&?. cl ; /f oc Regional Input-Outp Modeling System Estimation, Evaluation, and Application of a Disaggregated Regional Impact Model I : ■ ' U.S. DEPARTMENT.OF COMMERCE 7j / Bureau of Economic Analysis ■^eso^ Regional Economic Analysis Division BUREAU OF ECONOMIC ANALYSIS George Jaszi, Director Allan H. Young, Deputy Director Daniel H. Garnick, Associate Director for Regional Economics A. Ray Grimes, Chief, Regional Economic Analysis Division For sale by the Superintendent ol Documents, U.S. Government Printing Office, Washington, D.C. 2040^ r to 5» RIMSH Regional Input-Output Modeling System Estimation, Evaluation, and Application of a Disaggregated Regional Impact Model Joseph V. Cartwright Richard M. Beemiller Richard D. Gustely April 1981 U.S. DEPARTMENT OF COMMERCE Malcolm Baldrige, Secretary William A. Cox, Acting Chief Economist for the Department of Commerce BUREAU OF ECONOMIC ANALYSIS George Jaszi, Director Digitized by the Internet Archive in 2013 http://archive.org/details/rimsiiregionalinOOcart Foreword In response to a growing need for improved techniques for regional impact analysis, the Regional Economic Analysis Division of the Bureau of Economic Analysis developed the Regional Industrial Multiplier System (RIMS) in the mid-1970's. RIMS was designed to estimate input-output-type multipliers for use in estimating the secondary regional impacts of public and private economic development policies. RIMS was capable of estimating multipliers for any region composed of one or more contiguous counties and for any of the 478 industrial sectors in the national input-output (1-0) model. RIMS was a significant improvement over the more summary measures often used in regional impact analysis, and was capable of providing reliable multiplier estimates, without the costly expense of gathering survey data. The regional impact system described in this monograph--the Regional Input-Output Modeling System (RIMS II) — is a refinement of RIMS. The basic differences between RIMS II and RIMS are the use of a more recent national 1-0 table, the use of more detailed data for regionalizing the national 1-0 table, and greater flexibility in the derivation of regional impact estimates through the ability to apply either of two approaches—a shortcut method that provides aggregate impacts or a matrix inversion technique that provides industrial ly disaggregated impacts. This monograph documents the structure and performance of RIMS II and provides an example of its application in analyzing regional impacts of Federal programs and policies. The monograph assumes a knowledge of 1-0 techniques and focuses on the technical aspects of regional 1-0 modeling. April 1981 A. Ray Grimes, Chief Regional Economic Analysis Division Bureau of Economic Analysis Acknowledgments A number of individuals in the Bureau of Economic Analysis (BEA) and elsewhere have aided this research. We acknowledge the support of Daniel Garnick, Associate Director for Regional Economics at BEA, and A. Ray Grimes, Chief of the Regional Economic Analysis Division at BEA. We are especially grateful to Ronald Drake, Daniel Garnick, and Dennis Robinson, who, while in the Regional Economic Analysis Division, developed the original RIMS. Their extensive research greatly simplified our task. James Younger edited the monograph. Linda Adair typed the manuscript. Elsewhere in BEA, specific acknowledgment is expressed to Edward Trott, Jr., Duane Hackmann, Kenneth Johnson, Bruce Levine, and Patricia Schmitt of the Regional Economic Analysis Division; Edwin Coleman, Lowell Ashby, Elizabeth Queen, Wallace Bailey, and the staff of the Wage Branch of the Regional Economic Measurement Division; Philip Ritz, Howard Schreier, and Albert Walderhaug of the Interindustry Economics Divison; Frank DeLeeuw, Chief Statistician at BEA; Christian Ehemann of the Business Outlook Division; and Carol Carson, Sybella G'Schwend, and Karin Berndt of the Current Business Analysis Division. Among those outside of BEA, we thank especially the directors of the reseach teams in Texas, Washington, and West Virginia, who estimated the survey-based regional input- output tables used in the development of RIMS II. In addition, this monograph profited from comments on papers in which we described several aspects of RIMS II; we acknowledge the comments of Robert Bolton of Williams College, Philip Bourque of the University of Washington, Mark Henry of Clemson University, Geoffrey Hewings of the University of Illinois, R.C. Jenson of the University of Queensland (Australia), Joseph Katz of the University of Arizona, William Latham of the University of Delaware, James London of the College of Charleston, Karen Polenske of the Massachusetts Institute of Technology, Dennis Robinson of the U.S. Environmental Protection Agency, Benjamin Stevens of the Regional Science Research Institute, and Anthony Yezer of George Washington University. Also, our research profited from the comments on the original RIMS model made by Andrew Issermann of the University of Illinois, William Miernyk of the University of West Virginia, and William Schaffer of the Georgia Institute of Technology. Numerous users of the original RIMS model have provided support and comments that have enabled us to develop RIMS II. We acknowledge the support of the U.S. Water Resources Council, which, in publishing RIMS multipliers, has stimulated the use of input-output-type multipliers in regional impact analysis. For their comments and support, we wish to thank Peter Ashton of the U.S. Department of Agriculture, Louis Bykoski of the U.S. Nuclear Regulatory Commission, Hugh Knox of the U.S. Department of Commerce, John Lynch of the U.S. Department of Defense, John Ross of the U.S. Department of Housing and Urban Development, David Sandoval of the U.S. Department of Energy, Ajay Sanghi of the New York State Energy Office, and John Stutz and Steven Buchsbaum of the Energy Systems Research Group. TABLE OF CONTENTS Chapter Page 1. Introduction 1 Overview of the RIMS II Approaches 1 Scope of the Study 3 2. A Review of Regional Modeling Approaches 4 Overview of Model ing Approaches 4 Classification of Nonsurvey 1-0 Techniques 5 Previous BEA Research 9 3. Estimation of the Regional Direct Coefficients 11 Derivation of the National Tables 11 Regionalization of National Coefficients 15 Endogenizing Households 18 Industry Aggregation 23 RIMS II Regional Direct Coefficients 25 4. Estimation of Regional Multipliers 26 Leontief Inversion RIMS II Approach 27 Shortcut Techniques 28 Earnings Multipliers 34 RIMS II Regional Multipliers 38 5. Comparative Evaluation of RIMS II Performance 39 Description of RIMS II 39 Overview of the Evaluation Methodology 39 Column-Total -Level Accuracy Comparisons 44 Interindustry-Level Accuracy Comparisons 50 RIMS II Accuracy and Impact Analysis 55 6. Application of RIMS II 58 RIMS II Multipliers and Impact Analysis 58 RIMS II Estimated Impacts of LPW 60 7. Conclusions 71 Advantages of RIMS II 71 Limitations of RIMS II 71 Model Extensions 72 Bibliography 75 Appendix A. Sectoring of the Survey-Based Tables 83 Appendix B. Data for Several Accuracy Comparisons 95 Appendix C. Estimates of LPW Impacts 123 LIST OF TABLES Page 5.1 Alternative Techniques for Estimation of Direct Coefficients, Total Multiplier, and Earnings Multiplier 40 5.2 Distribution of Theil Statistics and Ratios (Nonsurvey/Survey) at the Column-Total Level, Texas 45 5.3 Distribution of Theil Statistics and Ratios (Nonsurvey/Survey) at the Column-Total Level, Washington 46 5.4 Distribution of Theil Statistics and Ratios (Nonsurvey/Survey) at the Column-Total Level, West Virginia 47 5.5 Distribution of Ratios of Column-Total Multipl iers (Nonsurvey/Survey) 49 5.6 Distribution of Ratios of Column Earnings Multipl iers (Nonsurvey/Survey) 51 5.7 Distribution of Theil Statistic 53 5.8 Decomposition of Theil Statistic 54 6.1 LPW Expenditures by Construction Type and SMSA 61 6.2 Column-Total and Earnings Multipliers by Construction Type and Area 63 6.3 Inversion RIMS II and Alpha Regression RIMS II Column-Total Multipliers by Construction Type and SMSA 65 6.4 Inversion RIMS II and Alpha Regression RIMS II Earnings Multipliers by Construction Type and SMSA 66 6.5 Gross Output and Earnings Impacts of LPW Expenditures by Industry and SMSA 67 6.6 Percent Distribution of LPW Earnings Impacts by Industry and SMSA 69 LIST OF TABLES— CONTINUED Page Al.l Input-Output Industry Definitions, Texas 85 A1.2 Input-Output Industry Definitions, Washington 9 2 A1.3 Input-Output Industry Definitions, West Virginia 9 4 Bl.l Ratios of the Column-Total Multipliers (Nonsurvey/Survey) , Texas 96 B1.2 Ratios of the Column-Total Multipliers (Nonsurvey/Survey) , Washington 101 B1.3 Ratios of the Column-Total Multipliers (Nonsurvey/Survey), West Virginia 103 B2.1 Ratios of the Earnings Multipliers (Nonsurvey/Survey) , Texas 105 B2.2 Ratios of the Value-Added Multipliers (Nonsurvey/Survey) , Washington 110 B2.3 Ratios of Earnings Multipliers (Nonsurvey/Survey), West Virginia 112 B3.1 Chi-Square Statistics, Texas 114 B3.2 Chi-Square Statistics, Washington 119 B3.3 Chi-Square Statistics, West Virginia 121 Cl.l Industry Designations for LPW Impact Appl ication 124 C2.1 RIMS II Multipliers—New Warehouses (49) 129 C2.2 RIMS II Multipliers — New Other Nonfarm Buildings (55) 130 C2.3 RIMS II Multipliers — New Sewer System Facilities (62) 131 LIST OF TABLES— CONTINUED Page C2.4 RIMS II Multipliers—New Highways and Streets (64) 132 C2.5 RIMS II Multipliers—New Construction and Development Facilities (70) 133 C2.6 RIMS II Multipliers— Maintenance and Repair, Residenti al (73) 134 C2.7 RIMS II Multipliers— Maintenance and Repair of Other Nonfarm Buildings (74) 135 C2.8 RIMS II Multipl iers— Maintenance and Repair of Highways and Streets (87) 136 C3.1 Gross Output and Earnings Impacts of Denver LPW Expenditures by Industry and Construction Type 137 C3.2 Gross Ouput and Earnings Impacts of Detroit LPW Expenditures by Industry and Construction Type 138 C3.3 Gross Output and Earnings Impacts of Wilmington LPW Expenditures by Industry and Construction Type 139 Chapter 1 INTRODUCTION Many types of public-sector and private-sector decisions require an evaluation of probable regional effects. For example, Federal requirements for environmental impact statements and urban impact analyses of Federal policies have substantially increased the need for regional impact analyses. Among the numerous aspects of a methodologically sound analysis is the consideration of indirect as well as direct impacts. Since important impacts are often economic ones, this increased concern has created a derived demand for regional economic impact models. As a result of this demand, economic impact models have been developed for many States and regions using a variety of methodologies. The three most common types of impact models are economic base, econometric, and input-output (1-0). These models vary considerably in terms of structure, reliability, sectoral and geographic detail, flexibility in application, and cost of development and use. The most important attributes of models used for the purpose of analyzing the regional impacts of Federal policy changes include reliability as well as sectoral and geographic detail. Specifically, it is important that the impact model can be consistently applied to a variety of regions to enable comparisons of impacts of Federal policies across these areas. Unfortunately, most impact models have been developed for individual areas, making this comparison difficult. The Regional Industrial Multiplier System (RIMS) was developed by the Bureau of Economic Analysis (BEA) in the mid-1970's to meet this analytical need. It was capable of producing 1-0 type industry-specific multipliers for use in impact analysis. Since its initial formulation, three changes have altered the environment within which RIMS was first developed. First, the national 1-0 table for 19 72 is now available upon which to base multiplier estimates. Second, more detailed data describing regional industrial structure are now available. Finally, significant advancements in the state of the art in regional 1-0 modeling have taken place against which the original RIMS estimating methodology needs to be evaluated. The purpose of the research described in this monograph was to develop a new version of RIMS that reflected these changes. This monograph focuses on the estimation, evaluation, and application of this new system--the Regional Input-Output Modeling System (RIMS II). Its primary use is to provide estimates of the impact of changes in the public sector (e.g., Federal policy) or in the private sector (e.g., private investment) on the economies of any county or group of counties in the United States and for any of the industrial sectors in the BEA national 1-0 table. Overview of the RIMS II Approaches As with most 1-0 techniques that rely on other than survey information, RIMS II estimates of regional industrial relationships are based on an existing national 1-0 table. For this purpose RIMS II employs the 19 72 BEA national 1-0 table, which shows the input and output structure of 496 U.S. industries. Since firms in all national industries are not found in each region, all direct requirements in a particular region typically cannot be supplied by that region's industries. Therefore, input requirements that are produced in a study region are identified, using BEA 4-digit Standard Industrial Classification (SIC) county wage and salary data. These data function as proxies for the industry-specific input and output data, which are seldom available at the small-area level. The resulting regional 1-0 table then can be aggregated, using these same wage and salary data, to the level of industrial detail appropriate for the impact study. More specifically, the RIMS II approach can be viewed as a three-step process. In the first step, the national direct-requirements-coefficients matrix is made region- specific by using corresponding 4-digit SIC location quotients (LQ's)._l/ For this purpose, RIMS II employs LQ's based on two types of data. According to this mixed-LQ approach, BEA county personal income data, by place of residence, are used for the calculation of LQ's in the service sectors, while BEA earnings data, by place of work, are used for the LQ's in the nonservice sectors. The LQ's are used to estimate the extent to which direct requirements are supplied by firms within the region. The second step involves estimations of the household row and the consumption column of the matrix. The direct household-earnings coefficients are estimated based on value- added gross-output ratios from the national table and introduced into each industry's coefficient column. In addition, a personal consumption expenditure column is constructed, based on national consumption and savings rate data and national and regional tax rate data. The last step in the RIMS II estimating procedure is to calculate the multipliers. RIMS II employs two alternative approaches for obtaining these multipliers. For some applications, it is necessary to trace the impact of changes in final demand on numerous individual directly and indirectly affected industries. RIMS II employs the Leontief inversion approach for obtaining multipliers in these cases. This inversion process produces both gross output and earnings multipliers. For other applications that require the calculation of only the gross output and earnings impact associated with a change in final demand for a specific industry, RIMS II employs a shortcut alpha-regression approach. According to this shortcut approach, the direct component of the multiplier is estimated as the sum of the coefficient column, including the household coefficient. Then, the indirect-induced component is derived, using a regression relationship involving the direct component in the reference industry, the average direct component for all industries, and the sum of the coefficients in the personal-consumption-expenditure column. From this estimate of the total multiplier, a shortcut formula is used to calculate the corresponding earnings multiplier. The blending of these two approaches (alpha regression and inversion) into RIMS II greatly enhances the flexibility of the system in terms of the range of applications for which it might be employed. Furthermore, based on comparative evaluations of the errors associated with these two techniques vis-a-vis their survey-based counterparts, such flexibility is gained with no apparent loss of accuracy. In addition to this flexibility of application, there are several other advantages to the RIMS II approaches. First, since RIMS II produces multipliers that are derived from secondary data sources, it is possible to provide estimates of economic impact without building a complete survey 1-0 model for each region under study. Second, the RIMS II multipliers are derived from a very limited number of secondary data sources, thus eliminating the costs associated with the compilation of data from a wide variety of these sources. Third, because of the relatively disaggregated sectoring plan employed by RIMS II, analysis may be performed at a detailed industrial level, thereby avoiding aggregation errors that often occur when different industries are combined. Fourth, the RIMS II multipliers are based on a consistent set of procedures and conventions across areas, thus making comparisons among areas more meaningful than would be the case if the results were obtained from incompatible impact models designed only for individual areas. 1. LQ's are measures of a regional industry's share of total regional economic activity relative to that national industry's share of national economic activity; LQ's are discussed in detail in chapter 3. ■2- Scope of the Study This monograph is divided into seven chapters. Chapter 2 presents an overview of regional modeling approaches that have historically been used in impact analysis. Specific attention is paid to the categorization of alternative nonsurvey 1-0 approaches, since RIMS II is an outgrowth of these approaches. Chapters 3 and 4 detail the methods that have been employed for estimating the direct and the indirect-induced components of 1-0 multipliers. Specifically, chapter 3 focuses on the manipulation of the national table and the approaches used for estimating the regional direct-requirements-coefficients matrix. Chapter 4 describes the techniques used for estimating the full multiplier matrix, as well as several shortcut techniques for estimating multipliers. Chapter 5 contains a description of the RIMS II approaches and a statistical evaluation of their accuracy vis-a-vis several other nonsurvey techniques and survey- based 1-0 tables for the States of Texas, Washington, and West Virginia. Chapter 6 demonstrates the application of RIMS II in the analysis of public policy impacts. Here, the system is employed to estimate the impacts of Local Public Works (LPW) expenditures in three SMSA's--Denver, Colorado; Detroit, Michigan; and Wilmington, North Carolina. Chapter 7 presents the conclusions of the study in terms of the strengths and weaknesses of RIMS II. The chapter also includes a description of possible extensions to the system. Tables defining the sectors included in each of the survey-based tables are contained in appendix A. The detailed accuracy comparisons of the alternative nonsurvey techniques appear in the tables in appendix B. The sector definitions and multipliers associated with the LPW application are included in appendix C. Chapter 2 A REVIEW OF REGIONAL MODELING APPROACHES Overview of Modeling Approaches One of the earliest types of economic models used in applied regional impact analysis is the economic base model. 1/ This model relates changes in indirectly affected local-service sectors to changes originating in basic (export) sectors. Because the economic base model is simple to understand and inexpensive to construct, these models have been widely used. However, a major weakness of the economic base model is that it divides local economic activity into only two broad sectors—the local-service sector and the export sector. This weakness gives rise to two significant problems in applying these models. First, the economic base multiplier is an average for the entire basic sector, and may not be the appropriate multiplier for output changes in an industry that is part of the basic sector. Second, the estimated impact is for the entire local- service sector. Therefore, the effects on specific local-service industries are not measured, even though estimating these industry-specific effects is often a major goal of impact analysis. The two problems can be overcome by the use of 1-0 models, which enable the analyst to examine the interindustry multipl ier differentials in detail. 2/ The consideration of these multiplier differentials is particularly important, since Cartwright (19 79) and others have shown that total gross-output multipliers can vary substantially among export-oriented industries, and that the industrial distribution of output and earnings effects depends on which export industry is initially affected. Given these advantages, numerous small-area and State-level 1-0 models were constructed during the 1960's and early 19 70's by surveying establishments for industry-specific sales and purchase data. However, not all of these models were of high quality; many were one-time, low-budget efforts, and several studies adopted 1-0 accounting procedures for the trade sectors that make their use in regional impact analysis questionable. 3/ Still, several States (for example, Kansas, Texas, Washington, and West Virginia) maintain an ongoing commitment to producing usable periodic survey-based tables. One major obstacle to the extensive use of small-area 1-0 models in regional impact analysis is their cost. For example, Glickman (1977) notes that approximately $250,000 was expended over a 5-year period for the collection and processing of data for the 1. Glickman (1977) discusses the conceptual basis of economic base models. In addition, he provides a thorough review of regional economic modeling techniques with numerous observations on the advantages and disadvantages of each technique. 2. For detailed presentations of 1-0 modeling methodology, see Miernyk (1965), Miernyk, et al . (19 70), and Bourque and Conway (1977). For summaries and bibliographies of regional 1-0 modeling techniques, see Richardson (19 72) and Giarratani, et al. (19 76). Schaffer, et al. (19 76) present a thorough discussion of the interpretation and use of regional 1-0 models. 3. See U.S. Water Resources Council (1977) for a partial bibliography of these tables; the trade sector accounting problems are also discussed in this source. See Bourque and Cox (1970) and Hewings (1970) for additional bibliographies of these early regional tables. 500-industry Philadelphia 1-0 study. Commenting on the construction of the 1958 Philadelphia table, Isard and Langford (1971) indicate that implementation costs were significant, especially those associated with maintaining experienced research personnel . During the same period, regional time-series econometric models were estimated for several States and metropolitan areas. 4/ In terms of industrial detail, econometric models represent a compromise between the simplistic two-sector economic base model and the industrially disaggregated 1-0 models. For example, the Tennessee econometric model developed by Gustely (19 78) has 23 endogenous industrial sectors. However, econometric models have two major limitations when used for regional analysis. First, the time series data used in constructing econometric models often are available only at the State and metropolitan-area levels, thus typically precluding county-level analysis. Second, like survey-based 1-0 models, econometric models are costly to build and maintain, particularly in terms of time and experienced research personnel. Thus, unless there is an ongoing need to analyze numerous projects or policy changes in a particular region, it is doubtful that constructing either a survey-based regional 1-0 model or an econometric regional model is cost effective. Additionally, because of time and research-personnel costs, the various single-region, survey-based 1-0 models and econometric models are often constructed by differing research teams. Thus, in most cases, the results of these models are not comparable, and interarea comparisons of policy changes are difficult because of the differing conceptual procedures adopted by the various research teams. At the State level, a notable exception is the National-Regional Impact Evaluation System (NRIES), for which the same structure was employed in each State model .5/ Classification of Nonsurvey 1-0 Techniques The demand for regional economic models that can be applied at the county level, estimated by using inexpensive techniques and applied across areas for interregional comparisons, often has been met by nonsurvey 1-0 techniques. These techniques frequently use a national 1-0 table as a basis for regional technology and then make adjustments that take into account various differences between the region's economy and that of the Nation. According to the specificity of their data input needs, these techniques can be classified into four broad groups. The first group of techniques estimates regional 1-0 coefficients, using detailed knowledge of local characteristics derived from data on industries or establishments whose technologies or trading patterns are suspected of differing from their national counterparts. The term, "mixed approach," is adopted in this monograph to describe the first group of techniques, because the regional 1-0 coefficients can be viewed as a mixture of purely national and purely regional interindustry relationships. As a first example of this group of techniques, the Multiregional Input-Output Model (MRIO) consists of linked 1-0 models for each State. 6/ MRIO is based on the following five data- estimation techniques: (1) detailed, State-specific, interindustry relationships 4. Glickman (19 77), Knapp, et al . (19 78), and Ballard, Gustely, and Wendling (1980) provide bibliographies, as well as discussions of the construction and use of regional econometric models. 5. The structural and performance characteristics of NRIES are discussed in Ballard, Gustely, and Wendling (1980). 6. Polenske (1980) summarizes the MRIO model and contains an extensive bibliography of the MRIO project, which began in 1967. It is important to recognize that unlike the other nonsurvey 1-0 techniques discussed in this monograph, which are exclusively single- region techniques, MRIO provides comprehensive and consistent State economic accounts to be used in multiregional economic analyses. (obtained from various Federal sources) for a number of industries, (2) State-specific output-weightings of national coefficients for other industries, (3) various estimation techniques based on Federal data sources for construction of the components of final demand, as well as industry-specific totals for output, employment, payrolls, and other measures related to value added, (4) special tabulations of the U.S. Census of Transportation for estimating interstate trade, and (5) reconciliation of the estimates obtained from the preceding four procedures with values from national economic accounts and 1-0 tables. In several respects, the MRIO methodology for constructing each State 1-0 table is similar to that used in constructing the national 1-0 table; that is, while no surveys of establishments are used directly in estimating MRIO or national 1-0 coefficients, numerous Federal data files are used. Because of the lack of actual data for some necessary components at the State level, when compared to national 1-0 tables, the MRIO methodology requires a more extensive use of estimation techniques to fill in the missing data.// Two major advantages of MRIO are its ability to make interstate comparisons because the same model structure is used in each State, and its ability to identify feedback effects because of State-to-State trade-flow matrices.8/ Two major disadvantages of the current MRIO system are its use of 1963 base-year data for several important components of the model and its inability to perform small-area, substate impact analysis. As a second example of this approach, the Georgia Economic Model 9/ was estimated by using the national 1-0 table as a first approximation to the State's table. This table was then adjusted with data on interindustry purchases and sales obtained by surveying a sample of firms. In addition, confidential industry-specific output, employment, and wage data were used to supplement the survey-based data and to serve as a further adjustment to the national table. These confidential data were gathered by various State government administrative agencies as part of their ongoing revenue and expenditure functions. As a third example, an Australian regional 1-0 modeling system, termed the Generation of a Regional Input-Output Table (GRIT)IO/, applied a number of mechanical procedures to a national 1-0 table for the purpose of estimating a prototype regional table. The mechanically-produced prototype table was then further regionalized by an analyst who had access to superior, but limited, data on regional interindustry relationships. A newer version of the modeling system, GRIT II, has an "accuracy- optimization" procedure, which can be used to identify the 1-0 cells that most affect multiplier size. Based on the procedure, an analyst can maximize the accuracy of a regional multiplier matrix, subject to a data-gathering budget constraint. The mixed approach of modifying a national table with limited survey or other region-specific data may require considerably less data gathering than a purely survey- based table and, therefore, may entail lower associated costs. However, in terms of the 7. For examples of the data sources and the manipulation techniques used in estimating personal consumption expenditures, see Polenski (19 72); for examples of data sources and the manipulation techniques used in estimating interregional trade, see Rodgers (19 73). 8. For an example of the advantages of MRIO, see Polenske and Rowan (1977). With respect to these advantages, the MRIO model is similar to the NRIES model mentioned above. 9. Schaffer, et al. (19 76) describe the Georgia Economic Model. 10. West, et al. (19 79) describe the GRIT and GRIT II procedures; in addition, the study contains a recent and extensive regional 1-0 bibliography. -6- need for experienced research personnel, the costs of the two approaches are similar. Thus, with the exception of the MRIO model, the mixed approach of nonsurvey data supplemented with primary data would require a different research team for each area to be studied, and interarea comparisons would be difficult unless each team agreed to use identical procedures. In addition, the mixed approach frequently cannot be applied for small areas because of the unavailability of administrative data for these areas. In these respects, the mixed approach has the same drawbacks as a purely survey-based methodology. In fact, tables that are viewed as "purely" survey-based often are based partially on extensive use of administrative records, especially for estimating control totals for industry-specific output. Moreover, Jensen (1980) argues that the purely survey component of some "survey-based" tables has not been sufficiently large to warrant their being considered as true survey-based tables. In application, the difference between "purely" survey-based and mixed-approach tables could be small. As a consequence, previous studies have not compared the results of the mixed approach with those from "purely" survey-based tables. The second broad group of national table adjustment procedures—the constraining of national technical coefficients, based on region-specific information — also requires a significant survey element. The RAS technique is an example of this type of adjustment procedure. The RAS technique was originally developed by Stone and Brown (1965) for projecting national technical coefficients with limited survey data; it has also been used to estimate regional tables. 11/ In the regional applications of the RAS technique, national coefficients are constrained to regional industry-specific intermediate output and input control totals. As applied by Morrison and Smith (1974), the control totals were obtained from survey data. While the RAS technique requires less primary data than the mixed approach, its data gathering costs often preclude its being applied in many small-area impact analyses, especially for a one-time set of changes in final demand. Several evaluations of the accuracy of the RAS technique have been performed. Morrison and Smith found that their semisurvey RAS approach generated Type II income multipliers that averaged 7 percent above the survey-based table estimates for the City of Peterborough, England. 12/ However, Miernyk (19 76) summarizes other research results that indicate that the RAS technique is less accurate. In addition, Hewings (1977) questions the industry-specific reliability of the RAS technique as well as the expense in gathering the data necessary for its use, although he generally confirms the aggregate validity of the technique. A third group of techniques for adjusting the national tables to generate regional tables can be used with no survey data, but it makes use of economic data gathered by the Federal Government. For example, a methodology proposed by Stevens and Trainer (1980) uses the Bureau of Labor Statistics 1 Consumer Expenditure Survey and the Bureau of the 11. For a more recent description of the RAS technique see Bacharach (19 70); for a discussion of its use with survey-based regional 1-0 tables see Malizia and Bond (19 74). While McMenamin and Haring (19 74) have refined the RAS procedure, their refinements, although lessening the data requirements, are only applicable to the problem of updating an earlier table. For many small areas, there is no earlier table to update. 12. Type II income multipliers are based on an 1-0 model with an endogenous household sector, while Type I income multipliers are based on an 1-0 model with an exogenous household sector. A detailed discussion of the distinction between Type I and Type II 1-0 multipliers can be found in Richardson (19 72) and Schaffer, et al . (19 76). Several aspects of the relationship between the household sector and the definitions of 1-0 multipliers are discussed in chapter 4 of this monograph. -7- Census' regional economic data (especially, the Census of Transportation ) for altering technical coefficients in the national table. For some States and metropolitan areas, these data are similar to those that would be gathered in an industry survey. For smaller areas, where there is a lack of data due to establishment confidentiality problems and incomplete tabulation of industry-specific data, Stevens and Trainer advocate the use of various estimation techniques to fill in the missing data. For example, Stevens and Trainer use regression techniques with ratios of weight to value of shipments, population density, and income as independent variables to explain industry-specific imports and exports. 21/ In addition, they estimate output in some sectors as a function of County Business Patterns employment data; these employment data often must be estimated for detailed sectors as functions of more aggregate, but disclosed, subtotals. This third group of nonsurvey techniques is similar to the first group; the major difference is that the adjustment data employed by the third group are not survey-based and often must be estimated for a particular study area. 14/ This group of techniques avoids the large costs of gathering survey data and can be applied on a consistent basis to many small areas for interregional comparisons. However, there are two potential problems with this group of techniques. First, since Census data often are available only every 5 years, estimating current import levels in regional tables may be difficult. Second, much of the data actually used in adjusting national tables to small-area tables are estimated by regression equations that are specified by the use of State or metropolitan-area data for aggregated industry control totals. The estimated data, therefore, may not reflect actual relationships at the small-area level. However, in spite of these potential problems, Stevens, et al. (1980) reported generally favorable results in comparing their technique with the 19 72 Washington State survey-based table; for example, the average value-added and column-total multipliers were 4 percent higher than the corresponding survey-based multipliers. 15/ The fourth group of national-table adjustment techniques makes use of generally available published data on industry-specific employment or earnings to estimate the level of industry-specific imports. The national table is then adjusted to the regional level by taking into account these imports. The major advantages of these techniques are their low application cost, and their ability to be applied even at the county level when making interarea multiplier comparisons. The LQ and the supply-demand pool techniques, as described in studies by Schaffer and Chu (1969), Schaffer (1972), and Morrison and Smith (1974), are examples of the fourth group of techniques. In comparing the LQ and supply-demand pool techniques with survey-based tables, the studies indicate that the simple LQ technique is the most accurate of the nonsurvey techniques analyzed. However, the average multiplier generated by this LQ technique is considerably higher than the average multiplier estimated from the survey-based tables. For example, Schaffer and Chu found that the average simple LQ Type II income multiplier was 47 percent higher than the survey-based multiplier, and Morrison and Smith found that it was 27 percent higher. 13. Stevens, et al . (19 79) present several refinements to the estimation techniques developed by Stevens and Trainer. 14. However, Stevens and Trainer (1980) do argue that if limited survey funds are available, they should be used to estimate likely direct ("first round") effects. See also Conway (19 77) on this point. 15. The inversion RIMS II results presented in chapter 5 of this monograph are similar to those reported by Stevens, et al. (1980). -8- Previous BEA Research Several researchers at BEA have undertaken studies of the feasibility of using techniques that can be classified in this fourth group. Walderhaug (19 72) constructed a synthetic technical coefficient table for Washington State. Using the 367-industry national technical-coefficient table for 1963, he aggregated the 270 industries present in the State to the 27 sectors identified in the Washington State table. He concluded that the differences between the synthetic and survey-based technical coefficients were within an acceptable range. 16/ Garnick (19 70) demonstrated that there are inexpensive techniques for augmenting basic-service multipliers so that industry-specific multipliers can be estimated. Using 2-digit SIC BEA earnings data and an 80-sector 1963 national technical-coefficient 1-0 table, he estimated industry-detailed economic base multipliers for two States for which survey-based 1-0 tables existed (Washington and Nebraska). He found that, with the exception of resource-oriented industries in both States, most differences between the two estimates appeared to be within tolerable limits. For example, for 18 directly comparable sectors in the 1963 Washington table, the average difference between the survey-based 1-0 Type II income multiplier and its augmented basic-service counterpart was 10 percent of the survey multiplier. Drake (19 76) combined Walderhaug's use of a very disaggregated sectoring plan and an extension of Garnick's relationship between direct (basic) effects and indirect-induced (local-service) effects. The resulting model, RIMS, employed (1) a variation of the 2- digit SIC LQ approach, to estimate the direct component, and (2) a regression equation based on survey-based tables, to estimate the indirect-induced component of the multiplier for each industry. To date, at least two studies, comparing RIMS multipliers with those from survey- based tables, have been undertaken. Among his other findings, Drake (19 76) reported that RIMS underestimated the mean multiplier for the New Mexico State model by 22.5 percent and overestimated the mean multipliers for the St. Louis SMSA and Nebraska State models by approximately 17 percent. Using an aggregate 86-industry national table, Latham and Montgomery (19 77) compared the results of two nonsurvey techniques (simple LQ's and RIMS) with the 1969 survey-based Kansas table. They found RIMS Type II gross-output multipliers outperformed the simple LQ multipliers, although both techniques recorded substantial errors when compared with survey-based table multipliers. For example, the average RIMS multiplier overestimation was 18 percent of the survey-based model multiplier, while the simple LQ multiplier overestimation was 26 percent. The orginial version of RIMS represented an inexpensive nonsurvey technique that could be generalized to any county-defined study area. However, there are at least three limitations associated with RIMS. First, unlike some nonsurvey models, RIMS could estimate only column-total multipliers. Thus, for a given initial final-demand change, 16. Bourque (19 72) noted that, because Walderhaug did not estimate import and export flows, his synthetic table could not be inverted to estimate State multipliers for use in impact analysis. -9- the industrial distribution of total effects could not be specif ied.I7/ Second, as Miernyk (19 76) comments, the differences between survey-based 1-0 multipliers and RIMS multipliers still may be too large for RIMS' widespread use in economic impact analysis. Third, since RIMS was initially developed in the mid-19 70's, more recent and detailed data have become available, including a 19 72 national 1-0 table and 4-digit SIC wage and salary estimates at the county level. The refinements to the original version of RIMS, which were incorporated in RIMS II to avoid the three limitations, are discussed in the remainder of this monograph. 17. Several nonsurvey techniques permit the estimation of a full 1-0 transactions table. The fourth group of nonsurvey techniques is generally used only for estimating the direct-coefficient and multiplier matrices. The RIMS technique was originally developed only for estimating the individual column totals of the direct-coefficient and multiplier matrices. However, an approximation procedure for estimating RIMS earnings and employment effects was developed at BEA. This procedure can be found in U.S. Water Resources Council (1977); the procedure is also discussed in chapter 4 of this monograph. -10- Chapter 3 ESTIMATION OF THE REGIONAL DIRECT COEFFICIENTS All purely nonsurvey techniques take a national 1-0 table as a first approximation of regional interindustry relationships. The national table can then be made region specific by removing those input requirements that are not produced in the region. The focus of this chapter is on the algebraic derivation of the national direct-requirements matrices, the regional ization of these matrices by several LQ techniques, and the estimation of row and column coefficients for the household sector. A brief discussion of the aggregation of the resulting regional table then follows. The chapter concludes with a summary description of how RIMS II estimates regional direct coefficients. Derivation of the National Tables In order to provide more information on the 1-0 structure of the economy (especially in terms of an industry's production of secondary products), the 19 72 national 1-0 tables differ from earlier national benchmark tables in terms of definitions and conventions. For this reason, a detailed derivation of the national tables is useful for indicating explicitly how the national 1-0 tables provide the basis for estimating regional 1-0 tables.JV This discussion of the national 1-0 tables concludes by showing the relationship between the detailed derivation's matrix notation and the more familiar 1-0 matrix notation, which is used elsewhere in this monograph in order to simplify the presentation of RIMS II. The derivation of the national table begins with two accounting identities that define total commodity and industry output. The total national output of a given commodity can be defined as: q = Ui + e where: q = a column vector showing total output by commodity U = the intermediate portion of the commodity-by-industry input matrix i = a unit vector e = a column vector showing total final demand purchases by commodity Similarly, the total national output of a given industry can be defined as: (3.1) g = Vi + h where: g = a column vector showing total output (including scrap) by industry (3.2) 1. The derivation of national 1-0 tables is taken from Ritz (1980). For additional details on the national 1-0 tables, see Ritz (19 79) and Ritz, et al. (19 79). -11- V = the industry-by-commodity output matrix with zero-filled columns for noncomparable imports and scrap2/ h = a column vector showing the total output of scrap by industry In order to convert the accounting identities of equations 3.1 and 3.2 into an economic model that determines the levels of industry and commodity output, the following three assumptions are made: (1) If inputs are required in proportion to output and the proportions are the same for an industry's primary and secondary products, then U = Cg* 3/ (3.3) where: C = a technical -coefficients matrix showing the amount of a commodity used by an industry per dollar of output of that industry (2) If each commodity (other than scrap) is produced by the various industries in fixed proportions, then V = Dq* (3.4) where D = a market-share matrix showing for a given commodity (excluding scrap) the proportion of the total output of that commodity produced in each industry4/ (3) If scrap output in each industry is proportional to total output of the industry, then h = p*g (3.5) where: p* = a square matrix with the ratio of the value of scrap produced in each industry to the total output of the industry on the main diagonal and zeros elsewhere Equations 3.1 through 3.5 represent an 1-0 model with three constants (C, D, and p), five endogenous variables (U, V, h, q, and g), and one exogenous variable (e). A model solution which relates total output and final demand can be derived as follows: Substituting 3.4 into 3.2 yields: g = Dq + h g - h = Dq (3.6) 2. This treatment of scrap prevents its requirement as an input from generating output in the industries in which it originates. 3. An asterisk (*) associated with the symbol for a vector indicates a square matrix in which the elements of the vector appear on the main diagonal and zeroes are entered elsewhere. 4. To allow for leakages from the domestic economy, D is defined here to include comparable imports. -12- Substituting 3.5 into 3.6 and solving for g yields: g - p*g = Dq (I - p*)g = Dq g = (I - p*) _1 Dq (3.7) where: I = the identity matrix To simplify the notation, if W = (I - p*)~ D, then g = Wq 5/ (3.8) Then, substituting 3.3 into 3.1 yields: q = Cg + e (3.9) Multiplying 3.9 by W and substituting 3.8 into this result yields: g = WCg + We (3.10) Solving for g yields: g = (I - WC) -1 We (3.11) The final model solution shown in equation 3.11 indicates the relationship among total output by industry (g), the direct-requirements matrix (WC), and the final demand vector (e). In that equation the expression WC is an industry-by-industry direct- requirements matrix for the Nation, and the expression (I - WC) is an industry-by- industry total-requirements matrix. Further, the multiplication of the final demand vector e by the W matrix has the effect of converting commodity demand into industry demand. The national 1-0 model described above is flexible in the sense that it can be used to derive variously-defined regional 1-0 models. For example, when comparing nonsurvey with survey regional tables, the national industry-by-industry matrix derived here is the appropriate starting point, since regional survey tables are typically constructed on an industry basis. 6/ However, when regional final demand is stated in terms of commodities rather than industries, an industry-by-commodity matrix is more appropriate. ]_/ 5. Since the matrix (I - p*)~ has values 2 1 on the main diagonal, W. . 2 D. . for all i,j; the difference between W. • and D- • is the dollar value of scrap output generated by industry i in producing its share of one dollar's worth of commodity j. 6. Establishments are classified by industry according to their primary activities in the three survey-based tables examined in this study. 7. An industry-by-commodity total-requirements matrix is derived as follows: Substituting (3.8) into (3.9) and solving for q yields: 13- In order to generalize and simplify the presentation of RIMS II, a more familiar 1-0 matrix notation is used in the remainder of this monograph, even though RIMS II is based on the flexible 1-0 model described in equations 3.1 through 3.11. In this more familiar notation, interindustry or intercommodity relationships are represented by the following equation : X = AX + Y (3.12) where: X = a column vector of gross output A = a matrix of direct requirements coefficients Y = a column vector of final demand Equation 3.12 states that total output (X) equals intermediate sales (AX) plus final sales (Y).8/ The dimensions of the square A matrix are equal to the total number of industries or commodities specified. Thus, for example, the direct industry requirements matrix can be represented by the following equation: M < 3 - i3 > A where: i,j = 1,2,...., n intermediate industries At this point, it is useful to describe the relationship between the notation in equations 3.1 through 3.11 and the more familiar notation in equations 3.12 and 3.13. For example, in equation 3.9, output and input are represented by q and g, while in equation 3.12, output and input are represented by X. Similarly, A corresponds to either of the matrix products (CW or WC) and Y corresponds to e or We. The relative complexity of the 1-0 model described by equations 3.1 through 3.11 is caused by this model's explicit treatment of the primary and secondary commodity output of each industry. Since the model expressed by equations 3.12 and 3.13 is defined exclusively on an industry basis, its notation can be considerably less complex. The discussion in the remainder of this monograph uses the more familiar matrix notation in equations 3.12 and 3.13, even though the national 1-0 model underlying RIMS II is expressed in equations 3.1 through 3.11. This less complex notation is adopted for three reasons. First, the less complex notation simplifies the presentation and, therefore, allows emphasis to be placed on the regionalizing techniques. Second, the less complex notation generalizes the discussion of the regionalizing techniques. Thus, q = (I - CW) _1 e (3.11a) where (I - CW) is a commodity-by-commodity total-requirements matrix. Substituting (3.11a) into (3.8) yields: g = W(I - CW) _1 e (3.11b) where W (I - CW) is an industry-by-commodity total requirements matrix. 8. See chapter 2, footnote 2, for references to studies that use this more conventional 1-0 notation. ■14- the A matrix can refer to either the industry-by-industry direct-requirements matrix (WC) or the commodity-by-commodity direct requirements (CW). Third, the less complex notation permits an easier comparison of RIMS II with previous regional 1-0 techniques. For example, the comparison of the multipliers from RIMS II and the survey-based tables presented in chapter 5 of this monograph must be performed on A matrices, which are defined on an industry-by-industry basis, since the survey-based tables adopt this convention. Regionalization of National Coefficients As indicated in chapter 2, several nonsurvey approaches can be used to adjust national 1-0 coefficients. Of these approaches, the LQ technique is most often used, since the data used to construct LQ's are often readily available. As shown by Schaffer and Chu (1969) and others, these LQ's can be defined in several ways. The most straightforward form, the simple location quotient approach (SLQ), assumes that the needs of regional industries for output in each industry i relative to the needs for output in each of these industries nationally are the same as the ratio of total regional to total national output. In addition, several variations in the form of the LQ have been used.9_/ One approach (the purchases-only LQ) defines the base of the LQ to be the outputs of those industries purchasing inputs from industry i instead of total regional and national outputs. Another approach (the cross-industry LQ) allows the import proportions to vary within rows by comparing the proportion of national output of selling industry i in the region to that of purchasing industry j in the region. However, past studies (summarized in chapter 2) of the accuracy of these alternatives indicate the relative superiority of the SLQ approach. A simple location quotient for each regional industry can be defined by the following equation: . "X (3.14) SLQ. 1 Q^/T" where: r Q. = a measure of the output of industry i in region r Q n . = a measure of the output of industry i in the Nation r T = a measure of aggregate economic activity in region r T = a measure of aggregate economic activity in the Nation Data on earnings or employment by industry are often used to specify Q r and Q. ; data on total income, population, earnings, or employment are used to specify T r and T n . Simple LQ's are one measure of the region's self-sufficiency in producing the output of a given industry. Referring to equation 3.14, an LQ of less than 1.0 means that the output of regional industry i represents a smaller share of regional economic activity than the output of national industry i represents of total national activity. Accordingly, LQ's are often used to identify regional industries that are net importers and exporters. Thus, if SLQ. is less than one, the region imports some of the output of 9. See Richardson (19 72) and Schaffer and Chu (1969) for a more detailed discussion of these variations. -15- industry i from elsewhere in the Nation. Similarly, if SLQ, is greater than one, the region exports some of the output of its industry to the rest of the Nation. If SLQ. equals one, the region, on a net basis, neither imports nor exports the output of industry i, and the region is viewed as self-sufficient with respect to industry i's output. The region's SLQ's are often used to regionalize the national 1-0 table in the estimation of the regional direct-purchase coefficients. This can be expressed by the fol lowing equation: »1j ■ SLQ', .Ifj (3.15) where: a-- = the proportion of the total output of the regional industry j that is accounted for by the purchases of inputs from regional industry i a-- = the national direct-requirements coefficient SLQ 1 , SLQ i if SLQ i 1.0 if SLQ i Thus, in those cases where SLQ, is less than one, a^, is less than a., for all j n r industries. The positive difference between a- • and a. ., when SLQ- is less than one, is a th 1 measure of the extent of importing the i industry's output. Similarly, if SLQ. is greater than or equal to one, then a., and a- . are equal, and the region is assumed to be tn self-sufficient in producing the i industry's output. 10/ The conceptual problems associated with the use of the SLQ technique (as well as the other LQ techniques) are well documented. 11/ The effects of some of these limitations can be lessened by the choice of the basis upon which the LQ is to be determined. For example, Nourse (1968) and others have argued that earnings-based LQ's take better account of regional productivity differences than do employment-based LQ's. Another limitation, that resulting from regional differences in industrial mixes, can often be due to the lack of adequate regionalizing data. For example, while the national 1-0 table is based on a 4-digit SIC classification scheme, industry-specific regional employment or earnings data are often available only at a more aggregate level. Therefore, regionalizing with aggregate LQ's ignores the differences between the region's and the Nation's disaggregated industry-specific output mix. For 10. In the notation of equations 3.1 through 3.11, the regional industry-by-industry direct requirements matrix is (SLQ* WC), and the regional commodity-by-commodity direct requirements matrix is (C SLQ* W), where SLQ* is a diagonal matrix with the vector SLQ'. on the main diagonal and zeros elsewhere. 11. Isard (1960) and Nourse (1968) discuss in more detail the limitations of using LQ's for estimating imports and exports. -16- example, aggregate LQ's are often defined on the basis of 2-digit SIC data. At this level of classification, approximately 60 industry-specific LQ's can be identified for regionalizing the national 1-0 table. Thus, SLQ- in equation 3.14 is defined where i is equal to 1 through 60. However, since the most disaggregated national table consists of 496 industries, the use of only 60 SLQ-'s in equation 3.15 means that the same SLQ- is often used for many disaggregated industries. 12/ The effect of the use of only 60 SLQ.'s is that the national and regional 1-0 tables (described in equation 3.15) have only 60 industries. Given the availability of more industrially disaggregated data, disaggregated SLQ-'s would seem to be more appropriate than aggregated SLQ-'s for estimating regional 1-0 tables. For example, using SLQ-'s for each industry in the national 1-0 table, 496 SLQ^s (rather than only 60 SLQ^s) would be used in estimating a matrix of regional direct-purchase coefficients at the 496-industry level .13/ A third limitation of some LQ's (notably earnings and employment LQ's) results from their failure to adequately reflect the regional level of aggregate demand. Earnings- based LQ's are widely used to identify regional imports, and they function as proxies for industry output and demand. However, for estimating the level of regional self- sufficiency in providing certain industry-specific outputs, Isard (1960), Nourse (1968), and Stevens and Trainer (1980) have argued that personal income-based LQ's are more appropriate. 14/ Specifically, when a large part of an industry's output is sold directly 12. For example, food manufacturing (SIC 20) is one 2-digit SIC industry, yet 44 food manufacturing industries are identified in the disaggregated national 1-0 table. For the application presented in chapter 6 of the monograph, the Denver SMSA's SLQ for SIC 20 is greater than 1.0, yet the disaggregated SLQ's for the 44 food manufacturing industries range from 0.0 to over 9.0; 14 of these SLQ's are zero, and 17 others are less than 1.0. Thus, the use of aggregate SLQ's overstates Denver's level of self-sufficiency in 31 disaggregated food manufacturing industries. 13. The original RIMS used a combination of aggregate and disaggregate SLQ's. In the original RIMS, County Business Patterns (CBP) data at the 4-digit SIC level were used to identify industries that were not present in the region; SLQ's for these industries were set equal to zero. SLQ's for the remaining industries were based on BEA's 2-digit SIC county earnings data. The reason for this combined approach is that the CBP data, while tabulated at the 4-digit SIC level, do not present employment or earnings estimates for many industries present in a given county because of disclosure regulations. Recently, the wage and salary component of BEA's county-earnings data base has been expanded to the 4-digit SIC level. While the expanded data base is subject to disclosure regulations and is not available for public use, it is used in RIMS II calculations. 14. Earnings consist of wages and salaries, other labor income, and proprietors' income. Personal income consists of earnings, plus transfer payments, dividends, interest, and rent, less personal contributions for social insurance. For details on the definitions and measurement of personal income at the regional level, see U.S. Department of Commerce (1980). Earnings-based LQ's are defined as: SLQ. E^/TE r i n n (3.14a) E"/TE n -17- to final demand, personal income LQ's may be more accurate than earnings LQ's in estimating regional self-sufficiency (and therefore imports) ._15/ For example, in a region where transfer payments are proportionately larger than in the Nation, retail trade self-sufficiency will be better estimated by a personal income LQ than an earnings LQ. This is because the personal-income-based LQ accounts for all sources of intermediate and final demand for retail trade, while the earnings-based LQ accounts for only the earnings-based demand for retail trade. Since LQ's function as proxies for regional output and demand, the appropriate LQ should be based on the regional source of demand for output. Therefore, a mixed-LQ approach that combines the use of earnings-based and personal income-based LQ's should be useful in estimating regional purchase coefficients. _16/ Thus, for industries that sell most of their output to intermediate demand, an earnings LQ may be more appropriate; in this case the level of regional total earnings would be a proxy for the level of total intermediate output. However, for industries that sell most of their output to final demand, a personal income LQ may be more appropriate; in this case the level of regional personal income would be a proxy for the level of final demand. Endogenizing Households When it is appropriate to indicate the effects of output changes in personal income or earnings, the direct-regional-purchase-coefficients matrix (A ) is expanded in where: E r , E n . = earnings in industry i in the region and the Nation, respectively TE r , TE n = total earnings in the region and the Nation, respectively Personal income-based LQ's are defined as: E r /PY r r SLQ. = (3.14b) i r n /nw n EV/PY' where: PY r , PY n = total personal income in the region and the Nation, respectively 15. For an example of the use of personal income LQ's see Cartwright (19 79), where, on the basis of earnings LQ's, most suburban areas appeared self-sufficient in providing retail trade and other service-type outputs. However, on the. basis of personal income LQ's, several suburban areas imported these services. The positive difference between earnings LQ's and personal income LQ's occurred because of the large positive residence adjustment component (that is, income earned in the urban central county by suburban residents) of suburban personal income. 16. For any given industry, it is impossible to construct an accurately mixed LQ without data on the total intermediate and final sales that are specific to that regional industry. As used in chapters 5 and 6 of this monograph, the RIMS II LQ's for the agriculture, mining, and manufacturing industries are equal to the earnings LQ's. The RIMS II LQ's for the remaining industries are equal to the personal income LQ's. -18- regional 1-0 analyses by the inclusion of a regional household row and a household column. Often A r is expanded to include the household sector when an analyst wants to indicate the additional effects induced by consumer spending as well as the direct and indirect interindustry effects. 17/ Based on equation 3.13, the expanded regional matrix can be represented by the following equation: A r ■ ajj (3.16) where: i,j = 1, n,n + 1 The inclusion of households in A r requires specifying the regional household-payments- row coefficients (a r -> •) and the regional household-expenditure-column coefficients v n + 1 ,j 3 (a. + .) .18/ Regional 1-0 models defined by equation 3.16 are often referred to as "closed with respect to households," and many regional 1-0 studies refer to A r (as defined in equation 3.16) as having an endogenous household sector. The discussion of endogenizing households presented below indicates how the national 1-0 tables' personal-consumption-expenditure (PCE) column can be adjusted to estimate a r . + -,, and how the national 1-0 table's value-added (VA) row can be adjusted to estimate a + •, -. Regional household expenditure coefficients A region's household coefficient column can be represented by the following identity: n+1 1 '° = a m,n + l + a s,n+l + a t,n + l + a i,n+l (3 ' 17) where: X m + , = the household import coefficier a£ , = the household savings coefficient a * «j.i = the household direct tax coefficient t,n+l 17. For a discussion of alternative treatments of households, see Schaffer, et al . (19 76), Richardson (19 72), and others mentioned in chapter 2 of this monograph. The effects of including the household sector on multiplier interpretation and size are discussed in chapter 4 of this monograph; the assumptions associated with an endogenous household row and column are discussed in chapter 6. 18. The cells of the household row U n+ i •) show the proportion of the total gross output of industry j that is accounted for by payments to households in the form of labor earnings or value added. The cells of the household column (a 1 ? ,,) show the industry- specific disposition of personal consumption expenditures per dollar of income by households. -19- Equation 3.17 states, in coefficient form, that imports, savings, direct personal tax payments, and total intraregional purchases sum to one. For use in most regional 1-0 analyses, the imports, savings, and tax coefficients represent leakages from the regional economy. 19/ The LQ techniques described above can be used to regionalize the national PCE column, and, therefore, to estimate a r - + -. , as described in equation 3.17. This approach assumes that the national consumption pattern is an appropriate proxy for the regional consumption pattern; it is 'also consistent with using national technology as a proxy for regional technology in estimating the other portions of the matrix. 20/ However, since the national PCE coefficient column is not defined to take into account explicitly personal taxes and savings, the national PCE column first is made region-specific by adjusting for these two leakage effects.21/ This is expressed in the fol lowing equation: ^l.n + 1 ■ a i,n + l l 1 - 7 "' C " < 3 - 18 ' where: a . + , = an initial estimate of the regional household-column coefficient T r = the average regional tax rate C r = the average regional aftertax consumption rate For use in equation 3.18, T r is the ratio of regional disposable personal income (DPI) to personal income, and C r is the ratio of national PCE to DPI. 22/ In equation 3.18, the 19. See Bourque and Conway (19 77), Grubb (19 78), and Loviscek, et al . (1979), for examples of the treatment of personal taxes and savings with respect to regional household expenditures in survey-based regional 1-0 tables. 20. Stevens and Trainer (1980) use Bureau of Labor Statistics Consumer Expenditure Survey (CES) data for constructing area-specific household column coefficients. However, for many areas CES data are not available, and the regional household column must be estimated from more industrially and geographically aggregated CES control totals. BEA is developing, at the State level, detailed PCE estimates, which can be used for constructing more region-specific household columns. 21. The 19 72 national 1-0 table is constructed with the household sector as part of final demand, and, therefore, its treatment of taxes and savings differs from that in many regional 1-0 tables. 22. National data are used to estimate C r , since regional PCE data are not presently available. However, since DPI, at the State level, is estimated by BEA, T r will vary across States. Furthermore, since T r varies across States, it is important to recognize that State 1-0 multipliers also will vary if only because of differences in the level of T r across States. To some extent, this is due to the lack of endogenous State and local government sectors in most regional 1-0 models. However, since import leakage differences across States are significantly larger than differences in T , the extent to r which 1-0 multipliers vary is far greater for import leakage differences than for T differences . -20- reduction of each national PCE coefficient (a" + i) by average tax and consumption rates provides estimates of the sum of a[ , and a r , in equation 3.17. t,n + 1 s,n +1 ^ r By the SLQ technique, a • + -, can be used to estimate a ^ + ,. This is represented in the following equation: a r r, o. _r SLQ',. a _ + 1 (3.19) i,n +1 JLW i Q i,n + 1 In equation 3.19, the regional ization of the household column by SLQ ' ^ corresponds to the regional ization of the other interindustry columns expressed by equation 3.15, where SLQ ' ^ is based on the mixed-LQ concept, as specified in equations 3.14a and 3.14b. When combined with the estimate of the sum of a!T , and a r , from equation 3.18, t,n + 1 s,n +1 ^ ' equation 3.19 provides an estimate of dL + , in equation 3.17. Therefore, equations 3.18 and 3.19 describe how the national PCE column can be used to estimate the regional household-coefficient column. Regional household-payment coefficients In specifying the household row (a , .) some regional 1-0 multiplier formulations use a value added definition, while others use an earnings definition. Since value added is greater than earnings, coefficients based on a value-added definition are larger than those based on an earnings definition. 23/ Bourque and Conway (1977) argue that the choice of a household-row definition should be made in the context of the type of impact to be studied. 24/ The regional value-added household-row ( a n + i J can be estimated by the industry-specific value added-to-gross output ratios from the national 1-0 table. The earnings household row is more difficult to estimate using national data. Ideally, the procedure used to construct the earnings household row would use proprietors' income data, wage and salary-to-employee compensation ratios, and disaggregate employee compensation-to-value added ratios for 1972. However, disaggregate ratios are not yet available for the 19 72 table. Since only aggregate ratios are available for 1972, disaggregate ratios from the 1967 national table can be 23. Value added is defined as the sum of employee compensation, profit-type income, and indirect business taxes. Earnings is defined as the sum of wages and salaries (a part of employee compensation), other labor income (another part of employee compensation), and proprietors' income (a part of profit-type income). 24. When using a value-added household-row definition, Bourque and Conway (1977) estimated the household column coefficients (a. -i ) by the household industry- i ,n + 1 ' J J specific purchases-to-total regional value added ratio (X. ,/VA ). When using an earnings household-row definition, the household-column coefficients are estimated by the household industry-specific purchases-to-total regional personal income ratio < X i,n ♦ l /PYr >- -21- controlled to the level of the corresponding aggregate 19 72 ratios by a procedure such as the fol lowing:25/ cv k 72 cv j 2= 17? cv f < 3 - 20 > k where: CV = an employee compensation-to-value added ratio In equation 3.20 and other equations presented below, the superscripts (67 and 72) refer to the base years of the national 1-0 tables; the subscript j refers to an industry in the 496-industry-level national table, and the subscript k refers to the industry of which j is a part in the 85-industry-level national table. In equation 3.20, the distribution of the 1967 employee compensation-to-value added ratios for disaggregate industries is used to allocate the 1967 to 19 72 corresponding aggregate industry change in those ratios. The employee compensation ratios estimated for 19 72 can then be further adjusted to reflect the exclusion from earnings of compensation other than wages and salaries and other labor income, and the inclusion in earnings of proprietors' income. Such an adjustment can be represented as: EV j 2 = CV j 2 WO k 2 PW k 2 (3,21) where: EV = the national earnings-to-value added ratio WO = the national wages and salaries and other labor income-to-employee compensation ratio PW = the national proprietors' income and wages and salaries-to-wages and salaries ratio In equation 3.21, WO is always less than one, because the sum of wages and salaries and other labor income is less than employee compensation; PW is greater than one for most industries, because proprietors' income is positive in most industries. Finally, earnings-to-gross output ratios can be estimated as follows: EG 72 = EV 72 VG 72 (3.22) J J J where EG = the national earnings-to-gross output ratio VG = the national value added-to-gross output ratio 25. Employee compensation-to-value added ratios for the 484-industry-level 1967 national 1-0 table can be found in Coughlin (19 78). Employee compensation-to-value added ratios for the 85-industry-level 19 72 national 1-0 table can be found in Ritz (19 79) and Ritz, et al. (19 79). When employee compensation-to-value added ratios for the 496- industry-level 19 72 1-0 table are available, they will be used directly in equation 3.21. -22- Thus, in cases where an earninqs-def ined household row is relevant, a 11 . . is n + l defined by the following equation: ' J a n + l,j * EG f < 3 ' 23 > In other cases, where a value-added household row is relevant, a + n ■ is defined by the following equation: aJ + lfJ - VGf (3.24) Whether a value-added or an earnings household-row definition is adopted, it is important to adjust the household row to reflect the region's loss of income that results from individuals working in the region but residing outside the region. 26/ Thus, commuters' income is viewed as a leakage from the regional economy. This additional adjustment is represented as follows: a n + l,j ■ SL Vl Cl.j < 3 - 25 > where: SLQ , = total personal income plus residence adjustment divided by total personal income, if residence adjustment is negative SLQ , = 1.0, if residence adjustment is not negative In equation 3.25, the amount of residence adjustment is used as the basis for constructing an LQ (SLQ + , ) to estimate the size of a region's labor imports. Industry Aggregation Previous sections of this chapter have described various techniques for estimating a disaggregated regional direct-purchase-coefficient (a..) matrix. However, a more r aggregated coefficient (a-, ) matrix is often useful .27/ Ideally, since the coefficients to be aggregated are defined in terms of output, columns of a disaggregated direct- coefficient matrix should be aggregated on the basis of industry-specific output data. However, since these data seldom are available at the regional level, industry-specific earnings data can be used to estimate proxies for regional output. This is represented in the following equation: E 5 r X. = x n J = E " J (3.26) 26. For a discussion of the residence-adjustment concept, and its relationship to commuting, see U.S. Department of Commerce (1980.) 27. For example, in the accuracy comparisons presented in chapter 5 of this monograph, the nonsurvey matrices were aggregated to a level of industry detail which is comparable to that of the survey-based matrices. In addition, an aggregated matrix may be appropriate, since impact studies may not require the industry detail provided in the national table. This is especially true for the row industry detail. For the application of RIMS II presented in chapter 6, the 496 rows of the regional matrices have been aggregated to 39 rows. -23- where : X. = a proxy for the output of industry j in region r \ n . = the output of industry j in the Nation •J E. = earnings in industry j in region r El- = earnings in industry j in the Nation J In equation 3.26, for each disaggregated industry the regional share of national earnings estimates a proxy for regional output to be used in the following aggregation procedure. 28/ In order to aggregate a matrix with j columns to one with m columns, the following equation can be used for all i rows: j" 3 r E ••)• The I ■ .••■■•il T . • 1 • ' J The multiplier matrix also permits the estimation of household-earnings multipliers for individual-row industries for a given column industry's final-demand change. These multipliers can be estimated by multiplying the individual row-industry multipl ier (b--) by the ratio of earnings to output in that industry (a , •). The sum of these i industry-specific earnings multipliers also equals the total-earnings multiplier (b r ,, ■) for a qiven column j. This is expressed in equation 4.13: n+l,j ; 3 n+1 b n+l,J E b ^ -Vi.i (4 - 13) i=l •34- where: r r ^ii a n+l i = tne earn "i n 9 s multiplier for industry i given a final -demand change J L > in industry j Earnings multipl iers--shortcut approaches In addition to showing how industry-specific earnings multipliers can be summed to the total-earnings multiplier, equation 4.13 is the basis for alternative formulas for calculating a household-earnings multiplier when a shortcut technique is used to estimate the column-total multiplier (b r -). Earnings-multiplier formulas are necessary since the shortcut techniques do not estimate the full-multiplier matrix (b. .), but rather only its column sums (b •)• The shortcut techniques, by themselves, provide no information about the relative size of the two parts of the column-total multiplier shown in equation 4.12. The alternative earnings formulas can be derived by expressing equation 4.13 as: n+l r _ h r r n+l,j D jj Vl,j i=l + E b iJ 3 n+l,i (4 ' 14) The first term on the right side of equation 4.14 represents that part of the earnings multiplier that occurs in the initially affected industry itself. The coefficient b.. is th ^ the diagonal element of the j column in the multiplier matrix, and the coefficient r th a , . is the household-row coefficient from the j column of the direct-coefficient matrix. The fact that the diagonal of the multiplier matrix is always greater than, or equal to, 1.0 can be used to express equation 4.14 as: b n+l,j = a n+l,j or h r r Vl,j Vl,j n+l (b r . - 1) a r xl . + V* b r . a 1 ^ . (4.15) i=l n+l E br 'a a n+i,i (4 - 16) 1=1 where: b r :. = b io if W b r :. = b io -1 if i=j ■35- Equation 4.16 indicates that the earnings multiplier for industry j is composed of two parts: the direct-earnings effect in industry j, and the sum of the additional earnings effects in all industries. Moreover, since the shortcut techniques make estimates of a n+l i " in estimating a -j (the sum of the direct coefficients in column j), equation 4.16 can be used to generate earnings-multiplier formulas based on the relationship between b r \. and a^ +lji . r ' Since b . . is not estimated by the shortcut techniques for any particular column j, the original formula 10/ for calculating the total-earnings multiplier is based on the simplifying assumption that aj^ + , . is constant across industries, and equal to the average of the direct household coefficients. Under this assumption, equation 4.16 becomes: n+1 E br ij (4 - 17) b n+l,j = Vl,j + a n+l i=l where: aL,, = the average a „,, , over the i industries n+1 3 n+l,i Furthermore, since from the conditions of equation 4.16, n+1 b r . (E b %) + i (4 - l8) the j column's earnings multiplier can be expressed as: b n + l,j ■ Vl,j + Vl '"j - 1) < 4 - 19 > As indicated in equation 4.19 (the original formula), the earnings multiplier is expressed as a function of the direct-earnings effect (a ■, .), the average direct- earnings effect (a ,), and the column-total multiplier (b .). n - ' i • j An alternative earnings-multiplier formula, which includes the same variables as equation 4.19, also can be derived. In order to see how this alternative formula might be derived, equation 4.16 can rewritten as: n ClJ ■ VlJ + Cl.j a n + l,n + l + E br U Vl.i (4 - 20) i=l 10. The term, original formula, is adopted here because it was employed in the original RIMS as described in U.S. Water Resources Council (1977). The original formula is also equivalent to one described by Burford and Katz (1977 and 19 78a). -36- By writing the (n+1) row outside the summation sign, a potential weakness of the original formula can be readily seen. Since a r ,, ,, (which represents the expenditures n+1, n+1 v K K of households, paid directly to households) is always a small coefficient relative to a ,-,, the use of the significantly larger a„.i as an estimate of a .-, „,-, could lead to an n+l 3 J 3 n+i n+i,n+i overestimate of the earnings multipl ier .11/ Given this overestimation bias, a modification of the original formula (eguation 4.19) is appropriate. Instead of assuming that a^ + i • is constant for all i industries, the modified formula is based on the assumption that a r Ll is constant only for the n+l,i J first n industries, and is equal to zero for the (n+1) industry. This latter assumption is based on the recognition that the intrahousehold-expenditure coefficient (a r .i , i ) is generally small and, therefore, has a small relative effect on the total- v n+1, n+1' 3 J earnings multiplier. r With a ., „,, equal to zero, and a ^i • constant only for the first i industries, n+1, n+1 M ' n+l,i J ' equation 4.20 becomes: b r ., . a r ., . + a x1 Y^ b r ' (4.21) n+1 / j ij v ' r r n+l,j n+1, j i=l Since, by equations 4.12 and 4.18, E b r .. = b r . -1 - b r x1 . (4.22) ij -J n+1, j v ' i=l then bLi i = a r x1 . + a (b r . - 1 - b r x1 .) (4.23) n+1, J n+1, j n+1 .j n+l,j y v ; Rearranging terms, equation 4.23 can be written as r . /L r c 'n+l,j b r Vl,j + a n+l ( b .j ' 1} (4.24) 1 + a ., n+1 As can be seen from equation 4.24, this modified formula differs from the original formula (equation 4.19) in that the former is divided by the amount 1 + a , . As a 11. In national 1-0 tables and most regional tables, a , , i i .. is above 0.30. n+i,n+i n+1 s less than 0.05, whi le -37- result, for a given column-total multiplier, earnings multipliers generated from this modified formula are less than those based on the original formula. For example, if "a , is equal to 0.3, then the multipliers generated from the modified formula are approximately 77 percent of the original formula's earnings multipliers. RIMS II Regional Multipliers RIMS II employs two alternative approaches for estimating column-total multipliers. For applications in which it is necessary to measure the impact of final-demand changes in numerous directly and indirectly affected industries, the inversion RIMS II approach (equation 4.4) is employed. This RIMS II approach estimates the full regional multiplier matrix (B r ). For other applications that require measuring only the gross-output and earnings impacts associated with an industry-specific final-demand change, the shortcut alpha regression RIMS II approach (equation 4.11) can be employed. According to this RIMS II approach, only the column-total multiplier (b •) is estimated. However, based on the • J alpha regression RIMS II column-total multiplier, the modified formula (equation 4.24) can be used to estimate the corresponding RIMS II earnings multiplier (b , .)• While the blending of these two approaches into RIMS II enhances the flexibility of the system, especially in terms of the range of applications for which it might be employed, the inversion RIMS II approach might be the more useful in impact studies for two reasons. First, the inversion RIMS II approach provides the industry-specific IT multipliers ( b - - ' s ) that are useful in many impact studies, while the alpha regression RIMS II approach does not. Second, in many instances, the time and computer costs required to calculate the alpha regression RIMS II and the inversion RIMS II multipliers may not differ significantly. For example, if the full A r matrix must be calculated — r r first in order to estimate a and a ,-, for use in the alpha regression RIMS II equation, then generating the full inversion RIMS II matrix is a relatively inexpensive computer calculation. However, it is important to recognize that there are instances where the alpha regression RIMS II approach may be more useful than the inversion RIMS II approach. If a and a , are known (for example, from a previous regional 1-0 study where A was estimated), then the alpha regression RIMS II multiplier can be estimated based on these Y* V values and an estimate of a .. Therefore, when there is no need to estimate A , the alpha regression approach is the more cost effective of the two RIMS II approaches. ■38- Chapter 5 COMPARATIVE EVALUATION OF RIMS II PERFORMANCE While chapters 3 and 4 describe various purely nonsurvey techniques for estimating regional 1-0 tables, chapter 5 presents a comparative evaluation of the RIMS II nonsurvey techniques with other nonsurvey techniques that are similar to RIMS and RIMS II. In order to do this, the first section of this chapter presents a summary description of the RIMS II approaches. The second section describes the general evaluation approach and the statistics used in comparing RIMS II and other nonsurvey techniques with survey-based 1-0 coefficients. The third and fourth sections present the results for column-total comparisons and full-multiplier-matrix comparisons, respectively. The fifth and last section summarizes the results of the comparative evaluation of RIMS II, and presents a discussion of the implications of the accuracy of RIMS II for its use in impact analysis. Description of RIMS II Table 5.1 lists the RIMS II techniques and various other nonsurvey techniques for estimating the regional 1-0 coefficients that are analyzed in this monograph. In estimating regional direct coefficients, RIMS II uses a disaggregated (i.e., based on 4- digit SIC data) mixed LQ approach. This is done for two reasons. First, as discussed in chapter 3 of this monograph, the use of disaggregated LQ's more fully takes into account the differences between the regional and national industrial mixes than do the more aggregated LQ's. Second, the use of mixed LQ's takes into account all sources of demand, rather than only the interindustry transactions accounted for by earnings-based LQ's. For estimating column-total multipliers, RIMS II uses one of two approaches. The shortcut alpha regression RIMS II approach is used when only aggregate impacts for selected industries are desired. Among the various shortcut techniques examined in chapter 4, the alpha regression approach (equation 4.11) is superior to the original RIMS (equation 4.8) and the reestimated RIMS (equation 4.9) in terms of stability and explanatory power. For more detailed applications, the RIMS II total multipliers are estimated by Leontief inversion of the regional direct-coefficients matrix. The inversion RIMS II approach provides an estimate of the full multiplier matrix and indicates the industry- specific effects of changes in final demand. When the total multipliers are estimated by the alpha regression RIMS II approach, the RIMS II earnings multipliers are estimated by the modified formula (equation 4.24). This formula (as discussed in chapter 4) recognizes that the average direct household coefficient is not the appropriate earnings-to-output ratio for all row industries. When the full multiplier matrix is estimated by the inversion RIMS II approach, the earnings multipliers are the household-row coefficients of the multiplier matrix. Overview of the Evaluation Methodology This section focuses on a discussion of the methodology adopted for the evaluation of the accuracy of the RIMS II approaches, relative to other nonsurvey techniques. Jensen (19 79) and others have pointed out the pitfalls of comparing survey and nonsurvey estimates of input-output coefficients. Such comparisons are particularly difficult, since significant measurement errors may be associated with both survey and nonsurvey estimates. More specifically, Jensen (1980) argues that the survey content of some survey-based tables may be too small to warrant viewing their results as accurate -39 Table 5.1. -Alternative Techniques for Estimation of Direct Coefficients, Total Multiplier, and Earnings Multiplier Variable/technique Equation number Direct coefficients A 2-Digit earnings LQ's B 4-Digit earnings LQ's C* 4-Digit mixed LQ's Total multiplier 2-Digit techniques D Inversion of direct coefficients from A E Original RIMS with direct coefficients from A F Reestimated RIMS with direct coefficients from C 4-Digit techniques G Original Burford-Katz Formula with direct coefficients from C H* Alpha regression with direct coefficients from C I* Inversion of direct coefficients from C Earnings multiplier 2-Digit techniques J Inversion of direct coefficients from A K Original RIMS--total multipliers from E with the original earnings multiplier formula L Original RIMS--total multipliers from E with the modified earnings multiplier formula 4-Digit techniques M Alpha regression—total multiplier from H with the original earnings multiplier formula N* Alpha regression—total multiplier from H with the modified earnings formula 0* Inversion of direct coefficient from C 3.15 with 3.14a where i=l,. . . ,60 3.15 with 3.14a where i = l,...,496 3.15 with 3.14a and 3.14b where i = l,...,496 4.4 4.8 4.9 4.10 4.11 4.4 4.12 4.19 4.24 4.19 4.24 4.12 ♦Indicates RIMS II approaches -40- measures of the true 1-0 relationships in a regional economy. Still, it is necessary to adopt some norm against which to compare the alternative techniques, and the survey-based tables are the most generally accepted basis for comparison. The remainder of this chapter focuses on the estimates produced by the nonsurvey techniques relative to those of three recent survey-based tables: Texas (19 72); Washington (19 72); and West Virginia (19 75). A general description of these tables, and of their respective sectoring designations, appears in appendix A. The choice of these tables reflects several considerations. First, they are relatively recent tables, and they use base years that are reasonably close to those used for the BEA national table. Second, they represent three distinct kinds of economies, in both size and industrial structure. Third, the tables are well documented so as to assure conformance with the national 1-0 table in terms of definitions and conventions. Fourth, they were estimated by experienced research personnel, thus lending credibility to the accuracy of the results.^/ Based on the three survey tables, an analysis is performed on the accuracy of three techniques for estimating the direct coefficients, six techniques for estimating the total multiplier (with households endogenous), and six techniques for estimating the total earnings multiplier. These estimation techniques are listed in table 5.1. They can be categorized into two broad groups: 2-digit techniques and 4-digit techniques. 2/ The accuracy comparisons of alternative estimation techniques are conducted both at the column-total level and at the disaggregated cell-by-cell level. The aggregate comparisons are presented first, for two reasons. First, the shortcut multiplier techniques, as indicated in chapter 4, do not estimate the full multiplier matrix (b. .), r but rather only column total multipliers (b .)• Therefore, only aggregate comparisons • J are possible for these shortcut techniques. Second, the focus on aggregate accuracy comparisons may be more appropriate when the multipliers are intended for use in impact studies. For example, Jensen (19 79) emphasizes the need for analyzing the holistic, rather than merely the partitive, accuracy of nonsurvey techniques. Jensen describes partitive accuracy as that which focuses primarily on cell-level comparisons of nonsurvey and survey results. He distinguishes this from holistic accuracy, which is more concerned with whether the application of a nonsurvey technique on the whole gives "reasonable" estimates of economic interrelationships. According to this latter approach, strict cell-by-cell accuracy comparisons are less important than considerations of the accuracy of the overall multipliers. Numerous techniques have been employed in previous studies for the purpose of measuring accuracy in nonsurvey techniques. Percent error, Theil statistics, chi-square 1. Although attempts were made to use a small-area (for example, an SMSA) table in the evaluation, none was found that met each of these four criteria. 2. For the purpose of a historical comparison with earlier BEA work, a strict formulation of the 2-digit LQ technique was not employed. Rather, a variation of the 2- digit LQ technique was used in estimating the multipliers analyzed in this chapter. According to this variation (part of the original RIMS technique), data on 4-digit industries are used to identify those that are not present in the study region. The remaining coefficients were then made more region-specific by the 2-digit LQ technique. -41- tests, as well as correlation and regression analysis, have been the most common approaches. 3/ The analysis in this chapter primarily employs the statistic developed by Theil (19 66). 4/ An important reason for using the Theil statistic is that it combines both the absolute prediction error (which is the basis for the percent error and chi- square tests) and the degree of association between the actual and predicted values (which is the basis for correlation and regression analysis). In addition, unlike other tests, the Theil statistic does not suffer from the "small-cell" problems discussed by Morrison and Smith (19 74) and others. The Theil statistic (U) is based on the relative mean-square prediction error, and, as used in the accuracy comparisons presented in this chapter, is defined as: U where : £(P. - A^ 2 Y 7 2 (5.1) P. = the value predicted by the nonsurvey table A- = the actual value for the survey table If the predicted and actual values are identical in all cases, then U equals zero; if the predicted and actual values are unequal in some cases, then U is not equal to zero. Furthermore, the larger the difference between P. and A-, the larqer the value of U. For this reason, the statistic is often referred to as the Theil inequality coefficient. The lower bound of U is zero; the statistic has no finite upper bound. One of the important features of the Theil statistic is that U can be decomposed into three sources of prediction error. If U is not equal to zero, errors of central tendency (U m ), unequal s c variation (U ). or incomplete covariation (U ) may occur . The three sources of error are defined as proportions that sum to one. Theil (1961 and 1966) argues that if predictions are not perfectly accurate the desirable distribution of the inequality proportions i s U = U =0 and U = 1. Small proportions for U and U indicate that systematic errors are not large, while a large proportion for U indicates that individual cell-level errors predominate. The Theil statistic is especially useful when comparing alternative nonsurvey techniques. For example, in general the technique with the lowest U value would be the preferred technique, especially if this technique also had the lowest values for U m and II s and the highest value for U c . Another indication of the accuracy of nonsurvey techniques relative to that of the survey-based multipliers can be obtained from the chi-square statistic. For each column, 3. For examples of the range of tests applied in analyzing the accuracy of nonsurvey techniques, see Schaffer and Chu (1969), Morrison and Smith (19 74), and Stevens, et al. (1980). 4. The Theil statistic has been employed in regional 1-0 analysis by Stevens and Trainer (1980). -42- this statistic measures the degree of association between the nonsurvey multipliers and the survey multipliers, where the multipliers in each of the rows are expressed as proportions of the column-total multiplier. The actual form of the statistic is given in equation 5.2. 5/ chi -square = i = l where: P. b r . s\ b r . • J b r . A i b r . t (p ^- A,) (5.2) The circumflex [ s\ ) refers to the nonsurvey multiplier matrix values. For a given column, if the nonsurvey and survey multipliers had the same proportional distribution of multipliers among affected row industries, P. would equal A. in all cases, and the value of the chi-square statistic would be zero. Alternatively, the greater the dissimilarity (in terms of the relative size of industry-specific multipliers for that column) between the nonsurvey and survey tables, the larger the statistic. In addition to the Theil and chi-square statistics, Spearman-rank correlation statistics are useful in assessing the accuracy of the estimation techniques. 6/ The Spearman-rank correlation coefficient (r ) can be defined as follows: N 6 E »* r = 1 - — (5.3) s l(N 2 - 1 where r . . r D. = the difference between the size rankings of b.- and b.. in column j N = the number of observations, that is, the number of rows in each column 5. The use of the chi-square statistic as a summary statistic in this context is similar to the chi-square goodness-of-f it test, discussed by Wonnacott and Wonnacott (19 77) and others. 6. For an example of the use of the Spearman statistic in 1-0 analysis, see Bezdek and Wend ling (19 76). -43- The Spearman-rank correlation measures the degree of association between two distributions of rankings; if the rankings were the same, the Spearman-rank correlation coefficient would equal one. In implementing this statistic, the multiplier values for the rows in each column are ranked from highest to lowest for both the survey and nonsurvey matrices. Spearman-rank correlation coefficients are then calculated for each column in each of the State matrices. Column-Total-Level Accuracy Comparisons The first three tables in this section present a summary of relevant error statistics associated with alternative techniques for estimating the direct coefficients, the total multiplier, and the earnings multiplier. These statistics have been calculated for three States at the column-total level. The statistics were based on 133 column observations for Texas, 50 column observations for Washington, and 41 column observations for West Virginia. The mean column values in these tables are the unweighted averages of the individual column values; the ratios of means are calculated as the mean nonsurvey value divided by the mean survey value. Focusing first on the accuracy of the estimates of the direct coefficients, tables 5.2-5.4 indicate several patterns that are apparent across each of the States. First, all the statistics indicate appreciably larger errors associated with the 2-digit SIC earnings LQ's than with either of the 4-digit techniques. Furthermore, a consistent, although slight, increase in accuracy is also associated with the use of mixed LQ's employed in the RIMS II approach. Second, a substantially greater portion of the error (as indicated by the Theil statistic) is associated with central tendency in the case of the 2-digit LQ's, as opposed to the 4-digit LQ's. Slight improvement in this measure is also evident when comparing the 4-digit mixed LQ's employed in the RIMS II approach with those of the 4-digit earnings LQ's. Turning to the consideration of the accuracy of the total multiplier results, similar conclusions are evident. With few exceptions, errors associated with the 2-digit techniques are consistently greater than those associated with the 4-digit techniques, and a large portion of the errors in the 2-digit techniques are attributable to errors in central tendency. Further, it should be noted that the alpha-regression RIMS II and the inversion RIMS II approaches generate total multiplier estimates that are quite similar. The results of the total multiplier analysis also suggest several other findings regarding the accuracy of alternative nonsurvey techniques. First, of the 2-digit techniques, none is clearly superior in all cases. For example, the accuracy of the inversion 2-digit technique is relatively poor in Washington and relatively good in West Virginia. Furthermore, while the reestimated RIMS approach is superior to the original RIMS approach in Texas and West Virginia, it is inferior in Washington. Second, of the 4- digit techniques, both the alpha regression and the inversion RIMS II approaches consistently outperform the original Burford-Katz formula, as measured by the Theil statistics and mean multiplier ratios. 7/ For example, the Theil statistic for central 7. For the original Burford-Katz approach these results are not as favorable as those for multipliers that were calculated without an endogenous household row and column; see Katz and Burford (1980) for these results with households exogenous. A probable cause for the relatively poor results generated by the original Burford-Katz formula, when households are endogenous, is that the large household-row coefficients (especially the value-added coefficients in Washington) violate the randomness assumptions used in deriving the formula; Jensen (1978a and 1978b) and Burford and Katz (1978b) contain ■44- Table 5. 2. -Distribution of Theil Statistics and Ratios (Nonsurvey/Survey) at the Column-Total Level Texas Variable/technique Theil statistic Mean Nonsurvey Survey Ratio of mean Direct coefficient 2-Digit earnings LQ's 0.3210 4-Digit earnings LQ's .2217 4-Digit mixed LQ's* .2187 Total multiplier Inversion with 2-digit earnings LQ's .2944 Original RIMS with 2-digit earnings LQ's .2923 Reestimated RIMS with 2-digit LQ's .1770 Original Burford-Katz with 4-digit mixed LQ's .1566 Alpha regression with 4-digit mixed LQ's* .1435 Inversion with 4-digit mixed LQ's* .1504 Earnings multiplier Inversion with 2-digit earnings LQ's .3078 Original RIMS with 2-digit earnings LQ's Original formula Modified formula Alpha regression with 4-digit mixed LQ's Original formula Modified formula* Inversion with 4-digit mixed LQ's* .2319 0.3435 0.0048 0.6517 0.7366 0.6176 .1320 .0290 .8390 .6685 .6176 .1217 .0327 .8456 .6659 .6176 5925 ,6094 ,0356 1289 ,2405 ,0020 .4055 3.4467 2.8036 ,0005 .3901 3.4509 2.8036 ,0848 .0307 .8844 2.9490 2.8036 1813 .0483 0248 7705 2.9928 2.8036 ,0648 .899 7 2.8804 2.8036 .8463 2.9569 2.8036 .0123 .7472 .8191 7074 1.19 27 1.0824 1.0782 1.2294 1.2309 1.0519 1.0675 1.0274 1.0547 1.1579 .6267 .7072 .0001 .29 26 1.0974 .7074 1.5514 .3413 .2191 .0386 .7423 .8256 .7074 1.1671 .4019 .4621 .0026 .5353 .9095 .7074 1.2857 .2717 .0132 .1051 .8817 .6843 .7074 .9674 ,0005 ,0559 .9436 7035 .7074 .9945 *Indicates RIMS II approaches. -45- Table 5. 3. -Distribution of Theil Statistics and Ratios (Nonsurvey /Survey) at the Column-Total Level Washington Variable/technique Theil statistic ,m Mean Nonsurvey Survey Ratio of means 0.3741 .1086 .0503 Direct coefficient 2-Digit earnings LQ's 0.2102 4-Digit earnings LQ's .1461 4-Digit mixed LQ's* .1408 Total multiplier Inversion with 2-digit earnings LQ's Original RIMS with 2-digit earnings LQ's Reestimated RIMS with 2-digit earnings LQ's Original Burford-Katz with 4-digit mixed LQ's .4688 Alpha regression with 4-digit mixed LQ' s* Inversion with 4-digit mixed LQ's* Value added multiplier Inversion with 2-digit earnings LQ's .2535 .4085 .3410 .7676 .1684 .4824 .1802 .5376 .4688 .9159 .1148 .2375 .1107 .0711 Original RIMS with 2-digit earnings LQ's Original formula .5647 .79 07 Modified formula .2101 .0184 Alpha regression with 4-digit mixed LQ' s Original formula .3441 .5442 Modified formula* .2660 .49 76 Inversion with 4-digit mixed LQ's* .1709 .1860 *Indicates RIMS II approaches. 0.0260 0.5999 0.8490 .0116 .8798 .7873 .0212 .9285 .7746 ,0117 ,0082 ,0048 ,0320 2207 3.9 715 ,0254 .4921 3.4108 ,0117 .4507 3.4604 ,0129 .0712 4.4373 ;0903 .6722 2.8776 0.7504 1.1314 .7504 1.049 2 .7504 1.0322 3.0502 1.3021 3.0502 1.1182 3.0502 1.1345 3.0502 1.4548 3.0502 .9434 .9207 3.1412 3.0502 1.0298 5867 1.3751 ,0078 .2015 1.7861 ,0484 .9 332 1.1449 ,0184 .4374 1.4861 ,0330 .4694 .9527 7820 1.0903 1.1794 1.1660 1.1794 1.5145 1.1794 .9708 1.1794 1.2601 1.1794 .8078 1.1794 .9 245 -46- Table 5. 4. -Distribution of Theil Statistics and Ratios (Nonsurvey/Survey) at the Column-Total Level West Virginia Variable technique Theil statistic Mean Jonsurvey Survey Ratios of means Direct coefficient 2-Digit earnings LQ s 0.3739 0.2116 4-Digit earnings LQ' s .3060 .0641 4-Digit mixed LQ s* .3029 .0575 Total multiplier Inversion with 2-digit LQ's .2789 .4601 Original RIMS with 2-digit LQ's Reestimated RIMS with 2-digit LQ's Original Burford-Katz with 4-digit mixed LQ's* Alpha regression with 4-digit mixed LQ' s* Inversion with 4-digit mixed LQ's* Earnings multiplier Inversion with 2-digit earnings LQ's 2789 .4601 4106 .7262 2931 .5568 19 46 .3111 1728 .1608 1821 .1526 .3542 Alpha regression with 4-digit mixed LQ' s Original formula .5679 Modified formula* .4043 Inversion with 4-digit mixed LQ's* .2848 2781 Original RIMS with 2-digit earnings LQ's Original formula .8650 .6510 Modified formula .5306 .3074 ,3626 ,0043 1014 0.0006 0.7879 0.5880 0.4990 1.1784 .0101 .9 259 .5391 .499 1.0804 .0125 .9300 .5366 1.0754 1.0754 .0134 .5265 2.3161 1.9448 1.1909 ,0173 0092 .0004 0005 ,0007 2564 2.6316 1.9448 1.3532 4340 2.3740 1.9448 1.2207 ,6884 2.1579 1.9448 1.1096 ,0030 .8362 2.0808 1.9448 1.0699 .8469 2.0845 1.9448 1.0918 7212 5700 ,4749 1.2003 ,0056 .3434 .8304 .4749 1.7486 ,0059 .6867 .6247 .4749 1.3155 .0 .6374 .6491 0499 .9458 .4883 0003 .8983 5211 ,4749 1.3669 4749 1.0283 4749 1.09 73 *Indicates RIMS II approaches. -47- tendency (L) c ) for the original Burford-Katz formula is significantly higher for each State than the Theil statistics for the RIMS II approaches. The earnings-multiplier results shown in tables 5.2-5.4 also indicate the superiority of the 4-digit techniques over the 2-digit ones, and the superiority of the RIMS II approaches over the other nonsurvey techniques. In addition, the tables show that the accuracy of the modified formula for calculating earnings multipliers is better than that of the original formula. Finally, in all cases, the Theil statistics for the earnings multipliers are somewhat greater than those for the corresponding total multipliers. This result suggests that, for a given column, the nonsurvey techniques are generally less accurate in estimating a given row element (in this case, the household row) than in estimating the column total itself. In summary, it is important to emphasize the significant accuracy improvements brought about by using the RIMS II 4-digit mixed LQ's when compared with the 2-digit earnings LQ's, as indicated in tables 5.2-5.4. For example, with respect to the survey total multipliers for all three States, the average overestimation associated with the inversion of the 2-digit direct coefficient matrix is 24 percent. 8/ For the inversion RIMS II approach, the corresponding overestimation is only 5.5 percent. Therefore, by using 4-digit SIC mixed LQ's, and thereby taking into account the disaggregated regional industrial structure, the accuracy of the purely nonsurvey LQ technique is significantly improved. In order to further evaluate the accuracy of the RIMS II, it is useful to consider the distribution of column-total-multiplier ratios for several nonsurvey techniques. Rather than presenting results for the entire range of techniques shown in tables 5.2- 5.4, the focus here is on the accuracy of two 2-digit approaches (original RIMS and inversion) and the two 4-digit RIMS II approaches (alpha regression and inversion). Since a basic purpose of this research is to improve the existing multiplier approach, the original RIMS approach is included here to facilitate historical comparison. The choice is made even though the reestimated RIMS approach performs slightly better than its earlier counterpart. The inversion 2-digit approach is included to facilitate the comparison of the 4-digit inversion RIMS II approach. Appendix tables B1.1-B1.3 present the industry-specific column total multiplier ratios for each State from which the results in table 5.5 were derived. As is readily evident from the results presented in table 5.5, a substantially larger proportion of ratios lie between .90 and 1.09 for the RIMS II approaches.9/ For preliminary discussions of this issue. Katz and Burford (1981) developed refinements to their original shortcut formula that explicitly take into account a correction factor for an endogenous household sector. The refined Katz-Burford approach for calculating earnings multipliers is similar to the modified formula for earnings multipliers, derived in chapter 4; based on that similarity, the refined Katz-Burford approach should be more accurate than the original formula. The original Burford-Katz formula is included in the analysis in this chapter in order to provide an additional historical comparison with the original RIMS approach, which was developed (as shown in chapter 4) from a similar conceptual basis. 8. This average is obtained by weighting the overestimation of the mean multiplier by the number of columns in each State. This result is consistent with (although somewhat lower than) the findings of Schaffer and Chu (1969) and Morrison and Smith (19 74). 9. The mean ratio is calculated as the unweighted average of the individual column ratios . ■48- Table 5. 5. -Distribution of Ratios of Column-Total Multipliers (Nonsurvey/Survey) Ratio range Mean State/technique Ratio Below .70- .80- .90- .95- 1.00- 1.05- 1.10- 1.20- Over .70 .79 .89 .94 .99 1.04 1.09 1.19 1.29 1.29 Texas Inversion 2-digit earnings LQ's 1 2 5 4 6 10 26 29 50 1.25 Original RIMS 2-digit earnings LQ's 1 1 5 2 1 8 7 30 30 48 1.26 Alpha regression 4-digit mixed LQ's* 2 4 10 17 17 19 25 20 11 8 1.04 Inversion 4-digit mixed LQ's* 2 1 7 14 20 14 24 28 11 12 1.07 Washington Inversion 2-digit earnings LQ's 1 1 2 6 16 24 1.32 Original RIMS 2-digit earnings LQ's 003143 12 13 86 1.13 1 1 3 1 4 3 9 14 12 1 4 1 10 Alpha regression 4-digit mixed LQ's* n ! 0.9 Inversion 4-digit mixed LQ's* i i 1.04 West Virginia Inversion 2-digit earnings LQ's 1 2 5 3 3 9 5 13 1.21 Original RIMS 2-digit earnings LQ's 1 1 2 7 6 24 1.38 Alpha regression 4-digit mixed LQ's* 1 3 6 5 3 4 9 4 6 1.09 Inversion 4-digit mixed LQ's* 1 3 7 3 3 8 5 5 6 1.09 Indicates RIMS II approaches. -49- example, only 20 observations for the 2-digit inversion technique fall between ratios .90 and 1 . 09 i n Texas, while 72 observations for the 4-digit inversion RIMS II approach fall into this range. As with the Theil statistics, the alpha regression RIMS II and the inversion RIMS II approaches have a similar ratio distribution. Finally, in terms of the overall accuracy of the RIMS II approaches for all three States, almost 60 percent of column-total multipliers are within 10 percent of the corresponding survey values. A comparison of the distribution of individual column-earnings-multiplier ratios (value-added-multiplier ratios for Washington) shows results similar to those for the total multiplier ratios. The distribution of column-earnings-multiplier ratios for each of four approaches is presented in table 5.6. (Appendix tables B2.1-B2.3 present the industry-specific earnings-multiplier ratios for each State.) With the exception of the original RIMS in Washington, both RIMS II approaches are superior to their 2-digit alternatives in estimating the earnings multipliers. However, the range of the distribution of the earnings multipliers is greater than that of the total-multiplier ratios. For example, approximately 60 percent of the inversion RIMS II earnings- multiplier ratios are within 15 percent of the survey values, while 60 percent of RIMS II total-multiplier ratios are within 10 percent of the survey values. 10/ Two of the results shown in table 5.6 should be discussed here more fully. First, in West Virginia, the high mean ratios for the RIMS II approaches primarily are due to a substantial overestimation of the earnings multiplier for the instruments industry. When this industry is deleted from the calculation, the mean ratio of the alpha regression RIMS II approach decreases from 1.15 to 1.08, and that of the inversion RIMS II decreases from 1.19 to 1.11. These large decreases show the sensitivity of this statistic to changes in a few extreme ratios, particularly in tables such as West Virginia's, which lists relatively few industries. Second, table 5.6 indicates that the alpha regression RIMS II approach significantly underestimates a large number of the value-added multipliers in Washington. Since this approach is considerably more accurate in estimating the column-total multiplier, underestimating the value-added multipliers probably is due to the inadequacy of the shortcut modified formula. More specifically, since the modified formula works better in Texas and West Virginia (where the household row is defined on an earnings basis) than in Washington, the incompatibility of the value-added household-row definition and the modified formula might be viewed as a basic cause of the underestimation in Washington. However, since the earnings household-row definition is used in many RIMS II applications, this shortcoming may be less serious. Still, further research into this problem would be useful. Interindustry-Level Accuracy Comparisons As described in the previous sections, aggregate comparisons of various nonsurvey techniques indicate the relative superiority of the RIMS II approaches, as well as their overall accuracy, when compared with survey-based counterparts. Since the shortcut techniques estimate only the column-total multiplier, disaggregated accuracy comparisons are impossible for these techniques. However, the inversion techniques estimate the full multiplier matrix, thereby enabling additional interindustry accuracy comparisons (based on the difference between b • ■ and b- -) to be made. Therefore, the purpose of this section 10. The greater range in the earnings-multiplier-ratio distribution is also reflected in the higher Theil statistic for the earnings multiplier when compared with those for the total multipl ier . -50- Table 5.6. -Distribution of Ratios of Column Earnings* Multipliers (Nonsurvey /Survey) Ratio range Mean State/technique Ratio Below .75- .85- .90- .95- 1.00- 1.05- 1.10- 1.15- Over .75 .84 .89 .94 .99 1.04 1.09 1.14 1.24 1.24 Texas Inversion 2-digit earnings LQ's 10 5 3 5 5 4 7 13 24 57 1.23 Original RIMS 2-digit earnings LQ's modified formula 8 6 4 3 5 6 10 8 76 65 1.25 Alpha regression 4-digit mixed LQ's modified formula** 18 11 14 11 8 16 14 11 12 18 1.03 Inversion 4-digit mixed LQ's** 18 10 10 11 14 6 13 19 13 19 1.04 Washington Inversion 2-digit earnings LQ's 2 2 3 10 1 14 16 1.21 Original RIMS 2-digit earnings LQ's modified formula 4 2 1 7 10 7 6 4 2 7 1.01 Alpha regression 4-digit mixed LQ's modified formula** Inversion 4-digit mixed LQ's** West Virginia Inversion 2-digit earnings LQ's 1 3 1 7 2 1 2 2 6 16 1.32 Original RIMS 2-digit earnings LQ's modified formula 300202151 27 1.49 9 23 6 7 2 1 2 .83 5 3 7 8 8 9 3 1 6 .9 5 Alpha regression 4-di mixed LQ's modified formula** 9" t 4 3 4 6 2 1 4 2 3 12 1.15 Inversion 4-digit mixed LQ's** 2 3 6 1 3 1 4 3 3 15 1.19 *Value added multipliers for Washington **Indicates RIMS II approaches. -51- is to determine how closely the inversion techniques (notably the inversion RIMS II approach) approximate their survey-based counterparts at the interindustry level. In this section, accuracy comparisons are first made on the basis of the Theil statistic calculated for each column, with observations being individual row elements of a column in the multiplier matrix. Thus, in Texas, 133 Theil statistics (one for each column) are calculated, each with 51 observations (one for each row) .11/ In addition, the chi -square results and the results of the Spearman rank correlation test are discussed in order to indicate the similarity of the survey and nonsurvey columns in the multiplier matrices. Finally, the accuracy of the inversion approach is analyzed, based on a comparison of the percent errors associated with the larger cells of the multiplier matrix and the percent errors associated with the smaller cells of the multiplier matrix. Table 5.7 presents the Theil statistic results for the inversion 2-digit and inversion RIMS II approaches. These results show that the inversion RIMS II approach records almost five times the number of Theil statistics in the lowest two groups when compared with its 2-digit counterpart. Similarly, in each State, substantially larger numbers of Theil statistics can be found in the .30-and-over group for the 2-digit technique, as compared with RIMS II. Table 5.8 presents the results of the decomposition of the Theil statistic for the two inversion techniques. As indicated above, if prediction errors were present, then the ideal distribution of U m , U s , and U c would be 0, 0, and 1. The results for each of the States again show the relative superiority of the inversion RIMS II approach when compared with its 2-digit counterpart. Further, this RIMS II approach exhibits little error associated with central tendency (U m ). However, a somewhat greater divergence from the ideal values is evident for the other Theil statistic components. In order to describe further the interindustry accuracy of RIMS II, chi-square statistics and Spearman-rank correlation coefficients were calculated. For all three States, the average chi-square for RIMS II was .27; the average chi-square statistic was 280 percent higher for the 2-digit technique, when compared with the inversion RIMS II approach. _12/ The low chi-square statistics for RIMS II indicate that RIMS II multipliers and multipliers from survey-based tables have similar proportional distributions of multipliers among affected row industries. In addition, Spearman-rank correlation coefficients calculated for the RIMS II approach indicate little significant difference between the survey and RIMS II multipliers in the rank ordering of row elements in each column. For example, in Washington, the Spearman coefficients were all significant at the .001 level, and greater than .9 for 43 of 50 column-total multipliers; the average coefficient was .94. In this context, the high coefficients indicate that the RIMS II approach shows a rank distribution of row industry-specific effects that is indistinguishable from that of the survey table. The results of the Spearman tests are not presented here, however, since the Spearman statistic is only a rank-size test, and, 11. For the analysis of aggregate multipliers in the previous section, one Theil statistic is calculated for each State. For example, in analyzing the column-total direct coefficients, there are 133 predicted and actual observations for calculating the Theil statistic in Texas. 12. Chi-square statistics for each column-multiplier comparison are presented in appendix tables B3.1-B3.3. ■52- Table 5. 7. -Distribution of Theil Statistic State/technique Theil statistic range .0000- .0500- .1000- .1500- .2000- .2500- Over .0499 .0999 .1499 .1999 .2499 .2999 .2999 Average Texas Inversion 2-digit earnings LQ's Inversion 4-digit mixed LQ's* 24 27 53 22 22 27 15 20 10 32 0.2403 1654 Washington Inversion 2-digit earnings LQ's Inversion 4-digit mixed LQ's* 13 23 16 13 10 2383 1309 West Virginia Inversion 2-digit earnings LQ's Inversion 4-digit mixed LQ's* 17 1944 149 3 Indicates RIMS II approach -53- Table 5. 8. -Decomposition of Theil Statistic State/technique Percentile range Average 01- .10- .20- .30- .40- .50- .60- .70- .80- .90- 09 .19 .29 .39 .49 .59 .69 .79 .89 1.00 56 54 23 38 23 28 13 10 1 6 8 9 17 96 36 1 56 22 19 13 6 1 6 11 5 Washington Inversion 2-digit earnings LQ's m u c Inversion 4-digit mixed LQ's* U m 35 5 9 1 U S 16 8 4 7 U 13 4 3 West Virginia Inversion 2-digit earnings LQ's U m 14 18 U s 15 8 U c Inversion 4-digit mixed LQ's* U m u s u c Texas Inversion 2-digit earnings LQ's U m u s U C : i: 8 9 17 16 22 Inversion 4-digit mixed LQ's* U m u c 0.12 5 .26 19 20 15 .63 .06 6 3 .21 16 27 20 38 .73 5 3 16 24 1 .28 6 6 11 11 7 5 3 1 .32 7 7 13 14 3 2 1 2 1 .39 .09 2 2 3 .28 6 7 8 7 9 .63 8 1 .13 7 4 4 2 1 .20 3 4 2 7 4 5 6 10 .67 25 15 1 .09 16 9 5 5 2 2 1 1 .20 1 2 3 4 6 6 10 9 .71 *Indicates RIMS II approach, ■54- therefore, weaker than the chi-square statistic, which evaluates the magnitude of multiplier errors. Another indication of the accuracy of the Inversion RIMS II approach can be made by comparing the size of the RIMS II estimation error with the size of the survey table's multipliers.^/ For most multiplier columns, RIMS II makes relatively small percent errors for those cells that are a large percent of the survey table's total multiplier. This can be seen in the generally small percent errors for the earnings multipliers, which are always a large proportion of the column-total multiplier. Similarly, when relatively large percent errors occur, these errors are associated with the row elements that represent a small proportion of the column-total multiplier. For example, in Washington, individual multiplier-matrix cells that register errors larger than 100 percent represent row elements that are always less than 0.5 percent of the column-total multiplier. The inverse relationship between percent error and relative multiplier size is consistent with the Theil statistic and chi-square results, and is a further indication of the accuracy of the inversion RIMS II approach in estimating industry- specific multipliers. RIMS II Accuracy and Impact Analysis Among the alternative nonsurvey 1-0 techniques analyzed, the degree of accuracy of the RIMS II approaches is clearly higher than that of the other techniques. In addition, the RIMS II average multipliers overestimate the average survey multipliers by a small amount, and, for the majority of individual multiplier columns, RIMS II and survey multiplier differences are small. Furthermore, for a given multiplier matrix column, as shown by the chi-square and Spearman correlation results, RIMS II and survey multipliers have statistically similar row distributions of the column-total multiplier. It is important to recognize that the RIMS II accuracy comparisons are based on results from survey tables, which, themselves, are estimates of the "true" 1-0 relationships in the economy. 14/ Therefore, since measurement errors may be associated with both RIMS II and survey estimates, it is incorrect to ascribe the entire difference between RIMS II and survey multipliers to the RIMS II estimation error. The major implications of the accuracy comparisons for the use of RIMS II multipliers in impact analysis is that, on average and in a large number of cases, RIMS II and survey techniques provide similar estimates of the "true" regional 1-0 relationships. 13. With multiplier size (defined as the survey table's row element divided by its column total multiplier) plotted on the y-axis, and with the percent error (defined as the RIMS II minus the survey table's row element divided by the survey table row element) plotted on the x-axis, this relationship, for each State, resembles a rectangular hyperbola. 14. Two sources of potential measurement error are associated with survey tables. First, since not all establishments are surveyed for data on industry-specific sales and purchases, the industry coefficients may refer only to the sampled establishments, whose activity may not be representative of the industry as a whole. For details on sampling procedures in constructing regional tables, see Miernyk, et al. (19 70), Bourque and Conway (1977), and Loviscek, et al. (19 79). Second, since industry-specific sales and purchases are seldom equal, in order to construct balanced regional transaction tables sales and purchase data must be reconciled by techniques that introduce either judgmental or stochastic error. For details on reconciliation techniques, see Gerking (1976), Jensen and McGurr (19 76), Miernyk (19 76), and Loviscek, et al. (19 79). ■55- Two additional observations on the accuracy of RIMS II for the purpose of impact analysis should be made. The first concerns the effects of multiplier errors on the size of impact errors. The second concerns the industry detail and base years used in accuracy comparisons, relative to the industry detail and time frames used in impact analysis. A discussion of these two points concludes this chapter. Multiplier error and impact analysis While RIMS II generally estimates multipliers that are similar to those in survey tables, for certain industries in each State RIMS II estimation errors may still be considered too large. ^5/ Conway (1977) and others have shown that the effect of a multiplier error on an estimated impact can be mitigated significantly by gathering primary data to detail the industry-specific final demand changes ( A Y^ ) associated with the initial impact to be analyzed. Thus, when detailed industry-specific final demand data are available, the appropriate equation for impact analysis using RIMS II multipliers can be expressed as: b ij * Y J (5.4) n+1 In equation 5.4, total estimated impact (AX.) depends more on the overall accuracy of B and less on the accuracy of any one individual column of B r .16/ Furthermore, since the final demand vector ( AY r ) represents a survey-based estimate of initial impacts, which n+1 A X r l = £ j-i where: J = l... 15. In a benefit-cost study, Henry (19 79) discusses the costs of multiplier-estimation errors with respect to impact analysis, and the benefits of gathering additional data for use in impact analysis. As indicated below, if time and money are available, gathering detailed data on industry-specific final demand changes may be especially cost effective. Mandeville and Jensen (19 78) provide examples of disaggregating initial effects for use in regional 1-0 impact analysis. Miernyk, et al. (19 70) use a similar concept in analyzing the impacts of a new firm or industry with a survey-based regional 1-0 model. Billings and Katz (1981) describe a similar technique, using an existing regional 1-0 model for estimating multipliers for an individual firm whose direct coefficients may deviate significantly from the average coefficients for the industry of which the firm is a part. 16. Often in 1-0 impact analysis, detailed industry-specific final demand data are not available. In this case, only the size of the final demand change for one industry (for example, industry j') is known, in which case the appropriate impact equation can be written as: AX r = b r . A Y r (5.4a) where: -56- are often a large proportion of total impacts, the effects of multiplier error on the total estimated impact can be small. Therefore, large gains in estimated impact accuracy can occur when survey data are first used to measure initial impacts; in that event, RIMS II multipliers are used to measure only additional or secondary impacts. Industrial detail, base years, and impact analysis The accuracy comparisons of RIMS II multipliers use the level of industry detail and the same base years as the survey 1-0 tables. This type of comparison may not present RIMS II in its best light for two reasons. First, RIMS II identifies considerably more individual industries than does the typical survey table. RIMS II estimates coefficients for 496 column industries, which then can be aggregated to the same level of industry detail as in the survey table. Therefore, if initial effects can be identified at a level of industry detail greater than that used in the survey table, RIMS II multipliers may be more useful in impact analysis than multipliers from survey tables. 1_7/ For example, if the initial final demand change occurs for the output of the Scientific Instruments (SIC 3811) industry, a RIMS II multiplier can be calculated for this industry in any region. In the Washington table, the corresponding industry is Other Manufacturing, whose multiplier values are based on the aggregation of several 2-digit SIC industries- Instruments (SIC 38), Rubber (SIC 30), Leather (SIC 31), and Miscellaneous Manufacturing (SIC 39). Thus, in application, the RIMS II multiplier for Scientific Instruments may be more appropriate than is the Other Manufacturing multiplier from the Washington table. Second, the survey 1-0 tables are estimated only for a fixed base year, while RIMS II multipliers can be estimated for any year. Conway (1980) shows that multipliers can be yery sensitive to import-pattern shifts, and, therefore, regional 1-0 models should take into account these shifting regional import patterns. Since RIMS II multipliers can be estimated by taking into account recent import patterns, RIMS II multipliers may be more useful than those from survey tables, when the impact to be studied occurs in a year which is not the same as the base year of the survey table. 18/ 17. The level of aggregation in the various regional survey 1-0 tables is based on the size of the regional industry and other important aspects of the regional economy. For example, in Washington, primary aluminum is separated from other primary metals. However, the level of aggregation that is appropriate for constructing a base-year transactions table may not be appropriate for the impact analysis. This is especially true for the regional impact analyses of either new industries or the expansion of existing small industries. 18. For any given quarter, the regional data base for RIMS II has a timelag of one year. -57- Chapter 6 APPLICATION OF RIMS II RIMS II multipliers, like multipliers from other regional 1-0 models, are intended to show the total economic impacts of initial changes in regional economic activity. More specifically, RIMS II multipliers show the effects on regional total gross output, earnings, and employment of changes in regional final demands for imports or exports, new investments, and government expenditures.^/ The purpose of this chapter is to indicate in general terms several important aspects of the relationship between RIMS II multipliers and estimated impacts, and to show how RIMS II multipliers can be used to estimate the regional impacts of a specific Federal program—Local Public Works (LPW) construction expenditures for 19 78. RIMS II Multipliers and Impact Analysis Any regional economic model makes certain assumptions about economic activity, and these assumptions affect the interpretation of the results estimated by the model .27 The purpose of this section is to discuss five important aspects of the relationship between RIMS II multiplier specification and impact analysis. The discussion of RIMS II multipliers also applies to multipliers estimated by most regional 1-0 models. Furthermore, the discussion of the relationship between the specification of RIMS II and impact analysis is not intended as a complete discussion of all the potential problems which might arise when using RIMS II; rather it is intended to indicate the general types of problems that can be encountered, and, more importantly, how to incorporate solutions to these problems into the impact analysis. First, the production function underlying RIMS II multipliers is the linear Leontief production function, which implies constant returns to scale and no substitution among inputs in producing each industry's output. 3/ This assumption may not be valid in all 1. Since RIMS II multipliers are often defined with an endogenous household sector, final demand in RIMS II can be categorized into three sectors: net export, investment, and government. However, the inversion RIMS II multipliers can be estimated with households exogenous, in which case final demand also includes the household personal- consumption (PCE) sector. 2. Glickman (1977) discusses the differing sets of assumptions for regional economic- base, regional 1-0, and regional econometric models. For specific regional 1-0 model assumptions, see U.S. Water Resources Council (1977), U.S. Department of Agriculture (19 78), and the studies referenced in chapter 2, footnote 2. For a more general discussion of the role of assumptions in models, see Ascher (19 78). 3. When household payments are endogenous, the "fixed input coefficient" assumption means that a marginal change in final demand affects income based on the average industry-specific income-to-output ratio. That is, labor productivity does not change when output changes. When household consumption is endogenous, the "fixed input coefficient" assumption means that an additional dollar of income is spent in the same way as an average dollar of income. That is, the consumption function is linear. For a general discussion of this assumption, see Richardson (1972). For a discussion of techniques used to relax this assumption, see Miernyk, et al . (1967) and Batey and Madden (1980). -58- cases. However, Humphrey (1977), at the national level, and Conway (1977), at the regional level, have shown that changes in technical coefficients over 5-to-10-year time periods are small. Therefore, adopting the "fixed-input coefficient" assumption may be reasonable for many impact studies. Furthermore, in cases where adopting this assumption is not warranted, individual coefficients can be altered, based on more realistic assumptions. Often, this can be done simply by gathering data that identify the regional industry-specific final demand changes associated with the initial impact to be studied. As used in equation 5.3, these final demand data would describe the region's production relationships that are associated with the initial impact; the "fixed-input coefficient" assumption then would apply only in estimating additional or secondary effects. Second, RIMS II multipliers are best used for analyzing the impacts of final demand changes that are small relative to the size of the impact region's economy. If the initial impact represents a small proportion of a regional industry's total output, then the impact will probably not be large enough to alter production technology, or change the regional source of inputs. However, this is not always the case. For example, a large construction project may exceed the output capacity of the region's construction- materials industries. Since import levels for such a project may be higher than average import levels for the region's economy, the multipliers for this project may be smaller than average. As in other cases, where the RIMS II multiplier specification is incompatible with the impact to be studied, the effects of this incompatibility can be mitigated by gathering survey data on project requirements. A third consideration in the use of RIMS II multipliers is that impact regions should be delineated so as to conform to the supply areas of the inputs to the directly affected industries. Since RIMS II is a single-region, rather than an interregional, model, it is not capable of analyzing feedback effects from adjacent regions. By specifying the impact region as the supply area for inputs, these feedback effects are kept to a minimum. Therefore, in many RIMS II impact studies it is necessary that an impact region consist of several counties that are interrelated in terms of intercounty trade and commuting. Fourth, RIMS II multipliers show the economic impacts of final demand changes on output and earnings in supplying industries. Thus, RIMS II multipliers, by themselves, do not show the effects of changes in regional economic structure. For example, in analyzing the regional impact of expanding a warehousing facility, the RIMS II multiplier for warehousing would show the regional effects of the increased output of industries that supply goods and services to the warehousing industry, but would not show the regional effects of additional manufacturing establishments that might locate near the expanded warehousing facility .4/ However, if the size of the final demand sales of these manufacturing establishments can be specified, and if appropriate RIMS II manufacturing multipliers are used, the additional manufacturing impacts can be estimated. In this case, the total regional impacts of the warehousing facility would equal the sum of the warehousing-only impacts and the manufacturing-only impacts. 4. RIMS II multipliers, by themselves, only account for "backward-linkage" effects. "Forward-linkage" effects are common in less developed economies, where, for example, output changes induce labor inmigration, which, in turn, stimulates new housing and infrastructure construction. In general, "forward-linkage" effects require a case-by- case analysis. A discussion of when "forward-linkage" effects are likely to occur, and how to incorporate them into an impact study, can be found in U.S. Water Resources Council (1977). -59- Fifth, RIMS II multipliers estimate regional impacts, based on final demand changes. However, RIMS II does not indicate the existence or magnitude of any final demand substitution effects occuring within the regional economy as a whole. For example, if the increased expenditures associated with a construction project were financed by increased local taxes, there would ensue a positive regional impact, due to the positive final demand change in the investment sector, and a negative regional impact, due to the effect of increased personal taxes in reducing the household consumption of locally produced goods and services .5/ However, if the size of these substitution effects can be identified, positive and negative regional impacts can be estimated, using RIMS II multipliers, and the impacts can be summed to form net regional impacts. RIMS II Estimated Impacts of LPW RIMS II multipliers can be used to estimate the regional economic impacts of numerous public-sector policies. The purpose of this section is to indicate how these multipliers can be used to estimate the regional gross-output and earnings effects of the Federal LPW program. First, the scope and objectives of the LPW program are described briefly; RIMS II multipliers for selected LPW construction projects in three SMSA's are then presented, followed by a discussion of the metropolitan-area impacts estimated by the RIMS II multipliers. The section concludes with several observations on the scope of the LPW economic impacts estimated by RIMS II. The LPW program was first enacted by Congress in 19 76 and was extended by the Public Works Employment Act of 19 77. The program's objectives were to create jobs, stimulate the economy out of the 19 75-77 recession, and create usable public infrastructure. In order to attain these objectives, almost $6 billion was expended during 19 77 and 19 78 on over 10,000 public-facility construction projects in areas of high unemployment. 6/ Table 6.1 presents selected LPW construction expenditures in three SMSA's--Denver, Colorado; Detroit, Michigan; and Wilmington, North Carolina. TJ In Denver, most expenditures were for new sewer construction. In Detroit, the expenditures were divided among five types of construction. In Wilmington, maintenance and repair of streets and highways was the only type of construction expenditure analyzed. The table shows expenditures in both current (19 78) and constant (19 72) dollars. Constant-dollar expenditures are included, because RIMS II coefficients and multipliers are based on 19 72 output prices. The estimated LPW impacts discussed in the remainder of this chapter are also in 1972 constant dollars. 5. The origin of the funds used to finance the final demand change provides an indication of whether substitution effects are relevant. In general, if the majority of funds originates from within (outside) the region, then substitution effects may be relevant (irrelevant). For a detailed presentation of the substitution effects, which are induced by various Federal urban policies, see Glickman (1980). 6. For additional details of the LPW program, see U.S. Department of Commerce (1977b). 7. These data were obtained from the Economic Development Administration (EDA). The construction types listed in table 6.1 represent some of the projects used by EDA in a detailed evaluation of the LPW program's effectiveness. For a list of all LPW expenditures, see U.S. Department of Commerce (1977a). Thus, the impacts analyzed here are not the impacts of the entire LPW program in each SMSA. For example, almost $25 million was expended in the Denver SMSA under the LPW program; the Denver expenditures shown in table 6.1 are approximately 25 percent of this total. -60- < 00 z: 00 ■o c (0 O) Q. >» * h- r-^ (/I cn C r— 1 o u X> c >» fO J3 CO CO r^ CD en f— i GJ Ql X XJ c 00 3 O cu Q. u -z> u +-> CO c: o C_J to 0) 10 03 O "O 03 CO 00 -t-> 03 *— . S 1^. (11 -£= CO 0) CTJ--^ i_ ce: o3 CO en OS c r 03 -o ; 3 -Q or e O) oa -o s: lo O) co CO S- O- O 03 CD (U s_ CO CO 03 — ^ 5 «* -C CD cn- — CO i_ ^^ CD CM 3 CD O) — - CO co CD lis o ■■- > - ' oo CD oo 13 --» O cn -E ^t" O) i_ 03 < CO to c\j co ^t O CO I*"* *» #\ >=J- CM O r-H cm co C\J i—l O CO ^f CM O CO en <— i co c\j o XJ #> 03 i- S- O) o > I — c o CD O Q CO CM CTi ■— I cn en rs. o CXI cn >^> OJ LT> co •— i co cn CO r-l oo cn CM CM r^ co CM «d- OJ O JC S- U -(-> T- CD 21 Q O c_> cn E 5- <— O CO rH CTJ VO 00 rH ro in CO r-l 00 LO O r-l CO CO CM —I CM CM cm ^» ^- CM o ro *r cm cm r^ r>« 1-1 10 cm 00 LO O ro CO r-l ro cm to +■> o 00 CU CU i_ 03 a. -a (64) (/Uj (73) (74) highways (87) Denver, Colorado Earnings multiplier Column-total multipl ier 0.704 2.814 0.710 2.79 6 0.646 2.649 0.644 2.679 0.699 2.566 0.660 2.545 0.702 2.547 0.781 2.709 Detroit, Michigan Earnings multipl ier Column-total multiplier .723 2.839 .714 2.772 .633 2.586 .619 2.538 .701 2.540 .649 2.470 .69 7 2.501 .768 2.615 Wilmington, North Carolina Earnings multipl ier Column-total multipl ier .540 2.174 .538 2.147 .489 2.081 .514 2.19 4 .591 2.182 .531 2.035 .590 2.137 .675 2.324 United States Earnings multipl ier Column-total multipl ier 1.066 4.447 1.074 4.434 .952 4.068 .917 3.9 50 .9 77 3.843 .9 64 3.9 42 1.028 4.025 1.040 3.9 20 -63- considerably among construction types (in Wilmington, for example, the earnings multipliers range from .489 to .675), and, therefore, LPW impacts will depend on the types of construction that were funded by the program. In Denver and Detroit, column-total multipliers are highest for new warehouse construction. In all three SMSA's, however, earnings multipliers are highest for the maintenance and repair of streets and highways. 10/ If the primary purpose of a study is to analyze impacts on local household earnings, this latter result indicates that focusing only on column-total multipliers may yield misleading conclusions about the relative magnitudes of impacts associated with various types of construction. For the purpose of comparison, column-total and earnings multipliers were also estimated, using the alpha regression RIMS II approach; these results are presented in tables 6.3 and 6.4. A comparison of the alpha regression and inversion RIMS II results indicate that multiplier levels estimated by the two techniques are quite similar. For example, the inversion RIMS II column-total multipliers average less than 3 percent higher than the alpha regression RIMS II multipliers, and the inversion RIMS II earnings multipliers average 5 percent higher. Since the inversion RIMS II approach estimates the full multiplier matrix, and the results of the two RIMS II approaches are similar, the inversion RIMS II multipliers are used in the remainder of this chapter for analyzing the metropolitan-area economic impacts of selected LPW expenditures. The initial LPW expenditures and RIMS II multipliers were multiplied to estimate the regional impacts of the LPW expenditures. 11/ The impacts for each construction type were then summed to show the impacts of all selected LPW expenditures in each SMSA. The industry-specific gross output and earnings impacts are presented in table 6.5. Three of the results presented in this table should be noted here. First, the industry-specific output impact in all three SMSA's is considerably greater than the earnings impact. This occurs because household earnings are always a small proportion of gross output, which, in 1-0 accounting, can be loosely defined as industry sales. 12/ Miernyk, et al . (19 70) and others have argued that focusing on gross output impacts is less important than focusing on earnings impacts. This is especially true for the regional impact analysis ofthe LPW program, since one of the objectives of 10. The high earnings multiplier for maintenance and repair of streets and highways occurs because this construction type has the highest labor intensity (as measured by the direct household row coefficient) of the construction types analyzed here. Labor services are one construction input that are generally supplied locally. For a discussion of the elasticity of multipliers with respect to the size of household-row coefficients, see Cartwright (1980). 11. Equation 5.4a was used to calculate the gross output and total earnings impacts. Equation 4.13 was used to calculate the industry-specific earnings impacts. Impacts by construction type are presented in appendix tables C3.1-C3.3. 12. For details on 1-0 accounting, see Ritz (19 79). Gross output in the 1-0 accounting framework includes all industry purchases. Gross regional product originating excludes intermediate purchases, and is similar in definition to regional value added. Since household earnings are a large percentage (at least 70 percent in most industries) of value added, the regional earnings impacts give an indication of the gross regional product originating and regional value-added impacts. For additional details on regional economic accounting, see Garnick and Grimes (19 79) and Romans and Trott (1980). -64- Table 6. 3. -Inversion RIMS II and Alpha Regression RIMS II Column-Total Multipliers by Construction Type and SMSA SMSA/mu ltiplier type De iver, Det roit, Wi Imington, Construction type Col. Drado Mic higan North Carolina Alpha regression Inversion Alpha regression Inversion Alpha regression Inversion Warehouses (49) 2.788 2.814 2.731 2.839 2.145 2.174 Other buildings (55) 2.748 2.796 2.685 2.772 2.103 2.147 Sewers (62) 2.589 2.649 2.508 2.586 2.042 2.081 Streets and highways (64) 2.612 2.679 2.469 2.538 2.140 2.194 Parks (70) 2.531 2.566 2.492 2.540 2.162 2.182 M & R residents (73) 2.504 2.545 2.452 2.470 2.013 2.035 M & R buildings (74) 2.512 2.547 2.487 2.501 2.124 2.137 M & R streets and highways (87) 2.684 2.709 2.607 2.615 2.315 2.324 -65- Table 6. 4. -Inversion RIMS II and Alpha Regression RIMS II Earnings Multipliers by Construction Type and SMSA SMSA/mult ipl ier type De river, Detroit, Wi Imir lgton, Const .ruction type Col Drado Michi gan North Carol ina Alpha regression Inversion Alpha regression Inversion Alpha regression Inversion Warehouses (49) 0.690 0.704 0.679 .723 0.528 0.540 Other bui ldings (55) .683 .710 .671 .714 .521 .538 Sewers ; (62) .618 .646 .602 .633 .481 .489 Street ;s and highv /ays (64) .620 .644 .588 .619 .501 .514 Parks (70) .678 .699 .672 .701 .581 .591 M & R residents (73) .641 .660 .632 .649 .515 .531 M & R bui ldings (74) .682 .702 .680 .69 7 .580 .590 M & R streets and highv /ays (87) .767 .781 .753 .768 .669 .675 ■66- Table 6. 5. -Gross Output and Earnings Impacts of LPW Expenditures by Industry and SMSA (Thousands of 19 72 dollars) Industry Denver, Colorado SMSA/impact category Detroit, Michigan Gross r Gross r output tunings output Earnings Wi lmington, North Carolina Gross output Earnings 1 Agriculture 2 Forestry and fisheries 3 Coal mining 4 Petroleum and natural gas mining 5 Other mining 6 New construction 7 Maintenance and repair 8 Food and kindred products 9 Textiles 10 Apparel 11 Paper 12 Printing and publishing 13 Chemicals 14 Rubber and leather 15 Lumber and furniture 16 Stone, clay, and glass 17 Primary metals 18 Fabricated metals 19 Nonelectrical machinery 20 Electrical machinery 21 Motor vehicles 22 Other transportation equipment 23 Instruments 24 Miscellaneous manufacturing 25 Transportation 26 Communication 27 Utilities 28 Wholesale trade 29 Retail trade 30 Eating and drinking establ ishments 31 Finance 32 Insurance 33 Real estate 34 Lodging and amusement 35 Personal services 36 Business services 37 Health services 38 Other services 39 Household Total* 17 4 35 7 4 2 1 2 1 9 1 1 38 9 69 21 42 13 2,704 868 7,680 2,611 45 20 3,009 1,335 726 340 126 18 346 50 8 2 1 8 2 7 2 11 3 19 5 11 3 8 2 22 6 1 40 14 86 35 3 2 57 11 437 82 11 2 12 4 155 40 10 3 100 29 3 I 285 85 438 130 14 3 104 36 528 140 144 35 801 251 2 108 37 164 62 12 5 58 19 323 44 1 15 6 1 12 4 10 4 8 2 45 14 172 70 664 302 59 21 64 20 199 64 14 5 72 9 361 46 21 3 241 100 771 325 34 14 225 103 947 438 62 27 102 35 351 121 26 8 11 24 214 67 11 3 84 36 296 130 8 3 167 8 431 22 40 2 36 12 97 33 7 2 37 18 151 73 5 2 221 93 1,037 456 21 9 48 18 360 137 14 4 123 51 408 156 23 8 1,767 8 7,288 25 483 2 5,423 1,767 20,636 7,288 1,179 483 *Gross output totals exclude earnings impacts to avoid double counting; see equation 4.12, -67- the program was job creation, which can be measured by the household earnings impacts of the program. 13/ Second, in table 6.3, the total-earnings impact (which is shown as the last row entry in the gross output column for each SMSA) is equal to the sum of the industry- specific earnings effects. For example, in the Denver SMSA, the total-earnings impact is $1,767 thousand, which is equal to the sum of the industry-specific earnings impacts. Third, it is useful to indicate the size of total-earnings impacts relative to the initial LPW expenditures. For example, in the Denver SMSA, the $2,703 thousand in LPW expenditures generated a total of $1,767 thousand in local area earnings. The ratio of local-area-earnings impacts to LPW expenditures is .65 in Denver; the ratios in Detroit and Wilmington are .69 and .68, respectively. The two higher ratios indicate that the LPW expenditures in the other two SMSA's were associated with construction types that have higher earnings multipliers than those in Denver. The gross-output and earnings impacts presented in table 6.5 indicate that a large proportion of the total impacts occurs within the construction industries (New Construction, and Maintenance and Repair) themselves. In order to show the relative size of the industry-specific impacts, the percent distribution of LPW earnings impacts by industry for each SMSA is presented in table 6.6. The table indicates that in Denver and Detroit, slightly more than 50 percent of the industry-specific impacts occur in the construction industries. In Detroit, the next largest earnings impacts occur in the Transportation, Wholesale and Retail Trade, and Business Services industries. In Wilmington, 70 percent of the total earnings impacts occur in the construction industries, a further indication that a large part of the initial LPW expenditure leaks out of Wilmington. In concluding this discussion, it is important to recognize that the analysis of regional gross-output and earnings impacts does not represent an analysis of all LPW regional economic impacts. For example, one important set of effects, fiscal impacts in terms of sales and income-tax receipts, cannot be measured by RIMS II itself. However, RIMS II estimated-output changes in retail trade can provide the basis for estimating sales-tax receipts, and estimated pretax household-earnings changes can provide the basis for estimating income-tax receipts. Furthermore, it is important to recognize that the RIMS II estimated impacts by themselves do not represent a cost-benefit analysis of the LPW program. 14/ For example, if the LPW expenditures in one region were financed by 13. Data on industry-specific earnings per worker and earnings impacts can be used to estimate industry-specific employment impacts. For example, if average earnings per worker in Denver is $10,000 (19 72 constant dollars) in retail trade, and the LPW retail- trade earnings impact is $103,000, then the LPW program could lead to the hiring of 10 retail-trade workers. However, employment impacts are particularly difficult to specify exactly, based on average earnings. For example, the $103,000 could accrue to workers already employed, in the form of overtime earnings, or it could be used to hire 20 part- time workers at $5,000 per worker. In all probability, the employment impacts of most final demand changes are a mixture of full-time, part-time, and overtime workers. 14. For additional details on the relationship of cost-benefit analysis and impact analysis, see Haveman (1977) and Haveman and Margolis (1977). Often regional impact analysis and national cost-benefit analysis are not linked in a policy study. For example, decisions on the opening and closing of military facilities are made on the basis of national defense considerations, while the regional impact analysis of a particular opening or closing is often undertaken in order to indicate the size of impact assistance required to ameliorate any unfavorable regional effects of those decisions. For a discussion of the impacts of military-base-spending cutbacks, see Cartwright and Beemiller (19 79). -68- Table 6.6. -Percent Distribution of LPW Earnings Impacts by Industry and SMSA (Percent) SMSA Industry Denver, Colorado 1 Agriculture 0.2 2 Forestry and fisheries 3 Coal mining .1 4 Petroleum and natural gas mining .1 5 Other mining .5 6 New construction 49.1 7 Maintenance and repair 1.1 8 Food and kindred products 1.0 9 Texti les 10 Apparel .2 11 Paper .1 12 Printing and publishing .8 13 Chemicals .6 14 Rubber and leather .2 15 Lumber and furniture .2 16 Stone, clay, and glass 4.8 17 Primary metals 2.0 18 Fabricated metals 2.0 19 Nonelectrical machinery 2.1 20 Electrical machinery .2 21 Motor vehicles 22 Other transportation equipment 23 Instruments .2 24 Miscellaneous manufacturing .1 25 Transportation 4.0 26 Communication 1.1 27 Utilities .5 28 Wholesale trade 5.7 29 Retail trade 5.8 30 Eating and drinking establ ishments 2.0 31 Finance 1.4 32 Insurance 2.0 33 Real estate .5 34 Lodging and amusement .7 35 Personal services 1.0 36 Business services 5.3 37 Health services 1.0 38 Other services 2.9 39 Household .5 Detroit, Wi lmington, Michigan North Carolina 0.1 0.2 .3 2.7 35.8 18.3 70.4 .7 .2 .2 .1 .6 .1 .5 .2 1.1 .4 .5 .4 .2 1.8 .6 1.9 3.5 .9 .3 .4 .1 .1 .2 4.1 4.3 .9 2.0 .6 .6 4.5 2.9 6.0 5.6 1.7 1.7 .9 .6 1.8 .6 .3 .4 .5 .4 1.0 .4 6.3 1.9 1.9 .8 2.1 1.7 .3 .4 Total 100.0 100.0 100.0 ■69- income taxes generated in other regions, there would be a positive impact in the one region, and negative impacts (through a decline in personal consumption expenditures) elsewhere; net national benefits could be viewed as the sum of the positive single-region impacts and the negative rest-of-Nation impacts. However, RIMS II results could be used in a national -level cost-benefit analysis of various programs, to estimate separately the positive and negative regional impacts in the above example. It it evident that in many regional economic-impact studies, RIMS II results can be crucial for estimating important economic effects that are not directly specified by RIMS II itself. Regional fiscal effects, labor migration effects, and environmental and energy effects are examples of important regional economic impacts that often depend on estimates of the regional gross-output and earnings effects of the initial stimulus. Since many of these important effects are often best analyzed on a case-by-case basis, one of the major advantages of using RIMS II is that valuable research resources can be used in the analysis of these effects, rather than on the construction of a gross-output and earnings impact model. Therefore, when using RIMS II a cost-effective impact study might devote most of its research budget to specifying initial impacts in industry- specific detail, and analyzing the implications of the RIMS II estimated gross-output and earnings impacts on other important aspects of regional economic activity. -70- Chapter 7 CONCLUSIONS The purpose of this chapter is to discuss the advantages and limitations of RIMS II and to indicate several extensions of the basic RIMS II model. Advantages of RIMS II Four major advantages of RIMS II should be mentioned; the first three concern the flexibility of the modeling system and the fourth concerns its accuracy. First, RIMS II was constructed as a highly disaggregated system, both spatially and industrially. Consequently, it can be used to evaluate regional impacts for any county or group of counties, and for any industry included in the 496-industry national 1-0 model. Second, RIMS II was constructed to rely on a minimal number of data sources, including the 19 72 national 1-0 table and the BEA 4-digit Standard Industrial Classification (SIC) earnings- by-county file. As a result, RIMS II is relatively inexpensive to implement, even though the industrial and spatial data contained in these files are substantial. Third, because the system is capable of generating multiplier estimates, using either the inversion approach or the shortcut alpha regression approach, RIMS II has greater flexibility in application than many other techniques. Fourth, both RIMS II approaches, when compared with the multipliers from survey- based 1-0 tables, are relatively accurate. J7 For example, the average error associated with the RIMS II approaches is well within an acceptable range (approximately 5 percent), and, for the majority of individual multiplier columns, RIMS II and survey multiplier differences are small; furthermore, for a given column in the multiplier matrix, both RIMS II and survey multipliers have similar row distributions of the column-total multipl ier. Limitations of RIMS II Like other regional models, RIMS II suffers from certain limitations that affect the manner in which it should be employed. 2/ Three of the more significant limitations are descibed here. First, RIMS II was developed as a single-region model, because the annual, detailed trade-flow data necessary to make RIMS II an interregional model are not available. Therefore, the impact estimates obtained from the modeling system do not take into 1. As indicated in chapters 4, 5, and 6 of this monograph, the accuracy of impacts estimated by RIMS II can be improved by gathering survey data on the initial economic change that is the subject of the impact study. For improving the accuracy of the RIMS II multipliers themselves, survey data can be gathered for specific regional interindustry linkages, and RIMS II results can be used as the purely nonsurvey component of a "mixed- approach" table (as described in chapter 2). In order to specify what survey data to gather, future research will be directed at identifying the interindustry coefficients that generate the larger differences between RIMS II and survey multipliers. 2. The limitations of RIMS II and most other 1-0 models (whether survey-based or nonsurvey-based) are the same. One group of 1-0 limitations, particularly those relating to the fixed-proportions production function, is discussed in chapter 6 and is not repeated here. -71- account feedback effects from adjacent or economically related regions. Second, RIMS II is a static model rather than a dynamic model. Consequently, the impact estimates generated by the system indicate the overall change that is likely to occur rather than the timing of such a change. Third, government and investment spending are exogenous in RIMS II and are viewed as elements of final demand. Therefore, RIMS II by itself cannot estimate changes in government spending that are induced by changes elsewhere in the model. The exogenous treatment of these sectors is due to the conventions adopted in ttie national 1-0 table and the lack of regional data for these sectors. Model Extensions While the limitations described in the previous section are significant, their effects can be ameliorated in particular applications of RIMS II. The remainder of this chapter describes three applications in which the basic modeling system can be extended to overcome partially its limitations. 3/ An interregional application In assessing regional impacts of urban public-expenditure programs, it is often useful to determine the impact in the urban-core county versus the impact in the remainder of the SMSA, and how the distribution of the impact would differ depending on whether the initial expenditure took place in the urban-core county or in surrounding suburban counties. Such an application was undertaken by BEA for the U.S. Department of Housing and Urban Development (HUD). 4/ In this application, industry-specific multipliers for the entire SMSA first were calculated. Next, direct requirements provided by suburban firms to the core county and by core-county firms to suburban counties were estimated, based on industrial structure and commuting data. The data on direct requirements then were used to estimate preliminary interregional matrices of multipliers for the core and suburban counties. Finally, the SMSA multipliers were allocated between the core county and suburban counties, based on the preliminary interregional matrices. The resulting final estimates indicate the impact of changes in one region (e.g., the core county) on an adjacent region (e.g., the suburban counties). A dynamic application Impact analysis often requires estimates of the timing and magnitude of the impacts of policy changes. While 1-0 models can be used to estimate the magnitude of impacts in considerable industrial detail, because they are static in structure, they do not address the timing of the impacts. Alternately, econometric models that identify explicitly the time path of impacts usually lack the industrial detail provided by 1-0 models. One approach for analyzing both the timing and the magnitude of impacts is to combine the results of a regional 1-0 model and a regional econometric model .5/ 3. While the extensions of the modeling system described below were initially made in applications of the original RIMS, they are presented here, since they will be employed, where appropriate, in future RIMS II applications. 4. See Cartwright (1980). 5. The advantages and limitations of the various techniques for combining 1-0 and econometric models are discussed in Kort and Cartwright (1981). -72- The above approach was employed by HUD in the analysis of the regional impacts of construction expenditures in Colorado. 6/ In this application, the BEA multiregional econometric model, NRIES, was used to estimate the timing and magnitude of the impacts on the 13 endogenous industries specified in the model, and the original RIMS model was used to estimate the magnitude of the impacts on over 300 endogenous industries specified in the model and present in Colorado. While it would have been preferable to obtain more industrially detailed data on timing, the estimates from NRIES and RIMS provided considerable information on which to base an evaluation of the overall dynamic impacts and the detailed industry-specific impacts. A government-sector application As indicated above, the national 1-0 table includes the government sector in final demand rather than as an endogenous activity. Therefore, it is not possible to analyze directly the effects on the remainder of the economy when the level of regional government expenditures is affected by final demand changes that originate in the private sector. However, it is possible to analyze the effects of changes in regional government expenditures, if information can be obtained on the type of regional government-sector purchases and payments to residents in the region. Such an approach was employed at BEA in assessing the regional impact of the cutbacks in military-base spending that were planned by the U.S. Department of Defense. 7/ In this application, region-specific information was obtained, identifying the local purchases made by the base and its personnel, as well as wage-and-salary payments to local residents. These expenditures then were treated as changes in final demand, and were employed in generating the industry-specific estimates of impacts that were associated with the reduction of military-base spending in the region. 6. See Ballard, Cartwright, Gustely, and Kort (1980) 7. See Cartwright and Beemiller (19 79). -73- Bibl iography -75- Ascher, W. Forecasting: An Appraisal for Policy-Makers and Planners . Baltimore: Johns Hopkins University Press, 19 78. Bacharach, M. Biproportional Matrices and Input-Output Change . Cambridge: Cambridge University Press, 19 70. Ballard, K. P., Cartwright, J. V., Gustely, R. D., and Kort, J. R. "Developing a Spatially Comprehensive Impact Modeling System: A Feasibility Study." Springfield, Virginia: National Technical Information Service, 1980. , Gustely, R. D., and Wendling, R. M. NRIES: Structure, Performance, and Application of a Bottom-Up Interregional Econometric Model . Washington, D.C.: U.S. Department of Commerce, 1980. Batey, P. W. 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"Regional Input-Output Multipliers Without a Full 1-0 Table: Comment." The Annals of Regional Science , Vol. 12 (November 19 78b), 98-99. . "The Concept of Accuracy in Regional Input-Output." Paper presented at the annual meeting of the Australian and New Zealand section of the Regional Science Association, 19 79. . "On Introspective Evaluation of the Regional Input-Output Technique." Paper presented at the First World Regional Science Congress, June 1980. and Mc Guarr, D. "Reconciliation of Purchases and Sales Estimates in an Input-Output Table." Urban Studies , Vol. 13 (February 1976), 61-62. Katz, J. L. and Burford, R. L. "A Comparison of Two Estimators of Output Multipliers From an Incomplete Input-Output Table." Paper presented at the annual meeting of the Western Regional Science Association, 1980. and . "A Method to Compute Output, Income and Employment Multipliers Without an Input-Output Table." Paper presented at the annual meeting of the Western Regional Science Association, February 1981. Knapp, J. L., Fields, T. W., and Jerome, R. T., Jr. A Survey of State and Regional Econometric Models. Charlottesville, Virginia: Tayloe Murphy Institute, 1978. -78- Kort, J. R. and Cartwright, J. V. "Modeling the Multiregional Economy: Integrating Econometric and Input-Output Models." Paper presented at the annual meeting of the Southern Regional Science Association, April 1981. Latham, W. R. and Montgomery, M. "Regional Industry Impact Multipliers: A Comparison of Alternative Methods." Paper presented at the annual meeting of the Southern Regional Science Association, April 19 77. Loviscek, A. L., Holliday, R. E., Robinson, L. A., and Wolford, M. A. The 19 75 West Virginia Input-Output Study: Modeling a Regional Economy . Morgantown, West Virginia: West Virginia University Library, 19 79. Malizia, E. and Bond, D. L. "Empirical Tests of the RAS Technique of Interindustry Coefficient Adjustment." Journal of Regional Science , Vol. 14 (December 19 74), 355-365. Mandeville, T. D. and Jensen, R. C. The Impact of Major Development Projects on the Gladstone/Calliope, Fitzroy, Queensland, and Australian Economies: An Application of Input-Output Analysis . St. Lucia, Australia: University of Queensland, 19 78. McMenamin, D. G. and Haring, J. V. "An Appraisal of Nonsurvey Techniques for Estimating Regional Input-Output Models." Journal of Regional Science , Vol. 14 (August 1974), 191- 205. Miernyk, W. H. Elements of Input-Output Economics . New York: Random House, 1965. "Comments on Recent Developments in Regional Input-Output Analysis." International Regional Science Review , Vol. 1 (Fall, 1976), 47-55. , Bonner, E. R., Chapman, J. H., Jr., and Shellhamer, K. L. Impact of the Space Program on a Local Economy: An Input-Output Analysis . Morgantown, West Virginia: West Virginia University Library, 1967. , Shellhamer, K. L., Brown, D. M., Coccari , R. L., Gallagher, C. J., and Wineman, W. H. Simulating Regional Economic Development . Lexington, Massachusetts: D.C. Heath and Company, 19 70. Morrison, W. I. and Smith, P. "Nonsurvey Input-Output Techniques at the Small Area Level: An Evaluation." Journal of Regional Science , Vol. 14 (February 1974), 1-14. Nourse, H. 0. Regional Economics . New York: McGraw-Hill, 1968. Polenske, K. R., ed. State Estimates of Gross National Product; 1947, 1958, and 1963 . Lexington, Massachusetts: D.C. Heath and Company, 19 72. The U.S. Multiregional Input-Output Accounts and Model . Lexington, Massachusetts: D.C. Heath and Company, 1980. and Rowan, R. E. Multiregional Multipliers for Massachusetts and New England . Report No. 17. Washington, D.C: Department of Transportation and Economic Development Agency, July 19 77. Richardson, H. W. Input-Output and Regional Economics . London: Weidenfeld and Nicholson, 1972. •79 Ritz, P. M. "Definitions and Conventions of the 1972 Input-Output Study." Bureau of Economic Analysis Staff Paper No. 34, July 1980. 'The Input-Output Structure of the U.S. Economy, 19 72." Survey of Current Business, Vol. 59 (February 19 79), 34-72. , Roberts, E. P., and Young, P. C. "Dollar-Value Tables for the 1972 Input-Output Study." Survey of Current Business , Vol. 59 (April 1979), 51-72. Rodgers, J. M. State Estimates of Interregional Commodity Trade, 1963 . Lexington, Massachusetts: D. C. Heath and Company, 1973. Romans, T. J. and Trott, E. A., Jr. "A Methodology for Estimating Gross State Product Originating." Unpublished paper, 1980. Schaffer, W. A. "Estimating Regional Input-Output Coefficients." The Review of Regional Studies , Vol. 2 (Spring 1972), 57-71. and Chu, K. "Nonsurvey Techniques For Constructing Regional Interindustry Models." Papers, Regional Science Association , 23 (1969), 83-101. , Laurent, E. A., Floyd, G. F., Sutter, E. M., Jr., Hamby, C. K., and Herbert, R. C. On the Use of Input-Output Models for Regional Planning . Leiden: Martinus Nijhoff, 19 76. Stevens, B. H. and Trainer, G. A. "Error Generation in Regional Input-Output Analysis and Its Implications for Nonsurvey Models." Economic Impact Analysis: Methodology and Appl ications . Edited by Saul Pleeter. Boston: Martin Nijhoff, 1980. , Treyz, G. I., and Ehrlich, D. J. "On the Estimation of Regional Purchase Coefficients, Export Employment, and Elasticities of Response for Regional Economic Models." Discussion Paper No. 114. Amherst, Massachusetts: Regional Science Research Institute, December 19 79. , , , and Bower, J.R. "Estimation of Regional Purchase Coefficients and Their Use in the Construction of Nonsurvey Input- Output Impact Models." Discussion Paper No. 119. Amherst, Massachusetts: Regional Science Research Institute, September 1980. Stone, R. and Brown, A. "Behavioral and Technical Change in Economic Models." Problems in Economic Development . Edited by E.A.G. Robinson. New York: MacMillan, 1965. Theil, H. Applied Economic Forecasting . Amsterdam: North Holland, 1966. . Economic Forecasts and Policy . Amsterdam: North Holland, 1961. U.S. Department of Agriculture. Regional Development and Plan Evaluation: The Use of Input-Output Analysis . Agriculture Handbook No. 503. Washington, D.C.: U.S. Department of Agriculture, 1978. U.S. Department of Commerce. Bureau of Economic Analysis. Local Area Personal Income: 19 73-78 . Washington, D.C.: Government Printing Office, 1980. -80- . Economic Development Administration. Directory of Approved Projects; Local Public Works Program: Round I and Round II . Washington, D.C.: U.S. Department of Commerce, 19 77a. "Study Plan: Evaluation of the Local Public Works Program." Unpublished paper, August 19 77b U.S. Water Resources Council. Guideline 5: Regional Multipliers (Industry-Specific Gross Output Multiliers for BEA Economic Areas, prepared by the U.S. Department of Commerce, Bureau of Economic Analysis). Washington, D. C: Government Printing Office, 19 77. Walderhaug, A. J. "State Input-Output Tables Derived from National Data." Proceedings of the Business and Economic Statistics Section 19 71 . American Statistical Association (19 72), 77-86. West, G. R., Wilkinson, J.T., and Jensen, R. C. Generation of Regional Input-Output Tables for the States and Regions of South Australia . St. Lucia, Australia: University of Queensland, 19 79 . Wonnacott, T. H. and Wonnacott, R. J. Introductory Statistics . New York: John Wiley and Sons, 19 77. -81- Appendix A SECTORING OF THE SURVEY-BASED TABLES ■83- Tables A1.1-A1.3 present the sectoring schemes employed in the Texas, Washington, and West Virginia survey-based 1-0 tables. Several observations concerning this sectoring scheme should be made here. In general, these regional tables, when compared to the national 1-0 table, provide more industrial detail in the trade sector and those sectors that are of special importance in the State. For example, in the Texas table, the trade sector is disaggregated into 17 industries as compared to only 2 in the national table. In Washington and West Virginia, more detail is provided for the natural resource related industries. Specifically, West Virginia makes a distinction between underground and strip mining whereas the national table does not. A similar sectoring problem is encountered in the Washington table, where forestry and fisheries are separate industries, unlike in the national table. Therefore, the survey tables were aggregated to a level of industrial detail that permited comparisons to be made with the nonsurvey tables. The manner in which the "owner-occupied dwellings" (1-0 industry 710100) sector is treated in the nonsurvey table, depended upon the convention adopted by the survey-based table. Since the Texas and West Virginia tables do not explicitly recognize this industry, in the nonsurvey tables, industry 710100 was deleted as a column industry, and the PCE column coefficients were based on a column total that excluded the row element associated with industry 710100. In the Washington table, industry 710100 was treated as part of the value-added component of PCE. Adjustments for this convention were made by deleting row industry 710100 and combining the column elements of industry 710100 with the respective PCE column elements. The resulting number of column industries is 133 for Texas, 52 for Washington, and 41 for West Virginia. The row industries of the regional tables were aggregated, where possible, to industry classifications that were consistent with those employed in the BEA OBERS projections program. J7 The aggregations of rows to insure conformability with the OBERS industries is part of RIMS II for two reasons. First, in future applications, this operation will permit the estimation of industry-specific employment impacts, since the OBERS regional data base includes compatibly estimated earnings and employment subfiles. Second, row aggregation assures that the confidential 4-digit SIC earnings data used to estimate the LQ's in RIMS II will not be disclosed inadvertently. As a result, for this analysis the Texas table contains 51 rows, the Washington table contains 26 rows, and the West Virginia table contains 34 rows. For the comparisons in chapter 5, the 19 75 West Virginia transactions table was deflated to 1972 dollars in order to minimize distortions due to interindustry differences in the rates of price change. 2/ In addition, the comparisons shown in chapter 5 are based on a value-added definition of the household row in Washington, and an earnings definition of the household rows in Texas and West Virginia. These definitions were employed to conform to the conventions adopted in the respective State tables. 1. See U.S. Department of Commerce, Bureau of Economic Analysis, Survey of Current Business (November 1980), for a description of OBERS. 2. The deflation of the 19 75 West Virginia table used a "double deflation" technique similar to the one described in BEA Staff Paper No. 32, Updated Input-Output Table of the U.S. Economy: 19 72 , by Paula C. Young and Philip M. Ritz, April 19 79. -84- Table Al.l. -Input-Output Industry Definitions Texas Industry number Column Row Industry name 19 72 SIC Agriculture, forestry, and fisheries 4 5 6 7 4 5 6 7 3 3 1 2 115 9 9 8 8 Mining 11 11 11 10 2 2 8 3 Construction 12 6 14 13 15 16 Irrigated cotton Irrigated food grains Irrigated feed grains Other irrigated crops Dryland cotton Dryland food grains Dryland feed grains Dryland crops and livestock not elsewhere classified Range livestock production Feedlot livestock production Dairy Poultry and eggs Agriculture supply except farm machinery Cotton ginning Agricultural services Primary forestry Fisheries Crude petroleum and natural gas Natural gas liquids Oil and gas field services Other mining and quarrying Residential construction Commercial, educational, and institutional construction Industrial construction Facility construction Maintenance and repair 0112 0119 0133,0134,0139,0161,0171,0172, ,0174,0175,0179,0191 0112 0119 0133,0134,0139,0161,0171,0172,0173, ,0175,0179,0191,0271,0272,0279,0291 0214,0219 0213 0252,0253,0254,0259 0131 0111, 0115, 0116, 0173 0131 0111, 0115, 0116, 0174 0212, 0211, 0241 0251, 5191 0724 0711,0721,0722,0723,0729,0741,0742,0751, 0752,0761,0762,0781,0782,0783,09 71 0811,0821,0843,0849,0851 0912,0913,0919,09 21 1311 1321 1381,1382,1389 1011,1021,1031,1051,1061,1081,109 2, 1094,1099,1211,1213,1411,1422,1423, 1429,1442,1446,1452,1453,1454,1455, 1459,1472,1473,1474,1475,1476,1477, 1479,1481,149 2,149 6,1499 1521,1522,1531 plus subcontractors parts of the two-digit SIC 17 1542, plus subcontractors parts of two- digit SIC 17 1541, plus subcontractors parts of two- digit SIC 17 1611,1622,1623,1629 Maintenance and repair part of 2-digit SIC 17 -85- Table Al.l. -Input-Output Industry Definitions — Continued Texas Industry number Column Row Industry name 19 72 SIC Manufactur ing 18 7 Meat products 19 7 Poultry products 20 7 Dairies 22 7 Grain milling 23 7 Animal feeds 24 7 Bakery products 21 7 Canned, preserved, pickled, dried, and frozen foods 25 7 Other food and kindred products 26 7 Beverages 27 8 Textile mill products 2011,2013 2016,2017 2021,2022,2023,2024,2026 2041,2043,2044,2045,2046 2047,2048 2051,2052 2032 , 2033 , 2034 , 2035 , 2037 , 2038 , 209 1 , 209 2 2061,2062,2063,2065,2066,2067,2074,2075, 2076,2077,2079,2095,209 7,2098,2099,2121 2082,2084,2086,2087 2211,2221,2231,2241,2251,2253,2254,2257, 2258,2259 ,2261,2262,2269 ,2271,2272,2279 , 2281,2283,2284,2291,229 2,229 3,2294,229 5, 2296,2297,2298,2299 28 9 Men and boys, women and misses, 2311,2321,2322,2323,2327,2328,2329,2331, and children furnishings 2335,2337,2339,2341,2342,2351,2352,2361, 2363,2369 29 9 Related apparel 2371,2381,2384,2385,2386,2387,2389,2391, 2392,239 3,2394,239 5,239 6,239 7,2399 Logging 2411 Lumber mills 2421,2426,2429 Millwork and wood products 2431,2434,2435,2436,2439,2441,2448,2449, 2452,2491,249 2,2499 Wood furniture and fixtures 2511,2512,2515,2517,2519,2521,2531,2541, 2591,2599 Metal furniture and fixtures 2514,2522,2542 Paper and paper mills 2611,2621,2631,2661 Paper products except boxes 2641,2642,2643,2645,2646,2647,2648,2649 and containers Boxes and paper containers 2651,2652,2653,2654,2655 Newspapers 2711 Publishing 2721,2731,2741 Printing 2732,2751,2752,2753,2795 Manifold business forms 2761 Other printing and publishing 2771,2782,2789,2791,2793,2794 Chlorine and alkalies 2812,2813 Cyclic crudes and intermediates 2865 and inorganic pigments Organic chemicals 2861,2869 Inorganic chemicals 2816,2819 Fibers and plastics 2821,2823,2824 Synthetic rubber 2822 Drugs 2831,2833,2834 Agricultural chemicals 2873,2874,2875,2879 -86- 30 10 31 10 32 10 33 11 34 11 33 12 36 12 37 12 38 13 39 13 40 13 41 13 42 13 43 14 43 14 45 14 43 14 47 14 48 14 49 14 44 14 Table Al.l. -Input-Output Industry Definitions — Continued Texas Industry number Industry name 19 72 SIC Column Row 50 14 51 14 46 14 52 15 53 15 54 16 55 16 56 16 57 17 58 18 60 18 61 18 59 18 62 19 64 19 67 19 Manufacturing (continued) Soaps, cleansers, and toiletries 2841,2842,2843,2844 Paints and varnishes 2851 Other chemicals 2891,2892,289 3,289 5,2899 Petroleum refining 2911 Other petroleum products 29 51,29 52,299 2,2999 Tires 3011 Fabricated rubber products 3021,3041,3069 Plastics products 3079 Leather and leather products 3111,3131,3142,3143,3144,3149,3151,3161, 3171,3172,3199 Glass 3211,3221,3229,3231 Clay 3251,3253,3255,3259,3261,3262,3269 Cut stone and other clay and 3281,3291,3292,3293,3295,3296,3297,3299, shell products 3274,3275 Cement and concrete products 3241,3271,3272,3273 Primary steel and iron 3313,3315,3316,3317 Foundries 3321,3322,3324,3325 Nonferrous primary and secondary 3331,3332,3333,3339,3341 smelting 68 19 Aluminum smelting and nonferrous 3334,3351,3353,3354,3356,3357 rolling and drawing Castings and forgings 3361,3362,3369,3398,3399 Fabricated steel 3441 Plate work 3443 Sheet metal and architectural 3444,3446,3448,3449 Metal doors 3442 Fabricated metal products 3411,3412,3421,3423,3425,3429 Plumbing 3431,3432,3433 Bolts, nuts, and screws 3451,3452,3461,3462,3463,3465,3466,3469 Electroplating, coating, 3471,3479 and engraving Valves and pipe fittings 3494,3498 Other fabricated metal 3493,3495,3496,349 7,3499 Farm, construction, and 3523,3524,3531,3537 industrial machinery 81 21 Materials handling machinery and 3534,3535,3536 equipment Mining machinery and equipment 3532,3533 Engines 3511,3519 Metal working machinery 3541,3542,3544,3545,3546,3547,3549 Industrial processing machinery 3551,3552,3553,3554,3555,3559 General industry machinery 3561,3562,3563,3564,3565,3566,3567,3568, 3569 Refrigerator machinery 3585 Computers, and accounting, office, 3572,3573,3574,3576,3579,3581,3582,3586, and service industry machinery 3589,359 2,3599 -87- 66 19 71 20 73 20 74 20 72 20 69 20 70 20 65 20 75 20 77 20 76 20 79 21 80 21 78 21 82 21 83 21 84 21 86 21 85 21 Table Al.l.- Input-Output Industry Definitions — Continued Texas Industry number Column Row Industry name 19 72 SIC Manufacturing (continued) 88 22 90 22 91 22 92 23 93 23 94 23 95 24 96 23 97 23 98 26 87 26 99 26 100 26 101 102 27 27 Electric household equipment Electronic communications equipment Other electrical apparatus Aircraft Aircraft engines Other aircraft Motor vehicles and parts Ship and boat building Other transportation equipment Scientific instruments Mechanical measuring devices Medical instruments Photographic time and optical instruments Other manufacturing industries Games and toys 3631,3632,3633,3634,3635,3636,3639 3651,3652,3661,3662,3671,3672,3673,3674, 3675,3676,3677,3678,3679 3691,3693,3694,3699 3721,3761 3724,3764 3728,3769 3711,3713,3714,3715 3731,3732 3743,3751,3792,3799,2451 3811 3821,3823,3824,3829,3825 3841,3842,3843 3832,3851,3861,3873 3911,3914,3915,39 31,39 51,39 52,39 53,3955, 3961,3962,3963,3964,3991,3993,399 5,3996 3999 3942,39444,3949 Transportation 103 23 104 29 117 39 106 31 107 32 108 33 104 29 109 34 Communi cation 110 35 111 33 110 35 113 36 112 36 114 36 Railroad transportation Intercity rural highway transportation Motor freight transportation and local trucking and storage Water transportation Air transportation Pipeline transportation Local and suburban transportation Other transportation services Telephone and telegraph Radio and television Other communications Gas services Electric services Water and sanitary services 4011,4013,4041 4131 4212,4213,4214,4222,4224,4225,4231 4411,4421,4441,4452,4453,4454,4459,4463, 4464,4469 4511,4521,4582,4583 4612,4613,4619 4111,4119,4121 4141,4142,4151,4171,4172,4712,4722,4723, 4742,4782,4783,4784,4789 4811,4821 4832,4833 4899 4922,4923,4924,4925,4932 4911,4931 4941,4952,49 53,49 59,4961 -88- Table Al.l. -Input-Output Industry Definitions — Continued Texas Industry number Column Row Industry name 19 72 SIC Wholesale trade 115 37 115 37 115 37 115 37 115 37 115 37 115 37 Wholesale auto, parts, and supplies Wholesale groceries and related products Wholesale farm products and farm product warehousing Wholesale livestock Wholesale machinery, equipment, and supplies Wholesale petroleum and petroleum products General wholesale Finance, insurance, and real estate 117 39 Banking and credit agencies 5012,5013,5014 5141,5142,5143,5144,5145,5146,5146,5148, 5149 4221,5152,5153,5159 5154 5081,5082,5084,5085,5086,5087,5088 5171,5172 5021,5023,5031,5039,5041,5042,5043,5051, 5052,5063,5064,5065,5072,5074,5075,5078, 5093,5094,5099,5111,5112,5113,5122,5133, 5134,5136,5137,5139,5161,5181,5182,5194, 5198,5199 Retail trade 116 38 Lumber yards 5211 116 38 Farm machinery and equipment 5083 116 38 Hardware, paint, and wallpaper 5231,5251 116 38 Department and variety stores 5311,5331, 116 38 Food stores 5411,5422, 5499 116 38 Automotive dealers and 5511,5521, repair shops 7542,7549 116 38 Gasoline service stations 5541 116 38 Apparel and accessory stores 5611,5621, 116 38 Furniture 5712,5713, 125 38 Eating and drinking places 5812,5813 116 38 Other retail 5261,5271, 5931,5941 5948,5949 5993,5994 5399,5961 5423,5431,5441,5451,5462,5463, 5531,7531,7534,7535,7538,7539, 5631,5641,5651,5661,5681,5699 45714,5719,5722,5732,5733 5551,5561,5571,5599,5912,5921, ,5942,5943,5944,5945,5946,5947, ,5962,5963,5982,5983,5984,5992, ,5999 6011,6022,6023,6024,6025,6026,6027,6028, 6032 , 6033 , 6034 , 6042 , 6044 , 6052 , 6054 , 6055 , 6056,6059,6112,6113,6122,6123,6124,6125, 6131,6142,6143,6144,6145,6146,6149,6153, 6159,6162,6163 -89- Table Al .1. -Input-Output Industry Definitions — Continued Texas Industry number Column Row Industry name 19 72 SIC Finance, insurance, and real estate (continued) 119 41 118 40 ices 124 50 120 42 121 43 123 44 122 44 122 44 122 44 122 44 122 44 127 46 126 45 126 45 121 43 121 43 128 47 129 47 130 26 * * 131 48 124 50 124 50 124 50 132 49 Insurance carriers FIRE not elsewhere classified Legal services Lodging services Personal services Advertising Duplicating and addressing Employment agencies, private Photographic services Research and development Other business services Motion picture, amusement, and recreation services Automobile rental services Automobile parking Electrical repair Miscellaneous repair services Physicians and dentists services Hospital and laboratory services Other health services Education (public and private) Colleges and universities Other educational services Engineering and architectural services Accounting, auditing, and bookkeeping Other professional services Other services 6311,6321,6324,6331,6351,6361,6371,6399, 6411 6211,6221,6231,6281,6512,6513,6514,6515, 6517,6519,6531,6541,6552,6553,6611,6711, 6722,6723,6724,6725,6732,6733,679 2,679 3, 6794,6799 8111 7011,7021,7032,7033,7041 7211,7212,7213,7214,7215,7216,7217,7218, 7219 , 7231 , 7241 , 7251 , 7261 , 7271 , 7299 7311,7312,7313,7319 7331,7332,7339 7361 7221,7333,7813,7814,7819,7823,7824,7829, 739 5 7319,89 22 7321 , 7341 , 7342 , 7349 , 7351 , 7362 , 7369 , 739 2 , 7393,739 4,7395,7396,739 7,7399 7832,7833,7911,79 22,79 29,79 32,79 33,79 41, 7948,799 2,799 3,7996,799 7,7999 7512,7513,7519 7523,7525 7622,7623,7629 7631,7641,769 2,7694,7699 8011,8021,8031,8041 8062,8063,8069,8071,8072 8042,8049,8081,8091 8211 8221,8222 8231,8241,8243,8244,8249,8299 8911 8931,7372,7374,7379 8999 8321,8331,8351,8361,8399,8411,8421,8611, 8621,8631,8641,8651,8661,8699 Other manufacturing 17 25 Ordnance and ordnance accessories 3482,3483,3484,3489,3761,379 5 -9 0- Table Al.l. -Input-Output Industry Definitions — Continued Texas Industry number Column Row Industry name 19 72 SIC Other services * Outdoor recreation 132 49 Final payments 133 51 Scrap Households The total public funds spent in the operation and administration of outdoor recreation facilities by the Texas Parks and Wildlife Department, plus those funds spent by counties, cities, and municipalities for the same purpose. Used and second-hand goods. Wages, salaries, rents, interest, and dividends paid to households and personal incomes of sole proprietors. *These State and local activities are not included in the endogenous portion of the table -91- Table Al. 2. -Input-Output Industry Definitions Washington Industry number Industry name 19 72 SIC Column Row 1 2 Field and seed crops 011,013 (exc. 0133), pt. 018, pt. 019 2 1 Vegetables and fruits 0133,016,017, pt. 019 3 1 Livestock and products 02 (exc. 027) 4 I Other agriculture pt. 018,027,071 5 1 Fisheries 09 (exc. 097) 6 2 Meat products 201 7 2 Dairy products 202 5 2 Canning and preserving 203,2091,2092 9 2 Grain meal products 204 10 2 Beverages 208 11 2 Other foods 205-207,209 5-2099 12 3 Texti les 22 13 4 Apparel 23 14 5 Mining 10-14 15 1 Forestry 08--includes national and State forests 16 6 Logging 241 17 6 Sawmi lis 242 16 6 Plywood 2435,2436 19 6 Other wood products 2431,2434,2439,244,245,249 5 20 7 Furniture and fixtures 25 21 8 Pulp mills 261 22 8 Paper mi 1 Is 262 23 8 Paperboard and other products 263-266 24 9 Printing and publishing 27 25 10 Industrial chemicals 281,286,287,289 26 10 Other chemicals 282-285 27 11 Petroleum 29 28 12 Glass products 321-323 ?9 12 Cement, stone, and clay 324-329 30 13 Iron and steel 331,332,339 31 13 Other nonferrous metals 3331-3333,3339,334 3351,3356,3357,3362,3369 32 13 Aluminum 3334,3353-3355,3361 33 14 Structural metal products 344 34 14 Other fabricated metals 341-343,345-349 35 15 Nonelectrical industrial equipment 355-358 36 15 Machine tools and shops 354,359 37 15 Nonelectrical industrial equipment 355-358 38 16 Electrical machinery 36 39 17 Aerospace 372,376 40 17 Motor vehicles and other 371,374,375,379 transportation equipment -9 2- Table Al. 2. -Input-Output Industry Def initions--Continued Washington Industry number Column Row muua li y name 41 17 Ship and boat building 42 18 Other manufacturing 43 19 Transportation services 44 20 Electric companies 45 20 Gas companies 46 20 Other utilities 47 21 Communication 48 22 Construction 49 23 Trade 50 24 Finance, insurance, and real estate 51 25 Services 52 26 Households 19 72 SIC 373--includes Puget Sound Naval Shipyard 30,31,38,39 40-47--includes Postal Services, State ferries, and public transit 491, pt. 493--includes BPA, PUD's, and municipal electric utilities 492, pt. 493--includes municipal gas companies pt. 493,494-49 7- -includes public water, sewage, sanitary, and irrigation systems 48 15-17 50-59--includes State liquor stores 60-67 072-079,09 7,70-89— excludes public hospitals and schools -9 3- Table Al. 3. -Input-Output Industry Definitions West Virginia Industry number Column Row Industry name 19 72 SIC 5 5 6 5 7 5 8 5 9 6 10 7 11 7 12 8 13 9 14 10 15 11 16 11 17 12 18 13 19 14 20 15 21 16 22 17 22 18 24 19 2 5 20 26 21 27 22 28 23 29 24 30 25 29 yt 31 26 32 27 33 28 34 29 35 30 36 31 3 7 32 33 33 39 33 40 33 41 34 Agriculture Coal mining (underground) Coal mining (strip and auger) Petroleum and natural gas Al 1 other mining General contractors (building) General contractors (nonbui lding) Special trades contractors Food and kindred products (n.e.c.) Food and kindred products (dairies) Food and kindred products (bakeries) Food and kindred products (beverages) Apparel and accessories Logging and sawmills Furniture and other wood fabrication Printing and publishing Chemicals Petroleum Glass Stone and clay products Primary metal products Fabricated metal products Machinery (except electrical) Electrical machinery and apparatus Transportation equipment Instruments and related products All other manufacturing Eating and drinking establishments Wholesale trade Al 1 other retail Banking Other finance Insurance agents and brokers Real estate All other FIRE Hotels and other lodging places Medical and legal services Educational services Rai lroads Trucking and warehousing All other transportation Communication Electric companies and systems Gas companies and systems Water and sanitary services Households 0133,0139 ,0143,0132,011,012, 0142,0144,019,07,08,09 121 121 13 10,14 15 16 17 201,203,204,209 202 2051 208 23 241,242 243,244,249,25 27 28 29 321,322 32 (excluding 321,322,329) 33 34 35 36 37 38 21,22,30,329,39,19,26,31 58 50 53,55 (except 5541), 56,57,59 60 61 64 65 62,63,66,67 70 80,81 82 (including 9182,9282,9382) 40 42 44,41,45,46,47 48 491 49 2 494,495,496 ( including 9249 ,9 349 ) -9 4- Appendix B DATA FOR SEVERAL ACCURACY COMPARISONS -95- Table Bl.l. -Ratios of the Column-Total Multipliers (Nonsurvey /Survey) Texas Industry Inversion 2-digit earnings LQ's Original RIMS 2-digit earnings LQ's Alpha regression 4-digit mixed LQ's Inversion 4-digit mixed LQ's 1.1475 1.1501 0.9402 0.9669 1.2528 1.1842 .8609 .9182 1.3038 1.2075 1.0167 1.1266 1.1243 1.1263 1.0029 1.0516 .8573 .8781 .7848 .8043 .89 60 .9081 .8101 .8386 1.0182 1.0312 .9054 .9321 1.2365 1.2138 1.0677 1.1101 1.2761 1.2665 1.1097 1.1408 1.1054 1.1183 .9 740 .9880 1.3299 1.3717 1.2174 1.2259 1.2567 1.2767 1.0914 1.1009 1.1479 1.1513 .9904 .9869 1.2197 1.2380 1.0532 1.0553 1.2164 1.2350 1.0471 1.0582 1.2590 1.2752 1.0940 1.1100 1.1039 1.09 56 .8913 .9155 1.2479 1.0409 .9251 1.1190 1.2135 1.0295 .7880 .8470 1.2507 1.1281 .7967 .8465 1.3613 1.3321 1.0941 1.1405 1.0824 1.1211 .9 572 .9 765 1 . 19 78 1.1573 .9 39 2 .9907 1.1193 1.1176 .9866 1.0179 1.6721 1.6525 1.4181 1.4814 1.4144 1.4053 1.2114 1.2258 1.3153 1.2760 .8846 .9161 1.9 610 1.89 59 1.4820 1.5214 1.5756 1.5346 1.0649 1.0782 .99 53 1.0197 .8661 .8722 1 2 3 4 5 6 7 S 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 -9 6- . Table Bl.l. -Ratios of the Column-Total Multipliers (Nonsurvey/Survey) — Continued Texas Industry Inversion Original RIMS Alpha Inversion 2-digit 2-digit regression 4-digit earnings LQ's earnings LQ's 4-digit mixed LQ's mixed LQ's 1.0147 1.0724 0.8492 0.8404 1.3741 1.4117 1.1599 1.1604 1.39 38 1.4028 1.0831 1.09 76 1.4195 1.4441 1.0733 1.0926 1.0928 1.1223 .9980 1.0143 1.2688 1.2980 1.0172 1.0461 1.2405 1.2815 1.1025 1.1216 1.2696 1.29 38 1.0663 1.0885 1.2032 1.2027 .9199 .9404 1.3253 1.3441 1.0894 1.1160 1.1742 1.19 72 .9 287 .9524 1.1261 1.1409 .9 752 .9944 1.0769 1.1078 1.0385 1.0619 1.0852 1.1209 1.0695 1.0982 1.2553 1.2865 1.0960 1.1046 1.3545 1.3750 1.2227 1.2612 1.3765 1.4230 1.2693 1.3037 1.3721 1.4221 1.2796 1.3125 1.2437 1.2422 1.0393 1.0746 1.5257 1.5287 1.2812 1.3215 1.3206 1.3503 1.2011 1.2327 1.1322 1.1825 1.1009 1.1038 .9866 1.0009 .9050 .9430 .9642 .9603 .8583 .9002 1.3162 1.3196 1.1071 1.1454 1.2311 1.2367 1.0508 1.0924 1.7041 1.6186 1.2568 1.3473 1.1357 1.1497 1.0442 1.0709 1.2393 1.2542 1.1576 1.2011 1.1907 1.2062 1.1228 1.149 6 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 -9 7- Table Bl.l. -Ratios of the Column-Total Multipliers (Nonsurvey /Survey) — Continued Texas Industry Inversion Original RIMS Alpha Inversion 2-digit 2-digit regression 4-digit earnings LQ's earnings LQ's 4-digit mixed LQ's mixed LQ's 1.3517 1.3692 1.2172 1.2490 1.2734 1.29 66 1.1142 1.1416 1.3461 1.389 5 1.0609 1.0744 1.1800 1.1916 1.0201 1.0387 1.4250 1.4658 1.1082 1.1226 1.3881 1.4330 1.2376 1.2443 .99 56 1.0842 .99 24 .9 730 1.2125 1.2703 1.0674 1.0596 1.3232 1.3648 .9918 1.0079 1.6143 1.6390 1.1781 1.2031 1.2389 1.2799 .9425 .9527 1.29 36 1.3271 .9 629 .9 750 1.4839 1.5262 1.1731 1.1848 1.2591 1.29 63 .9 550 .9683 1.0953 1.1081 .989 5 1.0217 1.4727 1.5111 1.1363 1.1535 1.3601 1.3840 1.0785 1.0928 1.5535 1.5377 1.09 28 1.1102 1.3562 1.3547 1.0150 1.0292 1.3386 1.3504 1.0838 1.0981 1.1780 1.1890 .9033 .9167 1.1338 1.1381 .9036 .9194 1.3311 1.3451 1.0749 1.0888 1.4114 1.4157 1.0936 1.1109 1.5304 1.5127 1.1981 1.2271 1.3928 1.3921 .9937 .9975 1.9923 1.9627 1.5691 1.6121 1.7165 1.7212 1.3068 1.3347 1.7206 1.7290 1.2656 1.2966 1.7056 1.6679 1.3410 1.3830 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 -98- Table Bl.l. -Ratios of the Column-Total Multipliers (Nonsurvey/Survey) — Continued Texas Industry Inversion Original RIMS Alpha Inversion 2-digit 2-digit regression 4-digit earnings LQ's earnings LQ's 4-digit mixed LQ's mixed LQ's 1.1630 1 . 19 64 0.9 720 0.9820 1.79 52 1.7253 1.3374 1.3887 1.3371 1.3047 .9426 .9677 1.3223 1.2951 1.0249 1.0575 2.2570 2.2425 1.5344 1.5563 1.4233 1.4294 1.1464 1.1602 1.2217 1.2308 .9430 .9 401 1.2242 1.2144 .9 742 .9967 1.3415 1.3358 1.0881 1.1206 1.3981 1.3992 1.1353 1.1645 1.29 64 1.3114 1.0694 1.0913 1.5139 1.5211 1.2301 1.2589 1.1155 1.0967 1.0143 1.0646 1.0055 1.0123 .8919 .9104 1.1447 1.1420 1.0218 1.0589 1.0201 1.0029 .9106 .9 649 1.0078 1.0001 .8844 .9 208 .9 59 2 .9407 .9001 .9331 1.1514 1.1657 1.0328 1.0526 1.1886 1.1794 1.0506 1.0855 1.2330 1.2485 1.0322 1.0459 .8201 .8219 .8680 .8834 .7879 .8297 1.0452 1.0684 .7250 .7153 .6575 .6866 1.1375 1.1467 1.0248 1.0471 1.0432 1.0598 .9 558 .9681 1.0907 1.1102 .9870 1.0038 .8914 .8988 .8104 .8317 1.3256 1.2776 1.1014 1.1692 1 . 189 3 1.2066 1.1039 1.1191 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 -99- Table Bl.l-Ratios of the Column-Total Multipliers (Nonsurvey/Survey) — Continued Texas Industry Inversion 2-digit earnings LQ's Original RIMS 2-digit earnings LQ's Alpha regression 4-digit mixed LQ's Inversion 4-digit mixed LQ's 1.0963 1.1045 0.9551 0.9 718 1.1434 1.1585 1.0150 1.0316 1.1375 1.1484 1.0009 1.0215 .8481 .8617 .7787 .7928 1.2871 1.2463 1.0925 1.1489 1.4196 1.4202 1.1177 1.1289 1.0874 1.0875 .9131 .9390 .6327 .6336 .5724 .5902 1.1398 1.1469 1.0011 1.0217 1.0553 1.0630 .9396 .9 585 1.2295 1.2568 1.1202 1.1283 1.1811 1.1946 1.0686 1.0835 1.0945 1.0691 .9285 .9 724 121 122 123 124 125 126 127 128 129 130 131 132 133 Average 1.2536 1.2567 1.0443 1.0709 -100- Table Bl. 2. -Ratios of the Column-Total Multipliers (Nonsurvey/Survey) Washington Industry Inversion Original RIMS Alpha Inversion 2-digit 2-digit regression 4-digit earnings LQ's earnings LQ's 4-digit mixed LQ's mixed LQ's 1.2855 1.1182 0.9647 1.0415 1.1862 1.0459 .9179 .9863 1.4620 1.1101 .8750 1.0392 1.2613 1.1575 1.0236 1.0572 1.9494 1.3216 .8863 1.0640 1.3153 .9 523 .8266 1.0135 1.2292 .9949 .8531 .9836 1.6036 1.2676 1.0877 1 . 2899 1.3139 1.1067 .9401 1.0282 1.3273 1.0963 .9661 1.1130 .9 529 .8670 .7664 .8096 1.2805 1.1810 .9686 1.0137 1.3362 1.2021 1.0328 1.0824 1.0092 .8590 .7331 .8164 1.1613 .9854 .8721 .9 769 1.2893 1.0771 .9491 1.0815 1.4187 1.1769 .99 79 1.1438 1.3404 1.1422 .9 607 1.0664 1.2625 1.0547 .9194 1.0474 1.3361 1.1303 .9891 1.1142 1.2728 1.0727 .9369 1.0599 1.3496 1.1640 1.0096 1.1098 1.2549 1.0912 .9479 1.0346 1.5209 1.2773 1.0708 1.19 71 1.5060 1.3642 1.2180 1.2951 1.2280 1.0865 .9 369 1.0013 1.29 30 1.089 6 .9 330 1.0443 1.1367 1.0022 .8076 .8648 .7985 .8094 .7270 .7209 1.5888 1.3614 1.1918 1.3359 1 2 3 4 6 7 8 9 10 11 12 13 14 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 -101- Table Bl. 2. -Ratios of the Column-Total Multipliers (Nonsurvey /Survey) — Continued Washington Inversion Original RIMS Alpha Inversion Industry 2-digit 2-digit regression 4-digit earnings LQ's earnings LQ's 4-digit mixed LQ's mixed LQ's 33 1.4069 1.2224 0.9013 0.9672 34 1.5824 1.3773 1.0380 1.1174 35 1.3235 1.1748 .9318 .9757 36 1.3492 1.2118 .9873 1.0272 37 1.3725 1.2173 .9852 1.0385 38 1.4158 1.2603 1.0286 1.0827 39 1.6462 1.4409 1.1543 1.2230 40 1.9283 1.6752 1.2466 1.3115 41 1.2801 1.1299 .9280 .9827 42 1.4131 1.2344 1.0137 1.0867 43 1.2364 1.0993 .9599 1.0214 44 1.0199 .9 284 .8045 .8379 45 1.1317 1.0358 .8702 .9033 46 1.1737 1.0641 .9331 .9 720 47 1.2222 1.1262 .9835 1.0058 48 1.3347 1.1517 .9866 1.0746 49 1.2151 1.0857 .9538 1.0000 50 1.19 66 1.0648 .9 300 .9863 51 1.2072 1.0750 .9148 .9642 52 1.2044 .9666 .8158 .9613 Average 1.3186 1.1341 .9535 1.0394 -102- Table Bl. 3. -Ratios of the Column -Total Multipliers (Nonsurvey/Survey) West Virginia Industry Inversion Original RIMS Alpha Inversion 2-digit 2-digit regression 4-digit earnings LQ's earnings LQ's 4-digit mixed LQ's mixed LQ's 1.0624 1.2337 0.9 247 0.9176 1.2722 1.4503 1.1603 1.1697 .9165 1.0588 .8711 .8525 1.19 69 1.3662 1.0944 1.0918 .9616 1.0735 .8405 .8463 .9035 1.0155 .9425 .9 353 1.2528 1.4398 1.0186 1.0221 1.5428 1.6649 1.2136 1.2621 1.0752 1.2241 .9425 .9408 1.1678 1.2833 .9814 1.0103 1.5025 1.6339 1.2175 1.2605 1.0781 1.2171 .8635 .8619 1.3755 1.5415 1.2041 1.2253 .9821 1.1576 .9312 .9099 1.2924 1.4677 1.1167 1.1217 1.3065 1.4718 1.1898 1.2272 1.4757 1.6637 1.3264 1.3486 1.5213 1.7032 1.3076 1.3383 1.2921 1.4635 1.1079 1.1164 1.3079 1.4627 1.1018 1.1148 1.4377 1.5833 1.1436 1.1660 2.0813 2.3619 1.7521 1.7575 1.7015 1.8986 1 . 3848 1.4026 1.2450 1.4668 1.1103 1.0981 1.0270 1.19 69 .9 750 .9 636 .9991 1.1666 .9 583 .9 387 1.1469 1 . 3089 1.0809 1.0723 1 . 149 2 1.3262 1.1043 1.0890 1.3687 1 . 569 3 1.3108 1.3011 .6440 .7012 .6437 .6317 .9 737 1.1548 .9334 .9073 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 -103- Table Bl. 3. -Ratios of the Column-Total Multipliers (Nonsurvey /Survey) — Continued West Virginia Industry 32 33 34 35 36 38 39 Inversion 2-digit earnings Original RIMS 2-digit earnings LQ's Alpha regression 4-digit mixed LQ's Inversion 4-digit mixed LQ's 1.1906 1.3901 1.1003 1.0841 1.1449 1.3578 1.0931 1.0620 1.3399 1.5386 1.2593 1.2527 1.4499 1.6633 1.3567 1.3718 1.1338 1.2902 1.0628 1.0585 1.0020 1.1460 .9624 .9 525 1.0574 1.2044 .9969 1.0001 1.0197 1.1312 1.0004 .9923 .9811 1.1079 .9431 .9420 1.1694 1.3041 1.0483 1.0712 40 41 Average 1.2134 1.3771 1.0872 1.0900 -104- Table B2.1. -Ratios of the Earnings Multipliers (Nonsurvey/Survey) Texas Industry Inversion 2-digit earnings LQ's Original 2-dig earning; RIMS it 5 LQ's Alpha regression 4-digit mixed LQ's Original Modified formula formula Inversion 4-digit Original formula Modified formula mixed LQ's 1 1.2666 1.7416 1.3102 1.4393 1.0828 1.0920 2 1.3675 1.8290 1.3760 1.2555 .9445 .9900 3 1.0811 1.5438 1.1614 1.2521 .9420 .899 5 4 .9 365 1.2509 .9411 1.1071 .8329 .8731 5 .7087 .9836 .7400 .8670 .6523 .6601 6 .6671 .9 258 .6965 .8121 .6110 .6181 7 .9 711 1.3040 .9810 1.1536 .8679 .8937 8 1.1779 1.5319 1.1525 1.3350 1.0044 1.0565 9 1.4706 1.9421 1.4611 1.7245 1.2974 1.3376 10 .9947 1.3397 1.0079 1.1564 .8700 .8802 11 1.3399 1.8216 1.3704 1.6133 1.2138 1.2362 12 1.1831 1.6231 1.2211 1.3813 1.0392 1.0456 13 1.0057 1.3620 1.0247 1.1718 .8816 .8715 14 1.1083 1.5194 1.1431 1.2905 .9 708 .9673 15 1.0448 1.4409 1.0840 1.2247 .9 214 .9 206 16 1.2485 1.6801 1.2640 1.4733 1 . 1084 1.1267 17 1.0253 1.3430 1.0104 1.1044 .8309 .8646 18 1.1315 1.5751 1.1850 1.3620 1.0247 .9 708 19 1.2816 1.6088 1.2103 1.1635 .8753 .8559 20 1.3558 1.6113 1.2122 1.0507 .7905 .8411 21 1.4631 1.9435 1.4622 1.5241 1.1466 1.1825 22 .9 645 1.4446 1.0868 1.1727 .8822 .8488 23 1 . 199 3 1.6812 1.2648 1.3286 .999 5 .9831 24 .9924 1.4011 1.0541 1.2132 .9127 .8914 25 2.0323 2.7590 2.0757 2.2814 1.7164 1.7441 26 1.3767 1.9253 1.4485 1.5810 1.1895 1.1370 27 1 . 2488 1.6513 1.2423 1.1060 .8321 .8636 28 2.1694 2.7676 2.0822 2.2133 1.6651 1.7575 29 1.5664 2.0690 1.5566 1.4018 1.0547 1.0774 30 .8191 1.1802 .8879 .9294 .6992 .6803 -105- Table B2.1. -Ratios of the Earnings Multipliers (Nonsurvey/Survey) — Continued Texas Industry Inversion 2-digit earnings LQ's Original RIMS 2-digit earnings LQ's Alpha regression 4-digit mixed LQ's Original Modified formula formula Inversion 4-digit Original Modified formula formula mixed LQ's 31 0.7789 1.2530 0.9426 0.9 399 0.7071 0.6436 32 1.2987 1.8861 1.4189 1.5159 1.1405 1.1007 33 1.3667 1.8809 1.4151 1.4415 1.0845 1.09 34 34 1.4264 1.9911 1.4980 1.4526 1.09 29 1.1044 35 1.0741 1.5357 1.1554 1.3466 1.0131 .9998 36 1.2239 1.7176 1.2922 1.3177 .9913 1.0123 37 1.3293 1.8890 1.4211 1.6110 1.2120 1.2105 38 1.2927 1.7325 1.3034 1.4521 1.0925 1.1345 39 1.2185 1.5618 1.1750 1.1600 .8727 .9 284 40 1.3178 1.7652 1.3280 1.4602 1.0985 1.1401 41 1.1321 1.5453 1.1626 1.1854 .8918 .9 29 2 42 1.1093 1.4804 1.1137 1.29 32 .9 729 1.0011 43 1.2375 1.7653 1.3281 1.6370 1.2316 1.2015 44 1.1870 1.7417 1.3103 1.6425 1.2357 1.1813 45 1.4837 2.1268 1.6001 1.7752 1.3355 1.3040 46 1.6095 2.2627 1.7023 1.9983 1.5034 1.4892 47 1.5382 2.2610 1.7010 1.9777 1.4879 1.4312 48 1.8125 2.6595 2.0008 2.3691 1.7823 1.7121 49 1.1022 1.4602 1.0985 1 . 19 34 .89 78 .9422 50 1.8353 2.5043 1.8841 2.0149 1.5159 1 . 5469 51 1.5403 2.2128 1.6648 1.9438 1.4624 1.4224 52 1.19 32 1.7249 1.2977 1.5677 1.1794 1.1362 53 1.0103 1.4453 1.0874 1.2751 .9 59 3 .9 550 54 1.0529 1.4184 1.0671 1.2430 .9 352 .9 711 55 1.3382 1.8189 1.3684 1.519 6 1.1433 1.1643 56 1.2488 1.7419 1.3105 1.4501 1.0910 1.0893 57 1.6275 2.1497 1.6173 1.6679 1.2548 1.2905 53 1.1218 1.5100 1.1360 1.3752 1.0346 1.0551 59 1.2179 1.6563 1.2461 1.5109 1.1367 1.1741 60 1.1884 1 . 589 1 1 . 19 56 1.4849 1.1172 1.1360 -106- Table B2.1. -Ratios of the Earnings Multipliers (Nonsurvey/Survey) — Continued Texas Industry Inversion 2-digit earnings LQ's Original 2-dig earnings RIMS it LQ's Alpha regression 4-digit mixed LQ' s Original Modified formula formula Inversion 4-digit Original formula Modified formula mixed LQ's 61 1.3460 1.8289 1.3759 1.6136 1.2140 1.2389 62 1.19 22 1.6355 1.2304 1.3799 1.0381 1.0645 63 1.1986 1.7120 1.2880 1.2507 .9410 .9 29 5 64 1.1087 1.4769 1.1111 1.2763 .9602 .9854 65 1.4039 1.9667 1.4796 1.4792 1.1129 1.1182 66 1.2523 1.7931 1.3490 1.5453 1.1626 1.1155 67 .6394 1.0814 .8135 .9612 .7232 .6181 68 1.1337 1.8278 1.3751 1.4715 1.1071 .9678 69 1.4253 2.0413 1.5358 1.4221 1.0699 1.0761 70 1.5090 2.1146 1.5909 • 1.4387 1.0824 1.1004 71 1.1738 1.6634 1.2514 1.1927 .89 73 .8984 72 1.3403 1 .9 199 1.4444 1.3787 1.0373 1.0287 73 1.3119 1.8365 1.3817 1.3805 1.0386 1.0445 74 1.2144 1.7362 1.3062 1.2348 .9 29 .9 285 75 .9 269 1.2693 .9 549 1.1299 .8501 .8585 76 1.5114 2.1568 1.6226 1.5557 1.1704 1.1684 11 1.2743 1.7483 1.3153 1.3447 1.0116 1.0253 78 1.4638 1.9394 1.4591 1.3364 1.0054 1.0307 79 1.1722 1.5609 1.1743 1.1454 .8617 .8826 80 1.3727 1.8351 1.3806 1.4750 1.109 7 1.1351 81 .8494 1.1442 .8608 .8667 .6521 .6666 82 .9 064 1 . 199 3 .9022 .9683 .7285 .7483 83 1.3022 1.7586 1.3231 1.4037 1.0560 1.0694 84 1.419 6 1.8867 1.419 4 1.4639 1.1013 1.1300 85 1.5043 1.9597 1.4743 1.5407 1.1591 1.2044 86 1.3787 1.8900 1.4219 1.2400 .9 329 .9215 87 2.9025 3.7285 2.8051 3.049 7 2.2944 2.4073 88 1.8394 2.4614 1.8518 1.8800 1.4144 1.4531 89 1.7336 2.3603 1.7757 1.669 5 1.2560 1.2872 90 1.7389 2.2061 1.6597 1.8153 1.3657 1.4401 -107- Table B2.1. -Ratios of the Earnings Multipliers (Nonsurvey/Survey) — Continued Texas Original RIMS Alpha Inversion 2-dig it regression Inversion Industry 2-digit earnings LQ's earnings LQ's 4-digit mixed LQ's Original Modified 4-digit Original Modified mixed LQ's formula formula formula formula 91 1.1373 1.6136 1.2139 1.3031 0.9803 0.9 628 92 1.799 2 2.2426 1.6872 1.7646 1.3276 1.4161 93 1.1109 1.4245 1.0717 1.0409 .7831 .8133 94 1.1045 1.4181 1.0669 1.1364 .8549 .89 78 95 3.3040 4.4360 3.3373 2.9 320 2.2059 2.2545 96 1.3583 1.8217 1.3705 1.5004 1.1288 1.1455 97 1.0504 1.4790 1.1127 1.0903 .8203 .7962 98 1,1580 1 . 5069 1.1337 1.2203 .9180 .9 547 99 1.4395 1 .9 19 1.4437 1.5491 1.1654 1.2035 100 1.3373 1.7631 1.3264 1.4336 1.0785 1.1222 101 1.2464 1.7045 1.2823 1.3813 1.0392 1.0544 102 1.3825 1.8755 1.4110 1.49 32 1.1234 1 . 1469 103 .9 787 .2478 .9 387 1.1611 .8736 .9469 104 .8687 1.1533 .8676 1.0236 .7701 .7921 105 1.1517 1.4857 1.1178 1.3486 1.0146 1.0799 106 .7816 1.0104 .7601 .9136 .6873 .739 4 107 .8590 1.1241 .8457 .99 70 .7501 .7880 108 .7714 .9 653 .7263 .9015 .6782 .7229 109 1.2160 1.6039 1.2066 1.4496 1.0906 1.1304 110 1.1725 1.5067 1.1335 1.3361 1.0052 1.0668 111 1.0865 1.4453 1.0873 1.19 33 .89 78 .9221 112 .5710 .7674 .5774 .8383 .6307 .6021 113 .7317 1.0757 .8093 1.4796 1.1132 .9679 114 .5584 .7079 .5326 .6436 .4842 .5261 115 1.0447 1.3760 1.0352 1.2435 .9 355 .9 710 116 .9901 1.3148 .9892 1.2029 .9050 .9 266 117 .9086 1.19 63 .9000 1.0734 .8076 .8425 118 .8275 1.0814 .8135 .9 766 .7347 .7738 119 1.1770 1.4554 1.0949 1.2658 .9 523 1.0457 120 1.1669 1.5424 1.1604 1.4117 1.0621 1.09 36 ■108- Table B2.1. -Ratios of the Earnings Multipliers (Nonsurvey/Survey) — Continued Texas Industry Inversion 2-digit jarnings LQ's Original 2-dig earnings RIMS it LQ's Alpha regression 4-digit mixed LQ's Original Modified formula formula Inversion 4-digit 6 Original formula Modified formula mixed LQ's 121 0.9292 1.2302 0.9255 1.0691 0.8043 0.8317 122 1.0341 1.3704 1.0310 1.2162 .9150 .9455 123 1.2146 1.6010 1.2045 1.4212 1.0692 1.109 5 124 .6175 .8202 .6171 .7405 .5571 .5782 125 1.2555 1.7021 1.2805 1.5002 1.1286 1.1270 126 1.6820 2.2435 1.6879 1.7613 1.3251 1.3524 127 .8538 1.1215 .8437 .9 371 .7050 .7363 128 .3664 .4785 .3600 .4214 .3170 .3383 129 .9613 1.2773 .9609 1.1400 .8577 .8795 130 1.0643 1.419 1.0676 1.2714 .9565 .9 776 131 1.0544 1.4055 1.0574 1.2825 .9649 .9845 132 1.1628 1.5343 1.1543 1.4003 1.0535 1.0812 133 .9 738 .449 7 .3383 .3644 .2742 .9191 Average 1.2264 1.6522 1.2486 1.3628 1.0252 1.0434 ■109- Table B2. 2. -Ratios of the Value-Added Multipliers (Nonsurvey /Survey) Washington Industry Inversion 2-digit earnings LQ's Original 2-dig earnings RIMS it LQ's Alpha regression 4-digit mixed LQ's Original Modified formula formula Inversion 4-digit Original formula Modified formula mixed LQ's 1 1.1472 1.5115 0.9 689 1.3047 0.8363 0.9429 2 .9937 1.3256 .849 7 1.1636 .7459 .8365 3 1.3713 1 . 59 60 1.0231 1.1987 .7684 .9 522 4 1.2608 1.7517 1.1229 1.5661 1.0039 1.0857 6 1.9647 2.1649 1.3877 1.2690 .8135 .9 330 7 1.3387 1.5658 1.0037 1.3222 .8476 .99 26 8 1.079 7 1.3147 .8428 1.0984 .7041 .8505 9 1 . 599 5 1.9016 1.219 1.5809 1.0134 1.259 5 10 1.2094 1.5622 1.0014 1.3075 .8381 .9404 11 1.2426 1.5746 1.0093 1.3676 .8767 1.0332 12 .7146 .9 684 .6208 .8304 .5323 .59 33 13 1.1186 1.5672 1.0046 1.2370 .79 30 .8703 14 1.2343 1.6860 1.0807 1.4542 .9332 1.0188 16 .8427 1.0633 .6816 .8836 .5664 .6747 17 1.0226 1.3506 .8658 1.1831 .7584 .8544 18 1.1634 1.5106 .9 683 1.3148 .8428 .9675 19 1.3397 1.7053 1.0931 1.4134 .9 060 1.0654 20 1.1789 1.5378 .9857 1.2733 .8162 .9 343 21 1.1755 1.5033 .9637 1.2859 .8243 .9 620 22 1.2179 1.5764 1.0105 1.3571 .8700 1.0044 23 1.1478 1.4886 .9 542 1.2807 .8210 .9459 24 1.1565 1.5175 .9 728 1.3108 .8403 .9557 25 1.0717 1.419 3 .9098 1.2225 .7836 .8844 26 1.3737 1.7508 1.1223 1.4365 .9 209 1.0701 27 1.7556 2.3745 1.5221 2.0333 1.3034 1.4504 28 1.0837 1.4705 .9426 1 . 2699 .8140 .89 60 29 1.2076 1.5381 .9859 1.3017 .8344 .9 737 30 .9092 1.2186 .7811 .9 540 .6115 .6845 31 .3760 .7639 .489 7 .6461 .4141 .3089 -110- Table B2.2. -Ratios of the Value-Added Multipliers (Nonsurvey/Survey)--Continued Washington Industry Inversion 2-digit earnings LQ's Original 2-dig earnings RIMS it LQ's Alpha regression 4-digit mixed LQ' s Original Modified formula formula Inversion 4-digit Original formula Modified formula mixed LQ's 32 1.6165 2.1532 1.3803 1.8436 1.1818 1.3305 33 1.2653 1.6984 1.0887 1.2076 .7741 .8605 34 1.4631 1.9678 1.2614 1.4398 .9 230 1.0258 35 1.2155 1.6465 1.0554 1.2823 .8220 .89 75 36 1 . 249 7 1.7175 1.1010 1.3986 .89 65 .9 69 2 37 1.2706 1.7173 1.1008 1.3755 .8817 .9 684 38 1.3217 1.79 53 1.1508 1.4522 .9 309 1.0200 39 1.5567 2.0713 1.3278 1.6324 1.0464 1.1565 40 2.1471 2.8898 1.8524 2.059 7 1.3203 1.4328 41 1.059 3 1.4318 .9178 1.1595 .7433 .8150 42 1.2417 1.6619 1.0653 1.3494 .8650 .9601 43 1.0817 1.4558 .9332 1.2732 .8162 .9 063 44 .9 219 1.279 3 .8200 1.1084 .7105 .7661 45 1.1571 1.6443 1.0541 1.3512 .8662 .9137 46 1.0292 1.4176 .9 087 1.2548 .8044 .8737 47 1.0965 1.5336 .9831 1.3572 .8700 .9296 48 1.2629 1.6664 1.0682 1.4139 .9 064 1.0206 49 1.0587 1.4454 .9265 1.2807 .8209 .89 28 50 1.0945 1.4668 .9 403 1.2910 .8276 .9227 51 1.0508 1.4193 .9098 1.2151 .7789 .859 5 52 1.0544 .4949 .3172 .3702 .2373 .9310 Average 1.2103 1.5770 1.0109 1.2996 .8331 .9479 -111- Table B2. 3. -Ratios of the Earnings Multipliers (Nonsurvey/Survey) West Virginia Industry Inversion 2-digit earnings LQ's Original 2-dig earnings RIMS it LQ's Alph regres 4-digit mi Original formula a si on xed LQ's Modified formula Inversion 4-digit Original formula Modified formula mixed LQ's 1 1.1890 1.869 5 1.4065 1.39 04 1.0460 1.0588 2 1.4520 2.1502 1.6177 1.7482 1.3152 1.3625 3 .9347 1.5017 1.1298 1.2040 .9058 .8662 4 1.2240 1.8683 1.4056 1.49 52 1.1249 1.1336 5 1.089 2 1.7199 1.2940 1.2128 .9124 .9487 6 .7670 1.2107 .9108 1.1033 .8300 .8160 7 1.4135 2.2596 1.7000 1.5237 1.1463 1.1802 8 1.6202 2.3388 1.7596 1.5878 1.1946 1.29 66 9 .8138 1.2240 .9 209 .9 322 .7013 .7196 10 1.0927 1.5622 1.1753 1.2038 .9057 .9620 11 1.8542 2.6837 2.0190 1.9 243 1.4477 1.5519 12 1.1992 1.7856 1.3433 1.2700 .9 555 .9830 13 1.5345 2.4122 1.8148 1.8219 1.3707 1.3640 14 .9021 1.6716 1.2576 1.2303 .9 256 .8169 15 1.2127 1.8178 1.3676 1.3996 1.0530 1.0775 16 1.2755 1.9090 1.4362 1.5311 1.1519 1.2127 17 1.5119 2.2653 1.7043 1.7867 1.3442 1.3933 18 1.59 53 2.3805 1.7909 1.8142 1.3649 1.4174 19 1.1803 1.7455 1.3132 1.3492 1.0150 1.0452 20 1.519 4 2.259 7 1.7000 1.6816 1.2651 1.3069 21 1.4055 2.0838 1.5677 1.4463 1.0881 1.1324 22 4.9 701 7.3374 5.5201 5.5863 4.2027 4.3250 23 2.2614 3.4142 2.5686 2.4406 1.8361 1.8837 24 1.4014 2.2170 1.6679 1.69 78 1.2773 1.2851 25 .9273 1.3773 1.0362 1.1632 .8751 .8913 26 .9811 1.4902 1.1211 1.2568 .9455 .9394 27 1 . 249 6 1.8600 1.3993 1.5473 1.1641 1.1834 28 .8832 1.4434 1.0859 1.1009 .8282 .8183 29 1.8912 2 .9 389 2.2110 2.3857 1.7948 1.8009 -112- Table B2. 3. -Ratios of the Earnings Multipliers (Nonsurvey/Survey) — Continued West Virginia Industry Inversion 2-digit earnings LQ's Original 2-dig earnings RIMS it LQ's Alpha regression 4-digit mixed LQ's Original Modified formula formula Inversion 4-digit Original formula Modified formula mixed LQ's 30 0.2254 0.4089 0.3076 0.3253 0.2447 0.2137 31 .9 302 1.4567 1.09 59 1.2046 .9062 .8833 32 1.2175 1.8279 1.3752 1.5045 1.1319 1.1426 33 1.1138 1.7119 1.2879 1.4300 1.0759 1.0580 34 1.5305 2.2984 1.7291 1.9106 1.4374 1.4582 35 1.7537 2.5574 1.9 240 2.1365 1.6074 1.6985 36 1.1186 1.7374 1.3071 1.3995 1.0529 1.0515 37 .9035 1.3449 1.0118 1.1428 .8598 .8708 38 .89 51 1.4790 1.1127 1.1567 .8702 .8450 39 .9003 1.4773 1.1115 1.19 66 .9003 .8642 40 1.0112 1.5151 1.1399 1.2733 .9 579 .9803 41 1.0584 .3764 .2832 .2509 .1887 1.0314 Average 1.3173 1.9 753 1.4861 1.5308 1.1517 1.1920 •113- Table B3.1.-Chi-Square Statistics Texas Inversion Inversion Industry 2-digit 4-digit earnings LQ's mixed LQ's 1 0.3955 0.2071 2 .3159 .1616 3 .3018 .1877 4 .5560 .3904 5 .5957 .4765 6 .4626 .3418 7 .4262 .2190 8 .5984 .4263 9 .6381 .3803 10 .3849 .2085 11 .8264 .4093 12 .4014 .2117 13 .3518 .1544 14 .4439 .2455 15. .3874 .1512 16 .3849 .1588 17 .4163 .1446 18 .2503 .1263 19 .2588 .1119 20 .3431 .2077 21 .3182 .1670 22 .3241 .1517 23 .3320 .1937 24 .3302 .1246 25 .6061 .2858 26 .4066 .189 5 27 .3174 .2029 28 .6999 .1545 29 3.5579 .4537 30 1.189 2 .5891 31 .5360 .2984 -114- Table B3.1. -Chi -Square Statistics — Continued Texas Inversion Inversion Industry 2-digit 4-digit earnings LQ's mixed LQ's 32 0.5057 0.1460 33 .4717 .1716 34 .8774 .4516 35 .5744 .2148 36 .4679 .2651 37 .3394 .1225 38 .3645 .1696 39 .5206 .3621 40 .4593 .1994 41 .2581 .0973 42 .3435 .1736 43 .5179 .2605 44 .3926 .2170 45 2.1069 1.2711 46 .7884 .4589 47 .6223 .2739 48 .619 5 .2746 49 .3525 .1215 50 .6446 .3669 51 .4679 .2052 52 .3157 .1375 53 .4800 .2203 54 1.019 4 .2749 55 .3846 .1543 56 .8289 .1441 57 .9016 .3615 58 .4328 .19 03 59 .4120 .1630 60 .4250 .1320 61 .8505 .4401 -115- Table B3.1. -Chi -Square Statistics — Continued Texas Inversion Inversion Industry 2-digit 4-digit earnings LQ's mixed LQ's 62 0.6045 0.2568 63 .7933 .4137 64 .6770 .2382 65 .6503 .1692 66 .5194 .2631 67 .6906 .5359 68 .3688 .1583 69 .4724 .2457 70 2.5080 .5218 71 .7824 .2155 72 .3516 .1886 73 1.2706 .3531 74 1.3249 .3719 75 .3572 .1680 76 .6573 .2069 77 .5323 .1580 78 1.1836 .3709 79 .3572 .1302 80 .3751 .1385 81 .7524 .2054 82 .7194 .1550 83 .4199 .1641 84 .5559 .1882 85 .7273 .2453 86 1.1470 .2240 87 1.7251 .5282 88 .6047 .1748 89 4.9 354 1.1786 90 .4821 .1841 91 .3850 .2010 •116- Table B3.1. -Chi -Square Statistics — Continued Texas Inversion Inversion Industry 2-digit 4-digit earnings LQ's earnings LQ's 92 0.5969 0.2105 93 1.5153 .3476 94 1.5259 .7521 95 2.5646 .5995 96 .7144 .1687 9 7 .59 20 .1815 98 .3810 .1934 99 2.2790 .5718 100 .8888 .3166 101 .3604 .1630 102 .9035 .3662 103 .7740 .6092 104 .7540 .4355 105 .8103 .6055 106 .4061 .2484 107 .3589 .1057 108 .3807 .1632 109 .4946 .1759 110 .5385 .2318 111 1.9417 .9271 112 .6424 .5387 113 .4184 .2864 114 .3977 .3244 115 .3681 .1728 116 .3345 .1282 117 .4228 .1640 118 .4287 .2126 119 .3936 .1427 120 .5421 .2699 121 .4365 .1601 •117- Table B3.1. -Chi -Square Statistics — Continued Texas Inversion Inversion Industry 2-digit 4-digit earnings LQ's mixed LQ's 122 0.4676 0.2078 123 .6572 .3151 124 .3652 .2129 125 .3683 .1456 126 1.5403 .6604 127 .4077 .1931 128 .4067 .3248 129 .3770 .2090 130 .4117 .1554 131 .5777 .3158 132 .4384 .19 31 133 .6284 .1966 Average .6906 .2799 ■118- Table B3. 2. -CHI-Square Statistics Washington Industry Inversion 2-digit earnings LQ's Inversion 4-digit mixed LQ's 1 2 3 4 6 7 8 9 10 11 12 13 14 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 .33 0.4578 .5162 .3855 .4488 .4224 .3943 .3313 .4705 .4772 .4266 .9475 .5556 .6761 1.2263 .5702 .5253 .9849 .8477 .5316 .4361 .4811 .6368 .5005 .5026 .9921 .9055 .6787 .49 78 .4400 .9 507 .5427 0.1804 .1383 .1099 .0866 .0569 .0754 .1303 .1397 .0919 .0925 .3293 .1721 .1643 .1831 .0755 .0829 .1640 .1639 .1509 .1028 .0985 .1781 .1285 .1292 .6002 .29 29 .1458 .1851 .4581 .4749 .1169 -119 Table B3.2.-Chi-Square Statistics — Continued Washington Inversion Inversion Industry 2-digit 4-digit earnings LQ's mixed LQ's 34 0.7185 0.1719 35 .2578 .0556 36 .6013 .1154 37 .5555 .1206 38 .3175 .1008 39 1.3397 .5940 40 .5937 .2363 41 .7599 .1899 42 .8428 .2081 43 .5186 .1314 44 .6199 .2414 45 .6789 .2205 46 .6328 .1790 47 .5208 .0965 48 .4598 .0782 49 .5276 .0998 50 .4704 .0536 51 .9469 .1242 52 .6753 .0733 Average .6160 .1718 120- : Table B3. 3. -Chi -Square Statistics West Virginia Industry Inversion 2-digit earnings LQ's Inversion 4-digit mixed LQ's 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 0.5871 .5894 1.3830 .7893 .7777 1.2656 .6669 5.3096 .3641 .6150 1.6027 5.5798 .5945 .9327 .6303 .2834 .5251 .5516 .5592 .8766 1.7211 5.2890 .8789 .4655 .3249 .2446 .3638 .5292 .7627 .3898 .5198 0.1107 .2797 .5515 .4024 .2035 .1377 .2152 2.2861 .1858 .2418 .8022 .2675 .1942 .9026 .2838 .1502 .2661 .2521 .1830 .2256 .3910 2.0730 .5279 .1539 .1115 .0841 .1179 .2548 .3468 .3807 .2138 -121- Table B3.3.-Chi-Square Statistics — Continued West Virginia Inversion Inversion Industry 2-digit 4-digit earnings LQ's mixed LQ's 32 0.8751 0.2046 33 .5444 .2378 34 .4114 .1842 35 .6056 .2194 36 .4702 .2067 37 .2140 .0842 38 .6958 .3377 39 .1791 .0916 40 .3340 .1588 41 .4985 .1707 Average .9951 .3584 122- Appendix C ESTIMATES OF LPW IMPACTS -123- Table CI. 1. -Industry Designations for LPW Impact Application Industry number Column Row Industry name 19 72 1-0 code 19 72 SIC - - 7 s 8 9 9 10 10 11 11 12 12 13 13 14 14 15 15 16 16 17 17 18 18 19 19 20 20 Agriculture products and services and forestry and fishery services Forestry and fishery products Coal mining Crude petroleum and natural gas Other mining New construction Maintenance and repair construction Food and kindred products and tobacco Textile mi 1 1 products Apparel Paper and allied products Printing and publishing Chemicals and refined petroleum Rubber and leather products Lumber and furniture products Stone, clay, and glass products Primary metals Fabricated metals Nonelectrical machinery Electrical machinery 010100-020702, 040000 030000 070000 080000 01-02,07 (excl. 074), 085, 092 081-4,091,09 7 1111, pt. 1112,1211, pt. 1212 131-1, pt. 133 050000,060100, 060200,090000, 100000 101-106, pt. 108, 109,141-5, pt.148. 149,147 110101-110508 pt. 15-17, pt. 138, pt. 1112, pt. 1213, pt. 148, pt. 108 120100-120216 pt. 15-17, pt. 138 140101-150200 20-21 160100-180300 221-9 180400-190306 231-9,39996 240100-25000 261-5 260100-26085 27 270100-310300 28-9 320100-340305 301-19 200100-230700 241-59 (excl. 2451) 350100-362200 321-9 370101-381400 331-9,3462-3,28195 390100-42110, 130200,130500- 130700 341-9, (excl. 3462-3) 430100-520500 35 530100-580500 36,3825 -124- Table CI .1.- Industry Designations for LPW Impact Application — Continued Industry number Column Row Industry name 19 72 1-0 code 19 72 SIC 21 21 Motor vehicles and equipment 22 22 Other transportation equipment 23 23 Instruments 24 24 Miscellaneous' manufacturing 25 25 Transportation, local government transit, and postal 26 26 Communication 27 27 Utilities 28 28 Wholesale trade 29 29 Retail trade 30 30 Eating and drinking establishments 31 31 Finance 32 32 Insurance 33 33 Real estate 34 34 Lodging and amusements 35 35 Personal services 36 36 Business services 37 37 Health services 38 38 Other services 590100-590302 371 600100-610700, 130100,130300 372-9.2451 620100-630300 38 (excl. 3825) 640101-641200 39 (excl. 39996) 650100-650700, 780100,790100 40-7 660000,67000 48 680100-680300, 780200,790200 491-7 690100 50,51 (excl. manufacturers' sales offices) 690200 52-7,59,7396, 8042 740000 58, pt. 70 700100-700300 60,62 (excl. 613), 67 700400,700500 63,64 710200 65-6, pt. 1531 720100,760100, 760200 70 (excl. dining) 78,79 720200,720300 72-4 (excl. 7396), 762-4, pt. 7699 730100-730300 73 (excl. 7396), 7692,7694, pt. 7699 81,89 (excl. 8922) 770100-770300 801-3,8041 074,8049,805-9 750000,770400- 770900 75,82-86,8922 074,8049,805-9 -125- Table CI. 1.- Indus try Designations for LPW Impact Application — Continued Industry number Column Row Industry name 19 72 1-0 code 19 72 SIC 39 40 41 39 6 42 6 43 6 44 6 45 6 46 6 47 6 48 6 49 6 50 6 51 6 52 6 53 6 54 6 55 6 56 6 57 6 58 6 59 6 60 6 Households 840000 New residential 1-unit structures, 110101 nonfarm New residential 2-4 unit structures, nonfarm 110102 New residential garden apartments 110103 New residential high-rise apartments 110104 New residential additions and alterations, nonfarm 110105 New hotels and motels 110106 New dormitories 110107 New industrial buildings 110201 New office buildings 110202 New warehouses 110203 New garages and service stations 110204 New stores and restaurants 110205 New religious buildings 110206 New educational buildings 110207 New hospital and institutional 110208 buildings New other nonfarm buildings 110209 New telephone and telegraph 110301 facilities New railroads 110302 New electric utility facilities 110303 New gas utility facilities 110304 New petroleum pipelines 110305 -126- pt. 15, pt. 17 pt. : L5, pt. 17 pt. ] 15-17 pt. : L5-17 P t. : .5. pt. 17 P t. : L5-17 P t. : .5, pt. 17 pt. ] L5-17 pt. '. L5, pt. 17 pt. : L5, pt. 17 pt. : L5, pt. 17 pt. ] L5, pt. 17 pt. ; L5, pt. 17 pt. ] L5, pt. 17 pt. '. L5, pt. 17 P t. ] L5, pt. 17 pt. ; .6, pt. 17 pt. 3 16, pt. 17 P t. ] 16, pt. 17 P t. i 16, pt. 17 pt. i 16, pt. 17 Table CI. 1. -Industry Designations for LPW Impact Application — Continued Industry number Column Row 61 6 62 6 63 6 64 6 65 6 66 6 67 6 Industry name 19 72 1-0 code 19 72 SIC 68 69 6 70 6 71 6 72 6 73 7 74 7 75 7 76 7 77 7 78 7 79 7 New water supply facilities New sewer system facilities New local transit facilities New highways and streets New farm housing units and additions New farm service facilities New petroleum and natural gas well drilling New petroleum, natural gas, and solid mineral exploration New military facilities New conservation and development facilities Other new nonbuilding facilities New access structures for solid mineral development Maintenance and repair, residential Maintenance and repair of other nonfarm buildings Maintenance and repair of farm residential buildings Maintenance and repair of farm service facilities Maintenance and repair of telephone and telegraph facilities Maintenance and repair of railroads Maintenance and repair of electric util ity faci 1 ities 110306 pt. 16, pt. 17 110307 pt. 16, pt. 17 110308 pt. 16, pt. 17 110400 pt. 16, pt. 17 110501 pt. 15, pt. 17 110502 pt. 15, pt. 17 110503 pt. 138 110504 pt. 138 1213, pt. pt. 148 138, 110505 pt. 15- 17 110506 pt. 15- 17 110507 pt. 15- 17 110508 pt. 108 1213, , pt pt. . 112, pt 148 120100 pt. 15, pt. 17 120201 pt. 15, pt. 17 120202 pt. 15, pt. 17 120203 pt. 15, pt. 17 120204 pt. 16, pt. 17 120205 pt. 16, pt. 17 120205 pt. 16, pt. 17 ■127- Table CI. 1. -Industry Designations for LPW Impact Application—Continued Industry number Column Row Industry name 19 72 1-0 code 19 72 SIC 80 81 82 83 84 85 86 7 7 89 Maintenance and repair of gas uti 1 ity facil ities Maintenance and repair of petroleum pipelines Maintenance and repair of water supply f aci lities Maintenance and repair of sewer f aci 1 ities Maintenance and repair of local transit facilities Maintenance and repair of military faci 1 ities Maintenance and repair of conservation and development facilities Maintenance and repair of highways and streets Maintenance and repair of petroleum and natural gas wells Maintenance and repair of other nonbuilding facilities 120207 pt. 16, pt. 17 120208 pt. 16, pt. 17 120209 pt. 16, pt. 17 120210 pt. 16, pt. 17 120211 pt. 16, pt. 17 120212 pt. 16, pt. 17 120213 pt. 15-17 120214 pt. 16, pt. 17 120215 pt. 138 120216 pt. 15-17 128- Table C2.1.-RIMS II Multipliers— New Warehouses (49) Industry United States Denver, Detroit, Wi lmington, Colorado Michigan North Carolina 1 Agriculture 0.078 0.006 0.005 0.007 2 Forestry and fisheries .003 .001 3 Coal mining .007 .001 4 Petroleum and natural gas .026 .005 5 Other mining .021 .009 .003 .010 6 New construction 1.000 1.000 1.000 1.000 7 Maintenance and repair .035 .018 .018 .013 8 Food and kindred products .132 .050 .034 .009 9 Textiles .030 .001 .007 10 Apparel .028 .004 .002 .013 11 Paper .035 .004 .002 .001 12 Printing .035 .019 .009 .004 13 Chemicals .135 .040 .044 .010 14 Rubber and leather products .035 .005 .015 15 Lumber and furniture .039 .010 .005 .005 16 Stone, clay, and glass .080 .055 .031 .034 17 Primary metals .147 .004 .084 .002 18 Fabricated metals .234 .157 .169 .045 19 Nonelectrical machinery .046 .008 .015 .001 20 Electrical machinery .055 .005 .006 .001 21 Motor vehicles .044 .032 22 Other transportation equipment .008 .002 .001 23 Instruments .011 .003 .001 24 Miscellaneous .012 .003 .003 25 Transportation .129 .077 .071 .066 26 Communication .042 .026 .020 .019 27 Utilities .067 .028 .037 .025 28 Wholesale trade .138 .088 .075 .054 29 Retail trade .142 .104 .096 .086 30 Eating and drinking establ ishments .061 .042 .035 .031 31 Finance .047 .031 .021 .013 32 Insurance .045 .030 .029 .009 33 Real estate .115 .070 .043 .050 34 Lodging and amusements .024 .015 .010 .008 35 Personal services .024 .015 .015 .006 36 Business services .143 .112 .107 .063 37 Health services .052 .019 .036 .015 38 Other services .075 .047 .039 .026 39 Household 1.006 .704 .723 .540 Total 4.448 2.815 2.839 2.175 -129 Table C2.2.-RIMS II Multipliers— New Other Nonfarm Buildings (55) Industry United States Denver, Colorado Detroit, Michigan Wilimington, North Carolina 1 Agriculture 0.077 0.005 0.003 0.005 2 Forestry and fisheries .004 .001 3 Coal mining .007 .001 4 Petroleum and natural gas .021 .003 5 Other mining .019 .007 .002 .008 6 New construction 1.000 1.000 1.000 1.000 7 Maintenance and repair .034 .018 .017 .014 S Food and kindred products .133 .051 .034 .009 9 Texti les .034 .001 .007 10 Apparel .029 .004 .002 .012 11 Paper .036 .003 .002 .001 12 Printing .034 .018 .009 .004 13 Chemical s .104 .020 .023 .009 14 Rubber and leather products .038 .006 .017 15 Lumber and furniture .072 .026 .017 .006 16 Stone, clay, and glass .103 .073 .040 .044 17 Primary metals .128 .004 .068 .001 18 Fabricated metals .146 .087 .102 .002 19 Nonelectrical machinery .065 .017 .023 .001 20 Electrical machinery .065 .006 .008 .001 21 Motor vehicles .045 .032 22 Other transportation equipment .007 .002 .001 23 Instruments .014 .003 .001 24 Mi seel laneous .012 .003 .003 2 5 Transportation .119 .067 .059 .054 26 Communication .043 .027 .020 .019 27 Utilities .066 .027 .036 .026 28 Wholesale trade .139 .089 .075 .054 29 Retail trade .138 .100 .091 .082 30 Eating and drinking establ i shments .063 .042 .035 .031 31 Finance .048 .032 .022 .013 32 Insurance .045 .030 .028 .009 33 Real estate .117 .072 .044 .051 34 Lodging and amusements .025 .015 .010 .008 35 Personal services .024 .015 .015 .006 36 Business services .178 .147 .142 .085 37 Health services .052 .019 .035 .015 38 Other services .076 .047 .039 .026 39 Household 1.074 .710 .715 .538 Total 4.435 2.796 2.773 2.143 130- Table C2.3.-RIMS II Multipliers—New Sewer System Facilities (62) Industry Un" ted States Denver, Colorado Detroit, Michigan Wilmington, North, Carolina 1 Agriculture 0.071 0.006 0.004 0.008 2 Forestry and fisheries .002 .001 3 Coal mining .008 .001 4 Petroleum and natural gas .020 .003 5 Other mining .031 .015 .005 .017 6 New construction 1.000 1.000 1.000 1.000 7 Maintenance and repair .031 .016 .016 .014 8 Food and kindred products .117 .046 .030 .008 9 Textiles .027 .001 .007 10 Apparel .025 .004 .002 .011 11 Paper .031 .003 .002 .001 12 Printing .029 .015 .007 .003 13 Chemicals .094 .019 .022 .011 14 Rubber and leather products .031 .004 .013 15 Lumber and furniture .023 .003 .002 .003 16 Stone, clay, and glass .158 .114 .070 .086 17 Primary metals .186 .044 .133 .012 18 Fabricated metals .078 .043 .050 .002 19 Nonelectrical machinery .080 .045 .024 .001 20 Electrical machinery .041 .005 .006 .001 21 Motor vehicles .042 .030 22 Other transportation equipment .007 .002 .001 23 Instruments .011 .005 .003 24 Miscellaneous .011 .003 .003 25 Transportation .111 .063 .057 .053 26 Communication .037 .023 .017 .016 27 Utilities .063 .027 .035 .028 28 Wholesale trade .133 .090 .074 .056 29 Retail trade .113 .081 .072 .064 30 Eating and drinking establishments .054 .037 .030 .027 31 Finance .042 .028 .019 .012 32 Insurance .045 .031 .029 .010 33 Real estate .101 .061 .036 .043 34 Lodging and amusements .021 .013 .008 .007 35 Personal services .021 .014 .013 .005 36 Business services .106 .078 .073 .045 37 Health services .046 .018 .031 .014 38 Other services .070 .045 .037 .026 39 Household .9 53 .646 .633 .490 Total 4.069 2.650 2.587 2.082 -131- Table C2.4.-RIMS II Multipliers— New Highways and Streets (64) Industry United States Denver, Colorado Detroit, Michigan Wilmington, North Carolina 1 Agriculture 0.066 0.005 0.003 0.006 2 Forestry and fisheries .002 .001 3 Coal mining .006 .001 4 Petroleum and natural gas .032 .007 5 Other mining .056 .037 .014 .047 6 New construction 1.000 1.000 1.000 1.000 7 Maintenance and repair .031 .017 .016 .015 8 Food and kindred products .113 .046 .029 .008 9 Texti les .025 .007 10 Apparel .024 .004 .002 .012 11 Paper .031 .003 .002 .001 12 Printing .030 .015 .008 .004 13 Chemicals .169 .051 .060 .016 14 Rubber and leather products .027 .003 .010 15 Lumber and furniture .023 .002 .001 .003 16 Stone, clay, and glass .148 .135 .075 .104 17 Primary metals .077 .002 .045 .001 18 Fabricated metals .093 .059 .070 .001 19 Nonelectrical machinery .025 .004 .007 .001 20 Electrical machinery .032 .002 .002 .001 21 Motor vehicles .038 .028 22 Other transportation equipment .006 .001 .001 23 Instruments .006 .002 24 Mi seel laneous .015 .007 .007 2 5 Transportation .128 .083 .072 .077 26 Communication .035 .022 .016 .016 27 Utilities .061 .027 .032 .031 28 Wholesale trade .133 .096 .078 .063 2*9 Retail trade .116 .087 .077 .073 30 Eating and drinking establ ishments .050 .035 .028 .026 31 Finance .039 .027 .017 .012 32 Insurance .041 .029 .027 .009 33 Real estate .099 .061 .034 .044 34 Lodging and amusements .020 .013 .008 .008 35 Personal services .020 .013 .013 .005 36 Business services .102 .076 .070 .044 37 Health services .044 .018 .031 .015 38 Other services .068 .046 .037 .028 39 Household .918 .644 .619 .514 Tot al 3.950 2.680 2.539 2.195 •132- Table C2.5.-RIMS II Multipliers — New Construction and Development Facilities (70) Industry United States Denver, Detroit, Wi lmington, Colorado Michigan North Carolina 1 Agriculture 0.068 0.005 0.003 0.006 2 Forestry and fisheries .002 .001 3 Coal mining .006 .001 4 Petroleum and natural gas .025 .004 5 Other mining .026 .014 .005 .018 6 New construction 1.000 1.000 1.000 1.000 7 Maintenance and repair .029 .016 .015 .013 8 Food and kindred products .119 .049 .032 .010 9 Textiles .026 .008 10 Apparel .026 .004 .002 .014 11 Paper .027 .002 .002 .001 12 Printing .029 .015 .007 .004 13 Chemicals .124 .026 .026 .010 14 Rubber and leather products .032 .005 .013 15 Lumber and furniture .029 .006 .001 .010 16 Stone, clay, and glass .050 .036 .025 .029 17 Primary metals .095 .002 .046 .001 18 Fabricated metals .098 .060 .068 .025 19 Nonelectrical machinery .029 .004 .009 .001 20 Electrical machinery .033 .002 .003 .001 21 Motor vehicles .041 .032 22 Other transportation equipment .006 .001 .001 23 Instruments .008 .004 .002 24 Miscellaneous .010 .003 .003 25 Transportation .099 .056 .050 .052 26 Communication .034 .022 .016 .017 27 Utilities .056 .024 .032 .025 28 Wholesale trade .119 .080 .067 .054 29 Retail trade .116 .088 .080 .076 30 Eating and drinking establ ishments .052 .036 .030 .029 31 Finance .039 .027 .018 .012 32 Insurance .042 .029 .028 .010 33 Real estate .096 .059 .036 .045 34 Lodging and amusements .021 .013 .009 .008 35 Personal services .021 .014 .014 .006 36 Business services .117 .092 .087 .056 37 Health services .047 .019 .035 .017 38 Other services .072 .049 .042 .031 39 Household .9 77 .700 .702 .59 2 Total 3.843 2.567 2.540 2.183 -133- Table C2.6.-RIMS II Multipliers — Maintenance and Repair, Residential (73) Industry United States Denver, Colorado Detroit, Michigan Wilmington, North Carolina 1 Agriculture 0.068 0.004 0.003 0.005 : Forestry and fisheries .003 .001 3 Coal mining .005 .001 4 Petroleum and natural gas .033 .008 5 Other mining .007 .001 .001 .001 6 New construction 7 Maintenance and repair 1.030 1.016 1.015 1.011 8 Food and kindred products .119 .047 .031 .009 9 Textiles .032 .001 .007 10 Apparel .027 .006 .003 .012 11 Paper .036 .004 .003 .001 12 Printing .032 .015 .008 .004 13 Chemicals .183 .082 .083 .008 14 Rubber and leather products .036 .007 .017 15 Lumber and furniture .049 .016 .005 .005 16 Stone, clay, and glass .031 .011 .010 .004 17 Primary metals .062 .001 .022 18 Fabricated metals .063 .029 .032 .001 19 Nonelectrical machinery .067 .013 .016 .001 20 Electrical machinery .059 .003 .004 .001 21 Motor vehicles .040 .028 22 Other transportation equipment .006 .001 .001 23 Instruments .011 .002 .001 24 Miscel laneous .019 .003 .004 25 Transportation .101 .057 .051 .048 26 Communication .037 .023 .017 .017 11 Utilities .057 .025 .031 .021 28 Wholesale trade .134 .092 .076 .060 29 Retai 1 trade .166 .135 .121 .121 30 Eating and drinking establ ishments .054 .037 .030 .028 31 Finance .041 .027 .018 .011 32 Insurance .042 .029 .027 .009 33 Real estate .102 .062 .037 .045 34 Lodging and amusements .021 .013 .008 .007 35 Personal services .021 .014 .013 .006 36 Business services .068 .040 .036 .019 37 Health services .047 .018 .032 .015 38 Other services .067 .043 .035 .025 39 Household .9 65 .661 .649 .531 Total 3.942 2.545 2.470 2.036 134- Table C2.7.-RIMS II Multipliers—Maintenance and Repair of Other Nonfarm Buildings (74) Industry United States Denver, Colorado Detroit, Michigan Wi lmington, North Carolina 1 Agriculture 0.073 0.005 0.003 0.005 2 Forestry and fisheries .002 .001 3 Coal mining .005 .001 4 Petroleum and natural gas .026 .005 5 Other mining .009 .001 .001 .001 6 New construction 7 Maintenance and repair 1.032 1.017 1.016 1.014 8 Food and kindred products .128 .051 .034 .010 9 Textiles .030 .001 .008 10 Apparel .027 .004 .002 .014 11 Paper .031 .003 .002 .001 12 Printing .032 .015 .008 .004 13 Chemicals .136 .042 .045 .008 14 Rubber and leather products .036 .005 .016 15 Lumber and furniture .039 .004 .002 .005 16 Stone, clay, and glass .065 .014 .018 .010 17 Primary metals .065 .001 .023 18 Fabricated metals .061 .026 .028 .002 19 Nonelectrical machinery .063 .011 .013 .001 20 Electrical machinery .070 .006 .006 .001 21 Motor vehicles .043 .031 22 Other transportation equipment .006 .001 .001 23 Instruments .011 .003 .001 24 Miscellaneous .012 .003 .003 25 Transportation .107 .059 .054 .054 26 Communication .041 .027 .020 .021 27 Utilities .060 .026 .032 .024 28 Wholesale trade .128 .084 .070 .056 29 Retail trade .145 .111 .100 .099 30 Eating and drinking establishments .062 .044 .036 .036 31 Finance .047 .032 .022 .014 32 Insurance .046 .032 .030 .011 33 Real estate .112 .070 .043 .056 34 Lodging and amusements .023 .014 .009 .009 35 Personal services .023 .015 .014 .006 36 Business services .077 .048 .044 .025 37 Health services .050 .019 .034 .017 38 Other services .075 .049 .040 .030 39 Household 1.028 .702 .698 .59 Total 4.025 2.548 2.502 2.137 ■135- Table C2.8.-RIMS II Multipliers — Maintenance and Repair of Highways and Streets (87) Industry United States Denver, Colorado Detroit, Michigan Wilmington, North Carolina : Agriculture 0.073 0.005 0.003 0.006 : Forestry and fisheries .002 .001 3 Coal mining .005 .001 4 Petroleum and natural gas .031 .007 5 Other mining .066 .046 .018 .059 6 New construction 7 Maintenance and repair 1.032 1.019 1.017 1.015 8 Food and kindred products .127 .055 .036 .011 9 Texti les .029 .001 .009 10 Apparel .027 .005 .002 .016 11 Paper .027 .003 .002 .001 12 Printing .030 .015 .008 .004 13 Chemicals .166 .050 .064 .015 14 Rubber and leather products .031 .005 .014 15 Lumber and furniture .031 .003 .001 .004 16 Stone, clay, and glass .039 .029 .018 .020 17 Primary metals .045 .001 .020 18 Fabricated metals .058 .035 .040 .002 19 Nonelectrical machinery .021 .003 .005 .001 20 Electrical machinery .023 .002 .001 .001 21 Motor vehicles .042 .033 .001 22 Other transportation equipment .006 .001 .001 23 Instruments .006 .002 24 Miscel laneous .012 .004 .004 2 5 Transportation .126 .085 .078 .083 26 Communication .037 .025 .019 .020 27 Utilities .059 .029 .035 .029 28 Wholesale trade .108 .073 .060 .048 S Retail trade .124 .098 .087 .086 30 Eating and drinking establ ishments .057 .043 .035 .036 31 Finance .044 .032 .021 .015 32 Insurance .043 .031 .029 .011 33 Real estate .107 .070 .042 .056 34 Lodging and amusements .022 .015 .010 .009 35 Personal services .022 .016 .016 .007 36 Business services .076 .052 .047 .030 37 Health services .050 .021 .038 .019 38 Other services .072 .051 .041 .032 39 Household 1.040 .781 .769 .676 Tot al 3.920 2.710 2.615 2.325 -136- Table C3.1. -Gross Output and Earnings Impacts of Denver LPW Expenditures by Industry and Construction Type (Thousands of 19 72 dollars) , Gross output impacts by Total imp acts cons truction type Industry Warehouses Sewers Parks Gross output Earnings (49) (62) (64) 1 Agriculture 1 15 1 17 4 2 Forestry and fisheries 3 Coal mining 2 2 1 4 Petroleum and natural gas mining 1 7 1 9 1 5 Other mining 2 34 2 38 9 6 New construction 213 2,359 132 2,704 868 7 Maintenance and repair 4 39 2 45 20 8 Food and kindred products 11 109 6 126 18 9 Textiles 1 1 10 Apparel 1 9 1 11 3 11 Paper 1 7 8 2 12 Printing and publishing 4 34 2 40 14 13 Chemicals 9 45 3 57 11 14 Rubber and leather 1 10 1 12 4 15 Lumber and furniture 2 7 1 10 3 16 Stone, clay, and glass 12 268 5 285 85 17 Primary metals 1 103 104 36 18 Fabricated metals 33 103 8 144 35 19 Nonelectrical machinery 2 105 1 108 37 20 Electrical machinery 1 11 12 5 21 Motor vehicles 22 Other transportation equipment 1 1 23 Instruments 1 11 12 4 24 Miscellaneous manufacturing 1 7 8 2 25 Transportation 16 149 7 172 70 26 Communication 6 55 3 64 20 27 Utilities 6 63 3 72 9 28 Wholesale trade 19 211 11 241 100 29 Retail trade 22 191 12 225 103 30 Eating and drinking establ ishments 9 88 5 102 35 31 Finance 7 66 4 77 24 32 Insurance 6 74 4 84 36 33 Real estate 15 144 8 167 8 34 Lodging and amusement 3 31 2 36 12 35 Personal services 3 32 2 37 18 36 Business services 24 185 12 221 93 37 Health services 4 41 3 48 18 38 Other services 10 107 6 123 51 39 Household 150 1,525 92 1,767 8 Total* 451 4,724 248 5,423 1,767 *Gross output totals exclude earnings impacts to avoid double counting; see equation 4.12. -137- Table C3. 2. -Gross Output and Earnings Impacts of Detroit LPW Expenditures by Industry and Construction Type (Thousands of 19 72 dollars) Gross cons Dutput impacts by truction type Total impacts M & R Industry Other Duildings (55) ' Streets and highways (64) M & R residents (73) M & R bui lding (74) ' streets and Gross s highways output (87) Earnings 1 Agriculture 18 8 1 4 4 35 7 : Forestry and fisheries 3 Coal mining - Petroleum and natural gas 1 1 5 Other mining 13 34 1 21 69 21 6 New construction 5,218 2,462 7,680 2,611 7 Maintenance and repair 89 39 523 1,175 1,183 3,009 1,335 8 Food and kindred products 177 72 16 39 42 346 50 9 Texti les 3 1 1 2 1 8 2 10 Apparel 9 4 2 2 2 19 5 11 Paper 12 5 1 2 2 22 6 12 Pri nting 45 19 4 9 9 86 35 13 Chemicals 120 147 43 53 74 437 82 1- Rubber and leather products 87 24 9 19 16 155 40 15 Lumber and furniture 91 3 3 2 1 100 29 16 Stone, clay, and glass 208 184 5 20 21 438 130 17 Primary metals 356 111 11 26 24 528 140 18 Fabricated metals 533 172 17 33 46 801 251 19 Nonelectrical machinery 119 16 8 15 6 164 62 20 Electrical machinery 43 5 2 7 1 58 19 21 Motor vehicles 166 68 15 36 38 323 44 22 Other transportation equipment 7 3 1 2 2 15 6 2 3 Instruments 7 1 1 1 10 4 24 Miscel laneous 16 18 2 4 5 45 14 25 Transportation 307 178 26 62 91 664 302 26 Communication 106 39 9 23 22 199 64 27 Utilities 187 80 16 38 40 361 46 28 Wholesale trade 390 19 2 39 81 69 771 325 29 Retail trade 478 189 62 116 102 947 438 30 Eating and drinking establ ishments 184 69 15 42 41 351 121 31 Finance 113 42 9 25 25 214 67 32 Insurance 147 66 14 35 34 296 130 Real estate 229 85 19 50 48 431 22 34 Lodging and amusement 52 20 4 10 11 97 33 35 Personal services 78 32 7 17 18 151 73 36 Business services 741 172 19 51 54 1,037 456 37 Health services 184 75 17 40 44 360 137 38 Other services 204 91 18 47 48 408 156 39 Household 3,728 1,525 334 807 89 4 7,288 25 Total* 10,737 4,726 939 2,089 2,145 20,636 7,288 *Gross output totals exclude earnings impacts to avoid double counting; see equation 4.12, -138- Table C3. 3. -Gross Output and Earnings Impacts of Wilmington LPW Expenditures by Industry and Construction Type (Thousands of 19 72 dollars) Industry Gross output impacts by construction type Total impacts M & R streets and highways -,.-..- ~..*~ + /o 7 v 3 J Gross output Earnings 1 Agriculture 4 2 Forestry and fisheries 1 3 Coal mining 4 Petroleum and natural gas 5 Other mining 42 6 New construction 7 Maintenance and repair 726 8 Food and kindred products 8 9 Textiles 7 10 Apparel 11 11 Paper 1 12 Printing 3 13 Chemicals 11 14 Rubber and leather products 15 Lumber and furniture 3 16 Stone, clay, and glass 14 17 Primary metals 18 Fabricated metals 2 19 Nonelectrical machinery 20 Electrical machinery 21 Motor vehicles 22 Other transportation equipment 1 23 Instruments 24 Miscellaneous 25 Transportation 59 26 Communication 14 27 Utilities 21 28 Wholesale trade 34 29 Retail trade 62 30 Eating and drinking establishments 26 31 Finance 11 32 Insurance 8 33 Real estate 40 34 Lodging and amusement 7 35 Personal services 5 36 Business services 21 37 Health services 14 38 Other services 23 39 Household 483 Total* 696 4 1 42 726 8 7 11 1 3 11 3 14 2 1 59 14 21 34 62 26 11 8 40 7 5 21 14 23 483 696 2 13 340 2 2 3 2 2 1 3 21 5 3 14 27 8 3 3 2 2 2 9 4 8 2 483 *Gross output total excludes earnings impacts to avoid double counting; see equation 4.12, -139- Bureau of Economic Analysis' Regional Programs and Services Personal Income by State, Metropolitan Area, and County Analysis: Robert Bretzfelder (202) 523-0948 Data: David Cartwright (202) 523-0966 Projections of State and Local-Area Economies Eugene Janisch (202) 523-0958 Lyle Spatz (202) 523-0950 Local-Area Input-Output Modeling System--RIMS II Richard Beemiller (202) 523-0514 Joseph Cartwright (202) 523-0594 National-Regional Econometric Modeling Systems--NRIES John Kort (202) 523-0591 Work Force Characteristics and Migration for States and Local Areas Bruce Levine (202) 523-0938 Regional Economic Accounts Edward Trott, Jr. (202) 523-09 73 Regional Economic Analysis Division Bureau of Economic Analysis U.S. Department of Commerce Washington, D.C. 20230 1>U.S. GOVERNMENT PRINTING OFFICE: 1 98 1 - 3 4 O " 9 9 7 / 1 6 1 O I AoaooiHS^im