C 3.<PP^ 
 
 by 
 
 Charles Nelson 
 
 and 
 
 Leon Litow 
 
 PENNSYLVANIA STATE 
 UNIVERSITY 
 
 APR2 11992 
 
 DOCUMENTS COLLECTION 
 U.S Depository Copy 
 
 CURRENT POPULATION REPORTS 
 Technical Paper 61 
 
 TP-61 
 
 Estimates of Median 
 
 Four-Person Family 
 
 Income, by State: 
 
 1974-89 
 
 ^ 
 
 & 
 
 :4 
 
 U.S. Department of Commerce 
 
 Economics and Statistics Administration 
 
 BUREAU OF THE CENSUS 
 
Acknowledgments 
 
 This report was prepared by Charles Nelson, Assistant Division Chief (Economic 
 Characteristics), Housing and Household Economic Statistics Division, and Leon 
 Litow, Division of Energy Assistance, Office of Community Services, Administration for 
 Children and Families, Department of Health and Human Services. 
 
 The model for estimating State median incomes was developed by Robert Fay, 
 Senior Mathematical Statistician, Office of the Director. Helen Ogle and Rose Mary 
 Schade provided statistical assistance. Shirley Smith and Deborah Largent provided 
 word processing assistance. 
 
 Data collection was conducted by Bureau of the Census field representatives, under 
 the overall direction of Joseph S. Harris, Chief, Field Division. 
 
 The staff of Administrative and Publication Services Division, Walter C. Odom, 
 Chief, provided publication planning, editorial review, design, composition, and printing 
 planning and procurement. 
 
 For further information on the Low Income Home Energy Assistance Program 
 (LIHEAP) and its eligibility requirements, contact Leon Litow, 202-401-5304. 
 
 For further information on the four-person family income estimates methodology, 
 contact Charles Nelson, 301-763-8029. 
 
 
 #• 
 
CURRENT POPULATION REPORTS 
 
 Technical Paper 61 
 
 TP-61 
 Issued January 1992 
 
 by 
 
 Charles Nelson 
 
 and 
 
 Leon Litow 
 
 Estimates of Median 
 
 Four-Person Family 
 
 Income, by State: 
 
 1974-89 
 
 4 
 
 / w *< 
 
 
 U.S. Department of Commerce 
 
 Robert A. Mosbacher, Secretary 
 
 Rockwell A. Schnabel, Deputy Secretary 
 
 Economics and Statistics Administration 
 
 BUREAU OF THE CENSUS 
 Barbara Everitt Bryant, Director 
 
0p2S*&. 
 
 ****££#** 
 
 Economics and Statistics 
 
 Administration 
 Michael R. Darby, Under Secretary 
 
 for Economic Affairs and Administrator 
 
 BUREAU OF THE CENSUS 
 
 Barbara Everitt Bryant, Director 
 C.L. Kincannon, Deputy Director 
 
 William P. Butz, Associate Director 
 for Demographic Programs 
 
 HOUSING AND HOUSEHOLD 
 ECONOMIC STATISTICS DIVISION 
 Daniel H. Weinberg, Chief 
 
 SUGGESTED CITATION 
 
 U.S. Bureau of the Census, Current Population Reports, Technical Paper No. 61. 
 Estimates of Median Four-Person Family Income, by State: 1974-89. 
 U.S. Government Printing Office, Washington, DC, 1991. 
 
 For sale by Superintendent of Documents, U.S. Government Printing Office, Washington, DC 20402. 
 
Ill 
 
 Contents 
 
 Page 
 
 Introduction 1 
 
 Methodology 2 
 
 Estimation Models 2 
 
 Time Frame 3 
 
 Household and Family Income Measures 3 
 
 TABLE 
 
 1 . Median Income for Four-Person Families, by State and Year 5 
 
 APPENDIXES 
 
 A. Definitions, Explanations, and Comparability of Data A-1 
 
 B. Multivariate Components of Variance Models as Empirical Bayes Procedures for 
 
 Small Domain Estimation B-1 
 
 APPENDIX TABLES 
 
 B-1 . Comparison of 1 979 Estimates of Median Income of Four-Person Familes B-7 
 
 B-2. Estimates of Median Income of Four-Person Families, Using Projected Census 
 
 Components of Variance B-8 
 
 B-3. Estimates of Median Income of Four-Person Families, Using Estimated 
 
 Components of Variance From CPS B-9 
 
 B-4. Comparison of Projected Components and MLE's, by Year B-1 
 
Digitized by the Internet Archive 
 
 in 2012 with funding from 
 
 LYRASIS Members and Sloan Foundation 
 
 http://archive.org/details/estimatesofmediaOOnels 
 
Estimates of Median Four-Person Family Income, 
 by State: 1974-89 
 
 INTRODUCTION 
 
 The Low Income Home Energy Assistance Program 
 (LIHEAP) is one of six block grant programs authorized 
 by the Omnibus Budget Reconciliation Act of 1981 
 (Public Law 97-35) and administered within the Depart- 
 ment of Health and Human Services (HHS). LIHEAP is 
 administered by the Division of Energy Assistance, 
 Office of Community Services within HHS' Administra- 
 tion for Children and Families. The Augustus F. Hawkins 
 Human Services Reauthorization Act of 1990 (Public 
 Law 101-501) reauthorized LIHEAP through fiscal year 
 (FY) 1994. 
 
 States and the District of Columbia, Indian tribes and 
 tribal organizations, and territories that wish to assist 
 low-income households in meeting the costs of home 
 energy may apply for a LIHEAP block grant. "Home 
 energy" is defined by the LIHEAP statute as "a source 
 of heating or cooling in residential dwellings." 
 
 Section 2605(b)(2)(B)(ii) of Title XXVI of the Omnibus 
 Budget Reconciliation Act of 1981 provides that 60 
 percent of the median income for each State, as 
 annually established by the Secretary of Health and 
 Human Services, is one of the income criteria that 
 States can use in determining a household's eligibility 
 for LIHEAP. 
 
 Under the provisions of section 2603(7) of the stat- 
 ute, HHS publishes each year in the Federal Register an 
 announcement of the estimated median income of a 
 four-person family for each State and the District of 
 Columbia in advance of the Federal FY that begins on 
 October 1 and ends on September 30. 
 
 Prior to the FY 1 983 State median income estimates, 
 the Bureau of the Census developed State median 
 income estimates for use in the former Title XX Pro- 
 grams of the Social Security Act which was adminis- 
 tered by the HHS Office of Human Development Ser- 
 vices. Since FY 1983, the Bureau of the Census has 
 developed the State median income estimates for use 
 in LIHEAP. Beginning with the FY 1984 estimates, HHS 
 has published State median income estimates as fol- 
 lows in the Federal Register. 
 
 FY 
 
 Vol. 
 
 No. 
 
 Date 
 
 Calendar year 
 of income 
 estimates 
 
 1984 
 
 48 
 
 222 
 
 11/16/83 
 
 
 1981 
 
 1985 
 
 49 
 
 236 
 
 12/06/84 
 
 
 1982 
 
 1986 
 
 50 
 
 232 
 
 12/03/85 
 
 
 1983 
 
 1987 
 
 51 
 
 213 
 
 11/04/86 
 
 
 1984 
 
 1988 
 
 52 
 
 160 
 
 08/19/87 
 
 
 1985 
 
 1989 
 
 53 
 
 64 
 
 04/04/88 
 
 
 1986 
 
 1990 
 
 54 
 
 50 
 
 03/16/89 
 
 
 1987 
 
 1991 
 
 55 
 
 71 
 
 04/12/90 
 
 
 1988 
 
 1992 
 
 56 
 
 46 
 
 03/08/91 
 
 
 1989 
 
 The method for adjusting median income for families 
 of different sizes is specified in 45 CFR 96.85(b), which 
 was published in the Federal Register on March 3, 
 1988, at 53 FR 6824. According to this method, each 
 State's estimated median income for a four-person 
 family is multiplied by the following percentages to 
 adjust for family size: 52 percent for one person, 68 
 percent for two persons, 84 percent for three persons, 
 100 percent for four persons, 116 percent for five 
 persons, and 132 percent for six persons. For family 
 sizes greater than six persons, 3 percent is added to 
 132 percent for each additional family member. 1 
 
 In addition to their use as an eligibility criterion, the 
 annual four-person family income estimates are impor- 
 tant to data users in general in that they represent the 
 only source of intercensal State-specific family income 
 estimates produced by the Census Bureau. As a result, 
 the estimates are widely used by analysts and research- 
 ers. However, since State family income estimates are 
 not published in a regular Census Bureau series, ana- 
 lysts often use these figures without a clear understand- 
 ing of their derivation. The purpose of this technical 
 paper is to (1) provide a brief overview of the method- 
 ology used to calculate State four-person family income 
 estimates and to summarize the ways in which the 
 calculation has changed over time; (2) describe how 
 these estimates are used for program purposes; and (3) 
 provide the entire set of estimates that are available at 
 this time — calendar years 1 974 to 1 989. 
 
 1 The adjustment of median income according to family size is 
 based on the same adjustment contained in 45 CFR 1396.60(d)(2) in 
 effect for the former Title XX program. These factors are shown in 
 appendix A of this report. 
 
METHODOLOGY 
 
 Data Sources 
 
 Estimates of four-person median family incomes by 
 State utilize the most recent data available from the 
 following three data sources: 
 
 • March Current Population Survey (CPS) from the 
 Bureau of the Census 
 
 • Decennial census of population from the Bureau of 
 the Census 
 
 • Per capita personal income estimates from the Bureau 
 of Economic Analysis (BEA) 
 
 CPS. The CPS is a monthly labor force survey of about 
 60,000 households across the country. Each March, the 
 monthly survey is supplemented with questions that ask 
 household respondents about their money income received 
 during the previous year. Survey results are published 
 annually by the Census Bureau. 2 
 
 The CPS utilizes a money income concept. Total 
 money income is the sum of the amounts received from: 
 wages and salaries, self-employment income (including 
 losses), Social Security, Supplemental Security Income 
 (SSI), cash public assistance, interest, dividends, rents, 
 royalties, estates and trusts, veterans' payments, unem- 
 ployment and workers' compensations, private and 
 government survivor, disability and retirement pensions, 
 alimony, child support, and any other source of money 
 income that is regularly received. Capital gains (or 
 losses) and lump-sums or one-time payments such as 
 life insurance settlements are excluded. Noncash ben- 
 efits are also excluded from the money income defini- 
 tion. Thus, the value of government noncash transfers 
 (food stamps, Medicaid, Medicare, public and subsi- 
 dized housing, etc.) and private sector in-kind benefits 
 (employer-subsidized health insurance, etc.) are excluded 
 from the CPS money income definition. The CPS pro- 
 vides sample survey estimates of median incomes for 
 four-person families annually at the national level. Though 
 CPS data may also be tabulated at the State level, the 
 sampling variability of State estimates from the CPS is 
 large enough to make their direct use inadvisable for 
 program purposes. 
 
 Decennial census. The decennial census provides income 
 values for calendar years 1969 and 1979 that utilize the 
 same money income concept as the annual CPS esti- 
 mates, with negligible sampling error at the State level. 
 
 BEA. The BEA produces a personal per capita income 
 series. The main difference between the BEA and CPS 
 income concepts is that BEA personal income relates to 
 income from all sources, while CPS income relates only 
 to money income. The BEA series is developed from a 
 variety of government statistics, the most important 
 being the Federal tax records of the Department of 
 Treasury, the insurance files of the Social Security 
 Administration, and State unemployment records col- 
 lected by the U.S. Department of Labor. Personal 
 income comprises wages and salaries (including cash 
 and in-kind payments), other labor income such as 
 employer contributions to private pensions, welfare, and 
 workers' compensation funds, self-employment income, 
 rental income, dividends and interest, and government 
 and business transfer payments (Social Security, food 
 stamps, corporate cash prizes, etc). Personal income is 
 equal to the sum of all of these items minus the amounts 
 paid by individuals for Social Security payroll taxes, 
 government retirement, and other social programs. 
 
 The BEA produces annual estimates of personal per 
 capita income based on this income concept for States 
 and other geographic areas. The estimates provide an 
 overall indication of relative incomes among States and 
 of change over time for particular States, even though 
 personal per capita income is only indirectly related to 
 median incomes of four-person families. 3 The BEA 
 estimates, though conceptually different from census 
 income data, are essentially free from sampling error. 
 
 ESTIMATION MODELS 
 
 Prior to 1984. Prior to 1984 the estimation procedure 
 consisted of five main steps: 
 
 1. State median family income estimates for four- 
 person families and respective standard errors were 
 directly calculated from CPS data. 
 
 2. Another set of State estimates of four-person family 
 income was developed by carrying forward census 
 median estimates using the percent change in 
 State BEA per capita personal income. 
 
 3. A regression estimate was then developed to pre- 
 dict the CPS estimates from the adjusted census 
 medians from the preceding step. 
 
 4. A composite estimate was formed as a weighted 
 average of the regression and CPS sample esti- 
 mates. 
 
 5. Finally, the composite estimate for each State was 
 constrained to a range which was equal to the CPS 
 estimate, plus or minus one standard error. 
 
 2 March 1990 CPS income estimates were published in a report 
 entitled, "Money Income and Poverty Status in the United States: 
 1989," Series P-60, No. 168. 
 
 3 For more details on the differences between the BEA and census 
 income concepts, see appendix A. 
 
1984 to present. The methodology as summarized 
 above was developed prior to the 1980 census. A 
 comparison of estimates from the model for income 
 year 1979 with comparable estimates from the 1980 
 census afforded an opportunity to assess the merits of 
 the estimation model. This comparison was the basis for 
 the modifications outlined below. The major impetus for 
 the revisions was the year-to-year variability of some of 
 the State estimates. As before, the revised methodol- 
 ogy employed sample estimates of four-person median 
 family income from the Current Population Survey. 
 Unlike the previous methodology, however, a second 
 sample estimate was considered for each State. This 
 second variable is a weighted average of estimated 
 State median incomes for three- and five-person fami- 
 lies. The weights, .75 for the medians of three-person 
 families and .25 for the medians of five-person families, 
 were selected on the basis of the approximate 3 to 1 
 ratio of the respective sample sizes. By introducing this 
 second variable into the estimation model, the amount 
 of sample information reflected in the estimate of four- 
 person medians for each State was roughly doubled. 
 
 Changes in the 1984-89 methodology are summa- 
 rized below 4 : 
 
 1. As in the earlier methodology, a regression equa- 
 tion was fitted to the CPS four-person estimated 
 medians. In the new equation however, two vari- 
 ables were used: 
 
 From the earlier methodology, 
 
 X 1 = (current BEA PCI/1979 BEA PCI)*census median 
 and 
 
 X 2 = unadjusted census median 
 
 It was found that the inclusion of the unadjusted 
 median improved the predictive power of the regres- 
 sion. The variable X., proportionally adjusted the 
 census median for changes in BEA per capita 
 income. The inclusion of X 2 permitted the adjust- 
 ment to be reduced in case of any "regression 
 toward the mean" which might arise if BEA per 
 capita income did not perfectly measure the propor- 
 tional changes in the income distribution. 
 
 2. In the revised model, a second regression equation 
 was simultaneously fitted to the weighted average 
 of three- and five-person medians. 
 
 4 Appendix B of this report contains a detailed explanation of the 
 revised four-person family income estimate methodology which pre- 
 viously appeared in Proceedings of the Survey Research Methods 
 Section, American Statistical Association, Washington, DC, 1986. 
 More recently, the problem was reviewed from a different technical 
 perspective by G. S. Datta, R. E. Fay, and M. Ghosh, "Hierarchical and 
 Empirical Bayes Analysis in Small Area Estimation," presented at the 
 1991 Annual Research Conference, U.S. Bureau of the Census, 
 Alexandria, Virginia, March 1991. 
 
 3. The composite estimate in the revised model uti- 
 lized both regression equations along with the CPS 
 sample estimates. 
 
 4. Since the revised methodology essentially doubled 
 the use of sample data in forming the composite 
 estimates, the standard error constraint of the 
 original equation model was eliminated. The com- 
 parison to the census results suggested that the 
 estimates were more accurate, on the average, 
 without the constraint. 
 
 TIME FRAME 
 
 In updating the State median income estimates annu- 
 ally, the Bureau of the Census uses the most recent 
 data available from its March CPS and BEA's per capita 
 income estimates. 5 However, the availability of such 
 data results in a 3-year difference between the time- 
 frame of the March CPS and BEA income data and the 
 fiscal year in which the estimates are in effect. For 
 example, the State median income estimates for FY 
 1992 were published in March 1991. The estimates are 
 based, in part, on 1989 family income from the March 
 1990 CPS which became available in August 1990 and 
 BEA's 1989 State per capita income estimates which 
 became available in September 1990. 
 
 Therefore, the State median income estimates do not 
 represent projected data for a fiscai year. Instead, the 
 estimates represent the most recent estimates available 
 for use in a fiscal year. 
 
 Table 1 can be used to identify State median income 
 estimates for a fiscal year by adding 3 to any calendar 
 year listed in the columns. For example, Alabama's 
 State median income for a four-person family in 1 989 
 was estimated to be $34,930. This is also the estimate 
 to be used for Alabama in FY 1992. 
 
 HHS publishes the updated estimates in the Federal 
 Register approximately 6 months before the beginning 
 of each fiscal year. This allows LIHEAP grantees suffi- 
 cient lead time in determining their income eligibility 
 levels for the upcoming fiscal year. 
 
 HOUSEHOLD AND FAMILY INCOME 
 MEASURES 
 
 Annual State median income estimates provided by 
 the Census Bureau for use in the Low Income Home 
 Energy Assistance Program are based on a family 
 income concept. A family consists of two or more 
 persons related by birth, marriage, or adoption who are 
 residing together. The Census Bureau also publishes 
 estimates of income based on a household income 
 concept. A household simply consists of all persons 
 
 5 lncome data from the 1990 Decennial Census for 1989 will be 
 available in 1 992 for updating and evaluating the State median income 
 estimates. 
 
who occupy a housing unit. Thus, a household may 
 consist of a family, several families residing together, a 
 person living alone, a group of unrelated persons living 
 together, or any combination of families and unrelated 
 persons. A major difference between households and 
 families is that persons residing alone are included in 
 the household universe and are excluded from the 
 family universe. Since persons living alone have, on 
 average, substantially lower incomes than families, their 
 inclusion in the household universe is a major reason for 
 the overall difference between median household and 
 family incomes. As shown in the following table, in 1989, 
 median family income ($34,213) for the United States 
 was 18 percent higher than median household income 
 ($28,906). 
 
 While the overall median incomes of households and 
 families are different, by size of unit they are quite 
 similar. As shown in the following table, there is no 
 
 statistically significant difference between the median 
 income of a four-person family and a four-person house- 
 hold. Thus, in the context of program eligibility, the use 
 of a household or family income concept is not a 
 tremendously important issue, as long as size of unit is 
 also used in the eligibility criteria. 
 
 Median Family and Household Income, by Size of 
 Unit: 1989 
 
 Size of unit 
 
 Total 
 
 1 person 
 
 2 persons 
 
 3 persons 
 
 4 persons 
 
 5 persons 
 
 6 persons 
 
 7 persons or more 
 
 Families 
 
 $34,213 
 (X) 
 28,834 
 35,963 
 40,763 
 39,077 
 35,801 
 32,259 
 
 Households 
 
 $28,906 
 14,829 
 29,862 
 36,277 
 40,744 
 39,281 
 35,305 
 32,643 
 
 X Not applicable. 
 
Table 1 . Median Income for Four-Person Families, by State and Year 
 
 Calendar year 1 
 Fiscal year 2 
 
 1989 
 1992 
 
 1988 
 1991 
 
 1987 
 1990 
 
 1986 
 1989 
 
 1985 
 1988 
 
 1984 
 1987 
 
 1983 
 1986 
 
 1982 
 1985 
 
 United States 
 
 Alabama 
 
 Alaska 
 
 Arizona 
 
 Arkansas 
 
 California 
 
 Colorado 
 
 Connecticut 
 
 Delaware 
 
 District of Columbia. 
 
 Florida 
 
 Georgia 
 
 Hawaii 
 
 Idaho 
 
 Illinois 
 
 Indiana 
 
 Iowa 
 
 Kansas 
 
 Kentucky 
 
 Louisiana 
 
 Maine 
 
 Maryland 
 
 Massachusetts 
 
 Michigan 
 
 Minnesota 
 
 Mississippi 
 
 Missouri 
 
 Montana 
 
 Nebraska 
 
 Nevada 
 
 New Hampshire 
 
 New Jersey 
 
 New Mexico 
 
 New York 
 
 North Carolina 
 
 North Dakota 
 
 Ohio 
 
 Oklahoma 
 
 Oregon 
 
 Pennsylvania 
 
 Rhode Island 
 
 South Carolina 
 
 South Dakota 
 
 Tennessee 
 
 Texas 
 
 Utah 
 
 Vermont 
 
 Virginia 
 
 Washington 
 
 West Virginia 
 
 Wisconsin 
 
 Wyoming 
 
 $40,763 
 34,930 
 48,411 
 38,347 
 31,853 
 42,813 
 40,265 
 53,313 
 42,790 
 40,574 
 37,399 
 40,019 
 44,988 
 33,633 
 42,609 
 38,201 
 36,736 
 37,938 
 34,390 
 34,406 
 38,336 
 50,145 
 51,799 
 42,825 
 42,365 
 32,300 
 38,478 
 33,882 
 37,902 
 39,737 
 47,983 
 53,229 
 31,156 
 43,693 
 38,068 
 34,806 
 41,469 
 34,470 
 38,723 
 40,404 
 43,278 
 36,113 
 32,829 
 34,882 
 34,978 
 36,562 
 40,397 
 45,090 
 41,728 
 31,811 
 40,557 
 35,620 
 
 $39,051 
 33,022 
 47,247 
 36,892 
 28,665 
 41,425 
 39,095 
 50,720 
 41,742 
 38,562 
 37,280 
 38,208 
 42,353 
 31,454 
 41,635 
 37,939 
 34,804 
 35,796 
 32,088 
 32,514 
 35,385 
 49,105 
 48,296 
 41,044 
 41,076 
 29,624 
 37,187 
 32,333 
 34,287 
 39,148 
 45,619 
 52,305 
 29,350 
 41 ,700 
 35,678 
 31,346 
 38,145 
 31,905 
 36,623 
 37,855 
 41,377 
 34,915 
 30,503 
 34,160 
 35,280 
 34,410 
 36,467 
 42,587 
 39,327 
 29,743 
 38,662 
 33,667 
 
 $36,812 
 31,221 
 47,106 
 35,711 
 27,415 
 40,218 
 37,778 
 47,195 
 39,794 
 36,523 
 35,247 
 35,529 
 40,878 
 29,701 
 39,891 
 35,016 
 34,094 
 34,474 
 30,257 
 31,964 
 31,957 
 46,384 
 44,329 
 40,105 
 39,775 
 27,416 
 35,437 
 31,015 
 32,969 
 37,810 
 40,833 
 47,846 
 27,675 
 38,992 
 33,253 
 31,152 
 36,344 
 30,772 
 34,555 
 35,638 
 37,814 
 32,417 
 29,142 
 31,916 
 35,656 
 32,980 
 33,983 
 39,913 
 38,308 
 28,71 1 
 36,674 
 33,692 
 
 $34,716 
 29,799 
 41,292 
 33,477 
 27,157 
 37,655 
 36,026 
 44,330 
 35,766 
 35,424 
 33,368 
 34,602 
 36,618 
 27,075 
 36,163 
 32,026 
 30,556 
 32,512 
 28,464 
 29,614 
 31,297 
 42,250 
 42,295 
 36,088 
 36,746 
 26,763 
 33,149 
 29,190 
 31,484 
 33,604 
 39,503 
 44,591 
 27,474 
 36,796 
 31,787 
 29,424 
 34,038 
 29,071 
 31,392 
 32,700 
 35,837 
 31,025 
 27,008 
 29,568 
 32,442 
 30,635 
 32,490 
 37,885 
 35,071 
 27,094 
 33,739 
 28,742 
 
 $32,777 
 28,407 
 42,897 
 32,129 
 26,255 
 36,223 
 35,214 
 40,677 
 34,104 
 32,610 
 31,364 
 31,907 
 34,636 
 27,383 
 34,374 
 31,369 
 29,425 
 31,114 
 27,307 
 29,910 
 28,537 
 40,055 
 39,079 
 33,908 
 34,376 
 25,716 
 31,414 
 27,999 
 30,655 
 32,314 
 35,702 
 40,800 
 27,127 
 34,478 
 30,290 
 28,993 
 33,478 
 29,050 
 30,741 
 32,265 
 34,154 
 29,417 
 26,153 
 27,917 
 32,189 
 29,634 
 30,019 
 35,353 
 32,791 
 26,170 
 32,007 
 30,741 
 
 $31,097 
 26,595 
 44,017 
 29,431 
 23,075 
 33,711 
 34,154 
 39,070 
 33,809 
 31,104 
 28,858 
 29,623 
 33,445 
 25,499 
 33,126 
 30,302 
 28,650 
 30,330 
 25,815 
 28,430 
 26,237 
 38,132 
 36,731 
 32,365 
 33,807 
 23,660 
 30,050 
 26,072 
 28,752 
 31,059 
 33,255 
 39,096 
 25,468 
 32,665 
 27,995 
 28,901 
 30,779 
 28,856 
 28,633 
 29,573 
 32,066 
 27,810 
 25,391 
 26,603 
 31,031 
 27,497 
 26,645 
 33,480 
 31,585 
 25,316 
 30,622 
 29,752 
 
 $29,184 
 25,117 
 38,238 
 27,551 
 21,524 
 31,967 
 32,294 
 37,703 
 31,676 
 28,701 
 25,455 
 27,463 
 31,614 
 24,009 
 30,736 
 26,924 
 25,800 
 27,569 
 24,096 
 27,953 
 24,178 
 35,475 
 33,990 
 29,472 
 30,785 
 21,957 
 27,789 
 25,278 
 26,100 
 34,504 
 30,414 
 36,448 
 23,906 
 30,539 
 25,363 
 26,327 
 28,305 
 27,169 
 26,404 
 28,274 
 29,167 
 25,756 
 23,998 
 24,081 
 29,290 
 25,678 
 25,441 
 31,451 
 30,185 
 22,153 
 28,979 
 28.480 
 
 $27,619 
 24,181 
 31,823 
 29,835 
 20,710 
 29,885 
 30,663 
 35,361 
 30,498 
 26,897 
 25,745 
 26,935 
 30,019 
 23,529 
 29,758 
 26,123 
 26,129 
 23,956 
 23,732 
 27,165 
 23,036 
 32,456 
 30,327 
 28,125 
 28,666 
 22,247 
 26,035 
 24,965 
 25,372 
 28,411 
 28,810 
 32,781 
 23,642 
 28,730 
 24,085 
 26,361 
 27,100 
 27,461 
 25,988 
 27,209 
 28,170 
 23,490 
 22,009 
 23,875 
 28,581 
 25,877 
 23,797 
 28,528 
 29,972 
 22,425 
 27,873 
 29,582 
 
 1 Refers to the calendar year for which estimates were calculated. See text for further details. 
 
 2 Refers to the fiscal year in which the estimates were in effect. See text for further details. 
 
 Note: 1969 data were published in the 1970 Census of Population and Housing reports. 1974-89 data were published in the Federal Register. 
 
Table 1 . Median Income for Four-Person Families, by State and Year— Continued 
 
 Calendar year 1 
 Fiscal year 2 
 
 1981 
 1984 
 
 1980 
 1983 
 
 1979 
 1982 
 
 1978 
 1981 
 
 1977 
 1980 
 
 1976 
 1979 
 
 1975 
 1978 
 
 1974 
 1977 
 
 1969 
 
 United States 
 
 Alabama 
 
 Alaska 
 
 Arizona 
 
 Arkansas 
 
 California 
 
 Colorado 
 
 Connecticut 
 
 Delaware 
 
 District of Columbia. 
 
 Florida 
 
 Georgia 
 
 Hawaii 
 
 Idaho 
 
 Illinois 
 
 Indiana 
 
 Iowa 
 
 Kansas 
 
 Kentucky 
 
 Louisiana 
 
 Maine 
 
 Maryland 
 
 Massachusetts 
 
 Michigan 
 
 Minnesota 
 
 Mississippi 
 
 Missouri 
 
 Montana 
 
 Nebraska 
 
 Nevada 
 
 New Hampshire 
 
 New Jersey 
 
 New Mexico 
 
 New York 
 
 North Carolina 
 
 North Dakota 
 
 Ohio 
 
 Oklahoma 
 
 Oregon 
 
 Pennsylvania 
 
 Rhode Island 
 
 South Carolina 
 
 South Dakota 
 
 Tennessee 
 
 Texas 
 
 Utah 
 
 Vermont 
 
 Virginia 
 
 Washington 
 
 West Virginia 
 
 Wisconsin 
 
 Wyoming 
 
 $26,274 
 22,443 
 35,834 
 25,163 
 20,583 
 27,763 
 28,756 
 31,108 
 27,174 
 28,312 
 23,504 
 25,131 
 29,295 
 22,821 
 29,403 
 24,832 
 26,678 
 24,842 
 22,409 
 26,144 
 22,201 
 30,019 
 28,839 
 27,976 
 29,261 
 22,509 
 25,339 
 24,953 
 24,835 
 28,829 
 25,332 
 30,793 
 21,488 
 26,030 
 23,625 
 25,364 
 26,851 
 24,701 
 24,516 
 26,519 
 25,625 
 22,060 
 21,708 
 22,336 
 26,492 
 24,171 
 23,551 
 28,850 
 28,254 
 22,842 
 27,232 
 27,553 
 
 $24,332 
 22,026 
 32,745 
 23,832 
 19,448 
 26,070 
 25,943 
 28,376 
 25,479 
 25,476 
 21,355 
 25,290 
 27,514 
 21,251 
 26,202 
 24,043 
 24,244 
 23,334 
 20,960 
 23,711 
 21,207 
 27,394 
 26,381 
 25,342 
 25,394 
 20,765 
 23,488 
 23,449 
 22,941 
 25,208 
 23,554 
 27,772 
 20,453 
 24,465 
 22,399 
 22,436 
 24,898 
 22,563 
 23,208 
 24,814 
 24,132 
 19,427 
 20,729 
 20,700 
 24,059 
 22,711 
 21,773 
 25,331 
 25,993 
 21 ,244 
 25,050 
 25,853 
 
 $22,395 
 18,613 
 31,037 
 23,000 
 18,493 
 25,109 
 25,228 
 24,410 
 21,184 
 21,310 
 20,757 
 21,578 
 24,582 
 20,429 
 24,265 
 22,614 
 22,567 
 22,848 
 19,138 
 20,166 
 18,074 
 24,686 
 23,786 
 24,422 
 24,409 
 17,672 
 21 ,294 
 20,051 
 20,749 
 25,457 
 22,335 
 24,640 
 21,032 
 21,082 
 19,648 
 19,520 
 22,528 
 20,852 
 24,031 
 22,314 
 21,636 
 20,154 
 19,209 
 19,437 
 23,416 
 21,250 
 19,314 
 22,976 
 24,410 
 18,876 
 23,518 
 22,673 
 
 $20,428 
 18,352 
 27,572 
 20,863 
 1 5,669 
 22,294 
 21,778 
 22,278 
 21,194 
 16,769 
 18,118 
 19,676 
 22,475 
 19,042 
 22,081 
 20,566 
 20,800 
 19,792 
 17,924 
 18,691 
 16,885 
 23,461 
 20,512 
 22,063 
 21,455 
 16,586 
 19,268 
 17,878 
 19,319 
 21,106 
 20,247 
 22,189 
 18,738 
 19,660 
 18,058 
 18,789 
 20,950 
 19,064 
 21,534 
 19,753 
 21,093 
 18,468 
 16,897 
 17,916 
 20,455 
 20,202 
 18,458 
 20,729 
 21,494 
 18,493 
 21,034 
 22,452 
 
 $18,723 
 16,629 
 32,119 
 19,101 
 15,068 
 20,858 
 20,181 
 20,469 
 18,245 
 19,047 
 17,874 
 16,835 
 21,718 
 16,601 
 20,243 
 19,131 
 18,441 
 18,379 
 16,264 
 16,511 
 15,025 
 21,193 
 19,508 
 20,908 
 20,715 
 14,635 
 17,862 
 16,389 
 16,523 
 20,308 
 18,190 
 21 ,409 
 16,801 
 18,216 
 16,252 
 16,008 
 19,195 
 17,144 
 19,771 
 18,348 
 17,910 
 16,573 
 15,733 
 15,677 
 18,930 
 18,250 
 16,381 
 19,244 
 20,207 
 16,793 
 20,109 
 20,755 
 
 $17,315 
 15,346 
 28,571 
 17,131 
 13,679 
 18,931 
 18,244 
 18,789 
 16,859 
 17,201 
 16,278 
 15,799 
 20,113 
 15,982 
 19,336 
 17,329 
 16,919 
 16,840 
 14,964 
 15,354 
 14,429 
 19,331 
 17,842 
 18,572 
 17,970 
 13,475 
 16,177 
 15,522 
 15,205 
 18,290 
 16,937 
 19,865 
 15,504 
 17,200 
 15,214 
 15,469 
 17,515 
 15,621 
 17,761 
 17,054 
 16,991 
 15,416 
 13,684 
 14,859 
 17,420 
 16,656 
 15,523 
 17,955 
 18,359 
 15,564 
 17,923 
 18,256 
 
 $15,848 
 14,018 
 25,638 
 15,829 
 12,969 
 17,393 
 16,928 
 17,781 
 16,243 
 16,554 
 15,303 
 14,538 
 18,825 
 14,664 
 17,793 
 15,731 
 16,536 
 15,709 
 13,625 
 13,992 
 12,948 
 18,132 
 16,546 
 16,919 
 16,871 
 12,174 
 14,996 
 14,900 
 15,381 
 16,945 
 14,954 
 17,984 
 13,954 
 16,105 
 13,883 
 15,321 
 15,848 
 14,436 
 16,349 
 15,753 
 15,691 
 13,879 
 13,351 
 13,646 
 15,802 
 15,352 
 14,294 
 16,348 
 16,818 
 14,064 
 16,593 
 16,818 
 
 $14,747 
 12,805 
 19,368 
 15,230 
 11,890 
 15,931 
 15,629 
 16,476 
 15,231 
 15,093 
 14,788 
 13,666 
 17,069 
 14,075 
 16,350 
 14,478 
 14,371 
 14,395 
 12,514 
 12,600 
 12,552 
 16,650 
 1 5,630 
 16,174 
 15,792 
 1 1 ,562 
 13,770 
 13,686 
 13,364 
 15,357 
 13,986 
 16,727 
 12,143 
 15,169 
 13,183 
 15,005 
 15,121 
 12,645 
 15,013 
 14,489 
 14,404 
 13,055 
 12,824 
 12,788 
 13,924 
 14,003 
 13,145 
 15,130 
 15,401 
 12,569 
 15,398 
 14,833 
 
 $10,782 
 
 8,825 
 
 13,048 
 
 10,543 
 
 7,951 
 
 11,918 
 
 10,612 
 
 12,668 
 
 11,166 
 
 10,302 
 
 9,990 
 
 9,650 
 
 12,411 
 
 9,323 
 
 11,912 
 
 10,941 
 
 10,173 
 
 9,941 
 
 8,712 
 
 8,874 
 
 8,964 
 
 1 1 ,988 
 
 11,683 
 
 11,955 
 
 1 1 ,029 
 
 7,825 
 
 10,277 
 
 9,337 
 
 9,651 
 
 11,565 
 
 10,647 
 
 12,456 
 
 8,934 
 
 1 1 ,654 
 
 9,104 
 
 8,736 
 
 11,185 
 
 9,219 
 
 10,638 
 
 10,514 
 
 10,721 
 
 8,939 
 
 8,582 
 
 8,781 
 
 9,998 
 
 9,910 
 
 9,746 
 
 10,256 
 
 1 1 ,392 
 
 8,514 
 
 11,025 
 
 9,966 
 
 1 Refers to the calendar year for which estimates were calculated. See text for further details. 
 
 2 Refers the the fiscal year in which the estimates were in effect. See text for further details. 
 
 Note: 1 969 data were published in the 1 970 Census of Population and Housing reports. 1 974-89 data were published in the Federal Register. 
 
A-1 
 
 Appendix A. 
 
 Definitions, Explanations, and Comparability of Data 
 
 DEFINITIONS AND EXPLANATIONS 
 
 Money income. The Census Bureau money income 
 concept consists of amounts received from the follow- 
 ing sources: (1) earnings from longest job (or self- 
 employment); (2) earnings from jobs other than longest 
 job; (3) unemployment compensation; (4) Social Secu- 
 rity; (5) Supplemental Security income; (6) public assis- 
 tance; (7) veterans' payments; (8) survivor benefits; (9) 
 disability benefits; (10) retirement pensions; (11) inter- 
 est; (12) dividends; (13) rents and royalties or estates 
 and trusts; (14) educational assistance; (15) alimony; 
 (16) child support; and (17) financial assistance from 
 outside of the household, and other periodic income. 
 
 It should be noted that although the income statistics 
 refer to receipts during the preceding calendar year, the 
 demographic characteristics such as age, labor force 
 status, and family or household composition are as of 
 the survey date. The income of the family/household 
 does not include amounts received by persons who 
 were members during all or part of the income year if 
 these persons no longer resided in the family/house- 
 hold at the time of interview. However, income data are 
 collected for persons who are current residents but did 
 not reside in the household during the income year. 
 
 Data on consumer income collected in the CPS by 
 the Bureau of the Census cover money income received 
 (exclusive of certain money receipts such as capital 
 gains) before payments for personal income taxes, 
 Social Security, union dues, Medicare deductions, etc. 
 Therefore, money income does not reflect the fact that 
 some families receive part of their income in the form of 
 noncash benefits such as food stamps, health benefits; 
 noncash benefits in the form of rent-free housing and 
 goods produced and consumed on the farm; or that 
 noncash benefits are also received by some nonfarm 
 residents which often take the form of the use of 
 business transportation and facilities, full or partial pay- 
 ments by business for retirement programs, medical 
 and educational expenses, etc. These elements should 
 be considered when comparing income levels. More- 
 over, data users should be aware that for many different 
 reasons there is a tendency in household surveys for 
 respondents to underreport their income. From an anal- 
 ysis of independently derived income estimates, it has 
 been determined that income earned from wages or 
 salaries is much better reported than other sources of 
 income and is nearly equal to independent estimates of 
 aggregate income. 
 
 The various sources for which income is reported are 
 defined as follows: 
 
 Longest job and other employment earnings can be 
 classified into the three types: 
 
 1 . Money wage or salary income is the total received 
 for work performed as an employee during the 
 income year. It includes wages, salary, Armed Forces 
 pay, commissions, tips, piece-rate payments, and 
 cash bonuses earned, before deductions were made 
 for taxes, bonds, pensions, union dues, etc. 
 
 2. Net income from nonfarm self-employment is the 
 net money income (gross receipts minus expenses) 
 from one's own business, professional enterprise, 
 or partnership. Gross receipts include the value of 
 all goods sold and services rendered. Expenses 
 include costs of goods purchased, rent, heat, light, 
 power, depreciation charges, wages and salaries 
 paid, business taxes (not personal income taxes), 
 etc. In general, inventory changes were considered 
 in determining net income; replies based on income 
 tax returns or other official records do reflect inven- 
 tory changes. However, when values of inventory 
 changes were not reported, net income figures 
 exclusive of inventory changes were accepted. The 
 value of saleable merchandise consumed by the 
 proprietors of retail stores is not included as part of 
 net income. 
 
 3. Net income from farm self-employment is the net 
 money income (gross receipts minus operating 
 expenses) from the operation of a farm by a person 
 on his own account, as an owner, renter, or share- 
 cropper. Gross receipts include the value of all 
 products sold, government farm programs, money 
 received from the rental of farm equipment to 
 others, rent received from farm property if payment 
 is made based on a percent of crops produced and 
 incidental receipts from the sale of wood, sand, 
 gravel, etc. Operating expenses include cost of 
 feed, fertilizer, seed, and other farming supplies; 
 cash wages paid to farmhands; depreciation charges; 
 cash rent; interest on farm mortgages; farm building 
 repairs; farm taxes (not State and Federal personal 
 income taxes), etc. The value of fuel, food, or other 
 farm products used for family living is not included 
 as part of net income. In general, inventory changes 
 were considered in determining net income only 
 
A-2 
 
 when they were accounted for in replies based on 
 income tax returns or other official records which 
 reflect inventory changes; otherwise, inventory changes 
 were not taken into account. 
 
 Unemployment compensation includes payments received 
 from government unemployment agencies or private 
 companies during periods of unemployment and any 
 strike benefits received from union funds. 
 
 Workers compensation includes payments received 
 periodically from public or private insurance companies 
 for injuries received at work. 
 
 Social Security includes Social Security pensions and 
 survivors' benefits, and permanent disability insurance 
 payments made by the Social Security Administration 
 prior to deductions for medical insurance. Medicare 
 reimbursements are not included. 
 
 Supplemental Security income includes payments 
 made by Federal, State, and local welfare agencies to 
 low-income persons who are (1 ) 65 years old or over, (2) 
 blind, or (3) disabled. 
 
 Public assistance or welfare payments include public 
 assistance payments made to low-income persons, 
 such as aid to families with dependent children and 
 general assistance. 
 
 Veterans' payments include payments made period- 
 ically by the Department of Veterans Affairs to disabled 
 members of the Armed Forces or to survivors of deceased 
 veterans for education and on-the-job training, and 
 means-tested assistance to veterans. 
 
 Survivor benefits include payments from survivor or 
 widows' pensions, estates, trusts, annuities, or any 
 other types of survivor benefits. Payments can be 
 reported from 10 different sources: (1) private compa- 
 nies or unions, (2) Federal government (Civil Service), 
 (3) military, (4) State or local governments, (5) railroad 
 retirement, (6) workers' compensation, (7) Black lung 
 payments, (8) estates and trusts, (9) annuities or paid-up 
 insurance policies, and (10) other survivor payments. 
 
 Disability benefits include all payments received as a 
 result of a health problem or disability. Payments can be 
 reported from 10 sources: (1) workers' compensation, 
 (2) companies or unions, (3) Federal government (Civil 
 Service), (4) U.S. Military, (5) State or local govern- 
 ments, (6) railroad retirement, (7) accident or disability 
 insurance, (8) Black lung payments, (9) State temporary 
 sickness, or (10) other disability payments. 
 
 Retirement benefits include payments reported from 
 eight sources: (1) companies or unions, (2) Federal 
 government (Civil Service), (3) U.S. Military, (4) State or 
 local governments, (5) railroad retirement, (6) annuities 
 or paid-up insurance policies, (7) IRA or KEOGH pay- 
 ments, or (8) other retirement income. 
 
 Interest income includes payments received or cred- 
 ited to savings accounts, bonds, treasury notes, IRA's, 
 certificates of deposit, interest-bearing checking accounts, 
 and all open investments that pay interest. 
 
 Dividends include income received from stockhold- 
 ings and mutual fund shares. Capital gains from the sale 
 of stockholdings are not included as dividends. 
 
 Rents, royalties, and estates and trusts include the 
 net income from the rental of a house, store, or other 
 property; receipts from boarders or lodgers; net royalty 
 income; and periodic payments from estate or trust 
 funds. 
 
 Educational assistance includes Pell Grants, other 
 government educational assistance, any scholarships 
 or grants, or financial assistance from employers, friends, 
 or relatives not residing in the students household. 
 
 Child support includes all periodic payments paid by 
 parents for the support of children, even if these pay- 
 ments are made through a State or local government 
 office. 
 
 Alimony includes all periodic payments to ex-spouses. 
 One-time property settlements are not included. 
 
 Financial assistance from outside of the household 
 includes periodic payments from nonhousehold mem- 
 bers. Gifts or sporadic assistance are not included. 
 
 Other income includes all other regularly received 
 payments that are not included elsewhere on the ques- 
 tionnaire. Some examples include State programs such 
 as foster child payments, military family allotments, 
 income received from foreign government pensions, 
 etc. 
 
 Receipts not counted as income include (1) capital 
 gains such as money received from the sale of property, 
 such as stocks, bonds, a house, or a car (unless the 
 person was engaged in the business of selling such 
 property, in which case the net proceeds would be 
 counted as income from self-employment), (2) withdraw- 
 als of bank deposits, (3) money borrowed, (4) tax 
 refunds, (5) gifts, and (6) lump-sum inheritances or 
 insurance payments. 
 
 Median income is the amount which divides the income 
 distribution into two equal groups, half having incomes 
 above the median, half having incomes below the 
 median. The medians for households, families, and 
 unrelated individuals are based on all households, fam- 
 ilies, and unrelated individuals. The medians for persons 
 are based on persons 15 years old and over with 
 income. 
 
 Households consist of all persons who occupy a 
 housing unit. A house, an apartment or other group of 
 rooms, or a single room is regarded as a housing unit 
 when it is occupied or intended for occupancy as 
 separate living quarters; that is, when the occupants do 
 not live and eat with any other persons in the structure 
 and there is direct access from the outside or through a 
 common hall. 
 
 A household includes the related family members 
 and all the unrelated persons, if any, such as lodgers, 
 foster children, wards, or employees who share the 
 
A-3 
 
 housing unit. A person living alone in a housing unit, or 
 a group of unrelated persons sharing a housing unit as 
 partners, is also counted as a household. The count of 
 households excludes group quarters. 
 
 Families are groups of two persons or more (one of 
 whom is the householder) related by birth, marriage, or 
 adoption and residing together; all such persons (includ- 
 ing related subfamily members) are considered as mem- 
 bers of one family. Beginning with the 1980 CPS, 
 unrelated subfamilies (referred to in the past as second- 
 ary families) were no longer included in the count of 
 families, nor are the members of unrelated subfamilies 
 included in the count of family members. 
 
 Size of household or family. The term "size of house- 
 hold" includes all persons occupying a housing unit. 
 "Size of family" includes the family householder and all 
 other persons in the living quarters who are related to 
 the householder by birth, marriage, or adoption. 
 
 Family size and adjustment. In defining program eligi- 
 bility for assistance in the LIHEAP program, the follow- 
 ing percentages are used to adjust incomes for families 
 containing other than four persons (from 45 CFR 1 396.60(d)(2) 
 in effect under the former Title XX Program): one 
 person, 52 percent; two persons, 68 percent; three 
 persons, 84 percent; five persons, 1 1 6 percent; and six 
 persons, 132 percent. 
 
 For each additional family member above six per- 
 sons, 3 percent is added to 1 32 percent. 
 
 COMPARABILITY OF CURRENT POPULATION 
 SURVEY INCOME DATA WITH BUREAU OF 
 ECONOMIC ANALYSIS (BEA) PERSONAL 
 INCOME SERIES. 
 
 Census Bureau money income estimates are not 
 directly comparable with estimates of per capita per- 
 sonal income prepared by the BEA, though BEA figures 
 on personal per capita income are used in the estima- 
 tion process. Differences between Census Bureau money 
 income estimates and BEA per capita income figures 
 are highlighted below. 
 
 Income definition. The personal income series include, 
 among other items, the following types of nonmoney 
 income which are not included in the census definition: 
 wages received in kind, the value of food and fuel 
 produced and consumed on farms, the net rental value 
 
 of owner-occupied homes, the property income received 
 by mutual life insurance companies, and the value of the 
 services of banks and other financial intermediaries 
 rendered to persons without the assessment of specific 
 charges. These items of income in kind account for 
 about 4 percent of total personal income. The Census 
 Bureau definition of income, however, includes such 
 items as regular contributions for support received from 
 persons who do not reside in the same living quarters, 
 income received from roomers and boarders residing in 
 households, and employee contributions for social insur- 
 ance, which are not included in the personal income 
 series. These items, however, represent a much smaller 
 income total than the nonmoney items included in 
 personal income. 
 
 Source of data. The personal income series is esti- 
 mated largely on the basis of data derived from busi- 
 ness and governmental sources. These sources include 
 the industrial and population censuses, employer's wage 
 reports under the Social Security programs, and records 
 of disbursements to individuals by governmental agen- 
 cies. The income data presented in the census reports, 
 on the other hand, are based directly on field surveys of 
 households. 
 
 Income data obtained in household interviews are 
 subject to various types of reporting errors which tend to 
 produce an understatement of income. It is estimated 
 that the income surveys conducted by the Bureau of the 
 Census during the past few years have obtained about 
 90 percent of the comparable total money income 
 aggregates and about 98 percent of the comparable 
 money wage or salary aggregates derived from the 
 personal income series prepared by BEA. 
 
 For a more detailed discussion of the differences 
 between distributions using Census money income and 
 BEA personal income, see "Size Distribution of Family 
 Personal Income: Methodology and Estimates for 1964," 
 by Edward C. Budd, Daniel B. Radner, and John C. 
 Hinrichs, Bureau of Economic Analysis, BEA-SP 73-21, 
 June 1973. 
 
 Population coverage. The Bureau of the Census excluded 
 from its sample inmates of institutions and military 
 personnel overseas or living on post in the United 
 States (except for a few families living on post). In 
 addition, the income of persons who died or emigrated 
 prior to the date of interview was not reported in the 
 census inquiry. The income of these groups is included 
 in the aggregate personal income series released by the 
 BEA. 
 
B-1 
 
 Appendix B. 
 
 Multivariate Components of Variance Models as Empirical 
 
 Bayes Procedures for Small-Domain Estimation 
 
 Robert E. Fay, U.S. Bureau of the Census 
 
 1. INTRODUCTION 
 
 Frequently, sample surveys produce estimates of char- 
 acteristics for the total population or for large domains 
 within the population, but interest extends beyond this 
 level of detail to small areas or domains. Often, design- 
 based estimators for the small domains are unsatisfactory 
 because of small sample sizes and associated high sam- 
 pling errors. Most attempts to address this problem have 
 involved the use of auxiliary information outside the survey 
 itself. Some, such as Sarndal (1984), have proposed 
 estimators incorporating the auxiliary information entirely 
 within a design-based framework. Most developments in 
 this area, however, have relied upon combining the sample 
 survey information with analytic models for the population. 
 A review article of Purcell and Kish (1979) summarizes 
 many of these modeling approaches. 
 
 Work of Ericksen (1973, 1974) on the use of linear 
 regression for small domain estimation represents one 
 example of modeling and has formed the basis for a 
 number of applications. In his original description of this 
 method, a sample survey is assumed to provide unbiased 
 sample estimates, Y,'s, for many or all of the small domains 
 of interest. The Yj's are presumed to have estimable, even 
 though generally large, sampling errors. Auxiliary informa- 
 tion, Xjj, is presumed to be available for each domain i and 
 for a specific number of characteristics j. In this formula- 
 tion, the Xjj's are presumed to be measured without error, 
 but they are also assumed to be typically imperfect linear 
 predictors of E(Y;), the underlying characteristic measured 
 by Y|. The predicted values from the linear regression of 
 the Yj's on the X^'s provide small domain estimates for the 
 population. Ericksen also presented an estimator of the 
 mean-squared error of prediction for these small domain 
 estimates. 
 
 Fay and Herriot (1 979) described some modifications to 
 the regression approach related to the methods presented 
 in this paper. By drawing parallels to the James-Stein 
 estimator when the Yj's have equal sampling variances, 
 they proposed an empirical Bayes estimator for the situa- 
 tion of unequal sampling variances. In the case of domains 
 with no sample data, the estimator is the regression 
 estimate, as before. For each domain with a sample 
 estimate, Y,, however, the empirical Bayes estimator takes 
 the form of a composite, that is, a weighted combination of 
 Y| with the predicted value from the regression, where the 
 weights for domain i depend on both the sampling variance 
 of Yj and the overall fit of the regression to the sample 
 estimates. 
 
 This paper considers extensions of this approach to the 
 instance in which some of the independent variables, the 
 Xjj's, are themselves stochastic. For example, some of the 
 independent variables may have also been measured by 
 the same or a different sample survey. Under limited 
 circumstances, use of the previous estimators developed 
 for fixed X^'s still proves appropriate, but a more general 
 solution requires that the effect of random variation in the 
 Xy's be explicitly included in the model. Specifically, the 
 method described here involves treating all stochastic 
 variables, both the Yj's and any stochastic Xjj's, as depen- 
 dent variables in a multivariate regression expressed as a 
 multivariate components of variance model. Separate vari- 
 ance components are included in the model to represent 
 sampling variability in the survey estimates and to repre- 
 sent the lack of fit or model error of the model. By 
 estimating the unknown variance components and then 
 applying the best linear unbiased estimator (Harville 1976, 
 1977) as if the estimated variance components were 
 known, an empirical Bayes estimator results. This estima- 
 tor again is in the form of composite between the sample 
 estimates and the regression estimates, although the 
 composite is now multivariate. A potential application of 
 this idea is to situations in which small domain estimates 
 are of interest for more than one characteristic. In many 
 instances, a more effective estimate of each characteristic 
 emerges than if each had been treated as a separate 
 estimation problem. In this case, the multivariate formula- 
 tion appears a natural extension of the regression method. 
 
 When only one characteristic is of interest, the multivari- 
 ate formulation is less obvious; yet, this approach generally 
 yields more effective estimates than does the univariate 
 regression of the Yj's on the non-stochastic Xjj's. The gain 
 comes from use, under the model, of the information 
 contained in the stochastic X^'s. 
 
 An earlier paper (Fay 1 985) outlined this methodology, 
 but did not contain the empirical results reported here. The 
 methods are related to and preceded by work of Fuller and 
 Harter (1 985). The major difference between their approach 
 and the one presented here reflects the level of analysis. 
 Fuller and Harter modeled the data at the level of the 
 individual observation, and derived small domain esti- 
 mates as a consequence, whereas the models in this 
 paper apply directly at the level of the small domain. 
 Although the approach in the Fuller and Harter paper may 
 be more effective in situations satisfying their conditions, 
 the models in this paper permit more general sample 
 designs. The two approaches are approximately equally 
 
B-2 
 
 well suited to applications in which the auxiliary information 
 is available only at the level of the small domain or cannot 
 be matched at the individual level to the sample survey 
 data. Additionally, models at the level of the small domain 
 are applicable to statistics, such as medians, defined at the 
 level of the small domain and not fitting into the formulation 
 at the individual level. Further remarks on the relationship 
 between the models considered in this paper and those of 
 Fuller and Harter appear at the end of the paper. The next 
 section of this paper provides the background for the 
 application to be presented in this paper, the estimation of 
 median income for four-person families by State. Section 3 
 describes the formulation of a components of variance 
 model for the problem. Section 4 presents the empirical 
 results and discusses alternative approaches to estimating 
 the components of variance by combining information over 
 years. The concluding section suggests other ways in 
 which these and similar models may be applied to prob- 
 lems of small domain estimation. 
 
 2. THE PROBLEM: ESTIMATION OF MEDIAN 
 INCOME FOR FOUR-PERSON FAMILIES, BY 
 STATE 
 
 2.1 Basic Objectives and Sources of Data 
 
 The Social Security Administration, Department of Health 
 and Human Services, administers a program, Low Income 
 Home Energy Assistance, to aid low-income families with 
 their energy costs. Eligibility for the program varies by 
 State and is determined by a formula employing an esti- 
 mate of the median income or four-person families by 
 State (and the District of Columbia) for the most recently 
 available year. 
 
 The Current Population Survey (CPS) provides direct 
 sample survey estimates of median income for four-person 
 families annually at the national level. The CPS data may 
 also be tabulated to produce separate estimates by State. 
 At the State level, however, the effect of sampling variabil- 
 ity is pronounced: in a few States the coefficient of 
 variation (c.v., that is, standard error divided by expected 
 value) is only 2 or 3 percent, but in most States it falls in the 
 range of 6 to 1 percent. 
 
 The models to be described for this problem have 
 employed two auxiliary sources of information: results from 
 the decennial censuses of population, and estimates from 
 the Bureau of Economic Analysis (BEA). The census 
 provides income values for the year immediately preceding 
 the census year. At the State level, the census estimates 
 of median income for four-person families have negligible 
 sampling error. Thus, the census values of median income 
 for 1979 constitute an obvious choice for inclusion in a 
 model of current State medians. 
 
 BEA produces annual estimates of per capita income 
 for States and other geographic areas on the basis of 
 aggregate statistics on earnings, transfer payments, etc. 
 
 The estimates furnish an overall indication of relative 
 income among States and especially change over time for 
 individual States, even though per capita income is only 
 indirectly related to median income of four-person families. 
 The BEA estimates, although subject to revision and 
 conceptual differences from census income, are essen- 
 tially free from sampling error. 
 
 Up to three independent variables, X,.,, X i2 , and X j3 , are 
 employed in this paper as predictors of E(Yi), where Y, 
 represents the expected value of median income from the 
 CPS. X M takes the value 1, serving as the independent 
 variable corresponding to the constant term; 
 
 X i2 = (BEA(t)j/BEA(c)i) Cen(c)i 
 
 (2.1) 
 
 where BEA(t)j and BEA(c), denote the values of BEA per 
 capita income in State i for the current income year and 
 census income year, respectively, and Cen(c)j represents 
 the median income for the year measured by the census; 
 and X i3 = Cen(c)i denotes the unadjusted census median. 
 X j2 represents an attempt to adjust the census values of 
 median income for change since the census according to 
 the proportional growth of BEA per capita income. 
 
 2.2 The Earlier Model 
 
 A few years before the 1980 census, a regression 
 estimator was developed for this problem. The CPS sam- 
 ple estimates, Yj, for the median income of four-person 
 families by State were fitted by a linear regression with Xj-, 
 and X i2 , where the latter were 1969 median incomes 
 adjusted by change in BEA per capita income. A compos- 
 ite estimate was formed from the sample estimates Y, and 
 the fitted regression estimates. The selection of the inde- 
 pendent variables and the assessment of this model were 
 based on fitting 1970 census values for 1969 median 
 income using X i2 expressed as the 1960 census values 
 adjusted for change from 1959 to 1969 in BEA income, as 
 in (2.1). The observed average error in fitting the 1970 
 census values was used as an estimate of the model error 
 for subsequent years, instead of estimating the model error 
 from the sample data, as suggested by Fay and Herriot 
 (1979). 
 
 If the composite estimator combining the sample and 
 regression estimates fell beyond one standard error of the 
 sample estimate, the final estimate was constrained to lie 
 within one standard error of the sample value. This proce- 
 dure was originally included to limit the individual risk to 
 any of the States in case the model failed seriously in a few 
 isolated instances. The application described by Fay and 
 Herriot (1979) also incorporated this constraint. A draw- 
 back of the procedure here, however, was that the con- 
 straint increased the year-to-year variability in the esti- 
 mates. 
 
 Comparison of the estimates from the model for income 
 year 1 979 with the 1 980 census afforded an opportunity to 
 assess the merits of the estimator. Several conclusions 
 emerged from this review: 
 
B-3 
 
 i. Although the original model attempted to distinguish 
 among States according to population size in assessing 
 the average model error, the distinction proved ineffective 
 for the 1979 estimates. The average error across all 
 States, however, agreed well with the previous experience 
 derived from fitting the 1970 census. Instead, it now 
 appeared appropriate to presume a single level of model 
 error across all States. 
 
 ii. The addition of X i3 , the unadjusted median from the 
 previous census, improved the predictive power of the 
 regression. The form of X i2 in (2.1) proportionally adjusts 
 the census median for changes in BEA income; inclusion 
 of X i3 permits this adjustment to be softened in case of any 
 "regression toward the mean," which might arise if BEA 
 income did not perfectly measure the proportional changes 
 in the income distribution. 
 
 iii. Use of the constraint of one standard deviation from 
 the sample estimate did not reduce the number of extreme 
 errors compared to the same model without the constraint. 
 Had the model produced extreme errors in a few States, 
 the constraint would have been effective, but, in the 
 absence of extreme errors, the constraint failed to be 
 beneficial. This experience suggested removing the con- 
 straint. 
 
 These three changes in the model could have been 
 expected to yield improvements in the performance for 
 post-1980 predictions. Nonetheless, the remaining year- 
 to-year variability provided the impetus to attempt addi- 
 tional modifications. The CPS sample estimates for three- 
 and five-person families represented an additional source 
 of information. Strong statistical relationships among the 
 median incomes of three-, four-, and five-person families at 
 the State level appear in both the 1970 and 1980 cen- 
 suses. In 1980, the ratio of medians for the four-person to 
 three-person families ranged only from 1.072 to 1.162 at 
 the State level. This ratio fell between 1.089 and 1.135 for 
 two-thirds of the States. Furthermore, some of the differ- 
 ences among States appeared structural, since almost all 
 of the higher ratios appeared in States with relatively large 
 Black populations. Similarly, the association between four- 
 and five-person medians at the State level was almost as 
 high. 
 
 Consequently, if CPS obtained three- and five-person 
 medians without sampling error, they would have made 
 excellent predictors to add to the regression. The sampling 
 error of these medians is comparable to those for four- 
 person families, however. The next section describes a 
 model incorporating the three- and five-person medians 
 while accounting for the effect of sampling error. 
 
 3. THE MODEL FOR FAMILY MEDIANS BY 
 STATE 
 
 As stated in the first section, the formulation of the 
 components of variance model includes stochastic predic- 
 tors as dependent variables in the regression. In a preced- 
 ing paper (Fay 1985), the original approach envisioned 
 
 four-, three-, and five-person family medians each as 
 separate dependent variables. When this model was applied, 
 however, it became evident that the greater sampling 
 variability of the five-person medians and especially the 
 instability of the estimated sampling error for these medi- 
 ans were problematic. Instead, the information from the 
 five-person medians was incorporated into the model by 
 averaging the five- with the three-person median at the 
 State level, with weights 1/4 and 3/4, respectively. The 
 weights were chosen on the basis of the approximate 1 to 
 3 ratio for the respective sample sizes. Thus, the regres- 
 sion was reduced to two dependent variables per State. 
 Although the notation presented here is specific to the 
 problem at hand, the methods are applicable to more than 
 two variables per domain. 
 
 Let ju. (i) = (/Lt (i)1 , /x ( i )2 )' denote the true values of the 
 medians in State i, where jx (i)1 is the true median for 
 four-person families and ju, (i)2 denotes the weighted aver- 
 age computed as 3/4 the three-person median and 1/4 
 the five-person median. Assume that /x (i)k , k=1,2, has 
 been sampled from a superpopulation with expected value 
 X (i) (k) /3( k) - For k= 1 , the elements X (j)(1)j of X (i)(1) are X^, j = 
 1, 2, 3, from the previous section. For k=2, the elements 
 of X (i)(2) are formed similarly, with Cen(c)j in (2.1) and as 
 X (j)(2)3 equal to the weighted average of the census three- 
 and five-person family medians. Assume that the distribu- 
 tions of /x (j) about their expected values are N(0, A) and 
 independent over i. 
 
 The corresponding CPS estimates Y (j) for State i are 
 assumed N(jn (i) , D (i) ), with known sampling covariance 
 matrix D (i) . The sampling errors will also be assumed 
 independent across States. 
 
 Under this superpopulation model, the unconditional 
 distribution of the Y's may be expressed as a mixed 
 components of variance model. Setting 
 
 ' = ('(1)1> Y(1)2» ' (2)1 •— ) ' 
 
 a column vector of 102 elements (for 50 States and DC), 
 and X to be the 1 02 by 6 matrix whose first rows are given 
 by 
 
 X = 
 
 Hi)(D 
 
 
 ^(2)0) 
 
 M1)(2) 
 
 the model is 
 
 Y = Xj3 + b + e 
 
 (3.1) 
 
 where b represents random effects arising from the pre- 
 sumed sampling of the /x (j) from the superpopulation (i.e., 
 the bias terms of the regression model when the true State 
 medians are considered fixed), and e denotes sampling 
 errors. The covariance matrix of b is assumed to be in the 
 block diagonal form 
 
B-4 
 
 A* = 
 
 A 
 A 
 A 
 
 and that of e in the form 
 
 D* 
 
 D (D 
 
 
 
 
 
 
 D( 2 ) 
 D 
 
 (3) 
 
 If A were known, the BLUE estimate of the fixed effects 
 would be given by 
 
 on maximum likelihood estimation in the next section, 
 although alternatives such as MINQUE may also be con- 
 sidered in other applications. 
 
 The log-likelihood, ignoring additive constants not depend- 
 ing upon the parameters, is 
 
 L(A,/J;Y) = - (1/2)log(det(A*+D*)) 
 
 - (1/2)(Y-X/3)'(D*+A*)- 1 (Y-X£). 
 
 (3.4) 
 
 One method to obtain the 
 to choose test values of A 
 examine the resulting log 
 mum can be obtained by 
 particularly easy for this 
 dimension of A. Harville (1 
 approaches to finding the 
 
 maximum likelihood estimate is 
 , compute fi from (3.2) and then 
 likelihood from (3.4). The maxi- 
 search procedures, which are 
 problem because of the small 
 977) reviewed more systematic 
 maximum. 
 
 /3 = (X'(D*+A*)- 1 X)" 1 X'(D*+A) 1 Y. 
 
 (3.2) 
 
 4. IMPLEMENTATION OF THE MODEL 
 
 Consequently, the BLUE of the superpopulation means 
 would be given by Xp . The objective, however, is to 
 estimate the actual true medians, 
 
 ju, = X/3 + b, 
 
 which is a linear combination of the fixed and random 
 effects. Again, assuming A* were known, the BLUE of \x is 
 given by 
 
 jx = X# + A*(D"+A*)- 1 (Y-X$) 
 
 (3.3) 
 
 (Harville 1976). Equation (3.3) gives the BLUE as the 
 regression estimate X/3 plus the multivariate residual (Y-Xp) 
 times a "shrinkage factor," actually a matrix, A*(D*+A*)" 1 • 
 Harville (1977) noted that this estimator corresponds to 
 the posterior mean of an analogous Bayes model with a 
 uniform prior on the fixed effects, y8. Because of the 
 block-diagonal form of A* and D* in this specific model, the 
 residuals of both components in State i will be incorpo- 
 rated in the estimation of each component in (3.3), unless 
 D (i) is a multiple of A, but the residuals of each State do not 
 affect the estimation in other States in (3.3). Indeed, it is 
 through the form of (3.3) that the information represented 
 in the CPS estimates of the three- and five-person family 
 medians can improve the estimation of the four-person 
 family medians. 
 
 In fact, A is generally not known. Substitutution of a 
 value of A estimated from the data into (3.2) and (3.3) 
 converts (3.3) into a parametric empirical Bayes estimator, 
 in the sense of Morris (1983). 
 
 The next section examines the relative merits of esti- 
 mating A directly from the data or from past experience, in 
 this case from the fit of the model to census data. In other 
 applications, however, direct estimation may be the only 
 available choice. Direct estimation from the data is based 
 
 4.1 Comparisons to 1980 Census 
 
 Since the 1 980 census provides State medians essen- 
 tially free from sampling error, evaluation of the fit of the 
 regression to the census values gives a relatively precise 
 determination, A , of A. Here, of course, 1970 census 
 medians are used as the census values in the definition of 
 the independent variables, X (i)(k) . The elements of A are 
 3.08 x 1 5 for A 01 ^ , the variance of the model error term for 
 four-person family medians, 2.86 x 10 5 for A 022 > the 
 corresponding variance for the weighted combination of 
 three and five-person medians, and 2.63 x 10 5 for A 012 . As 
 expected, A gives a high correlation between the two 
 components, .89. 
 
 The diagonal elements of D (i) , the sampling variances 
 for the census medians, were estimated according to a 
 methodology documented in an internal memorandum by 
 Fay and Burkhead (1985). Because the four-person medi- 
 ans and the weighted average of three- and five-person 
 medians were derived from mutually exclusive sets of 
 households, their sampling covariance was taken to be 
 zero. It is possible that a correlation in fact exists from 
 clustering effects in the CPS design, but this correlation is 
 certainly small and decidedly much less than that of A. 
 
 Maximum likelihood estimates, computed directly from 
 the 1 980 CPS data and using the estimated D (i) as if they 
 were known, give A u as 1.15 x 10 5 , k 22 as 3.26 x 10 5 , and 
 A\ 2 as 1.93 x 10 5 . The estimated correlation is 1.00. 
 Although the MLE estimate, A, is somewhat different from 
 A , the difference in the the log-likelihood (3.4), multiplied 
 by two, is only 1.13, indicating no statistically significant 
 difference. As will be shown later, the likelihood surface is 
 quite flat for A for this problem, implying wide confidence 
 regions for A. 
 
 The shrinkage factor, A*(D*+A*)"\ in (3.3) makes con- 
 siderable use of the sample estimates for the weighted 
 three- and five-person family medians in estimating the 
 
B-5 
 
 four-person family medians, because both A and A have 
 such different correlations from D (l) . Table B-1 compares 
 the 1980 census values for the median income of four- 
 person families in 1979 with three sets of estimates: 
 estimates derived under the earlier regression methodol- 
 ogy using only CPS data for four-person medians, (3.3) 
 based upon A , and (3.3) based upon A. The second set of 
 estimates is dependent, through A on results from the 
 1 980 census, while the first and third were derived entirely 
 independently of the 1980 census. 
 
 Generally, the two sets of new estimates are closer to 
 each other than to the previous methodology. Table B-1 
 shows substantial improvements over the earlier approach. 
 One of the first set of estimates is in error by over 10.0 
 percent and 11 additional estimates are in error by 5.0 
 percent or more. The new estimates have no errors over 
 10.0 percent and only three each in the -ange of 5.0-9.9 
 percent. 
 
 4.2 Estimates for Income Years 1981-1984 
 
 Table B-1 shows A to do quite well against A . Even 
 though the two estimated covariance matrices are quite 
 dissimilar, their difference has little effect on the log- 
 likelihood function. The flatness of the log-likelihood func- 
 tion implies the possibility of large variation in A from year 
 to year. A more stable estimate of A, although not neces- 
 sarily superior, may be derived by multiplying A by the 
 square of the proportional growth in national median 
 income, thus assuming approximately the same average 
 relative error of the regression model over time. Table B-2 
 presents estimates based on these projected error com- 
 ponents; table B-3 gives those based on the MLE. The 
 projected error components give a somewhat smoother 
 series of estimates, although the contrast between the 
 sets is not dramatic. 
 
 Table B-4 compares the projected components and 
 MLE estimates for these 4 years. The MLE estimates vary 
 substantially over time, but the overall test of difference 
 from the projected components based on a chi-square test 
 with three degrees of freedom is not significant in each 
 case. Again, the likelihood surface is quite flat. In 1984, the 
 MLE of the correlation, r, drops substantially, but not 
 necessarily significantly. Because of this low estimated r, 
 the estimates in table B-3 for 1 984 based on the MLE of A 
 make little use of the CPS estimates for the three- and 
 five-person medians in predicting the four-person medians. 
 Use of the projected error components assures that the 
 three- and five-person medians will be used to approxi- 
 mately the same degree in each year. The estimates in 
 table B-2 based on projected components have been 
 selected as the preferred set. Estimates from the 1986 
 CPS for income year 1 985 will provide additional perspec- 
 tive on this choice, when they become available. 
 
 5. CONCLUDJNG REMARKS 
 
 The representation of the estimation problem in terms 
 of a components of variance model allows auxiliary infor- 
 mation with random error to be suitably combined into the 
 estimation. The use of this information depends upon the 
 form of the factor A*(D*+A) 1 in (3.3). For small domain 
 applications in which A* and D* take the same block 
 diagonal form as in this example, the auxiliary information 
 will have effect on the estimation of the k-th characteristic 
 when the k-th row of A(D;+A) 1 has nondiagonal elements. 
 The importance of the auxiliary information in this instance 
 resulted from the high correlation of the characteristics in 
 the population and from a negligible correlation of the 
 sample estimates about the true values. It is precisely this 
 combination of circumstances that would favor application 
 of this methodology to other problems. 
 
 Research is underway to adapt these methods to the 
 estimation of median fair-market rent for two-bedroom 
 units for larger SMSA's and regions from the Annual 
 Housing Survey (AHS). These medians are computed from 
 a subset of rental units meeting a number of criteria. The 
 situation differs somewhat from the CPS application since 
 the 1 980 census did not collect sufficiently detailed data to 
 determine which units satisfy the definition of this quantity 
 exactly. The census does provide related data, however. 
 Additionally, rentals for two-bedroom units not satisfying 
 the definition and rentals for units of other sizes should be 
 statistically related to the variable of interest at the SMSA 
 level. The sample estimates for such related variables 
 should have low sampling covariances with each other. 
 This situation appears to offer the same potential gains 
 from the components of variance approach as in the 
 application to median incomes for four-person families 
 from CPS. 
 
 As mentioned in the introduction of this paper, Fuller 
 and Harter (1985) proposed a similar use of components 
 of variance models for small domain estimation, where the 
 model is stated at the individual level. In some applica- 
 tions, particularly when the interest is in domain means and 
 when auxiliary information can be matched at the individual 
 level, their approach should be more effective than the one 
 presented here. In cases in which modeling at the individ- 
 ual level is inappropriate or proves difficult, such as the 
 estimation of medians, modeling at the level of the small 
 domain becomes a feasible and effective alternative. 
 
 ACKNOWLEDGEMENTS 
 
 The author is grateful to Charles H. Alexander and 
 Beverley D. Causey for thoughful comments and to Alice 
 W. Coburn for assistance with typing. 
 
 REFERENCES 
 
 Ericksen, E.P. (1973), "A Method of Combining Sample 
 Survey Data and Symptomatic Indicators to Obtain Popu- 
 lation Estimates for Local Areas," Demography 10, 137- 
 160. 
 
B-6 
 
 (1974), "A Regression Method for Estimating 
 
 Population Changes for Local Areas," Journal of the 
 American Statistical Association 69, 867-875. 
 
 Fay, R.E. (1985), "Application of Multivariate Regression 
 to Small Domain Estimation," paper presented at the 
 International Symposium on Small Area Statistics, Ottawa, 
 Ontario, Canada, May 22-24. 
 
 and Burkhead, D. (1985), "Summary of Research 
 
 Completed on Estimating Median Income for 4-Person 
 Families by State," undated draft memorandum to Roger 
 A. Herriot, Chief, Population Division, U.S. Bureau of the 
 Census. 
 
 and Herriot, R. (1979), "Estimates of Income for 
 
 Small Places: An Application of James-Stein Procedures 
 to Census Data," Journal of the American Statistical 
 Association 74, 269-277. 
 
 Fuller, W.A. and Harter, R.M. (1985), "The Multivariate 
 Components of Variance Model for Small Domain Estima- 
 tion," paper presented at the International Symposium on 
 Small Area Statistics, Ottawa, Ontario, Canada, May 22-24. 
 
 Harville, D.A. (1976), "Extension of the Gauss-Markov 
 Theorem to Include the Estimation of Random Effects," 
 Annals of Statistics 4, 384-395. 
 
 (1 977), "Maximum Likelihood Approaches to Vari- 
 
 ance Component Estimation and to Related Problems," 
 Journal of the American Statistical Association 72, 320- 
 338. 
 
 Morris, C. (1983), "Parametric Empirical Bayes Inference: 
 Theory and Applications," Journal of the American Statis- 
 tical Association 78, 47-55. 
 
 Purcell, N.J. and Kish, L. (1979), "Estimation for Small 
 Domains," Biometrics 35, 365-384. 
 
 Sarndal, C.E. (1984), "Design-Based Versus Model-Dependent 
 Estimation for Small Domains," Journal of the American 
 Statistical Association 79, 624-631. 
 
B-7 
 
 Table 8-1. Comparison of 1979 Estimates of Median Income of Four-Person Families 
 
 State 
 
 1980 
 census 
 
 Original 
 method 
 
 Comparison of 
 variance methods 
 
 Percent error 
 
 Original 
 
 ME 
 
 NH 
 
 VT 
 
 MA 
 
 Rl. 
 
 CT 
 
 NY 
 
 NJ 
 
 PA 
 
 OH 
 
 IN. 
 
 IL . 
 
 Ml. 
 
 Wl. 
 
 MN 
 
 IA. 
 
 MO 
 
 ND 
 
 SD 
 
 NE 
 
 KS 
 
 DE 
 
 MD 
 
 DC 
 
 VA 
 
 WV 
 
 NC 
 
 SC 
 
 GA 
 
 FL. 
 
 KY 
 
 TN 
 
 AL 
 
 MS 
 
 AR 
 
 LA 
 
 OK 
 
 TX 
 
 MT 
 
 ID. 
 
 WY 
 
 CO 
 
 NM 
 
 AZ 
 
 UT 
 
 NV 
 
 WA 
 
 OR 
 
 CA 
 
 AK 
 
 HI. 
 
 18,319 
 22,027 
 19,424 
 23,772 
 22,107 
 25,712 
 22,669 
 26,014 
 22,266 
 23,279 
 23,014 
 25,410 
 25,111 
 23,320 
 24,044 
 22,351 
 21,891 
 20,511 
 18,674 
 21,438 
 22,127 
 23,627 
 26,203 
 21,862 
 22,757 
 20,214 
 19,772 
 19,944 
 20,668 
 21,086 
 19,685 
 19,693 
 19,926 
 18,150 
 17,893 
 21,412 
 20,659 
 22,521 
 20,776 
 19,961 
 24,641 
 23,757 
 19,257 
 21,924 
 21,572 
 24,438 
 24,394 
 22,688 
 24,752 
 31,018 
 24,966 
 
 18,074 
 22,335 
 19,314 
 23,786 
 21,636 
 24,410 
 21,082 
 24,640 
 22,314 
 22,528 
 22,614 
 24,265 
 24,422 
 23,518 
 24,409 
 22,567 
 21,294 
 19,520 
 19,209 
 20,749 
 22,848 
 21,184 
 24,686 
 21,310 
 22,976 
 18,876 
 19,648 
 20,154 
 21,578 
 20,757 
 19,138 
 19,437 
 18,613 
 17,672 
 18,493 
 20,166 
 20,852 
 23,416 
 20,051 
 20,429 
 22,673 
 25,228 
 21,032 
 23,000 
 21,250 
 25,457 
 24,410 
 24,031 
 25,109 
 31,037 
 24,582 
 
 18,810 
 22,626 
 20,297 
 23,809 
 22,022 
 25,623 
 22,313 
 25,440 
 22,657 
 22,986 
 22,489 
 24,611 
 24,716 
 24,108 
 23,840 
 22,561 
 21,688 
 19,910 
 19,346 
 20,922 
 22,404 
 22,007 
 25,306 
 22,184 
 23,076 
 19,210 
 19,507 
 19,498 
 20,902 
 20,798 
 19,423 
 19,155 
 19,317 
 18,024 
 18,149 
 20,154 
 20,655 
 22,519 
 20,106 
 20,517 
 24,236 
 24,370 
 19,960 
 22,733 
 21,234 
 24,351 
 24,341 
 23,308 
 24,393 
 30,012 
 25,115 
 
 18,842 
 22,559 
 20,426 
 23,714 
 21,908 
 25,585 
 22,438 
 25,337 
 22,384 
 23,051 
 22,499 
 24,602 
 24,687 
 24,124 
 23,884 
 22,451 
 21,753 
 20,031 
 19,370 
 20,807 
 22,409 
 21,940 
 25,152 
 22,202 
 22,895 
 19,308 
 19,447 
 19,532 
 20,692 
 21,086 
 19,422 
 19,143 
 19,532 
 17,948 
 18,101 
 20,229 
 20,770 
 22,429 
 20,068 
 20,407 
 24,334 
 24,145 
 20,007 
 22,731 
 21,280 
 24,278 
 24,234 
 23,242 
 24,570 
 30,020 
 25,091 
 
 -1.3 
 
 1.4 
 
 -0.6 
 
 0.1 
 
 -2.1 
 
 -5.1 
 
 -7.0 
 
 -5.3 
 
 0.2 
 
 -3.2 
 
 -1.7 
 
 -4.5 
 
 -2.7 
 
 08 
 
 1.5 
 
 1.0 
 
 -2.7 
 
 -4.8 
 
 2 9 
 
 -3.2 
 
 3.3 
 
 -10.3 
 
 -5.8 
 
 -2.5 
 
 1.0 
 
 -6.6 
 
 -0.6 
 
 1.1 
 
 4.4 
 
 -1.6 
 
 -2.8 
 
 -1.3 
 
 -6.6 
 
 -2.6 
 
 3.4 
 
 -5.8 
 
 0.9 
 
 4.0 
 
 -3.5 
 
 2.3 
 
 -8.0 
 
 6.2 
 
 9.2 
 
 4.9 
 
 -1.5 
 
 4.2 
 
 0.1 
 
 5.9 
 
 1.4 
 
 0.1 
 
 -1.5 
 
 2.7 
 2.7 
 
 4.5 
 
 0.2 
 
 0.4 
 
 0.3 
 
 -1.6 
 
 -2.2 
 
 1.8 
 
 -1.3 
 
 -2.3 
 
 -3.1 
 
 -1.6 
 
 3.4 
 
 0.8 
 
 0.9 
 
 -0.9 
 
 -2.9 
 
 3.6 
 
 -2.4 
 
 1.3 
 
 -0.9 
 
 3.4 
 
 1.5 
 
 1.4 
 
 -5.0 
 
 -1.3 
 
 -2.2 
 
 1.1 
 
 -1.4 
 
 -1.3 
 
 -2.7 
 
 -3.1 
 
 -0.7 
 
 1.4 
 
 -5.9 
 
 0.0 
 
 0.0 
 
 -3.2 
 
 2.8 
 
 -1.6 
 
 2.6 
 
 3.7 
 
 3.7 
 
 -1.6 
 
 -0.4 
 
 -0.2 
 
 2.7 
 
 -1.5 
 
 -3.2 
 
 0.6 
 
 2.9 
 
 2.4 
 
 5.2 
 
 0.2 
 
 0.9 
 
 0.5 
 
 -1.0 
 
 -2.6 
 
 0.5 
 
 -1.0 
 
 -2.2 
 
 -3.2 
 
 -1.7 
 
 3.4 
 
 -0.7 
 
 0.4 
 
 -0.6 
 
 -2.3 
 
 3.7 
 
 -2.9 
 
 1.3 
 
 -7.1 
 
 -4.0 
 
 1.6 
 
 0.6 
 
 -4.5 
 
 -1.6 
 
 -2.1 
 
 0.1 
 
 0.0 
 
 -1.3 
 
 -2.8 
 
 -2.0 
 
 -1.1 
 
 1.2 
 
 -5.5 
 
 0.5 
 
 -0.4 
 
 -3.4 
 
 2.2 
 
 -1.2 
 
 1.6 
 
 3.9 
 
 3.7 
 
 -1.4 
 
 0.7 
 
 -0.7 
 
 2.4 
 
 0.7 
 
 -3.2 
 
 0.5 
 
B-8 
 
 Table B-2. Estimates of Median Income of Four-Person Families, Using Projected Census Components 
 of Variance 
 
 State 
 
 1979 
 census 
 
 1981 
 estimate 
 
 • 1982 
 estimate 
 
 1983 
 estimate 
 
 1984 
 estimate 
 
 Percent change 
 
 1979-84 1979-81 1981-82 1982-83 
 
 1983-84 
 
 ME 
 NH 
 VT 
 MA 
 Rl. 
 CT 
 NY 
 NJ. 
 PA 
 OH 
 IN. 
 IL . 
 Ml. 
 Wl. 
 MN 
 IA. 
 MO 
 ND 
 SD 
 NE 
 KS 
 DE 
 MD 
 DC 
 VA 
 WV 
 NC 
 SC 
 GA 
 FL. 
 KY 
 TN 
 AL- 
 MS 
 AR 
 LA. 
 OK 
 TX 
 MT 
 ID. 
 WY 
 CO 
 NM 
 AZ 
 UT 
 NV 
 WA 
 OR 
 CA 
 AK 
 HI. 
 
 18,319 
 22,027 
 19,424 
 23,772 
 22,107 
 25,712 
 22,669 
 26,014 
 22,266 
 23,279 
 23,014 
 25,410 
 25,111 
 23,320 
 24,044 
 22,351 
 21,891 
 20,511 
 18,674 
 21,438 
 22,127 
 23,627 
 26,203 
 21,862 
 22,757 
 20,214 
 19,772 
 19,944 
 20,668 
 21,086 
 19,685 
 19,693 
 19,926 
 18,150 
 17,893 
 21,412 
 20,659 
 22,521 
 20,776 
 19,961 
 24,641 
 23,757 
 19,257 
 21,924 
 21,572 
 24,438 
 24,394 
 22,688 
 24,752 
 31,018 
 24,966 
 
 21,433 
 25,980 
 23,080 
 28,409 
 25,655 
 30,431 
 26,224 
 30,498 
 25,607 
 26,413 
 25,567 
 29,493 
 28,862 
 27,349 
 27,864 
 25,824 
 25,276 
 24,443 
 21,326 
 24,995 
 25,353 
 27,730 
 30,909 
 25,059 
 27,052 
 22,730 
 23,227 
 22,578 
 24,470 
 24,410 
 23,01 1 
 22,915 
 22,773 
 21,020 
 20,672 
 25,108 
 24,712 
 26,574 
 24,512 
 23,159 
 29,174 
 28,310 
 22,355 
 25,494 
 24,700 
 28,321 
 28,091 
 25,832 
 20,502 
 36,958 
 24,324 
 
 22,842 
 26,881 
 24,053 
 29,441 
 27,116 
 32,077 
 27,615 
 31,547 
 26,691 
 27,771 
 26,827 
 30,736 
 29,362 
 28,372 
 28,582 
 26,780 
 26,173 
 25,557 
 22,505 
 26,080 
 26,480 
 29,078 
 31,843 
 26,217 
 28,111 
 23,764 
 24,257 
 23,258 
 25,719 
 25,023 
 24,361 
 24,039 
 24,309 
 22,102 
 21,503 
 25,904 
 25,700 
 27,761 
 24,980 
 24,111 
 29,435 
 29,264 
 23,093 
 26,924 
 25,981 
 29,160 
 29,228 
 27,356 
 29,603 
 37,234 
 30,236 
 
 23,852 
 29,337 
 24,466 
 33,258 
 29,093 
 35,474 
 30,140 
 35,141 
 28,221 
 28,556 
 27,545 
 31,615 
 30,230 
 28,846 
 30,652 
 26,766 
 27,602 
 27,012 
 22,849 
 26,253 
 27,769 
 31,320 
 35,223 
 28,949 
 30,591 
 23,265 
 25,944 
 26,719 
 26,874 
 26,800 
 24,245 
 24,313 
 25,014 
 22,135 
 21,822 
 27,554 
 26,809 
 28,884 
 25,465 
 26,244 
 29,256 
 31,526 
 23,974 
 27,586 
 25,528 
 30,488 
 30,102 
 27,497 
 31,734 
 42,867 
 32,030 
 
 26,237 
 33,255 
 26,645 
 36,731 
 32,066 
 39,070 
 32,665 
 39,096 
 29,573 
 30,779 
 30,302 
 33,126 
 32,365 
 30,622 
 33,817 
 28,650 
 30,050 
 28,901 
 25,391 
 28,752 
 30,330 
 33,809 
 38,132 
 31,104 
 33,480 
 25,316 
 27,995 
 27,810 
 29,623 
 28,858 
 25,815 
 26,603 
 26,595 
 23,660 
 23,075 
 28,430 
 28,856 
 31,031 
 26,072 
 25,499 
 29,752 
 34,154 
 25,468 
 29,431 
 27,497 
 31,059 
 31,585 
 28,633 
 33,711 
 44,017 
 33,445 
 
 43.2 
 51.0 
 37.2 
 54.5 
 45.0 
 52.0 
 44.1 
 50.3 
 32.8 
 32.2 
 31.7 
 30.4 
 28.9 
 31.3 
 40.6 
 28.2 
 37.3 
 40.9 
 36.0 
 34.1 
 37.1 
 43.1 
 45.5 
 42.3 
 47.1 
 25.2 
 41.6 
 39.4 
 43.3 
 36.9 
 31.1 
 35.1 
 33.5 
 30.4 
 29.0 
 32.8 
 39.7 
 37.8 
 25.5 
 27.7 
 20.7 
 43.8 
 32.3 
 34.2 
 27.5 
 27.1 
 29.5 
 26.2 
 36.2 
 41.9 
 34.0 
 
 17.0 
 17.9 
 18.8 
 19.5 
 16.0 
 18.4 
 15.7 
 17.2 
 15.0 
 13.5 
 11.1 
 16.1 
 14.9 
 17.3 
 15.9 
 15.5 
 15.5 
 19.2 
 14.2 
 16.6 
 14.6 
 17.4 
 18.0 
 14.6 
 18.9 
 12.4 
 17.5 
 13.2 
 18.4 
 15.8 
 16.9 
 16.4 
 14.3 
 15.8 
 15.5 
 17.3 
 19.6 
 18.0 
 18.0 
 16.0 
 18.4 
 19.2 
 16.1 
 16.3 
 14.5 
 15.9 
 15.2 
 13.9 
 15.2 
 19.2 
 17.5 
 
 6.6 
 3.5 
 4.2 
 3.6 
 5.7 
 5.4 
 5.3 
 3.4 
 4.2 
 5.1 
 4.9 
 4.2 
 1.7 
 3.7 
 2.6 
 3.7 
 3.5 
 4.6 
 5.5 
 4.3 
 4.4 
 4.9 
 3.0 
 4.6 
 3.9 
 4.5 
 4.4 
 3.0 
 5.1 
 2.5 
 5.9 
 4.9 
 6.7 
 5.1 
 4.0 
 3.2 
 4.0 
 4.5 
 1.9 
 4.1 
 0.9 
 3.4 
 6.0 
 5.6 
 5.2 
 3.0 
 4.0 
 5.9 
 3.9 
 0.7 
 3.1 
 
 4.4 
 9.1 
 1.7 
 
 13.0 
 7.3 
 
 10.6 
 9.1 
 
 11.4 
 5.7 
 2.8 
 2.7 
 2.9 
 3.0 
 1.7 
 7.2 
 
 -0.1 
 5.5 
 5.7 
 1.5 
 0.7 
 4.9 
 7.7 
 
 10.6 
 
 10.4 
 8.8 
 
 -2.1 
 7.0 
 6.3 
 4.5 
 7.1 
 
 -0.5 
 1.1 
 2.9 
 0.1 
 1.5 
 6.4 
 4.3 
 4.0 
 1.9 
 0.6 
 
 -0.6 
 7.7 
 1.2 
 2.5 
 
 -1.7 
 4.6 
 3.0 
 0.5 
 7.2 
 
 15.1 
 5.9 
 
 10.0 
 13.4 
 8.9 
 10.4 
 10.2 
 10.1 
 8.4 
 11.3 
 4.8 
 7.8 
 10.0 
 4.8 
 7.1 
 6.2 
 10.3 
 7.0 
 8.9 
 7.0 
 11.1 
 9.5 
 9.2 
 7.9 
 8.3 
 7.4 
 9.4 
 8.8 
 7.9 
 12.5 
 10.2 
 7.7 
 6.5 
 9.4 
 6.3 
 6.9 
 5.7 
 3.2 
 7.6 
 7.4 
 2.4 
 5.2 
 1.7 
 8.3 
 6.2 
 6.7 
 7.7 
 1.9 
 4.9 
 4.1 
 6.2 
 2.7 
 4.4 
 
B-9 
 
 Table B-3. Estimates of Median Income of Four-Person Families, Using Estimated Components of Variance 
 From CPS 
 
 State 
 
 
 
 
 
 
 
 Percent change 
 
 
 1979 
 census 
 
 1981 
 estimte 
 
 1982 
 estimate 
 
 1983 
 estimate 
 
 1984 
 estimate 
 
 
 
 
 
 
 1979-84 
 
 1979-81 
 
 1981-82 
 
 1982-83 
 
 1983-84 
 
 18,319 
 
 21,386 
 
 22,980 
 
 24,058 
 
 26,055 
 
 42.2 
 
 16.7 
 
 7.5 
 
 4.7 
 
 8.3 
 
 22,027 
 
 25,908 
 
 26,623 
 
 29,040 
 
 33,701 
 
 53.0 
 
 17.6 
 
 2.8 
 
 9.1 
 
 16.1 
 
 19,424 
 
 22,936 
 
 24,400 
 
 24,448 
 
 26,770 
 
 37.8 
 
 18.1 
 
 6.4 
 
 0.2 
 
 9.5 
 
 23,772 
 
 28,226 
 
 29,624 
 
 33,664 
 
 36,652 
 
 54.2 
 
 18.7 
 
 5.0 
 
 13.6 
 
 8.9 
 
 22,107 
 
 25,743 
 
 27,037 
 
 29,024 
 
 31,832 
 
 44.0 
 
 16.4 
 
 5.0 
 
 7.3 
 
 9.7 
 
 25,712 
 
 30,345 
 
 32,490 
 
 35,613 
 
 39,573 
 
 53.9 
 
 18.0 
 
 7.1 
 
 9.6 
 
 11.1 
 
 22,669 
 
 26,349 
 
 27,541 
 
 30,152 
 
 33,214 
 
 46.5 
 
 16.2 
 
 4.5 
 
 9.5 
 
 10.2 
 
 26,014 
 
 30,460 
 
 31,501 
 
 35,044 
 
 39,588 
 
 52.2 
 
 17.1 
 
 3.4 
 
 11.2 
 
 13.0 
 
 22,266 
 
 25,628 
 
 26,636 
 
 28,199 
 
 29,815 
 
 33.9 
 
 15.1 
 
 3.9 
 
 5.9 
 
 5.7 
 
 23,279 
 
 26,460 
 
 27,713 
 
 28,442 
 
 30,583 
 
 31.4 
 
 13.7 
 
 4.7 
 
 2.6 
 
 7.5 
 
 23,014 
 
 25,862 
 
 26,613 
 
 27,432 
 
 30,751 
 
 33.6 
 
 12.4 
 
 2.9 
 
 3.1 
 
 12.1 
 
 25,410 
 
 29,413 
 
 30,923 
 
 31,786 
 
 31,902 
 
 25.5 
 
 15.8 
 
 5.1 
 
 2.8 
 
 0.4 
 
 25,111 
 
 28,774 
 
 29,242 
 
 30,172 
 
 31,781 
 
 26.6 
 
 14.6 
 
 1.6 
 
 3.2 
 
 5.3 
 
 23,320 
 
 27,145 
 
 28,572 
 
 28,751 
 
 30,774 
 
 32.0 
 
 16.4 
 
 5.3 
 
 0.6 
 
 7.0 
 
 24,044 
 
 27,780 
 
 28,352 
 
 30,686 
 
 33,655 
 
 40.0 
 
 15.5 
 
 2.1 
 
 8.2 
 
 9.7 
 
 22,351 
 
 25,850 
 
 26,780 
 
 26,946 
 
 28,530 
 
 27.6 
 
 15.7 
 
 3.6 
 
 0.6 
 
 5.9 
 
 21,891 
 
 25,269 
 
 25,983 
 
 27,601 
 
 29,953 
 
 36.8 
 
 15.4 
 
 2.8 
 
 6.2 
 
 8.5 
 
 20,511 
 
 24,497 
 
 25,698 
 
 26,913 
 
 28,682 
 
 39.8 
 
 19.4 
 
 4.9 
 
 4.7 
 
 6.6 
 
 18,674 
 
 21,392 
 
 22,535 
 
 22,877 
 
 25,419 
 
 36.1 
 
 14.6 
 
 5.3 
 
 1.5 
 
 11.1 
 
 21,438 
 
 24,984 
 
 26,094 
 
 26,005 
 
 28,657 
 
 33.7 
 
 16.5 
 
 4.4 
 
 -0.3 
 
 10.2 
 
 22,127 
 
 25,430 
 
 26,562 
 
 27,801 
 
 30,713 
 
 38.8 
 
 14.9 
 
 4.5 
 
 4.7 
 
 10.5 
 
 23,627 
 
 27,636 
 
 29,250 
 
 31,476 
 
 34,048 
 
 44.1 
 
 17.0 
 
 5.8 
 
 7.6 
 
 8.2 
 
 26,203 
 
 30,828 
 
 32,048 
 
 35,445 
 
 38,664 
 
 47.6 
 
 17.7 
 
 4.0 
 
 10.6 
 
 9.1 
 
 21,862 
 
 25,220 
 
 25,764 
 
 28,876 
 
 31,093 
 
 42.2 
 
 15.4 
 
 2.2 
 
 12.1 
 
 7.7 
 
 22,757 
 
 26,878 
 
 28,313 
 
 30,779 
 
 33,146 
 
 45.7 
 
 18.1 
 
 5.3 
 
 8.7 
 
 7.7 
 
 20,214 
 
 22,858 
 
 23,437 
 
 22,625 
 
 25,102 
 
 24.2 
 
 13.1 
 
 2.5 
 
 -3.5 
 
 10.9 
 
 19,772 
 
 23,077 
 
 24,325 
 
 26,375 
 
 28,322 
 
 43.2 
 
 16.7 
 
 5.4 
 
 8.4 
 
 7.4 
 
 19,944 
 
 22,778 
 
 22,806 
 
 24,435 
 
 28,051 
 
 40.6 
 
 14.2 
 
 0.1 
 
 7.1 
 
 14.8 
 
 20,668 
 
 24,259 
 
 25,953 
 
 26,849 
 
 28,820 
 
 39.4 
 
 17.4 
 
 7.0 
 
 3.5 
 
 7.3 
 
 21,086 
 
 24,552 
 
 24,761 
 
 26,709 
 
 28,188 
 
 33.7 
 
 16.4 
 
 0.9 
 
 7.9 
 
 5.5 
 
 19,685 
 
 22,914 
 
 24,672 
 
 24,330 
 
 25,220 
 
 28.1 
 
 16.4 
 
 7.7 
 
 -1.4 
 
 3.7 
 
 19,693 
 
 22,848 
 
 24,042 
 
 24,289 
 
 26,121 
 
 32.6 
 
 16.0 
 
 5.2 
 
 1.0 
 
 7.5 
 
 19,926 
 
 22,873 
 
 24,488 
 
 25,129 
 
 27,060 
 
 35.8 
 
 14.8 
 
 7.1 
 
 2.6 
 
 7.7 
 
 18,150 
 
 20,935 
 
 21,858 
 
 22,158 
 
 23,429 
 
 29.1 
 
 15.3 
 
 4.4 
 
 1.4 
 
 5.7 
 
 17,893 
 
 20,619 
 
 21 ,409 
 
 21,872 
 
 22,505 
 
 25.8 
 
 15.2 
 
 3.8 
 
 2.2 
 
 2.9 
 
 21,412 
 
 25,155 
 
 25,730 
 
 27,553 
 
 29,108 
 
 35.9 
 
 17.5 
 
 2.3 
 
 7.1 
 
 5.6 
 
 20,659 
 
 24,599 
 
 25,766 
 
 27,111 
 
 30,118 
 
 45.8 
 
 19.1 
 
 4.7 
 
 5.2 
 
 11.1 
 
 22,521 
 
 26,632 
 
 27,887 
 
 28,729 
 
 32,014 
 
 42.2 
 
 18.3 
 
 4.7 
 
 3.0 
 
 11.4 
 
 20,776 
 
 24,378 
 
 24,914 
 
 25,373 
 
 26,626 
 
 28.2 
 
 17.3 
 
 2.2 
 
 1.8 
 
 4.9 
 
 19,961 
 
 23,118 
 
 24,174 
 
 24,329 
 
 25,718 
 
 28.8 
 
 15.8 
 
 4.6 
 
 0.6 
 
 5.7 
 
 24,641 
 
 29,049 
 
 29,485 
 
 29,383 
 
 31,432 
 
 27.6 
 
 17.9 
 
 1.5 
 
 -0.3 
 
 7.0 
 
 23,757 
 
 28,206 
 
 29,467 
 
 31,739 
 
 34,117 
 
 43.6 
 
 18.7 
 
 4.5 
 
 7.7 
 
 7.5 
 
 19,257 
 
 22,348 
 
 23,850 
 
 24,074 
 
 25,046 
 
 30.1 
 
 16.1 
 
 6.7 
 
 0.9 
 
 4.0 
 
 21,924 
 
 25,497 
 
 27,079 
 
 27,601 
 
 29,067 
 
 32.6 
 
 16.3 
 
 6.2 
 
 1.9 
 
 5.3 
 
 21,572 
 
 24,686 
 
 26,101 
 
 25,282 
 
 26,898 
 
 24.7 
 
 14.4 
 
 5.7 
 
 -3.1 
 
 6.4 
 
 24,438 
 
 28,235 
 
 29,317 
 
 31,015 
 
 31,145 
 
 27.4 
 
 15.5 
 
 3.8 
 
 5.8 
 
 0.4 
 
 24,394 
 
 28,093 
 
 29,132 
 
 30,060 
 
 32,167 
 
 31.9 
 
 15.2 
 
 3.7 
 
 3.2 
 
 7.0 
 
 22,688 
 
 25,825 
 
 27,668 
 
 27,819 
 
 28,847 
 
 27.1 
 
 13.8 
 
 7.1 
 
 0.5 
 
 3.7 
 
 24,752 
 
 28,612 
 
 29,511 
 
 31,738 
 
 33,325 
 
 34.6 
 
 15.6 
 
 3.1 
 
 7.5 
 
 5.0 
 
 31,018 
 
 36,985 
 
 36,820 
 
 42,068 
 
 43,760 
 
 41.1 
 
 19.2 
 
 -0.4 
 
 14.3 
 
 4.0 
 
 24,966 
 
 29,193 
 
 30,440 
 
 32,338 
 
 34,000 
 
 36.2 
 
 16.9 
 
 4.3 
 
 6.2 
 
 5.1 
 
 ME 
 NH 
 VT 
 MA 
 Rl. 
 CT 
 NY 
 NJ. 
 PA 
 OH 
 IN. 
 IL . 
 Ml. 
 Wl. 
 MN 
 IA. 
 MO 
 ND 
 SD 
 NE 
 KS 
 DE 
 MD 
 DC 
 VA 
 WV 
 NC 
 SC 
 GA 
 FL. 
 KY 
 TN 
 AL- 
 MS 
 AR 
 LA. 
 OK 
 TX 
 MT 
 ID. 
 WY 
 CO 
 NM 
 AZ 
 UT 
 NV 
 WA 
 OR 
 CA 
 AK 
 HI. 
 
B-10 
 
 Table B-4. Comparison of Projected Components and MLE's, by Year 
 
 (All variance components shown divided by 10 5 ) 
 
 Year 
 
 Four-person 
 
 Wtd. avg. 
 3- and 5- 
 
 Covariance 
 
 r 
 
 Difference 
 2*log-Lklhd 
 
 1981: 
 
 
 
 
 
 
 Projected 
 
 MLE 
 
 4.154 
 2.069 
 
 3.747 
 2.591 
 
 3.500 
 2.315 
 
 0.89 
 1.00 
 
 0.49 
 
 1982: 
 
 
 
 
 
 
 Projected 
 
 MLE 
 
 4.590 
 7.082 
 
 4.003 
 12.038 
 
 3.803 
 9.234 
 
 0.89 
 1.00 
 
 3.19 
 
 1983: 
 
 
 
 
 
 
 Projected 
 
 MLE 
 
 5.125 
 8.774 
 
 4.412 
 9.749 
 
 4.219 
 9.248 
 
 0.89 
 1.00 
 
 1.67 
 
 1984: 
 
 
 
 
 
 
 Projected 
 
 MLE 
 
 5.819 
 18.058 
 
 5.244 
 13.616 
 
 4.900 
 2.160 
 
 0.89 
 0.14 
 
 5.57 
 
 :• 
 
 ~ 
 
 ADQ0QnE733m 
 
 * U.S. G.P.0.:1992-311-892:60203 
 
U.S. Department of Commerce 
 BUREAU OF THE CENSUS 
 Washington, D.C. 20233 
 
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 COM 202 
 
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