College and Research Libraries I· Forecasting Academic Library Growth -Forecasting techniques develor}ed by_ _· government · and · ind~,Y a~e being applied to various 'library statistics. These techniq~s are _ ex- plained and examples of their use discussed. B ~ETING . AN~ PJ,..ANNING PROCESS~ in academic libraries are under great stress due to tight budgets·, inflation, and un- certainty about the future. University administrators are stressing the need for cost justification and the necessity ·for short- and long-range planning. The fu- ture appears . to .-be characterized by in- creasing stress because of higher prices for materials, demands for .higher sal- aries, and growilig uncertainty about availability of fQllding. The need for planning assumes a greater importance in times of decreas- ing resources and ·retrenchment. The li- brary manager; confronted with smaller budgets and higher prices on the one hand and demands for better service on the other, must devote considerable en- ergy and effort to systematic planning. Thoughtful · and informed planning de- cisions are imperative if libraries are to continue to . function effectively as an interface between ·information and the student or researcher. The planning process is a systematic and purposeful endeavor ' which in- volves the setting of goals for the fu- ture and strategies for realizing those goals. University- . libraries function within a dynamic environment in which teaching and research goals and methods are changing. · Library planners must plan within . this environment at;1d with- in the · framework · of the university's Miriam A. Droke . is · Mad, Research De- velopment - Unit, Purdue · University Li- braries and .... Audio:.VisutJl Center, West La- fayette, Indiana. goals. The role of forecasting in plan- ning is critical. Analyses of the past and present and forecasts of probable fu- ture · events and situations give the plan- ner the framework within which deci- sions about future courses of action are made. Good information will riot neces- sarily guarantee good decisio~ or effec- tive planning; but no information or poor information may well result in bad decisions. At the present time, when the need for accurate predictive infor- mation is so great, library managers and planners have little an~lytical data about the past and ··poor forecasts · for the future. 1 · The purpose of this paper is to dis- cuss one type of information needed by library planners, namely, forecasts . of library grow~h and related factors. Fore- casting techniques will be .discussed, and examples of their use in libraries will be reviewed. The purpose of forecasting is to de- scribe what is likely to occur . under a given ··set of circumstances . at some fu- ture time. The forecast provides an in- dication 'of results at a specified time in the future if conditions · are not changed. The manager can change the likelihood of given results by ,cha~ging · go~ls · and. making deCisions · which will influence the course of events: G«imeral- ly, there are three types of forecasting techniques used in· libraries: qualitative, time series, anQ. :causal. T4ese. techniques may be used individually or in combina- tion. · /53 54 I College & Research Libraries • January 1976 QUALITATIVE TECHNIQUES Qualitative techniques are used when data are sketchy or nonexistent. They rely solely on human experience and judgment to assess the future. Some- times they are formalized by the use of rating schemes to transfer ·qualitative factors into quantitative estimates ifl: a systematic fashion. Examples of quali- tative methods are the Delphi approach, "visionary forecast," and historical anal- ogy.2 It is difficult to find examples of systematic qualitative forecasting in ac- ademic libraries; however, judgmental forecasts have been used extensively be- cause librarians do not have sufficient familiarity with quantitative techniques to use them effectively or to interpret the results. QUANTITATIVE TECHNIQUES Quantitative forecasting techniques fall into two categories, time series analysis and causal methods. Time Series Analysis Time series analysis is a statistical technique . which assumes that patterns in the past can be identified and that these patterns. will be repeated in the future. Forecasts of library growth have relied primarily on time series analysis to identify trends and to determine growth rates of trends. The technique involves fitting a line or curve to the past data and projecting the line by means of its mathematical equation. The simplest trend line is a straight line in which the variable being projected increases or decreases by the same amount in each · time period. The line is fitted by the method of least squares, so called because the sum of the squares of the deviations from the line is less than the sum of the sq~ared deviations from any other straight line. 3 The .devi- ations are the differences between the actual or observed values and the values produced by the straight line equation for each point in the past. The straight line l:s described mathe- matically as where: Y is the variable to be . forecast; a is the value of Y at the x origin; b is the slope of the line or the value to be added or subtracted in each time period; and x is the value of time; The elements a and b are both Constants as their values do not change; therefore, the projection is based on the same amount of growth or decline in each period. Figure 1 illustrates a straight line pro- jection of nonprofessional staff size in the median Association of -Research Li-- braries library. The median library is not a specific library; rather, it repre- sents a library which is at the midpoint on a scale in which Association of Re- search Libraries libraries are ranked from highest to lowest. Half the li- braries rank above the median in non- professional staff siz·e~ and ·half · rank be- low the median. The straight line shown was plotted · from a mathematical equa- tion calculated from data for the years 1962-1973. The dots on the graph show the actual or observed values for the median library. The straight line which has been drawn is that whiCh "fits" most closely the dots representing actual val- ues. The line has been extrapolated to 1980, giving an estimate of the number of nonprofessional staff in the median library assuming that · the trends of 1962-1973 remain unchanged. In reality, library growth indicators such as volumes added or volumes held do not show a- straight line · trend. Non- linear trends can exhibit constant growth rates or changing growth rates. A straight line shows a constant amount of growth, while a curve may be based on a constant annual rate {e.g., 20 per- cent) of growth or a changing rate of growth. A constant growth rate will pro- duce an exponential curve because of the effect of compounding. ·Figure 2 illustrates a projection of volumes added for the· median com- ·I l Fore casting Academic Library Growth I 55 ~ 150 .s en <; -~ ~ 8 0. 5 z 'C 100 .. 1951- 1980: A Statistical Study of Growth and Change and shows growth at an increas- ing rate; that is; a percentage growth which is increasing each year. It is clear that neither curve is suitable for a short-range forecast of volumes added for the median library. Observed values are declining, and qualitative judgment regarding library budgets, inflation, etc., would indicate that these values will de- cline further. In this case, the forecast- er must ·raise questions regarding both the long-range and short-run significance of the decline. How long will it contin- ue? Does it represent a major change in pattern? Will long-run .growth at pre- vious rates resume? This case clearly il- lustrates the importance .of experience and judgment in forecasting. The num- bers alone. do not tell the story. Time series analysis, because it as- sumes that the future will repeat the past, "is more likely to be correct over the short term than it is over · the long term, and for this reason these tech- niques provide us · with reasonably ac- curate forecasts for the immediate fu- ture but do quite poorly further into the future."5 The validity of that state- ment can be shown by looking at the forecasts shown in Figures 2 and 3. An- other shortcoming of time series analy- sis for libraries is that it cannot predict irregular change in the rate of growth. It can predict only on past rates. Fig- ure 2 clearly shows that actual values for 1972 and 1973 are deviating substan- tially from the trend line; These deviations indicate that growth 56/ College &·Research Librarief • January 1976 150 ~ 100 s:: ~ :;1 0 ..c: c "' Q) "' "' < "' Q.l E ..2 50 ~ Fig. 2 Volumes Added in Median Composite Library (Constant Growth Rate), 1951-1975 Sources: 0. C. Duqn, D. L. Tolliver, and M. A. Drake, The Past and Likely Futt~rfJ of 58 .R~search Li- bmrles, 1951-1980: A Stou.tlcal Study of Growth and Change, 9th ed. (West Lafayette, Ind.: Purdue UDi- versity Libraries and Audio-Visual Center, .1973), p.43; ' and .Q, C. Dunn,. W. F •. Seibert, and J. A. 'Scheuneman, The Past and Likely Future of 58 Research Li.brtuiu, 1951-1980: A Stati8tical Study of Growth and Change, 5th ed. (West Lafayette, Ind.: Purdue University Ll'brt¢es and Audio-Vis1,1al Center, 1969), p.43 .. may be ' 'changing. ' If . the forecast~r knows that there are factors which will change the rate of trend, suCh as bud- get. conStraints, then other · methodS ·or combinations of methods· muSt be used to forecast the particular variables in question. Caus~l Models · · The most sophisticated forecasting techniques are called causal models be- cause they relate the values of one vari- able ·to' two or more other variables. Ee0nomi.Sts use a varietY ·of these mod- els in different . applications, ·including input-output, multiple regression; and econometric models. Only multiple re- gression · models will . be considered here. The multiple ·· regression technique · as- sumes that a dependent variable, the variable ·· to be forecast (e.g·., volumes added; total operating expenditures, etc. ) , is related .to '.two or more' inde- pendent ·or causal variables whicli ·are assum~ to be "exogenous,'' that is, mit- side the control of . th~: dependent vari- ·able. The · variables which are · defined as independent are those for which val- ues are known. These values generally will not be affected directly by changes in the dependent variable. The variable to: be forecast is the dependent or "re- sultant" variable. Its ·value ·is related to and may be estimated from changes in 'the causal variables. 6 Mathematically, a functional relationship is assumed. · The standard equation is Y = a t b1x1 + b2X2 + .. ·. hmXm where: Y is the dependent variable; a is a .constant; X1, X2, Xs, ••• , Xm represent independent variables; and bh b2, ba, . . . , bm represent net regression coeffi- cients, i.e., the effect on Y of a · change in x when "allowance has been made for other independent variables.', The choice of . independent variables -will depend on. the variable to be fore- FOrecasting ·Academtc Library · Growth / ·. 57 . ' 150 Fig. 3 Volume·s Ad