College and Research Libraries MAURICE P. MARCHANT University Libraries as Economic Systems The possibility of developing an economic theo~y of libraries is ex- plored. The concepts of economic theory, economic system, and eco- nomic model are discussed as potentially applicable to libraries. Two types of such models are developed from data drawn from university libraries. One predicts professional staff size from two variables: col- lect-ion size and collection decentralization. The other identifies a set of library inputs composed of professional staff size, subprofessional staff size, and annual acquisitions rate as a consistently good predictor of library expenditures and a stable measure of library input. THE FEASIBILITY OF AN ECONOMIC THE- ORY of the library has recently been sug- gested. 1 Were such a theory to be devel- oped sufficiently to provide mathemati- cal models, it is suggested that library planning and budgeting might be mea- surably improved. Economic theory attempts to define and generalize the relationship existing among variables having to do with the production and distribution of wealth. Its method is largely deductive: on the basis of a set of known or assumed facts, a hypothesis is established and a model is set up. While the model may be simple or complex, it is a simplifica- tion of the real world to the extent that it does not include all the variables that could possibly be included. It is likely Maurice P. Marchant is acting .director, School of Library and Information Sciences, Brigham Young University, Provo, Utah. This . article was one of two winners of the 1975 Research Competition sponsored by the ALA Library Research Round Table and was p1'esented by the author on June 30, 1975, at the Annual Conference of the association in San Francisco. to emphasize those that are important to the needs of the study and those that are readily measurable. The effect of those not included cumulates as error variance in the model. An ex~mple of an economic theory is that price tends to move to the level at which demand is equal to supply. Another is that a rise in price tends, sooner or later, to decrease demand and to increase supply. Such theories require checking against data obtained from the real world. If empirical data support the relationship proposed by the theory, we may accept the theory as a useful assumption until additional evidence appears which con- flicts with the theory, requiring its modi- fication or abandonment. Because of the difficulties associated with environ- mental control in economic studies, eco- nomic theories indicate tendencies rath- er than universal laws. Two different concepts are covered by the term "economic system." Both are concerned with the interrelationship of a set of economic variables. One is con- cerned with the ways in which a given society organizes its means of produc- tion and distribution of materia] wealth I 449 L------------------------------------------------------------------- - - - ,-----------------------------------------------------------------------------~ 450 I College & Research Libraries • November 1975 and services and might be referred to as, for example, the American or British economic system. The other concept ad- heres to general systems theory and is concerned with identifying interrela- tionships between variables within a sys- tem: the processing of inputs into out- puts, the effect of change in one vari- able on others, and so forth. This paper is concerned with the second concept, but is limited largely to the study of inputs. The kinds of variables incorporated into economic models are those associat- ed with production. They might be mea- sures of wealth or productivity or those thought to affect or to be affected by them. Obviously, personnel, materiel, and money are important economic vari- ables. For example, the model presented later in this paper in which physical de- centralization serves as a predictor of staff size is an economic model because the emphasis is on personnel as a repre- sentation of funding. In another con- text, physical decentralizati0n might be fitted into a political, rather than an economic, model in which the object is to study faculty influence. In model building, theoretical as- sumptions of cause and effect relation- ships are made and tested. In doing so, within the concept of general systems theory, variables become categorized as input, intervening, and output vari- ables. Speaking generaUy, they might be described as follows. Inputs are those things that enter the system from out- side, such as books and personnel in a library. Outputs are products which are created in the system with the use of in- puts and exported back into the en- vironment, such as library service. Inter- vening variables are affected by inputs and, in turn, affect outputs. But the label given a variable under one set of circumstances may not apply in another. Thus an input variable in one system might be an intervening or output vari- able in another system. Variables are also categorized as in de- pendent and dependent. An indepen- dent variable has the capacity to predict the value of a dependent variable, and there is often a presumption of causal relations between them. These terms are more general than, but not unrelated to, the concepts of input, intervening, and output. Within a systems study, one would expect inputs to be independent variables, outputs to be dependent vari- ables, and intervening variables to be both. Two relevant research projects regard- ing libraries have emerged recently. One computed the annual growth rates of several variables in academic libraries and developed prediction equations for estimating various staff, collection, and cost values. 2 The other, noting that the distribution of many library statistics is skewed, approached the study of those statistics with improved success through their logarithmic values. 3 These studies provide a sense of con- fidence to the assumption that general- ized influences are at work which affect all or large groups of academic li- braries. If so, their identification and measurement may help in the construc- tion of an economic theory of the li- brary which librarians might find useful in decision making. The thrust of this paper is to provide recently identified eVidence supportive of that position. However, these studies have been confined to academic libraries of limited size range, above 500,000 vol- umes. They were undertaken to explore a set of readily available data for evi- dence that might support the concept that libraries are economic systems and to identify points of departure for fur- ther research. Two groupings of predic- tive models will be discussed, one deal- ing with the size of the professional staff and the other with measures of in- put. PRoFESSIONAL STAFF SIZE It was found in a study of twenty- two libraries of Association of Research Libraries ( ARL r member institutions that the ratio of professional staff mem- bers (mostly librarians) to 1,000 stu- dents was 4.4 (with a standard deviation of 3.5). 4 Comparisons with other vari- ables in the study demonstrated that the ratio had a high relationship with sev- eral funding measurements. It took its place among them as a measure of li- brary wealth, indicating that it reflects financial input in relation to the num- ber of students who have a potential call on the library. This relationship was confirmed by factor analysis as well as by the magnitude of the Pearson product-moment correlation coefficients, which was as high as .99.5 It was appar- ent that funding is a fairly good pre- dictor of professional staff size. The high standard deviation relative to the mean of the librarian-to-student ratio results from both high variance in wealth among libraries and a skewing toward high wealth caused by a few es- pecially wealthy libraries. The number of professional staff members was also found to be highly related to several other organizational variables. Moreover, when their interre- lationships were graphically depicted, number of librarians occupied a central position among them much like the axle of a wheel. 6 These variables, .along with their correlations with professional staff size, were: ( 1) collection size, .72; (2) currently received serial titles, .54; ( 3) number of volumes acquired during the school year, .56; ( 4) physical decentral- ization of the collection, . 71; and ( 5) number of doctoral degrees . (excluding law, medical, and dental doctorates) granted that year by the university to which the library belongs, .62. It is not difficult to imagine staff size being affected by these variables. The size and growth rate of the collection generate work to process .and service it. . A large graduate program, which is the primary justification of a large collec- tion, would be expected to generate ser- vice demands. Overfragmentation of Economic Systems I 451 the collection could cut down on the efficient use of personnel. However, considering these variables' lack of independence from each other and the small number of libraries in the study, it would be surprising if they could all fit significantly into a formula predicting professional staff size. The easiest procedure for constructing an optimum predictive equation is through linear multiple regression analysis, in which combinations of independent variables are tested for significance and compared for predictive capacity. The best combination, as it turned out, in- cluded two variables: collection size and decentralization. Together, they explain .almost 80 percent of the variance in professional staff size. If these relation- ships are causal and accurate, they offer help in predicting staff needs under changing conditions of collection size and decentralization. The predictive equation is Y = 22.9 + 0.235Xl + 67.8X2 in which Y is number of professional staff members, xl is collection size in 10,000s of volumes, and X2 is the decen- tralization index. The decentralization index is computed from the formula D = B2 /Ct in which D is the decentralization index .and is equal in this case to X2, B is the number of branches, and Ct is the total number of volumes (in 1,000s) in the university library system and is ten times the value of X1 in this case. The deriva- tion of the formula for decentraliza- tion ·is explained in the dissertation. 7 While the correlation between the inde- pendent variables was insignificant ( .28), the involvement of collection size in both made the formula nonlinear. The prediction equation has certain limitations. First, it was derived from libraries varying in size from 500,000 to 2,100,000 volumes and with a mean size of 1,160,000 volumes. The mean of the decentralization indexes was 0.084, and 452 I College & Research Libraries • November 1975 the indexes ranged from 0.000 to 0.586. The equation functions best with li- braries having values close to the mean, and the extent of error can be expected to increase as the values deviate from it. There is also a certain potential for error in the prediction due to the 20 percent of the variance which was un- accounted for. The expected error is as much as 17 about once iil twenty cases. SETS OF LIBRARY INPUTS The usefulness of professional staff size as a measure of input requires test- ing. But it is part of a more general question which asks what measurements constitute interrelated sets of inputs. It would be helpful if a set of mutually complementary inputs could be identi- fied which are stable over time. Inputs in this case consist of resources entering the library from the environ- ment. Funding can be thought of as an input. So can the resources the budget provides, such as personnel and library collection components. The dollar has been used as a measure of input by most libraries; but it has both advantages and disadvantages. As a means of exchange, it can stand for many different inputs, including person- nel playing different roles and drawing differing salaries, books and serials, and various other materials and services li- braries need. Consequently, the dollar can be used as a unit of input by which, in one sense, various inputs can be com- pared. For example, a librarian costing $10,000 a year can be equated to 1,000 books averaging $10 each. But the potentially available freedom to choose what inputs to exchange the library's budget for may be delusionary. If a given set of goals is desired, its ac- tualization may predetermine the opti- mum mix of inputs required. If so, and we understand the optimum system that will achieve it, the choice of inputs and their quantities have already been deter- mined, and the inputs are not indepen- dent of each other. Another weakness in using money as a measure of input is its instability dur- ing periods of inflation or recession. Consequently, it ~ould be helpful if other, more stable, inputs could be iden- tified. RESEARCH METHODOLOGY To study input stability, two sets of data were subjected to regression analy- sis. The first had been collected for the dissertation. It included three measure- ments of funding (total operating ex- penditures, staff expenditures, and li- brary materials expenditures) and five measurements of the basic groups of re- sources funded by libraries ( the total number of staff members, professional staff size, subprofessional staff size, the number of volumes acquired, and the number of current serials received). However, it was also limited to one year's data from only twenty-two li- braries. The second set was the data based on punched cards regarding the libraries of fifty-eight ARL member in- stitutions compiled by the Purdue Uni- versity Library and Audio Visual Cen- ter. 8 While it lacked measurements for number of current serials received, the sample size was much larger and the data covered twenty-one years. Conse- quently, the smaller data base was used for a series of preliminary analyses to determine whether the lack of that one measurement might be a serious loss. The second set was then analyzed, first, to see to what extent it confirmed the preliminary analyses and, second, to de- termine the extent to which the relation- ships might have varied over time. PRELIMINARY ANALYSIS SERIES Total operating expenditures were best predicted, using the first set of data, by the size of the professional staff and number of acquisitions. Once they had entered the regression analysis, none of the other measurements had a significant further predictive capability. The two, as a set, accounted for 83 per- cent of the variance in total operating expenditures. Expenditures for library materials were best predicted by annual number of acquisitions and the professional staff size, which accounted for 76 per- cent of the variance in library materials expenditures. Staff expenditures (including salaries and wages) were best predicted by the size of the professional staff alone, which accounted for 77 percent of the variance in these expenditures. None of the other potential dependent variables, including the number of subprofession- al staff members, contributed significant- ly to the prediction. The relationships between the three expenditures were also probed. Adding the staff and library materials expendi- tures together accounted for nearly 90 percent of the total operating expenses in the average of the libraries studied and would be expected, therefore, to provide an excellent prediction. Staff ex- penditures alone explained 91 percent of the variance in total expenditures, and library materials expenditures add- . ed 8 percent more to the explanation, for a total control of 99 percent. Anticipating that the relationships identified in these preliminary analyses would be generally consistent with those in the larger study, several insights were possible. First, the number of current serial titles offered little supplementary pre- dictive potential to any of the expendi- ture variables. This is not to say that the cost of serials is unimportant. Rather, it suggests that ( 1) the number of serial titles is not a good indication of serial cost, and ( 2) the number of serial titles varies with such other variables as nmn- ber of professional librarians to such an extent that its predictive potential, such as it is, is largely duplicative. Economic Systems I 453 Second, the strongest predictors of to- tal operating expenditures are profes- sional staff size and number of volumes acquired. Of these, professional staff size appears to be the stronger. Number of volumes acquired affects expendi- tures largely through library materials expenditures, as would be expected; but professional staff size is an important predictor for both library materials and staff expenditures. Third, with an increase in the num- ber of libraries in the study, number of subprofessional staff members might emerge as a significant predictor of total operating and staff expenditures. . Fourth, total staff size did not provide a useful index for this study. The com- ponents of it, professional and subpro- fessional staff size, are more useful. ANALYSIS OF SERIES OvER TIME The preliminary analyses provided a sense of confidence that the lack of data regarding serials from the larger data base would not result in the lack of an important variable for the pur- pose of this study. As the regression analyses were completed, using the data for each year for making a set of re- gression .analyses like . those in the pre- liminary series, the patterns that had been expected emerged. Since there was some overlap between the libraries rep- resented in the two data bases, this should not come as a surprise. But nei- ther was it certain beforehand. Of the twenty-two libraries in the preliminary series, four were not among the fifty- eight libraries of the larger series. No library over 2,100,000 volumes in size in 1968 was among the twenty-two in the preliminary series, whereas twelve of the fifty-eight in the larger data base were above that size in 1968. That the pattern was similar between the two samples and from year to year in the second sample suggests that the pattern can be relied upon, within limits, from year to year and across a fairly wide 454 I College & Research Libraries • November 1975 size range. Moreover, predictions of in- dividual library expenditures and their confidence intervals were made possible. It is that measure of consistency, sup- plemented by the Baumol and Marcus and Pr.att observations, which provides encouragement to persist in the search for a theory of library economy. One purpose of this study was to try to determine whether the staff size and acquisitions measurements might have greater stability over time th.an the ex- penditures measurements. One way to test stability is to see how constant the cumulative proportionate variance, as a measure of predictive capacity, remains from year to year as compared with the regression coefficients which are generat- ed in sets of yearly regression analyses in which the staff size and acquisitions v.aria hies serve to predict the expendi- tures levels. Another evidence is the ex- tent to which variance in the cumulative proportionate variance and regression coefficients is a function of time. If the ability of a set of independent variables to predict the value of a dependent variable remains constant, the cumulative proportionate variance would not change. But the effect of in- flation on the cost of the independent variables over the years would cause changes in the regression coefficients. The magnitude of variance from year to year is measured by the standard de- viation. The extent to which the vari- ance is constant over time would be ex- pressed by a simple correlation between value of the variable .and the year. Summaries of the sets of analyses are given in Tables 1 through 4. They pro- vide the data required to evaluate ( 1 ) the ability of specific sets of indepen- dent variables to predict library expend- itures, ( 2) variance over time in that predictive capacity, ( 3) the mean value of regression coefficients associated with each independent variable in the set, ( 4) variance in the regression coeffi- cients, and ( 5) the extent to which vari- ance was a function of time. In addi- tion, in order that a rough comparison can be made of the difference in vari- ance between the regression coefficients and cumulative proportionate variance, the standard deviations were normalized by showing them as a ratio of their mean values. This normalized value is known as a coefficient of variation. Table 1 summarizes data regarding the relationships of total operating ex- penditures with staff and library materi- als expenditures during the twenty-one- year period. These data are presented largely to provide a basis for compari- son with the other three tables. This set of independent variables is shown to be an excellent predictor of total operat- ing expenditures (predicting, in an av- erage year, with 98.47 percent accuracy) with little deviation in predictive capaci- ty from year to year ( 1.94 percent stan- dard deviation). Staff expenditures is the more stable predictor. (Comparing the coefficients of variation determines their relative variability.) Neither the regression coefficients nor the cumula- tive proportionate variance changed in TABLE 1 SuMMARY OF ANALYSES RELATING ToTAL OPERATING ExPENDITUREs TO STAFF AND LIBRARY MATERIALS ExPENDITURES OvER TwENTY-ONE YEARS Standard Correlation Mean Deviation S.D./Mean with Year Regression coefficients Staff expenditures 1.1553 0.1281 0.1114 -0.1390 Library materials expenditures 1.1085 0.2383 0.2150 -0.1951 Cumulative proportionate variance 0.9847 0.0194 0.0197 -0.1089 Economic Systems I 455 TABLE 2 SuMMARY OF ANALYSES RELATING ToTAL OPERATING ExPENDITURES TO PROFESSIONAL AND SuB- PROFESSIONAL STAFF SIZE AND NuMBER OF VoLUMES AcQUffiED OvER TwENTY- ONE YEARS Regression coefficients Professional staff size Subprofessional staff size Acquisitions Cumulative proportionate variance a pattern associated with time. (The correlations with year were low and not significant at the .05 level, which was the lowest significance level tested throughout the study.) Since all three variables were affected by inflation, these nonsignificant correlations were expected. Regression coefficients associated with more constant inputs as predictors of expenditures, being immune to infla- tion, should be more highly correlated with time because the resources acquired will increase at .a slower rate than the funding expended to acquire them. Ta- bles 2, 3, and 4 provide the data gen- erated to test the constancy of three such input variables and their predictive capacity. In each case, the input vari- ables listed are those which contributed significantly, at the .05 level or better, to the prediction and which, as a set, provided the best prediction available. All three input variables were .able to enter the analyses, in Table 2, predict- ing total operating expenditures. Note that the larger sample size and breadth of years covered allowed for the inclu- Standard Correlation Mean Deviation S.D./Mean with Year 12418. 6028. 0.4854 0.9179 3915. 1601. 0.4088 0.4658 4.0917 2.1690 0.5301 0.2736 0.9309 0.0309 0.0385 -0.2194 sion here of subprofessional staff size, which did not emerge in the preliminary study. In seventeen of the twenty-one yearly analyses, it emerged as a better primary supplement to professional staff size than did number of volumes .acquired. Together they explained an average of 93.09 percent of the variance with a standard deviation of 3.09 percent, a substantial improvement over the pre- liminary analysis results of 83 percent. The inclusion of the larger number of libraries appears to have improved the statistical measurements of the relation- ships. While the prediction is lower than was attributed to the two expenditures variables in Table 1, it is remarkably high and stable. In only one year did it drop below 90 percent. The coefficients of variation (S.D ./ Mean) of the regression coefficients were much higher than those in Table 1 and indicate a fairly high variation in regression coefficients over the years. Much of the variation was not random but, rather, was the result of increases TABLE 3 SUMMARY OF ANALYSES RELATING LIBRARY MATERIALS EXPENDITURES TO PROFESSIONAL STAFF SrzE AND NuMBER OF VoLUMES AcQumED- ovER TwENTY-ONE YEARs Standard Correlation Mean Deviation S.D ./ Mean with Year Regression coefficients Professional staff size 3491. 1691. 0.4844 0.8186 Acquisitions 2.7042 1.1832 0.4375 0.5000 Cumulative proportionate variance 0.7508 0.1441 0.1919 -0.5109 456 I College & Research Libraries • November 1975 TABLE 4 SuMMARY OF ANALYSES RELATING STAFF ExPENDITURES To PROFESSIONAL AND SUBPROFESSIONAL STAFF SIZE OVER TWENTY-ONE YEARS Regression coefficients Professional staff size Subprofessional staff size Cumulative proportionate variance over the years that are the result of in- flation. That was particularly true of the regression coefficients associated with professional staff size and, to a more moderate extent, with subprofessional staff size. Tables 3 and 4 summarize the data from the sets of analyses predicting li- brary materials expenditures and staff e~penditures, respectively. As expected from the preliminary analysis, profes- sional staff size entered both sets. In ad- dition, subprofessional staff size entered the staff expenditures set, and acquisi- tions entered the library materials set. - In each set, the correlations between year and regression coefficients for both input variables were positive and signifi- cant, indicating that the regression co- efficients grow larger over the years. The staff size variables explained 93.71 per- cent of the variance in staff expendi- tures, which is comparable with the pre- dictive power of the three input vari- ables in Table 2. But control over vari- ance in library materials expenditures, of 75.08 percent, was less strong and was assoCiated with a standard deviation more than four times as large as was found in total operating expenditures. The correlations of year with the cumulative proportionate variance asso- ciated with staff and library materials expenditures indicate a tendency for a decline in predictive power in recent years. The decline is more pronounced regarding library materials expendi- tures, with which the correlation is sig- Standard Correlation Mean Deviation S.D./Mean with Year 8845. 4549. 0.5143 0.9198 3119. 955. 0.3062 0.6896 0.9371 0.0495 0.0528 -0.3576 nificant at the .05 level, than regarding staff expenditures. Overall, the data support the hypothe- sis that the staff size and acquisitions in- put variables have retained their powers to predict library expenditures. But their control has been better over total operating and staff expenditures than over library materials expenditures. Ap- parently, stability of prediction is great- er for more general funding measures than for more specific ones. CONCLUSIONS A pattern of relationship between major personnel and materials inputs with library expenditures has persisted in American university libraries for two decades. The major inputs are profes- sional and 'subprofessional staff size and number of volumes acquired. Together, they constitute a set of inputs that are stable over time and can be used in sys- tems studies comparing conditions in one year with those in another in place of the expenditures variables which are not stable. While a budget officer may not be willing to predict next year's funding needs in a specific library without great- er specificity than these three gross mea- surements provide, that officer could probably estimate this year's expendi- tures within a margin of error as small as 6 percent with 95 percent confidence and as small as 7.5 percent with 99 per- cent confidence. With some experience, he or she could likely improve substan- tially. Such accuracy is possible because many other expenditures are reflected in these three. Materials, such as paper, pencils, and card stock, are a function of the number of personnel and books acquired. While an administrator might control the costs involved in such items somewhat by bulk purchases and watch- ing for bargains, control · through these types of activities is only marginal. Moreover, attempts to economize un- duly in these areas can readily result in operational bottlenecks that inhibit ef- fective service. When a library acquires a new reference assistant, the resource commitment that will result, after the library has adjusted to the stress im- posed by that increase, will be a great deal more than that staff member's sal- ary and fringe benefits. It is more likely to be nearer $20,000 than a $10,000 an- nual salary. The demonstration, in the first part of this paper, that professional staff Economic Systems I 457 size is a function of decentralization and collection size is a minor contribu- tion to a developing economic theory of libraries. It suggests that organizational patterns might be a fruitful area for future study into that development. An- other area would be to identify the in- terrelationships between the three staff and acquisitions input variables and other resources, perhaps as part of the type of systems analysis studies and model building carried out with the use of techniques and concepts used in econometrics. Radical changes in the pattern of li- brary organizational behavior might af- fect the basic economic patterns identi- fied in this study. But the pattern has re- mained fairly constant over a twenty- year span characterized by constant change. At least for the near future, those relationships are likely to persist and to provide a basis from which fu- ture costs can be predicted. REFERENCES 1. Michael K. Buckland, "Toward an Economic Theory of the Library," in Robert S. Taylor, ed., Economics of Information Dissemina- tion: A Symposium ( Frontiers of Librarian- ship 16 [Syracuse, N.Y.: School of Library Science, Syracuse University, 1974]), p.68- 80; 2. William J. Baumol and Matityahu Marcus, Economics of Academic Libraries ( Wash- ington: American Council on Education, 1973 ). 3. Allan D. Pratt, "A Theory of Lognormal Size Distribution of Academic Libraries in the United States" (Ph.D. dissertation, Univ. of Pittsburgh, 1974) . 4. Maurice P. Marchant, "The Effects of the Decision Making Process and Related Orga- nizational Factors on Alternative Measures of Performance in University Libraries" (Ph.D. dissertation, Univ. of Michigan, 1970), p.108-11. 5. Ibid., p.120-21. 6. Ibid., p.123. 7. Ibid., p.96-97. 8. Oliver C. Dunn ~nd others, The Past and Likely Future of 58 Research Libraries, 1951-1980: A Statistical Study of Growth and Change (8th issue; Lafayette, Ind.: University Libraries and Audio Visual Cen- ter, Purdue University, 1972), p.5.