I nput-output analysis is a tec h n ique designed to examine the output of a system when the variable i np uts are changed. Cohn and Millman ( 1 975) surveyed the development of the educational production function (output) for elementary and secondary education in the U nited States and summarized the major studies using input-output analysis. The emphasis is placed on studies utilizing production functions based on simultaneous equation systems (Cohn & Millman, 1 975, pp. 31 -46). Some of the inputs used in more than one of the 23 studies are class size, student-staff ratio, teachers' experience, teachers' salary , teache r tu rnover, school building size o r age , library and textbook supply. Outputs are evaluations of pupil performance usually measured by standardized achievement tests, verbal ability tests, reading ability, school holding power, or students going on to higher education. There is a lack of consistent results from the studies; however, the authors point out that some school components (inputs) have been shown to have a positive influence "in a number of places and at a number of times" (p. 47). Those compone,liIts are teacher experience, salary, and facilities.
Averch and his associates (quoted in Cohn & Millman, 1 975) conciude after reviewing these and other existing studies:
Research has not identified a variant of the existing system that is consistently related to students' educational outcomes (p. 47).
They state that the answer lies not in g iving up educational research but in "refining m easures of cognitive ability ... non-cognitive functioning ... better data col/ection ... and more sophisticated data manipulation and analysis" (p. 48). Perhaps the largest and most controversial of i nput-output studies is the Coleman report published in 1 966 (discussed in Cohn & Millman, 1 975, pp. 37- 38). It was criticized for the choice of measurem e nt and handling of data. Many conten d that the manner i n which the regression technique was used made any strong showing by the school factors difficult to determine.
Ste pw i s e reg ress i o n req u i re s t h e statistical ass u m pt i o n of i ndepe ndence of variables ... Where such i ndepende nce i s not present ... the first variables to be entered (in t his case nonschool factors) will appear most potent ... In fact, the nonschool and school factors may be so nested within each other that their effects cannot be so arbitrarily separated (Cohn & Millman, 1 975, p. 37).
An input-output educational model was developed in 1 971 using data from 53 Pennsylvania secondary schools (Coh n & Mi"man , 1 975). It used the most extensive number of i nputs and outputs ever analyzed i n a simultaneous equation context. The 31 input variables listed as examples of those used in the model is only a subset of the Pennsylvania Department of Education data which were used. Other i nput variables (nonschool) are compressed into a set of four socioeconomic variables. N ot a" i n put variables are used i n every analysis. OutPl,.lt variables are related to twelve g oals which are interactive and feedback (or input) into other models .
... endogenous (output) variables were chosen in a given equation when they appeared to have relatively high correlations with the respective dependent variable - provided, however, that an a priori arg u ment cou ld su pport the i r i nclusion i n the mode l (Co h n & Mi"man, 1 975, p.61 ).
Specifyi ng the set of exogenous variables "was i nfluenced by the desire to i nvestigate as many of the instrumental (manipulative) variables as possible" (p. 6 1 ). The authors observe that while "non-school variables contribute a l arge po rtion of the explanatory powe r of the model, it is equally beyond question that school related factors are also important" (p. 75). The authors suggest that changes in the internal reallocation of resources within schools might affect changes in output (pp. 76-77). They also state that the main thrust of the analysis is that when compari ng schools, those "with diffe rent input levels ought to expect different output levels" (pp. 78-79). Cohn and Mi"man ( 1 9 75) co nclude, howeve r, that "reg ressio n a n alysi s o n ly d escri bes the educational production process, and does not explicitly accou nt for managerial objectives and constraints" (Cohn & Mi"man, 1 975, p. 91 ).
Mathematical programming is recommended by Cohn and Mi"man (1 975) for modeling the decision making process for manag erial objectives. Although linear programmi ng is the most widely used mathematical technique, goal prog ram ming may be more re levant. G oal prog ra m m i ng is described as follows:
Goal prog ramming is a special type of linear programming. I n li near prog ramming o nly o ne goal can b e i ncorporated i nto the o bj ective fu ncti o n to be m ax i m i ze d or m i n i m i z e d . I n g o a l pro g ramming more than o n e g oal can b e incorporated i nto the objective function. Envi ro n m e ntal conditi ons such as resource availability are put as con strai nts. Each goal is set at a level desired by the decision maker. This level need not be the best possible o n e , and it m ay o r m ay n ot be attai n ab l e d u e to the limitations of available resources. Goal programming wi" provide
the set of x values that satisfied the constraints and comes closest to the targets of the decision maker as represented by the stipulated levels of the different goals" (Cohn & Millman, 1 975, p. 93). .
One of the conclusions reached in this study is that "the technique of goal programming is particularly suitable for implementation at the district level" (Cohn & Millman, 1 975, p. 97). However, the difficulty of estimating the educational production function (output) is such that large changes in educational manipulative variables (input) based on using this technique are not recommended (p. 97).
Other authors also recommend input-output analysis and linear programming for solving educational problems involving the allocation of resources "in such a way that the outcome is optimized (maximized or minimized)" (Van Dusseldorp, et aI., 1 971 , p. 58). They also distinguish between an "open" system and a "closed" system, the criteria bei ng that an open system is one "exchanging energy with the environment in any form", (Van Dusseldorp, et aI., 1 971 , p. 1 6). By this definition, school districts are open systems. Input-output analysis has been used extensively in educational research and, therefore, will be used in the literature-based integrated financial planning model presented i n this chapter.
When using input-output analysis for integrated financial planning for school districts, all of the above-mentioned items are inputs to the model:
Mission Statement
Long Term Goals and Objectives Exogenous Factors
SWOT or SWOP Analysis
GAP Analysis Strategies
Academic Plan Financial Plan
When manipulation of primary planning variables results i n satisfactory endogenous outputs (cash balances) of the sub model, the output of the main integrated financial planning model will be integrated academic and financial plans.