Input Output in Education
Doctoral Scholar, Jawaharlal Nehru University, New Delhi
One type of analogy that has been brought into economics of education is the production function analogy. The production function claims that there exists a technical relationship between different combinations of input and output thus produced. There is some merit in viewing an institution of higher education in the context of traditional theory of the firm, whereby the university is hypothesized to maximize net social product to a set of production relations. This paper seeks to ask whether it is safe to use this economic analogy in the context of higher education, drawing parallels between universities and firms, students and customers, and so on. The discussion here seeks to identify the key economic features of higher education that make it different from for-profit industries. The task here is to make economic sense of an unusual industry. The first section explains and outlines the concept of input output used in case of firms as well as in educational institutions. The second section talks about the identification of outputs and a discussion at length of the three different outputs and the problems encountered in their valuation. It further discusses about the identification and valuation of inputs thereby leading to a deliberation on education production function which is viewed as a function of input and output. The next section brings forth the difference in productivity and efficiency in education. Hence, the arguments based from the literature are thus put forward.
An educational institute is engaged in the delivery of education as a service and helps in the formation of human capital. The delivery of service is supposed to be guided by an input-output relation in the form of production function. In familiar microeconomics the firm’s inputs and outputs are measurable, inputs are substitutable, guided by profit motive, buyers are anonymous and sellers don’t care which buyers they serve and entrepreneurs are decision makers. Well as far as higher education institutions are concerned the question that arises is then what drives institutions to strive for best if their objective is not to maximize profit.
Marginson (2009a: 208) analyses the objective function of a university as status competition. A degree from a high ranking university commands high value as the seats are limited in these institutions. Colleges thus have a control to whom they sell to by generating excess demand and then selecting the students with the characteristics they most desire (Klitgaard, 1985; Rosovsky, 1990; Litten, 1991; Duffy and Goldberg, 1998; Bowen and Bok, 1998). The competition for status adds altogether different dimensions to the nature of competition. The fight for high ranking ensures high quality institutions. These institutions thus become selective through generation of excess demand and restricting supply. This is analogous to efficiency wage where a "too high" wage rate is paid so that an employer can select individual workers on the basis of their desirable characteristics. Student quality has an efficiency wage answer – the existence of too high wage rate for student quality allows the institution to control what quality is and who they think has it (Akerlof and Yellin, 1988). Non-profit means they care about objectives- equal opportunity through educational access (Bowen and Bok, 1998). In higher education, managers appear motivated by what Cloffelter (1996) calls "the pursuit of excellence," a general goal which in practice means maintaining or improving the quality of the educational services they supply and the equity with which they are provided (Bowen and Breneman, 1993). Further, higher education market is strongly hierarchical with firms differentiated initially by their access to donative resources-the subsidy rankings. At the top of the hierarchy are the schools well-endowed with donative wealth-large endowments in the case of private schools and large government subsidies in the case of public schools-that offer expensive and high quality education at highly subsidized prices and that therefore disproportionately attract high quality students (Winston 1999). In sharp contrast to the business firm, donative commercial nonprofits can and do subsidize their customers, selling them a product at a price that is below the costs of its production (This can usefully be made more precise. The all-purpose equation for the sources and uses of funds in a firm, whether profit or nonprofit, is p + dr + g = c + v + d, where p is commercial revenue, dr is donative revenue, g is the extent of grants, c is cost of education, v is retained earnings or institutional savings, and d is dividends. Thus, the left-hand side of the equation is sources of revenue, and the right-hand side is uses. For a government aided institution, d=v=0 even dr=0. In that case g=c-p. If p is recovered from students and c is the cost incurred on them them c-p is the extent of subsidy. In case of privately funded institution g=o and dr=c-p. If dr is low, given c, p would be higher or given p, there would be pressure on the management to press c.). Thus, ‘non-profit universities are prestige maximizers, performance maximizers and revenue maximizers’ (Marginson 2009a).
Identifying and Valuing Outputs:
Bear (1974), Attiyeh (1974) and Archibald (1974) provided a list of outputs produced by a university. They can be classified into three broad categories: i) Educational output which leads to formation of human capital, having both a yield appropriable by the individual and a stream of benefits to society as a whole. ii) Informational output: in screening model, the output is information about the relative abilities of students. iii) Research output: increment in stock of knowledge which contributes towards economy’s productivity. Measurement of educational outcome is extremely important. But in the absence of any units of measurement, the valuation problem is of serious nature. As Woodhall and Blaug (1965) observe: “the first problem in considering the education industry is to define output. What is the end product of a period of schooling? One of the peculiar features of universities is that they represent a vast multiproduct industry, providing teaching and research in a wide range of subjects at many different levels. The final product is intangible, and at first sight, incapable of being quantified. When physical measures are not available, as in case of all service industries, the common procedure is to use money values adjusted by a price index as an estimate of quantity. But there is no market mechanism for universities so no money valuation of output”. Existing works on education has used a wide variety of measures of output (Output measured in terms of test scores, grade point, number of credit hours, student’s degree etc.) But comparison over the years becomes difficult if the grades of a batch of students are not subject to some kind of standardization. However, a persuasive argument for use of test scores relate to continuation in schooling (Hanushek). If one takes the number of diploma holders emerging from an educational process as the outcome, then the analogy is close; a possible difference is that no industrial process would normally survive the proportion of rejects that a formal education system often accepts not only as usual but actually as an indicator of its high standard of production (Majumdar 1983). Economists have however concentrated on measurement of investment in human capital via rate of return. This procedure may be proper for engineers but premature for liberal arts. However, human capital is a black box and the measurement of the contents of the box can be only in terms of one or more outputs that flow from it. And as for externalities they are hard to quantify. Education contributes towards making better citizens who take well informed decisions for a more stable society.
Secondly, it is not at all safe to assume that the market value of a degree reflects investment in productive capital: it may be a screening device. The schooling earning relationship is highlighted by screening aspect whereby schools may produce more qualified individuals or simply identify the more able. Thus the attention paid to screening model arise from the implication that the social value of schooling may be less than the private value if schools were merely identifying the more able rather than changing their skills. A rival to screening hypothesis is the hypothesis that the university’s output is an input into subsequent training: a man with a degree in economics will be a cheaper on the job trainee than one without (Archibald 1974).
The third type of output is the research output. Well, research is discovery and dissemination of new knowledge. Measuring research output is also a problem. The published pages may be a unit by which the quantity of disseminated knowledge is measured. But this is not a sufficient condition for its dissemination as many published papers are read far less than unpublished papers. However, we are faced with the need to set a price on each page. Although certain journals pay authors according to number of pages, such a value per page is unacceptable for measuring societal benefits. It is even difficult to accept as some journals like Econometrica does not pay its authors. There is thus no method of valuing stock of knowledge, or of an increment to it. If however any idea or research is patented valuation becomes easy and at the same time it contributes to the revenue of the government. However valuation would be incomplete as the impact on societal well being cannot be quantified easily. Hence market is not true measure of research output. This creates problem for resource allocation between teaching and research output. Attiyeh (1974) argues that the cost of neglecting research through reallocation of budgetary resource from research to teaching may be counterproductive particularly for a university. Massy (2004:28) draws attention to a similar type of problem where research is increasingly getting prioritized at the cost of teaching. Academic ratchet refers to steady irreversible shift of faculty allegiance away from the goals of a given institution, toward those of an academic specialty (Zemsky and Massy 1990:22 quoted in Massy 2004). It can however be measured by what universities may be paying for research. Hierarchy in institutions suggests that across institutions of different ranks and status, salaries and teaching loads are negatively correlated. In the graph below teaching loads are measured on x-axis and salaries on the y-axis. Loads increase as the rank of the institution diminishes. The vertical lines correspond to some scatter of salaries. Let us assume that PhD is required in all ranks except D. If we consider an individual of rank R in a C-class institution, who is located at Q, teaches OC hours for CQ. Thus an individual of rank R in a B-class institution, located at R’, is being paid R’Q’ for his nonteaching contribution and similarly for A class institution can be interpreted.
It is however difficult to identify and further value the output as there is no single simple measure of output whether provided by market price or otherwise.
Identification and Valuation of Inputs:
The typical conceptual model depicts the achievement of a given student at a particular point in time as a function of cumulative inputs of the family, of peers, and of schools and teachers. These inputs also interact with the innate abilities, or learning potential of the student (Hanushek 1972, 1979). No studies have adequate measures of learning capacity. Many educational inputs (example family educational inputs) are not measured directly but instead are proxied by other observable attributes, such as socioeconomic background of the family and past research suggests that learning environment in the home is highly correlated with socioeconomic status. Further time is an important input as argued by Becker (1964). There could be two components of time spent-student time and faculty time. For students, time spent would vary with their IQs and preparation time and also the opportunity cost is taken into consideration. Faculty time is to be valued at the prevailing salary level. However, a problem with teacher’s salary is that it is administered as decided by the government. Hence, they do not reflect scarcity as a price of a product reflects in a free market. In educational production function, peer quality is an input to a college's production and one that cannot be bought from anyone other than its own customers. Peer quality is an input that costs and that have no substitutes (Winston1999). College can buy inputs to their production only from those customers who buy their products. In the process the students educate both themselves and the peers. The quality of the education any student gets from college depends on the quality of that student's peers. Further, school inputs are measured by class size, teacher education, availability of computers, textbooks etc.
Education Production Function:
Production function implies maximum feasible output that can be obtained from a given set of inputs. Studies of production function are referred to as input output analysis. These are conceptual constructs used in analyzing resource allocation decision of firms. The reality faced by education is however different. Production function is unknown and estimated using imperfect data. The education production function attempts to establish a statistical relationship between education resources and measures of student outcome. Results from these studies have had a significant impact on policy debates about how and how much public funding should be provided for education (Harris 2010). The step towards specification of the EPF is to express the relationship between input and output mathematically. Education output for individual student i at time t as which is a function f (.) of the school inputs S and family inputs F from current and all previous time periods, a fixed student contribution, is the innate ability of the student, and an error term is expressed in the form of following equation:-
In case of institutions producing multiple products, EPF was formulated by Bear (1964). Let be the non negative vector where the components pertain to quantities of educational output like the number of undergraduates, post graduates and doctoral students and the quantity of research in each of the disciplines per period. Let denote the non- negative vector of input quantities in terms of hours per period of faculty time in various disciplines, hours per period of non faculty labor, hours of utilization of lab equipment, hour of student’s time, and material inputs. Let be the vector of prices of output and is the price of inputs. The dimensions of all the vectors are required to be greater than 2. Therefore, the value of net social product of the educational firm is expressed as follows:
The firm should maximize w.r.t (ỹ, ), subject to the production relation linking outputs and inputs as:
F ( , )=0
So the objective problem can be stated as:
The central fiscal agency assists each institute by supplying information on certain and . Q is the number of academic disciplines and professional schools. The output is categorized into three branches of education delivery undergraduate, postgraduate and research (b, p, r) respectively. Administration is denoted by ‘a’. While administrative input is essential for all three lines of production, it is shown that teaching experience at the UG and PG level is not only important for other levels of teaching but they also contribute to research. Similarly, research activity strengthens teaching programmes. After designing the production function we delve further into the question of measuring efficiency and productivity.
Productivity and Efficiency Dilemma:
Productivity and efficiency are not synonyms. There is a difference between the two. Efficiency implies optimum combination of inputs that is required to produce a given output i.e. producing output at least cost. It is measured at any one point in time. Productivity on the other hand is measured over a period of time. Therefore an activity that is conducted inefficiently at a point in time enjoys productivity improvement as time passes. What we can say is that decline in productivity is a certain sign of inefficiency and the failure of an industry to improve its productivity may result in rise in costs.
Staff student ratio is an important indicator of measuring productivity of teaching. Improvement in staff student ratio implies a decline in productivity. Smaller classes improve quality of teaching as classroom interactions may be more and faculty time given to a student on an average may not fall. However, measurement of productivity is meaningless unless input and output are measured in terms of constant quality. Some are however convinced that quality of university teaching has been rising as subjects now are taught in ways unimaginable 10 years ago, subject itself is evolving and better textbooks are constantly being available. But if we are serious in measuring university’s productivity, we need to standardize the quality of student as well as teachers time. Group effect plays an important role on the quality of education. To produce five good sports cars, it would not be necessary to produce them in a larger group with fifteen other cars. But to produce five good physicists it may be necessary to put them in a class of twenty or so. This is not only necessary to keep up and improve upon but they can also learn from one another (Majumdar 1983).
Efficiency in production has important policy implications. Two concepts of efficiency are considered- economic and technical efficiency. Economic efficiency refers to correct choice of input mix given the prices of inputs; technical efficiency on the other hand refers to operating on the production frontier i.e. maximizing output for a given set of inputs. Achieving technical efficiency is difficult in government funded institutions as decision makers are not guided by either to maximize profit or to minimize cost. A greater degree of centralization might be more efficient as compared to where forecast can be made but where there is no central planning. If for example there is increase in demand to study a certain subject at the university level, to meet this demand, we must start to increase graduate programmes at some earlier dates and fulfill it. Further unit cost reflects efficiency, cost varies inversely with productivity and quality is positively related with the cost of education. Therefore advocates favor in promoting market mechanism for achieving efficiency. Vouchers in this context are argued to be a better instrument to help an educational institute achieve efficiency in the use of resources. Attiyeh (1974) however questions whether a greater reliance on market mechanism would take a university towards an efficient functioning unit?
One would suspect the usefulness of the production function analogy in education. One who thinks that university is like any other business will work in all the wrong places. One problem that completely breaks down the analogy between the firm and a school as Woodhall and Blaug (1965) stated, “is that the student is both an input and an output of the system”. Output however is an estimate of the value added in the process. A more vexing problem is that students are also investment decision makers in their own domain. This paper however sketches a framework within which fruitful research on higher education might take place because having constructed the production function, each institute request of the central fiscal agency the funds necessary for out of pocket expenses. This in turn will help in formulating resource allocation decisions and further would help in developing some of the issues that must be resolved before meaningful policies can be designed for the higher education industry.
CONFLICT OF INTEREST:
The author declares no conflict of interest.
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Received on 15.09.2018 Modified on 16.11.2018
Accepted on 24.12.2018 ©AandV Publications All right reserved