تحلیل تئوریک بازی ها از تعاملات بحش عمومی یا دولتی در شکل گیری سرمایه انسانی

Despite that the influence of the education and innate capabilities of workers on production has always been a principal concern of educational researchers and economists, not all relevant aspects of the topic have been sufficiently covered. For example, the influence exerted by government as the supplier of education and the responses of the public to the government’s decisions have not been studied in detail. This paper attempts to fill this gap. The interaction of government and the public is analyzed using an elementary game theoretic model. The empirical validity of the model is evaluated using information from other studies on workers’ productivity and education.

The analysis of the influence of workers’ education and innate capabilities on their productivity has always been and still is one of the main concerns of educational researchers and economists interested in what the latter call the economics of education. In this field the topic is studied from three different points of view: (a) the human capital, (b) the human resources and (c) the screening, sorting or signaling (SSS) approaches. To locate the content of this paper within the field, some observations about these approaches are presented in this section. The foundation of the human capital and human resources approaches is the assumption that knowledge transmitted by education does contribute to workers’ productivity and, as a consequence, to their income. This provides a basis for applying concepts and methods of analysis based on the assumption of rational behavior the study of educational decisions. This has been done in studies by Becker (1964) and Schultz (1960), in which the human capital approach was introduced. In these initial studies, the emphasis was on evaluating the contribution of educational transmitted knowledge to workers’ productivity. A theoretically more solid foundation was provided some time later by Ben-Porah (1967), who explicitly studied behavior assuming that individuals pursue the maximization of their well being over their lifetimes. The measurement of the contribution of education to a worker’s output and data on the public and private, paid and non-paid costs of education, which by definition are considered as investments in human capital, make it possible to compute the rates of return to those investments. This information provides a basis for policy recommendations. Specifically, if the rates of return to investments in physical capital are larger than those in human capital, society would benefit from transfers from the former to the latter up to the point where the marginal returns to the two types of investment are equal. This means that the human capital approach recognizes that investments in education, like any other type of investment, are subject to decreasing marginal returns although some important implications of this assumption have not been explicitly operationalized in applications of the approach. The descriptions of the current state of the approach presented by Correa (1995) and Woodhall, 1995 and Woodhall, 2001 show that the basic assumption, the methods of analysis, and the main objectives of the human capital approach have not been substantially modified since its inception, despite that much progress has been made in (a) statistical evaluation of the contribution to labor productivity of all its determinants, including knowledge obtained in education, (b) decomposing the overall rates of return to investments in human capital into rates of return for segments of the population defined by innate abilities, age, sex, race, etc., and (c) elaborating the approach introduced by Ben-Porah. Examples of the first type of analysis are presented by Ashenfelter and Rouse (2000) and Winship and Korenman (1999), of the second by Heckman (1999) and Carneiro and Heckman (2003), and of the third by Killingsworth (1983, pp. 207–230), Rosen (1977, pp. 3–40) and Weiss (1986, pp. 603–640). The human resources approach to the analysis of the relationship between education and economic conditions, despite that it uses the same basic assumption as the human capital approach, does not take into consideration the rational behavior of either suppliers or demanders of education, and does not emphasize measurement of the contribution of education to productivity. Its main objective, as shown in the models presented by Correa and Tinbergen (1962) and Correa (1963), and in the more recent description presented by Hinchliffe (1995), is to determine the number of workers with different levels of education needed to achieve economic objectives, and as a consequence, the number of students that should attend the educational system. This information is intended for the use of planning authorities for integrating education into the overall development policies of a society. The SSS point of view, initially conceptualized by Berg (1970) and formalized, among other authors, by Arrow (1973), is based on the antithesis of the assumption used in the first two approaches. Its point of departure is the denial that educational knowledge contributes to worker productivity. The higher incomes of workers with more education are due to their innate abilities and to desirable behavioral characteristics that may even have been acquired in the educational processes. Workers obtain education because it certifies that they have the natural abilities and forms of behavior that employers want, not that they have acquired the knowledge needed for high productivity. These assumptions are used as the basis for an analysis of the interactions between educated job applicants and their potential employers. With its emphasis on the behavior of suppliers and demanders of qualified labor, the SSS approach fills a vacuum in both the human capital and human resources approaches, but particularly in the latter. In addition, it has been an important motivation for the statistical studies whose objective is to allocate the salary differentials of workers with different levels of education among the different factors that may originate them. It follows that, in this respect, the human capital and the SSS points of view converge toward the common goal of identifying and evaluating the determinants of workers’ productivity. This brief review of the three main points of view used in economics to analyze the influence of education on worker productivity shows that two related topics have not been properly addressed. The first deals with the impact of the supply of qualified labor on workers’ income, and through it on the demand of individuals for education. Specifically, a comparison of the human capital and human resources approaches shows that they complement each other. Human capital analyses do not produce recommendations for the investments that should be made in education to equate its returns to those being obtained with physical investments. On the other hand, the human resources approach does not take explicitly into consideration the impact of education on the workers’ income, i.e., it omits from the analysis the principal motivation for investing in education. The second topic not properly addressed deals with the role of government in determining the supply of qualified labor in order to achieve economic objectives for society. An attempt is made in this paper to fill these gaps. The point of departure is the game theoretic model presented in Section 2. In this model it is assumed that the demand and supply of qualified labor is determined by the behavior of two actors: the public and the government. The public is represented by one typical individual whose objective is to maximize his/her income as determined by the amount of education that he/she demands and acquires and the total number of workers with similar qualifications that offer their services in the market. In this respect, the model extends the human capital approach to consider not only the objectives that individuals pursue, but also the collective impact of all the individuals operating in a market. On the other hand, it is assumed that the government’s objective is to maximize the total income of the community it governs. This means that an implicit assumption of the human resources approach is adopted. To describe the way this model is expressed, it is useful to recall that Yunker (1998) indicates that economic models can be presented and analyzed in three basic forms: (1) general function models, (2) a functionally specific but parametrically general form, and (3) a functionally and parametrically specific form. The presentation here uses type (2) and (3) forms. The second type of expression is used in the model in Section 2 and in its analysis in Section 3, in which the Nash–Cournot and the Nash–Stackelberg equilibriums of the model, i.e., the strategies that maximize the average number of years of education for the public and the number of educated workers for the government, are specified. A preliminary analysis of these results showed that, due to their complexity, general conclusions cannot be derived from them. To circumvent this problem, a functionally and parametrically specific form of the model in adopted, with data from the U.S.A and information obtained from studies made using the human capital, the human resources and the SSS approaches used to calibrate the parameters of the model. This information is presented in Section 4 and used in Section 5 for a detailed analysis of the characteristics and sensitivity of the equilibriums specified in Section 3. Section 6 includes some conclusions and some suggestions for future research.

The model and analyses presented in this paper are based on a systematic view of the interest and motivations of the government and the public. This basis is implicit in all applications of the human capital, human resources and SSS concepts of educational policy-making, but does not seem to have been properly operationalized, as is done here. The results obtained show an overall consistency between the model in 2 and 3 and the empirical information presented in Section 4 and used in Section 5. This indicates that the game theoretic model introduced here is a more useful instrument for a systematic study of the interactions between education and other socio-economic processes than the approaches that have been used previously. Despite the rather intensive efforts made in the last 4–5 decades, a clear, comprehensive and systematic view of the supply and demand of education and of their equilibrium does not seem to have been developed. It would be pretentious to say that this paper fills this vacuum; however, it does contribute by calling attention to the existence of the gap, and presents a possible way to deal with it. Nonetheless, the model and the analyses presented have several important limitations whose removal are worthwhile topics for future research. Some of these are mentioned below, proceeding from improvements that can be introduced in the model as it currently stands or with only minor modifications, to those that require more significant alterations. One obvious limitation of the quantitative analysis of the model is that it does not have an appropriate empirical basis. A first, but minor, problem is that the equilibrium functions in Table 1 do not satisfy the identifiability conditions needed for the estimation of their parameters. This problem can easily be solved by introducing into these functions exogenous determinants of the public’s and government’s behavior. However, even if this is done, the experience of the numerous statistical studies of human capital formation and related topics previously mentioned indicates that at least some of the data needed are not likely to be available, and even if they were, the actual statistical analysis is full of sand traps that are not likely to be avoided until several attempts have been made. Supporting evidence for this observation is presented by Harmon et al. (2001, pp. 1–37). It should also be observed that only two types of one isolated public/government interaction are analyzed here. This limitation can and should be removed. This can easily done easily by assuming that the public and the government in each current period respond to the behavior of their counterparts in the previous period. With this, the conditions for the Cournot and Stackelberg equilibriums become a system of difference equations that can probably be solved with well-known methods. It is also possible to use the methods of dynamic optimization applied by Ben-Porah (1967) and others for investigations based on the human capital approach to the analysis of the model presented here. The simplicity of the model in Section 2 is simultaneously one of its virtues and one of its most important defects. The former point will not be argued, since this would be outside the main purpose of this paper. On the other hand, the model has the serious defect that the two payoff functions used consider only the financial benefits of education for the persons that receive it, and through them, the society to which they belong. The payoff function for the public could be extended by considering other determinants of the well-being of individuals and that for the government could be modified to consider explicitly a production function of education, instead of the more easily quantified output of the educational process, i.e., the number of students with different educational levels. This could be attempted first by expanding the static model analyzed in this paper, and then, proceeding to dynamic analyses along the lines suggested above. In view of the mathematical complexity of these studies, it would more appropriate to do so in numerical studies based on the conceptual framework used here or on some of its possible extensions. Finally, reference will be made to the possibility of important extensions of the basic structure of the model in 2 and 3. First, it should be observed that this model does not consider the demand in the economic system for workers with different levels of education. This means that it leaves out a particularly important determinant of the demand for education and that, as a consequence, it does not completely integrate the human capital, human resources and SSS approaches to the interaction between education and the economy. In principle this can be done by adapting the methods used in the SSS approach to the analysis here. Second, it should be clear that, with few if any exceptions, the supply of education, and as a consequence of educated people, is controlled by the government. In most cases, the government and the private sector fulfill this function. This means that the realism of the model would be substantially increased by taking into consideration the existence of parallel public and private education systems. These two topics clearly constitute important areas for future research. In conclusion, this paper takes a large step in the right direction in the study of areas in which economic and educational concerns overlap. However, as shown by the suggestions for improvement of the model and its analysis, a substantial amount of work remains to be done. This is left as a challenge for future research.