This research examines scholastic performance within the context of an individual’s production function. A constant partial elasticity of substitution production function for academic achievement is presented and estimated with non linear maximum likelihood methods. We find that ability and time devoted to various aspects of the learning process are the most important determinants of students’ accomplishments. Our results underscore the potential for students to compensate for relatively “poor” educational backgrounds by spending more time on study and class attendance.

Educational Production Functions

We construct a one-sector growth model where the technology is described by a Variable Elasticity of Substitution (VES) production function. This framework allows the elasticity of factor substitution to interact with the level of economic development. First, we show that the model can exhibit unbounded endogenous growth despite the absence of exogenous technical change and the presence of non-reproducible factors. Second, we provide some empirical estimates of the elasticity of substitution, using a panel of 82 countries over a 28-year period, which admit the possibility of a VES aggregate production function with an elasticity of substitution that is greater than one and consequently of unbounded endogenous growth.

http://chrispapageorgiou.com/papers/finalves1.pdf

Variable Elasticity of Substitution and Economic Growth: Theory and Evidence

This is a sequel to an earlier paper by the author, Dhrymes (1990). Using the LRD sample, that paper examined the adequacy of the functional form specifications commonly employed in the literature of US Manufacturing production relations. The "universe" of the investigation was the three digit product group; the basic unit of observation was the plant; the sample consisted of all "large" plants, defined by the criterion that they employ 250 or more workers. The study encompassed three digit product groups in industries 35, 36 and 38, over the period 1972-1986, and reached one major conclusion: if one were to judge the adequacy of a given specification by the parametric compatibility of the estimates of the same parameters, as derived from the various implications of each specification, then the three most popular (production function) specifications, Cobb-Douglas, CES and Translog all fell very wide of the mark. The current paper focuses the investigation on two digit industries (but retains the plant as the basic unit of observation), i.e., our sample consists of all "large" manufacturing plants, in each of Industry 35, 36 and 38, over the period 1972-1986. It first replicates the approach of the earlier paper; the results are basically of the same genre, and for that reason are not reported herein. Second, it examines the extent to which increasing returns to scale characterize production at the two digit level; it is established that returns to scale at the mean, in the case of the translog production function are almost identical to those obtained with the Cobb-Douglas function.1 Finally, it examines the robustness and characteristics of measures of productivity, obtained in the context of an econometric formulation and those obtained by the method of what may be thought of as the "Solow Residual" and generally designated as Total Factor Productivity (TFP). The major finding here is that while there are some differences in productivity behavior as established by these two procedures, by far more important is the aggregation sensitivity of productivity measures. Thus, in the context of a pooled sample, introduction of time effects (generally thought to refer to productivity shifts) are of very marginal consequence. On the other hand, the introduction of four digit industry effects is of appreciable consequence, and this phenomenon is universal, i.e., it is present in industry 35, 36 as well as 38. The suggestion that aggregate productivity behavior may be largely, or partly, an aggregation phenomenon is certainly not a part of the established literature. Another persistent phenomenon uncovered is the extent to which productivity measures for individual plants are volatile, while two digit aggregate measures appear to be stable. These findings clearly calls for further investigation.

The Structure Of Production Technology Productivity And Aggregation Effects

On the economic growth theory with Kadiyala production function

This paper contributes to the environmental literature by (i) demonstrating that the estimated coefficients and the statistical significance of the non-leading terms in quadratic, cubic, and quartic logarithmic environmental Kuznets curve (EKC) specifications are arbitrary and should therefore not be used to choose the preferred specification and (ii) detailing a proposed general-to-specific type methodology for choosing the appropriate specifications when attempting to estimate higher-order polynomials such as cubic and quartic logarithmic EKC relationships Testing for the existence and shape of the well-known EKC phenomenon is a hot topic in the environmental economics literature The conventional approach widely employs quadratic and cubic specifications and more recently also the quartic specification, where the variables are in logarithmic form However, it is important that researchers understand whether the estimated EKC coefficients, turning points, and elasticities are statistically acceptable, economically interpretable, and comparable In addition, it is vital that researchers have a clear structured non-arbitrary methodology for determining the preferred specification and hence shape of the estimated EKC We therefore show mathematically and empirically the arbitrary nature of estimated non-leading coefficients in quadratic, cubic, and quartic logarithmic EKC specifications, being dependent upon the units of measurement chosen for the independent variables (eg dependent upon a rescaling of the variables such as moving from $m to $bn) Consequently, the practice followed in many previously papers, whereby the estimates of the non-leading terms are used in the decision to choose the preferred specification of an estimated EKC relationship, is incorrect and should not be followed since it potentially could lead to misleading conclusions Instead, it should be based upon the sign and statistical significance of the estimated coefficients of the leading terms, the location of turning point(s), and the sign and statistical significance of the estimated elasticities Furthermore, we suggest that researchers should follow a proposed general-to-specific type methodology for choosing the appropriate order of polynomials when attempting to estimate higher-order polynomial logarithmic EKCs

/pdf/estimating-different-order-polynomial-logarithmic-1f801ijv70.pdf

Estimating different order polynomial logarithmic environmental Kuznets curves.

Theoretical and empirical works dealing with production functions have found it convenient, if not a necessity, to work with specific parametric forms. Beginning with the early Leontief and Cobb-Douglas forms, successive generalizations of the form of a production function first allowed constant elasticities of substitution (CES) other than zero or unity (K. J. Arrow, H. Chenery, B. S. Minhas, R. Solow [1]) and then introduced the variable elasticity of substitution (VES) form in which the elasticity of substitution is linearly dependent on the input ratio (Y. Lu and L. B. Fletcher [7]) or on time (R. Sato and R. F. Hoffman [12]). A generalized production function (GPF) modification by use of a composite function approach provides variable returns to scale as well as a variable elasticity of substitution (A. Zellner and R. S. Revankar [14]). Recently K. R. Kadiyala [6] has pointed out a direct generalization of the familiar CobbDouglas and CES functions which contains both as special cases. In addition, the KRK function allows for a more general variable elasticity of substitution and thus provides added flexibility to earlier VES modifications. Aside from its theoretical features the KRK function presents the possibility for a

R. A. Meyer

Papers

Linear and Nonlinear Estimation of Production Functions