Nonparametric Statistical Inference in Production Functions

Konishi Yoko, Nishiyama Yoshihiko, Ando Tomohiro, Kawasaki Yoshinori

doi:10.5023/jappstat.33.157

Production functions play many important roles both in economic theory and in empirical econometrics. Usually, a production function is postulated as a mapping from several input variables to a scalar 'output'. In its simplest form, the output level (y) is assumed to be dependent on capital (x1) and labor (x2). When it comes to empirical analysis, the most commonly used specification is the so-called Cobb-Douglas function, which was extended to the translog production function long afterward. Though the great bulk of past empirical works on the estimation of production function heavily relies on a parametric specification such as Cobb-Douglas or translog, it is often singled out as a major flaw that the statistical analysis under model misspecification may give rise to incorrect statistical inference and therefore, to fallacious economic implications. In consideration of this possible danger, this article addresses two issues. At first, we apply the nonparametric misspecification test (proposed by Hong and White, 1995) to investigate whether or not the parametric specifications (Cobb-Douglas and translog) are appropriate for the production functions of firms. Data are the cross section of y, x1, x2 by companies whose stocks are listed on the first division of the Tokyo Stock Exchange. Firms are classified into two groups (manufacturing and non-manufacturing), and the misspecification test is performed separately on each group, year by year from 1965 to 2001. To summarize the results of the test, parametric specifications are considered reasonable and proper until the 1970's, while they do not fit well after 1980. Observing these results, we proceed to the nonparametric estimation of production functions as the second step. We exploit the generalized additive model (GAM) employing B-spline basis functions. In model estimation, we make use of a penalized likelihood approach where smoothness constraints on the coefficients of basis functions are imposed. What is essential in the estimation of such smoothing spline models as the GAM is the objective choice of smoothing parameter. In this article a version of generalized information criteria (GIC) is derived to determine the smoothing parameter and the number of basis functions. As is expected, the estimated production functions exhibit substantial nonlinearities after 1980. As an application of nonparametric analysis, we investigate the inefficiency of the companies that went bankrupt during the sample period.

Nonparametric Statistical Inference in Production Functions

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