M.Sc Thesis
M.Sc Student Katseva Galina Nonparametric Estimation of Production Functions The Quasiconcave Case Department of Industrial Engineering and Management Professor Ury Passy

Abstract

In economic theory the production function is a mathematical statement that relates quantitatively the technological relationship between the output of a process and the inputs of the different factors of the process.

A production technology consists of certain alternative means, arrangement of these means and uses of materials and services by which goods or services may be produced.

When using production function it is implicitly assumed that the output of the technology is a single good/service.

The literature is entirely parametric. However, in the last 20 years nonparametric approach has grown in popularity. In the present approach we assume that the production function is nonnegative, nondecreasing, and Quasiconcave. And the technology is Well Behaved Technology, thus the induced level sets are convex but the Production Function is merely Quasiconcave.

In this work we solve the following problems:

a.    Nonparametric Estimation of Quasiconcave Production Function.

b.    Nonparametric Estimation of Quasiconcave  Production Function assuming also an error in the input due to input inefficient usage of resources.

c.    Nonparametric Estimation of Quasiconcave Production Function  with simultaneous errors by producing lower  products, outputs, and utilizing higher inputs due to inefficient production processes

To demonstrate the feasibility of our approach we reported two empirical applications.

The first data set contained of 448 units, DMUs. The output was the value added in different manufacturing sectors in the United States (downloaded from the website of NBER- National Bureau of Economic Research) in 1954. Three sets of data were generated by random sampling with repetition of the NBER data: 100 sets each of 20 DMUs, 100 sets each of 50 DMUs, 100 sets each of 100 DMUs.

The second data set (25 DMUs) was taken from the work of Zellner and Ryu (1957). The data set consists of two inputs (labour - man hours and capital services) and single output (value added of transportation equipment).

The developed method produces a consistent estimator of the true production function.

The experiments showed that large Quasiconcave models can be solved in reasonable time for Estimation of Production Function.