Efficiency Measurement William Greene Stern School of Business New York University

Session 1 Introduction

Course Overview  Inefficiency  Production Functions  Frontier Functions  Stochastic Frontier Model  Functional Form; Cost Functions  Efficiency Measurement  Modeling Heterogeneity  Model Extensions  Panel Data, Distance Functions  Applications  Summary and Review

Modeling Inefficiency

The Production Function “A single output technology is commonly described by means of a production function f(z) that gives the maximum amount q of output that can be produced using input amounts (z 1,…,z L-1 ) > 0. “Microeconomic Theory,” Mas-Colell, Whinston, Green: Oxford, 1995, p See also Samuelson (1938) and Shephard (1953).

Thoughts on Inefficiency Failure to achieve the theoretical maximum  Hicks (ca. 1935) on the benefits of monopoly  Leibenstein (ca. 1966): X inefficiency  Debreu, Farrell (1950s) on management inefficiency All related to firm behavior in the absence of market restraint – the exercise of market power.

A History of Empirical Investigation  Cobb-Douglas (1927)  Arrow, Chenery, Minhas, Solow (1963)  Joel Dean (1940s, 1950s)  Johnston (1950s)  Nerlove (1960)  Berndt, Christensen, Jorgenson, Lau (1972)  Aigner, Lovell, Schmidt (1977)

Inefficiency in the “Real” World Measurement of inefficiency in “markets” – heterogeneous production outcomes:  Aigner and Chu (1968)  Timmer (1971)  Aigner, Lovell, Schmidt (1977)  Meeusen, van den Broeck (1977)

Production Functions

Defining the Production Set Level set: The Production function is defined by the isoquant The efficient subset is defined in terms of the level sets:

Isoquants and Level Sets

The Distance Function

Inefficiency in Production

Production Function Model with Inefficiency

Cost Inefficiency y* = f(x)  C* = g(y*,w) (Samuelson – Shephard duality results) Cost inefficiency: If y < f(x), then C must be greater than g(y,w). Implies the idea of a cost frontier. lnC = lng(y,w) + u, u > 0.

Specification

Corrected Ordinary Least Squares

Modified OLS An alternative approach that requires a parametric model of the distribution of u i is modified OLS (MOLS). The OLS residuals, save for the constant displacement, are pointwise consistent estimates of their population counterparts, - u i. Suppose that u i has an exponential distribution with mean λ. Then, the variance of u i is λ 2, so the standard deviation of the OLS residuals is a consistent estimator of E[u i ] = λ. Since this is a one parameter distribution, the entire model for u i can be characterized by this parameter and functions of it. The estimated frontier function can now be displaced upward by this estimate of E[u i ].

COLS and MOLS

Principles  The production function resembles a regression model (with a structural interpretation).  We are modeling the disturbance process in more detail.