Topics in Microeconometrics Professor William Greene Stern School of Business, New York University at Curtin Business School Curtin University Perth July 22-24, 2013

1. Efficiency

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.

Frontier Functions

Deterministic Frontier: Programming Estimators

Estimating Inefficiency

Statistical Problems with Programming Estimators They do correspond to MLEs. The likelihood functions are “irregular” There are no known statistical properties – no estimable covariance matrix for estimates. They might be “robust,” like LAD. Noone knows for sure. Never demonstrated.

An Orthodox Frontier Model with a Statistical Basis

Extensions Cost frontiers, based on duality results: ln y = f(x) – u  ln C = g(y,w) + u’ u > 0. u’ > 0. Economies of scale and allocative inefficiency blur the relationship. Corrected and modified least squares estimators based on the deterministic frontiers are easily constructed.

Data Envelopment Analysis

Methodological Problems with DEA Measurement error Outliers Specification errors The overall problem with the deterministic frontier approach

DEA and SFA: Same Answer? Christensen and Greene data N=123 minus 6 tiny firms X = capital, labor, fuel Y = millions of KWH Cobb-Douglas Production Function vs. DEA (See Coelli and Perelman (1999).)

Comparing the Two Methods.

Total Factor Productivity