Topics in Microeconometrics
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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.

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Topics in Microeconometrics Professor William Greene Stern School of Business, New York University

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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 functionf(z) that gives the maximum amount q of output that can be produced using input amounts (z1,…,zL-1) > 0.

“Microeconomic Theory,” Mas-Colell, Whinston, Green: Oxford, 1995, p. 129. 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 ui is modified OLS (MOLS).

The OLS residuals, save for the constant displacement, are pointwise consistent estimates of their population counterparts, - ui. Suppose that ui has an exponential distribution with mean λ. Then, the variance of ui is λ2, so the standard deviation of the OLS residuals is a consistent estimator of E[ui] = λ. Since this is a one parameter distribution, the entire model for ui can be characterized by this parameter and functions of it.

The estimated frontier function can now be displaced upward by this estimate of E[ui].


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 Modelwith 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


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