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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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slide1
Topics in Microeconometrics

Professor William Greene

Stern School of Business, New York University

at

Curtin Business School

Curtin University

Perth

July 22-24, 2013

the production function
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
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
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
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)
defining the production set
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:

cost 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.

modified ols
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].

principles
Principles
  • The production function resembles a regression model (with a structural interpretation).
  • We are modeling the disturbance process in more detail.
statistical problems with programming estimators
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.
extensions
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.
methodological problems with dea
Methodological Problems with DEA
  • Measurement error
  • Outliers
  • Specification errors
  • The overall problem with the deterministic frontier approach
dea and sfa same answer
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).)
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