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.
Professor William Greene
Stern School of Business, New York University
Curtin Business School
July 22-24, 2013
“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).
Failure to achieve the theoretical maximum
All related to firm behavior in the absence of
market restraint – the exercise of market
Measurement of inefficiency in “markets” – heterogeneous production outcomes:
The Production function is defined by the isoquant
The efficient subset is defined in terms of the level sets:
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.
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].
ln y = f(x) – u ln C = g(y,w) + u’
u > 0. u’ > 0. Economies of scale and
allocative inefficiency blur the relationship.