Nonparametric Measures of Scale and Technical Change for Competitive Firms Under Uncertainty

Measures of scale elasticity and rate of technical change can be obtained nonparametrically in the Sandmo model of competitive firms with nonlinear risk preference responding to output price risk. Information on risk attitudes is not needed for measurement of scale elasticity because it is observable as the ratio of average to marginal cost, as in certainty models. The cross section of panel data sets can be used to develop a nonparametric marginal cost measure, which permits identification of scale elasticity; the technical change measure then follows from the scale measure and the time-series portion of the panel data set. Key words: nonparametric measurement, risk, scale elasticity, technical change. Measurement of the elasticity of scale and the rate of technical change without estimation is possible if a competitive firm is assumed to maximize profits when no uncertainty exists (see, e.g., Hulten or Chambers 1988). Problems arise, however, if the firm maximizes expected utility of profit under output price uncertainty, as in Sandmo or Batra and Ullah. Specifically, Chambers (1983) argues that the usual measures of scale and technical change with risk aversion depend upon knowledge of, or some assumption about, the firm's utility function or its technol-ogy when output price uncertainty exists. While Chambers shows that the expression for the rate of technical change under certainty holds under output price uncertainty only if the firm's tech-nology has constant returns to scale, Tressler and Menezes show that constant returns to scale is incompatible with the assumption of risk aver-sion under price uncertainty and free entry. The purpose of this paper is to demonstrate The authors are, respectively, a senior lecturer, Department of Op