Econometric tests of firm decision making under uncertainty - optimal output and hedging: comment.

• Author: Dalal, Ardeshir J.
• Position: Comment on Timothy Park and Frances Antonovitz, Southern Economic Journal, Jan. 1992, pp. 593

1. Introduction

   In recent years there has been an increasing number of theoretical contributions to the analysis of behavior in the presence of uncertainty. Unfortunately, empirical testing of these models has been virtually non-existent. A recent exception is an article in this journal by Park and Antonovitz [6] which attempts to conduct an empirical analysis of a firm which engages in transactions in a futures market and is subject to basis risk. Park and Antonovitz [6] (hereafter PA) obtain estimating equations for optimal output and hedging from the indirect expected utility function using a procedure introduced by Dalal [3] which permits the derivation of uncertainty analogues of Hotelling's Lemma.(1) Unfortunately, the PA paper contains several errors. Among the most important of these is the fact that the parameter restrictions they impose on the indirect function contradict rather than confirm (as PA assert) the existence of constant absolute risk aversion (CARA). Moreover, the specification of their estimating equation for output supply would be correct only if an unnecessarily restrictive assumption (independence of the second period futures price from the future spot price) is made.

   The purpose of this article is to provide a more general formulation for the empirical testing of finn behavior in the presence of basis risk which will, it is hoped, be useful to future researchers in the field. The next section derives estimating equations based on an explicit dependence of the second period futures price on the future spot price and also derives a corrected test for the presence of CARA.

2. Estimating Equations and Hypothesis Tests

   In order to facilitate comparison with the PA paper I have used their notation throughout. The firm is assumed to maximize the expected utility of profits, i.e., the firm's problem is

   [Mathematical Expression Omitted],

   where Q is the production function, [r.sub.1] and [X.sub.1] are vectors of input prices and quantities respectively, [Mathematical Expression Omitted] is the stochastic future spot price, [Mathematical Expression Omitted] is the first period futures price which is known, [Mathematical Expression Omitted] is the stochastic second period futures price, f is the amount hedged, and K is a shift parameter with an initial value of 0.(2)

   A salient characteristic of models with basis risk is that the second period futures price is dependent on the future spot price. This is ignored by PA but is made quite explicit by Paroush and Wolf [7]. Using the latters' formulation,

   [Mathematical Expression Omitted],

   [Mathematical Expression Omitted],

   where [Sigma], [Tau], [Gamma] and [Delta] are positive constants, [Epsilon] and [Eta] are random variables with E[[Epsilon]] = E[[Eta]] = 0, E[[[Epsilon].sup.2]] = E[[[Eta].sup.2]] = 1, and E[[Epsilon][Eta]] = 0. Consequently, [Mathematical Expression Omitted], the spot price ([Mathematical Expression Omitted]) has variance [Mathematical Expression Omitted], the second period futures price ([Mathematical Expression Omitted]) has variance [Mathematical Expression Omitted], and the covariance between [Mathematical Expression Omitted] and [Mathematical Expression Omitted] is [Mathematical Expression Omitted]. The solution to (1) implies the existence of an indirect expected utility function, and (1), (2) and (3) imply that it will be given by [Mathematical Expression Omitted]. However, since [Mathematical Expression Omitted], we may still write (with...