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

The expected utility model of the competitive firm under price uncertainty has yielded a rich set of implications for optimal firm decision making. Recent research has focussed on modeling the complete sources of risk influencing firms along with the alternative institutions and marketing strategies available for managing risk.

The authors of the comment on Park and Antonovitz [4] continue this line of research by incorporating an alternative assumption about the relationship between the spot and futures prices directly into the model of output and hedging decisions. Other assumptions about spot and futures prices are also reasonable and can be empirically justified but we did not pursue these assumptions in our paper.

For example, Lapan, Moschini and Hanson [3] discussed how optimal decisions are affected by the decision maker's expectations about futures prices relative to the current futures price. One reasonable assumption is that the producer's expectations of the second period futures price equals the price of the current futures contract. This assumption implies that [Mathematical Expression Omitted]. Comparative statics results can be developed for this case of unbiased expectations. As the authors demonstrate additional assumptions about the structure of the decision model will change the form of the derived output and hedging decisions and the set of testable restrictions on optimal output and hedging decisions by the firm.

The relationship between spot and futures prices has been specified in at least two different forms. Both Lapan, Moschini, and Hanson [3] and Benninga, Eldor, and Zilcha [1] write the cash price as a linear function of the futures price:

[Mathematical Expression Omitted]

where [Mathematical Expression Omitted] is independent of [Epsilon] and [Mathematical Expression Omitted]. Theoretical and empirical models to derive and estimate the optimal minimum variance hedge using ordinary least squares regressions are based on this specification relating spot and futures prices. However, this common specification is the reverse of that proposed by the authors of this comment. A non-linear relationship for basis movements is another alternative specification that could be incorporated into the model.

The direction of regressability has important implications about the relationship between spot and futures prices and does change the structure of the decision model. Consider the specification proposed by Lapan, Moschini, and Hanson [3] in which the spot price is a linear function of the futures price.

In this case, basis risk influences the spot price and the futures price is unaffected. Basis risk is an exogenous addition to the risky output price and is modelled by Briys, Crouhy, and Schlesinger [2] as an independent background risk. If the utility function is consistent with constant absolute risk aversion (CARA) and the spot and futures prices are related as in (1), the production and hedging decision can be separated. Lapan, Moschini, and Hanson [3] showed that the optimal output decision is independent of the distribution of the random futures price in this case. The expected futures prices along with the variance of the futures price and the covariance between the spot and futures price does not appear in the optimal output decision.

The authors of this comment assume that the direction of regressability between spot and futures prices is reversed. Under this assumption the output price is not affected by basis risk. Instead, basis risk shifts the distribution of the futures price while the output price is considered as primary. Clearly additional empirical evidence is needed to decide on the validity of these competing assumptions and this avenue was not pursued in our paper.

In our second point, the proposed empirical tests of the expected utility model of output and hedging decisions are implemented using the series of restrictions formulated by the authors. The model incorporates the assumption proposed by the authors that the futures price is a linear function of the spot price. The output and hedging decisions in equations (9) and (10) of the comment are estimated in a nonlinear seemingly unrelated regression. The tests are performed using the bivariate autoregressive expectations model presented in the original paper.

The parameter restrictions on output and hedging decisions in (12) were not rejected since the calculated test statistic value was 11.03 with a critical [Mathematical Expression Omitted] value of 11.07 at the 5 percent level. Conditional on the chosen flexible functional form, the hypothesis that output and hedging decisions are consistent with expected utility maximization was not rejected.

The restrictions in (12) and (15) are also not rejected. The calculated test statistic was 11.88 with a critical [Mathematical Expression Omitted] value of 12.59 at the 5 percent level. However, the additional restrictions implied by separability are rejected. The set of interaction terms between fixed costs and the parameters of the indirect expected utility function are not jointly zero.

Following the sequence of tests developed by the authors of this comment, the output and hedging decisions are consistent with CARA, conditional on the bivariate autoregressive expectations model.

It is important to note that more complete tests of the expected utility model for optimal output and hedging decisions can be derived as additional assumptions are imposed on the model. Future work could examine how shifts in the mean preserving spread parameters of output and futures prices effect output and hedging decisions. The indirect utility framework used here and clarified by the authors of this comment should be a useful tool in developing testable restrictions on decision making.

Timothy A. Park University of Georgia Athens, Georgia

References

1. Benninga, Simon, Rafael Eldor, and Itzhak Zilcha, "The Optimal Hedge Ratio in Unbiased Futures Markets." Journal of Futures Markets, August 1984, 155-59.

2. Briys, Eric, Michel Crouhy, and Harris Schlesinger, "Optimal Hedging in a Futures Market with Background Noise and Basis Risk." European Economic Review, June 1993, 949-60.

3. Lapan, Harvey, Giancarlo Moschini, and Steven D. Hanson, "Production, Hedging, and Speculative Decisions with Options and Futures Markets." American Journal of Agricultural Economics, February 1991, 66-74.

4. Park, Timothy and Frances Antonovitz, "Econometric Tests of Firm Decision Making under Uncertainty: Optimal Output and Hedging Decisions." Southern Economic Journal, January 1992, 593-609.