ECONOMETRICS

In the previous chapters we have examined various models of optimizing behavior. Here we examine hob one can use the theoretical insights developed in those chapters to help estimate relationships that may have been generated by optimizing behavior.

Theoretical analysis and econometric analysis can interact in several ways. First, theory can be used to derive hypotheses that can be tested econometrically. Second, the theory can suggest ways to construct better estimates of model parameters. Third, the theory helps to specify the structural relationships in the model in a way that can lead to more appropriate estimation. Finally, the theory helps to specify appropriate functional forms to estimate.

12.1. The optimization hypothesis

We have seen that the model of optimizing choice imposes certain restrictions on observable behavior. These restrictions can be expressed in a number of ways: 1) the algebraic relationships such as WAPM, WACM, GARP, etc.; 2) the derivative relationships such as the conditions that certain, substitution matrices must be symmetric and positive or negative semi definite; 3) the dual relationships such as the fact that profits must be a convex function of prices.

The conditions implied by the maximization models are important for at least two reasons. First, they allow us to test the model of maximizing behavior. If the data don’t satisfy the restrictions implied by the particular optimization model we are using, then we generally would not want to use that model to describe the observed behavior.

Second, the conditions allow us to estimate the parameters of our model more precisely. If we find that the theoretical restrictions imposed by optimization are not rejected in some particular data set, we may want to re-estimate our model in a way that requires the estimates to satisfy the restrictions implied by optimization.

Suppose, for example, we have an optimizing model that implies that some parameter α equals zero. First, we might want to test this restriction, and see if the estimated value of α is significantly different from zero. If the parameter is not significantly different from zero, we may want to accept the hypothesis that α = 0 and re-estimate the model imposing this hypothesis. If the hypothesis is true, the second set of estimates of the other parameters in the system will generally be more efficient estimates.