A two-stage pooled panel data estimator of demand elasticities

In those cases where the first-stage estimates of the structural parameter vector is at the boundary of the parameter space, we switch in the second stage to an estimator that depends on which boundary that is binding in the first stage. [...] When α = 1, the probability of a boundary solution is 40 percent and the NRMSE is about twice that of the corresponding unbiased FE estimator (not displayed) and between 10 and 40 percent of the F/S estimator. [...] In fact, by comparing Table 6 and 7, we see that the NRMSE of the 2SP estimator in a sample with NT = 1250 observations 28 is of the same magnitude as the NRMSE with the F/S estimator in a sample with NT = 5000. [...] There is a high probability of the 2SP estimator switching in the second stage if the true parameter is at the boundary of the parameter space, but it seldom switches if the true parameter is away from the boundary. [...] There are complementarities between the two refinements we have made: choosing many reference varieties not only reduces RMSE directly, it also increases 29 the probability of the 2SP estimator switching to a more efficient FE estimator when the true parameter is at the boundary of the parameter space, and of an admissible first-stage estimate when the true parameter is away from the boundary.