Essays in econometric theory
The first essay in the dissertation deals with the finite sample properties of the partially restricted reduced form estimator (PRRF). The technique of fractional calculus is used to derive a general expression for the exact moments of a linear function of the PRRF estimator. The model considered here is less restrictive than the ones studied by other authors. In fact, it is shown that the results obtained by Nagar and Sahay (1978) for the exact bias and mean squared errors of the PRRF estimator are only valid for the restricted model considered by them, and can not be extended to the more general cases. The second essay compares the deterministic and stochastic predictors of nonlinear models when the disturbances are small. Large sample properties of these predictors have been analyzed extensively by Mariano and Brown. While the deterministic predictors are asymptotically biased, there are some Monte Carlo experiments that suggest that the magnitude of this bias is rather insignificant. Here, we offer a possible explanation of the smallness of the deterministic bias. It is shown that when the error terms have small standard deviation, the deterministic predictor turns out to be asymptotically unbiased. The results are based on deriving asymptotic expansions for alternative predictors. The asymptotic expansions carried out here are similar to the large sample asymptotic expansions in Mariano and Brown (1983) and Brown and Mariano (1984). However, the expansions here are in terms of the standard deviation of the disturbance terms. The results are then used to obtain the asymptotic bias and asymptotic mean squared prediction errors of the deterministic and stochastic predictors of a model containing the Box-Cox transformation.
Arvin-Rad, Hassan, "Essays in econometric theory" (1990). Dissertations available from ProQuest. AAI9026515.