| This dissertation studies panel data and spatial models. The panel data models pool the observations on a cross-section of households, states, countries, etc. over a few time periods. The spatial models are cross sectional models dealing with spatial dependence and spatial heterogeneity.; There are four essays in this dissertation.; The first essay proposes the double length artificial regression (DLR) tests for testing spatial dependence (including both spatial lag dependence and spatial error dependence) in a cross sectional model. DLRs are useful econometric tools for deriving LM and equivalent test statistics. These DLR's can be applied to more general models than some of the other artificial regression counterparts.; The second essay derives Lagrangian Multiplier tests to jointly test for functional form and spatial error correlation. In particular, this essay tests for linear and loglinear models with no spatial error dependence against a more general Box-Cox model with spatial error correlation. Conditional LM tests and modified Rao-Score tests that guard against local misspecification are also derived. These tests are easy to implement. The performance of these tests is also compared using Monte Carlo experiments.; The third essay considers the problem of prediction in a panel data regression model with spatial auto correlation. In particular, I consider a simple demand equation for cigarettes based on a panel of 46 states over the period 1963–1992. I use the first 25 years for estimation and the last 5 years for out-of-sample forecast. I derive the best linear unbiased predictor for the random effects with spatial correlation. Based on the mean-squared error forecast performance, it is important to take into account spatial correlation and heterogeneity across the states.; The fourth essay considers the problem of estimating a partially linear semiparametric (dynamic) panel data model with fixed effects. Using the series method, I establish the root N normality result for the estimator of the parametric component, and I show that the unknown function can be consistently estimated at the standard nonparametric rate. |
