Three Essays on Spatial Econometric Models with Missing Data

This dissertation is composed of three essays on spatial econometric models with missing data. Spatial models that have a long history in regional science and geography have received substantial attention in various areas of economics recently. Applications of spatial econometric models prevail in urban, developmental and labor economics among others. In practice, an issue that researchers often face is the missing data problem. Although many solutions such as list-wise deletion and EM algorithm can be found in literature, most of them are either not suited for spatial models or hard to apply due to technical di¢ culties. My research focuses on the estimation of the spatial econometric models in the presence of missing data problems. The rst essay, GMM Estimation of Mixed Regressive, Spatial Autoregressive Models with Missing Observations in Dependent Variables, develops a GMMmethod based on linear moments for the estimation of mixed regressive, spatial autoregressive (MRSAR) models with missing observations in the dependent variables. The estimation method uses the expectation of the missing data, as a function of the observed independent variables and the parameters to be estimated, to replace the missing data themselves in the estimation. The proposed GMM estimators are shown to be consistent and asymptotically normal. Feasible optimal weighting matrix for the GMM estimation is given. We extend our estimation method to MRSAR models with heteroskedastic disturbances, high order MRSAR models and unbalanced spatial ii panel data models with random e¤ects as well. From these extensions, we see that the proposed GMM method has more compatibility, compared with the conventional EM algorithm. Monte Carlo experiments show that the estimation method works well for nite sample. Although it is not as e¢ cient as the EM algorithm when the disturbances are i:i:d:, it outperforms the EM algorithm in presence of heteroskedasticity. The second essay, A Group Interaction Model with Endogenous, Exogenous, Group Fixed E¤ects and Group Heteroskedasticity A Random Sample Framework, considers a group interaction model rst proposed by Lee (2006); this model is a special case of the spatial autoregressive (SAR) models. The essay is a rst attempt to estimate the model in a more general random sample setting, i.e. a framework in which only a random sample rather than the whole population in a group is available. We incorporate group heteroskedasticity along with the endogenous, exogenous and group xed e¤ects in the model. We prove that, under some basic assumptions and certain identi cation conditions, the quasi maximum likelihood (QML) estimators are consistent and asymptotically normal when the functional form of the group heteroskedasticity is known. Two types of misspeci cations are considered, and, under each, the estimators are inconsistent. We also propose IV estimation in the case that the group heteroskedasticity is unknown. A LM test of group heteroskedasticity is given at the end, and Monte Carlo experiments are designed to check the nite sample performance of the estimations and the test. The third essay, GMM Estimation of a Group Interaction Model with Endogenous, Exogenous, Random E¤ects and Random Samples Large Group Scenarios, considers the same group interaction model as that in the second essay, but focuses