Model Selection and Adaptive Lasso Estimation of Spatial Models

摘要

Various spatial econometrics models have been proposed to characterize spatially correlated data. As economic theories provide little guidance on constructing a true model, we are often faced with the problem to choose among spatial econometrics models. My dissertation develops a Vuong-type test and an adaptive Lasso procedure that complement existing spatial model selection methods in several aspects.;Chapter 1 develops a likelihood-ratio test for model selection between two spatial econometrics models. It generalizes Vuong (1989) to models with spatial near-epoch dependent (NED) data. We measure the distance from a model to a data generating process by Kullback-Leibler Information Criterion and test the null hypothesis that two models are equally close to the data generating process. We make no assumption on the model specification of the truth and allow for the cases where both, either or neither of the two competing models is mis-specified. As a prerequisite of the test, we first show that the quasi-maximum likelihood estimators (QMLE) of spatial econometrics models are consistent estimators of their pseudo-true values and are asymptotically normal under regularity conditions. In particular, we study spatial autoregressive models with spatial autoregressive errors (SARAR) and matrix exponential spatial specification (MESS) models. With asymptotic properties of QMLEs and limit theorems for NED random fields, we then derive the limiting null distribution of the test statistic. A spatial heteroskedastic and autoregressive consistent estimator of asymptotic variance of the test statistic under the null, which is necessary to implement the test, is constructed. Monte Carlo experiments are designed to investigate finite sample performance of QMLEs for SARAR and MESS models, as well as the size and power of the proposed test.;Chapter 2 proposes a penalized maximum likelihood approach with adaptive Lasso penalty to estimate SARAR models. It allows for simultaneous model selection and parameter estimation. With appropriately chosen tuning parameter, the resulting estimators enjoy the oracle properties, in other words, zero parameters are estimated as zeros with probability approaching one and nonzero parameters possess the same asymptotic distribution as if the true model is known. We extend Zhu, Huang and Ryes (2010)'s work to account for models with spatial lags. We also allow the number of parameters to grow with sample size at a relatively slow rate. As maximum likelihood estimation is computationally demanding, we generalize the least squares approximation (LSA) algorithm (Wang and Leng, 2010) to spatial linear models and prove that the LSA estimators perform as efficiently as the oracle as long as a consistent initial estimator with proper convergence rate is adopted in the algorithm. By using the LSA algorithm with a computationally simple initial estimator, we can perform penalized maximum likelihood estimation of SARAR models much faster than Zhu, Huang and Ryes (2010) without sacrificing efficiency.