Essays on semi-parametric panel data and lasso-based instrumental variables selection in spatial economics

Abstract

In the first chapter, I consider a semiparametric panel data model with the heterogeneous time-varying trend across individuals and homogeneous slope coefficients. A novel data-driven approach - adaptive discrete smoothing kernel regression - is introduced. This approach allows us to use the whole data sample to estimate the individual specific trending functions. To do that, a two-step estimation based on local linear approximation is needed, where a two-dimensional similarity indices of each trend are constructed in the first step. In the second step, a crosssectional kernel weight determined by these similarity indices between individual time-varying trends is employed. The asymptotic distribution of the parametric slope coefficient and the nonparametric trend is established. The performance of the proposed method in the finite sample data is illustrated by simulation demonstration. One empirical application is provided. The second chapter studies a LASSO-based two-stage least squar estimation of spatial autoregressive models when some or all regressors are endogenous in the presence of many instruments. To handle the biasvariance tradeoff caused by the presence of many available instruments, we use LASSO methods in the first stage to select the most informative instruments and obtain the prediction of conditional expectation of regressors. We show that if the conditional expectation is approximate sparse, i.e., only a small set of instruments can explain the most portion of conditional expectation, our Lasso-based 2SLS estimation will be root-n consistent and asymptotically normal. Our method will be still valid even when the number of instruments increases at the same rate or faster thanthe sample size. The performance of proposal estimation in finite sample is illustrated by a simulation demonstration.