Nonstationary panels with unobserved heterogeneity
The dissertation comprises 3 papers which are available at:
1. Identifying latent grouped patterns in cointegrated panels. (2018). Working paper.
2. Nonstationary panel models with latent group structures and cross-section dependence. (2019). Working paper.
Abstract
This dissertation develops several econometric techniques to address the unobserved heterogeneity in nonstationary panels, namely identifying latent group structures in cointegrated panels, studying nonstationary panels with both cross-sectional dependence and latent group structures, and estimating panel error-correction model with unobserved dynamic common factors.
Chapter 1 considers a panel cointegration model with latent group structures that allows for heterogeneous long-run relations across groups. We extend Su et al. (2013) classifier-Lasso (C-Lasso) method to the nonstationary panels and allow for the presence of endogeneity in both the stationary and nonstationary regressors in the model. In addition, we allow the dimension of the stationary regressors to diverge with the sample size. We show that we can identify the individuals’ group membership and estimate the group-specific long-run cointegrated relationships simultaneously. We demonstrate the desirable property of uniform classification consistency and the oracle properties of both the C-Lasso estimators and their post-Lasso versions. The special case of dynamic penalized least squares is also studied. Simulations show superb finite sample performance in both classification and estimation. In an empirical application, we study the potential heterogeneous behavior in testing the validity of long-run PPP hypothesis in the post-Bretton Woods period from 1975-2014 covering 99 countries. We identify two groups in the period 1975-1998 and three ones in the period 1999-2014. The results confirm that at least some countries favor the long-run PPP hypothesis in the post-Bretton Woods period.
Chapter 2 proposes a novel approach, based on Lasso, to handle unobserved parameter heterogeneity and cross-sectional dependence in nonstationary panel models. We propose a penalized principal component method to jointly estimate group-specific long-run relationships, unobserved common factors and to identify unknown group membership. Our Lasso-type estimators are consistent and efficient. We provide a bias-correction procedure under which our estimators are centered around zero as both dimensions of the panel tend to infinity. We establish a mixed normal asymptotic distribution for our estimators, which permit inference using standard test statistics. Finally, we apply our approach to study the international R&D spillovers model with unobserved group patterns. The results shed new light on growth convergence puzzle though the channel of technology diffusions.
Chapter 3 proposes a novel econometric model that accounts for both long-run and short-run co-movements in panel error correction models. By imposing latent group structures, we achieve efficient estimation for long-run cointegration vectors in the presence of unobserved heterogeneity. The short-run co-movements are driven by unobserved dynamic common factors, which can be consistently estimated by principal components. We propose a penalized generalized least squares method that jointly estimates long-run cointegration vectors and infers unobserved group structures. We establish asymptotic properties for two Lasso-type estimators. In an empirical application, we estimate longrun cointegration relationships between bid and ask quotes in stock market. We introduce a new measure for efficient price, which is weighted average of bid and ask quotes.