Heterogeneous Panel Data Models with Cross--Sectional Dependence

Abstract

This paper considers a semiparametric panel data model with heterogeneous coefficients and individual-specific trending functions, where the random errors are assumed to be serially correlated and cross-sectionally dependent. We propose mean group estimators for the coefficients and trending functions involved in the model. It can be shown that the proposed estimators can achieve an asymptotic consistency with rates of root−N T and root−N T h, respectively as (N, T ) → (∞, ∞), where N is allowed to increase faster than T . Furthermore, a statistic for testing homogeneous coefficients is constructed based on the difference between the mean group estimator and a pooled estimator. Its asymptotic distributions are established under both the null and a sequence of local alternatives, even if the difference between these estimators vanishes considerably fast (can achieve root-N T 2 rate at most under the null) and consistent estimator available for the covariance matrix is not required explicitly. The finite sample performance of the proposed estimators together with the size and local power properties of the test are demonstrated by simulated data examples, and an empirical application with the OECD health care expenditure dataset is also provided.

Spiked Eigenvalues of High-Dimensional Separable Sample Covariance Matrices

“…Empirical results show that dependent variable HE, the regressor variables GDP and DR y , and the residual u it possess factor structures, while DR o and GHE follow unit root structures. These results are consistent with the relevant literature using a factor structure to model healthcare expenditure (HE), such as [8] and [18]. Furthermore, we analyze the eigenvalues of the sample covariance matrices for HE, GDP , DR y , DR o , GHE, and the residual u it , which are provided in Figures 21-26, respectively.…”

“…Meanwhile, mortality data indicate non-stationary temporal trending behavior. Another popular dataset is healthcare expenditure data accumulated from certain countries and observed over several years, which are usually modeled as panel data in econometrics (see Gao, Xia and Zhu [18]).…”

An Integrated Panel Data Approach to Modelling Economic Growth

“…In the second case, as in Pedroni (2007) we assume that different countries have different types of time trends. This case has been partially discussed in Chen et al (2012) and Gao et al (2018). In particular, Gao et al (2018) allow the regressors x it to have the following form…”

“…This case has been partially discussed in Chen et al (2012) and Gao et al (2018). In particular, Gao et al (2018) allow the regressors x it to have the following form…”