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-NT and root-NTh, respectively, 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-NT 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.
Highlights
Unobserved heterogeneity is a pervasive feature among microeconomic individual responses as suggested by Heckman (2001), see Durlauf et al (2001) for an example of multi-country studies
The test, ∆, by Pesaran and Yamagata (2008) is not generally applicable to our situation where there are deterministic trending as well as crosssectional dependence (CSD) and serial correlation (SC) involved in the model we are studying in this paper, it is workable in some specific cases
We study the determinants of health care expenditure in OECD countries where those elasticities and underlying progresses are allowed to be heterogeneous
Summary
Unobserved heterogeneity is a pervasive feature among microeconomic individual responses as suggested by Heckman (2001), see Durlauf et al (2001) for an example of multi-country studies. Pesaran (2006) considers panel data models with i.i.d. random coefficients across individuals, where the common population mean is estimated with root-N consistency. Boneva et al (2015) impose the heterogeneous covariate functions with a common component structure, where the basis functions can be estimated with a root-N T h rate, see Vogt and Linton (2015) for a nonparametric panel data model with a group structure. Instead of imposing restrictions on the heterogeneity structure, we utilize the panel data information by using the weighted averaging or mean-group estimators based on individual regressions. Where Σβ is the covariance matrix involved in the asymptotic distribution of lNT (βmg − βp), in which lNT → ∞ is a sequence of real numbers One difficulty with such approach is that the difference (βmg − βp) can be too small under both the null and the alternative.
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