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.

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“…Therefore, future studies suggest using another estimator or model to address heterogeneity and the cross-dependency problem simultaneously. For example, consider the spatial panel modeling or another model such as the heterogeneous panel data models with cross-sectional dependence 40 that can address this problem to avoid biased test results.…”

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“…Each region possesses unique characteristics, such as distinct healthcare policies, economic conditions, and demographic profiles. Panel data models allow for the inclusion of these differences, ensuring more accurate and reliable estimates compared to models that use only cross-sectional or time-series data [ 19 , 44 , 104 ]. Enhanced data informative: by combining cross-sectional and time-series data, panel data models provide more informative datasets.…”

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“…Similarly, statisticians have developed various panel unit root and cointegration tests to circumvent the problem (Liven &Lin, 1993;Quah, 1994;McCoskey & Kao, 1998;Chieng & Kao, 2002). Despite the efforts by applied econometricians, it appears that the panel unit roots test cannot provide an appropriate account of the cross-sectional dependence problem (Gao et al, 2020;Su& Chen, 2013;Pesaran & Yamagata, 2008;Ando & Bai, 2015;Breitung et al, 2016;Dikgraaf & Vollebergh, 2005). Breusch and Pagan (1979) and Pesaran (2004) are often implemented to resolve the problem.…”