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Identifying latent grouped patterns in panel data models with interactive fixed effects. (English) Zbl 1452.62960

Summary: We consider the estimation of latent grouped patterns in dynamic panel data models with interactive fixed effects. We assume that the individual slope coefficients are homogeneous within a group and heterogeneous across groups but each individual’s group membership is unknown to the researcher. We consider penalized principal component (PPC) estimation by extending the penalized-profile-likelihood-based C-Lasso of the first author et al. [Econometrica 84, No. 6, 2215–2264 (2016; Zbl 1410.62110)] to panel data models with cross section dependence. Given the correct number of groups, we show that the C-Lasso can achieve simultaneous classification and estimation in a single step and exhibit the desirable property of uniform classification consistency. The C-Lasso-based PPC estimators of the group-specific parameters also have the oracle property. BIC-type information criteria are proposed to choose the numbers of factors and groups consistently and to select the data-driven tuning parameter. Simulations are conducted to demonstrate the finite-sample performance of the proposed method. We apply our C-Lasso to study the persistence of housing prices in China’s large and medium-sized cities in the last decade and identify three groups.

MSC:

62P20 Applications of statistics to economics
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62H30 Classification and discrimination; cluster analysis (statistical aspects)
62J07 Ridge regression; shrinkage estimators (Lasso)

Citations:

Zbl 1410.62110
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References:

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