Specification Tests for Time-Varying Coefficient Panel Models

This paper provides a nonparametric test for the commonly-used structure, the homogeneity and stability, on the parameters in panels. We ?rst get the augmented residuals by estimating the model under the null hypothesis of homogeneity and stability, then run auxiliary time series regressions of residuals on the regressors with time-varying coe?cients via sieve methods. The test statistic is constructed by averaging the squared ?tted values, which is close to zero under the null and deviates from zero under the alternative. We show that the test statistic, after being appropriately standardized, is asymptotically normally distributed under the null and a sequence of Pitman local alternatives as both cross-sectional and time dimensions tend to in?nity. A bootstrap procedure is proposed to improve the ?nite sample performance of our test. Monte Carlo simulations indicate that our test performs reasonably well in ?nite samples. We apply the test to study the Environmental Kuznets Curve in U.S. and reject the homogeneity and stablility of the coe?cients for all states. In addition, we extend the procedure to test other structures such as the homogeneity of time-varying coe?cients or the stability of heterogeneous coe?cients.