A Joint Test for Slope Homogeneity and Stability in Panel Data Models with Fixed Effects

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This paper provides a nonparametric joint test for slope homogeneity across individuals and stability along time in panel data models with fixed effects based on auxillary semi-parametric time series regressions. We first estimate the model under the null hypothesis of slope homogeneneity and stability, and obtain the augmented residual which consistently estimates the sum of fixed effect and the disturbance under the null. Then we run a time series regression of the augmented residuals on a time trend and a set of regressors with time-varying coefficients by the sieve methods for each cross-sectional unit. The proposed test statistic is obtained by averaging all the squared fitted values across inviduals and time periods, which is close to 0 under the null and deviates from 0 under the alternative. We show that the test statistic, after being appropriately standardized, is asymptotically normally distributed under both the null and a sequence of Pitman local alternatives when both cross-sectional dimension N and time dimension T tend to infinity. A bootstrap procedure is proposed to improve the finite sample performance of the test. Monte Carlo simulations indicate that the proposed test performs reasonably well in finite samples. We apply our test to a financial data set and reject the assumption of homogeneous and time-invariant coefficients.

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