COWLES FOUNDATION FOR RESEARCH IN
ECONOMICS Box 208281
COWLES FOUNDATION DISCUSSION PAPER NO. 1832 Testing for Common Trends in Semiparametric Panel Data
Models Younghui Zhang, Liangjun Su, and Peter C.B. Phillips October 2011 This paper proposes a nonparametric test for common trends in
semiparametric panel data models with fixed effects based on a measure of nonparametric
goodness-of-fit (Rē). We first estimate the model under the null hypothesis of common
trends by the method of profile least squares, and obtain the augmented residual which
consistently estimates the sum of the fixed effect and the disturbance under the null.
Then we run a local linear regression of the augmented residuals on a time trend and
calculate the nonparametric Rē for each cross section unit. The proposed test statistic
is obtained by averaging all cross sectional nonparametric Rē's, which is close to zero
under the null and deviates from zero under the alternative. We show that after
appropriate standardization the test statistic is asymptotically normally distributed
under both the null hypothesis and a sequence of Pitman local alternatives. We prove test
consistency and propose a bootstrap procedure to obtain p-values. Monte Carlo simulations
indicate that the test performs well in finite samples. Empirical applications are
conducted exploring the commonality of spatial trends in UK climate change data and
idiosyncratic trends in OECD real GDP growth data. Both applications reveal the fragility
of the widely adopted common trends assumption. |
