Testing for parameter constancy in the time series direction in panel data models

Abstract

We propose tests for parameter constancy in the time series direction in panel data models. We construct a locally best invariant test based on Tanaka [Time series analysis: nonstationary and noninvertible distribution theory. New York: Wiley; 1996] and an asymptotically point optimal test based on Elliott and Müller [Efficient tests for general persistent time variation in regression coefficients. Rev Econ Stud. 2006;73:907–940]. We derive the limiting distributions of the test statistics as T→∞ while N is fixed, and calculate the critical values by applying numerical integration and response surface regression. Simulation results show that the proposed tests perform well if we apply them appropriately.

Keywords:

• parameter constancy
• panel data
• locally optimal test
• point optimal test
• characteristic function
• response surface regression

JEL Classification:

• C12
• C32
• C33

Acknowledgements

The authors are grateful to In Choi, Tatsushi Oka, Pierre Perron, Zhongjun Qu, Yohei Yamamoto and the participants at the 2012 Hitotsubashi-Sogang Conference on Econometrics, SETA 2013, EEA-ESEM 2013, and seminar participants at Boston University and Hitotsubashi University. All errors are our responsibility.

Notes

1. Juhl and Xiao [39] proposed to choose $\overline{c}$ such that ${\int }_0^M(\varphi (c,c)-\varphi (c,\overline{c}))\mathrm{d}c$ is minimized, where $\varphi (c,\overline{c})=P(qLL<x;c)$ is a power function of the qLL test and $\varphi (c,c)$ is a power envelope. We can easily see that this strategy is the same as the one considered in this study.

2. Simulation results with serially correlated errors are available upon request.

3. Under the null hypothesis, DGP2 and DGP4 are equivalent to DGP1 and DGP3, respectively, and thus we omit the results under DGP2 and DGP4.

4. It can be shown that ${\widetilde{\mathrm{LM}}}_{\mathrm{homo}}$ and $-{\widetilde{qLL}}_{\mathrm{homo}}$ do not diverge to infinity but are stochastically bounded even in the presence of heterogeneity in the slopes with constant parameters in the time series direction. We omit the proof to save space.

Additional information

Funding

Daisuke Yamazaki gratefully acknowledges the financial support by the JSPS Research Fellowship for Young Scientists [grants-in-aid no. 12J04741]. Kurozumi's research was partially supported by JSPS and BA under the Japan-Britain Research Cooperative Program and by the Ministry of Education, Culture, Sports, Science and Technology [grants-in-aid nos. 23243038 and 24243031].