Abstract
This paper considers the problem of hypothesis testing in a simple panel data regression model with random individual effects and serially correlated disturbances. Following Baltagi et al. (Econom. J. 11:554–572, 2008), we allow for the possibility of non-stationarity in the regressor and/or the disturbance term. While Baltagi et al. (Econom. J. 11:554–572, 2008) focus on the asymptotic properties and distributions of the standard panel data estimators, this paper focuses on testing of hypotheses in this setting. One important finding is that unlike the time-series case, one does not necessarily need to rely on the “super-efficient” type AR estimator by Perron and Yabu (J. Econom. 151:56–69, 2009) to make an inference in the panel data. In fact, we show that the simple t-ratio always converges to the standard normal distribution, regardless of whether the disturbances and/or the regressor are stationary.
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References
Baltagi, B.H., Kao, C.: Nonstationary panels, cointegration in panels and dynamic panels: a survey. Adv. Econom. 15, 7–51 (2000)
Baltagi, B.H., Kao, C., Liu, L.: Asymptotic properties of estimators for the linear panel regression model with random individual effects and serially correlated errors: the case of stationary and non-stationary regressors and residuals. Econom. J. 11, 554–572 (2008)
Baltagi, B.H., Kao, C., Na, S.: Supplementary appendix to test of hypotheses in panel data models when the regressor and disturbances are possibly nonstationary. Working paper, Syracuse University (2010)
Baltagi, B.H., Krämer, W.: A simple linear trend model with error components. Econom. Theory 13, 463 (1997)
Baltagi, B.H., Li, Q.: A transformation that will circumvent the problem of autocorrelation in an error component model. J. Econom. 48, 385–393 (1991)
Bresson, G., Hsiao, C., Pirotte, A.: Assessing the contribution of R&D to total factor productivity—a Bayesian approach to account for heterogeneity and heteroscedasticity. Adv. Stat. Anal. (2011 this issue)
Canjels, E., Watson, M.W.: Estimating deterministic trends in the presence of serially correlated errors. Rev. Econ. Stat. 79, 184–200 (1997)
Fuller, W.A., Battese, G.E.: Transformations for estimation of linear models with nested error structure. J. Am. Stat. Assoc. 68, 626–632 (1973)
Hsiao, C.: Analysis of Panel Data. Cambridge University Press, Cambridge (2003)
Kao, C.: Spurious regression and residual-based tests for cointegration in panel data. J. Econom. 90, 1–44 (1999)
Kao, C., Emerson, J.: On the estimation of a linear time trend regression with a one-way error component model in the presence of serially correlated errors: part I. J. Probab. Stat. Sci. 2, 213–243 (2004)
Kao, C., Emerson, J.: On the estimation of a linear time trend regression with a one-way error component model in the presence of serially correlated errors: part II. J. Probab. Stat. Sci. 3, 59–96 (2005)
Perron, P., Yabu, T.: Estimating deterministic trends with an integrated or stationary noise component. J. Econom. 151, 56–69 (2009)
Phillips, P.C.B., Moon, H.R.: Linear regression limit theory for nonstationary panel data. Econometrica 67, 1057–1111 (1999)
Vogelsang, T.J.: Trend function hypothesis testing in the presence of serial correlation. Econometrica 66, 123–148 (1998)
Wansbeek, T.J., Kapteyn, A.: A note on spectral decomposition and maximum likelihood estimation of ANOVA models with balanced data. Stat. Probab. Lett. 1, 213–215 (1983)
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Baltagi, B.H., Kao, C. & Na, S. Test of hypotheses in panel data models when the regressor and disturbances are possibly non-stationary. AStA Adv Stat Anal 95, 329–350 (2011). https://doi.org/10.1007/s10182-011-0170-5
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DOI: https://doi.org/10.1007/s10182-011-0170-5