Abstract
This chapter presents the methodology for the construction of the large battery of panel unit root and stationarity tests employed in the first part of the analysis, which explicitly allow for cross-sectional dependence. Smith et al. (J Appl Econometrics 19:147–170, 2004) and Hadri (Econom J 3:148–161, 2000) control for general forms of cross-dependence through bootstrap methods, Breitung and Das (Statistica Neerlandica 59:414–433, 2005) control for contemporaneous cross-correlation through seemingly-unrelated methods, Chang (J Econom 110:261–292, 2002) allows for cross-correlation by using a nonlinear instrumental variables method, Choi (Econometric theory and practice: frontiers of analysis and applied research: essays in honor of Peter C.B. Phillips, pp 311–334, 2002) considers a restrictive one-factor model in which all cross-sectional units are equally affected by the common factor, Pesaran (J Appl Econom 22(2):265–312, 2007) also allows for one common factor but with different factor loadings across units, and Moon and Perron (J Econom 122:81–126, 2004) and Harris et al. (J Bus Econ Stat 23:395–409, 2005) incorporate multiple common factors.
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Notes
- 1.
See Smith et al. (2004, pp. 165–166) for details on the bootstrap procedure in a similar spirit to that in Maddala and Wu (1999). This method generates bootstrap innovations through resampling using a block size of 30 and 20,000 replications. The maximum lag order of autocorrelation used to compute the statistics is set at 8.
- 2.
All the five tests take the presence of a unit root for all individuals as the null hypothesis vs. the alternative hypothesis of stationarity for at least one individual unit.
- 3.
For expositional simplicity we abstract from lagged augmented terms.
- 4.
Asymptotic independence of individual t-statistics is achieved by establishing asymptotic orthogonalities of the nonlinear instruments used in the construction of individual IV t-statistics. As a result, in a panel setting, one does not need to impose independence across units or to rely on sequential asymptotics in order to be able to construct panel unit root tests based on averaging across individual statistics.
- 5.
These are obtained non-parametrically using the Quadratic Spectral kernel with fixed bandwidth.
- 6.
Hadri’s statistic must be compared with the upper tail of the standard normal distribution.
- 7.
\( P_{m} \) must be compared with the critical values from the upper tail of the standard normal distribution, and Z and \( L^{*} \) with the critical values from the lower tail of the standard normal distribution.
- 8.
The panel unit root tests of Moon and Perron (2004) take the null hypothesis of nonstationarity for all cross-sectional units, versus the alternative of stationarity for all units. In contrast, the tests of Chang (2002), Choi (2002), Smith et al. (2004), Breitung and Das (2005) and Pesaran (2007) described in this chapter and Bai and Ng (2004a) employed in chapter 5, all take the null hypothesis of nonstationarity for all units, versus the alternative hypothesis of stationarity for at least one unit.
- 9.
The long-run variance of the residuals is computed with both the Barlett and Quadratic Spectral kernels with non-parametric Newey-West (1994) bandwidth selection. As a result, we present two sets of Moon and Perron (2004) statistics.
- 10.
The null hypothesis implies that all cross-sectional units are stationary against the alternative that at least one unit is nonstationary.
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Hernández-Salmerón, M., Romero-Ávila, D. (2015). Econometric Methods. In: Convergence in Output and Its Sources Among Industrialised Countries. SpringerBriefs in Economics. Springer, Cham. https://doi.org/10.1007/978-3-319-13635-6_3
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DOI: https://doi.org/10.1007/978-3-319-13635-6_3
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