Least Squares Asymptotics in Spurious and Cointegrated Panel Regressions with Common and Idiosyncratic Stochastic Trends*

Abstract

This article makes an analytical study of the effects of the presence of both common and idiosyncratic stochastic trends on the pooled least squares estimator. The results suggest that the usual result of asymptotic normality depends critically on the absence of the common stochastic trend.

Demographics and Business Cycle Volatility: A Spurious Relationship?

“…After replicating their results, we still find no clear evidence in favor of cointegration. Although the richer panel dimension allows the authors to pool over a larger number of cross-sections, cross-sectional dependence can still render their estimation results spurious (see Urbain and Westerlund, 2011). However, Banerjee and Carrion-i-Silvestre (2015) show that consistent estimation is possible once cross-sectional dependence is controlled for using the CCEP approach of Pesaran (2006).…”

“…When using panel data, a consistent estimate of the long‐run relation can thus be obtained even if there is no cointegration. Besides a sufficiently large cross‐sectional dimension, an important condition for this asymptotic result to hold is that the error terms are independent over cross‐sections (see also Urbain and Westerlund, ). The bottom left panel of Table shows that although there are signs of cross‐sectional dependence in the error terms this is not overwhelming, especially when using the SW volatility measure.…”

Testing for Panel Cointegration Using Common Correlated Effects Estimators

“…Two other articles are worth mentioning to put our work in context. First, Urbain and Westerlund () look at the asymptotics of least squares regressions in spurious and cointegrated panels with cross section dependence driven by common and idiosyncratic stochastic trends or factors that may be integrated or stationary. Second, Gengenbach et al () study a panel cointegration test based on the error correction model approach where the cross section dependence is modelled via the use of cross section averages.…”

Testing weak exogeneity in cointegrated panels

“…In the international business cycle literature, for example, global technology shocks -widely assumed the primary force driving world business cycles -are typically viewed as persistent but stationary (see, e.g., Kehoe and Perri, 2002); the same applies to global demand (spending) shocks (e.g., Boileau et al, 2010). In other situations, it may be more difficult to rule out common stochastic trends; for example, panel tests of purchasing power parity usually involve country-specific I(1) variables defined relative to a reference country, and this tends to introduce common stochastic trends in the analysis (e.g., Urbain and Westerlund, 2011).…”