Abstract
In this paper, we develop tests for structural change in cointegrated panel regressions with common and idiosyncratic trends. We consider both the cases of observable and nonobservable common trends, deriving a Functional Central Limit Theorem for the partial sample estimators under the null of no break. We show that tests based on sup-Wald statistics are powerful versus breaks of size , also proving that power is present when the time of change differs across units and when only some units have a break. Our framework is extended to the case of cross correlated regressors and endogeneity. Monte Carlo evidence shows that the tests have the correct size and good power properties.
Highlights
Since the seminal contributions by Perron (1989) and Rappoport and Reichlin (1989), the literature has produced a comprehensive set of results on the changepoint problem in a time series framework - we refer, inter alia, to the articles by Andrews (1993), Andrews and Ploberger (1994), Bai and Perron (1998), and Kejriwal and Perron (2008, 2010)
We show that asymptotic mixed normality is preserved when we allow for cross-dependence among the s, even though asymptotic orthogonality between − and − does not hold any more
This section considers extending the framework to incorporate the case of endogeneity; we develop a fully-modified OLS (FMOLS) estimator and we show that the null distribution of the Wald-type test statistic is the same as in Theorem 2
Summary
Since the seminal contributions by Perron (1989) and Rappoport and Reichlin (1989), the literature has produced a comprehensive set of results on the changepoint problem in a time series framework - we refer, inter alia, to the articles by Andrews (1993), Andrews and Ploberger (1994), Bai and Perron (1998), and Kejriwal and Perron (2008, 2010). We show that our framework can be accommodated to allow for endogeneity Whilst this involves modifying the estimation technique, i.e., from ordinary least squares (OLS) to fully-modified OLS (FMOLS), the limiting distribution of the test and the power versus local alternatives remain unaltered. Results are extended to the case of endogeneity by proving an FCLT for the partial sample FMOLS estimators These results are of independent interest: ordinary large panels asymptotic theory (Phillips and Moon, 1999; Kao, 1999) cannot be applied in our framework due to the strong cross-sectional dependence introduced by the common shocks. We prove that our tests, albeit designed for the common changepoint alternative , have nontrivial power versus alternatives where series have a break at potentially different points in time This is a desirable property, since a break could be induced by a change common to all units, but each unit could have different levels of hysteresis and respond with different lag.
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