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• W2034758977 abstract "ABSTRACT In this article, a parametric framework for estimation and inference in cointegrated panel data models is considered that is based on a cointegrated VAR(p) model. A convenient two-step estimator is suggested where, in the first step, all individual specific parameters are estimated, and in the second step, the long-run parameters are estimated from a pooled least-squares regression. The two-step estimator and related test procedures can easily be modified to account for contemporaneously correlated errors, a feature that is often encountered in multi-country studies. Monte Carlo simulations suggest that the two-step estimator and related test procedures outperform semiparametric alternatives such as the fully modified OLS approach, especially if the number of time periods is small. Key Words: Cointegrated systemsEstimationInferencePanel dataJEL Classification: C33C12C13 ACKNOWLEDGMENT The research for this article was carried out as part of the DFB research project “Unit roots and cointegration in panel data” and the METEOR research project “Macroeconomic Consequences of Financial Crises” at the University of Maastricht. I wish to thank Harald Badinger, Oliver Fries, Uwe Hassler, Simon Junker, Michael Massmann, and two referees for helpful comments and suggestions. Notes 1I am gratefull to a referee who suggested this possibility to me. 2Although it has not been shown that the finite sample moments of the two-step estimator exist, one may conjecture that the results of Mariano (Citation1972) for the two-step estimator in classical systems of simultaneous equations carries over to the two-step estimator of cointegrated systems. 3As noted by Boswijk (Citation1996), this normalization may be invalid. To check the validity of the normalization, the tests of Boswijk (Citation1996) and Saikkonen (Citation1999) may be used. 4One may think of situations where theoretical considerations suggest a different cointegration rank across, say, countries. This case is beyond the scope of our analysis, as it implies a heterogenous cointegration framework not considered here. 5Phillips and Moon (Citation1999, p. 1092) state that “… when there are strong correlations in a cross section (as there will be in the face of global shocks) we can expect failures in the strong laws and central limit theory arising from the nonergodicity.” 6A similar apparch can be employed for the Wald version of the cointegration test based on Eq. (Equation10). 7As pointed out by a referee, the poor performance of the FMOLS estimator may be improved by applying parametric (VAR based) estimator of the nuisance parameters. Note: The entries display the estimated bias of the cointegration parameter b = 1 based on 5000 replication of the model (21). “two-step” indicates the two-step estimator suggested in Section 3, “FMOLS” denotes the Fully-modified panel cointegration estimator suggested by Pedroni (Citation2000), “DOLS” is the dynamic OLS estimator of Kao and Chiang (Citation2000), and “OLS” indicates the ordinary least-squares estimator of the pooled model. Note: Rejection frequency for tests of the null hypothesis r = 1. “REG” indicates the regression based test suggested in Theorem 2 and “LLL” denotes the LR-bar statistic suggested by Larsson et al. (Citation2001). The local power is computed by simulating the data under the local alternative . The critical values are used that yield tests with an exact size of 0.05 under the null hypothesis (size adjusted power). 5000 replications are used to compute the rejection frequencies. Note: Rejection frequency for tests of the null hypothesis b = 0 in model (Equation21). “2S-OLS” indicates rejection frequencies of a t-test where the errors are assumed to be i.i.d., whereas “2S-robust” indicates a t-test based on robust standard errors computed from (Equation20). The column “GM-FMOLS” reports rejection frequencies of the group mean FMOLS t statistic suggested in Proposition 3.1 of Pedroni (Citation2000) assuming contemporaneously uncorrelated errors. The nominal size is of the tests is 0.05 and 5000 replications are used to compute the rejection frequencies. 8The countries are Australia, Austria, Belgium, Canada, Denmark, Finland, France, Germany, Greece, Ireland, Italy, Japan, Mexico, New Zealand, The Netherlands, Norway, Spain, Sweden, Switzerland, U.K. and the U.S. 9It should be noted that the variable p 0t is identical for all countries and, thus, this variable does not have a panel dimension. The analysis was therefore repeated by using a bivariate system with y t = [e t , p it − p 0t ]′. It was found that the estimated cointegrating vector is not significantly different from β = [1, −1]′ and, therefore, the conclusions remain the same. However, it is interesting to note that the standard errors of βˆ2 are larger than those of βˆ1. This may be due to the lack of country specific variation of the variable p 0t . Note: IPS indicates the test statistic of Im et al. (Citation2003), LL denotes the test suggested by Levin and Lin (Citation1992). LL* is the bias-adjusted LL test of Breitung (Citation2000) and LL*-CC is the same statistic computed by using robust standard errors. Note: This table displays the estimation results of the PPP relationship (Equation22). The standard errors (s.e.) resp. marginal significance level (p-value) are given in parentheses. The column “robust two-step” reports the results based on the robust standard errors computed from (Equation20). The Wald statistic tests the hypothesis β1 = 1 and β2 = −1. Note: The cases refer to the classification of the software EViews 5: Case (2) assumes that the variables have no time trends (restricted constant). Case (3) assumes that at least one variable has a linear time trend. Case (4) assumes that the variables and the cointegration relationships have a time trend." @default.
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• W2034758977 date "2005-04-01" @default.
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• W2034758977 title "A Parametric approach to the Estimation of Cointegration Vectors in Panel Data" @default.
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