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This paper employs response surface regressions based on simulation experiments to calculate asymptotic distribution functions for the Johansen-type likelihood ratio tests for cointegration. These are carried out in the context of the models recently proposed by Pesaran, Shin, and Smith (1997) that allow for the possibility of exogenous variables integrated of order one. The paper calculates critical values that are very much more accurate than those available previously. The principal contributions of the paper are a set of data files that contain estimated asymptotic quantiles obtained from response surface estimation and a computer program for utilizing them. This program, which is freely available via the Internet, can be used to calculate both asymptotic critical values and P values. JEL Classification Number: C22 Keywords: cointegration tests, Johansen tests, vector autoregressions, exogenous variables, response surfaces, critical values, approximate

This paper argues that probability forecasts convey information on the uncertainties that surround macro-economic forecasts in a straightforward manner which is preferable to other alternatives, including the use of confidence intervals. Probability forecasts obtained using a small benchmark macroeconometric model as well as a number of other alternatives are presented and evaluated using recursive forecasts generated over the period 1999q1-2001q1. Out of sample probability forecasts of inflation and output growth are also provided over the period 2001q2-2003q1, and their implications discussed in relation to the Bank of England’s inflation target and the need to avoid recessions, both as separate events and jointly. The robustness of the results to parameter and model uncertainties is also investigated by a pragmatic implementation of the Bayesian model averaging approach.

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This paper proposes a pair-wise approach to testing for output convergence that considers all N(N-1)/2 possible pairs of log per capita output gaps across N economies. A general probabilistic definition of output convergence is also proposed, which suggests that all such output gap pairs must be stationary with a constant mean. The approach is compatible with individual output series having unit roots, or other non-stationary common components and does not involve the choice of a reference country in computation of output gaps. It is also applicable when N is large relative to T (the time dimension of the panel). After providing some encouraging Monte Carlo evidence on the small sample properties of the pair-wise test, the test is applied to output series in the Penn World Tables over 1950-2000. Overall, the results do not support output convergence, and suggest that the …ndings of convergence clubs in the literature might be spurious. However, significant evidence of growth convergence is found, a result which is reasonably robust to the choice of the sample period and country groupings. Non-convergence of log per capita outputs combined with growth convergence suggests that while common technological progress seems to have been diffusing reasonably widely across economies, there are nevertheless important country-specific factors that render output gaps highly persistent, such that we can not be sure that the probability for the output gaps to lie within a fixed range will be non-zero.

This paper considers estimation and inference in panel vector autoregressions (PVARs) where (i) the individual effects are either random or fixed, (ii) the time-series properties of the model variables are unknown a priori and may feature unit roots and cointegrating relations, and (iii) the time dimension of the panel is short and its cross-sectional dimension is large. Generalized Method of Moments (GMM) and Quasi Maximum Likelihood (QML) estimators are obtained andthencomparedintermsoftheirasymptoticandfinite sample properties. It is shown that GMM estimators based only on standard orthogonality conditions break down if the underlying time series contain unit roots. Extended GMM estimators making use of further moment conditions are not subject to this problem. However, their finite sample performance is shown to deteriorate as a ratio of cross-section to time-series variation is increased, while the performance of the fixed effects QML estimator is invariant to this ratio. The QML estimators also tend to outperform the various GMM estimators in finite sample. Overall, our findings favor the use of the fixed effects QML estimator, given that it does not impose any restrictions on the distribution generating the individual effects. The paper also shows how the fixed effects QML

This paper continues the investigation of Giles and Williams (2000) on export-led growth (ELG). In the first part, we surveyed the empirical export-led growth literature; it was evident that Granger noncausality tests are commonly applied as a test for ELG. In this paper, we explore the sensitivity of the test for exclusions restrictions often used as the Granger noncauality test for ELG by reconsidering two applications: Oxley’s (1993) study for Portugal and Henriques and Sadorsky’s (1996) analysis for Canada. We focus on robustness to the method adopted to deal with nonstationarity, including the choice of deterministic trend degree. We show that different noncausality outcomes are easy to obtain, and consequently we recommend that readers interpret the empirical ELG literature with care. Our analysis also highlights the importance of examining the robustness of Granger noncauality test results to avoid spurious outcomes in applications.

This paper provides a review of the literature on unit roots and cointegration in panels where the time dimension (T), and the cross section dimension (N) are relatively large. It distinguishes between the …rst generation tests developed on the assumption of the cross section independence, and the second generation tests that allow, in a variety of forms and degrees, the dependence that might prevail across the di¤erent units in the panel. In the analysis of cointegration the hypothesis testing and estimation problems are further complicated by the possibility of cross section cointegration which could arise if the unit roots in the di¤erent cross section units are due to common random walk components.

This paper provides a synthesis and further development of a global modelling approach introduced in Pesaran, Schuermann and Weiner (2004), where country speci…c models in the form of VARX * structures are estimated relating a vector of domestic variables, xit, to their foreign counterparts, x it, and then consistently combined to form a Global VAR (GVAR). It is shown that the VARX * models can be derived as the solution to a dynamic stochastic general equilibrium (DSGE) model where over-identifying long-run theoretical relations can be tested and imposed if acceptable. This gives the system a transparent long-run theoretical structure. Similarly, short-run over-identifying theoretical restrictions can be tested and imposed if accepted. Alternatively, if one has less con…dence in the short-run theory the dynamics can be left unrestricted. The assumption of the weak exogeneity of the foreign variables for the long-run parameters can be tested, where x it variables can be interpreted as proxies for global factors. Rather than using deviations from ad hoc statistical trends, the equilibrium values of the variables re‡ecting the long-run theory embodied in the model can be calculated. This approach has been used in a wide variety of contexts and for a wide variety of purposes. The paper also provides some new results. Keywords: Global VAR (GVAR), DSGE models, VARX*.

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