A Principal Components Approach to Cross-Section Dependence in Panels

6 Conclusions

In the context of large N and T panels it is important to confront the is-
sue of cross-section dependence. Such dependence may arise from omitted
unobservable global variables or common shocks which may be correlated
with each group regressor. In this paper we propose a two-stage estimation
method to deal with these. First one extracts principal components from the
residuals of the model of interest. These factors can be used to augment the
original regression equations to proxy possible omitted variables. A compar-
ison of parameter estimates across the regression models with and without
factors may provide some insights into the nature of these group depen-
dences, namely, whether they represent exogenous world shocks or omitted
global variables correlated with the regressors. In contrast to two-way FE,
this approach can be used in models with heterogeneous slope coefficients
across countries and when there are multiple omitted variables to which each
country reacts differently. Moreover, in contrast to SURE-GLS it can be
applied to large N panels. Using sequential limit theory it is shown that, for
a simple DGP with no autocorrelation or groupwise heteroskedasticity, the
POLS slope coefficient estimator of the augmented regression is consistent.
For panel dimensions typical of the PPP literature and using POLS, FE and
MG estimators, Monte Carlo simulations also confirm the bias reduction for
a DGP with serial dependence and heteroskedasticity.

The proposed approach is illustrated by means of a PPP application
for a group of 17 OECD countries 1973:1-1998:12. We find that between-
group dependence is clearly significant in PPP equations and that it is much
stronger in the US dollar than in the German mark panels. In all panels
and PPP equations a minimum of one of the unobserved factors is clearly
significant. Moreover, the impact of the factors on the augmented regression
coefficients seems to strengthen support for long run PPP.

Finally the paper suggests various issues which warrant further research.
One is to derive the appropriate asymptotic covariance matrix of the above
panel estimators for the augmented regression. Absent the latter, another is
to investigate whether a bootstrap technique might provide consistent stan-
dard errors in this setup. The case where the omitted variables are I(1) also
needs consideration. It is hoped that the present contribution may motivate
a more formal treatment of the ideas and approach elaborated in this paper.

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