Grouped Variable Approximate Factor Analysis

We introduce a generalization of the approximate factor model for which the observable variables belong to a nite number of groups. The error terms of variables that belong to di erent groups are assumed to be at most weakly correlated, but the correlation between the errors of variables that belong to the same group is not restricted. We propose an approximate instrumental variables method to estimate the model, prove consistency and provide rates of convergence. Monte carlo simulations provide evidence of the performance of the approximate instrumental variables estimator relative to the principal components estimator of Stock and Watson (2002a). We nd that if the grouped variable structure exists and is exploited in the construction of the estimator, then the approximate instrumental variables estimator is superior to the principal components estimator. In cases where the variables have an approximate factor structure, the approximate instrumental variables estimator has a similar performance to the principal components estimator.