Common Trends and Common Cycles in Latin America: A 2-step vs an Iterative Approach

We are interested in determining the number of common trends and common cycles in the output of a set of Latin American countries. In order to work with homogeneous and reasonably good series however, we should rely on annual data. Consequently, the number of variables is relatively large compared to the number of observations to blindly trust the asymptotics. For several years, the panel data literature proposes tools to tackle this problem, mainly for the study of long-run co-movements. We take another road here and we test for cointegration and common cyclical features in a time series framework using an iterative strategy that maximizes the likelihood function by successively imposing long and short-run restrictions until convergence is achieved. Monte Carlo simulations stress advantages of this approach over the two-step one. In practice however, the cost of implementing this more complicated procedure must be evaluated with the expected benefits. Overall, simple adjustments for the degrees of freedom and the use of information criteria are helpful "cheap" alternatives