Testing for public debt sustainability using a time-scale decomposition analysis

In this paper we estimate the response of primary surplus to lagged debt to test for debt sustainability within the 17 EMU countries by using a factor model. The analysis is split into two stages. In the first stage we retrieve the cyclical and long-run components of primary surplus and debt ratios of each EMU country using a wavelet decomposition for each fiscal covariate, based on the Maximal Overlapping Discrete Wavelet Transform. In the second stage, we use Full Information Maximum Likelihood for a factor decomposition of thecross covariance matrix of the wavelet coefficients of primary deficit and debt to GDP ratios in order to measure the short run and the long run reaction of the primary surplus to (lagged) debt. The empirical evidence shows a positive response of primary surplus to debt within EMU as a whole. Country specific factor decomposition confirms Germany as the one of the most virtuous countries, and, Italy, as the only PIIGS member on a long-run sustainable path for debt