Fractional Output Convergence, with an Application to Nine Developed Countries

We argue that cross-country convergence of output per capita should be examined in a fractional-integration time-series context and we propose a new empirical strategy to test it, which is the first one that discriminates between fractional long-run convergence and fractional catching-up. The starting point of the paper is: since there are reasons to believe that aggregate output is fractionally integrated, the usual testing strategy based on unit-root or traditional I(1)-I(0) cointegration techniques is too restrictive and may lead to spurious results. We then propose a new classification of output convergence processes which is valid when outputs are fractionally integrated and which nests the usual definitions built for an I(1)-versus-I(0) world. The new testing strategy, which can identify the precise type of convergence, is based on the combined use of new inferential techniques developed in the fractional integration literature. The advantage of these new techniques is that of being robust both to the presence of a trend and to a memory parameter d above 0.5. We explain in detail the importance of this advantage for testing convergence. This strategy applied on a group of developed countries (G-7, Australia and New Zealand) shows that these countries converged in the last century; it also determines the type of convergence for each one. The main result is that per-capita-output differentials are typically mean-reverting fractionally I(d), with d significantly above 0 but below 1. This contrasts with the results of divergence obtained with six unit-root tests and by other authors with I(1)-I(0) (co)integration techniques. The paper therefore contributes to solve the puzzling negative or inconclusive results about convergence usually obtained with I(1)-I(0) tests; our results also prove that the proposed widening of the statistical definition of output convergence is necessary and that convergence does take place but is slower than traditionally expected