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Discriminating Short and Long Memory in Finite Samples Using Sensitivity Analysis: An Application to Growth Convergence

The standard linear model y_t = x_tβ u_t , where u_t is generated from an ARFIMA process, is considered. The sensitivity of the predictor and sensitivity of variance estimates of the linear model to long memory are investigated by constructing the statistical measures B_L/S and D_L/S, respectively. B_L/S and D_L/S is interpreted as a sensitivity measure for the long-memory process without the short memory effects. As an application, the memory characteristics of per capita GDP of 30 countries are investigated from the Maddison GDP dataset. It is found that per-capita GDP exhibits long memory characteristics, and the long-run growth estimates are sensitive to the long memory characteristics.