Nonlinearities and Fractional Integration in the US Unemployment Rate*

Abstract

This paper proposes a model of the US unemployment rate which accounts for both its asymmetry and its long memory. Our approach introduces fractional integration and nonlinearities simultaneously into the same framework, using a Lagrange multiplier procedure with a standard null‐limit distribution. The empirical results suggest that the US unemployment rate can be specified in terms of a fractionally integrated process, which interacts with some nonlinear functions of labour‐demand variables such as real oil prices and real interest rates. We also find evidence of a long‐memory component. Our results are consistent with a hysteresis model with path dependency rather than a non‐accelerating inflation rate of unemployment (NAIRU) model with an underlying unemployment equilibrium rate, thereby giving support to more activist stabilization policies. However, any suitable model should also include business cycle asymmetries, with implications for both forecasting and policy‐making.