Unit root tests and persistence of unemployment: Spain vs. the United States

Abstract

In this article, we investigate the existence of infrequent shocks and the degree of persistence of unemployment in the US and Spain over the period 1976–2004. We first apply the minimum Lagrange Multiplier unit root test with up to two endogenous changes in level. The evidence gives support to the hysteresis hypothesis for Spain and to regime-wise stationarity for the US. The computation of median unbiased estimates of half-lives directly from the impulse-response function indicates a much higher degree of persistence of unemployment in Spain than in the US. Our results thus give an indication that aggregate demand policies may have different effects in these two countries.

Acknowledgements

The authors would like to thank seminar participants at the Pablo de Olavide University, Centro de Estudios Andaluces and DG-Economics at the European Central Bank. Carlos Usabiaga acknowledges financial support from Centro de Estudios Andaluces. Special thanks go to Junsoo Lee and Nikolay Gospodinov for providing the codes to implement some of the techniques used in the article. The usual disclaimer applies.

Notes

¹ The search for breaks is carried out over the interval [0.1T, 0.9T] where T is the sample size and a trimming value of 10% is employed to eliminate endpoints. By choosing the most negative t-statistic it is ensured that if the null of a unit root cannot be rejected at the break location determined by the grid search, it will not be rejected at any other break location.

² We begin with the LM unit root t-statistic with two breaks proposed by Lee and Strazicich (2003) and examine the significance of the dummy coefficients on the basis of the conventional t-statistics. If less than two breaks are significant at 10% we apply the minimum LM unit root t-statistic with one break proposed by Lee and Strazicich (2001), and if the break is insignificant we employ the LM unit root t-statistic without breaks proposed by Schmidt and Phillips (1992).

³ Generally, half-lives are calculated using the expression ln(0, 5)/ln(α), where the parameter α is the sum of the coefficients of the underlying autoregressive (AR) process. This can be appropriate for an AR(1) process that decays monotonically, but it is inappropriate for higher order AR processes for which shocks do not generally decay at a constant rate.

⁴ This method provides better coverage rates of the confidence intervals in small and large samples than conventional bootstrap methods when large AR roots are present (Inoue and Kilian, 2002). This is achieved by making the persistence parameter a function of the sample size.