Testing for persistence in aggregate and sectoral Canadian unemployment

Abstract

Persistence in aggregate and sectoral Canadian unemployment is tested for. Using the corrected for short-range dependency modified rescaled-range test, it is concluded that the fluctuations in aggregate and sectoral Canadian unemployment exhibit persistence. Policies aimed at reducing inflation should embody and account for the extra cost of sustained unemployment due to its persistence.

Acknowledgements

The first author is grateful to the McGill Major Fellowship for financial support, to John W. Galbraith and to the seminar participants at the University of Central Florida for helpful comments.

Notes

¹ The most widely used notion of short-range dependence is the concept of `strong mixing' due to Rosenblatt (1956). It measures the decline of statistical dependence between events separated by successively longer spans of time. As the time span increases and the maximal dependence between events becomes trivially small, then the time series is a strong-mixing one, such as the class of ARMA models wherein the autocorrelations decay exponentially. Dependence between events over a long span defines long-range dependence, such as long-memory processes.

² See Mandelbrot (1972) for the superiority of the rescaled range test statistic over analysing variance ratios. An application of eight test statistics to six exchange-rate daily series, showed that the modified R/S statistic is the most robust test against short-run effects, but has the disadvantage of relatively smaller power (Hauser, 1997, p. 269).

³ The variables of interest are total unemployment, and unemployment in the manufacturing and services sectors for Canada. All the series are in log-level form. The CANSIM labels are D980712, D980737 and D980739, for total, manufacturing and services unemployment, respectively. The quarterly data covers the period 1976–1999. This sample period is focused on for the following reasons. Prior to 1976, the Canadian government undertook an overhaul to the unemployment insurance benefits. Post 1999, CANSIM changed the labelling of the series to D968140 and D968141.

⁴ By correcting for short-range dependency, the limiting distribution of the modified statistic is invariant to many forms of short-range dependency but sensitive to the presence of long-range dependency.

⁵ The modified rescaled and range test procedure was written in RATS^©. The data and the routine code are available at <http://www.bus.ucf.edu/omikhail>