Permanent and Transitory Movements in Output and Unemployment: Okun’s Law Persists

This paper develops a bivariate correlated unobserved components model to investigate the interaction between output and unemployment. The model separates these two key macroeconomic variables into permanent and transitory components and provides estimates of the correlations among these components. The results for the US indicate that fluctuations in both output and unemployment are largely permanent and there exists a negative relationship between these permanent components similar to the Okun’s Law relationship between the transitory components. These results call into question macroeconomic theories that imply zero correlation between the different components, as well as theories that consider recessions as purely transitory movements in either output or unemployment. The author wishes to thank James Morley for constant help and guidance, Gaetano Antinolfi, Lee Benham, Marcus Berliant, Art Carden, Steve Fazzari, Neville Francis, Ed Greenberg, Tom King, Michael Owyang, Jens Sondergaard, Houston Stokes, and the participants in the Applied Time-Series Research Group at Washington University, the Midwest Economics Association 68 Annual Meeting in Chicago, and the Western Economic Association International 79 Annual Conference in Vancouver. I especially thank Christoph Schleicher for help with the proof of identification of the model. All remaining errors are my own. Section 1: Introduction Many macroeconomic models and theories separate the study of economic growth from that of fluctuations. They also often separate the study of permanent movements in the unemployment rate (the natural rate of unemployment or the NAIRU—NonAccelerating Inflation Rate of Unemployment) from the study of transitory unemployment. The connection between output and unemployment comes through Okun’s Law which suggests that an increase in transitory output is accompanied by a decrease in transitory unemployment. Thinking of the economy in this manner implicitly assumes that the components of output and unemployment are uncorrelated except for a negative correlation between the two transitory components. Theories do exist, however, which suggest the existence of additional nonnegative correlations between the components of output and unemployment. For example, some real business cycle theories, such as the one presented by Kydland and Prescott (1982), imply a negative correlation between the permanent and transitory components of output. In these theories, transitory movements in the series arise primarily from adjustment to permanent changes. Other theories suggest a positive correlation between permanent and transitory movements. For example, a temporary increase in investment may lead to both transitory and permanent increases in output. Hysteresis may also imply a positive correlation between transitory and permanent movements where, for instance, a temporary increase in unemployment may partially persist and become permanent (e.g. Blanchard and Summers 1986). Economists thus need empirical evidence to distinguish between these different theories. Until recently, however, time series models of output and unemployment have primarily reflected the thinking that the components of major macroeconomic time series are uncorrelated. Clark (1987), Stock and Watson (1988), and others supposed that 1 Some researchers (for example Blanchard and Quah 1989) assume that the unemployment rate is stationary and thus does not have a permanent component. This assumption will be considered in Section 4.4. 2 One major exception to this is the Beveridge and Nelson decomposition (1981), which does not assume anything about the correlation between the components. The innovations in the estimated components of the Beveridge and Nelson decomposition are perfectly negatively correlated, however the implied correlation between the true components can take on any value. It is possible to solve for this correlation in the univariate case, as shown by Morley, Nelson, and Zivot (2003). The multivariate case has been examined by Schleicher (2003) and will be discussed here in Section 3.

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