Persistence in U.S. state unemployment rates.

• Author: Sephton, Peter S.

1. Introduction

   Midway through 2008, the U.S. national economy was in jeopardy of decline. Interest was renewed in historical business cycle dating, and many questions arose. Would there be a recession, and how long might it last? How would changes in growth be distributed across the country, and how might state legislators ameliorate the shocks that were about to come? What role would the election of a new president play, and in conjunction with the ongoing financial crisis and the government's unprecedented policy actions, what might happen to unemployment rates? Would they rise, and would the changes be permanent or just seem so? Would confidence return quickly, or would the U.S. economy fall into a protracted decline, with macroeconomic multipliers exacerbating distress across globally integrated supply chains? Could consumers keep the economic expansion moving forward, or was it time for another period short-lived, it is hoped--of creative destruction?

   The United States learned just how serious the situation had become when, in early December 2008, the National Bureau of Economic Research's Business Cycle Dating Committee announced that the recession had begun nearly a year prior. It appears that economists had difficulty extracting the signal from the noise, particularly given revisions to the data. For example, in late September the Bureau of Economic Analysis reduced the second-quarter estimate of real growth to 2.8% from the initial estimate of 3.3%. While this reduction represented only one-half of a percent, the media was quick to report an increased risk of recession (Englund and MacDonald 2008). Calling the third strike of the third out in the bottom of the ninth inning of the seventh game of the World Series is surely bound to test one's inner strength; so, too, would officially pronouncing that a recession had begun. Business cycle dating committees want to be sure before making the call--and we economists generally take our time, hoping the data will eventually provide clarity.

   For obvious reasons, state legislators watch local unemployment rates closely, since those rates have an important bearing on revenue generation and the near-term economic and financial outlook. If economists can provide a useful characterization of the processes describing how unemployment rates evolve over time, policy makers can interpret changes with greater precision and introduce policies that can hasten the adjustment back to the desired path. Until recently, much of the empirical literature suggested many states had unemployment rates that behaved as though macroeconomic shocks had a permanent effect on the unemployment rate; that is, they were path-dependent and subject to hysteresis. The other prevalent view, at least from a theoretical standpoint, was that the real side of the economy determined the unemployment rate and that shocks to the economy could have structural effects that could make the "equilibrium" unemployment rate shift over time. This "natural rate" view allows the unemployment rate to move in more or less a stable pattern around a shifting mean or perhaps trend, if one subscribes to the view that economic development and structures evolve at different rates over time.

   In an important paper, Romero-Avila and Usabiaga (2007) use sophisticated tests for nonstationarity to demonstrate that many states had unemployment rates that seemed to fluctuate over time around a mean that shifted twice over the period 1976-2004. Their use of a multivariate test is novel, and their results indicate that many unemployment rates were highly persistent but not the result of some random process generating trend-like behavior. They report that many unemployment rates were indeed mean-reverting so that they would return to the previous paths, given sufficient time.

   The purpose of this note is to extend the analysis of Romero-Avila and Usabiaga to the concept of fractional integration to demonstrate that the empirical evidence supports both structuralist and hysteresis models in many states, depending on the time period under examination. Generally speaking, over the last 30 years, most states had unemployment rates that were stationarity fluctuations around a shifting trend. In some cases, the unemployment rate process was well described by a random walk during some periods. Indeed, since the late 1980s the unemployment rates in Connecticut, Massachusetts, and New Hampshire appear to be random walks, a result that might not bring much solace to policy makers in those states. Most other states appear to have unemployment rates that were mean-reverting, suggesting that the process of creative destruction is on going in the United States.

   Section 2 describes fractional integration and outlines a relatively new univariate approach to testing for fractional integration. This is followed by a novel method of estimating the degree of fractional integration when allowance is made for breaking means in section 3. Conclusions and suggestions for further work follow in section 4.

2. Tests for Fractional Integration

   A fractionally integrated process exhibits behavior that may appear to be a random walk but may actually be mean-reverting. The concept of non-integer differencing allows a series to be characterized as being covariance stationary when the degree of fractional integration is below one-half or non-covariance stationary yet mean-reverting when it lies between one-half and one. Visual inspection of the history of the series might suggest that it shares many characteristics of a random walk: long decays in the...