Unit root tests, persistence, and the unemployment rate of the U.S. States.

• Author: Romero-Avila, Diego
• Position: Author abstract

1. Introduction

   The high persistence in unemployment rates observed in the developed world since the first oil shock has led to a vivid debate over which paradigm can better explain the behavior of unemployment rates. The traditional strand of the literature that forms the basis of the natural rate theory (Phelps 1967, 1968; Friedman 1968) assumes that the unemployment rate evolves around an equilibrium level describing stationary fluctuations. This equilibrium level, or natural rate, is set depending on fundamentals of the economy. While initially the absence of theories explaining the determination of the natural rate meant that in practice it was taken to be constant and exogenous, subsequent developments have attempted to identify the structural factors behind differences across economies and over time, including labor productivity, technological change, real interest rates, real exchange rates, and energy prices, to name a few (see Phelps 1994; Phelps and Zoega 1998). According to the structuralist view (Phelps 1994), most shocks to unemployment are temporary, but occasionally the natural rate permanently changes and is affected by variations in the aforementioned structural factors. As a consequence, the unemployment rate may be characterized as a process that is stationary once a small number of structural breaks are allowed for.

   In contrast to the natural rate and structuralist approaches, the hysteresis hypothesis (see Blanchard and Summers 1986, 1987) implies that the unemployment rate is path-dependent, and temporary shocks can affect unemployment permanently. (1) While hysteresis is thought to imply that the natural rate is conditioned by the level of unemployment recorded in the past, persistence in unemployment--which is a special case of the natural rate hypothesis--entails a slow adjustment process of reversion toward the mean. Thus, hysteresis implies that unemployment is characterized by a unit root, while persistence is characterized by a near unit root. In the latter case, shocks to unemployment, though long-lasting, would not have a permanent effect.

   To discriminate among theories explaining the behavior of unemployment rates, unit root tests have been widely applied. The hysteresis hypothesis has been formulated as a unit root process, and its rejection lends support to the natural rate hypothesis (if no breaks are included in the specification) and the structuralist hypothesis (if breaks are allowed for).

   The purpose of this article is to investigate which theoretical paradigm most closely represents the behavior of unemployment rates in the states of the United States over the period 1976-2004. We first apply the individual Lagrange multiplier (LM) t-statistic proposed by Schmidt and Phillips (1992) to monthly data, and we fail to reject the null hypothesis of a unit root in unemployment for forty states. Perron (1989) pointed out that the presence of structural changes could favor the nonrejection of the unit root null if they are not properly accounted for. Therefore, we employ the minimum LM t-statistic, allowing for up to two endogenous changes in level proposed by Lee and Strazicich (2003). However, these tests continue to fail to reject the null hypothesis of a unit root for forty states.

   It is also well known that time series unit root tests have low power, especially in small samples (see Campbell and Perron 1991; DeJong et al. 1992). In order to tackle this problem, we use panel unit root tests. We first employ the panel LM t-statistic without breaks, and we fail to reject the null hypothesis of joint nonstationarity for data adjusted for cross-correlations. Second, in order to combine the best of both worlds, we employ the panel LM t-statistic with up to two level shifts recently developed by Im, Lee, and Tieslau (2005). Only in this case does our panel test have enough power to reject the joint hysteresis hypothesis in favor of regimewise stationarity.

   Since unit root tests are incomplete measures of the degree of persistence of a series, we also compute the half-life of a shock to U.S. state unemployment. This definition measures persistence as the number of years for a unit impulse to decay by one half. In this regard, we try to overcome certain methodological problems with the computation of half-lives by computing impulse-response functions following the procedure proposed by Gospodinov (2004). (2) The estimated half-lives are finite in all but three states, but the magnitude is quite large, which indicates the high degree of persistence in U.S. state unemployment. In order to measure the precision of half-life point estimates, we compute percentile grid-bootstrap confidence intervals for the half-life of the impulse-response function. The upper bound of the 95% confidence interval of half-lives normally exceeds two decades, which points to high uncertainty in the half-life estimates.

   The remainder of the paper is structured as follows. Section 2 briefly reviews the literature testing the hysteresis hypothesis. Section 3 outlines the methodology of individual and panel LM unit root tests with breaks and presents the main results of the tests applied to monthly unemployment rate series for U.S. states. Section 4 reports the results of the half-lives of shocks to U.S. state unemployment. Section 5 puts forward some policy implications and conclusions.

2. Evolution of the Literature Testing the Hysteresis Hypothesis

   Chronologically, the first studies testing the hysteresis hypothesis apply the traditional unit root tests, basically of the augmented Dickey and Fuller (1979) and Phillips and Perron (1988) type (see, for instance, Blanchard and Summers 1986; Alogoskoufis and Manning 1988; Jaeger and Parkinson 1994; Roed 1996, for countries of the Organization of Economic Co-operation and Development [OECD]). Mostly, the evidence supports the hypothesis of hysteresis for the European Union (EU) economies and is mixed for the United States. However, those conclusions are based on unit root tests that under the alternative assume a constant, unique, natural rate of unemployment. In other words, these unit root tests are not robust to the presence of structural breaks (see Perron 1989; Perron and Vogelsang 1992; Zivot and Andrews 1992). To overcome this limitation, Mitchell (1993), Bianchi and Zoega (1998), Arestis and Biefang-Frisancho Mariscal (1999, 2000), Ewing and Wunnava (2001), and Papell, Murray, and Ghiblawi (2000) applied unit root tests that allowed for structural breaks in the unemployment rate of OECD countries. In general, the number of breaks allowed is higher in the most recent papers. (3) Once structural breaks are considered in the analysis, the null hypothesis of hysteresis is rejected in favor of the alternative of stationarity around a changing equilibrium rate for the majority of the countries analyzed, and particularly for the United States, which usually shows a low degree of persistence in unemployment. Such a finding seems to be in accordance with the structuralist theories of unemployment.

   A third group of empirical studies is based on the recent panel unit root tests, which try to exploit the cross-section variation of the series. On the one hand, there is a group of studies that employs panel unit root tests that do not allow for structural breaks. Song and Wu (1998) applied the test of Levin, Lin, and Chu (2002) to a sample of 15 OECD countries with seasonally adjusted quarterly data over the period 1960-1992 and rejected the null of nonstationarity for the panel as a whole. Song and Wu (1997) applied several univariate unit root tests and the Levin, Lin, and Chu (2002) test to annual data (1962-1993) of 48 U.S. states. In general, the univariate tests could not reject the null hypothesis of hysteresis, whereas the panel data test rejected it overwhelmingly. In addition, Leon-Ledesma (2002) analyzed the 50 U.S. states plus the District of Columbia and 12 EU countries (quarterly data, 1985-1999). He applied univariate augmented Dickey and Fuller (1979) tests for unadjusted and adjusted (for cross-sectional correlation) data, and a panel unit root test that did not allow for structural breaks (Im, Pesaran, and Shin 2003). The main results of the study indicate that for the majority of U.S. states and EU countries, the univariate tests do not reject the null hypothesis of hysteresis, whereas the panel test suggests that the most plausible hypotheses are hysteresis for the EU countries and the natural rate for the U.S. states.

   More recent contributions have incorporated one or two structural breaks for the analysis of OECD unemployment under a panel framework. Murray and Papell (2000) employed the test of Levin, Lin, and Chu (2002), which was extended to allow for a homogeneous break in the unemployment mean, to annual data of 17 OECD countries over the period 1955-1990; this test strongly rejected the joint null hypothesis of hysteresis. Strazicich, Tieslau, and Lee (2001) applied the panel LM unit root test, allowing for up to two mean shifts in unemployment, to annual data for 17 OECD countries over the period 1955-1999 and provided evidence of stationarity around a changing equilibrium rate. (4)

   In summary, the inclusion of structural breaks, reinforced by the panel dimension, in unit root testing leads to the rejection of the hypothesis of hysteresis. In this line, the objective of this study is to contribute to this literature by applying individual and panel unit root tests that allow for structural breaks in the level of the unemployment rate of U.S. states. (5) In our analysis, we impose the maximum limit of two structural breaks--three different unemployment regimes--because we think that a higher number of breaks would not match adequately with the structuralist theory; note that this theory suggests the existence of infrequent shocks that are captured by structural breaks. Finally, we emphasize that this is the first time that...