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

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 panel data unit root tests allowing for structural breaks have been applied to the unemployment rates of U.S. states.

3. LM Unit Root Tests: Methodology and Results

Econometric Methodology

Individual LM Unit Root Tests with Breaks

According to the LM score principle, we obtain the unit root t-statistic from the following regression:

[DELTA][Y.sub.t] = [delta]'[DELTA][Z.sub.t] + [phi][[??].sub.t - 1] + [k.summation over (i)] [[gamma].sub.i][DELTA][[??].sub.t - 1] + [[epsilon].sub.t], (1)

where [delta], [phi], and [[gamma].sub.i] for i = 1, ..., k are parameters to be estimated and [[??].sub.t - 1] represents the detrended series such that [[??].sub.t] = [Y.sub.t] - [??] - [Z.sub.t][??], for t = 2, ..., T. [??] is a vector of coefficients estimated from the regression of [DELTA][Y.sub.t] on [DELTA][Z.sub.t] and [??] = [Y.sub.1] - [Z.sub.1][??], where [DELTA] is the first difference operator and [Y.sub.1] and [Z.sub.1] are the first observations of [Y.sub.t] and [Z.sub.t], respectively. [Z.sub.t] is a vector of exogenous variables defined by the data generation process of the unemployment rate series. The "crash" model allows for two shifts in the intercept such that [Z.sub.t] = [1,t,[D.sub.1t],[D.sub.2t]]', where [D.sub.jt] = 1 for t [greater than or equal to] [T.sub.Bj] + 1, j = 1,2 and [D.sub.jt] = 0 otherwise. The specification also includes a deterministic trend so as to allow for the possibility of trend-stationarity in the unemployment rate under the alternative. (6)

The unit root null hypothesis is given by [phi] = 0 versus the alternative that [phi] < 0, and the LM t-statistic is defined by:

[??] = t--statistic testing the null hypothesis that [phi] = 0. (2)

The minimum LM unit root t-statistic determines the endogenous location of two breaks ([[lambda].sub.j] = [T.sub.Bj]/T, j = 1,2) by using a grid search over all possible break points as follows:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (3)

The search for breaks is carried out over the interval [0.1 T, 0.9T], where T is the sample size and a trimming value of 10% is employed to eliminate endpoints. To correct for serial correlation in Equation 1, we control for a sufficiently large number of augmentation terms ([DELTA][[??].sub.t - i], i = 1, ... k). At each combination of breaks [lambda] = ([[lambda].sub.1], [[lambda].sub.2])', we determine k by employing the general-to-specific approach initially proposed by Perron (1989) and later extended by Ng and Perron (1995). (7) Once the location of the breaks is endogenously established, we follow a general-to-specific approach in order to determine the optimal number of breaks for each panel member on the basis of the significance of the dummy coefficients.

Panel LM Unit Root Tests with Breaks

Following Im, Lee, and Tieslau (2005), in a panel framework the null hypothesis is given by [H.sub.0] : [[phi].sub.i] = 0 for all i (implying that all the individual series have a unit root), versus the alternative [H.sub.1] : [[phi].sub.i] < 0 for i = 1,2, ..., [N.sub.1] and to [[phi].sub.i] = 0 for i = [N.sub.1] + 1, [N.sub.1] + 2, ..., N (implying that at least one of the series is stationary). The panel LM t-statistic is computed by averaging the minimum LM t-statistic for each panel member ([LM.sup.[tau].sub.i]) as follows:

[[bar.LM].sub.NT] = [N.summation over (i = 1)] [LM.sup.[tau].sub.i]/N. (4)

As in Im, Lee, and Tieslau (2005), a standardized panel LM unit root t-statistic can be constructed by letting E([LM.sup.[tau].sub.i]) and V([LM.sup.[tau].sub.i]) represent the expected value and variance of [LM.sup.[tau].sub.i] under the null as follows:

[[GAMMA].sub.LM] = [square root of]N[([bar.LM].sub.NT] - E([LM.sup.[tau].sub.i]))/[square root of]V([LM.sup.[tau].sub.i]) [right arrow] N(0, 1). (5)

Simulated values for E([LM.sup.[tau].sub.i]) and V([LM.sup.[tau].sub.i]) are given in Im, Lee, and Tieslau (2005), and are the same irrespective of the number of breaks identified in each panel member. In case of heterogeneous serial correlation in panel members, they recommend using a weighted average of E([LM.sup.[tau].sub.i][[k.sub.i]]) and V([LM.sup.[tau].sub.i][[k.sub.i]]) on the basis of the unit-specific optimal values of [k.sub.i]. As with the Im, Pesaran, and Shin (2003) test, the panel LM unit root test follows asymptotically a standard normal distribution and assumes no cross-correlations in the error terms across panel members. However, because this latter assumption is unlikely to hold in practice, we follow Jewell et al. (2003) and employ the panel LM unit root test with two changes in level and control for time effects, which help account for any cross-sectional dependencies in the data (see Hakkio 1984). This is equivalent to de-meaning the data by subtracting the average value of the unemployment rate from each observation in each period. (8) Furthermore, as with the Im, Pesaran, and Shin (2003) test, the inclusion of time effects does not change the values for E([LM.sup.[tau].sub.i]) and V([LM.sup.[tau].sub.i]) for the panel LM unit root test, with or without structural breaks. (9)

To sum up, the use of panel LM unit root tests with breaks presents the following advantages. First, the distribution of the t-statistic does not depend on nuisance parameters on the break location under the null hypothesis, and the distribution of the panel LM test is unaffected by the number of breaks. (10) Second, individual and panel LM t-statistics allow for breaks under the null and alternative hypotheses, which avoids the possibility of spurious rejections caused by size distortions (see Nunes, Newbold, and Kuan 1997; Lee and Strazicich 2001). Third, the panel LM t-statistic allows for the presence of heterogeneous intercepts, deterministic trends, and persistence parameters across panel members. Fourth, the optimal number of break points, the location of the break points, and the degree of augmentation are left completely heterogeneous across panel members and are endogenously and jointly determined.

Empirical Results

We employ seasonally adjusted monthly data on unemployment rates for 50 U.S. states plus the District of Columbia over the period 1976-2004. (11) Table 1 presents the results of individual and panel LM unit root t-statistics without breaks. We are able to reject the null hypothesis of a unit root at the 10% significance level or better in only eleven states. The panel LM t-statistic without breaks computed with unadjusted data is able to reject the null at the 1% level, whereas the panel t-statistic computed with data adjusted for cross-correlations does not reject the null even at the 10% level. This preliminary evidence favors the hypothesis of hysteresis in U.S. state unemployment rates versus the natural rate and structuralist views.

Since it is well-known that nonstationarity may conceal the existence of stationarity with breaks, Table 2 shows the results of individual and panel LM tests allowing for up to two changes in level. The results from individual LM t-statistics point to the rejection of the null hypothesis of a unit root in eleven states, of which seven were found stationary without the need to control for breaks. (12) These states are Arizona, California, District of Columbia, Georgia, New Hampshire, Pennsylvania, and Texas. For Iowa, Kansas, Nevada, and Tennessee, the inclusion of breaks leads to the decrease in the persistence of the series, thus rejecting the null of nonstationarity. This provides evidence against the hypothesis of a constant natural rate of unemployment in these states. Nonetheless, as shown at the bottom of Table 2, we are able to reject the hysteresis hypothesis for the panel of U.S. states at the 1% level with unadjusted data and at the 5% level with adjusted data. This serves to confirm that the use of panel LM t-statistics that take advantage of the within and between variability of the data is more important than allowing for breaks in individual tests in rejecting the null of hysteresis in U.S. states.

Given the way the alternative hypothesis is defined in the panel LM unit root test, the results need to be viewed with caution since rejection of the null hypothesis of joint nonstationarity may be caused by the stationarity of as few as a single panel member. Thus we compute the panel LM t-statistics (for both the case without breaks and the case with a heterogeneous number of breaks) after removing from the panel those states for which the null of nonstationarity could be rejected at the individual level. We thus make sure that the rejection of the null of nonstationarity with the panel LM t-statistic is not driven by a small number of states exerting a relatively large influence on the panel, but it is due to the increase in power brought about by the cross-sectional variability of the data.

At the bottom of Tables 1 and 2, we present the panel LM unit root t-statistic with and without breaks computed for the forty states for which we could not individually reject the null of a unit root. (13) The panel tests without breaks computed with unadjusted and adjusted data both point to the nonstationarity of the panel. In contrast, the LM t-statistic computed with a heterogeneous number of up to two breaks for the reduced panel rejects the null of joint nonstationarity at the 1% level for the case of unadjusted data, and at the 10% level for the case of adjusted data; this lends support to the structuralist theory of unemployment for U.S. states. (14) We again observe the tendency to reject the null of joint nonstationarity once we allow for the appropriate number of endogenous breaks across states.

Taken as a whole, our results from individual LM unit root t-statistics are generally consistent with the hysteresis hypothesis, whereas the panel LM tests with up to two breaks point to the empirical validity of the structuralist theories, suggesting the existence of infrequent changes in the natural rate of U.S. state unemployment. (15) This corroborates the fact that the inclusion of structural breaks, reinforced with the panel dimension of the data, in unit root testing leads to the rejection of the hysteresis hypothesis. (16)

Discussion of the Breaks

Looking at the number of breaks, we observe that only twelve states are characterized by two significant breaks, twenty-five states have one break, and fourteen have zero breaks. (17) This provides evidence for the existence of only a few permanent changes in unemployment in the U.S. states after the first oil shock. We can also observe some clustering of the break dates. Of the forty-nine breaks detected, seventeen structural changes took place between the end of 1978 and 1981, thirteen occurred between 1982 and 1985, and ten during the period 1990-1993. The decade involving the years 1995-2004 shows much fewer fluctuations than previous years and only four significant breaks are detected, of which three are positive; these coincide with a sharp increase in the unemployment rate in Kansas, North Carolina, and South Carolina in recent years.

We now look at the local means of the unemployment rate in each regime (calculated before the first break and after each subsequent break), which are shown in columns 5 to 7 of Table 2. Among the forty-nine significant breaks, fourteen are positive and thirty-five are negative; this shows the prevailing tendency of unemployment rates to fall from the level reached after the first oil shock. The exceptions are Kansas, Mississippi, North Carolina, Oklahoma, and Wyoming, for which we find that the unemployment rate has risen with respect to the level reached before the first break identified in each case. Of the twelve states that are characterized by having two level shifts, Alaska, Arizona, and Connecticut show a drop in the unemployment rate each time the series shifts, while Kansas shows a rise in each break. In Idaho, Ohio, South Dakota, Wisconsin, and Wyoming, we find a rise in the natural rate of unemployment coinciding with the recessionary period that followed the second oil shock. These states further experienced a negative shift in the natural rate of unemployment in the mid-eighties when the recovery commenced in the United States. In Colorado, Hawaii, and South Carolina, a downward shift in unemployment rates was followed by an upward shift.

Overall, our results lend support to the existence of highly persistent and infrequent shocks in unemployment rates in U.S. states from the mid-seventies to 2004. In this regard, Lilien (1982) found evidence that part of the shifts in the natural rate of unemployment over the seventies and eighties was caused by the slow adjustment of labor to shifts of employment demand between sectors of the U.S. economy. Brainard and Cutler (1993) also provided evidence that intersector reallocation shocks have accounted for a large share of fluctuations in long-duration unemployment in the United States over the postwar period. Partridge and Rickman (1995) found that employment shifts in the eighties caused by national restructuring policies could partly explain state unemployment rate differences, but most of the changes in state unemployment were state-specific. Along similar lines, Partridge and Rickman (1997) showed that the considerable degree of persistence and dispersion in U.S. state unemployment--despite its relatively high degree of regional labor mobility and labor market flexibility--can be explained by some state-idiosyncratic factors. Some of the most important factors are the percentage of the population living in an owner-occupied residence, which increases the state equilibrium rate of unemployment, and the larger proportion of college educated labor, which reduces it.

In general, the natural rate of unemployment has tended to fall throughout U.S. states following the long-lasting recovery periods that commenced after the recessions that have occurred in the late seventies and early nineties to the present. The results from individual LM t-statistics test stand in stark contrast to the common belief held among scholars that the U.S. state unemployment rate is closer to the natural rate paradigm than to the hysteresis paradigm. In order to back up these findings, in the next section, we calculate half-lives of a shock, which constitute a more complete measure of the degree of persistence of U.S. state unemployment.

4. The Persistence of Shocks to U.S. State Unemployment Rates

Since unit root tests provide an incomplete picture of the persistence of a macroeconomic series, we also provide estimates of the half-life of a shock, leading to deviations from the natural rate of unemployment. In this regard, Cheung and Lai (2000) recommend computing half-lives directly from the impulse-response function. We follow the recently proposed method by Gospodinov (2004) for constructing confidence intervals for impulse-response functions and half-lives of near nonstationary processes. This method is based on the inversion of the acceptance region of the likelihood ratio statistic under a sequence of null hypotheses that restrict the values of the half-life or impulse-response to a shock. By reparameterizing the leading time of the impulse-response function as a function of the sample size, the order of the polynomial constraint by the null hypothesis is not constant but rises linearly with the sample size. (18)

This procedure improves on conventional bootstrap methods (see, for instance, Inoue and Kilian 2002) in that the confidence intervals are correctly computed for the sum of the autoregressive (AR) coefficients rather than for individual slope coefficients of the AR(p) model. This method also provides correct coverage rates of the confidence intervals in large samples and good coverage rates in small samples compared to conventional bootstrap methods when large AR roots are present. This is achieved by making the persistence parameter a function of the sample size. Finally, the inversion of the likelihood ratio statistic provides tighter confidence intervals by shifting them away from the upper boundary more often than other methods.

As reported in column 8 of Table 2, the estimated half-lives indicate the existence of considerable variation in the persistence of unemployment among states. On the basis of the magnitude of estimated half-lives, we can observe some clustering of the degree of persistence of unemployment (see Table 3). The three states characterized by the lowest persistence, with a half-life lower than three years, are Arizona, Colorado, and Kansas, of which Arizona and Kansas were found to be stationary with the LM tests with breaks, and Colorado, with the LM tests without breaks. These states appear to converge to their natural rate of unemployment at a speed of more than 20.6% per year. In addition, we find twenty-nine states with a half-life in the range of three to six years, and eleven states with a half-life greater than six years and lower than ten years. Half-lives appear to be greater than ten years and lower than twenty years in only five states (Arkansas, Iowa, Massachusetts, Nevada, and Tennessee). Finally, the states in which unemployment is more persistent are Idaho, Montana, and New Mexico, which have half-lives greater than twenty years. (19)

Among the forty-eight states for which we find finite half-lives, the median half-life equals 4.86 years, with a speed of convergence toward the natural rate of unemployment of 13% per year. The median lower bound of the 95% confidence interval for half-lives of deviations from the natural rate of unemployment equals 3.32 years, which implies that shocks to unemployment decay at a rate of about 19% per year. (20) In addition, an upper bound of the confidence interval that exceeds two decades in all but nine states is consistent with a high degree of persistence in unemployment. The widths of the confidence intervals associated with the point estimates of half-lives indicate the high degree of uncertainty in half-life estimation, since they would be congruent with a wide range of degrees of unemployment persistence in the states of the U.S.

Taken as a whole, the relatively large median value of the half-life and an upper bound of the confidence interval greater than twenty years in all but nine states point to the existence of a high degree of persistence across the U.S. states. These results confirm our previous findings derived from individual LM t-statistics, which supported unemployment hysteresis in most states of the United States.

5. Concluding Remarks

The purpose of this paper has been to investigate the existence of infrequent shocks and the degree of persistence of U.S. state unemployment over the period 1976-2004. First, we applied individual LM t-statistics without breaks, and we failed to reject the hysteresis hypothesis for forty states. Since Perron (1989) demonstrated that the omission of structural breaks can favor the nonrejection of the unit root null, we employed the minimum LM t-statistic, allowing for up to two mean shifts. However, these tests still provided evidence for the hysteresis hypothesis for forty states.

Since individual unit root tests normally lack power to reject a false null, we employed panel unit root tests. We first used the panel LM t-statistic without breaks, and we failed to reject the null of joint nonstationarity for data adjusted for cross-correlations. Second, we employed the panel LM t-statistic with up to two changes in level, and only in that case was our panel test powerful enough to reject the joint hysteresis hypothesis in favor of regime-wise stationarity.

Since unit root tests do not provide a complete picture of the degree of persistence of U.S. state unemployment, we also calculated the half-life of deviations from the natural rate of unemployment. In doing so, we tried to circumvent some methodological problems with the computation of half-lives that result from the requirement that the series follow an AR(1) process. We computed half-lives directly from the impulse-response functions following Gospodinov (2004), who constructed median unbiased confidence intervals for impulse-response functions and half-lives for near unit root processes. This was achieved by inverting the acceptance region of the likelihood ratio statistic under a sequence of null hypotheses that restrict the values of the half-life or impulse-response to a shock. Even though the estimated half-lives are finite in all but three states, they mask a considerable degree of variation in unemployment persistence across U.S. states. However, the relatively large median value of the half-life (4.86 years) together with an upper bound of the confidence interval that exceeds two decades in most states point to the existence of a high degree of persistence in U.S. state unemployment, thereby reinforcing the results from individual LM unit root tests.

Taken as a whole, our analysis on a state-by-state basis favors the hypothesis of hysteresis, which contrasts with the common belief among scholars in the field that U.S. state unemployment is closer to the natural rate paradigm than to the hysteresis paradigm. Only when the panel dimension and level shifts are brought into the analysis do our results favor the structuralist hypothesis, for which unemployment is stationary around an infrequently changing mean.

An important policy implication of our results is that stabilization policy may have permanent (or at least long-lasting) effects on the unemployment rates of U.S. states. The presence of a high degree of persistence or even hysteresis implies that the rise in unemployment due to restrictive demand policies could become permanent, thus leading to a higher natural rate of unemployment. Our results have also revealed the prevailing tendency of U.S. state unemployment rates to fall from the high level reached after the first oil shock. This gives an indication that labor market reforms and stabilization policies have been implemented in the right direction.

The authors would like to thank seminar participants at the Pablo de Olavide University and DG-Economics at the European Central Bank. Carlos Usabiaga acknowledges the financial support from Centro de Estudios Andaluces (ECOD1.05/033). Special thanks go to Junsoo Lee and Nikolay Gospodinov for making available to us the codes to implement some of the techniques used in the paper, and to two anonymous referees for suggestions that substantially improved the paper. The usual disclaimer applies.

Received July 2005; accepted December 2005.

References

Alogoskoufis, George S., and Alan Manning. 1988. On the persistence of unemployment. Economic Policy 7:427-69.

Arestis, Philip, and Iris Biefang-Frisancho Mariscal. 1999. Unit roots and structural breaks in OECD unemployment. Economics Letters 65:149-56.

Arestis, Philip, and Iris Biefang-Frisancho Mariscal. 2000. OECD unemployment: Structural breaks and stationarity. Applied Economics 32:399-403.

Bai, Jushan, and Pierre Perron. 1998. Estimating and testing linear models with multiple structural changes. Econometrica 66:47-78.

Bianchi, Marco, and Gylfi Zoega. 1998. Unemployment persistence: Does the size of the shock matter? Journal of Applied Econometrics 13:283-304.

Blanchard, Olivier J., and Lawrence H. Summers. 1986. Hysteresis and the European unemployment problem. NBER Macroeconomics Annual 1986:15-78.

Blanchard, Olivier J., and Lawrence H. Summers. 1987. Hysteresis in unemployment. European Economic Review 31:288-95.

Brainard, S. Lael, and David M. Cutler. 1993. Sectoral shifts and cyclical unemployment reconsidered. Quarterly Journal of Economics 108:219-43.

Campbell, John Y., and Pierre Perron. 1991. Pitfalls and opportunities: What macroeconomists should know about unit roots. NBER Macroeconomic Annual 1991:141-201.

Cheung, Yin-Wong, and Kon S. Lai. 2000. On the purchasing power parity puzzle. Journal of International Economics 52:321-30.

Coakley, Jerry, Ana M. Fuertes, and Gylfi Zoega. 2001. Evaluating the persistence and structuralist theories of unemployment. Studies in Nonlinear Dynamics and Econometrics 5:179-202.

DeJong, David N., John Nankervis, N. Eugene Savin, and Charles H. Whiteman. 1992. The power problems of unit root tests in time series with autoregressive errors. Journal of Econometrics 53:323-43.

Dickey, David A., and Wayne A. Fuller. 1979. Distribution of the estimators for autoregressive time series with a unit root. Journal of the American Statistical Association 74:427-31.

Diebold, Francis X., and Glenn D. Rudebusch. 1991. On the power of Dickey-Fuller tests against fractional alternatives. Economics Letters 35:155-60.

Ewing, Bradley T., and Phanindra V. Wunnava. 2001. Unit roots and structural breaks in North American unemployment rates. North American Journal of Economics and Finance 12:273-82.

Friedman, Milton. 1968. The role of monetary policy. American Economic Review 58:1-17.

Gil-Alana, Luis A. 2001. The persistence of unemployment in the USA and Europe in terms of fractionally ARIMA models. Applied Economics 33:1263-9.

Gil-Alana, Luis A., and S. G. Brian Henry. 2003. Fractional integration and the dynamics of the UK unemployment. Oxford Bulletin of Economics and Statistics 65:221-40.

Gospodinov, Nikolay. 2004. Asymptotic confidence intervals for impulse responses of near-integrated processes. Econometrics Journal 7:505-27.

Hakkio, Craig S. 1984. A re-examination of purchasing power parity. Journal of International Economies 17:265-77.

Hansen, Bruce E. 1997. Inference in TAR models. Studies in Nonlinear Dynamics and Econometrics 2:1-14.

Hassler, Uwe, and Jurgen Wolters. 1994. On the power of unit root tests against fractional alternatives. Economics Letters 45:1-5.

Im, Kyung-So, Junsoo Lee, and Margie Tieslau. 2005. Panel LM unit root tests with level shifts. Oxford Bulletin of Economies and Statistics 67:393-419.

Im, Kyung-So, M. Hashem Pesaran, and Yongcheol Shin. 2003. Testing for unit roots in heterogeneous panels. Journal of Econometrics 115:53-74.

Inoue, Atsushi, and Lutz Kilian. 2002. Bootstrapping autoregressive processes with possible unit roots. Econometrica 70:377-91.

Jaeger, Albert, and Martin Parkinson. 1994. Some evidence on hysteresis in unemployment rates. European Economic Review 38:329-42.

Jewell, Todd, Junsoo Lee, Margie Tieslau, and Mark C. Strazicich. 2003. Stationarity of health expenditures: Reexamination using panel unit root tests with heterogeneous structural breaks. Journal of Health Economics 22:313-23.

Lee, Junsoo, and Mark C. Strazicich. 2001. Break point estimation and spurious rejections with endogenous unit root tests. Oxford Bulletin of Economics and Statistics 63:535-58.

Lee, Junsoo, and Mark C. Strazicich. 2003. Minimum Lagrange multiplier unit root test with two structural breaks. Review of Economics and Statistics 85:1082-9.

Leon-Ledesma, Miguel. 2002. Unemployment hysteresis in the US states and the EU: A panel approach. Bulletin of Economic Research 54:95-103.

Levin, Andrew, Chien-Fu Lin, and Chia-Shang Chu. 2002. Unit root tests in panel data: Asymptotic and finite-sample properties. Journal of Econometrics 108:1-24.

Lilien, David M. 1982. Sectoral shifts and cyclical unemployment. Journal of Political Economy 90:777-93.

Mitchell, William F. 1993. Testing for unit roots and persistence in OECD unemployment rates. Applied Economics 25:1489-501.

Murray, Christian J., and David H. Papell. 2000. Testing for unit roots in panels in the presence of structural change with an application to OECD unemployment. In Nonstationary panels, panel cointegration and dynamic panels (Advances in econometrics 15), edited by Badi H. Baltagi. Amsterdam: JAI Press, pp. 223-38.

Ng, Serena, and Pierre Perron. 1995. Unit root tests in ARMA models with data-dependent methods for the selection of the truncation lag. Journal of the American Statistical Association 90:268-81.

Nunes, Luis, Paul Newbold, and Chung-Ming Kuan. 1997. Testing for unit roots with breaks: Evidence on the great crash and the unit root hypothesis reconsidered. Oxford Bulletin of Economics and Statistics 59:435-48.

O'Connell, Paul. 1998. The overvaluation of purchasing power parity. Journal of International Economics 44:1-19.

Papell, David H., Christian J. Murray, and Hala Ghiblawi. 2000. The structure of unemployment. Review of Economics and Statistics 82:309-15.

Partridge, Mark D., and Dan S. Rickman. 1995. Differences in state unemployment rates: The role of labor and product market structural shifts. Southern Economic Journal 62:89-106.

Partridge, Mark D., and Dan S. Rickman. 1997. The dispersion of US state unemployment rates: The role of market and non-market equilibrium factors. Regional Studies 31:593-06.

Perron, Pierre. 1989. The great crash, the oil price shock, and the unit root hypothesis. Econometrica 57:1361-401.

Perron, Pierre, and Timothy J. Vogelsang. 1992. Non-stationarity and level shifts with an application to purchasing power parity. Journal of Business and Economic Statistics 10:301-20.

Phelps, Edmund S. 1967. Phillips curves, expectations of inflation and optimal unemployment. Economica 34:254-81.

Phelps, Edmund S. 1968. Money-wage dynamics and labor-market equilibrium. Journal of Political Economy 76:678-711.

Phelps, Edmund S. 1994. Structural slumps: The modern equilibrium theory of unemployment, interest and assets. Cambridge, MA: Harvard University Press.

Phelps, Edmund S., and Gylfi Zoega. 1998. Natural-rate theory and OECD unemployment. Economic Journal 108:782-801.

Phillips, Peter C. B., and Pierre Perron. 1988. Testing for a unit root in a time series regression. Biometrika 75:335-46.

Roed, Knut. 1996. Unemployment hysteresis--Macro evidence from 16 OECD countries. Empirical Economics 21:589-600.

Roed, Knut. 1997. Hysteresis in unemployment. Journal of Economic Surveys 11:389-418.

Rothman, Philip. 1998. Forecasting asymmetric unemployment rates. Review of Economics and Statistics 80:164-8.

Schmidt, Peter, and Peter C. B. Phillips. 1992. LM tests for a unit root in the presence of deterministic trends. Oxford Bulletin of Economics and Statistics 54:257-87.

Skalin, Joakim, and Timo Terasvirta. 2002. Modelling asymmetries and moving equilibria in unemployment rates. Macroeconomic Dynamics 6:202-41.

Song, Frank M., and Yangru Wu. 1997. Hysteresis in unemployment: Evidence from 48 U.S. states. Economic Inquiry 35:235-43.

Song, Frank M., and Yangru Wu. 1998. Hysteresis in unemployment: Evidence from OECD countries. The Quarterly Review of Economics and Finance 38:181-92.

Strazicich, Mark C., Margie Tieslau, and Junsoo Lee. 2001. Hysteresis in unemployment? Evidence from panel unit root tests with structural change. University of North Texas, Department of Economics Working Paper No. 01-08.

Tschernig, Rolf J. V., and Klaus F. Zimmermann. 1992. Illusive persistence in German unemployment. Centre for Economic Policy Research Discussion Paper No. 739.

U.S. Department of Labor, Bureau of Labor Statistics. Employment and Earnings. Washington, D.C.: U.S. Government Printing Office, various issues.

Zivot, Eric, and Donald W. K. Andrews. 1992. Further evidence on the great crash, the oil-price shock and the unit root hypothesis. Journal of Business and Economic Statistics 10:251-70.

(1) There are three main approaches to explain the sources of hysteresis: insider-outsider theory, long-run unemployment, and capital scrapping. See Roed (1997) for a survey on the theories of hysteresis.

(2) Traditionally, half-lives are calculated with the formula ln(0.5)/ln([alpha])--rather than through impulse-response functions--where the parameter [alpha] is the sum of the coefficients of the underlying autoregressive (AR) process. Even though this is appropriate for an AR(1) process that decays monotonically, it is inappropriate for higher-order AR processes for which shocks do not generally decay at a constant rate.

(3) Bai and Perron (1998) developed a univariate test that allows for multiple breaks. However, this test has the limitation that it is only applicable to stationary series, so it is not of much use if one wants to test the hysteresis hypothesis versus natural rate alternatives.

(4) Analysis at the univariate level of the degree of persistence in unemployment is not confined to unit root testing. Other possible alternatives include: (i) fractional integration techniques (see Tschernig and Zimmermann 1992; Gil-Alana 2001; and Gil-Alana and Henry 2003 among others), (ii) nonlinear models, such as the Markov switching regression models of Bianchi and Zoega (1998) and the nonlinear threshold AR models of Coakley, Fuertes, and Zoega (2001), and (iii) models based on smooth transition mechanisms (see Hansen 1997; Rothman 1998; Skalin and Terasvirta 2002).

(5) Given the features of the unemployment rate variable, we only consider mean shifts as structural breaks; this assumption is generally denoted in this literature as the "crash" model. This is congruent with the structuralist explanation of the natural rate of unemployment.

(6) Our model allows for structural breaks under the null and alternative hypothesis, thus controlling for a change in level under the alternative and for a one-period jump under the null hypothesis.

(7) The location of breaks and the degree of augmentation are endogenously determined from the data prior to the computation of the LM unit root t-statistic.

(8) As noted by Jewell et al. (2003), an alternative way to control for cross-correlations in the error terms would be to use the generalized least squares procedure proposed by O'Connell (1998). However, they correctly point out that this procedure is not feasible for large-N panels because there would be too many parameters of the variance-covariance matrix to estimate.

(9) At this point, it is necessary to acknowledge that we are applying asymptotic results to a sample consisting of 348 monthly observations, which may be regarded as a finite sample. However, this is unavoidable when implementing panel unit root tests that are based on asymptotic normality, given that the length of existing macroeconomic series is limited.

(10) Therefore, the critical values associated with the panel LM unit root test without breaks are the same asymptotically for the panel LM unit root test with one or two breaks, irrespective of the number and location of break points in each panel member.

(11) The data were obtained from the U.S. Department of Labor, Bureau of Labor Statistics. As noted by a referee, the fact that we seasonally adjust the data may lead to a loss of information. However, given that we are more interested in long-term information from the data--to help us discriminate among theories of unemployment behavior--than in short-term information, we prefer to employ seasonally adjusted data. In this regard, we keep up with most of the extant literature in the field.

(12) It is necessary to mention that conventional unit root tests usually have low power against fractional alternatives (see Diebold and Rudebusch 1991; Hassler and Wolters 1994). Under fractional integration, with orders of integration smaller than one, the unemployment rate would show mean reversion. Since it is not clear how the presence of level shifts in the series affects the fractional integration properties of the series, we prefer to focus on studying the case of a unit root versus regime-wise stationarity.

(13) The states left out from the computation of the panel LM test without breaks are Arizona, California, Colorado, District of Columbia, Georgia, Maryland, Minnesota, New Hampshire, Pennsylvania, Texas, and Virginia. Likewise, the states omitted from the computation of the panel LM test with up to two breaks are Arizona, California, District of Columbia, Georgia, Iowa, Kansas, Nevada, New Hampshire, Pennsylvania, Tennessee, and Texas.

(14) From this result, we cannot infer that the aggregate U.S. unemployment rate is regime-wise stationary, since that would require every single unemployment series to be stationary.

(15) Our results appear broadly in line with those of Song and Wu (1997) and Leon-Ledesma (2002), which both reject the null hypothesis of hysteresis in U.S. state unemployment, thus favoring the existence of a constant natural rate of unemployment. By allowing for a more plausible alternative hypothesis, our results support the existence of an infrequently changing natural rate of unemployment.

(16) The different results when using the individual and panel LM unit root tests derive from the greater power brought about by the cross-section variation of the data. This is confirmed by the fact that we are able to reject the null hypothesis of joint nonstationarity even after removing from the panel those states for which we could reject the unit root null at the individual level.

(17) Arguably, these findings show that the use of tests that allow for multiple breaks is not strictly necessary for U.S. states, since two breaks were significant in only twelve states.

(18) See Gospodinov (2004) for more details on the computation of half-lives.

(19) For these states, we tried to extend the lead time of the impulse-response function to the limit imposed by the length of our data sample, but we did not find a finite half-life value. This appears consistent with the LM unit root tests, which also pointed to the nonstationarity of unemployment in these three states. In addition, we tried to detect some geographical pattern related to economic factors that could explain the considerable variation in the degree of persistence in unemployment across the U.S. states, but we could not find any. However, our findings strongly support the general tendency for the unemployment rate to fall across U.S. states over the past three decades.

(20) The average half-life is about six years, with a speed of convergence of 11% per year. The average lower bound is 4.43 years, implying a speed of adjustment toward the natural rate of unemployment of around 14.5% per year.

Diego Romero-Avila * and Carlos Usabiaga ([dagger])

* Department of Economics, Carretera de Utrera, Km. 1, Pablo de Olavide University, 41013 Seville, Spain; E-mail [e-mail].

([dagger]) Department of Economics, Carretera de Utrera, Kin. 1, Pablo de Olavide University, 41013 Seville, Spain; E-mail [e-mail]; corresponding author.

Table 1. Lagrange Multiplier (LM) Unit Root Tests without Structural
Breaks on the Unemployment Rate for U.S. States 1976-2004

                       Univariate
                        LM Unit                                Mean
State                  Root Test     Optimal Lag Length    Unemployment

Alabama                -1.927                3                6.878
Alaska                 -1.946                3                8.252
Arizona                -4.080 ***            5                6.146
Arkansas               -1.931                7                6.670
California             -2.910 *              3                7.144
Colorado               -2.878 *              8                5.375
Connecticut            -1.907                5                5.041
Delaware               -1.509                2                5.122
District of Columbia   -4.812 ***            4                7.688
Florida                -1.989                3                6.205
Georgia                -3.200 **             3                5.510
Hawaii                 -1.104                1                4.877
Idaho                  -1.607                6                6.101
Illinois               -2.319                4                6.857
Indiana                -1.586                2                5.900
Iowa                   -1.233                5                4.787
Kansas                 -2.737                3                4.580
Kentucky               -1.831                8                6.710
Louisiana              -1.564                8                7.592
Maine                  -2.032                6                5.800
Maryland               -2.849 *              7                5.239
Massachusetts          -2.720                7                5.555
Michigan               -1.856                4                8.005
Minnesota              -2.929 *              8                4.845
Mississippi            -1.678                7                7.825
Missouri               -2.333                3                5.746
Montana                -1.545                8                6.043
Nebraska               -1.807                5                3.468
Nevada                 -2.573                8                6.100
New Hampshire          -3.092 **             8                4.394
New Jersey             -2.122                3                6.222
New Mexico             -2.049                6                7.134
New York               -2.350                4                6.713
North Carolina         -2.314                3                5.384
North Dakota           -1.486                1                4.211
Ohio                   -1.866                3                6.735
Oklahoma               -2.318                3                5.374
Oregon                 -2.436                8                7.148
Pennsylvania           -2.863 *              6                6.648
Rhode Island           -2.75                 7                5.983
South Carolina         -2.737                7                6.045
South Dakota           -1.476                1                3.786
Tennessee              -1.887                8                6.430
Texas                  -3.154 **             3                6.224
Utah                   -2.425                8                5.106
Vermont                -1.822                6                4.864
Virginia               -2.901 *              5                4.662
Washington             -2.277                4                7.128
West Virginia          -2.339                6                8.984
Wisconsin              -2.039                4                5.363
Wyoming                -2.191                4                5.182
Panel mean                                                    5.994
Panel LM t-statistic   -4.087 ***   Panel LM t-statistic      1.346
  with unadjusted                     with adjusted data
  data
Panel LM t-statistic   -0.722       Panel LM t-statistic      1.976
  with unadjusted                     with adjusted data
  data for reduced                    for reduced panel
  panel

The specifications include an intercept and time trend. The 1%, 5%, and
10% critical values for the LM unit root test without breaks are: -3.63,
-3.06, and -2.77. The 1%, 5%, and 10% critical values for the panel LM
unit root test (with or without breaks) are: -2.326, -1.645, and -1.282.
*, **, and *** imply rejection of the null hypothesis of
nonstationarity at the 10%, 5%, and 1% significance level, respectively.

Table 2. LM Unit Root Tests with Structural Breaks on the Unemployment
Rate for U.S. States 1976-2004

                                      Optimal      Optimal
                 Univariate LM          Lag       Number of
State            Unit Root Test        Length       Breaks

Alabama          -1.927                  3            0
Alaska           -2.203                  5            2

Arizona          -4.386 **               8            2

Arkansas         -1.931                  7            0
California       -2.910 *                3            0
Colorado         -3.215                  8            2

Connecticut      -2.518                  6            2

Delaware         -3.116                  8            1

District of      -5.909 ***              4            1
  Columbia
Florida          -2.202                  3            1

Georgia          -3.345 *                3            1

Hawaii           -1.325                  1            2

Idaho            -3.485                  7            2

Illinois         -2.319                  4            0
Indiana          -1.751                  2            1

Iowa             -3.308 *                6            1

Kansas           -3.513 *                5            2

Kentucky         -1.831                  8            0
Louisiana        -1.676                  8            1

Maine            -2.501                  4            1

Maryland         -2.952                  7            1

Massachusetts    -2.720                  7            0
Michigan         -1.856                  4            0
Minnesota        -3.201                  8            1

Mississippi      -2.182                  3            1

Missouri         -2.333                  3            0
Montana          -1.545                  8            0
Nebraska         -2.086                  5            1

Nevada           -4.646 ***              4            1

New              -3.092 **               8            0
  Hampshire
New Jersey       -2.732                  7            1

New Mexico       -2.049                  6            0
New York         -2.500                  4            1

North Carolina   -2.881                  5            1

North Dakota     -1.604                  1            1

Ohio             -2.802                  8            2

Oklahoma         -3.175                  5            1

Oregon           -2.56                   8            1

Pennsylvania     -3.641 **               6            1

Rhode Island     -2.75                   7            0
South Carolina   -3.381                  8            2

South Dakota     -2.09                   5            2

Tennessee        -3.899 **               8            1

Texas            -3.154 **               3            0
Utah             -2.425                  8            0
Vermont          -2.363                  5            1

Virginia         -3.046                  5            1

Washington       -2.88                   6            1

West Virginia    -2.471                  6            1

Wisconsin        -2.519                  4            2

Wyoming          -3.129                  3            2

                 Mean Unemployment
State            before the Break    Break 1      Break 2

Alabama                6.878
Alaska                 9.231         8.881        8.094
                                     1979 M08     1980 M03
Arizona                8.093         7.481        5.565
                                     1979 M01     1983 M12
Arkansas               6.610
California             7.144
Colorado               5.853         4.622        5.343
                                     1979 M04     1980 M03
Connecticut            5.468         4.799        3.974
                                     1993 M03     1999 M08
Delaware               5.986         4.163
                                     1991 M04
District of            7.881         7.502
  Columbia                           1989 M12
Florida                6.915         5.212
                                     1992 M12
Georgia                6.434         5.318
                                     1981 M01
Hawaii                 7.418         4.255        4.735
                                     1979 M11     1992 M09
Idaho                  6.691         8.482        5.809
                                     1983 M05     1984 M01
Illinois               6.857
Indiana                7.114         4.074
                                     1993 M06
Iowa                   5.843         4.318
                                     1984 M12
Kansas                 3.600         4.639        5.404
                                     1980 M03     2001 M12
Kentucky               6.710
Louisiana              7.901         7.479
                                     1983 M10
Maine                  6.302         5.280
                                     1990 M10
Maryland               5.672         4.718
                                     1991 M11
Massachusetts          5.555
Michigan               8.005
Minnesota              5.007         4.825
                                     1979 M03
Mississippi            6.833         7.965
                                     1979 M08
Missouri               5.746
Montana                6.043
Nebraska               4.208         3.004
                                     1987 M03
Nevada                 6.307         6.065
                                     1980 M03
New                    4.394
  Hampshire
New Jersey             6.743         5.475
                                     1993 M02
New Mexico             7.134
New York               7.080         6.325
                                     1990 M12
North Carolina         5.299         5.842
                                     2000 M07
North Dakota           4.182         4.215
                                     1979 M03
Ohio                   6.390         11.021       6.156
                                     1980 M04     1983 M07
Oklahoma               4.318         5.559
                                     1980 M05
Oregon                 8.861         6.346
                                     1985 M04
Pennsylvania           8.479         5.999
                                     1983 M08
Rhode Island           5.983
South Carolina         7.389         5.415        6.123
                                     1983 M10     2000 M11
South Dakota           3.390         4.649        3.375
                                     1978 M11     1988 M03
Tennessee              8.057         5.800
                                     1984 M02
Texas                  6.224
Utah                   5.106
Vermont                5.425         4.283
                                     1990 M10
Virginia               5.209         3.446
                                     1996 M01
Washington             7.637         7.043
                                     1980 M03
West Virginia         10.246         8.446
                                     1984 M09
Wisconsin              5.157         8.021        4.295
                                     1980 M07     1987 M11
Wyoming                3.533         6.974        5.584
                                     1982 M03     1983 M02

State                  Half-life

Alabama           9.574 [5.369, >20.000]
Alaska            4.647 [2.948, >20.000]

Arizona           1.627 [1.417, 3.458]

Arkansas         12.491 [7.101, >20.000]
California        4.041 [3.060, 14.210]
Colorado          2.519 [1.7884, >20.000]

Connecticut       3.286 [2.345,7.771]

Delaware          8.223 [4.536, >20.000]

District of       4.250 [3.316, >20.000]
  Columbia
Florida           4.346 [2.975, >20.000]

Georgia           3.061 [2.136, 9.541]

Hawaii            3.076 [2.241, 5.500]

Idaho             >20.000 [13.465, >20.000]

Illinois          5.450 [3.350, >20.000]
Indiana           8.157 [4.452, >20.000]

Iowa             12.116 [6.514, >20.000]

Kansas            2.418 [1.736, >20.000]

Kentucky          7.970 [4.391, >20.000]
Louisiana         8.558 [4.747, >20.000]

Maine             3.382 [2.426, >20.000]

Maryland          5.319 [3.432, >20.000]

Massachusetts    11.081 [10.591, 16.339]
Michigan          8.453 [5.039, >20.000]
Minnesota         4.368 [2.869, >20.0001

Mississippi       5.507 [3.334, >20.000]

Missouri          4.450 [2.913, >20.000]
Montana           >20.000 [14.504, >20.000]
Nebraska          4.0390 [2.423, >20.000]

Nevada           13.863 [6.229, >20.000]

New               9.601 [7.747, 9.944]
  Hampshire
New Jersey        5.375 [3.779, >20.000]

New Mexico        >20.000 [12.513, >20.000]
New York          3.834 [2.851,7.093]

North Carolina    3.787 [2.518, >20.000]

North Dakota      4.887 [2.806, >20.000]

Ohio              7.391 [4.333, >20.000]

Oklahoma          3.289 [2.135, >20.000]

Oregon            4.181 [3.0007, >20.000]

Pennsylvania      7.329 [4.820, >20.000]

Rhode Island      8.855 [8.165, >20.000]
South Carolina    4.824 [3.107, >20.000]

South Dakota      5.803 [3.397, >20.000]

Tennessee        18.344 [9.668, >20.000]

Texas             3.4581 [2.698, 6.460]
Utah              5.017 [2.950, >20.000]
Vermont           3.261 [2.374, 9.881]

Virginia          4.519 [2.924, >20.000]

Washington        5.734 [3.681, >20.000]

West Virginia     6.854 [4.260, >20.000]

Wisconsin         4.790 [2.876, >20.000]

Wyoming           3.1190 [1.960, >20.000]

Panel LM t-statistic     -8.311 ***   Panel LM t-statistic   1.879 **
  with unadjusted data                          with adjusted data

Panel LM t-statistic     -5.571 ***   Panel LM t-statistic   -1.445 *
  with unadjusted data                       with adjusted data
  for reduced panel                            for reduced panel

The specifications include an intercept and time trend. The 1%, 5%,
and 10% critical values for the LM unit root test without breaks
are: -3.63, -3.06, and -2.77. The 1%, 5%, and 10% critical values for
the minimum LM test with one break are: -4.239, -3.566, and -3.211.
The 1%, 5%, and 10% critical values for the minimum LM test with two
breaks are: -4.545, -3.842, and -3.504, respectively. The 1%, 5%, and
10% critical values for the panel LM unit root test (with or without
breaks) are: -2.326, -1.645, and -1.282. *, **, and *** imply
rejection of the null hypothesis of nonstationarity at the 10%, 5%,
and 1 % significance level, respectively. The entries that appear in
columns 6 and 7 are the local mean following the break, with the
break date reported in italics. The entries in column 8 are the
estimates of the half-life measured in years and the 95% confidence
interval based on the computation of impulse-response functions as
in Gospodinov (2004).

Table 3. Persistence of Shocks to Unemployment: Half-Lives (HL) for
U.S. States 1976-2004

HL: < 3    HL: 3-6 years    HL: 6-10        HL: 10-20       HL > 20
years                       years           years           years

Arizona    HL: 3-4 years    Alabama         Arkansas        Idaho
Colorado                    Delaware        Iowa            Montana
Kansas     Connecticut      Indiana         Massachusetts   New Mexico
           Georgia          Kentucky        Nevada
           Hawaii           Louisiana       Tennessee
           Maine            Michigan
           New York         New Hampshire
           North Carolina   Ohio
           Oklahoma         Pennsylvania
           Texas            Rhode Island
           Vermont          West Virginia
           Wyoming

           HL: 4-5 years

           Alaska
           California
           District of
             Columbia
           Florida
           Minnesota
           Missouri
           Nebraska
           North Dakota
           Oregon
           South Carolina
           Virginia
           Wisconsin

           HL: 5-6 years

           Illinois
           Maryland
           Mississippi
           New Jersey
           South Dakota
           Utah
           Washington

HL denotes the half-life of a shock, which is the time that takes for
a unit impulse to dissipate permanently by half.