Unemployment hysteresis in OECD countries: Centurial time series evidence with structural breaks

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Economic Modelling 25 (2008) 312 – 325 www.elsevier.com/locate/econbase

Unemployment hysteresis in OECD countries: Centurial time series evidence with structural breaks Chien-Chiang Lee a,⁎, Chun-Ping Chang b b

a Department of Applied Economics, National Chung Hsing University, Taichung, Taiwan Department of Business Administration, Shih Chien University Kaohsiung Campus, Kaoshiung, Taiwan

Accepted 26 June 2007

Abstract This paper re-examines the hypothesis of unemployment hysteresis in which the endogenously determined break points are incorporated in 14 major OECD countries by using annual data over one century in length, so as to avoid the seasonal adjustment shortcoming and be free from any local features of a short sample period. We utilize a new powerful Lagrange Multiplier unit root test that endogenously determines structural breaks in level and/or trend, as proposed by Lee and Strazicich [Lee, J., Strazicich, M.C., 2003. Minimum Lagrange Multiplier unit root test with two structural breaks, The Review of Economics and Statistics 85, 1082– 1089, Lee, J., Strazicich, M.C., 2004. Minimum LM unit root test with one structural break, Department of Economics, Appalachian State University Working Paper Series]. Our empirical findings provide significant evidence that unemployment rates are stationarity and these results do not change in the robustness test process—that is, the unemployment hysteresis hypothesis is strongly rejected. We also construct the half-lives to investigate the persistence of deviations of unemployment rate. Overall, we discover several critical economic affairs which cause unemployment rates to fluctuate significantly in 14 OECD countries. Some policy implications are proposed through our observations. © 2007 Elsevier B.V. All rights reserved. JEL classification: C22; C23; J64 Keywords: Hysteresis; Unemployment rate; Unit root tests; Structural breaks; Half-lives

1. Introduction There are several explanations for a phenomenon of high levels and the persistence of unemployment rates in European countries, especially among Economic Co-operation and Development (OECD) members (Camarero and Tamarit, 2004; Arestis and Mariscal, 1999). From theoretical viewpoints, one can realize through two main hypotheses on the time path of unemployment that this relates to economic development (Røed, 1997; Murray and Papell, 2000). One hypothesis is the so-called ‘natural’ rate of unemployment or non-accelerating inflation rate of unemployment (NAIRU) hypothesis, characterizing unemployment dynamics as a mean reverting process, which is therefore consistent with a stable inflation rate. The other hypothesis is the unemployment hysteresis as revealed by Blanchard ⁎ Corresponding author. Tel.: +886 4 22840352x308; fax: +886 4 22860255. E-mail address: [email protected] (C.-C. Lee). 0264-9993/$ - see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.econmod.2007.06.002

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and Summers (1986), who proposed that cyclical fluctuations will have permanent effects on the level of unemployment due to labor market restrictions. Thus, under this hypothesis they suggest that the level of unemployment is characterized as a non-stationary or unit root process. However, level stationarity supports the natural rate theories, whereas the presence of a unit root is compatible with the hysteresis hypothesis (Camarero and Tamarit, 2004).1 This study's major contribution is the use of a unit root test with multiple structural breaks and annual data collection over one century in length to re-examine the hypothesis of unemployment hysteresis. If the hypothesis of hysteresis is rejected, then the shocks only cause deviations around a mean value or deterministic trend. In other words, a shock affects unemployment only temporarily.2 Previous research has, in general, concluded that unemployment rates are non-stationary in OECD countries (Elmskov and MacFarlan, 1993; Mitchell, 1993; Røed, 1996; Camarero and Tamarit, 2004). However, there still is a contrarily large amount of papers supporting the stationarity on unemployment rates, such as Røed (1997) and Papell et al. (2000). These mixed findings may be called into question, for instance, since few previous research studies have properly allowed for the possibility of structural breaks in unit root tests on the unemployment rate.3 In this case, despite the fact that the unemployment hysteresis must not exist, unit root tests of the unemployment rate which ignore the possibility of structural breaks may erroneously show the presence of hysteresis.4 Applications of unit root tests which account for the presence of structural breaks have recently found controversial evidence for the previously perceived persistence in macroeconomic time series.5 Thus, the purpose and contribution of this paper are to empirically re-examine the time path of the unemployment rate in 14 major OECD countries by using the Lagrange Multiplier (LM hereafter) univariate unit root test developed by Lee and Strazicich (2003) that allows for endogenous structural breaks and can significantly increase the power of the test.6 Next, we collect annual data over one century in length, so as to avoid the seasonally adjustment shortcoming and be free from any local features of a short sample period (Hakkio and Rush, 1991; Lothian and Taylor, 1996). In testing the stationarity property, one needs a longer data span especially if the speed of convergence to equilibrium is slow. For this reason, researchers may prefer to work with data that span a century or more (Lau et al., 2006). Third, via finding the structural change points, we can discover several critical economic affairs which cause unemployment rates to fluctuate significantly in 14 major OECD countries. Finally, although the evidence presented in previous studies supports the stationarity of unemployment, it offers little information about the speed at which the unemployment rate dies out. To provide such information, a computation of persistence is needed and the half-life is used to quantify this. The half-life provides a summary measure of how long it takes for the unemployment rate, after facing a unit of shock, to dissipate by half. Our initial motivation is from Cross (1995), who claimed that ever since the seminal work of Blanchard and Summers (1986), tests of unemployment hysteresis have been conducted as unit root tests. Conceptually, the hysteresis intuition denotes a situation in which the equilibrium state of a system depends on the past history of the system. Actually, based on anterior experience, several previous wisdoms have attempted to test the presence of hysteresis in unemployment for Western developed countries.7 In general, the studies cannot reject the null of a unit root for most of the OECD countries, but the results for the U.S. are mixed. For instance, Neudorfer et al. (1990) employed standard Dickey–Fuller (DF hereafter) unit root tests, but they are unable to reject the unit root null and therefore the hysteresis hypothesis for Austria exists. Furthermore, Jaeger and Parkinson (1994) used augmented DF (Dickey and Fuller, 1979; ADF hereafter) unit root tests to unemployment rates in Canada, Germany, the U.K., and the U.S. Camarero et al. (2006) allowed for a different number of endogenous break points in the unemployment series, as they examined the hysteresis hypothesis in unemployment rates by using panel data for 19 OECD countries covering the period 1956– 1

The existence of hysteresis should not be confused with persistence (Song and Wu, 1997), as persistence implies that, although the speed of adjustment towards the equilibrium level is slow, the unemployment rate shows mean reversion. 2 Because hysteresis is consistent with non-stationary unemployment rates, unit root tests provide a convenient methodological framework in which to empirically examine this hypothesis. 3 The aspect of structural breaks is a common problem in macroeconomic series as they are usually affected by exogenous shocks or regime changes in economic events. The arguments such as those mentioned above have already been gradually confirmed. 4 Perron (1989) argued that if there is a structural break, then the power to reject a unit root decreases when the stationary alternative is true and the structural break is ignored. 5 Ohara (1999) provided two reasons for extending the unit root test towards multiple trend breaks. 6 Table 2 lists the details for all countries’ data spans. 7 For example, Blanchard and Summers (1986) for France, Germany, the United Kingdom, and the United States; Brunello (1990) for Japan; and Røed (1996) with a sample of OECD countries.

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Table 1 The comparison of empirical results from unit root tests for OECD countries Authors

Empirical method

Period

Countries

Hysteresis

Arestis and Mariscal (2000)

Perron's (1997) unit root test

1960Q1–1997Q2

22 OECD countries

Blanchard and Summers (1986) Brunello (1990) Camarero et al. (2006)

DF and ADF unit root tests DF unit root tests More endogenous break points' unit root test Breuer et al.'s (2001) Panel SURADF unit root tests Generalization of the ADF test Tsay's (1988) intervention model ADF and KPSS unit root tests Systems estimates of structural parameters Yamamoto (1996) augmented step-wise Chow test Univariate and panel unit root test with and without breaks Multivariate SURE unit root tests Perron's (1989) unit root test Zivot and Andrews (1992) Exact maximum likelihood stationarity test ADF and KPSS unit root tests LL and IPS unit root tests Panel unit root test

1953–1984 1955–1987 1956–2001

France, Germany, UK, U.S. Japan 19 OECD countries

No: Australia, Belgium, Canada, Denmark, Finland, Germany, Luxembourg, Switzerland and the UK No: U.S. Yes: France, Germany, UK

1961–1999

10 European countries

No: Belgium and the Netherlands. Yes: Other countries.

1966Q1–1999Q1

21 OECD countries

1960–1999

21 OECD countries

No: Australia, Belgium, Canada, Denmark, Finland, Netherlands, Norway, U.S. No

1974M4–2002M12

UK

Yes

1966Q3–1988Q4

Australia

No

1955Q1–1998Q2

Japan

No

1991M1–2001M5

No

1956–2001

12 Central and Eastern European Countries and 15 EU 19 OECD countries

1960s–1991Q3

15 OECD countries

1955–1997

16 OECD countries

1970Q1–1994Q4

16 OECD countries

No: Belgium, Canada, Denmark, Finland, Ireland, Norway, Sweden, Spain, U.S., UK No: U.S.

1960s–1995

10 OECD countries

No: U.S. Yes: Other countries

1983Q2–2002Q1 1972Q1–1992Q2

Australian states 15 OECD countries

Yes No

Chang et al. (2005)

Fève et al. (2003) Everaert (2001) Gray (2004) Groenewold and Taylor (1992) Hayashi (2005)

Leon-Ledesma and McAdam (2004) Camarero and Tamarit (2004) Mitchell (1993) Papell et al. (2000) Røed (1996)

Røed (2002) Smyth (2003) Song and Wu (1998)

Yes No

Yes: Austria, Germany, Italy, Japan, Norway, New Zealand and Switzerland. Yes

2001. The findings give support to the natural rate hypothesis of unemployment for the majority of the countries analyzed. In the path, Camarero et al. (2005) offered similar detections for European Union countries. As Table 1 shows, Mitchell (1993) used Perron's (1989) unit root test, which assumes one exogenously given structural break, and found similar support for the unit root hypothesis and hysteresis in several OECD countries. Gray (2004) adopted ADF and KPSS (Kwiatkowski et al., 1992) unit root tests for the UK's unemployment rates and also achieved a similar conclusion. Studies that use long-term data, such as Ben-David and Papell (1995), cannot determine if and when post-war slowdowns occurred, because the breaks are dominated by the two World Wars and the onset of the Great Depression (Ben-David et al., 2003). However, the low power of these tests against the stationary alternative, when the process is near-integrated, is a well-known problem (see, for example, Cochrane, 1991; DeJong et al., 1992; Camarero and Tamarit, 2004). Such as with the seasonal problems for monthly and quarterly data (Fève et al., 2003; Røed, 1996; Groenewold and Taylor, 1992), they all only have post-war data and do not consider the structural breaks in the data span. Even after assuming one exogenously given structural break (Mitchell, 1993), or using panel data unit root tests to extend the extra power in the panel properties of the data, we also can discover some weaknesses in most cases. On example is that although the panel unit root rejects the hysteresis, the univariate unit root result is mixed (Song and Wu, 1998).

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Camarero et al. (2006) reviewed the structuralist school that emphasizes the natural rate of unemployment often is endogenously affected by market forces like any other economic variable, such as real interest rates, productivity growth rates, oil prices, and stock prices, etc. Furthermore, Akram (2005) indicated that unemployment displays an asymmetric response to large positive and negative shocks, while the response is symmetric to small positive and negative shocks. From these pioneering viewpoints, while hysteresis is consistent with unit root or near-unit root processes, the previous wisdom is in line with the existence of structural breaks of the steady-state path of a stochastic stationary process (Phelps, 1999). These results induce an enormous amount of studies that are starting to seriously consider the existence of a structural change in the series of the unemployment rate (see as Perron, 1989; Zivot and Andrews, 1992; Perron, 1997). Unemployment rates might have been exposed to one or more structural breaks caused by either huge magnitude shocks or some political changes. Smyth (2003) indicated that two distinct parallel literature strains have emerged, which use more powerful tests to address this problem. One of them starts with Perron (1989),8 introducing one or more structural breaks into the unit root test. Immediately after that, Zivot and Andrews (1992, ZA hereafter) offered some decisive methods for selecting the break point endogenously from the data. Lumsdaine and Papell (1997, LP hereafter) extended the ZA test to allow for two breaks in level and trend. Papell et al. (2000) and Summers (2003) then efficiently applied these unit root tests with structural breaks to test for hysteresis in OECD unemployment rates. However, Lee and Strazicich (2003) claimed that in the presence of a unit root with breaks, the same outcome occurs as in the one-break tests. As a result, when utilizing these ADF-type endogenous break unit root tests, researchers might conclude that a time series is trend stationary, when in fact the series is non-stationary with a break (Smyth, 2003; Lee and Strazicich, 2003; Smyth and Inder, 2004), which is a disturbing condition to us. To avoid problems of biased and spurious rejections, we apply the endogenous two-break LM unit root test proposed by Lee and Strazicich (2003, LS hereafter) in this paper. We follow Strazicich et al. (2004) and Payne et al. (2005) to find empirical results from both the two-break and onebreak minimum LM unit root tests. There are some advantages in this new econometric method which can be summarized as follows (Strazicich et al., 2004). In the beginning, the break points are endogenously determined from the data. Hence, the test is not subject to spurious rejections in the presence of a unit root with break(s). The most important thing is that when the alternative hypothesis is true, spurious rejections are absent. According to the test results, if we fail to reject the unit root null hypothesis indicating that evidence supports hysteresis hypothesis, then the rejection of a unit root supports the alternative hypothesis that shocks to unemployment rate are temporary. By using annual data spanning over one century for OECD unemployment, we find strong evidence of a stationarity path of the unemployment rate, which incorporates structural changes. At the same time, it explains whether it yields a different hysteresis hypothesis in a country at the same developmental level. The remainder of the paper is organized as follows. Section 2 briefly describes the minimum LM unit root tests of Lee and Strazicich (2003, 2004) used in the paper, and Section 3 presents the empirical results and policy implications. Finally, Section 4 reports the main conclusions. 2. Minimum Lagrange Multiplier unit root tests Ever since the renowned paper offered by Perron (1989),9 previous literature has been aware of the importance of allowing for a structural break when testing for a unit root. Interestingly, subsequent studies changed the test to allow for one unknown break point that is determined endogenously from the data. One widely used endogenous procedure is the minimum test of ZA, which selects the break point where the t-statistic testing the null of a unit root is the most negative.10 According to these observations, Lumsdaine and Papell (1997) extend Perron's basic one structural break model to allow for two structural breaks. The one important drawback about the ZA and LP endogenous break tests is that they assume no break under the unit root null and derive their critical values accordingly. On the other hand, Lee and Strazicich (2003, 2004) pointed out that the alternative hypothesis would be ‘structural breaks are present’, which 8

The other one is the panel unit root test. These are: Model A (the crash model), which allows for a one-time change in the intercept of the trend function; Model B (the changing growth model), which allows for a change in the slope; and Model C (the crash-cum-growth model), which allows for a change in both intercept and slope (one can see a detailed discussion in Perron, 1989; Lee and Strazicich, 2003; Fève et al., 2003; Smyth and Inder, 2004). 10 The ZA test selects the break point where the t-statistic that tests the unit root null is minimized. A similar test is developed by Perron (1997), which selects the break point where the absolute value of the t-statistic on the break term is maximized. 9

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includes the possibility of a unit root with break. As Lee and Strazicich (2004) suggested, if we lose the power from ignoring one-break, it may let us extend that the query has a similar loss of power from ignoring two or more breaks in the one-break test (Smyth and Inder, 2004).11 This is reasonable as recently researchers have suggested that many economic time series might contain some structural breaks, but the incorrect determination of the break may distort the behavior of the statistics of any series (Montañés et al., 2005).12 The rejection of the null does not necessarily imply a rejection of the unit root in regard to itself, but rather implies a rejection of a unit root without breaks.13 Therefore, we must be careful to cite these conclusions in this empirical work. In the presence of a break under the null, researchers might incorrectly conclude that a rejection of the null indicates evidence of a trend-stationary time series with breaks, including those such as Ashworth et al. (1999) covering the Lee and Strazicich (2003) cognition. Overall, an important feature of the endogenous break LM unit root test is that unlike the competing DF-type endogenous break tests,14 the minimum LM test is not subject to spurious rejections in the presence of a break under the null (Nunes et al., 1997; Lee and Strazicich, 2001). Following Lee and Strazicich (2003), Strazicich et al. (2004), and Lee et al. (2006), in principle the two-break minimum LM unit root test process is as follows.15 In the beginning, they consider the DGP proposed by Perron (1989), of which Model A allows for two shifts in level and Model C includes two changes in level and trend. yt ¼ gVZt þ vt

vt ¼ bvt1 þ et ;

ð1Þ

where yt is the unemployment rate, Zt is a vector of exogenous variables defined by the data generating process (DGP hereafter), εt ∼ iid N(0, σ2) is an error term, and the DGP includes breaks under the null and alternative hypothesis in a consistent manner. Model C includes two breaks in level and trend and is described by Zt = [1,t, D1t, D2t, DT1t, DT2t]V, where Djt = 1 for t ≥ TBj + 1, j = 1,2, and 0 otherwise; DTjt = t − TBj for t ≥ TBj + 1, j = 1,2, and 0 otherwise; and TBi is the location at which the break occurs for country i. Note that the DGP includes breaks under the null ( β = 1) and alternative ( β b 1) hypothesis in a consistent manner. For example, in model C, depending on the value of B, we have: Null : yt ¼ l0 þ d1 B1t þ d2 B2t þ yt1 þ v1t ; Alternative : yt ¼ A1 þ gt þ d1 D1t þ d2 D2t þ N1 DT1t þ N2 DT2t þ v2t

ð2Þ

where v1t and v2t are stationary error terms. Lee and Strazicich (2003) held that the two-break LM unit root test statistic can be estimated by regression according to the LM (score) principle as follows: ∼ Dyt ¼ gVDZt þ / St1 þ ut ;

ð3Þ

∼ ∼ ∼ where St is a de-trended series, St ¼ yt  Wx  Zt ∼ g; t ¼ 2; N ; T ; ∼ g is a vector of coefficients in the regression of Δyt ∼ on ΔZt; Wx is given by y1  Z1 ∼ g; and y1 and Z1 denote the first observations of yt and Zt, respectively.16 Corrections ∼ for autocorrelated errors are accomplished via augmented terms D Stj , j = 1,...,k, in Eq. (3), as with the ADF test. The unit root null hypothesis is described by ϕ = 0 (implying a unit root with two breaks), and the LM test statistics are given by: ∼ s ¼ t2statistic for the null hypothesis / ¼ 0: 11

ð4Þ

The examples of the existence of multiple breaks are as follows. Ben-David and Papell (2000) found evidence of multiple breaks in per capita real GDP of the G7 countries over the past 120 years. Papell et al. (2000) showed more than one structural break in macroeconomic time series data in 16 OECD countries. Li (2000) used a unit root test with two structural breaks when examining the stationarity of China's real GDP. 12 Hansen (2001) pointed out that the distinction between a series with a unit root and a stationary series with non-constant deterministic components is less clear when we consider the case of more than one break. 13 Similarly, when the unit-root null hypothesis is rejected, it may be erroneous to conclude that all series in the panel are stationary (Breuer et al., 2001). 14 The hypotheses implied in the above endogenous break unit root tests differ from those in Perron's (1989) exogenous break unit root test, which allows for the possibility of a break under both the null and alternative hypotheses. 15 Lee et al. (2006) indicated that there are technical difficulties in obtaining relevant asymptotic distributions and the corresponding critical values of endogenous break unit root test with three or more breaks. 16 Vougas (2003) showed that the LM type test using the above de-trending method is more powerful than the DF type test.

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Table 2 Two-break minimum LM unit root test for Model C Country (period)

ˆk

ˆB T

Test statistic

dˆ1⁎

Australia (1901–2004) Belgium (1921–2004) Canada (1919–2004) Denmark (1910–2004) France (1895–2004) Germany (1887–2004) Italy (1947–2004) Japan (1930–2004) Netherlands (1911–2004) Norway (1904–2004) Sweden (1919–2004) Switzerland (1926–2004) United Kingdom (1855–2004) United States (1890–2004)

8 8 3 1 8 7 2 8 6 8 2 3 4 7

1928,1942 1937,1975 1938,1951 1929,1941 1990,1994 1922,1969 1959,1994 1958,1996 1929,1949 1928,1946 1933,1960 1937,1952 1937,1982 1928,1941

− 5.489⁎⁎ − 6.030⁎⁎ − 5.666⁎⁎ − 7.105⁎⁎ − 4.433 − 5.607⁎⁎ − 5.465⁎⁎ − 6.403⁎⁎ − 6.950⁎⁎ − 7.823⁎⁎ − 5.636⁎⁎ − 7.436⁎⁎ − 4.847 − 8.442⁎⁎

2.238⁎⁎ − 3.819⁎⁎ − 2.795⁎⁎ 3.394⁎⁎ 1.798⁎⁎ − 2.350⁎⁎ − 3.008⁎⁎ 3.117⁎⁎ 2.550⁎⁎ 4.828⁎⁎ − 2.742⁎⁎ − 5.135⁎⁎ − 1.256⁎⁎ 3.874⁎⁎

dˆ2⁎ (3.484) (− 5.599) (− 5.393) (5.488) (2.811) (− 5.171) (− 4.340) (6.093) (4.276) (5.926) (− 4.869) (− 8.502) (− 4.068) (7.030)

− 0.874⁎⁎ 2.797⁎⁎ 2.615⁎⁎ − 3.331⁎⁎ − 1.581⁎⁎ 2.753⁎⁎ 1.565⁎⁎ 2.441⁎⁎ − 3.293⁎⁎ − 3.028⁎⁎ 1.634⁎⁎ 2.566⁎⁎ 1.061⁎⁎ − 3.796⁎⁎

(−2.156) (5.707) (5.355) (−5.872) (−2.306) (5.760) (2.589) (4.234) (−5.350) (−5.707) (5.464) (6.896) (2.906) (−6.979)

Notes: ⁎⁎and ⁎ denote significance at the 5% and 10% levels, respectively. Term A ˆk is the optimal number of lagged first-differenced terms included ˆ B denotes the estimated break points. The 5% and 10% critical values for the minimum LM test in the unit root test to correct for serial correlation. T with two breaks (Model C) are − 5.286 and − 4.989, respectively. Standardized coefficients (dˆ⁎i = dˆi / ˆσ are reported. T-statistics for dˆi = 0 are given in parentheses. Term dˆ is the coefficient of dummy variables under the unit root null in Lee and Strazicich (2003). The period lists under a national denomination.

From this, the LM unit root test can endogenously determine the two breaks by utilizing a grid search as follows: sðkÞ; LMs ¼ inf ∼ k

ð5Þ

There is a repeated procedure at each combination of break points, λj = TBj / T, j = 1,2. As shown in Lee and Strazicich (2003), the critical values for Models A and C depend on the location of the breaks (λ). Therefore, we utilize critical values that correspond to the location of the breaks. Since only one structural break is found for the sample countries, we will repeat the tests for those countries using the minimum one-break LM test which is proposed by Lee and Strazicich (2004). We list the null and alternative hypothesis of Model C as: Null : yt ¼ l0 þ d1 B1t þ yt1 þ v1t ; Alternative : yt ¼ A1 þ gt þ d1 D1t þ N1 DT1t þ v2t

ð6Þ

However, regardless of whether we use the two or one-break test, if the vector of exogenous variables shows Zt = [1,t]V, then the DGP is the same as that shown in the no break LM unit root test of Schmidt and Phillips (1992; SP). 3. Empirical results 3.1. Unit root test with breaks This section applies the two-break minimum LM unit root test to data on 14 major OECD countries.17 All data are taken from The Global Financial Database, and Table 2 shows the available sample period of each country. The annual time series range from 1855 (or later) to 2004, which is according to the specific procedure offered by Perron (1989) and suggested in Ng and Perron (1995). Following Lee and Strazicich (2003), in the beginning, like the other examination process, we determine the number of lagged augmentation terms and we start from a maximum of k = 8 lagged terms. As such, the procedure looks for the significance of the last augmented term. We then use the 10% asymptotic normal value of 1.645 on the t-statistic of the last first-differenced lagged term. After determining the

17

The remaining OECD countries are excluded from our sample, because there is not enough unemployment data.

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Table 3 Two-break minimum LM unit root test for Model A Country

ˆk

ˆB T

Test statistic

dˆ1⁎

Australia Belgium Canada Denmark France Germany Italy Japan Netherlands Norway Sweden Switzerland United Kingdom United States

1 6 3 8 7 8 1 3 1 6 2 7 1 7

1924,1933 1950,1953 1935,1939 1920,1950 1982,1992 1930,1932 1959,1980 1956,1974 1934,1942 1933,1939 1929,1931 1937,1943 1925,1939 1920,1941

− 3.781⁎ − 3.507⁎ − 3.799⁎ − 4.190⁎⁎ − 3.671⁎ − 3.498 − 2.598 − 2.461 − 3.252 − 4.850⁎⁎ − 3.738⁎ − 5.210⁎⁎ − 4.107⁎⁎ − 5.372⁎⁎

2.333⁎⁎ − 0.625⁎⁎ 1.672 3.349⁎⁎ 0.629 2.731⁎ − 5.675⁎⁎ − 1.778⁎ 3.971⁎⁎ 2.396⁎ 4.902⁎⁎ 3.300⁎⁎ 1.849⁎ 2.348⁎⁎

dˆ2⁎ (2.320) (− 1.969) (1.429) (3.177) (0.599) (1.716) (− 5.549) (− 1.698) (3.615) (1.942) (4.765) (2.123) (1.833) (2.242)

0.263 −1.307 −3.542⁎⁎ −1.650 2.812⁎⁎ 5.080⁎⁎ 2.626⁎⁎ 0.820 −3.862⁎⁎ 3.823⁎⁎ 2.744⁎⁎ 3.698⁎⁎ −2.414⁎⁎ −0.166

(0.233) (−1.309) (−3.251) (−1.476) (2.652) (3.689) (2.594) (0.796) (−3.823) (3.098) (2.613) (2.817) (−2.389) (−0.152)

Notes: The 5% and 10% critical values for the minimum LM test with two breaks (Model A) are −3.842 and −3.504, respectively.

optimal k at each combination of two break points, we can determine the breaks where the endogenous two-break LM t-test statistic is at a minimum. To do so, we examine each possible combination of two break points over the time interval [0.1T, 0.9T] while eliminating the endpoints. Here, T is the sample of size.18 We utilize the endogenous two-break LM unit root test to examine the unemployment rate series. Throughout, we first consider Model C, which allows for two changes in level and trend. Table 2 presents the results, where the estimated break points are shown under the column “Tˆ B”. We find that nearly all unemployment rate series reject the unit root null at the 5% significance level, except for France (1895–2004) and UK (1855–2004). An examination reveals that two structural breaks in level and/or trend are significant (t-values significant at 5%) in all countries. Table 3 shows the results of employing the two-break LM unit root test (Model A—which allows for two changes in level). Ten of the fourteen unemployment rate series reject the unit root null at the 10% significance level. This reveals that two structural breaks in level and/or trend are significant (t-values significant at 10%) in seven countries, while only one structural break is significant in the seven remaining countries (Australia, Belgium, Canada, Denmark, France, Japan, and the United States). For these seven countries, a one-break unit root test appears more appropriate.19 Therefore, we want to determine if including two breaks instead of one can adversely affect power to reject the null for these seven countries using the onebreak minimum LM unit root test (Model A) developed in Lee and Strazicich (2004). Table 4 presents the results. The one-break test results are essentially unchanged from the two-break results, except that Japan now does not reject the unit root null, while Belgium, Canada, and France now reject the unit root null at the stronger 5% significance level as compared to the previous 10% level. One country (Japan) out of these seven fails to reject the null in the one-break test, suggesting that a loss of power is not a factor in this case. No matter if there is one-break or two breaks existing in the series, we should authentically take into account the break points in our empirical works. As compared to previous univariate time series tests that do not allow for structural breaks, we find stronger support for stationarity. An examination of the break points in Tables 2 and 3 reveals some interesting observations. From Table 2, in one country (Germany) the first structural break occurs around and after the World War I period of 1912–1927. In four countries (Belgium, Canada, Switzerland, and the UK) the first structural break occurs around the World War II period of 1937–1949. In three countries (Denmark, Netherlands, and Sweden) the first structural break occurs around the Great Depression period of 1929–1939. Aside from this, in five countries (Australia, Denmark, Netherlands, Norway, and the U.S.) the second structural break occurs around the World War II period of 1937–1949. In Belgium and U.K., the second one is associated with two great oil crises, whereas for France, Italy, and Japan this occurs during the

18

The empirical results draw upon code which is available from http://www.cba.ua.edu/~jlee/. The code was modified for the present exercise. We implement Strazicich's et al. (2004) procedure, and we estimate the test equation including two breaks and if the level and the trend dummies’ coefficients are not significant at 10% for one break, then we re-estimate the test equation with just one break. 19

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Table 4 One-break minimum LM unit root test for Model A Country

ˆk

ˆB T

Test statistic

dˆ1⁎

Australia Belgium Canada Denmark France Japan United States

1 0 3 0 7 3 7

1933 1945 1939 1950 1992 1956 1941

− 3.475⁎ − 3.900⁎⁎ − 3.592⁎⁎ − 3.447⁎ − 3.900⁎⁎ − 2.497 − 4.843⁎⁎

0.073 (0.065) − 1.808⁎ (−1.791) − 3.855⁎⁎ (−3.566) − 1.616 (−1.605) 3.060⁎⁎ (2.879) − 1.845⁎ (−1.762) 0.183 (0.166)

Notes: The 5% and 10% critical values for the minimum LM test with two breaks (Model A) are − 3.566 and − 3.211, respectively. Term dˆ is the coefficient of dummy variables under the unit root null in Lee and Strazicich (2004).

recovery of the mid-nineties under improved unemployment records. From the above, it is apparent that most structural breaks in the unemployment rate occur around the Great Depression and World War II. The findings are similar for Table 3 with Model A. However, what is worth paying attention to is this: in Germany and Sweden, two structural breaks occur around the Great Depression period; and for Switzerland it occurs around World War II. 3.2. Half-lives Our other one interest in this paper concerns the persistence of shocks to the unemployment rate. It is likely that although the unit root hypothesis is rejected, deviations are still persistent. As a result, our focus should not be on whether the unemployment rate has a unit root, but on whether it should be on the degree of its persistence. A measure of persistence typically applied in the literature is the half-life, which indicates how long it takes for the impact of a unit shock to dissipate by half. Following Holmes (2000), Ceglowski (2003), Zhang and Lowinger (2006), and Lau et al. (2006) on the measurement of half-lives, Table 5 reports calculations of the half-lives of random shocks to the unemployment rate for each of the countries based on the two-break minimum LM unit root test. These calculations use the estimated value of ϕ in Model C of Eq. (3) of the two-break model and are used to calculate the “approximate” halflives for the unemployment rate via the expression ln(0.5) / ln(1 + ϕ). Once the hysteresis effects in unemployment have been ruled out, we estimate the half-lives. Thus, for France and UK we use Model A to replace Model C, while Model C is not calculated as it is unable to reject the null of unit root.

Table 5 Half-lives in unemployment rate adjustment for two-break minimum LM unit root test Country

Two-break model Estimated ϕ

Years of half-lives

Australia Belgium Canada Denmark France Germany Italy Japan Netherlands Norway Sweden Switzerland United Kingdom United States

− 0.536 − 0.883 − 0.611 − 0.789 − 0.256 − 0.880 − 0.773 − 0.994 − 0.584 − 0.945 − 0.363 − 0.616 − 0.275 − 0.794

0.903 0.323 0.734 0.445 2.344 0.327 0.466 0.137 0.790 0.239 1.537 0.724 2.155 0.439

Notes: The reported value for ϕ is estimated from Eq. (3) and used to calculate the reported half-lives, ln(0.5) / (1 + ϕ). We use Model C of the twobreak unit root test to compute the half-lives, except for France and UK which use Model A.

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Table 6 Two-break minimum LM unit root test for Model C (robustness test: 1946–2004) Country

ˆk

ˆB T

Test statistic

dˆ1⁎

Australia Belgium Canada Denmark France Germany Italy Japan Netherlands Norway Sweden Switzerland United Kingdom United States

1 5 1 2 3 1 2 4 1 7 7 6 6 1

1973,1994 1958,1979 1961,1982 1970,1982 1981,1998 1960,1981 1959,1994 1974,1996 1970,1983 1986,1998 1960,1990 1960,1990 1978,1985 1968,1984

− 5.527⁎⁎ − 6.057⁎⁎ − 4.586 − 6.542⁎⁎ − 6.224⁎⁎ − 6.025⁎⁎ − 5.465⁎⁎ − 5.677⁎⁎ − 5.984⁎⁎ − 5.332⁎⁎ − 8.420⁎⁎ − 6.557⁎⁎ − 7.593⁎⁎ − 6.060⁎⁎

1.243⁎⁎ − 5.070⁎⁎ − 1.586⁎⁎ − 1.520⁎⁎ 3.941⁎⁎ − 1.747⁎⁎ − 3.008⁎⁎ − 0.003 − 0.058 2.690⁎⁎ − 1.239⁎⁎ 3.554⁎⁎ 7.593⁎⁎ 0.748

dˆ2⁎ −1.384⁎⁎ 3.437⁎⁎ 0.969⁎⁎ −0.656⁎ −3.198⁎⁎ 0.504 1.565⁎⁎ 3.077⁎⁎ −1.621⁎⁎ −1.398⁎ 6.267⁎⁎ 4.971⁎⁎ −6.845⁎⁎ −2.116⁎⁎

(3.228) (− 5.679) (− 3.120) (− 2.983) (4.541) (− 3.440) (− 4.340) (− 0.008) (− 0.150) (4.515) (− 2.494) (5.614) (9.394) (2.151)⁎⁎

(− 3.285) (5.125) (2.085) (− 1.755) (− 4.540) (1.530) (5.760) (4.267) (− 4.014) (− 1.732) (8.090) (6.403) (− 10.253) (− 4.715)

Note: Same as Table 2.

In Table 5 the estimated half-lives range from 0.137 years (Japan) to 2.344 (France), but the majority are well under one year. On another measure, Japan, Norway, and Germany have lower persistence and shorter half-lives, whereas Sweden, U.K., and France show higher persistence. The differences found across countries may be explained by the institutional framework in the labor market (Camarero et al., 2005). Those countries that enjoy more social benefits and higher minimum wages are those which exhibit the largest half-lives. All of the observations so far can be viewed in the context of calculations for unemployment in other countries reported in previous studies. In particular, Leon-Ledesma and McAdam (2004) applied the Perron (1997) unit root test with endogenous break in 12 Eastern European Countries (CEECs) and 15 European Union (EU) members. Their findings reject the null of non-stationarity for 6 countries and the half-lives are in the range of 0.25 and 1.75 years. Camarero et al. (2005) also showed that deviations from the NAIRU are corrected for quite rapidly in the EU, as the half-lives are less than two years. Overall, our findings are impressive and shed light on the validity of the natural rate theories. 3.3. The robustness analysis In order to provide a robust analysis for our results, we repeat the two-break unit root tests utilized above for smaller sub-samples: the post-World War II years of 1946–2004. The purpose is to show that our results are not sensitive to the sampling periods selected. Tables 6, 7, 8, and 9 display the results. Table 6 shows Model C for the period from 1946– 2004, similar to Table 2, in full spans. We also find that nearly all unemployment rate series reject the unit root null at the 5% significance level, except for Canada. An examination reveals that two structural breaks in level and/or trend are significant (t-values significant at 10%) in eleven countries, while only one structural break is significant in the 3 remaining countries (Germany, Japan, and the Netherlands). Therefore, the one-break minimum LM unit root test is continued to be adopted, and the results are in Table 7. The one-break test results are essentially unchanged from the two-break results, except for the Netherlands failing to reject the null in the one-break test, suggesting that the loss of power is not a factor in this case. The evidence provides significant support on stationarity for the unemployment rate, which means the ‘natural’ rate of the unemployment hypothesis in our selected sample countries. As suspected, the

Table 7 One-break minimum LM unit root test for Model C (Robustness test: 1946–2004) Country

ˆk

ˆB T

Test statistic

dˆ1⁎

Germany Japan Netherlands

1 8 1

1965 1979 1984

− 4.607⁎⁎ − 4.590⁎⁎ − 3.527

0.097 0.775⁎⁎ − 0.310

Note: The 5% and 10% critical values for the minimum LM test with two breaks (Model C) are − 4.50 and − 4.21, respectively.

(0.333) (2.514) (−1.089)

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Table 8 Two-break minimum LM unit root test for Model A (Robustness test: 1946–2004) Country

ˆk

ˆB T

Test statistic

dˆ 1⁎

Australia Belgium Canada Denmark France Germany Italy Japan Netherlands Norway Sweden Switzerland United Kingdom United States

8 7 5 2 1 3 1 4 1 5 3 1 1 1

1966,1969 1957,1975 1981,1993 1958,1976 1980,1994 1993,1997 1959,1980 1984,1992 1970,1974 1981,1987 1959,1980 1981,1995 1988,1993 1973,1983

− 2.229 − 3.155 − 3.672⁎ − 5.395⁎⁎ − 2.461 − 2.739 − 2.598 − 3.662⁎ − 2.822 − 3.911⁎⁎ − 2.686 − 3.126 − 2.327 − 4.910⁎⁎

− 1.708 4.854⁎⁎ 5.456⁎⁎ − 1.515 1.705⁎ − 0.872 − 5.675⁎⁎ 0.563 0.868 2.287⁎⁎ − 0.499 0.737 0.101 2.681⁎⁎

dˆ2⁎ (− 1.307) (3.459) (4.958) (− 1.488) (1.666) (− 0.827) (− 5.549) (0.553) (0.857) (2.244) (− 0.474) (0.728) (0.095) (2.653)

− 2.116⁎ 0.229 − 2.212⁎⁎ 0.881 0.806 − 0.889 2.626⁎⁎ 1.235 0.782 2.932⁎⁎ 0.487 3.701⁎⁎ − 0.865 0.804

(−1.693) (0.206) (−2.050) (0.872) (0.756) (−0.860) (2.594) (1.181) (0.768) (2.833) (0.478) (3.405) (−0.830) (0.706)

Note: Same as Table 3.

most structural breaks occur around the energy crisis period of 1970–1982.20 This clearly shows that the energy crises had a huge shock to unemployment in OECD countries. Re-checking for Model A as in Table 8, only five countries (Canada, Denmark, Japan, Norway, and the United States) reject the unit root null at the 10% significance level, as the evidence of a stationary path for unemployment rates appears to be slightly weak. Naturally, an examination reveals that two structural breaks in level and/or trend are significant (t-values significant at 10%) in three countries, while only one structural break is significant in the eleven remaining countries. Based on the one-break minimum LM unit root test, as reported in Table 9, two countries (Denmark and US) reject the unit root null at the 5% significance level.21 Our empirical findings overall provide significant support for unemployment rate stationarity among 14 OECD countries. From this, the evidence clearly supports several previous findings. For example, Papell et al. (2000) utilized Bai and Perron (1998) to test multiple structure change for 16 OECD countries from 1955–1997, though they found that all of the countries have at least one significant break, as well as the one-break greatly takes place during an oil crisis period. However, the method of Bai and Perron (1998) has to confirm that the series is I(0) first, and then it can come into use to test for multiple breaks. One should examine the process, but hold that one-break firstly and then carry on multiple break tests again. Distinctly, this examining method might be inconsistent logically. To overcome this shortcoming, we carry on differently with the two-break test directly in this paper's unit root test process. Although Røed (2002) reported that only U.S. unemployment hysteresis is non-existent using the ADF and KPSS unit root tests for 10 OECD countries, Fève et al. (2003) advanced the discussion in 21 selected OECD countries. Comparing these studies, the evidence that we provide is more obvious and severe in OECD countries. Camarero and Tamarit (2004) themselves found hysteresis in 7 countries out of 19, but when we use annual data spanning over one century of an unemployment series, we find strong evidence of the stationarity properties of the unemployment rate in Germany, Italy, Japan, Norway, and Switzerland, which Camarero and Tamarit (2004) claimed to have non-stationarity and hysteresis on the unemployment rate. By contrast, our empirical findings provide significant support for unemployment rate stationarity among OECD countries while allowing for structural breaks in series; in a word, the findings provide stronger support for stationarity. 4. Concluding remarks and policy implications Unemployment is a major source of concern among policymakers and society as a whole. Since a long data span is particularly important in the unit root test, this paper re-examines the hysteresis of unemployment's endogenously 20

This is similar to Strazicich et al. (2001), who found about 80% of all breaks occur during the years 1973–1974 and 1980–1982, both periods that associated with significant recessions. 21 Sen (2003) reported that Model C is preferable to Model A when the break data are treated as unknown, and indicated that Model C may achieve more reliable estimates of the break point.

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Table 9 One-break minimum LM unit root test for Model A (robustness test: 1946–2004) Country

ˆk

ˆB T

Test statistic

dˆ 1⁎

Australia Belgium Denmark France Germany Japan Netherlands Sweden Switzerland United Kingdom United States

8 7 2 3 8 3 1 3 1 1 1

1969 1957 1976 1998 1994 1992 1970 1956 1995 1987 1969

− 2.182 − 3.146 − 5.202⁎⁎ − 2.425 − 2.251 − 2.982 − 2.721 − 2.664 − 3.055 − 2.079 − 4.571⁎⁎

− 1.958 4.656⁎⁎ 0.822 − 2.249⁎⁎ 2.708⁎⁎ 1.126 0.833 2.724⁎⁎ 3.716⁎⁎ − 0.926 2.470⁎⁎

(−1.623) (3.329) (0.813) (−2.133) (2.767) (1.090) (0.821) (2.365) (3.428) (−0.858) (2.438)

Note: Same as Table 4.

determined break points that are incorporated in 14 major OECD industrialized countries, by using annual data over one century in length in order to avoid the seasonal adjustment shortcoming and be free from any local features of a short sample period. The focal point of the paper is that the stationary properties in the long-term path of the unemployment rate quantify the degree of persistence and account for possible breaks. We test the hypothesis with a careful selection of both data and methodology. Thus, to perform our examinations, we utilize an LM unit root test that endogenously determines structural breaks in level and/or trend as proposed by Lee and Strazicich (2003, 2004). Our empirical findings provide significant evidence that the unemployment rate presents stationarity when we control for breaks in 14 major OECD countries. These results are in contrast with other time series tests that do not allow for structural breaks and structural breaks are identified in each country. By allowing for two structural breaks in each country, our tests benefit from a greater ability to reject a unit root null. Additionally, we find that most shocks to unemployment rates are temporary and soon converge when we control for breaks, and that the unemployment rates show stationarity and these results are consistent in a robustness test process. Thus, shocks only cause deviations around a mean or deterministic trend. In other words, a shock only temporarily affects unemployment. In addition, related to the persistence measures, the estimated approximate half-lives of the unemployment rate are less than one year for 11 of 14 OECD countries, which indicate that the deviations from the NAIRU are corrected for quite rapidly. Important policy implications emerge from our empirical results of the unit root test with multiple structural breaks. First, as Leon-Ledesma (2002) reported, if most shocks to unemployment rates are temporary, then the stabilization of labor and macroeconomic policies do not have long lasting effects on the unemployment rates of the selected OECD countries based upon our results. Next, if the unemployment rate is mean (or trend) reverting, then it follows that the series will return to its mean value (or trend path), and it might be possible to forecast future movements in the unemployment rate based on past behavior. Moreover, other macroeconomic variables linked to the unemployment rate via flow-on effects will not inherit that non-stationarity condition and transmit it to major economic variables, such as the inflation rate. When combined with Okun's law—which describes the relation between unemployment and output in detail—a low output growth is often cited as the reason for the rise in unemployment. Third, the unemployment rate showing trend stationarity suggests that the aggregate demand policies may not be over-implemented in the sample countries since we fail to discover evidence to support the unemployment hysteresis hypothesis. We believe this represents that the trade-off impact does not exist, implying there is a restriction on the government's selected target, and that the independence of the policy will increase significantly. Fourth, if there are structural breaks, then we must try to both date these and ensure that we distinguish them from normal business-cycle fluctuations (Leon-Ledesma and McAdam, 2004). Our result implies that models which ignore breaks in the trend of unemployment cannot avoid the wasted costs of interference, which can also increase fluctuations in other macroeconomic variables. As part of the labor policy implemented by a government, it is not necessary for the authority to pay attention to the unemployment issue. Fifth, if the data were erroneously treated as I(1) and the causality tests for unemployment rate and macroeconomics were applied to the first difference, then a spurious causality would result. Our empirical test

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supports the crucial role played by institutional factors in determining the persistence of unemployment. Thus, labor market institutions matter not only to the determination of the unemployment rate, but also to the speed of adjustment. Sixth, according our findings, more breaks occurred from the effects of the global economy on our selected economies—for instance, the two World Wars, the Great Depression, and the two great oil crises. We find that most shocks to unemployment rates are temporary and soon converge, no matter in full span samples or the robustness test in a sub-period analysis. In a word, most structural breaks occur by historic events from global shocks, and the implications tell policymakers that once the unemployment rate series deviate from its deterministic trend briefly with short half-lives, they should stand in the position of neutrality, because there are no structural reasons to adopt more interventions under the stationarity properties of the unemployment rate. Finally, we are reminded that when we conduct research into the estimated relationship between unemployment and macroeconomics, we should take structural breaks into account as they can reflect the true current status. Some interesting areas for future research might be to identify precisely which events caused the structural breaks and to investigate the commonality of structural breaks in unemployment and macroeconomics. 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