In this empirical note we use a more powerful nonlinear (logistic) unit root test advanced by Leybourne et al. (1998) to investigate the hysteresis in unemployment for ten European countries for the period 1961-2003. The hypothesis is confirmed for all the European countries for which Leybourne et al.¡¯s (1998) nonlinear (logistic) unit root test is performed, except for Belgium and the UK.Hysteresis in Unemployment, European Countries, Logistic Unit Root Tests

Chung-Ju Huang

Tsangyao Chang

Yuan-Hong Ho

English

Research Papers in Economics

JOURNAL  OF  ECONOMIC  DEVELOPMENT                              49 
Volume 32, Number 1, June 2007 
 
 
REVISITING HYSTERESIS IN UNEMPLOYMENT FOR TEN 
EUROPEAN COUNTRIES: AN EMPIRICAL NOTE ON A MORE 
POWERFUL NONLINEAR (LOGISTIC) UNIT ROOT   
 
TSANGYAO CHANG, YUAN-HONG HO AND CHUNG-JU HUANG
*
 
Feng Chia University 
 
 
In this empirical note we use a more powerful nonlinear (logistic) unit root test advanced 
by Leybourne et al. (1998) to investigate the hysteresis in unemployment for ten European 
countries for the period 1961-2003. The hypothesis is confirmed for all the European 
countries for which Leybourne et al.’s (1998) nonlinear (logistic) unit root test is performed, 
except for Belgium and the UK. 
 
Keywords: Hysteresis in Unemployment, European Countries, Logistic Unit Root Tests 
JEL Classification: C22, C23 
 
 
1.  INTRODUCTION 
 
The issue of unemployment has clearly become the most pressing problem for the 
majority of countries over the past decade. In the case of the European countries, the 
average unemployment rate has increased from less than 4% in the 1960s to over 10% in 
the 1990s. The dominant feature of unemployment is its high persistence even in times 
of relative booms. Since confirming the validity of the hypothesis of hysteresis in 
unemployment is critical for both empirical researchers and policymakers, what actually 
causes this higher persistence has been the focus of numerous theoretical and empirical 
studies. In considering the assumptions inherent in the hysteresis hypothesis in relation 
to unemployment, if unemployment follows an I (1) process, then the shocks affecting 
the series will have permanent effects, thus shifting the unemployment equilibrium from 
one level to another. Should this be the case, from a policy perspective, policy action is, 
indeed, required to return unemployment to its original level. On the other hand, if 
unemployment follows an I (0) process, the effects of the shock will merely be transitory, 
thus rendering the need for policy action less mandatory since unemployment will 
eventually return to its equilibrium level. The I (0) process has commonly been referred 
to as the natural rate of unemployment hypothesis (NAIRU), for it characterizes 
 
* Valuable comments of an anonymous referee are greatly appreciated.
 
 TSANGYAO CHANG, YUAN-HONG HO AND CHUNG-JU HUANG  50 
unemployment dynamics as a mean reversion process. 
Because hysteresis is associated with non-stationary unemployment rates, unit root 
tests have been widely used to investigate its validity. For example, Blanchard and 
Summers (1986), for example, using data for France, Germany, the United Kingdom and 
the United States for the 1953 to 1984 period, were pioneers in presenting the first 
empirical study that employed conventional unit root tests to investigate the effect of 
hysteresis on unemployment. In so doing, they were unable to reject the non-stationarity 
of unemployment rates for the countries they studied except for the Untied States where 
they did find evidence of stationarity. A little later, Brunello (1990), using Japanese 
unemployment data for the 1955 to 1987 period, was unable to reject the null hypothesis 
of a unit root. Mitchell (1993) later used Perron’s (1989) unit root test, which assumes 
one exogenously given structural break and similarly confirmed support for hysteresis in 
several OECD countries. Likewise, Jaeger and Parkinson (1994) reported results, again 
indicating that unemployment hysteresis exists in Germany, the United Kingdom and 
Canada, but not in the United States. On the other hand, Arestis and Mariscal (2000) 
applied the structural break univariate unit root test of Perron (1997) to unemployment 
rates from twenty-two OECD countries. Although their results are mixed, they mostly 
reject the unit root and hysteresis. Using data from 1970 to 1994, Roed (1996) 
empirically investigated the presence of unemployment hysteresis in 16 OECD countries 
and strongly suggested that hysteresis prevails in Australia, Canada and Japan, as well as 
in several European countries; however, once again, hysteresis was rejected in the case 
of the United States. 
While most of the empirical studies to date support the existence of a unit root in 
unemployment, critics have claimed that this conclusion may be due to the low power of 
the conventional unit root tests employed. Recently, there has been a growing consensus 
that macroeconomic variables exhibit nonlinearities and, consequently, conventional 
unit root tests, such as the ADF test, have low power in detecting mean reversion. To 
solve this problem, stationarity tests based on a nonlinear framework must be applied.     
This empirical note contributes to this line of research by determining whether 
hysteresis in unemployment is a characteristic of the European labor market. We test the 
hysteresis hypothesis in unemployment for 10 European country data sets using a more 
powerful nonlinear (logistic) unit root test advanced by Leybourne et al. (1998). Our 
empirical results strongly reject the unit root process for only two of the countries 
examined, indicating that hysteresis in unemployment holds true for 8 of the 10 
European countries. 
The remainder of this empirical note is organized as follows. Section 2 presents the 
data used, and Section 3 describes the methodology adopted, while also discussing the 
empirical findings and policy implications. Finally, Section 4 presents some concluding 
remarks. 
 
 
 REVISITING HYSTERESIS IN UNEMPLOYMENT  51 
2.  DATA 
 
This empirical note employs the 1961-2003 unemployment rates for ten European 
countries, namely Belgium, Denmark, France, Ireland, Italy, the Netherlands, Portugal, 
the UK, Norway and Finland. All the data are from the AREMOS database of Taiwan’s 
Ministry of Education, and summary statistics are provided in Table 1. The 
unemployment data indicates that Ireland and Norway have the highest and lowest 
average unemployment rates, respectively. The Jarque-Bera test results meanwhile 
indicate that, except for Ireland, Norway and Finland, all the unemployment data sets are 
approximately normal. Figure 1 and Figure 2 plot the actual values and the fitted smooth 
transition of the unemployment rates for France and the UK, two leading countries in 
terms of their higher political and economic status in Europe, respectively. Due to space 
constraints, we do not report the figures for the remaining countries, but these are 
available from the authors upon request. 
 
 
Table 1.    Summary Statistics of Unemployment Data Sets: 1961-2003 
Country Mean  Std  Maximum Minimum Skewness Kurtosis  J-B 
Belgium 6.105  3.281  10.811  1.336  -0.197  1.564  3.968 
Denmark 4.783  2.934  10.048  0.589  -0.079  1.731  2.931 
France 6.654  3.857  12.399  1.163  -0.088  1.476  4.215 
Ireland 9.390  4.358  16.809  3.900  0.435  1.654  4.603* 
Italy 7.611  2.471  11.837  3.536  0.196  1.827  2.741 
Netherlands 4.519  2.909  11.693  0.444  0.179  2.128  1.592 
Portugal 5.004  2.233  8.709  1.619  0.007  1.550  3.766 
UK 5.754  3.404  11.396  1.081  0.186  1.671  3.415 
Norway 2.877  1.459  5.959  1.295  0.711  2.156  4.893* 
Finland 6.204  4.608  17.031  1.197  0.944  2.842  6.437** 
Notes: Std denotes standard deviation and J-B denotes the Jarque-Bera Test for Normality.*, ** and *** 
indicate significance at the 10%, 5% and 1% levels respectively. 
 
 
 
 
 
 
 
 
 
 
 
 TSANGYAO CHANG, YUAN-HONG HO AND CHUNG-JU HUANG  52 
.00
.02
.04
.06
.08
.10
.12
.14
65 70 75 80 85 90 95 00
X3 X3HATB
                                                         
.00 
                   
.02 
.04 
.06 
.08 
.10 
.12 
65  70 75 80 85 90 95 00
X 8 X8HATC
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
                                                                                                                
Figure 1.    Actual Values of Unemployment and Fitted Smooth Transition-France 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 2.    Actual Values of Unemployment and Fitted Smooth Transition-The U.K REVISITING HYSTERESIS IN UNEMPLOYMENT  53 
3.  METHODOLOGY 
 
Following Leybourne et al. (1998), we consider the following three logistic smooth 
transition regression models: 
 
Model A:  ,                                      ( 1 )   t t t v S Y + + = ) , ( 2 1 τ γ α α
 
Model B:  ,                                  ( 2 )   t t t v S t Y + + + = ) , ( 2 1 1 τ γ α β α
 
Model C:  ,                        ( 3 )   t t t t v tS S t Y + + + + = ) , ( ) , ( 2 2 1 1 τ γ β τ γ α β α
 
where   is a zero-mean I (0) process, and   is the logistic smooth transition 
function, based on a sample of size T, where 
t v ) , ( τ γ t S
 
1 )}] ( exp{ 1 [ ) , (
− − − + = T t St τ γ τ γ ,   0 > γ .                                ( 4 )  
 
While the S function controls the smooth transition between regimes, the parameter 
τ  determines the timing of the transition midpoint; for example, for  0 > γ , we have 
 and  . The speed of transition is then 
determined by the parameter 
1 ) , ( , 0 ) , ( = = ∞ + ∞ − τ γ τ γ S S 5 . 0 ) , ( = τ γ τT S
γ . If  γ  is small, then the transition is slow -   
takes a long period of time to traverse the interval (0,1). In the limiting case, with 
) , ( τ γ t S
0 = γ , 
 for  all  t. On the other hand, for large values of  5 . 0 ) , ( = τ γ t S γ ,   traverses  the 
interval (0,1) very rapidly. As 
) , ( τ γ t S
γ  approaches +∞, this function changes value from 0 
to 1 instantaneously at time  T t τ = . 
If we assume that   is a zero-mean I (0) process, then Model A implies that   is 
stationary around a mean which changes from   to  . Model B also allows the 
intercept to change from   to  , but include a fixed slope term. Model C is the 
most flexible model, for it allows the intercept to change from   to   and allows 
the slope parameter to change, with the same speed of transition, from   to . If 
t v t Y
1 α 2 1 α α +
1 α 2 1 α α +
1 α 2 1 α α +
1 β 2 1 β β +
0 < γ , the initial and final model states are reversed but the interpretation of the parameters 
remains the same. 
The tests of Leybourne et al. (1998) are based on the following hypothesis: 
 
ϕ ε = + + = = − 0 1 0 , , : U U K U U Y H t t t t t ,                                  ( 5 )  
 
a H :   M o d e l   A ,   M o d e l   B   o r   M o d e l   C ,                                     ( 6 )  
 TSANGYAO CHANG, YUAN-HONG HO AND CHUNG-JU HUANG  54 
where   and   are both assumed to be stationary autoregressive moving average 
(ARMA) processes with zero mean. The test statistics are calculated in two steps: 
t ε t v
Step 1. Using a nonlinear least squares (NLS) algorithm, estimate the deterministic 
component of the model and compute residuals ( ) from Models A, B or C.  t v ˆ
Step 2. Compute the ADF statistic, the t-ratio associated with   in the ordinary 
least squares (OLS) regression, 
ρ ˆ
 
. ˆ ˆ ˆ ˆ ˆ ˆ
1
1 ∑
=
− − + Δ + = Δ
K
i
i t i t t v v v η θ ρ                                            ( 7 )  
 
The ADF statistics are denoted by  ,   and  , respectively, if the 
residuals are calculated from Models A, B or C. Leybourne, et al. (1998) provided 
critical values for the tests calculated using Monte Carlo simulation. 
α S ) (β α S αβ S
 
 
4.  EMPIRICAL  RESULTS 
 
For purposes of comparison, we first apply several conventional unit root tests to 
examine the null of a unit root in the unemployment level for each country. We select the 
lag order of the test based on the Schwarz criterion (SC). The results in Table 2 clearly 
indicate that the ADF, DF-GLS (Elliott et al. (1996)), P-P and NP (Ng and Perron 
(2001)) tests all fail to reject the null of non-stationarity of unemployment for all 10 
countries. The KPSS test also yields the same results. Table 3 presents Leybourne et al.’s 
(1998) nonlinear (logistic) unit root test results and the corresponding Model A, B, or C 
selected based on the Schwarz criterion. The empirical results strongly reject the unit 
root process for only two of the data series, indicating that a unit root in unemployment 
holds true for 8 out of the 10 countries studied here.
1 These results provide strong 
evidence in support of the hysteresis hypothesis given the European countries’ 
unemployment data. 
 
 
 
 
 
 
 
1 The non-rejection by several conventional unit root tests and emphatic rejections by Leybourne et al.’s test 
(1998) points suggestively towards these being stationary around a smooth transition where, as was shown in 
Table 4, conventional unit root tests can have very lower power. REVISITING HYSTERESIS IN UNEMPLOYMENT  55 
 
 
Table 2.    Linear Unit Root Tests (ADF, DF-GLS, P-P, KPSS and NP) 
Country ADF  DF-GLS  P-P KPSS NP 
Belgium -1.894(1)  -1.413(1) -1.359[3] 0.585[5]**  -4.668 
Denmark -1.796(1) -1.376(1) -1.503[1] 0.526[5]**  -4.034 
France -1.263(1)  -0.515(1)  -1.238[3] 0.738[5]**  -0.736 
Ireland -1.713(1)  -1.527(1)  -1.203[3] 0.415[5]**  -4.888 
Italy -1.727(1)  -0.009(1)  -1.073[0] 0.742[5]*** -2.411 
Netherlands -1.561(0)  -1.089(0) -1.604[1] 0.373[5]**  -1.806 
Portugal -2.297(1)  -1.766(1) -1.731[1] 0.403[5]**  -4.293 
UK -1.405(2)  -0.973(2)  -1.401[0] 0.500[5]**  -1.888 
Norway -1.509(1)  -1.295(1) -1.022[0] 0.617[5]**  -5.293 
Finland -1.566(2)  -1.209(2) -1.475[1] 0.623[5]**  -3.428 
Notes: *, ** and *** indicate significance at the 10%, 5% and 1% levels respectively. The numbers in 
parentheses indicate the lag order selected based on the recursive t-statistic, as suggested by Perron (1989). 
The NP test was based on the MZa statistic. 
 
 
Table 3.    Nonlinear (Logistic) Unit Root Tests 
Country t-statistic  K  SC  AIC  Model 
Belgium -5.172**  1  -5.912  -6.117  B 
Denmark -4.234  1  -5.704  -5.908  B 
France -3.983  1 -6.533  -6.738  B 
Ireland -4.498  1  -5.293  -5.497  B 
Italy -4.398 1  -6.797  -7.043 C 
Netherlands -3.293  0  -6.059  -6.036  C 
Portugal -4.151  1  -6.032 -6.237  B 
UK -5.802**  1  -6.037  -6.283  C 
Norway -4.376  1  -7.469 -7.715  C 
Finland -3.854  1  -5.609 -5.856  C 
Notes: *, ** and *** indicate significance at the 10%, 5% and 1% levels respectively. Critical values are 
taken from Leybourne, et al. (1998). SC and AIC indicate the Schwarz criterion and Akaike information 
criterion, respectively. K is the order of lag-length. Models A, B or C are selected based on both SC and AIC. 
 
 
Table 4.    Empirical Powers for Series Generated from the Estimated   
Smooth Transition Model for both Belgium and UK Unemployment (T=43) 
 Model  C  ADF  DF-GLS  P-P  KPSS 
K 0.10  0.05  0.10  0.05 0.10  0.05 0.10 0.05 0.10 0.05 
0  0.95 0.93 0.16 0.13 0.27 0.26 0.22 0.21 0.34 0.31 
1  0.92 0.87 0.12 0.09 0.25 0.19 0.18 0.16 0.29 0.25 
Notes: Detailed procedures see Leybourne et al. (1998). The values in bold indicate the mean values of the 
powers. The Model C of Leybourne et al. (1998) clearly has considerable power to reject the (false) unit root TSANGYAO CHANG, YUAN-HONG HO AND CHUNG-JU HUANG  56 
hypothesis. On the other hand, other conventional unit root tests have no ability to distinguish the actual 
generating process from one with a unit root. Results from both Models A and B are similar to those found 
here, not reported here to save space but are available upon request. Normal sizes are 0.10 and 0.05. 
5. SUMMARY AND CONCLUSION 
 
In this empirical note we employ the Lebyourne et al. (1998) nonlinear (logistic) unit 
root tests to investigate the hysteresis in unemployment for ten European countries for 
the period 1961-2003. The results from five conventional unit tests provide strong 
evidence in support of the hysteresis hypothesis given the European countries’ 
unemployment data. The hypothesis is also confirmed for all the European countries 
except for Belgium and the UK when Leybourne et al.’s (2001) nonlinear (logistic) unit 
root test is conducted. As far as major policies are concerned, our study implies that a 
fiscal stabilization policy and/or monetary policy would possibly have permanent effects 
on the unemployment rates of these European countries. 
 
 
 
 
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Mailing Address: Department of Public Finance, Feng Chia University, Taichung, Taiwan. Tel: 
886-4-2451-7250(4306). E-mail: yhho@fcu.edu.tw. 
 
Manuscript received January, 2005; final revision received January, 2007. 

Efficient Tests for an Autoregressive Unit Root,”

final revision received

Further Evidence on Breaking Trend Functions in Macroeconomic Variables,”

Hysteresis and ‘the Japanese Unemployment Problem’:

Hysteresis and the European Unemployment Problem,”

Lag Length Selection and the Construction of Unit Root Tests with Good Size and Power,”

Lag Selection in

Some Evidence on Hysteresis in Unemployment Rates,”

Testing for Unit Roots and Persistence

Testing the Null Hypothesis of Stationarity Against the Alternative of a Unit Root: How Sure are We that Economic Time Series Have a Unit Root?”

Unemployment Hysteresis -

REVISITING HYSTERESIS IN UNEMPLOYMENT FOR TEN EUROPEAN COUNTRIES: AN EMPIRICAL NOTE ON A MORE POWERFUL NONLINEAR (LOGISTIC) UNIT ROOT

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REVISITING HYSTERESIS IN UNEMPLOYMENT FOR TEN EUROPEAN COUNTRIES: AN EMPIRICAL NOTE ON A MORE POWERFUL NONLINEAR (LOGISTIC) UNIT ROOT

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