2009 Oxford Business & Economics Conference Program
ISBN : 978-0-9742114-1-1
Mean reversion of unemployment rates:
Evidence for Colombia using regional data
Jesús Otero
Facultad de Economía
Universidad del Rosario
Bogotá, Colombia
Juan Carlos Guataqui
Facultad de Economía
Universidad del Rosario
Bogotá, Colombia
February 2009
ABSTRACT
In this paper, we test for the stationarity of unemployment rates in Colombia over the
period 1984Q1 to 2004Q4, using a panel of seven cities. Our testing strategy
addresses key concerns with regard to unit root panel data testing, namely the
presence of serial correlation and cross-sectional dependency across the
unemployment rates in the panel. To address these concerns, we employ an AR-based
bootstrap approach that allows us to test the null hypothesis of joint stationarity
allowing for cross sectional dependencies. In contrast to the existing literature, we
find that unemployment rates in Colombia can be characterised as stationary
processes, providing support to the view that they exhibit mean reversion, and
therefore appear consistent with the natural rate hypothesis.
JEL classification: C12; C15; C22; C23; E31
Keywords:
Unemployment; panel stationarity test; cross section dependence;
Colombia.

Corresponding author:
Jesús Otero
Facultad de Economía
Universidad del Rosario
Calle 14 # 4-69
Bogotá, Colombia
Phone: (+571) 297 02 00 Ext. 661
E-mail: jotero@urosario.edu.co
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2009 Oxford Business & Economics Conference Program
ISBN : 978-0-9742114-1-1
1. INTRODUCTION
The question of whether unemployment rates should be treated as stationary or nonstationary processes has received a great deal of attention ever since the publication of
the paper by Nelson and Plosser (1982). Indeed, classifying unemployment rates as
one or the other has a number of important statistical and economic implications.
From a statistical point of view, stationary series have a finite (non-zero) variance and
exhibit temporary memory in the sense that the effect of a perturbation disappears as
time passes. In contrast, non-stationary series have an unbounded variance and exhibit
a permanent memory. From an economic perspective, a stationary unemployment rate
has been commonly associated with the natural rate of unemployment hypothesis
(NAIRU), for it may be viewed as a mean reverting process that fluctuates around its
long-run equilibrium value, while non-stationarity has been associated with the
hysteresis hypothesis, whereby long lasting unemployment effects arise from cyclical
fluctuations (see Blanchard and Summers, 1986).
For these reasons, empirical examinations of unemployment behaviour have
typically fallen into one of two categories. The first category of studies has examined
the possibility of non-stationarity in unemployment by conducting univariate tests of
unit roots. Studies such as Blanchard and Summers (1986), Brunello (1990), Jaeger
and Parkinson (1994) and Røed (1996) consistently reject the null hypothesis of a unit
root for the US (favouring the natural rate hypothesis) but are unable to reject the unit
root hypothesis for other OECD countries (supporting the presence of unemployment
hysteresis effects). Within a regional context, and allowing for the presence of
structural breaks, Clemente et al. (2005) find favourable evidence to the rejection of
the unit root hypothesis in US states, while Reis and Gomes (2008) find hysteresis
effects in five out of six Brazilian regional unemployment rates.
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The second group of studies has applied panel unit root techniques to test for
stationarity since univariate tests suffer from low power. In recent years a number of
alternative procedures have been proposed to test for the presence of unit roots in
panels that combine information from the time-series dimension with that from the
cross-section dimension, such that fewer time observations are required for these tests
to have power. The most commonly used unit root test applied to panels include
Maddala and Wu (MW) (1999) and Im, Pesaran and Shin (IPS) (2003), which test the
joint null hypothesis of a unit root against the alternative of at least one stationary
series, by using the augmented Dickey–Fuller (ADF) (1979) statistic across the crosssectional units of the panel. A recent study that employs panel data methods is LeónLedesma (2002), who confirms that hysteresis for 11 EU countries and the natural rate
for 51 US states are the most plausible hypothesis using the IPS test. It should,
however, be noted that IPS (2003, p.73) warn that due to the heterogeneous nature of
the alternative hypothesis in their test, one needs to be careful when interpreting the
results, because the null hypothesis that there is a unit root in each cross section may
be rejected when only a fraction of the series in the panel are stationary. A further
issue of concern is that the presence of cross-sectional dependencies can undermine
the asymptotic normality of the IPS test and lead to over-rejection of the null
hypothesis of joint non-stationarity. To some extent, these concerns are addressed by
Camarero and Tamarit (2004) and Chang et al. (2005) who conduct ADF unit root
tests within a seemingly unrelated regression framework. Camarero and Tamarit
(2004) reject hysteresis effects in 12 out of 19 OECD countries, while Chang et al.
(2005) confirm the hysteresis hypothesis for 8 out of 12 European countries.
This paper aims to study regional unemployment in Colombia. In particular,
we test for stationarity of unemployment rates using data for a panel of seven
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ISBN : 978-0-9742114-1-1
metropolitan areas. Since unit root tests applied to single series suffer from low
power, panel unit root techniques offer a way forward in terms of enhanced test
power. A distinctive feature of our analysis is that we apply the Hadri (2000) tests of
the null hypothesis that all individual series are stationary, against the alternative of at
least a single unit root in the panel. The Hadri tests offer the key advantage that if the
null hypothesis is not rejected, we may conclude that all the city relative prices in the
panel are stationary. In addition to this, an important novel feature of our analysis is
that we allow for the presence of potential cross-sectional dependencies. More
specifically, we consider a procedure based on a bootstrap of the Hadri tests because
failure to account for cross-sectional dependencies leads to size distortion and overrejection by the Hadri test.
We believe that the study of the Colombian case is interesting because
Colombian regions are often characterised by a “centre–periphery” dichotomy, where
the central region (which consists of the three main cities of Bogotá, Medellín and
Cali) comprises the largest concentration of population, economic activity and
infrastructure (see e.g. Galvis, 2008). In earlier papers, Arango and Posada (2002)
examined the univariate time series properties of the unemployment rate in Colombia
and were unable to reject the unit root hypothesis. Gamarra (2006) also finds support
for the unit root hypothesis when using unemployment rates for the seven main
metropolitan areas of the country. Our paper differs in that we study the stationarity
issue within a panel context and allowing for the potential effects of cross-sectional
dependencies.
The paper is organised as follows. Section 2 presents an overview of the Hadri
(2000) panel stationarity tests. Section 3 describes the dataset and presents the results
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of applying the panel stationarity tests to the city unemployment rates in major
Colombian cities. Section 4 concludes.
2. TESTING FOR PANEL STATIONARITY
Hadri (2000) proposes residual-based Lagrange Multiplier tests for the null hypothesis
that all the time series in the panel are stationary (either around a level or a
deterministic time trend), against the alternative that some of the series are
nonstationary. The Hadri tests are panel versions of the Kwiatkowski, Phillips,
Schmidt and Shin (KPSS) (1992) stationarity tests. Following Hadri (2000), consider
the models:
yit  rit   it
(1)
yit  rit  i t   it
(2)
and
where rit is a random walk, rit  ri ,t -1  uit , and  it and uit are mutually independent
normal distributions. Also,  it and uit are i.i.d across i and over t , with E  it   0 ,
E  it2    2,i  0 , E uit   0 , E uit2    u2,i  0 , t  1,..., T and i  1,..., N . The null
hypothesis that all the series are stationary is given by H 0 :  u2,i  0 , i  1,..., N , while
the alternative that some of the series are nonstationary is H1 :  u2,i  0 , i  1,..., N1
and  u2,i  0 , i  N1  1,..., N .
Let ˆit be the residuals from the regression of yi on an intercept, for model (1)
(or on an intercept and a linear trend term, for model (2)). Then, the individual
univariate KPSS stationarity test is given by:
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i ,T ,k
ˆ   
ISBN : 978-0-9742114-1-1
T
t 1
2
Sit2
T ˆ 2i
i
,
where Sit denotes the partial sum process of the residuals given by Sit   j 1 ˆij , and
t
ˆ 2 is a consistent estimator of the long-run variance of ˆit from the appropriate
i
regression. In their original paper, KPSS propose a nonparametric estimator of ˆ 2i
based
on
a
Bartlett
window
having
a
truncation
lag
parameter
of
14
lq  integer q T 100  , with q  4,12 . However, Caner and Kilian (2001) have


pointed out that stationarity tests, like the KPSS tests, exhibit very low power after
correcting for size distortions. Thus, in our paper we follow recent work by Sul,
Phillips and Choi (2005), who propose a new boundary condition rule that improves
the size and power properties of the KPSS stationarity tests. In particular, Sul et al.
suggest the following procedure. First, an AR model for the residuals is estimated,
that is:
ˆit  i ,1ˆi ,t 1  ...  i , p ˆi ,t  p  it
i
i
(3)
where the lag length of the autoregression can be determined for example using the
general-to-specific algorithm proposed by Campbell and Perron (1991). Second, the
long-run variance estimate of ˆ 2i is obtained with the boundary condition rule:

2
i


,
2
ˆ
1


1


 i  
ˆ
2
ˆ   min T ˆ ,
2
i
i
where ˆi 1  ˆi ,1 1  ...  ˆi , pi 1 denotes the autoregressive polynomial evaluated at
L  1 . In turn, ˆ2i is the long-run variance estimate of the residuals in equation (3)
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that is obtained using a quadratic spectral window Heteroscedastic and
Autocorrelation Consistent (HAC) estimator.1
The Hadri (2000) panel stationarity test statistic is given by the simple average
of individual univariate KPSS stationarity tests:
LM T , N 
1
N
N

i 1
i ,T
,
which after a suitable standardisation, using appropriate moments, follows a standard
normal limiting distribution.2 That is:
Z
where  
1
N

N

N LM T , N  

  N  0,1
 and  2  N1 i 1 i2 .
N
i 1 i
The Monte Carlo experiments of Hadri (2000) illustrate that these tests have
good size properties for T and N sufficiently large. However, Giulietti et al. (2008)
show that even for relatively large T and N the Hadri (2000) tests suffer from severe
size distortions in the presence of cross-sectional dependence, the magnitude of which
increases as the strength of the cross-sectional dependence increases. This finding is
in line with the results obtained by Strauss and Yigit (2003) and Pesaran (2007) on
both the Im, Pesaran and Shin and the Maddala and Wu panel unit root tests. In order
to correct for the size distortion caused by cross-sectional dependence, Giulietti et al.
(2008) apply the bootstrap method and find that the bootstrap Hadri tests are
approximately correctly sized.
To implement the bootstrap method in the context of the Hadri tests, we start
off by correcting for serial correlation using equation (2) and obtain ˆit , which are
1
Additional Monte Carlo evidence reported by Carrion-i-Silvestre and Sansó (2006) also indicates that
the proposal in Sul et al. (2005) is to be preferred since the KPSS statistics exhibit less size distortion
and reasonable power.
2
Asymptotic moments can be found in Hadri (2000) while finite sample critical values appear in Hadri
and Larsson (2005).
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centred around zero. Next, as suggested in Maddala and Wu (1999), the residuals ˆit
are resampled with replacement with the cross-section index fixed, so that their crosscorrelation structure is preserved; the resulting bootstrap innovation ˆit is denoted ˆit* .
Then, ˆit* is generated recursively as:
ˆit*  ˆi ,1ˆi*,t 1  ...  ˆi, p ˆi*,t  p  it* ,
i
i
where, in order to ensure that initialisation of ˆit* , i.e. the bootstrap samples of ˆit ,
becomes unimportant, we follow Chan (2004) who advocates generating a large
number of ˆit* , say T  Q values and discard the first Q values of ˆit* (for our
purposes we choose Q  30 ). Lastly, the bootstrap samples of yit* are calculated by
adding ˆit* to the deterministic component of the corresponding model, and the Hadri
LM statistic is calculated for each yit* . The results shown in Table 1 are based on
1,000 bootstrap replications used to derive the empirical distribution of the LM
statistic.
3. DATA AND EMPIRICAL ANALYSIS
The data set, obtained from Departamento Administrativo Nacional de Estadística–
DANE, consists of seasonally unadjusted monthly observations on unemployment
rates for the seven major metropolitan areas in Colombia: Bogotá, Medellín, Cali,
Barranquilla, Bucaramanga, Manizales and Pasto. The sample period runs from
1984Q1 to 2004Q4 (for a total of 84 observations), and the series are considered in
percentage terms.
Table 1 presents the results of applying the KPSS stationarity test to the
unemployment rates of the metropolitan areas listed above (based on the model with
intercept only). As can be seen from the table, the null hypothesis of stationarity is
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rejected for three out of the seven metropolitan areas under consideration, namely
Bogotá, Bucaramanga and Cali. The evidence here is mixed and does not provide a
clear indication of stationarity.
Next, we apply the Hadri test to the unemployment rates of Bogotá,
Bucaramanga and Cali, which are found to be non-stationary on the basis of the
individual KPSS tests discussed before. The results indicate that the null hypothesis
that all of series in the panel are stationary is clearly rejected (the test statistic is
2.053; p-value 0.000). However, as indicated above, an important assumption
underlying the Hadri test is that of cross section independence among the individual
time series in the panel. To allow for potential cross section dependence and
subsequent size distortion, we apply the bootstrap method to the Hadri test as
described in the previous section. In particular, based on the results of the bootstrap
Hadri test reported in the second line of Table 2, we are now unable to reject the null
hypothesis of panel stationarity for a panel consisting of the metropolitan areas of
Bogotá, Bucaramanga and Cali. This finding provides support to the view that the
unemployment rates exhibit mean reversion, and therefore appear consistent with the
natural rate hypothesis.
4. CONCLUDING REMARKS
This paper applies the Hadri (2000) tests for panel stationarity to examine evidence on
stationarity for unemployment rates in seven Colombian cities. The Hadri tests offer
the key advantage insofar as we may conclude that all the city relative prices in the
panel are stationary, if the joint null hypothesis is not rejected. In addition to this,
another important feature of our analysis is that we allow for the presence of serial
correlation and cross-sectional dependency across the city relative prices in the panel,
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by means of the implementation of an AR-based bootstrap. In contrast to the existing
literature for Colombia, we find support for the view that unemployment rates appear
stationary in the long run after allowing for cross sectional dependencies. An
implication of this finding is that it provides support to the view that the
unemployment rates exhibit mean reversion, and therefore appear consistent with the
natural rate hypothesis.
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Table 1. Individual KPSS tests for mean stationarity
City
Lags Statistic
Barranquilla
4
0.060
Bogotá
5
0.518 **
Bucaramanga
5
0.350 *
Cali
6
0.466 **
Manizalez
4
0.253
Medellín
5
0.142
Pasto
7
0.188
* and ** indicate 10 and 5 per cent
levels of significance, respectively,
based on the response surfaces in
Sephton (1995).
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Table 2. Hadri test for unemployment rates
Test
Statistic p-value
Hadri
2.053 [0.000]
Bootstrap Hadri
2.053 [0.364]
The p-value of the Hadri test is based on the
standard normal distribution. The p-value of
the bootstrap Hadri test was calculated as
described in Section 2, using 2,000
replications.
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REFERENCES
Blanchard, O., & Summers, L. (1986) Hysteresis and the European unemployment
problem. In S. Fischer (Ed.), NBER Macroeconomics Annual 1986,
Cambridge MA: MIT Press, 15-78.
Brunello, G. (1990) Hysteresis and the Japanese unemployment problem: A
preliminary investigation, Oxford Economic Papers, 42, 483–500.
Camarero, M., & Tamarit, C. (2004) Hysteresis vs. natural rate of unemployment:
New evidence for OECD countries. Economics Letters, 84, 413-417.
Campbell, J., & Perron, P. (1991), Pitfalls and opportunities: what macroeconomists
should know about unit roots. In O. Blanchard and S. Fischer (Eds.), NBER
Macroeconomics Annual 1991. Cambridge MA: MIT Press, 141-201
Caner, M., & Kilian L. (2001). Size distortions of tests of the null hypothesis of
stationarity: Evidence and implications for the PPP debate. Journal of
International Money and Finance, 20, 639–657.
Carrion-i-Silvestre, J.L., & Sansó, A. (2006). A guide to the computation of
stationarity tests. Empirical Economics, 31, 433-448.
Chang, Y. (2004). Bootstrap unit root tests in panels with cross-sectional dependency.
Journal of Econometrics, 120, 263-293.
Chang, T., Lee, K-C., Nieh, Ch-Ch., & Wei, Ch-Ch. (2005). An empirical note on
testing hysteresis in unemployment for ten European countries: Panel
SURADF approach. Applied Economics Letters, 12, 881-886.
Clemente, J., Lanaspa, L., & Montañés, A. (2005). The unemployment structure of the
US states. The Quarterly Review of Economics and Finance, 45, 848-868.
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Dickey, D.A., & Fuller, W.A. (1979). Distribution of the estimators for autoregressive
time series with a unit root. Journal of the American Statistical Association,
74, 427-431.
Giulietti, M., Otero, J., & Smith, J. (2008). Testing for stationarity in heterogeneous
panel data in the presence of cross section dependence. Journal of Statistical
Computation and Simulation, 79, 195-203.
Hadri, K. (2000). Testing for stationarity in heterogeneous panels. The Econometrics
Journal, 3, 148-161.
Hadri, K., & Larsson, R. (2005). Testing for stationarity in heterogeneous panel data
where the time dimension is finite. The Econometrics Journal, 8, 55-69.
Im, K., Pesaran, M.H., & Shin, Y. (2003). Testing for unit roots in heterogeneous
panels. Journal of Econometrics, 115, 53-74.
Jaeger, A., Parkinson, M. (1994) Some evidence on hysteresis in unemployment rates,
European Economic Review, 38, 329–42.
Kwiatkowski, D., Phillips, P.C.B., Schmidt, P., & Shin, Y. (1992). Testing the null
hypothesis of stationarity against the alternative of a unit root. Journal of
Econometrics, 54, 159-178.
León-Ledesma, M. (2002) Unemployment hysteresis in the US states and the EU: a
panel approach, Bulletin of Economic Research, 54, 95–103.
Maddala, G.S., & Wu, S. (1999). A comparative study of unit root tests with panel
data and a new simple test. Oxford Bulletin of Economics and Statistics, 61,
631-652.
Mitchell, W. F. (1993) Testing for unit roots and persistence in OECD unemployment
rates, Applied Economics, 25, 1489–501.
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Nelson, C.R., & Plosser, C.I. (1982). Trends and random walks in macroeconomic
time series: Some evidence and implications. Journal of Monetary Economics,
10, 139-162.
Reis, F.A., & Gomes, C. (2008). Hysteresis versus NAIRU and convergence versus
divergence: The behaviour of regional unemployment rates in Brazil. The
Quarterly Review of Economics and Finance, forthcoming.
Røed, K. (1996) Unemployment hysteresis – macro evidence from 16 OECD
countries, Empirical Economics, 21, 589–600.
Sul, D., Phillips, P.C.B., & Choi, C.Y. (2005). Prewhitening bias in HAC estimation.
Oxford Bulleting of Economics and Statistics, 67, 517-546.
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