This study investigates the relationship between the female labour force participation and the female employment rate in Italy by adopting non-linear econometric modelling. In our specification we are unable to reject a nonlinear relationship. This implies that the discouraged worker effect is timevarying.Discouraged Workers, Non-linearity

Antonio Garofalo

Carlo Altavilla

Concetto Paolo Vinci

English

Research Papers in Economics

  1 
Università degli Studi di Salerno 
Centro di Economia del Lavoro e di Politica Economica 
Carlo Altavilla – Antonio Garofalo – Concetto Paolo Vinci  
 
University of Naples Parthenope 
 
 
Is the Discouraged Worker Effect Time-Varying? 
Discussion Paper 97 
Settembre, 2005   2 
 
CELPE 
Centro di Economia del Lavoro e di Politica Economica 
Università degli Studi di Salerno 
Via Ponte Don Mellillo, 84084 Fisciano, I- Italy 
Web Page:http://www.celpe.unisa.it/ 
E-mail: celpe@unisa.it  
 
Scientific Commitee: 
Adalgiso Amendola, Guido Cella, Ugo Colombino, Cesare Imbriani, 
Giancarlo Marini, Pasquale Persico, Nicola Postiglione, Enrico Pugliese, 
Salvatore Vinci 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
   3 
 
 
 
 
 
 
 
 
 
 
 
 
 
Indice 
 
 
 
 
 
 
 
1. Introduction................................................................................................5 
2. The Econometric Methodology .................................................................5 
3. Conclusions..............................................................................................12 
References....................................................................................................13 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
   4 
 
 
 
 
 
 
Is the Discouraged Worker Effect Time-Varying? 
 
 
 
 
 
Carlo ALTAVILLA
*   Antonio GAROFALO
**   Concetto Paolo VINCI
*** 
 
 
 
 
Abstract 
This study investigates the relationship between the female labour force 
participation and the female employment rate in Italy by adopting non-linear 
econometric modelling. In our specification we are unable to reject a non-
linear relationship. This implies that the discouraged worker effect is time-
varying. 
 
 
 
 
 
Keywords: Discouraged Workers, Non-linearity 
JEL Classification: J23, C32 
                                                 
* Corresponding author: University of Naples "Parthenope", Via Medina, 40 - 80133 Naples (Italy). E-
mail: Altavilla@uniparthenope.it; Phone: (+)39 0815474733, fax (+)39 0815474750. 
** University of Naples ''Parthenope'', E-mail: Garofalo@uniparthenope.it.  
*** University of Naples ''Parthenope'', E-mail: cpvinci@uniparthenope.it.  
 
   5 
1. Introduction 
Recent years have been characterised by some improvements in labour 
market performances. A variety of stylised facts characterised European 
labour market. First, European unemployment rate covers deep cross-
country asymmetries. Second, it particularly affects specific population 
segments (males, females, adults and youngest) and for rather long time 
periods.  
In principle, there are several ways the labour market can react to a 
negative shock. When a recession occurs, workers who lose their jobs can 
react in three different ways. First, they can keep looking for a job in the 
area, thus remaining unemployed; second, they can migrate to another 
area; or third they can stop looking for a job, thereby exiting the labour 
force (and becoming “discouraged workers”). The discouraged worker 
hypothesis (Long, 1953) assumes that since searching for a job is a very 
expensive activity, a persistent period of unemployment reduce the   
probability of finding a job and may induce groups of secondary workers not 
to enter in the labour market waiting, instead, for better opportunities.  
 A large number of empirical studies exist for different countries reporting 
evidence consistent with the discouraged worker hypothesis (Benati, 2001; 
Darby, Hart and Vecchi, 2001; Blundell, Ham and Meghir, 1998; Clark and 
Summers, 1982). None of the previous studies, however, use non-linear 
techniques in order to ascertain the existence of time-dependence in the 
discouraged worker effect. What will be the aim of the present paper.  
2. The Econometric Methodology 
Before employing non-linear econometric methodology we estimate a 
linear VECM with the maximum likelihood technique and test for possible 
non-linearity in the residuals. The data used in the empirical analysis are 
quarterly observations drawn from the Labour Force Survey (LFS) 
produced by ISTAT. The sample period goes from 1959:1 to 2004:4. The 
benchmark linear model we used to characterize the long-run dynamic 
adjustments is a finite-order VECM of the following form:   6 
[1]   () ()
α
γ
α
−
−−
−
ΔΔ ⎡ ⎤ ⎡⎤ ⎡ ⎤ ⎡⎤
=Γ + − − +⎢ ⎥ ⎢⎥ ⎢ ⎥ ⎢⎥ ΔΔ ⎣⎦ ⎣ ⎦ ⎣⎦ ⎣ ⎦
11 1
11
12 1
e
tt t
tt p
tt t
ee u
Le p t
pp u
 
Where  [] Δ Δ
'  , tt ep  is a vector of stationary variables containing the 
female employment rate ( t e ) and the female participation rate ( t p );  Δ  is 
the first difference operator; α11and α21 indicate the speed of adjustment 
of each variable back to its long-run value. The estimation results are 
reported in table 1.  
The two adjustment coefficients ( 11 α  and α21) are significantly different 
from zero, meaning that both the female participation rate and female 
employment rate adjust to restore the long-run equilibrium. The absolute 
value of α  gives information about the number of quarters needed to 
restore the long-term equilibrium. In our case, after almost four years, 50 
percent of the disequilibrium gap created by the shock has been closed by 
the adjustment in the female participation rate
1. This time pattern suggests 
that, in the long-run, the employment rate is increasingly driven by the 
participation rate. 
 
Table 1: Linear VECM Estimates 
Coeff. St.  Error Coeff.  St.  Error
c 0.495 [0.12] 0.605 [0.21]
Δp t-1 0.546 [0.15] 0.506 [0.17]
Δp t-2 0.611 [0.25] 0.488 [0.15]
Δe t-1 -0.740 [0.28] -0.684 [0.38]
Δe t-2 -0.833 [0.63] -0.657 [0.77]
α -0.033 [0.015] 0.036 [0.018]
σ
2  0.38 0.47
Δe t Δp t
 
 
It is now possible to check the non-linearity of the residuals by using 
three widely used tests. We apply the BDS, the Reset and Tsay test to the 
residuals of each equation in the VECM system. The null hypothesis for 
                                                 
1 In order to obtain the number of quarters (τ ) required to dissipate x% of a shock we use the following 
formula:  () ( ) 11 % x
τ α −= − , where α  is the absolute value of the estimated speed adjustment 
parameter.    7 
these tests is that the residual generating process is linear. Table 2 and 
table 3 show the results. 
Table 2: BDS Test statistics 
 
Table 3: Tsay and Reset Test statistics 
 
The tables report, for each equation from the VECM, the p-values under 
the null hypothesis that the corresponding residual is a serially i.i.d. 
process. Table 2 also reports the bootstrapped p-values for the BDS test 
statistic. All tests reject the null hypothesis of a linear generating 
mechanism for the residuals of the selected variables. The analysis 
altogether suggests the presence of non-linearity in the residuals. This 
evidence corroborates the decision of estimating the model in non-linear 
form. 
We account for non-linearity by estimating a multivariate Markov-
switching model. The asymmetry of the effects is captured by allowing for 
state-dependent parameters where the latent state variable follows a 
Markov-switching process. The idea behind this class of models is that the 
parameters underlying the data generating process of the observed time 
series vector depend upon the unobservable regime variable  t s , which 
represents the probability of being in a different state of the world. 
Residuals from Employment Rate Equation
Dimension  BDS Statistic Std. Error Z-Statistic Asymptotic Bootstrap 
2  0.03  0.01 3.44 2.5E-02 6.3E-02 
3  0.08  0.02 5.18 0.0E+00 8.0E-04 
4  0.24  0.02 5.28 0.0E+00 0.0E+00 
5  0.18  0.03 8.26 0.0E+00 0.0E+00 
6  0.31  0.03 7.98 0.0E+00 0.0E+00 
Residuals from Participation Rate Equation
Dimension  BDS Statistic Std. Error Z-Statistic Asymptotic Bootstrap 
2  6.88E-04  4.17E-04 6.13 3.32E-02 3.59E-02 
3  3.26E-04  2.04E-04 5.17 3.04E-02 4.70E-02 
4  -2.05E-04 2.96E-05 -7.35 0.00E+00 4.66E-02 
5  -2.04E-05 3.52E-06 -4.24 1.20E-03 8.27E-02 
6  -8.80E-07 5.90E-07 -5.00 4.55E-02 9.56E-02 
Distribution  Statistic P-value Statistic P-value
Tsay F( 1 , 98 )  27.15 2E-06 34.34 3E-08
Reset  F(3,96)  2.963 0.04619 24.093 9E-11
Employment rate Participation rate   8 
This variable  t s  is governed by a discrete state of a Markov stochastic 
process, which is defined by the following transition probabilities: 
() + == = 1 Pr ij t t p sj s i        
⎡ ⎤
⎢ ⎥
⎢ ⎥ =
⎢ ⎥
⎢ ⎥
⎣ ⎦
L
L
MM O L
K
11 12 1
21 22 2
12
m
m
mm m m
pp p
pp p
P
pp p
 
where  ij p  is the probability that state i is followed by state j and P is the 
corresponding transition matrix. The idea is that the relation between the 
employment and participation rate is time-varying but constant conditional 
on the stochastic and unobservable regime variable. We then proceed to 
estimate a Markov-switching vector equilibrium correction model (MS-
VECM) of the form
2: 
()
μα
δγ
μα
−−
ΓΓΔ − ⎡⎤ ⎡⎤ ⎡ ⎤ ⎡ ⎤
=− − − + ⎢⎥ ⎢⎥ ⎢ ⎥ ⎢ ⎥ ΓΓΔ − ⎣⎦ ⎣ ⎦ ⎣ ⎦ ⎣⎦
11 12 11
11
21 22 21
() () ()
()
() () ()
e
tt t
tt t p
tt t
LL e s u
ep st
LL p s u
 
where residuals are conditionally Gaussian,  tt us~ ( ) ( ) Σ 0, t NID s ; 
[ ] δ γ −− =− − 11 () tt t sE e p t represents the state-dependent deviation from the 
trend in employment and captures the correction to the long-term 
equilibrium; μ() t s  describes the regime-dependent mean.  
Following the two-stage procedure suggested by Krolzig (1997) the 
results obtained in the linear VECM concerning the cointegration analysis 
are used in this stage of the analysis. The maximum likelihood estimates of 
the model are reported in table 2. Standard bottom-up procedure hints 
three as the number of regimes.  
The estimated quarterly growth of the employment rate is -0.29% in 
regime 1, 0.32% in regime 2 and 0.31% in regime 3. Table 4 also reports 
the quarterly growth of the labour force participation associated with regime 
1 (-0.3%) regime 2 (0.38%) and regime 3 (0.18%).  
                                                 
2 We also estimated the model allowing for a shift in the intercept of the variables. The results we 
obtained from the two specifications are very similar with respect to the regime classification as well as to 
the parameter values.    9 
Table 4: ML estimates of the MSMH (3)-VECM (2) 
Coeff.  St. Error Coeff.  St. Error
μ 1 -0.292 [0.09] -0.298 [0.09]
μ 2 0.322 [0.06] 0.377 [0.06]
μ 3 0.314 [0.08] 0.176 [0.05]
Δp t-1 -0.552 [0.15] -0.255 [0.12]
Δp t-2 0.007 [0.15] 0.062 [0.12]
Δe t-1 0.457 [0.16] 0.138 [0.14]
Δe t-2 -0.624 [0.15] -0.710 [0.13]
α -0.101 [0.04] 0.104 [0.03]
σ
2 (Reg.1) 0.853 0.897
σ
2 (Reg.2) 0.385 0.320
σ
2 (Reg.3) 0.664 0.562
log-likelihood -161.75 vs. linear -225.76
AIC criterion 2.18 vs. linear 2.72
HQ  criterion 2.40 vs. linear 2.83
SC  criterion 2.73 vs. linear 2.99
LR linearity test: 128.0179 Chi(10) =[0.0000] **
  Chi(36)=[0.0000] **  DAVIES=[0.0000] **  
Δe t Δp t
 
 
The speed of the adjustment coefficient is higher than the one estimated 
by using the linear VECM: approximately 10% of the adjustment takes 
place each period. The participation rate restores 50% of the pre-shock 
long-run equilibrium level after almost 6 quarters. Moreover, the pace at 
which the employment rate moves to restore the long-run equilibrium is 
very similar.   
Once we have estimated the model, the transition matrix may be 
computed to analyse the probability of moving from one state to another. 
As the estimated process follows a 3-state Markov chain it is then possible 
to collect the transition probabilities in a 33 ×  transition matrix (table 5 -left): 
Table 5: Matrix of transition probabilities and Regime Properties 
Regime 1 Regime 2 Regime 3 N. Obs Prob. Duration
Regime 1 0.970 0.000 0.030 Regime 1 65.8 0.2955 33.04
Regime 2 0.020 0.980 0.000 Regime 2 53.9 0.4509 50.42
Regime 3 0.000 0.035 0.965 Regime 3 57.3 0.2537 28.36  
The regimes are estimated to be quite persistent. The least persistent 
regime is the last one. The expected duration
3 and the ergodic probabilities 
                                                 
3 The expected duration can be easily calculated from the estimated transition probabilities. The expected 
duration of regime 1, for example, can be derived as follows:   () ()
∞
− −
=
−= − ∑
1 1
11 11 11
1
11
z
z
zp p p .   10 
are also shown in table 5 (right). The above table shows respectively the 
expected duration for regime 1 (33 quarters), regime 2 (50 quarters) and 
regime 3 (28 quarters). 
The further step consists of characterizing the timing of the regimes. The 
resulting smoothed probabilities are given in Figure 1. 
Figure 1: Smoothed Regime Probabilities 
Regime 1
1962 1969 1976 1983 1990 1997 2004
0.00
0.25
0.50
0.75
1.00
Regime 2
1962 1969 1976 1983 1990 1997 2004
0.00
0.25
0.50
0.75
1.00
Regime 3
1962 1969 1976 1983 1990 1997 2004
0.00
0.25
0.50
0.75
1.00
 
 
Regime 1 coincides with the decrease in the employment rate and 
participation rate from the 1960s to the first half of the 1970s. Regime 2 and 
3 are characterized by a positive growth in both employment and 
participation rate.  
We now turn to the impulse response analysis. Following Krolzig and 
Toro (1998) we compute the effects of a regime-wide shock on the 
employment and participation rate (Figure 2). This methodology allows us 
to investigate the dynamic responses of the employment and participation 
rate in transition across regimes. We first analyse the response of all 
variables in the system to a shock that induces a movement from the 
ergodic
4 distribution to a specific regime. A 40-quarter horizon is 
considered. 
Figure 2 shows the response of the female employment (dashed lines) 
and participation rate (solid lines) when they move from steady-state 
probabilities to the three estimated regimes. Here, we observe the different 
dynamics governing the two selected variables during high- and low-
employment periods. The upmost left graph (shift to regime 1), for example, 
represents the reaction of the employment and participation rate to the 
                                                 
4 Note that as the Markov chain is stationary, the conditional distribution of the different states converges 
to the ergodic distribution.   11 
information that  =1 t s . Then, the time profile of the reactions illustrates the 
pattern of employment reduction and the subsequent labour force 
movements when the system moves to regime 1.  The middle graph of the 
second column, reports the response of the variables when moving from 
equilibrium to regime 2. Finally, the lowest right graph reports the response 
of the variables when the system moves from steady-state to the third 
regime. 
As it clearly emerges, there are asymmetries in the reaction of the 
selected variables when employment falls (shift to regime 1) with respect to 
when the employment rate moves to regime 3 (shift to regime 3). In 
particular, the occurrence of regime 1 produces a larger deviation from the 
long-term equilibrium if compared with a shift to regime 3. In other words, a 
shock that leads to employment reduction has a bigger impact on the long-
run equilibrium than a shock that induces an increase in the employment 
rate.  
Figure 2: Responses to Regime Shifts: Employment (dashed) - 
Participation (solid) 
Shift to Regime 1
0 5 10 15 20 25 30 35 40
-0.48
-0.32
-0.16
0.00
Transition Regime 1 to 2
0 5 10 15 20 25 30 35 40
0.00
0.25
0.50
0.75
Transition Regime 1 to 3
0 5 10 15 20 25 30 35 40
0.00
0.16
0.32
0.48
0.64
Transition Regime 2 to 1
0 5 10 15 20 25 30 35 40
-0.75
-0.50
-0.25
0.00
Shift to Regime 2
0 5 10 15 20 25 30 35 40
-0.09
0.00
0.09
0.18
0.27
Transition Regime 2 to 3
0 5 10 15 20 25 30 35 40
-0.32
-0.16
0.00
0.16
Transition Regime 3 to 1
0 5 10 15 20 25 30 35 40
-0.64
-0.48
-0.32
-0.16
0.00
Transition Regime 3 to 2
0 5 10 15 20 25 30 35 40
-0.1
0.0
0.1
0.2
0.3
Shift to Regime 3
0 5 10 15 20 25 30 35 40
0.04
0.08
0.12
0.16
0.20
 
 
Figure 2 also suggests a different time pattern of the selected variables 
to a regime shift. During regime 1 and 3 the employment rate reacts more   12 
than the participation rate. In contrast, during regime 2, the simulated 
response of the employment rate is smaller than the one observed for the 
participation rate. 
The main implication arising from impulse response analysis is that a 
shock producing a shift from the steady state probabilities to the estimated 
regimes will have a greater effect when it leads to a decrease in the 
employment rate than when the shock produces an increase in both 
employment and participation rate. Finally, when the employment rate 
increases, the dynamic responses of the two variables might generate 
either an increase in the unemployment (when the change in the 
participation rate is larger than the employment rate response – regime 3) 
or a decrease in the unemployment rate (i.e. when the labour force 
participation react less than the employment rate – regime 2). 
 
3. Conclusions 
The estimated model characterizes the employment adjustment process 
toward its long-run equilibrium. The main implication arising from the 
analysis suggests the presence of nonlinear mean reversion. As a 
consequence the relative strength of the participation rate to act as driving 
force for employment long-term equilibrium is consistently time-varying. 
 
 
 
 
 
 
   13 
References 
 
1.  Benati L., 2001,  Some empirical evidence on the 'discouraged 
worker' effect, Economics Letters, vol. 70, issue 3, pages 387-
395  
2. Blundell R., Ham J, and Meghir C., 1998, Unemployment, 
Discouraged Workers and Female Labour Supply”, Research 
in Economics, 52, 103-131. 
3.  Clark K.B. and Summers L.H., 1982, Labour Force Participation: 
Timing and Persistence, Review of Economic Studies, vol. 49, 
issue 5, pages 825-44.  
4.  Darby, J., Hart, R., Vecchi, M., 2001, Labour Force Participation 
and Business Cycle Fluctuations: A Comparative Analysis of 
Europe, Japan and the United States, Japan and the World 
Economy, 13, 113-133. 
5. Krolzig H.-M. (1997), Markov-Switching Vector Autoregressions 
Modelling, Statistical Inference, and Application to Business 
Cycle Analysis, Springer Verlag, pp. 357. 
6. Krolzig, H.-M., and Toro, J. (1998), A new approach to the 
analysis of shocks and the cycle in a model of output and 
employment, Working paper eco 99/30, EUI, Florence. 
7.  Long, C., 1953, Impact of effective demand on the labour supply, 
American Economic Review, Papers and Proceedings, 43, 
458-467.  

A new approach to the analysis of shocks and the cycle in a model of output and employment, Working paper eco 99/30,

Impact of effective demand on the labour supply,

Labour Force Participation and Business Cycle Fluctuations: A Comparative Analysis

Labour Force Participation: Timing and Persistence,

Markov-Switching Vector Autoregressions Modelling, Statistical Inference, and Application to Business Cycle Analysis,

Some empirical evidence on the 'discouraged worker' effect,

Unemployment, Discouraged Workers and Female Labour Supply”,

Is the Discouraged Worker Effect Time-Varying?

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Is the Discouraged Worker Effect Time-Varying?

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