REVIEW OF ECONOMIC PERSPECTIVES – NÁRODOHOSPODÁŘSKÝ OBZOR
VOL. 15, ISSUE 2, 2015, pp. 197-220, DOI: 10.1515/revecp-2015-0017
Measuring Inefficiency of the Czech Labour Market1
Daniel Němec2
Abstract:
This paper aims to quantify the performance of the Czech regional labour markets and
to reveal the most influential economic factors standing behind its dynamics in the last
fifteen years. Investigated labour markets are described using matching function approach.
The successful matches are treated as an output of production process, where
the unemployed are paired with vacancies. Efficiency of this matching process plays an
important role in determining unemployment outflows. Using stochastic frontier model
approach, dynamics of quantified efficiency terms is revealed and differences among
regions are evaluated. The model specification includes a fixed effect term, where individual
effect terms and inefficiency terms are estimated jointly. The stochastic frontier
is estimated using monthly and quarterly regional panel data of 77 districts for the period
1999-2014. Matching efficiency of the Czech regional labour markets is negatively
influenced people who have been unemployed for a long time and by the unemployed
aged over 50 years. Although all districts were able to operate at their stochastic frontiers
of matching, an upward trend in the inefficiency has been found within the investigated
period. These tendencies are accompanied by rising disparities among the regions.
Low levels of estimated matching inefficiency do not necessary mean the low unemployment
in the corresponding districts.
Key words: Matching efficiency, Matching function, Regional labour markets, Stochastic
frontier model, Panel data, Czech Republic
JEL Classification: R23, J41, C23, E24
Introduction
Labour market in the Czech Republic has experienced significant changes in the last
fifteen years. General unemployment rate of people from 15 to 64 years of age, which is
published by the Czech statistical office, reached 7.9 percent in January 1999, and 6
percent at the end of November 2014. During this period, one could observe the unemployment
rate of 4.3 percent in the months of 2008 or 9.3 percent in 2000. Of course,
the most important part of this variability may be explained by business cycles. But on
the other hand, strong disparities have appeared in unemployment rates of the Czech
1
This work is supported by funding of specific research at Faculty of Economics and Administration;
project MUNI/A/1235/2014.
2
Masaryk University, Faculty of Economics and Administration, Department of Economics,
Lipová 41a Brno 62100, nemecd@econ.muni.cz
REVIEW OF ECONOMIC PERSPECTIVES
198
regions and districts in this period. As an illustration, let us take a look at regional statistics
provided by the Czech Ministry of Labour and Social Affairs. In 2005, the average
unemployment rate (computed as a ratio of the unemployed to the population of people
from 15 to 64 years of age) in the Czech Republic was 6.59 percent but the regional
unemployment rates were 2.64 percent in Praha, 3.85 percent in Beroun, 5.37 percent in
the district of Domažlice, 10.3 percent in Hodonín, and 16.49 percent in Most. In the
year 2013, unemployment rates of 5.14 percent in Praha, 6.78 percent in Beroun, 6.42
percent in Domažlice, 11.81 percent in Hodonín, and finally, 13.51 percent in Most, can
be observed. The average unemployment rate in the Czech Republic was 8.17 percent in
2013. The differences in regional unemployment rates are evident. Moreover, the relative
distance in the unemployment measures have been changing as well.
How to explain the differences in regional unemployment rates in the Czech Republic?
The answer to this question may be connected to the problem of efficiency of labour
markets. Labour market efficiency is one of the most important factors influencing
labour market dynamics and its performance. There are many approaches of how to deal
with the ‘efficiency’ concept. Most of them are based on the matching function framework.
In this framework, successful labour market matches are treated as an outcome of
interactions between unemployed job seeker and vacancies.
The main goal of this article is to quantify the inefficiency of the Czech regional labour
markets and to evaluate its development in the last 15 years. Finding the main sources
standing behind the regional disparities in efficiency is one of the highly relevant tasks
in labour market analysis that allow us to answer many important questions: Are labour
markets with higher average unemployment rate less efficient than those with low unemployment
rate? What are the effects of unemployment benefits, age structure of unemployed
and the length of unemployment on the efficiency? What about the impact of
overall economic growth on the labour markets performance?
All the questions mentioned previously may be answered using the estimates of the
matching efficiency of the Czech regional labour market. The degree of efficiency, or
inefficiency, to be more precise, is estimated using the stochastic frontier panel data
model approach with monthly district-level regional data and explicitly treated fixed
effects term in the matching function model equation. On the one hand, this approach
extends the previous investigations of the efficiency of the Czech labour market carried
out by Němec (2013a), Němec (2013b) or by Tvrdoň and Verner (2012). Their results
have been based on aggregate labour market statistics. On the other hand, using the data
from monthly regional labour market statistics and stochastic frontier panel data model
methodology offers a new insight into the outcomes of the Czech labour market in the
last 15 years, and extends the detailed analysis of Galuščák and Münich (2007) in a
specific way - by dealing with efficiency issues.
Stochastic frontier model approach has been used by Ilmakunnas and Pesola (2003) in
their study of regional labour markets in Finland. They used annual data and did not
take into account explicitly possible individual fixed effects of the examined regions.
Gorter et al. (1997) investigated the efficiency in the Dutch labour market in the Netherlands
along the same lines. They observed that the estimated labour market efficiency
increases during recession and recovery periods and decreases during economic booms.
This interesting feature is considered in this article as well.
Volume 15, Issue 2, 2015
199
The main contribution of this article consists in quantification of inefficiency of the
Czech regional labour, evaluating its changes in the last 15 years, and in identification
of the main sources of estimated inefficiency disparities among the regions. Using the
stochastic frontier model approach, the districts are classified regarding their inefficiency
patterns. Matching function parameters and the inefficiency terms are estimated
jointly. Inefficiency terms are treated as a function of district specific labour markets
factors and common economic factors (like overall economic activity). Robustness of
results is checked using the models with monthly and quarterly regional panel data from
1999 to 2014 and providing the estimates on the full sample and the samples covering
the periods before and after the economic slowdown starting in 2008.
The structure of this article is as follows: the first section gives a short overview of
matching function approach to analyse labour market dynamics. It provides a short
introduction to efficiency analysis as well. Stochastic frontier model with individual
effects is explained in more detail in the second part of this article. The third part contains
data description and methodology of model estimates. The models are then estimated
in the fourth part of the paper and the results are interpreted. The final section
concludes.
Matching Efficiency of the Regional Labour Markets
The matching function expresses the interaction mechanism between the unemployed
and vacancies. This concept is based on the fact that both the flows of unemployed and
the flows of unfilled job vacancies are able to meet each other. The matching function
can be thus viewed as a standard production function with two inputs: the unemployed
and the vacancies. New matches are an outcome of this matching process. In this contribution,
the regional labour markets are represented by a Cobb-Douglas matching function
in log-linear form:
log = + log + log + , (1)
where the subscripts = 1, … , denote the districts and = 1, … , represents the time
period. Parameters are treated as the district specific fixed effects. The term is a
stochastic factor discussed below. The number of successful matches, , is influenced
by the number of unemployed, , and by the number of unfilled vacancies, . Parameters
and denote the matching elasticity of unemployed and matching elasticity
of vacancies respectively.
Due to the fact that the matching function can be perceived as a production function, we
are able to measure the efficiency of this production process. We can suppose that the
firms (or production units) maximise the output for a given level of inputs and available
production technology. Any deviations from the optimal production may thus indicate
inefficiency in the production process. The empirical problem is how to estimate the
production frontiers and the possible inefficiency given observable data. In general,
frontier analysis follows the idea that there exists a function mapping inputs and outputs
resulting to the set of all optimal production plans. We can denote them as the production
possibility frontier. After estimating it we could evaluate the inefficiency as the
deviations of observable production from the potential level.
REVIEW OF ECONOMIC PERSPECTIVES
200
Treating the production possibility frontier as a deterministic frontier is connected with
data envelopment analysis or free disposable hull technique. There is no possibility of
observations exceeding the frontier (efficiency above 100 percent). These nonparametric
techniques are not robust with regards to the outliers. On the other hand,
stochastic frontier analysis is one of the stochastic parametric methods allowing the
presence of super-efficient observations. It is thus robust to outliers. Using stochastic
frontier analysis (model), we try to find the highest achievable level of production
where most of observations may be found below the estimated production frontier.
Estimated differences are thus the corresponding technical inefficiency terms.
The aforementioned form of matching function in the equation (1) may be extended and
modified in many ways. Ilmakunnas and Pesola (2003) implemented regional and labour
force characteristics directly into the matching function by the means of other
explanatory variables. The resulting efficiency was thus a linear function of regional
fixed effects and various regional characteristics. In their view, the term was treated
purely as white noise process. Similar approach may be found in the work of Gorter et
al. (1997). Galuščák and Münich (2007) enhanced the basic matching function form by
the flow factors (i.e. unemployment and vacancy inflows realized during the time peri-
od).
Stochastic frontier model approach tries to model the stochastic term 	as consisting of
combination of random variations in the matching process and the region specific inefficiency
term. Regional and labour force characteristics are then implemented directly
into this inefficiency term. This approach was used by Ilmakunnas and Pesola (2003).
But they did not include the fixed (or random) region effects. In this paper, the inefficiency
of the Czech regional labour market is estimated using fixed effect panel stochastic
model. This model approach is able to capture region specific individual effects,
basic matching function characteristics and time-varying regional inefficiency terms at
once. Equation (1) could be enhanced by the time effect as well. But, incorporating the
time-specific variables, which are common to all regions, might lead to some identification
issues. Time-specific effect in the matching function cannot be distinguished easily
from the time-specific factors incorporated into the inefficiency term. Time effects are
used to control for business cycle dynamics. For these purposes, business cycle variables
(like GDP growth or growth of industrial production) are implemented into the
inefficiency term.
Stochastic Frontier Model with Panel Data
Panel data models are powerful tools to identify relationships among variables in cases
where lack of observations for individual cross-sectional units does not allow obtaining
efficient estimates of model parameters. Moreover, using panel data models, we are able
to control unobservable individual heterogeneity in our sample.
Working with panel data structure is necessary in stochastic frontier models framework.
It is really hard to estimate stochastic frontier within a model using the data for a single
cross-sectional unit only. Unobservable individual effects thus play an important role in
estimation of panel stochastic frontier model. In many applications, these individual
Volume 15, Issue 2, 2015
201
effects may be connected to inefficiency term. All time-invariant individual heterogeneity
across observed cross-sectional units is treated as a part of estimated inefficiency.
The pioneering work on stochastic frontier models (using the last mentioned approach)
was written by Aigner et al. (1977). After estimating stochastic frontier, it is possible to
conditionally compute inefficiency terms on estimated residuals. These estimates may
be used to determine the factors standing behind the inefficiency by the means of ordinary
regression. Wang and Schmidt (2002) showed that this two-stage procedure leads
to heavily biased results. As a consequence, it is crucial to estimate the stochastic frontier
and the determinants of inefficiency simultaneously. Battese and Coelli (1993)
specified a model where inefficiency determinants form a part of stochastic frontier
model framework. Their framework assumes that all production units face the same
production possibility frontier. Greene (2005) suggested an alternative approach where
all time-invariant heterogeneity across production units was removed before estimating
the stochastic frontier and the inefficiency factors. His approach was capable of correcting
the likely overestimated inefficiency terms resulting from the methodology of
Battese and Coelli (1993). Amsler et al. (2009) offer a detailed review of the history and
development of stochastic frontiers models.
In this article, we take advantage of an alternative approach that is used to remove
cross-sectional heterogeneity from the estimates of inefficiency. Wang and Ho (2010)
proposed a consistent methodology to deal with individual effects and efficiency terms
separately. This approach is used in presented paper. Wang and Ho (2010) specify a
stochastic frontier model as follows:
= + + , (2)
= − " , (3)
∼ (0, &'
(
), (4)
" = ℎ ⋅ "∗
, (5)
ℎ = -(. /), (6)
"∗
∼ 0(1, &2
(), (7)
where = 1, … , and = 1, … , . In this model specification, is the individual fixed
effect for the unit , is a 1 × 4 vector of explanatory variables, is a random error
term with zero mean, " is a stochastic variable measuring inefficiency, and ℎ is a
positive function of a 1 × 5 vector of non-stochastic determinants of inefficiency, . .
Constant term is excluded from explanatory variables and from determinants of inefficiency.
It should be noted that the notation 0
means truncated normal distribution for
positive values only. The realized values of the variable "∗
are positive. In case of
1 = 0 the variable "∗
follows half-normal distribution.
Wang and Ho (2010) showed how to remove the fixed individual effect from the model.
Their procedure allows estimating all the model parameters. Of course, the individual
effect term may be recovered from the final parameter estimates. Wang and Ho (2010)
REVIEW OF ECONOMIC PERSPECTIVES
202
presented two possible approaches to model transformation: first-differencing and within-transformation.
Both methods are asymptotically equivalent, which was proven by
Wang and Ho (2008). First-differencing and within-transformation are standard methods
used in panel models applications to remove individual effects before estimating the
key model parameters. But, these approaches are more complicated in nonlinear models
like stochastic frontier models.
The first-differencing approach is applied in the empirical part of this article. It may be
thus useful to discuss this method in greater detail. As the first step, one first has to
define differences of corresponding variables as Δ789 = 7 − 7 :;	and the stacked
(column) vector of Δ7 for given and = 2, … , as => = (Δ7 (, Δ7 ?, … , Δ7 @)A
.
Assuming that the function ℎ is not constant, i.e. the vector . contains at least one
time-varying variable, the model in its first-difference form may be expressed as:
B> = > + Δ ̃ , (8)
DE = F> − G> , (9)
F> ∼ (0, H), (10)
G> = IJ "∗
, (11)
"∗
∼ 0(1, &2
(), (12)
where = 1, … , . First-differencing procedure, described by the equations (8)-(12),
leads to the correlations of differenced error terms in many applications of panel data
models. As an example, one can consider the dynamic panel data model and ArrelanoBond
estimator derived by Arellano and Bond (1991). In the case of the firstdifferencing
approach proposed by Wang and Ho (2010), one can observe correlations
of Δ within the th panel. Resulting covariance matrix of the multivariate normal
distribution of F> = (Δ (, … , Δ @)′ is
H =
L
M
M
M
M
N
2&'
(
−&'
(
0 ⋯ 0
−&'
(
2&'
(
−&'
(
⋯ 0
0 −&'
(
2&'
(
⋱ ⋮
⋮ ⋮ ⋱ ⋱ −&'
(
0 0 ⋯ −&'
(
2&'
(
R
S
S
S
S
T
.
This ( − 1) × ( − 1) matrix has the elements 2&'
(
on the diagonal and −&'
(
on the
off-diagonals. Knowing the exact form of the covariance matrix is essential for the
efficiency of maximal likelihood estimates discussed later. Moreover, one does not have
to use any kind robust covariance matrix to correct final estimates and their standard
errors.
The main point of Wang and Ho (2010) is that the truncated normal distribution of the
part of inefficiency term, "∗
, is not affected by this transformation. This fact allows us
to derive the likelihood function of the model. To be more specific, the marginal loglikelihood
function for the th cross-sectional unit is
Volume 15, Issue 2, 2015
203
ln 5 =		−
1
2
( − 1) ln(2V) −
1
2
ln( ) −
1
2
( − 1)ln	(&'
(
)
−
;
(
DEA
H:;
DE +
;
(
W
X∗
Y
Z∗
Y −
XY
Z[
Y\ + ln ]σ∗Φ W
X∗
Z∗
\`
− ln ]&2Φ W
X
Z[
\`	,
(13)
where
1∗ =
1
&2
( − DEA
H:;
IJ
IJA
H:;IJ + 1/&2
(
	,
&∗
(
=
1
IJA
H:;IJ + 1/&2
(
	,
DE = B> − > 	.
As for the notation, Φ(⋅) is the cumulative distribution function of a standard normal
distribution. Log-likelihood function of the model may be obtained by summing the
above function over all cross-sectional-units, = 1, … , . The model parameters are
estimated by maximizing the log-likelihood function of the model.
For practical purposes, one wishes to estimate observation-specific technical inefficiency.
Wang and Ho (2010) approximated this kind of inefficiency as a conditional expectation
c(" |DE ) evaluated at estimated values of DE :
c(" |Δ ̃ ) = ℎ e1∗ +
f W
1∗
&∗
\ &∗
Φ W
μ∗
σ∗
\
h	,
where f(⋅) represents the density function of standard normal distribution. This estimator
is a modified estimator of inefficiency terms which uses differenced error terms
stacked into the vector Δ ̃ , instead of as the conditional term. The original estimator
of inefficiency based on model residuals was derived by Jondrow et al. (1982).
The main advantage of the modified approach to computing inefficiency lies in the fact
that the vector DE contains all information of individual unit in the sample and does not
depend on individual effect term, . Wang and Ho (2010) argue that the individual
effect term has the variance of higher order in the case of small time dimension of the
sample (variance of order 1/ ) in comparison to the variance of 1/(( − 1) ) for
parameters estimator, i. The modified estimator of inefficiency is based on the parameter
estimates i, and is thus more efficient than the standard one. Wang and Ho (2010)
derived the expression for individual fixed effects terms. However, the modified version
of inefficiency estimator does not contain the individual effect terms which can be thus
omitted in practical applications. Technical efficiency may be obtained in accordance
with other studies. Battese and Coelli (1993) and Battese and Coelli (1995) proposed the
expression exp(−" ).
REVIEW OF ECONOMIC PERSPECTIVES
204
Data and Methodology
The stochastic frontier model of the Czech regional labour markets is estimated using
the monthly and quarterly data set covering a sample of 77 districts from January 1999
to June 2014. When compared to models of other authors, the models proposed estimate
inefficiency of the labour markets using “high” frequency data set. Galuščák and Münich
(2007) worked with quarterly Czech regional data only, Ilmakunnas and Pesola
(2003) and Gorter et al. (1997) focused on annual data of regions in Finland and the
Netherlands, respectively. The reason is that aggregation may lead to some loss of information.
Moreover, proving the relationship among the variables using the monthly
data should provide us with more efficient estimates.
The original labour market data come from the database of the Ministry of Labour and
Social Affairs (MLSA). This database covers the monthly and quarterly data from regional
Employment offices. In our empirical analysis, the models are estimated using
three groups of data types. The first group covers the core data for matching function
specification:
• Number of registered successful matches for each district in the corresponding
month (source MLSA);
• Number of registered unemployed at the beginning of the month (source
MLSA);
• Number of registered vacancies at the beginning of the month (source MLSA).
The second group of the data represents the district specific labour market fundaments:
• Number of registered unemployed receiving the unemployment benefits in the
corresponding month (source MLSA);
• Number of registered unemployed of age 50 and older in the corresponding
quarter (source MLSA);
• Number of the registered unemployed who have been unemployed for more
than 12 months in the corresponding quarter (source MLSA).
The third data group captures the overall economic conditions and economic activity in
the Czech Republic:
• Index of industrial production (base year 2010 = 100, source Czech National
Bank and International Financial Statistics);
• Quarterly real gross domestic product (source Czech National Bank).
All the data are seasonally unadjusted. Seasonal pattern of the variables constitutes an
integral part of the stochastic frontier model. Treating the seasonality as a source of
inefficiency is in accordance with the econometric methodology advocated by Kalman
(1979). In his opinion, an adequate model should incorporate all behavioural aspects of
the data. From this point of view, seasonal adjustment of the variables done by researcher
outside model framework may be misleading and may influence the final results.
Seasonal behaviour is removed by averaging using the final model estimates. In
this way, one can obtain overall tendencies in inefficiency development.
Stochastic frontier models are estimated using monthly and quarterly data. Number of
successful matches and number of vacancies are computed as monthly averages due to
Volume 15, Issue 2, 2015
205
lack of quarterly counterparts of these statistics. Time series of the index of industrial
production is based on index provided by the Czech National Bank. Only values starting
in 2000 were available. The values for 1999 were thus computed using the industrial
production index provided by International Monetary Fund in its International Financial
Statistics.
All the district specific labour market variables are expressed relatively to the pool of
unemployed people in the corresponding month or quarter. It means that ratios of these
variables have been used. Models consist of quarterly dummies as well. The first quarter
of the year is the basic quarter (category).
The estimates are carried out using the monthly and quarterly data. To be more specific,
the models are formulated in accordance with the equations (2)-(7) as:
= log 	,
= (log , log )	,
= m , n	,
ℎ
= opqrsrt uvwv- + pxyzzΔ{||
+ pxyzz}~
Δ{|| :; + p•€r•‚0 ƒ„v50
+ δ‡ ˆ 	 5‰w„ + pŠ(‹( + pŠ?‹? + pŠŒ‹Œ 	o
for the model with monthly data, and
ℎ
= opqrsrt uvwv- + px•Ž•Δ•‘|
+ px’“z}~
Δ•‘| :; + p•€r•‚0 ƒ„v50
+ δ‡ ˆ 	 5‰w„ + pŠ(‹( + pŠ?‹? + pŠŒ‹Œ 	o
for the model with quarterly data. The specification of inefficiency function ℎ does not
contain time trend. Unlike the specification of inefficiency function ℎ proposed by
Němec (2014a) and Němec (2014b), no time trend is used and instead of that, regional
labour market specifics are implemented. This approach should provide a more reliable
and detailed view of the sources of labour market inefficiency. The model variables are
denoted as follows:
• number of registered successful matches, , in the corresponding month (averaged
in the quarterly models);
• number of unemployed at the beginning of the month, (averaged in the
quarterly models);
• number of vacancies at the beginning of the month, (averaged in the quarterly
models);
• ratio of registered unemployed receiving the unemployment benefits in the corresponding
month, uvwv- (averaged in the quarterly models), to the total
unemployed;
• ratio of the registered unemployed of age 50 and older in the corresponding
quarter, ƒ„v50 , to the total number of unemployed people;
REVIEW OF ECONOMIC PERSPECTIVES
206
• ratio of the registered unemployed who have been unemployed for more than
12 months in the corresponding quarter, 5‰w„ , to the total number of unemployed
people;
• seasonal (quarterly) dummies for the 2nd
, 3rd
and 4th
quarter (‹( , ‹? , ‹Œ );
• monthly growth of the industrial production, Δ{|| , and quarterly growth of
real gross domestic product, Δ•‘| .
Subscripts denote a district and corresponds to the month or quarter. Moreover, to
check the robustness of the results and to evaluate the possible changes in parameters
and inefficiency terms, the estimates are based on a full sample of the years from 1999
to 2014, and on the sample covering both the pre-crisis period of 1999-2007 and the
period of 2008-2014, respectively. The results will be used for finding the basic tendencies
and distributional inefficiency changes among the districts.
As for the estimation techniques, parameter estimates were obtained by nonlinear optimization
techniques in Matlab 2013b, applied on the log-likelihood of the models defined
as the sum of marginal log-likelihoods from the equation (13). Standard deviation
of the parameter estimates are based on inverted negative Hessian of log-likelihood
evaluated at the maximal likelihood estimates. All first and second derivatives were
computed numerically within the optimization procedure. The algorithm converged very
well in all cases.3
For computational purposes, the variance parameters were parameterised
as log &'
(
and log &2
(
respectively. Parameter 1 is defined as 1 = 0. This calibration
leads to a half-normal representation of the model.
Efficiency Estimates of the Czech Regional Labour Markets
Parameter estimates of the matching function and the inefficiency term for the Czech
regional labour markets are presented in Table 1 and Table 2. The models have been
estimated using the monthly and quarterly data using both the full sample and restricted
samples.
The results in Table 1 do not confirm the empirical findings presented by Ilmakunnas
and Pesola (2003) who claim that with regional data it may be more likely to find increasing
returns in matching. The Czech regional labour market proves the diminishing
returns in matching. The elasticity of matches to vacancies, 	( ), is extremely low. It
means that the vacancy creation is not a sufficient condition to diminish unemployment.
This kind of conclusion may be justified by the hypothesis that new vacancies do not
correspond to qualification structure of the unemployed. Using the full sample estimates,
we reach the value of 0.109. It means that only 10 percent of new monthly vacancies
may be matched with the unemployed. This effect is lower using the restricted sample
estimates of the pre-crisis period. It seems that the economic slowdown that started at
the end of 2009 led to a more efficient utilization of the unfilled vacancies. Estimated
elasticity matching to the unemployed, 	( ), shows that approximately half of the
3
Data and programme files are available from the author upon a request.
Volume 15, Issue 2, 2015
207
new unemployed might be able to find a new job immediately. Comparison of the estimates
of 0.569 and 0.522 in the pre-crisis and post-crisis period indicates modest
changes in matching elasticity of unemployed. Unfortunately, these changes tend to
worsen the matching conditions of regional labour markets.
Table 1 Parameter estimates – stochastic frontier model (monthly data)
Parameter 1999 – 2014 1999 – 2007 2008 – 2014
	( ) 0.493 (0.013) 0.569 (0.016) 0.522 (0.026)
	( ) 0.109 (0.005) 0.044 (0.005) 0.083 (0.011)
pqrsrt -0.338 (0.016) 0.024 (0.012) -0.365 (0.037)
pxyzz -2.874 (0.049) -3.238 (0.025) -2.953 (0.090)
pxyzz}~ -1.987 (0.034) -1.448 (0.105) -1.859 (0.086)
p‡”•–—˜™ 2.073 (0.055) 1.034 (0.042) 0.526 (0.022)
p‡š›œ• 0.353 (0.029) 0.303 (0.027) 1.748 (0.010)
pŠY -0.380 (0.021) -0.526 (0.016) -0.571 (0.007)
pŠ• 0.081 (0.014) 0.111 (0.005) 0.014 (0.017)
pŠž 0.416 (0.013) 0.350 (0.010) 0.472 (0.017)
log	(&'
(
) -2.761 (0.012) -3.382 (0.016) -2.458 (0.018)
log	(&2
(
) -0.940 (0.163) -0.920 (0.162) -0.911 (0.163)
Source: Own calculations (standard errors in parenthesis, grey shaded parameter estimates are
statistically insignificant at 5 percent level of significance).
Inefficiency of the regional labour markets is strongly influenced by region (district)
specific factors and common economic factors. The ratio of the registered unemployed
receiving unemployment benefits has a positive impact on efficiency (i.e. it reduces
inefficiency level) using the post-crisis and full sample data. The value of the corresponding
parameter pqrsrt means that a ten-percent increase of the ratio of unemployed
receiving benefits tends to lower the inefficiency by 3.3 percent for the full sample
estimates (we can treat the inefficiency term of 1 as a sign of absolute inefficiency).
This surprising result may be explained by stating that these unemployed people are
mostly short-term unemployed who are willing to get themselves a job as soon as possible.
This behaviour leads to increasing matching creation. As Table 1 suggests, this
effect is prevailing in the period of economic slowdown, where the unemployed prefer
getting a worse job rather than staying in the pool of the unemployed. It is clear that precrisis
value of 0.024 suggests the opposite behaviour of the unemployed, which was
caused by the fact that the labour market had not been so tight. Of course, the positive
influence on inefficiency is not so evident.
The ratio of the registered unemployed of age 50 and older, 䇔•–—˜™
, and the ratio of
the long-term unemployed, δ‡š›œ•
, both have a negative effect on matching efficiency.
Using the full sample data shows that the effect of the older unemployed prevails the
effect of long-term unemployed. On the other hand, the estimates based on restricted
REVIEW OF ECONOMIC PERSPECTIVES
208
samples indicate the changes of their relative strength. The predominant role of the
older unemployed in the pre-crisis period was replaced by the increasing influence of
the long-term unemployed. It is a logical outcome of the retirement process. The older
unemployed in the pre-crisis period were leaving the labour market after the economic
slowdown in 2008 (and consecutive years). The role of long-term unemployed was thus
more important in the determining of labour markets inefficiency. Ten percent increase
of ratio of the long-term unemployed may cause 17 percent (0.17) rise in inefficiency.
As for the parameters of economic activity, δxŸ•• and δxŸ••}~
, we can see that the marginal
effects of the monthly growths of industrial production in the last two periods
diminish the matching inefficiency. Positive economic development supports the vacancies
creation and lowers the unemployment inflows. These vacancies can be filled immediately.
The structure of the skills of the unemployed registered at the employment
office seems to be not a problem at the regional level. As pointed out by Polasek and
Sellner (2013), the economic growth may be inducted by many other factors connected
to openness of the Czech economy.
The inefficiency within the year tends to be accompanied by important seasonal patterns,
especially by a positive effect on the matching function outcomes in the second quarters.
Quarterly dummies show a substantial jump in the last quarter of the year (compared
with the first quarter).
Higher variability of the inefficiency term, &2
(
, in comparison to the white noise process
variability, &'
(
(i.e. &2
(
/&'
(
), contributes to the satisfying identification of the stochastic
frontier model as stated by Wang and Ho (2010).
Table 2 Parameter estimates – stochastic frontier model (quarterly data)
Parameter 1999 – 2014 1999 – 2007 2008 – 2014
	( ) 0.449 (0.018) 0.478 (0.018) 0.404 (0.042)
	( ) 0.054 (0.007) 0.074 (0.006) -0.001 (0.015)
pqrsrt -0.287 (0.064) -0.009 (0.014) -0.386 (0.019)
px•Ž• -2.268 (0.496) -2.050 (0.008) -1.380 (0.032)
px•Žz}~ -4.630 (1.043) -2.489 (0.015) -5.988 (0.014)
p‡”•–—˜™ 0.595 (0.129) 1.713 (0.010) 0.908 (0.073)
p‡š›œ• 0.404 (0.088) -0.332 (0.020) 0.586 (0.071)
pŠY -0.360 (0.075) -0.131 (0.013) -0.704 (0.006)
pŠ•
0.471 (0.106) 0.397 (0.008) 0.434 (0.008)
pŠž 0.346 (0.077) 0.401 (0.013) 0.234 (0.012)
log	(&'
(
) -3.434 (0.021) -4.573 (0.028) -3.157 (0.033)
log	(&2
() 0.634 (0.425) -0.573 (0.186) 1.178 (0.184)
Source: Own calculations (standard errors in parenthesis, grey shaded parameter estimates
are statistically insignificant at 5 percent level of significance).
Table 2 shows stochastic frontier model estimates which use quarterly data. The results
are very similar with regard to the estimated coefficients signs. As for some remarkable
Volume 15, Issue 2, 2015
209
difference, higher influence of the GDP growth on the inefficiency term can be observed.
Moreover, the lagged GDP growth contributes to diminishing inefficiency with
a remarkable extent. This property could not be detected using the monthly data only.
Compensating changes in the parameter at seasonal dummy, pŠ•
,	can be viewed as other
consequences of the GDP growth effects. The long-term and the older unemployed
influence the inefficiency in a more balanced way. There is a surprisingly negative
effect of the long-term unemployed on the inefficiency in the period from 1999 to 2007.
Unemployment rate declined (see Figure 1) and the labour market experienced an extremely
low tightness. As a result, for people who have been unemployed for a long
time, but are younger, finding a job was easier than for the older ones. This explanation
may be proved by the estimates mentioned above.
Estimated parameters in stochastic efficiency variability have changed dramatically.
Standard values obtained previously using the monthly data may be found for the precrisis
sample only. Estimates resulting from full data set show statistically insignificant
parameter of variance, log	(&2
(
). It means that the estimated variance, &2
(
, could equal
one.
Figure 1 Unemployment rate in the Czech Republic
Source: Own calculations.
4
5
6
7
8
9
10
1998
1999
2000
2001
2002
2003
2004
2005
2006
2007
2008
2009
2010
2011
2012
2013
2014
Generalunemploymentrate[%]
REVIEW OF ECONOMIC PERSPECTIVES
210
Figure 2 Inefficiency range (full sample 1999-2014, monthly data)
Source: Own calculations.
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
Praha
Benešov
Beroun
Kladno
Kolín
Kutná Hora
Mělník
Mladá Boleslav
Nymburk
Praha-východ
Praha-západ
Příbram
Rakovník
České Budějovice
Český Krumlov
Jindřichův Hradec
Písek
Prachatice
Strakonice
Tábor
Domažlice
Klatovy
Plzeň-město
Plzeň-jih
Plzeň-sever
Rokycany
Tachov
Cheb
Karlovy Vary
Sokolov
Děčín
Chomutov
Litoměřice
Louny
Most
Teplice
Ústí nad Labem
Česká Lípa
Jablonec nad Nisou
Liberec
Semily
Hradec Králové
Jičín
Náchod
Rychnov nad Kněžnou
Trutnov
Chrudim
Pardubice
Svitavy
Ústí nad Orlicí
Havlíčkův Brod
Jihlava
Pelhřimov
Třebíč
Žďár nad Sázavou
Blansko
Brno-město
Brno-venkov
Břeclav
Hodonín
Vyškov
Znojmo
Jeseník
Olomouc
Prostějov
Přerov
Šumperk
Kroměříž
Uherské Hradiště
Vsetín
Zlín
Bruntál
Frýdek-Místek
Karviná
Nový Jičín
Opava
Ostrava-město
25% quantile
median
75% quantile
Volume 15, Issue 2, 2015
211
Figure 3 Inefficiency range (full sample 1999-2014, quarterly data)
Source: Own calculations.
Estimated distribution of the monthly inefficiency among the Czech districts is depicted
in Figure 2. The presented interquartile range of inefficiency terms distributions for all
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
Praha
Benešov
Beroun
Kladno
Kolín
Kutná Hora
Mělník
Mladá Boleslav
Nymburk
Praha-východ
Praha-západ
Příbram
Rakovník
České Budějovice
Český Krumlov
Jindřichův Hradec
Písek
Prachatice
Strakonice
Tábor
Domažlice
Klatovy
Plzeň-město
Plzeň-jih
Plzeň-sever
Rokycany
Tachov
Cheb
Karlovy Vary
Sokolov
Děčín
Chomutov
Litoměřice
Louny
Most
Teplice
Ústí nad Labem
Česká Lípa
Jablonec nad Nisou
Liberec
Semily
Hradec Králové
Jičín
Náchod
Rychnov nad Kněžnou
Trutnov
Chrudim
Pardubice
Svitavy
Ústí nad Orlicí
Havlíčkův Brod
Jihlava
Pelhřimov
Třebíč
Žďár nad Sázavou
Blansko
Brno-město
Brno-venkov
Břeclav
Hodonín
Vyškov
Znojmo
Jeseník
Olomouc
Prostějov
Přerov
Šumperk
Kroměříž
Uherské Hradiště
Vsetín
Zlín
Bruntál
Frýdek-Místek
Karviná
Nový Jičín
Opava
Ostrava-město
25% quantile
median
75% quantile
REVIEW OF ECONOMIC PERSPECTIVES
212
77 districts is based on the estimates using the full sample period. Minimum inefficiency
values for each district (which are not presented here) are almost zero for all investigated
labour markets. All investigated districts thus can match the unemployed with the
vacancies at the full rate. Of course, it is often caused by seasonal factors in the second
quarter of the year. There are some districts with exceptionally good efficiency of
matching (e.g. Praha, Benešov, Trutnov or Jablonec nad Nisou) and some districts
showing bad efficiency performance (e.g. Jeseník, Znojmo or Bruntál).
It may be surprising that districts such as Karviná or Ústí nad Labem are among the well
performing districts, and it is necessary to say that the two districts are not to be classified
to come from regions with low unemployment properties. But, it should be stressed
that low inefficiency does not automatically mean low unemployment. It expresses the
potential for new created matches which can be constituted by the interaction between
unemployed and available vacancies.
From this point of view, these results imply that the potential of labour market is utilized
quite well. There may be an appropriate structure of unemployed people and vacancies,
unobserved characteristics of the unemployed support their willingness to actively
search for a job, and finally, the surrounding regions may offer other possibilities
for employing unemployed job applicants (this spatial dependency is not implemented
in estimated models so far). The unfavourable efficiency outcomes of the Jeseník,
Znojmo or Bruntál districts may be thus explained in a similar way.
Similar inefficiency patterns may be found in quarterly estimates which are presented in Figure 3.
Quarterly estimates show sharper disparities in inefficiency distribution. The best way to illustrate
the development of the labour market inefficiency and its variability is to compute the yearly
averages for each district. These aggregated results are presented in Figure 4 and
Figure 5. The revealed tendencies are almost the same for the monthly and quarterly
estimates.
In the period from 1999 to 2007, the Czech regional labour markets may be described as
labour markets with rising inefficiency patterns and rising heterogeneity among them.
These tendencies are more significant when monthly estimates are used (see Figure 4).
When looking at the development of unemployment rate in the Czech Republic, one
cannot conclude that rising inefficiency tends is accompanied by higher unemployment.
The increase before 2007 is a result of very low tightness at the Czech labour market.
The overall positive economic conditions made it problematic for companies to find
appropriate workforce. The structure of unfilled vacancies could not match the structure
of the unemployed. 2008 and 2009 are connected with the beginning of the global financial
crisis and worldwide economic slowdown. This exogenous shock forced firms
to think about their employment policies. Facing the uncertainty of expected length and
amplitude of the economic slowdown, they were not willing to dismiss their employees
immediately. Instead of that they reduced their vacancy creation. Available stock of
vacancies was thus reduced. From this point of view, successful matches operate closer
to production frontier (in comparison with the precedent years). The years from 2010 to
2012 reversed the positive efficiency patterns of the matching process due to prevailing
economic uncertainty.
Volume 15, Issue 2, 2015
213
Figure 4 Average inefficiency distributions (full sample 1999-2014, monthly data)
Source: Own calculations.
Figure 5 Average inefficiency distributions (full sample 1999-2014, quarterly data)
0
0.2
0.4
0.6
0.8
1
1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013
Year
Inefficiency
0
0.2
0.4
0.6
0.8
1
1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013
Year
Inefficiency
REVIEW OF ECONOMIC PERSPECTIVES
214
Source: Own calculations.
Table 3 and Table 4 show the changes in the inefficiency of Czech labour market in a
more compact way. Presented standard deviations illustrate the overall rise of inefficiency
disparities among the Czech districts.
Table 3 Average inefficiency and its variability among districts (monthly data)
Year Mean Std. deviation Year Mean Std. deviation
1999 0.213 0.045 2007 0.395 0.096
2000 0.248 0.054 2008 0.430 0.104
2001 0.239 0.052 2009 0.325 0.072
2002 0.248 0.056 2010 0.342 0.075
2003 0.286 0.066 2011 0.377 0.085
2004 0.293 0.067 2012 0.421 0.097
2005 0.349 0.079 2013 0.390 0.090
2006 0.366 0.085 1999 - 2013 0.328 0.102
Source: Own calculations.
Table 4 Average inefficiency and its variability among districts (quarterly data)
Year Mean Std. deviation Year Mean Std. deviation
1999 0.210 0.077 2007 0.350 0.126
2000 0.245 0.098 2008 0.361 0.131
2001 0.288 0.103 2009 0.426 0.140
2002 0.290 0.110 2010 0.360 0.117
2003 0.290 0.109 2011 0.429 0.136
2004 0.307 0.110 2012 0.515 0.167
2005 0.314 0.113 2013 0.481 0.156
2006 0.316 0.112 1999 – 2013 0.346 0.148
Source: Own calculations.
The differences across the regions were rising since 1999. We can observe some differences
in the results depending on the time frequency of the model. But the basic tendencies
are very similar. These results do not indicate that the estimated labour market
inefficiency may rise during periods of recession and recovery while it decreases during
the economic booms. Regarding the fact that Gorter et al. (1997) used annual data, it
should be noted that this contradiction is not conclusive.
Volume 15, Issue 2, 2015
215
Table 5 Labour market inefficiency across districts (monthly data, yearly averages)
District 99–13 99–07 08–13 District 99–13 99–07 08–13
Praha 0.193 0.182 0.209 Liberec 0.241 0.221 0.271
Benešov 0.253 0.236 0.278 Semily 0.213 0.188 0.249
Beroun 0.240 0.218 0.272 Hradec Králové 0.314 0.277 0.370
Kladno 0.233 0.212 0.265 Jičín 0.296 0.266 0.340
Kolín 0.323 0.303 0.353 Náchod 0.325 0.286 0.382
Kutná Hora 0.400 0.359 0.462 Rychnov nad Kněžnou 0.333 0.298 0.385
Mělník 0.270 0.244 0.308 Trutnov 0.198 0.179 0.227
Mladá Boleslav 0.264 0.221 0.329 Chrudim 0.412 0.382 0.458
Nymburk 0.309 0.282 0.349 Pardubice 0.305 0.266 0.364
Praha-východ 0.163 0.153 0.177 Svitavy 0.459 0.397 0.553
Praha-západ 0.199 0.185 0.218 Ústí nad Orlicí 0.354 0.320 0.405
Příbram 0.372 0.329 0.437 Havlíčkův Brod 0.371 0.339 0.419
Rakovník 0.343 0.306 0.399 Jihlava 0.341 0.293 0.412
České Budějovice 0.272 0.237 0.324 Pelhřimov 0.287 0.241 0.356
Český Krumlov 0.431 0.398 0.481 Třebíč 0.429 0.385 0.494
Jindřichův Hradec 0.427 0.378 0.501 Žďár nad Sázavou 0.373 0.339 0.424
Písek 0.409 0.359 0.483 Blansko 0.304 0.267 0.360
Prachatice 0.336 0.302 0.387 Brno-město 0.242 0.213 0.285
Strakonice 0.335 0.295 0.395 Brno-venkov 0.264 0.232 0.311
Tábor 0.340 0.291 0.415 Břeclav 0.410 0.354 0.494
Domažlice 0.309 0.258 0.385 Hodonín 0.383 0.343 0.442
Klatovy 0.341 0.303 0.398 Vyškov 0.322 0.286 0.375
Plzeň-město 0.235 0.216 0.262 Znojmo 0.548 0.500 0.619
Plzeň-jih 0.360 0.314 0.427 Jeseník 0.477 0.431 0.547
Plzeň-sever 0.355 0.314 0.417 Olomouc 0.348 0.311 0.402
Rokycany 0.306 0.282 0.343 Prostějov 0.415 0.365 0.489
Tachov 0.395 0.367 0.437 Přerov 0.376 0.320 0.460
Cheb 0.363 0.326 0.419 Šumperk 0.362 0.324 0.420
Karlovy Vary 0.351 0.331 0.382 Kroměříž 0.312 0.280 0.359
Sokolov 0.332 0.293 0.390 Uherské Hradiště 0.405 0.349 0.489
Děčín 0.316 0.280 0.369 Vsetín 0.378 0.325 0.456
Chomutov 0.323 0.292 0.370 Zlín 0.369 0.322 0.439
Litoměřice 0.336 0.306 0.382 Bruntál 0.460 0.418 0.522
Louny 0.343 0.305 0.400 Frýdek-Místek 0.326 0.287 0.385
Most 0.252 0.219 0.300 Karviná 0.245 0.219 0.283
Teplice 0.290 0.274 0.315 Nový Jičín 0.312 0.282 0.356
Ústí nad Labem 0.215 0.196 0.245 Opava 0.404 0.352 0.481
Česká Lípa 0.322 0.292 0.367 Ostrava-město 0.288 0.260 0.329
Jablonec nad Nisou 0.203 0.179 0.239
Source: Own calculations.
REVIEW OF ECONOMIC PERSPECTIVES
216
Table 6 Labour market inefficiency across districts (quarterly data, yearly averages)
District 99–13 99–07 08–13 District 99–13 99–07 08–13
Praha 0.131 0.111 0.160 Liberec 0.284 0.255 0.328
Benešov 0.102 0.084 0.131 Semily 0.304 0.242 0.397
Beroun 0.159 0.129 0.204 Hradec Králové 0.298 0.251 0.368
Kladno 0.215 0.187 0.256 Jičín 0.301 0.240 0.392
Kolín 0.350 0.308 0.412 Náchod 0.369 0.299 0.473
Kutná Hora 0.466 0.408 0.553 Rychnov nad Kněžnou 0.386 0.312 0.497
Mělník 0.219 0.188 0.267 Trutnov 0.250 0.209 0.311
Mladá Boleslav 0.196 0.150 0.264 Chrudim 0.395 0.334 0.486
Nymburk 0.279 0.238 0.341 Pardubice 0.276 0.222 0.357
Praha-východ 0.069 0.059 0.085 Svitavy 0.447 0.361 0.578
Praha-západ 0.178 0.147 0.225 Ústí nad Orlicí 0.420 0.362 0.507
Příbram 0.398 0.325 0.508 Havlíčkův Brod 0.349 0.295 0.430
Rakovník 0.356 0.282 0.466 Jihlava 0.274 0.217 0.359
České Budějovice 0.232 0.176 0.314 Pelhřimov 0.234 0.177 0.320
Český Krumlov 0.652 0.570 0.774 Třebíč 0.490 0.417 0.600
Jindřichův Hradec 0.464 0.379 0.590 Žďár nad Sázavou 0.412 0.341 0.519
Písek 0.401 0.306 0.543 Blansko 0.305 0.246 0.392
Prachatice 0.317 0.259 0.405 Brno-město 0.214 0.183 0.260
Strakonice 0.300 0.241 0.389 Brno-venkov 0.171 0.136 0.222
Tábor 0.357 0.278 0.475 Břeclav 0.421 0.342 0.539
Domažlice 0.249 0.175 0.361 Hodonín 0.451 0.399 0.529
Klatovy 0.340 0.273 0.440 Vyškov 0.322 0.269 0.402
Plzeň-město 0.158 0.133 0.195 Znojmo 0.588 0.499 0.722
Plzeň-jih 0.387 0.310 0.503 Jeseník 0.684 0.595 0.816
Plzeň-sever 0.285 0.233 0.363 Olomouc 0.371 0.322 0.446
Rokycany 0.266 0.232 0.317 Prostějov 0.372 0.306 0.470
Tachov 0.392 0.329 0.486 Přerov 0.376 0.301 0.488
Cheb 0.406 0.333 0.515 Šumperk 0.490 0.421 0.594
Karlovy Vary 0.453 0.415 0.509 Kroměříž 0.302 0.263 0.360
Sokolov 0.416 0.346 0.521 Uherské Hradiště 0.407 0.335 0.515
Děčín 0.423 0.364 0.511 Vsetín 0.453 0.387 0.551
Chomutov 0.390 0.331 0.479 Zlín 0.390 0.335 0.472
Litoměřice 0.438 0.382 0.523 Bruntál 0.604 0.516 0.736
Louny 0.423 0.371 0.502 Frýdek-Místek 0.391 0.337 0.472
Most 0.297 0.251 0.366 Karviná 0.297 0.266 0.343
Teplice 0.366 0.325 0.426 Nový Jičín 0.352 0.312 0.411
Ústí nad Labem 0.293 0.256 0.348 Opava 0.445 0.372 0.555
Česká Lípa 0.412 0.358 0.493 Ostrava-město 0.289 0.256 0.338
Jablonec nad Nisou 0.189 0.159 0.233
Source: Own calculations.
Volume 15, Issue 2, 2015
217
Table 5 and Table 6 contain a detailed view on average inefficiency estimates for all
Czech districts. The aggregate regional inefficiency changes are presented in a straightforward
way. All investigated districts have experienced the rise in their inefficiency. A
comparison of the inefficiency estimates to the unemployment rates does not confirm a
direct connection between unemployment rate and inefficiency of the matching process.
In the introductory section of this paper, regional unemployment rates for selected districts
and their changes have been mentioned. As an example, let us take a look at the
districts of Domažlice and Most. Unemployment rate in the Domažlice district reached
5.37 percent in 2005 and 6.42 percent in 2013. Average inefficiency rose from 0.258 to
0.385 when using the monthly estimates and from 0.175 to 0.361 when using the more
distinctive quarterly data. Unemployment rate in the Most district was 16.49 percent in
2005 and 13.51 percent in 2013. Average inefficiency increased from 0.219 to 0.300
when using the monthly estimates, and from 0.251 to 0.366 when using the quarterly
data. Low matching inefficiency does not lead to lower unemployment automatically.
Its dynamics may only help to improve the tendencies of unemployment dynamics. Bad
news is that regions with relatively satisfactory matching inefficiency and high unemployment
rate cannot improve their performance through the factors influencing the
effective matching process. Overall economic growth or diminishing ratio of long-term
unemployed would have only a little effect on the matching experience there.
Conclusion
This paper presented an alternative approach to measure the efficiency of the matching
process on the Czech regional labour markets. Obtained results show that the stochastic
frontier model approach is able to capture some interesting patterns of these labour
markets controlling individual fixed effects of examined districts and possible timevarying
changes in the inefficiency terms. The model estimates uses full sample displays
increasing tendency of matching inefficiency in all districts with strong seasonal
patterns. These tendencies are accompanied by rising disparities among the regions
although low inefficiency does not necessary mean low unemployment in the investigated
districts. The differences across the regions were rising since 1999. Surprisingly,
the estimated labour market inefficiency does not indicate that it may rise during the
recession and recovery period while it decreases during the economic booms.
In the period from 1999 to 2007, the Czech regional labour markets may be described as
labour markets with rising inefficiency patterns and rising heterogeneity among them.
The increase before 2007 was a result of very low tightness at the Czech labour market.
The structure of unfilled vacancies could not match the structure of the unemployed.
2008 and 2009 are connected with the beginning of economic slowdown. Firms were
not willing to dismiss their employee immediately. Instead of that they reduced their
vacancy creation. The successful matches operated closer to the production frontier.
From 2010 to 2012, the positive efficiency patterns of the matching process reversed
due to prevailing economic uncertainty.
Matching function of the Czech regional labour markets may be characterized by diminishing
returns in matching. The elasticity of matching to vacancies is extremely low
within the whole period of 1999-2014. These results are similar to those presented by
REVIEW OF ECONOMIC PERSPECTIVES
218
Galuščák and Münich (2007) or Münich et al. (1999). Empirical findings presented by
Ilmakunnas and Pesola (2003) that with regional data it may be more likely to find increasing
returns in matching are not confirmed in the case of the Czech Republic.
Moreover, it means that the vacancy creation is not a sufficient condition to diminish
unemployment. The main reason for that is that new vacancies do not correspond to the
qualification structure of the unemployed.
Inefficiency of the regional labour markets is strongly influenced by district specific
factors and common economic factors. The ratio of the registered unemployed receiving
the unemployment benefits has a positive impact on efficiency. It seems that that these
unemployed people are mostly short-term unemployed who are willing to find themselves
a job as soon as possible. The main sources of inefficiency may be connected
with the ratio of the unemployed in the age of 50 and older, and with the ratio of the
long-term unemployed. In the pre-crisis period, older unemployed people were actually
leaving the labour market after the economic slowdown in 2008 (and consecutive years).
In determining of labour markets inefficiency, the role of the long-term unemployed
was thus more important. All regional labour markets were able to operate at their
matching function frontiers due to seasonal factors.
Some key results may be found when taking advantage of the estimates of the matching
inefficiency using the pre-crisis data (prior to 2008) and the data covering the period of
global economic slowdown that started in 2008. Overall matching efficiency is lower
during the period of economic slowdown. As pointed out by Ilmakunnas and Pesola
(2003), this conclusion has strong policy implications: supporting job creation through
new vacancies is less efficient in the period of economic recession. Unfortunately, regions
with relatively satisfactory matching inefficiency and high unemployment rate
cannot improve their performance through factors influencing the effective matching
process. Overall economic growth or diminishing ratio of the long-term unemployed has
little effect on the matching experience there.
It will be of great importance in further research to focus on model outcomes using the
aggregate yearly data that allow including more region-specific variables. Münich et al.
(1999) suggested that TRANSLOG matching function be used as an alternative to the
standard Cobb-Douglas specification. Moreover, spatial properties of labour markets
dynamics should be investigated, i.e. efficiency terms should incorporate the influence
of neighbouring districts. This kind of model enhancements could provide us with more
detailed and precise view of the sources of labour market efficiency.
References
AIGNER, D., LOVELL, C.A.K., SCHMIDT, P. (1977). Formulation and Estimation of
Stochastic Frontier Production Function Models. Journal of Econometrics 6, 21–37.
AMSLER, C., LEE, Y. H., SCHMIDT, P. (2009). A Survey of Stochastic Frontier
Models and Likely Future Developments. Seoul Journal of Economics 22 (1), 5–27.
ARELLANO, M., BOND, S. (1991). Some tests of specification for panel data: Monte
Carlo evidence and an application to employment equation. Review of Economic Studies
58, 277–297.
Volume 15, Issue 2, 2015
219
BATTESE, G. E., COELLI, T. J. (1993). A Stochastic Frontier Production Function
Incorporating a Model For Technical Inefficiency Effects. Working Papers in Econometrics
and Applied Statistics. No. 69. University of New England.
BATTESE, G. E., COELLI, T. J. (1995). A Model for Technical Inefficiency Effects in
a Stochastic Frontier Production Function for Panel Data. Empirical Economics 20,
325–332.
Czech National Bank. Public time series database ARAD available at
http://www.cnb.cz/docs/ARADY/HTML/index_en.htm.
GALUŠČÁK, K., MÜNICH, D. (2007). Structural and Cyclical Unemployment: What
Can Be derived from the Matching Function. Czech Journal of Economics and Finance
57, 102–125.
GORTER, C., NIJKAMP, P., PELS, E. (1997). Vacancy Dynamics and Labor Market
Efficiency in the Dutch Labor Market. Growth and Change 28, 173–200.
GREENE, W. H. (2005). Reconsidering heterogeneity in panel data estimators of the
stochastic frontier model. Journal of Econometrics 126 (2), 269–303.
ILMAKUNNAS, P., PESOLA, H. (2003). Regional Labour Market Matching Functions
and Efficiency Analysis. Labour 17, 413–437.
International Financial Statistics. Database of International Monetary Fund available at
http://www.imf.org/external/data.htm.
JONDROW, J., LOVELL, C. A. K., MATEROV, I. S., SCHMIDT, P. (1982): On the
Estimation of Technical Inefficiency in the Stochastic Frontier Production Function
Model. Journal of Econometrics 19, 233–238.
KALMAN, R. E. (1979): A system-theoretic critique of dynamic economic models.
Lecture Notes in Control and Information Sciences 19, 3–24.
Ministry of Labour and Social Affairs. Unemployment statistics (quarterly and monthly)
available at http://portal.mpsv.cz/sz/stat/nz
MÜNICH, D., ŠVEJNAR, J., TERELL, K. (1999): Worker-Firm Matching and Unemployment
in Transition to a Market Economy: (Why) Are the Czechs More Successful
than Others? (January 1999). CERGE-EI Working Paper No. 141. Available at
http://dx.doi.org.sci-hub.org/10.2139/ssrn.164555
NĚMEC, D. (2013a). Evaluating labour market flexibility in V4 countries. In Vojáčková,
H. (ed.) Proceedings of 31st International Conference Mathematical Methods in
Economics. College of Polytechnics Jihlava, Jihlava, 661–666.
NĚMEC, D. (2013b). Investigating Differences between the Czech and Slovak Labour
Market Using a Small DSGE Model with Search and Matching Frictions. The Czech
Economic Review 7, 21–41.
NĚMEC, D. (2014a). Efficiency of the matching process on the Czech regional labour
markets. In Reiff, M., Gežík. P. (eds.) Proceedings of the International Scientific Conference
QUANTITATIVE METHODS IN ECONOMICS Multiple Criteria Decision
Making XVII. Vydavateľstvo EKONÓM, Bratislava, 188–195.
REVIEW OF ECONOMIC PERSPECTIVES
220
NĚMEC, D. (2014b) Efficiency of the European labour markets: The Case of Czech
Republic (A Stochastic frontier model approach). In Talašová, J., Stoklasa, J., Talášek,
T. (eds.) 32nd International Conference Mathematical Methods in Economics Conference
Proceedings. Palacký University, Olomouc, 703–708.
POLASEK, W., SELLNER, R. (2013): Does Globalization Affect Regional Growth?
Evidence for NUTS-2 Regions in EU-27. DANUBE: Law and Economics Review 4 (1),
23-65.
TVRDOŇ, M., VERNER, T. (2012). Regional unemployment disparities and their
dynamics: Evidence from the Czech Republic. In Ramík, J., Stavárek, D. (eds.) Proceedings
of 30th International Conference Mathematical Methods in Economics. Silesian
University in Opava, School of Business Administration in Karviná, 938–943.
WANG, H.-J., HO, C.-W. (2010). Estimating fixed-effect panel stochastic frontier models
by transformation. Journal of Econometrics 157, 286–296.
WANG, H.-J., Schmidt, P, (2002). One-step and Two-Step Estimation of the Effects of
Exogenous Variables on Technical Efficiency Levels. Journal of Productivity Analysis
18 (20), 1296–144.