Using microsimulation model to get things right: a wage equation for Poland.
Preliminary version
September 2007
Not for quotation
Leszek Morawski, Warsaw University1
Michał Myck, DIW - Berlin
Anna Nicińska, Warsaw University
Keywords: wage equation, sample selection bias, return to education
JEL classification: J24, J30
Abstract
We present an application of the Polish microsimulation model SIMPL to estimating the wage
equation on data from the Polish Household Budget Survey for year 2005. And yet, research
in Poland has so far failed to address two key issues in this area. Because all household level
surveys collect information on net incomes some papers analysed net rather than gross wages.
Apart from that all known to us estimations of the wages equation using Polish data have so
far failed to control for selection, which since Heckman’s seminal paper (1979) has been
recognised as a crucial correction in appropriate identification of the parameters of the wage
equation. SIMPL allows us to do both: we can compute gross incomes on the basis of net
incomes information in the data, and use income in out-of-work scenario generated in the
model (together with a set of demographic factors) as an instrument in the selection-corrected
equation. The paper demonstrates the degree of bias induced in the approaches taken in the
past, presents the first set of selection-corrected wage equation parameters and stresses the
importance of the simulated out-of-work incomes as an instrument in controlling for selection.
1
Acknowledgement: Financial support from the EFS by the Polish Ministry of Labor and Social Policy in a
project entitled “Model mikrosymulacyjny jako narzędzie wspierające polityki rynku pracy” is gratefully
acknowlegded. The data availability from Ministry of Economy, Ministry of Finance, Central Statistical Office,
Social Insurance Institution is gratefully appreciated. The usual disclaimer applies.
Introduction
The tradition of estimating microeconomic wage equation dates back to the paper by Mincer
(1974) where both theoretical background and empirical results are provided. Such analyses
were popular in 70’s and 80’s (eg. Willis, 1986). However, this hardly concerns Poland. At
that time Poland was not a free market economy, and wages were established arbitrary by a
planner, thus wages under socialism may be treated as a separated field of economics. On the
other hand, it was also possible that despite central planning wages were determined i a
similar way to free market economies (Rutkowski, 1994). Once the economical system in
Poland transformed, there has not been as much discussion on the determinants of expected
wages neither in the Polish economy nor in other ones as in 1980’s since many countries had
already investigated the issue in details.
In order to properly capture decisions that people make on the labor market one needs to
model not only what happens in the labor force, but also what makes people enter or leave
labor market. For this reason one needs to be able to predict a wage for everybody regardless
whether she or he declares a positive wage. Moreover, the knowledge about potential income
outside work for those who work is necessary. Both conditions may be satisfied if there exists
a microsimulation model enabling estimation of wage equation corrected for sample selection
and simulating incomes from social benefits and assistance if not working. A microsimulation
model for Poland (SIMPL2) has been recently developed in cooperation among researchers
from Warsaw University, IZA-Bonn and DIW-Berlin (see Bargain et al. (2006)) with
financial support by the Polish Ministry of Labour and Social Policy, Ministry of Economy
and Ministry of Finances. The additional advantage of SIMPL is a distinction between gross
wages, income taxes and benefits from tax and benefit policies. This makes estimation of
gross wages possible, thus the impact of wealth distribution within economy is controlled and
income taxation is irrelevant for expected wage rate.
The way in which wages depend on individual characteristics is the matter of both
microeconomic and macroeconomic policies, including inflation, unemployment and labor
force participation issues. The knowledge of the way in which wages in Poland are yielded is
2
The model is currently extended in a project called "Microsimulation model as an instrument support labor
market policies" financed from the EFS by the Polish Ministry of Labour and Social Policy (see www.simpl.pl).
1
fundamental for understanding the processes that are taking place at the moment and its future
consequences. This knowledge seems to be insufficient.
This paper aims to provide results of wage estimation using most adequate methodology that
has not been employed in such analysis in Poland, as far as we know, and to present basic
studies on wages together with most important publications on Poland. First part of this paper
describes briefly tradition and methodology of estimating wage equation. Then studies
concerning Poland in this field are presented. Following chapter describes methodology and
data employed in the research. Than empirical results are provided and interpreted. Final
chapter concludes.
1. Review of the most important studies concerning wages
Basic studies
According to microeconomics, wage is the price of the labor, which is a factor of production,
thus wage is equal to the marginal productivity of labor. Keeping in mind all reservations
connected with the uniqueness of the production factor supplied by human beings, the wage
reflects one’s productivity, which is a function of one’s human capital. There are other factors
affecting level of wages, such as inflation rate, trade unions, and regulations such as a
minimum wage and so on, but they are not captured directly by the human capital theory. It is
said that the level of human capital accumulated is a matter of decision made by a student that
can choose between continuing studies for another year subject to forgone earnings and quit
schooling. It is assumed that all individuals formulate their human capital in the process of
full-time schooling and the cost of each year of schooling related to foregone earnings from
that period is constant over time and equal to one for everyone (Becker and Chiswick, 1966).
The opportunity cost states a budget constraint for a student maximizing her stream of
lifetime earnings conditional of hers human capital. The wage after S years of schooling,
assuming constant interest rate is determined in a following way:
2
K
Costt
 const ; r  const
Waget
Wage1  Wage0  rCost1  Wage0  rKWage0  Wage0 (1  rK )
Wage2  Wage1  rCost1  Wage1  rKWage1  Wage1 (1  rK )  Wage0 (1  rK )(1  rK )
...
WageS  Wage0 (1  rK ) S
ln(WageS )  ln(Wage0 )  ln(1  rK ) S
The above equation was used by Mincer (1974) in his empirical research for the US keeping
the theoretical log-linear relation between earnings and schooling (Heckman and Polachek,
1974). The assumption of the opportunity cost being a solely cost of education can be relaxed
by adding direct costs and cost of student loans (K greater than one) or distracting tax
remissions for students (lowering K) (Chiswick, 1997). Moreover, the way in which human
capital is generated might be broadened by the inclusion of skills developed at work after
finishing formal education. The later paper extends the functional form proposed by human
capital theory by the potential experience measured by the time spent potentially at work
(one’s age above the age of finishing formal education) (Mincer, 1974) according to the
following equation:
ln(Wagei )  Const  1Schoolingi   2 Experiencei  3 Experiencei2   i
The paper discussed in such detail above was the beginning of a stimulating discussion. Most
controversial issue was raised by Heckman in his paper on a sample selection bias as an
omitted variable (1976, 1979). It was claimed that the estimates might be biased, as the
expected wage was estimated upon the selected sample of those only, who declare positive
wage. It is very likely that those who work are equipped with more human capital than those
who fail to find a job due to greater ability that cannot be observed and the selection to the
employment is not random. If so, sample on which study is conducted is not random and the
estimates are inconsistent as a consequence of an omitted variable. Heckman (1979) extends
the wage equation model by the participation equation with an instrumental variable allowing
for sample selection correction. His method is connected with the reservation wage concept
claiming that if one faces wage that is positive but lower than her reservation wage, one is not
going to enter the labor market and her wage will not be observed. The nonrandom selection
3
is revealed by positive statistically significant correlation between the two random terms of
the two equations.
 w *i  xi  i

 y *i  xi1  zi 2   i
 y  1 if y *  0
i
 i
2
s N (0, 1 )  i N (0,  22 )
corr (s ,  s )  
i  1, 2,..., I
The proper instrumental variable partially correlated with participation decision but
insignificant for the wage is crucial for the identification of an omitted variable in the sub
sample of workers and the consistency of whole model (Heckman, 1979). There are not many
variables that affect decision of entering or leaving job without posing any impact on the
wage. However, there is a number of recognized and widely employed instruments such as a
non-labor income of an individual, income of a spouse, household wealth or having children,
the later especially for women (Puhani, 2000a). The new techniques have been developed and
two-step procedure in sample selection models even thought still used (eg. Shonkwiler and
Yen, 1999) may be replaced by more efficient but demanding large sample (Puhani, 2000a)
full-information or limited-information maximum likelihood methods (eg. Jensen et al.,
2001). The maximum likelihood methods are more sensitive to assumption of linear
relationship between random terms in wage and participation equation than two-step
procedure. However sophisticated described methods are, it is still easier to predict expected
wages of those who work (so called two-part model, see: Duan et al. 1983, 1984a, 1984b)
than expected wages for the whole population including those with unobserved wages
(Hartman, 1991). The most recent studies in methodology of dealing with non-random
selection improve self-selection correction estimation (Cunha and Heckman, 2007) while
others develop non-parametric methods (Blundell and Powell, 2004).
The discussion has raised not only methodological issues. Many doubts concern the linearity
of the relation between human capital and earnings. There is still no unanimity on this topic as
there are arguments pro (Heckman and Polachek, 1974; Card and Krueger, 1992) and contra
linearity (Heckman et al. 1996; Trostel, 2005). The other way of accumulation human capital,
4
which is experience gained during work, seems to be related to wages in a much more
complex way as both third and sometimes even fourth power of potential experience are
statistically significant (Lemieux, 2004). This has to do with the imperfection of the measure
employed by Mincer as the proxy for potential experience making many assumptions
criticized in the literature, namely homogeneity of skills (Willis and Rosen, 1979),
differentiation of schooling institutions’ efficiency (Psacharopoulos, 1989), life histories and
probability of being unemployed through a lifetime which in fact differ, thus the costs of
education (Chiswick, 1997) and consequently the rate of return to education may be treated as
a variable changed throughout lifetime (Murphy and Welch, 1992). The question whether
education is a proper metric of human capital has been raised often (eg. Kroch and Sjoblom,
1994). Furthermore, there is a controversy about the way in which schooling should be
measured as the marginal revenue from different levels of education does not need to be
constant over generations (Connelly and Gottschalk, 1995) nor over time for a given cohort
thus more popular metric of education became the highest level of education obtained instead
of years at full-time education (eg. Trostel, 2005).
Studies on Polish wages
The price regulation mechanism responsible for production factors market equilibrium was
not officially in operation in nationalized and centrally planned economy that was present in
Poland since the Second World War till 1989. There are few papers concerning determinants
of wages under central planning which is a question raised by Rutkowski (1994). It is claimed
there that despite the low variation of wages, their determination does not vary much from
those under free market rules. However, this study is not based upon human theory solely as it
distinguishes a number of additional explanatory variables such as value of fixed assets per
employee, firm size, structure of the industry of the firm, ratio of final profit to sales revenue
(Rutkowski, 1994).
In 1989 the trade has been liberalized and free market was introduced successfully in Poland.
Economy was ruled by few regulations; wages could develop freely. The private sector grew
rapidly from 29% of GDP in 1989 to 60% of GDP in 1995 (Keane and Prasad, 2002) which
was the result of an immediate and full liberalization. Transition has been a period of many
deep adjustments in the economy. However interesting there were from the economists’ point
5
of view, there was little tradition (Rutkowski, 1994) and no urgent need to investigate
expected wage determinants.
However, the case of Polish economy transformation has been recognized as relatively
successful and all processes that took place between 1989 and 1996 (when macroeconomic
indicators reached stable level) have been interesting to many scientists. Among studies
concerning Polish transformation, there is some focusing on wage dynamics and structure of
earnings differentiation (eg. Goh and Javorcik, 2005, Newell and Socha, 2005; Puhani,
2000b). Most of them are recent and usually approach the topic from the macroeconomic
perspective. The direct result of a free market introduction was an increase in households’
earnings polarization, which was on average greater in private sector than in public sector by
10% and 20% respectively for small and medium firms (Keane and Prasad, 2002). The
stronger impact on private enterprises is explained by the fact that public firms were less
vulnerable to free market competition, modern management and marketing.
The estimation led by Keane and Prasad (2002) was an extended version of standard Mincer
equation, controlling for levels of education, rural or urban area, sex, industry and experience
in a quadratic form. However, the research was based on cross-sections individual net income
over period 1985-1992 and 1994-1996 without sample selection correction for there was no
proper instrument available. The most recent estimation of Mincerian equation for Poland
explains determination of monthly gross wages of full-time workers of companies employing
9 and more workers controlling for gender, years in formal education and on-the-job training
(Rogut and Roszkowska, 2007). The empirical evidence confirms predictions of human
capital theory noticing that in case of men the work experience has greatest impact on their
wages while in case of women that would be the formal education (Rogut and Roszkowska,
2007).
The analysis of wage inequality by Newell and Socha (2005, 2007) are based on individual
Poles’ net incomes from work. The research investigates hourly wage rates, and states that
their differentiation has not changed much after the transition (Newell and Socha, 1998). It is
iclaimed that the increase in the household earnings differentiation was caused not by the
change of hourly wage rate, but most of all by the drop of labor supplied by a household due
to unemployment (in case of older adults) and decision of continuing education (in case of
younger adults). This way of reasoning has been confirmed by Newell (2001) and is in line
6
with the empirics showing significantly greater revenue from higher education level after
transition than before it (Keane and Prasad, 2002). Moreover, the revenue from education was
greater in private sector than public one in Poland in 1995 (Socha and Weisberg, 2002). The
issue of revenue from education is still investigated and there are numerous cross-national
studies aiming to compare cultural and national differences between educational systems (eg.
Trostel, 2005). One of them estimates extended Mincer equation for male full-time full year
workers and self-employed aged 30-55 coming from a number of countries, among them also
from Poland, based on data on annual earnings gross of taxes and employee’s social insurance
contribution (Hartog et al., 2004). The definition of the correct measure of education is crucial
for that comparative research. Note also, that the sample covers very limited part of
population so it is not random which means that results shall not be generalized over whole
society.
The expected wage determination is a field where discrimination might be investigated. Many
concepts have been developed in order to explain reasons for which gender is important for
the wages and the gender pay gap has been widely examined (eg. Plasman and Sissoko, 2004)
also for Poland (Grajek, 2001). Empirical studies on net incomes of full-time employees show
that there was a decline in female employment outcomes while the average gender gap
remained stable at the 22-23 per cent level between 1993 and 1998 in Poland (Adamchik and
Bedi, 2003). The paper by Latuszyński and Woźny (2006) applies Oaxacia decomposition
method (1973) in order to find determinants of hourly net wages of employees working in 221
private firms in Poland. The region, actual experience (measured in years at an enterprise and
in the industry of the enterprise), level of education and number of children are controlled for.
The study focuses solely on the decomposition, so it concerns not what has been explained by
qualifications, experience, industry and regional differentiation, but just the opposite: on what
can not be explained by the observed individual characteristics other than gender. According
to Latuszyński and Woźny (2006) the main reason for lower average female wages is the
structure of labor supply, where women usually work in low skills occupations whereas man
in high skills occupations and the gender gap in earnings vanishes in marketing, research and
development.
Another question raised in the literature is relation between unemployment and wages. Such
analysis for Poland must take into account regional differences in unemployment rate and
labor demand structure and that is the case of estimation of Polish wage curve for period
7
1991-1996 (Duffy and Walsh, 2001). According to the non-accelerating inflation rate of
unemployment concept (Stiglitz, 1997), such unemployment rate would not affect level of
wages. This macroeconomic perspective involves additional agents to the standard
microeconomic framework such as a central bank with its inflation policy and trade unions
with their wages rigidity aiming to verify whether the rate of unemployment reached the
natural level neutral for inflation or its nature is structural, difficult to remove and unfavorable
for the economy as a whole. Results of the Granger causality test suggest that Polish wage
level depended on the unemployment rate, thus unemployment in Poland between 1993 and
2004 was of the later kind (Gaweł, 2006). However macroeconomic analysis of inflation,
wages and unemployment are common (eg. Commander and Coricelli, 1992; Welfe and
Majsterek, 2002), the functional form of the estimated wage equation is not derived directly
from the human capital theory and does not tell much about the individual characteristics
affecting marginal productivity of labor.
The research presented in the following chapters is a unique one in the light of thus far
achievements of Polish labor market analysis. None of them covers such wide sample of parttime and full-time both gender individuals employed by all types of companies with their
gross incomes nor proper instrumental variable enabling sample selection correction.
2. Methodology and the data
According to empirical studies concerning selection to the labor market, decision whether to
work or not is logically and statistically significantly correlated with the level of expected
earnings from that work. For this reason Heckman two-step procedure is a proper method of
dealing with the estimators’ bias. Linear estimators are also provided in order to make
possible adequate comparisons. The dependent variable is a logarithm of monthly wage rate
in gross and net terms.
 w *i  xi  i

 y *i  xi1  zi 2   i
 y  1 if y *  0
i
 i
s N (0, 12 )  i N (0,  22 )
corr (s ,  s )  
i  1, 2,..., I
8
The instrumental variables used for model identification are: family disposable income if not
working, other household members’ equivalized income and whether a household contains
more than one family. There are multifamily households and wealth of household members
that does not belong to a family may affect participation decision within this family. In order
to distinguish between no other families in household income due to lack of income and due
to lack of other families, we control whether a household is a one or more family unit. The
disposable income of family if not working is generated by SIMPL as a weighted sum of all
benefits and social assistance that a family is entitled to, judging from its financial and
demographical situation. It is expected that the greater the non-labor income, the lower
probability of entering labor market. The disposable income if not working is calculated at the
family level, as a spouse income affects participation decision. Moreover, eligibility to some
benefits depends on number of not working partners, thus non-labor income is generated for
all possible scenarios (both not working, one is working, both are working) and the value of
instruments consistent with observation is chosen for given family. The non-labor income for
one family households captures all benefits that whole households are entitled to, such as for
instance housing benefit. Other household’s memebers disposable income if a consireded
family is not working might be more important for two generation families, where
grandparents’ income shall also be taken into account while making labor market
participation decision that is why number of families in one household is also included. All
these instrumental variables are assumed to be uncorrelated with the individual marginal
productivity.
The dataset comes from the Household Budget Survey (BBGD) 2005 provided by the Central
Statistical Office (GUS). The gross wages are generated by SIMPL according to the Polish
income taxation patterns from 2005. The grossed up wages contain income tax, employee’s
social and health insurance contributions (Morawski, 2007). It is assumed that all part time
workers are exactly half-time workers. The sample contains persons that may be treated as a
part of labor force, so children, pensioners and persons unable to work due to health
conditions are not taken into account. The category of self-employed is also excluded from
the sample as their income from employment cannot be distinguished from their profits. That
is why their earnings shall not be treated as wages. The sample is composed of individuals
aged 18-59 who are neither retired nor unable to work for health reasons nor self-employed.
However, all disabled persons that are able to work are included in the sample, regardless
from their disability level.
9
The shape of employees’ gross wage distribution presented in graph 1 is typical, similar to
log-normal, which is in line with a theoretical assumption of the econometric model. The
income from self-employment does follow this pattern, which is another reason for which
self-employees are not taken into account. However, information form Ministry of Finance
reveal that the grossing up does not match official data for highest centiles. This makes our
estimation biased for individuals with highest wages.
.0003
.0002
0
.0001
Density
.0004
.0005
Graph 1. Distribution of employees’ gross wage in Poland in 2005
0
5000
10000
d_ipermemp
15000
20000
Source: Authors’ own calculation based upon BBGD 2005.
The sample contains 49 593 individuals, among which 26 656 are female, which states
53.75% of the labor force. Education structure within genders is presented in table 1. There
are six levels of completed education and three age groups distinguished:
-
low, aged 18-26
-
medium, aged 27-38
-
high, aged 39-59.
The number of women with tertiary level of education exceeds the number of men with the
same education level by 16.44 percentage points in the 27-38 age group, while in other
cohorts there are fewer women with higher education than man on average. The fraction of
persons without education or those who have finished primary school is greater for the oldest
10
age group and equals 13% in whole population. The gymnasium graduates are
underrepresented due to the innovation in schooling system that was introduced in 1999 and it
concerns only individuals younger than 22. In general, the majority of whole population has
completed secondary technical education and here share of all cohorts and both genders is
symmetric. The second most numerous group are vocational education graduates, but here
domination of elderly male labor force is very strong as in highest age group almost half of
men declares this education level. This category becomes less numerous as age decreases.
Table 1. Education structure of Polish labor force for genders within age groups in 2005.
Age group
18-26
27-38
39-59
General
Male Female Male Female Male Female
%
%
%
%
%
%
%
Completed education level:
- none or primary
- gymnasium
- vocational
- secondary academic
- secondary technical
- post-secondary professional
- higher
10.38
16.05
24.19
17.16
24.40
1.71
6.11
6.95 9.82
13.94 0.00
14.01 43.17
29.61 4.66
21.28 23.76
3.11 1.68
11.11 16.90
9.02 12.62
0.03 0.01
29.62 49.36
9.62 2.67
24.20 24.35
4.17 1.10
33.34 9.88
15.85
0.03
29.50
9.87
26.53
4.77
13.45
13.27
2.90
24.32
11.80
31.98
4.41
11.32
Source: Authors’ own calculation based upon BBGD 2005.
The sample consists mostly of employees, who state 62% of whole population examined. In
the highest age group 80% of men and 67% of women are employed and similar pattern of
male majority in employment holds for all age groups. This is the most popular category in all
age groups for both genders, however in case of youngest labor force members, it is less
numerous as more individuals seek for work due to the lack of experience, fresh start at the
labor market and greater mobility. The group of unoccupied is greatest in youngest age group
and levels 44% in case of men and 55% for women. Traditionally, there are more women than
men unoccupied for the reason of taking care of house or children, and that is why women are
more often inactive as the fractions of non-participants for other than family reasons are
similar for both genders.
11
Table 2. Employment status structure of Polish labor force for genders within age
groups in 2005.
Age group
18-26
27-38
39-59
General
Male Female Male Female Male Female
%
%
%
%
%
%
%
Current employment status:
- employee
- seeking work and available
to start work
- waiting to start job already
obtained
- unoccupied – takes care of
house or family
- unoccupied – other reason
38.68
30.52 85.23
64.60 79.21
66.67
61.66
16.15
13.86 10.91
11.95 11.40
9.47
12.02
0.93
0.54
0.56
0.59
0.41
0.34
0.53
0.13
44.12
9.12
45.96
0.43
2.87
20.22
2.64
0.44
8.54
12.95
10.57
7.63
18.16
Source: Authors’ own calculation based upon BBGD 2005.
Table 3. Family situation of individuals in Polish labor force within age groups in 2005.
18-26
Age group
27-38
39-59
General
%
41.48
%
18.54
%
11.89
%
22.42
4.19
26.10
18.40
6.75
6.40
28.13
32.94
10.24
27.92
27.80
21.57
7.67
15.01
27.39
23.77
8.11
3.08
3.75
3.16
3.30
Family composition:
- singles without children
- individuals in couples
without children
- individuals with 1 child
- individuals with 2 children
- individuals with 3 children
- individuals with 4 and more
children
Note: Child is a person aged less than 18 or full time student aged less than 26 and not married.
Source: Authors’ own calculation based upon BBGD 2005.
The sample consists of 11 118 singles without kids, 7 446 married individuals without
children and remaining 31 029 observations are persons with al least one child. Among
youngest age group persons without children state 45%. In case of the highest age group,
almost 40% of all individuals do not have a dependent child, but among them are usually
married persons whose children are aged more than 18. Note that child is defined as a not
married person younger than 18 years old or full time student aged less than 26. The most
popular family composition is one child family (27%) and two children family (24%).
12
3. Results and discussion
The estimated wage equations employ a set of explanatory variables controlling for the
highest level of formal education obtained in terms of dummies and age in a cubic form as a
proxy of potential experience. The voyevoidships are included as well as town size, which
captures local differences, such as a probability of being unemployed. Individuals at the same
age coming from regions with different unemployment rates have different work experience,
so the geographic measures improve efficiency of age as an instrumental variable. Also
disability level is important for the wage received. The age and number of children are
significant as far as marginal productivity is concerned, especially if there is a young child
that needs care. Marital status is also taken into account as it captures new roles that
individuals start to play with starting a family that cannot be explained by the fact of having
children.
The results of estimations are provided in following tables. Table 4 presents estimates of net
wage determinants using ordinary least squares linear regression and two step Heckman
model with sample selection. The outliers defined as wages greater than 99.5 centil are
excluded from estimations. Wages lower than first centil are replaced with the first cetile’s
value. The linear regression is based upon 26 872 observations and employs 40 explanatory
variables, which is not much as for such big sample, thus all statistics have relatively high
degree of freedom. All of them are statistically significant at least at 5% significance level
except from the dummies for second, third, fourth and young child. The fit of the model is
high, as it reaches almost 30%, which confirms together with the F statistic that the set of
explanatory variables is statistically significant. Moreover, the high number of independent
variables raises the fit of the model.
As far as the linear regression of net monthly wages, the most important variable affecting
wage rate in a positive way is education. In comparison to person with primary or none
education, wage rate of an employee with high education grows by 72%, while wage of an
employee with post-secondary degree by 42%. Secondary education brings similar benefit
regardless whether one has an academic or technical nature and raises net wage growth by
34%. Linear regression is in line with the theoretical relation between wage that is positive
but diminishing with age. In comparison to inhabitants of biggest towns, other individuals
earn less and this impact is the stronger the smaller the town is. Similar pattern is observed for
13
persons living in another than capital voyevoidship. This reflects general local economy
condition of regions with heterogeneity within them controlled by the town size. Disability
may affect productivity in a negative way, and the more severe disability is the greater
negative impact on net wage it has. However, negative coefficients on disability levels might
also reflect discrimination. Women’s earnings grow slower than men by 22% and married
people’s wages grow faster than singles by 10%.
The estimates described above are inconsistent, as the t-Student test for correlation between
participation and wage equations states that the hypothesis of a lack of such correlation is
rejected with probability equal to 1. The correlation is high (almost 83%) and positive which
confirms theoretical expectations that unobserved characteristics affect both wage and
participation decision is a positive way. The statistical significance of rho estimate and of
coefficients on instrumental variables suggests that they state a proper way of identification of
the Heckman two equation model.
According to results corrected for sample selection bias, the impact on net wage of education
is stronger than predicted by simple linear regression. The estimate on higher education is
higher now by 23 percentage points and equals 0.95. The second strongest factor increasing
net earnings is post-secondary professional education with coefficient 0.60. Heckman
selection estimation reveals that secondary technical education might seem slightly more
beneficial than the secondary academic as far as net wage is concerned, as coefficient on first
one is 0.48 while the other one is 0.43.
The remaining levels of education do not bring dramatic change to net wage and the
gymnasium seems to lower expected net wage. One shall remember that gymnasium is
relatively new element of Polish schooling system thus persons declaring it are usually very
young. Gymnasium does not form human capital that affects directly one productivity by
developing skills and knowledge necessary for further education but irrelevant for employers.
If education is not continued after graduating from gymnasium, this schooling does not make
any difference. Moreover, school is relatively costly, as full time education prevents from
gaining work experience without bringing any benefit. For these reasons finishing education
after gymnasium does not make much sense.
14
Table 4. Estimators of log net wage determinants with and without sample selection
correction.
Heckman two-step
Wage
Participation
constant
higher education
post-secondary professional
secondary technical
secondary academic
vocational education
gymnasium
age
age squared
age cubed/1000
town size 200,000 - 499,999
town size100,000 - 199,999
town size 20,000 - 99,999
town up to 19,999
village
one child
two children
three children
four children
five or more children
child aged less than 7
dolnoslaskie
kujawsko-pomorskie
lubelskie
lubuskie
lodzkie
malopolskie
opolskie
podkarpackie
podlaskie
pomorskie
slaskie
swietokrzyskie
warminsko-mazurskie
wielkopolskie
zachodniopomorskie
married
significant disability
medium disability
low disability
female
3.41190**
.94838**
.59843**
.47845**
.42964**
.21859**
-.31462**
.19838**
-.00381**
.02367**
-.07557**
-.12278**
-.16026**
-.18773**
-.18665**
.02875**
.02649*
-.03426*
-.07024*
-.14517**
.02319*
-.15934**
-.22800**
-.21592**
-.16044**
-.15486**
-.13922**
-.06674**
-.20950**
-.20587**
-.11110**
-.12516**
-.25459**
-.18324**
-.11853**
-.12258**
.22611**
-.55326**
-.28772**
-.26827**
-.32184**
family non-labor income
household income
multifamily household
Number of observations
Rho
Adjusted R2
Lambda
-3.18703**
1.2944**
.89276**
.67432**
.45555**
.33893**
-.28871**
.18365**
-.00201**
-.00320
-.01148
-.05986
-.10997**
-.14502**
-.09135**
-.04408*
-.13686**
-.24090**
-.30430**
-.41736**
-.15410**
-.24587**
-.20184**
-.24592**
-.08441
-.07132*
-.11674**
-.11290*
-.26456**
-.19147**
-.16519**
-.21922**
-.32054**
-.20473**
.00484
-.18568**
.74963**
-.61502**
-.19442**
-.05364
-.56467**
OLS
Wage
5.08180**
.72574**
.42417**
.34572**
.34630**
.14136**
-.12182
.11047**
-.00212**
.01391**
-.07798**
-.11841**
-.14585**
-.16979**
-.17727**
.04923**
.06728**
.02458
.00229
-.04891
.04736**
-.11763**
-.19441**
-.17561**
-.14917**
-.14880**
-.12219**
-.04663*
-.16943**
-.17590**
-.08283**
-.08977**
-.20511**
-.15081**
-.11946**
-.09342**
.10164**
-.41902**
-.23823**
-.25358**
-.22160**
-.00014**
-.00006**
-.08916**
26872
.829**
39300
26872
.302
.44976
Note: ** statistically significant at 1% significance level; * statistically significant at 5% significance level.
Source: Authors’ own calculation based upon BBGD 2005.
15
Potential experience increases with age, however capacity of skills and knowledge adaptation
is limited and starting from certain age, one’s productivity does not increase despite
cumulated time spent at work is growing. In some cases this might even cause a drop in
productivity, especially in occupations where fresh attitude and new technologies are crucial.
The estimation confirms that marginal productivity reflected by net wage grows at pace 15%
per year at the beginning of career then this rate is diminishing. The magnitude of potential
experience was underestimated in the linear regression. Results presented in table 4 are in line
with other estimations stating that third power of age is statistically significant as far as wage
rates are concerned.
The last factor increasing wages is marital status, which is also underestimated in linear
regression as it reaches 0.10 while under Heckman 0.23 respectively. The fact of being
married lowers one’s mobility, as such family situation affects flexibility in a negative way.
Similar reasoning explains positive coefficients on having a young child, but the later
mechanism is relatively weaker than pure fact of being married. Employers’ perception of
such individuals is favorable, as now they are perceived as more reliable, loyal and more
stable. That makes employers more willing to invest more in trainings for this group of
employees. In the following estimations the distinction between marital status of women and
men is made.
The application of Heckman’s selection correction allows identification of factors affecting
decision whether to work or not. The estimates provided in table 5 are calculated on the basis
of gross monthly wage rates. The higher family non-labor income prevents persons living in
one family household from entering labor market as there are lower financial incentives to
earn additional money. Similar mechanism holds for households with more than 1 family.
Severely disabled persons are substantially less likely to work than healthy individuals
whereas medium and low disability level does not affect participation as the coefficients are
statistically insignificant and low. The fact of being married facilitates work, but having
children, especially more than 2 or at least one aged less than 7, prevents from working. That
is because children demand care and it is often more expensive to hire a babysitter than take
care of home alone. Probability of being employed is the lower, the smaller the town is. Due
to migration from villages to towns, the fact of living at the countryside does not affect
participation decision in a way it does in small towns. The most unwilling to enter
16
Table 5. Estimators of log gross wage determinants with and without sample selection
correction.
Heckman two-step
Wage
Participation
constant
higher education
post-secondary professional
secondary technical
secondary academic
vocational education
gymnasium
age
age squared
age cubed/1000
town size 200,000 - 499,999
town size100,000 - 199,999
town size 20,000 - 99,999
town up to 19,999
village
one child
two children
three children
four children
five or more children
child aged less than 7
dolnoslaskie
kujawsko-pomorskie
lubelskie
lubuskie
lodzkie
malopolskie
opolskie
podkarpackie
podlaskie
pomorskie
slaskie
swietokrzyskie
warminsko-mazurskie
wielkopolskie
zachodniopomorskie
married
significant disability
medium disability
low disability
female
3.30089**
1.05668**
.67457**
.54096**
.48000**
.24928**
-.35432**
.22262**
-.00426**
.02604**
-.07913**
-.12949**
-.17258**
-.20341**
-.20260**
.01774
.01390
-.05569**
-.09675**
-.19092**
.01644
-.17716**
-.24942**
-.23709**
-.17307**
-.16654**
-.15098**
-.07392**
-.22983**
-.22369**
-.12584**
-.13989**
-.28189**
-.19939**
-.12648**
-.13472**
.25791**
-.61535**
-.33363**
-.31153**
-.35673**
family non-labor income
household income
multifamily household
Number of observations
Rho
Adjusted R2
Lambda
-3.18703**
1.29436**
.89276**
.67432**
.45554**
.33893**
-.28871**
.18365**
-.00202**
-.00320
-.01148
-.05986
-.10997**
-.14502**
-.09134**
-.04408*
-.13686**
-.24090**
-.30430**
-.41735**
-.15410**
-.24587**
-.20185**
-.24593**
-.08441
-.07132*
-.11675**
-.11290*
-.26456**
-.19147**
-.16519**
-.21922**
-.32054**
-.20473**
.00485
-.18568**
.74963**
-.61502**
-.19442**
-.05364
-.56467**
OLS
Wage
5.25367**
.79633**
.47081**
.38574**
.38255**
.15897
-.12886**
.11982**
-.00228**
.01462**
-.08194**
-.12437**
-.15573**
-.18243**
-.19163**
.04168**
.06160
.01311
-.01192
-.07836**
.04471**
-.12838**
-.21014**
-.18996**
-.15989**
-.15945**
-.13108**
-.05041*
-.18298**
-.18865**
-.09173**
-.09850**
-.22402**
-.16147**
-.12757**
-.10061**
.11235**
-.45837**
-.27576**
-.29436**
-.23950**
-.00014**
-.00006**
-.08916**
26872
.850**
39300
26872
.309
.50606
Note: ** statistically significant at 1% significance level;* statistically significant at 5% significance level.
Source: Authors’ own calculation based upon BBGD 2005.
17
labor
are
inhabitants
of
Swietokrzyskie,
Podkarpackie
and
Kujawsko-Pomorskie
voyevoidships while the most willing are in Mazowieckie, Lubuskie and Wielkopolskie.
The participation and gross wage equations are strongly positively correlated and the
hypothesis of no correlation between them is again rejected with probability 1. Similarly to
the net wage regressions, the linear estimates are underestimated due to the sample selection
bias. As far as the gross wage rate is concerned, the impact of all explanatory variables is not
interfered by the progressive taxation and health insurance. That is why the estimates from
Heckman two equation model presented in table 5 reflect impact of explanatory variables on
the expected gross wage in an adequate way. However, there are only minor differences
between results for net and gross specifications.
The coefficients of education levels are underestimated in case of net wage regressions, only
gymnasium and vocational training estimates do not differ between the two alternative
dependant variables. The revenue from higher education reaches 1.06, while contribution to
gross wage from post secondary professional schooling equals 0.95 and the difference in
estimates’ values is statistically significant. The positive difference between benefits coming
from secondary technical than academic education is slightly greater than in case of net
wages. Higher revenues from education for gross wages are in line with the progressive tax
system, as better educated persons pay higher taxes as their wages are greater due to
productivity driven by high qualifications.
The potential experience affects the gross wage rate in a slightly different way than net wages,
however dynamics remain similar, and the starting point is lower and equals 0.22 at the
beginning of working life. All regions other than Warsaw value labor less, especially in
smaller towns. The lowest gross wage rates in comparison to capitol voyevoidship are
observed in Swietokrzyskie and Kujawsko-pomorskie, as the unemployment rates there are
relatively high. The smallest gap in gross wages between Mazowieckie is present in Opolskie,
but if we take into account the fact that in that region there are usually towns smaller than
200000 inhabitants the difference between Warsaw gross wage rates becomes more
significant.
18
Table 6. Estimators of log gross wage determinants with sample selection correction in
genders.
Men
Wage
constant
higher education
post-secondary professional
secondary technical
secondary academic
vocational education
gymnasium
age
age squared
age cubed/1000
town size 200,000 - 499,999
town size100,000 - 199,999
town size 20,000 - 99,999
town up to 19,999
village
one child
two children
three children
four children
five or more children
child aged less than 7
dolnoslaskie
kujawsko-pomorskie
lubelskie
lubuskie
lodzkie
malopolskie
opolskie
podkarpackie
podlaskie
pomorskie
slaskie
swietokrzyskie
warminsko-mazurskie
wielkopolskie
zachodniopomorskie
married
significant disability
medium disability
low disability
3.28402**
.88628**
.48764**
.47242**
.39563**
.23216**
-.65947**
.23206**
-.00499**
.03458**
-.03270
-.10048**
-.12033**
-.16935**
-.16196**
.04899**
.07023**
.04233
.01890
-.03752
.03184*
-.11540**
-.23402**
-.22843**
-.14917**
-.15515**
-.11994**
-.05884
-.20327**
-.24948**
-.09260**
-.05664**
-.27825**
-.17200**
-.09056**
-.08693**
.52159**
-.61843**
-.38306**
-.40913**
family non-labor income
household income
multifamily household
Number of observations
Rho
Lambda
Participation
-4.9945**
.83797**
.48166**
.47751**
.16874**
.29438**
-.48515**
.35304**
-.00742**
.04665**
.03575
.01256
-.03612
-.09137*
.05663
-.07892**
-.19343*
-.10751
-.11642
.18251
.21758**
-.18483**
-.17090**
-.23812**
-.04265
-.07745
-.12600*
-.10008
-.23525**
-.27208**
-.06144
-.07320
-.29604**
-.19469**
.09613
-.11136
1.22796**
-.46451*
-.19461*
-.15317
Wage
Women
Participation
3.40200**
1.0465**
.66293**
.53263**
.48953**
.18359**
.03087
.21183**
-.00406**
.02523**
-.11862**
-.14412**
-.21481**
-.23051**
-.22907**
-.03852**
-.05064**
-.14906**
-.19559**
-.30627**
-.03259*
-.20910**
-.24657**
-.22364**
-.18017**
-.17464**
-.16206**
-.05541
-.23102**
-.18692**
-.12819**
-.19906**
-.24430**
-.21302**
-.15258**
-.15913**
.08738**
-.43227**
-.24489**
-.20279**
-.00005**
-.00008**
-.06542*
18842
.850**
.49957
14305
-3.52312**
1.48533**
1.03010**
.80033**
.57413**
.32787**
-.03022
.16765**
-.00102
-.01608
-.04162
-.11021*
-.17365**
-.19391**
-.19685**
-.14951**
-.21844**
-.39500**
-.48759**
-.79758**
-.36704**
-.28584**
-.22851**
-.27236**
-.11516
-.09099*
-.09205*
-.09038
-.29775**
-.15624*
-.21934**
-.29751**
-.29369**
-.19186**
-.06508
-.22170**
.50658**
-.64288**
-.23958*
.01784
-.00018**
.00001
-.09501**
12567
.660**
.34185
20458
Note: ** statistically significant at 1% significance level; * statistically significant at 5% significance level.
Source: Authors’ own calculation based upon BBGD 2005.
19
The situation of women in terms of gross wages is slightly worse than in net wage, as the
coefficient on gender for gross and net wage equals respectively 0.36 and 0.32 in favor for
men. The fact of being married controlling for children remains at the similar level for gross
and net wage. Also estimates on number of children in family and the presence of a child
younger than 7 years old are not affected by the change in dependent variable because
personal tax and health insurance system does not differ much for different number of
children. This does not hold for disability levels, as the net wage estimates on them are
underestimated. A person with severe disability is paid less and his or hers gross wage is
lower by 61 percentage points in comparison to not disabled. This negative impact is
weakened with the less significant disability, but even persons with low level receive gross
wages lower by 41 percentage points than others’. It is not trivial to distinguish whether these
differences occur due to actual difference in productivity or due to discrimination. Such
decomposition may be conducted as far as female labor force is concerned. In order to
distinguish more precisely where does the difference between genders gross wage comes
from, two separated regressions are made. The results are presented in table 6.
The correlation between participation and expected gross wage is positive and statistically
significant for both genders, however in case of women is greater by 19 percentage points
than in case of men, for whom it equals 85%. The strongest impact on decision whether to
work comes from formal qualifications and the greater schooling one has completed, the
greater incentives to work. Formal education affects male’s work decision weaker than female
especially with high education levels, because in case of man the experience is substantially
more important than for women. That is probably due to the labor force division in so called
male and female occupations. The jobs traditionally taken by men demand usually more
responsibility and formal qualifications are relatively less important than experience. The
coefficient on age, which is a proxy for potential experience, is substantially greater for men
than women.
The most evident difference between genders is the traditional role in growing children up.
Women are usually expected to provide care, while men salary. The fact of having child aged
less than 7 prevents women from working while facilitates men’s labor supply. Such behavior
might be Pareto optimal if female expected hourly wage rate is lower than male and
professional child care is more expensive than potential net earnings of a carer. Moreover,
20
once a family is eligible for child care suplement, decision of taking a job is connected with a
loss of the benefit. For women each child makes her less likely to work not only for the child
care reason, but also due to interruptions to work experience. The fact of being married makes
women more prone to work and impact of marriage is twice as big in case of man. In fact,
marital status is even more important for participation decision for men than higher education
completed.
The expected gross wage for women with higher education level grows faster by 16
percentage points than for man with the same characteristics. The same pattern of greater
female than male revenues from education holds for all its levels, except from vocational as
the group of occupations where vocational training is needed are usually perceived as better
performed by men. These mechanisms would explain relatively great number of highly
educated women. The age reflecting potential experience does not favor any gender, as the
coefficient on age variables are similar for men and women. The dynamics are similar, as the
second and third power of age have similar impact on gross wages. One shall remember that
despite more experienced women are more likely to earn more than men; they are also less
likely to work. Disability affects men stronger than women for all disability levels, which also
may be credited to male occupations usually demanding specific skills.
The favorable revenues from qualifications and experience of women remains at the same
level regardless from their marital status as long as they do not have children. The coefficient
on being married for women equals 0.09 whereas for men reaches 0.52. This major difference
results from different expectations towards married man and women. The later one is
expected to give a birth while the former one to work hard for his family. That may result in a
different perception of productivity according to gender with the change of marital status. All
coefficients on number of children and having a young child are negative for women while for
men are positive.
However, the constant in wage equation for women is actually greater than for men. If we
neglect wage difference coming from potential experience the expected gross monthly log
gross wage of a single women without children and no education living in Warsaw is
estimated at the 3.40 level while for men with the same remaining characteristics it reaches
3.28.. The place of living does matter more for women than men, due to their lower mobility,
as they are expected to stay with family once father or husband may work outside his place of
21
living. The other explanation is that discrimination of women is greater in smaller towns and
villages than in cities. The same disproportion in magnitude of place of living holds as far as
regions are concerned as for almost all voyevoidships except from two, negative coefficients
are lower for women than men.
Conclusions
The estimations described in this paper confirm that the selection to work is not random and
wage determinants obtained by ordinary least squares method are inconsistent. The
application of Heckman two-step procedure eliminates this bias as estimates are corrected for
the sample selection treated as an omitted variable. The instrumental variables employed in
identification of two-equation models are family non-labor income and income of other
household members controlling whether a household consists of one or more families.
Positive and statistically significant estimate on correlation between wage and participation
equation for all specifications confirm that these instruments are correct.
Results obtained in Heckman model are in line with theory and also with other empirical
results in the field. Positive returns to education grow with its level. The gymnasium is an
exception as it includes also cohort effect, as it is observed only for persons aged less than 22
as it has been introduced in 1999. Potential experience behaves according to theory and brings
positive but diminishing marginal return to productivity. Married persons and public sector
workers earn on average more than private sector while disabled individuals earn less
according to their disability level. The family situation affects productivity in different way
for different genders. The number of children makes women less willing to work while fathers
are more likely to work than childless men. Children make men more productive, which is
true for women only for her first and second child. Controlling for family composition, female
wages are lower than those of men. The regression of gross wage determinants ran separately
for men and women reveal that women benefit more than men from formal education, which
is especially strong for its high levels.
The estimates on explanatory variables corrected for sample selection reveal that returns to
education, especially for it high levels, were underestimated in linear models. Also the impact
of disability on expected earnings is stronger than predicted using ordinary least squares
models. The discrimination of women on labor market is observed in lower wages on average
22
and corrected estimates suggest that gender gap is greater if we take into account whole
population, not only individuals whose wages are observed.
Another conclusion derived from the research is that distinction between gross and net wages
is important as results obtained for the two alternative specifications of explanatory variables
are significantly different.
23
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