Modeling Labor Supply in the Netherlands:
The Effect of Tax Credits for Employees as a First Application
Henk-Wim de Boer
Ministry of Social Affairs and Employment
The Netherlands
Email: [email protected]
Tel: 0031-703335170
Paper presented at the 3rd General Conference of the International Microsimulation
Association, Stockholm, Sweden, June 8th to 10th, 2011
May 2011
*********** PRELIMINARY RESULTS: PLEASE DO NOT QUOTE ***************
Abstract
This paper presents a recently developed Dutch labor supply model, with labor tax credits for
employees as a first application. In the Netherlands, the tax benefit model MICROS is used almost
on a daily basis to support the decision making process of policy makers. Until now, the analysis
with MICROS has been static without behavioral responses of individuals. The current model is
extended by modelling labour supply effects in a discrete choice framework (Van Soest 1995). This
paper starts with a presentation of this model. The labour supply model estimates wage elasticities
for men and women of approximately 0.1 and 0.2% respectively. These elasticities are surprisingly
low compared to findings in other studies. Next, this paper focuses on the effect of tax credits for
employers in the Netherlands as a first application.
1. Introduction
In the Netherlands, the Ministry of Social Affairs and Employment uses the micro simulation model
MICROS almost on a daily basis to support the decision making process of policy makers. MICROS
is a tax benefit model which has been developed in the late eighties by the Ministry of Social Affairs
and Employment. The model is primarily used for simulating income effects of proposed policy
measures. In this way, policy makers get a better understanding of the effects of their (proposed)
policy measures for different types of households. Until now, the analysis with MICROS has been
static without behavioral responses of individuals. Many policy measures, however, have labor
supply effects as well. An increase in the labor tax credit, for instance, results in some employees
adjusting their labor supply. Obviously, policy makers are interested in these labor supply effects
as well 1. For that reason the current model MICROS is extended by modelling labour supply effects
in a discrete choice framework (Van Soest 1995).
The tax benefit model MICROS uses data from the Dutch survey WOON (In Dutch: Woononderzoek
Nederland) in 2005. WOON is a representative survey for the Dutch population with administrative
data from the Dutch Tax Administration. MICROS adjusts the population by static weighting on a
yearly basis. Static weighting means that decomposition of households, sources of income and
living situation of the individual cases in the survey remains unchanged. Only income of the
individuals is adjusted on a yearly basis. In this way, one can monitor the development of
purchasing power of households as a result of changes in regulations, wages, taxes, social security
premiums and prices. The structure of the population, such as the number of households,
unemployed and employees, is adjusted by changing the weight factors of individual cases.
The main goal of this study is to extend the simulation model MICROS with a labor supply module.
It is important to note that the labor supply model is restricted to direct labor supply effects of
individuals only. In reality, an increase in labor supply may contribute to wage restraints which in
turn result in a higher demand for labor and this effect is not taken into account. Moreover, the
demand side of the labor market is excluded as well. In order to take these effects into account, a
general equilibrium model is needed which is beyond the scope of this study. As a first application
of the recently developed labor supply model, the labor supply effects of tax credits for employees
are estimated. Employees in the Netherlands receive a labor tax credit AK (In Dutch:
Arbeidskorting) which depends on their income. In addition, secondary earners and sole parents,
who combine work with the care of children, receive an extra income dependent tax credit IACK (In
Dutch: Inkomensafhankelijke Combinatiekorting).
The structure of this paper is as follows. Section 2 provides background information on labour force
participation in the Netherlands and results from other scientific studies. Section 3 presents the
underlying theory of the labour supply model. In section 4, a description of the data is given and
section 5 contains the first preliminary results. The labour supply effects of tax credits for
employees are shown in section 6. Section 7 concludes.
1
The Netherlands Bureau for Economic Policy Analysis (CPB) does take behavioral responses into account in
their analysis. By using a general equilibrium model the effects of several policy measures can be simulated.
2
2. Background
Labour force participation in the Netherlands is high compared to other OECD countries. In 2005,
the labour force participation rate for men was 84.1% and for women 69.0%. The OECD averages
are 83.2 and 61.9 respectively 2. However, the majority (70%) of these women work part-time 3.
On average men worked 37.1 hours per week whereas women worked 24.2 hours per week in
2005. From a policy’s perspective, the latter group is particularly interesting. For these part-timers
there is still room to increase their labour supply and this group is relatively elastic with respect to
income.
Many studies on labor supply models use the discrete choice framework developed by Van Soest
(1995). He uses a discrete choice model to estimate a basic labor supply model, in which
individuals choose their working hours from a finite set of alternatives. Van Soest uses cross
section data for Dutch couples from 1987. This basic model produces median elasticities for an
average family of 0.15 and 1.03 for men and women respectively. Van Soest shows that the basic
labor supply model strongly overpredicts the number of part-time jobs. In order to correct for this,
alternative specific dummies for small part-time jobs are added. As a result, the median elasticities
drop to 0.10 and 0.52 for men and women respectively. A later study by Van Soest (2000) with
data from 1995 estimates a higher elasticity (0.7) for cohabiting/married women in the
Netherlands. Nelissen et al (2005) use panel data from 1990 to 2001 and estimate an elasticity of
0.30-0.40 for women (with a partner) in the Netherlands.
Evers et al (2008) apply a meta analysis in order to estimate labor supply elasticities in the
Netherlands. The analysis is based on 32 scientific studies, 6 of which refer to the Netherlands. The
authors conclude that labor supply elasticities are 0.10-0.20 for men and 0.50 for women. The
studies above show that women’s labor supply is more elastic and that they respond more heavily
to financial incentives than men. A possible explanation is the relatively low participation rate for
women.
As stated earlier, several recent studies on labor supply use the discrete choice framework by Van
Soest (1995). Some of these studies use cross section data meaning that the labor supply decision
is not intertemporal. In reality however, the time dimension of labor supply is important and we
can regard the labor supply decision as an intertemporal choice. Consider women, for instance,
who often reduce their labor supply on a temporary basis due to the birth of children and the care
afterwards. In addition, many studies assume that gross wage is exogenous and does not vary
between the labor supply alternatives. However, gross wage is endogenous for the following
reasons:
•
‘Simultaneity’: wages affect labor supply but labour supply influences wages as well (due
to progressivity of the tax system).
•
Unobserved heterogeneity: there are unobserved characteristics like talent and social skills
that influence labor supply.
2
3
OECD Employment Outlook
Statistics Netherlands (emancipatiemonitor 2009).
3
The methodology used by Blundell et al (1998) does take the time dimension of labour supply and
endogeneity of wages into account. The authors investigate how several tax reforms in the United
Kingdom affected labor supply of females in the 1980s. A tax reform results in exogenous variation
in income. In this way, we have a natural experiment which makes it highly suitable to study the
effect of net wages on labor supply. In particular, a tax reform is independent from individual
characteristics, or working hours, which makes it extremely suitable to study labor supply.
Van der Klaauw and Bosch (2009) follow Blundell’s approach in studying labor supply of females.
By using repeated cross section data for the period 1999-2003, the authors use a large, Dutch tax
reform in 2001 to study labor supply effects of cohabiting/married females. The tax reform in 2001
resulted in a sharp reduction in the maginal tax rates in the Netherlands. Furthermore, the general
allowance was replaced by a tax credit. With the old system prior to 2001, individuals only paid
taxes on income above the general allowance. Hence, individuals with a high marginal tax rate
benefited the most from this general allowance. With the old system it was possible for non
working individuals to transfer this allowance to their partner (with a higher marginal tax rate).
This was extremely beneficial in terms of reducing tax payments and in turn influenced non
working individuals’ decision to participate. For some non working individuals, with a relatively low
expected wage (conditional on participation) and hence a low marginal tax rate, it was profitable
not to participate on the labor market. Hence, the old tax system contained an opposing financial
incentive not to work. Van der Klaauw en Bosch estimated a negative wage elasticity which means
that the income effect dominates the substitution effect. The main reason for this is that the tax
reform primarily reduced high marginal tax rates. Especially employees with a relatively high
income profited from the drop in marginal tax rates and these employees were relatively inelastic.
Despite the negative income elasticity, the average number of working hours increased after the
tax reform from 17.92 to 18.28 hours per week. The authors showed that the increased
participation rate was responsible for this result. The participation rate increased because the
financial incentive to work was increased by replacing the general allowance by a tax credit. Hence,
the effect of the increased participation rate dominates the effect of the negative wage elasticity
and as a result, the tax reform increased labor supply.
A disadvantage of the studies by Van der Klaauw and Blundell is that marginal utility of income is
considered constant. In reality, marginal utility is decreasing in income. Many recent studies, based
on the discrete choice framework, allow for diminishing marginal utility of income. Another
drawback is that both studies assume that labor supply of males is fixed which is unreasonable.
Many households make a joint decision with respect to labor supply. The pooling hypothesis for
instance 4 holds that the source of income in the household is not relevant. Finally, the method
described above is not suitable to simulate proposed policy measures, such as expenditure cuts on
child care or the introduction of a flat tax in the future. By contrast, the discrete choice labor
supply models estimate the preferences of individuals for leisure and income. That is, these models
estimate the parameters of the (quadratic) utility function which can be used to simulate proposed
4
Lungerd, S, Pollak, R. and T.Wales (1997), Do Husbands and Wives Pool Their Resources? Evidence from the
United Kingdom Child Benefit, Journal of Human Resources, 32(3) pp. 463-479.
4
policy measures. This is the main reason for opting for a labor supply with discrete choices. For the
Ministry of Social Affairs and Employment, it is important that the labor supply model can simulate
future policy measures as well and develops into an essential instrument to support the decision
making process of policy makers in the Netherlands.
The choice for a discrete choice model instead of a continuous labor supply model is motivated as
follows. Firstly, the system of taxes and social security premiums creates a non-linear budget
constraint seriously complicates estimation. In practice, the calculations in continuous labor supply
models become too complex. Creedy and Duncan (2002) provide a nice technical survey of recent
developments in behavioural microsimulation. In their survey, they also concentrate on the pros
and cons of continuous labor supply models and discrete labor supply models. Secondly, the labor
supply decision of employees is not a continuous choice in practice. In reality, employees only have
a limited number of options (discrete choice).
3. Theory
Section 3.1 sets out the underlying theory of the labor supply model. In the end, the model should
not only focus on the decision of individuals to work more or less (intensive margin) but also on the
decision of individuals to participate or not (extensive margin). For non-working individuals it is
impossible to observe wage rates in the sample and we have to estimate these wages. Section 3.2
describes the theory of this wage estimation.
3.1 Labor supply model
Starting point of the analysis is an individual who maximizes utility with respect to leisure and
income, taking a budget constraint into account. The budget constraint is as follows 5:
Y = w * L + y non = w(80 − H ) + y non
(1)
Income (Y) equals the sum of the product of net wage (w) and labor supply (L) and other income
(ynon), such as wealth and family allowances. Here, the following time restriction holds: L+H=80 6,
where H represents hours of leisure per week. An individual chooses a combination of income (Y)
and leisure (H) so that his/her utility is maximized. For this we take the following quadratic utility
function:
U (Y , H ) = α yy Y 2 + α hh H 2 + α yhYH + β y Y + β h H
(2)
The advantage of a quadratic utility function is that this function is flexible and that the marginal
utility of income is not constant, as opposed to the linear utility function.
5
The gross wage is considered fixed throughout the analysis. In reality, one can argue that the gross wage is
endogenous.
6
Experimentation with other time endowments hardly affected the results.
5
We are not able to observe utility of the individuals. We only observe the actual working hours and
some relevant properties such as net salary, age, sex, education level and number and age of
children. Suppose we can observe all relevant properties (and we do not suffer from measurement
errors, etc.), then the model is deterministic. In that case, we can calculate utility for all individuals
in each of the alternatives and simply pick the alternative which yields the highest utility. In reality,
however, we have to deal with measurement error and unobserved heterogeneity. There are
properties that we can not observe, such as talent and social skills, that affect wages and hence
the utility of the individuals. Hence, utility consists of a deterministic component and an error term:
V (Y , H ) = U (Y , H ) + v
(3)
The error term ν here represents measurement errors and unobserved heterogeneity. An individual
i chooses labor supply option k if utility is higher than for the other alternatives:
pik = P(Vk > Vi ) = P(U k − U i > vi − v k )
(4)
If we assume that the error terms vi are independent and identically distributed over all
alternatives, then it follows that the difference in utility between the alternatives follows a logistic
distribution 7. The probability of alternative k,
pik , is a conditional probability. This probability is
conditional with respect to the error term. The unconditional probability is obtained by taking into
account the distribution of the error term. In discrete choice models of labor supply it is often
assumed that the error terms follow an extreme value distribution. McFadden (1973) showed that
in this case the probability for alternative k,
pik , for individual i equals:
n
pik = P(Vik > Vij ) = exp(Vik ) / ∑ exp(Vij )
(5)
j =1
In order to calculate the probabilities for the alternatives, we must first estimate the parameters of
the utility function. In other words, we must determine the preferences of individuals for leisure
and income. These parameters can be estimated by a conditional logistic regression (using
maximum likelihood) 8. The joint probability that all M individuals choose alternative k is thus equal
to the product of each individual’s probability for alternative k:
M
n
i =1
j =1
P(h1k ,...hmk ) = p1k p 2 k .... p mk = ∏ exp(Vik ) / ∑ exp(Vij )
(6)
7
See for instance Cameron and Trivedi (2005)
In a conditional logit the properties vary over the alternatives (alternative varying regressors). Characteristics
such as education and age only vary by individuals and not by alternatives. These properties interacted with
leisure ensure that we are dealing with properties that vary over the alternatives. The interpretation is that the
preference for leisure varies with these properties. This results in estimated parameters β that are the same
for all individuals and over the alternatives. By comparison, a multinomial regression with alternative invariant
regressors results in parameters that vary by alternative.
8
6
The equation above is the likelihood function that we want to maximize over the parameters β of
the utility function. We are looking for the parameters of the utility function with the highest
likelihood given the observed disribution of labor supply. The log likelihood is as follows:
M
n
i =1
j =1
log( L) = ∑ Vik − log(∑ exp(Vij )
(7)
It is expected that the preferences of individuals for income and leisure depend on characteristics
such as age, education, ethnicity and the presence of children. Individuals with children will
probably (on average) have a higher preference for leisure than someone without children. In
addition, unobserved heterogeneity (ε) plays an important role as well. Here we assume that ε is
normally distributed. The utility function then becomes 9:
U (Y , H ) = α yy ln 2 (Y ) + α hh ln 2 ( H ) + α yh ln(Y ) ln( H ) +
β y 0 ln(Y ) + {β h 0 + β h1 ln( Age) + β h 2 ln 2 ( Age) + β h 3 Educlow + β h 4 Educhigh +
(8)
β h 5 Child 04 + β h 6 Child 412 + β h 7 Child1218 + β h8 Re gion + β h 9 Etnic + ε } ln( H )
where:
•
Y = net income per week
•
H = leisure per week
•
Age = age (natural logarithm, ln)
•
Age2 = ln(age)*ln(age)
•
Educlow = dummy low education
•
Educhigh = dummy high education
•
Child04 = age youngest child 0-4 year
•
Child412 = age youngest child 4-12 year
•
Child1218 = age youngest child 12-18 year
•
Region = dummy for region West in the Netherlands
•
Etnic = dummy for non-Western immigrant
10
The quadratic utility function allows marginal utility of income and leisure not to be constant. For
age a quadratic term is included as well since it is expected that the relationship between age and
the preference for leisure is not constant. That is, for younger people the preference for leisure
probably declines with age whereas for older people this relationship is reversed. In addition, the
utility function contains dummy variables for education, children, region and non-Western
immigrants. One would expect that lower education, the presence of children and a non-Western
background raises the preference for leisure. Finally, a dummy for the region west is included as
9
For the variables income, leisure and age, the natural logarithm is taken
Medium education is the reference category
10
7
well since the Western part of the Netherlands is characterized by high economic activity and high
population density.
Unobserved heterogeneity is a property that, like age and education, is constant over the
alternatives and is therefore multiplied by the natural logarithm of leisure. The additional random
term ε, with a normal distribution, complicates the estimation. By adding a random error term ε,
the likelihood function must take the distribution of this random term into account (as an integral
in the likelihood function). This likelihood function has no closed form solution and therefore we
must use simulated maximum likelihood. For each draw of the random term ε we calculate the
likelihood and then take the average of the likelihood over R draws 11. The average maximum
likelihood is then maximized:
R
log( L) = (1 / R)∑
r =1
n




V
V
log(
exp(
)
−
∑
∑
ikr
ijr


i =1 
j =1

M
(9)
For the draw of the random terms, Halton sequences are used as they provide better coverage
than pseudo-random draws. Train (2003) provides a good description of this method. Haan and
Uhlendorf (2006) provide a good description of STATA routines for simulated maximum likelihood
and Halton draws.
Once the parameters of the utility function are estimated (including the random terms for
unobserved heterogeneity), the actual choice of all individuals must be calibrated. Creedy and Kalb
(2005) present a nice overview of the calibration process. Error terms are drawn from the extreme
value distribution and added to the calculated utility for each alternative. A draw is accepted when
the actual choice for an individual yields the highest utility. This exercise should be repeated
several times (eg 100 draws). Calibration results in a distribution of predicted labor supply that is
perfectly consistent with the observed distribution of labor supply in the sample. Next, we can
calculate labor market effects of policy measures by using the same (calibrated) error terms again.
This results in a new probability for each of the alternatives, given the characteristics (including
random terms for unobserved heterogeneity), calibrated error terms and the labor supply in the
baseline scenario.
3.2 Estimate expected wages non-working individuals
The labor supply model should also be able to model the participation decision of individuals, the
so-called extensive margin. For the inactive population in the sample the gross wage conditional on
participation is unknown and must be estimated. This section describes the theory of this wage
estimation.
For the wage estimation we use the observed wage distribution of workers in the sample. We can
estimate the determinants of gross wages for this group and use these results to estimate
11
As R approaches infinity, the maximum likelihood estimation is consistent.
8
expected gross wages for non-working individuals. Here, we have to consider a (possible) selection
effect. The population of workers will probably differ from the inactive population. By using the socalled Heckman selection model (1979), it is possible to correct for selection bias.
The Heckman selection model consists of a wage and participation equation. The wage equation for
gross wages is as follows 12:
ln(W ) = Xβ + ε
(12)
where X is a vector of explanatory variables (such as age and education) and ε is the unexplained
part, which is assumed to be normally distributed with mean 0 and variance σ2. We estimate the
vector β of the wage equation.
The participation equation estimates the probability of participation, given certain characteristics Z.
The participation equation is estimated using a Probit regression13:
Pr( Active = 1 | Z ) = Φ ( Zγ )
(13)
where Z is a vector of explanatory variables (age, education etc.). The unexplained portion is equal
to ν, assuming that ν is (standard) normally distributed. The vector γ contains the coefficients of
the participation equation while Φ is the cumulative distribution function. With respect to the error
terms of both equations, the following holds:
Corr[ ε ,υ ] = ρ
(14)
That is, the correlation between the two error terms of the wage equation and participation
equation equals rho. That is, rho is the correlation between unobserved determinants of the
probability of participation and unobserved determinants of wages. If rho is positive, it means that
unobserved characteristics are positively correlated. Take for instance the characteristic talent in
both equations. Talent has a positive effect on the gross wage and the probability of participation,
with a positive rho as a result. If rho is negative, then there are unobserved characteristics that
have a positive impact on participation, but a negative effect on the gross wage (or vice versa). If
rho is equal to 0, then the error terms are independent and selection bias is not present.
The conditional expected value of gross wage (that is, provided that the individual works) can be
approximated by:
E[ W * | Active = 1] = Xβ + E[ε | X , Active = 1] = Xβ + ρσM
12
13
(15)
The wage equation is estimated by OLS.
The participation regression can also be estimated by a logistic regression.
9
where
M = φ (Zγ ) / Φ(Zγ )
The second term on the right hand side of the equation is a variant of the Inverse Mill's Ratio. Here
φ
is the probability density function whereas
Φ represents the cumulative probability density
function. Both functions use the vector of explanatory variables Z as input for each individual. The
participation equation makes sure that the effect of the characteristics (Z) from the participation
equation on wages is taken into account. That is, a correction is made for selection bias. The
Heckman selection model is estimated for single women, single men and couples (again
differentiated between men and women). The explanatory variables are as follows:
Wage equation:
o
Dummies education
o
Age
o
Age squared
o
dummy non-Western immigrant
o
dummy Western region
Participation equation:
o
Dummies education
o
Age
o
Age squared
o
dummy non-Western immigrant
o
dummy Western region
o
dummy youngest child 0-4 year
o
dummy youngest child 4-12 year
o
dummy youngest child 12-18 year
It is expected that individuals with a higher education have a higher probability of participation and
receive higher wages on average. A similar story holds with respect to age. However, the positive
relationship between age and participation and wages is expected to weaken when individuals
become older (diminishing returns). Furthermore, dummies for Non-Western immigrans (negative
relationship) and Western region (positive relationship) are included as well. Finally, one expects
that the presence of children lowers the probability of participation.
10
4. Data
This section describes the dataset in more detail. As stated earlier, labor supply will be estimated
for singles and couples separately where a distinction is made between men and women. For
singles there are 6 alternatives to choose from: 0, 8, 16, 24, 32 and 40 hours 14. Couples are
offered 15 alternatives in the model where a distinction is made between men and women. For
men, there are 3 alternatives (0, 30 and 40 hours of work) whereas for women there are 5
alternatives (0, 10, 20, 30 and 40 hours of work), bringing the total number of alternatives to 15.
The gross hourly wage of workers can be calculated by by dividing the gross annual income in the
sample by 52 (number of weeks per yaer) times the working hours per week. For non-working
individuals the gross hourly wage is estimated by using the Heckman Selection model. Next, net
income has to be calculated for each of the alternatives. The simulation model MICROS offers a
comprehensive gross/net income module by which net income for households in each of the
alternatives can be calculated accurately.
The micro dataset contains the following relevant information for the labor supply model: working
hours, age, education, region, ethnicity and age and number of children. For this study, only
individuals aged between 23 and 60 years are included. Self-employed individuals and individuals
with multiple sources of income (for example wages and profits) are not included. This is because
the budget constraint becomes very complex if multiple income sources are present. Inactive
people are part of the population, but only if they receive social assistance or unemployment
benefits. For couples, non-working partners are included as well. Finally, disabled individuals are
also excluded. The reason for this is that some of these disabled individuals are permanently
disabled, with no prospect of recovery, and it is not possible to distinguish this group in the sample
in a proper way.
Table 1 shows the descriptive statistics of the singles population. For single men and women holds
that non-working individuals are relatively low educated. That is, 75.8% of non-working individuals
has a low education, while the share of individuals with a low education is only 31.5% in the active
population of single women. Furthermore, non-working individuals are older on average and often
have a non-Western background. An important difference between single men and women is the
the employment rate. Approximately 14% of single men are inactive while 24% of single women is
not working. One possible explanation is the presence of children. The share of single men with
children is very small (4%) while more than half of single women have children (54.5%).
Table 2 shows a similar table with descriptive statistics for couples, again differentiated between
men and women. As expected, most men work (94%) and average working hours is high (36.6
hours). Approximately one quarter of women are inactive. As with singles, we see that ethnicity
and low education are relatively common in the inactive population. Inactivity comes in two
different ways for couples: (1) both persons in the household do not work and the household
14
The results are quite robust with respect to the number or design of the alternatives. The fit of the model, in
terms of the predicted labor supply distribution, is highest for the current design. However, the differences are
small.
11
receives social assistance or unemployment benefits and (2) either one of the partners does not
work while the other partner does have a job.
Table 1: Descriptive statistics singles
Total
42,3
26,8
31,0
Low education
Medium education
High education
Singles men
(# 3.276)
Active
Inactive
37,4
71,9
28,1
18,6
34,5
9,5
Total
42,1
25,8
32,1
Singles women
(# 3.647)
Active
Inactive
31,5
75,8
27,6
20,1
40,9
4,1
No children
Youngest child 0-4 yr
Youngest child 4-12 yr
Youngest child 12-18 yr
96,1
0,2
1,7
2,0
96,1
0,2
1,8
1,9
95,9
0,4
1,5
2,2
70,0
5,2
13,6
11,2
77,8
2,8
9,5
9,9
45,5
12,9
26,5
15,2
Other
Non-Western immigrant
88,6
11,4
91,7
8,3
69,7
30,3
83,0
17,0
89,0
11,0
64,2
35,8
Region West
Other region
50,4
49,6
50,7
49,3
48,1
51,9
54,4
45,6
55,2
44,8
51,9
48,1
Age (average)
39,6
39,2
42,3
40,5
40,1
41,6
Active
Inactive
Working hours (average)
Working hours (average),
only active population
85,9
14,1
32,9
76,0
24,0
25,5
38,3
33,5
Table 2: Descriptive statistics couples
Low education
Medium education
High education
Total
34,4
30,0
35,6
Couples, men
(# 14.184)
Active
Inactive
33,3
51,5
30,5
21,6
36,1
26,9
Total
39,8
31,2
29,0
Couples, women
(# 14.184)
Active
Inactive
33,1
60,6
33,6
23,8
33,3
15,5
No children
Youngest child 0-4 yr
Youngest child 4-12 yr
Youngest child 12-18
yr
41,3
22,5
22,8
41,3
22,5
22,8
41,3
21,8
23,7
41,3
22,5
22,8
42,2
22,5
21,9
38,4
22,3
25,8
13,4
13,4
13,3
13,4
13,4
13,5
Other
Non-Western
immigrant
90,6
92,2
65,3
90,5
93,0
82,7
9,4
7,8
34,7
9,5
7,0
17,3
Region West
Other region
44,5
55,5
44,3
55,7
47,6
52,4
44,5
55,5
45,0
55,0
43,0
57,0
Active
Inactive
Age (average)
Working hours
(average)
Working hours
(average), only active
population
94,1
5,9
42,1
42,1
75,7
24,3
42,5
39,8
39,1
36,6
18,2
38,9
24,0
42,0
12
5. Estimation results
This section presents the first preliminary results of the recently developed labor supply model.
Section 5.1 shows the results for the wage estimation from the Heckman Selection Model. The
estimated parameters of the utility function are presented in section 5.2.
5.1. Results Heckman Selection Model
Table 3 shows the results for the wage and participation equation for single men and women. Most
of the coefficients of the wage equations for singles are highly significant (at 1% level) and have
the expected sign. The only exception is that the coefficient for ethnicity is not significant (and
slightly positive) for single women.
Table 3:
Estimation results Heckman Selection Model singles (by maximum
likelihood)
Men
Women
(# 10.464)
(# 10.216)
Wage equation
Dummy education 1+
- 0.459**
-0.558**
- 0.362**
-0.448**
Dummy education 2
Dummy education 3
- 0.296**
-0.313**
Dummy education 4
- 0.111**
-0.154**
Age (ln) ++
3.896**
2.523**
Age squared (ln) ++
- 0.484**
-0.307**
Ethnicity
- 0.061**
0.004
Region West
0.064**
0.058**
Constant
- 4.833**
-2.203**
Participation equation
Dummy education 1+
Dummy education 2
Dummy education 3
Dummy education 4
Age (ln) ++
Age squared (ln) ++
Ethnicity
Region West
Youngest child 0-4 years
Youngest child 4-12 years
Youngest child 12-18 years
Constant
rho (ρ)
sigma (σ)
lambda (λ= ρ*σ)
Log Likelihood
- 0.843**
- 0.274**
- 0.038
0.117*
7.728**
-1.187**
-0.512**
0.099**
-0.475*
0.021
0.015
-11.517**
-1.043**
-0.519**
-0.112
0.165**
13.667**
-2.023**
-0.444**
0.253**
-0.842**
-0.459**
-0.254**
-22.051**
-0.073
0.351
-0.026
-0.0977
0.369
-0.036
-8401.5
-8458.4
+ Category university is the reference category.
++ natural logarithm
** significant at 1%, * significant at 5%
Coefficients of the wage equation are directly interpretable. For instance, the average wage in the
Western region of the Netherland is 6.6% higher than in the rest of the Netherlands (exp (0064)).
Furthermore, we see that a higher education results in a higher predicted wage. The relationship
between wage and age is positive as well, but diminshing in age. Finally, there is a negative
relationship between wages and ethnicity.
13
In the participation equation, we see that most coefficients are significant as well. Only the
coefficient for the third education dummy (medium education) is not significant for single men and
women. We also see that people with higher vocational education (education dummy 4) have a
higher participation probability than those with a university degree (education dummy 5 which is
the reference category). One possible explanation is that some university graduates are searching
longer for a job compared to graduates with higher vocational education, since more studies are
offered that less fit the needs of the labor market. As a result, the probability of finding a job is
lower. The coefficients for age of the youngest child have the expected sign: as the youngest child
is older, the probability of participation increases. For men, we see that these coefficients are not
significant at the 5% level. This is probably due to the low number of observations of men with
young children in the sample. Furthermore, cultural factors may also play an important role. The
relationship between the probability of participation and age (positive, but declining), ethnicity
(negative) and region (positive) is as expected. It is important to note that the coefficients of the
participation equation are not directly interpretable. The participation equation is estimated with a
Probit model, where the marginal effects are not constant and depend on the level of explanatory
variables.
The coefficient rho is less than 0, but not significant at the 5% level. This means that we cannot
reject the null hypothesis that unobserved characteristics are not negatively correlated. The
coefficient for lambda is equal to the product of rho and sigma, and equal to -0.026 for men. The
final correction varies by individual as it is equal to the quotient of the probability density function
(PDF) and cumulative distribution function (CDF), multiplied by lambda. The model described
above results in an estimated wage rate for active and inactive individuals, while taking selection
bias into account.
14
Table 4 shows the results for the wage and participation equation for couples, again estimated
separately for men and women.
Table 4:
Estimation results Heckman Selection Model couples (by
maximum likelihood)
Men
Women
(# 17.669)
(# 19.777)
Wage equation
Dummy education 1+
- 0.711**
-0.745**
Dummy education 2
- 0.576**
-0.598**
Dummy education 3
- 0.444**
-0.374**
Dummy education 4
- 0.195**
-0.121**
Age (ln) ++
5.101**
9.283**
Age squared (ln) ++
- 0.622**
-1.282**
Ethnicity
- 0.189**
-0.130**
Region West
0.073**
0.065**
Constant
- 7.134**
-13.906**
Participation equation
Dummy education 1+
Dummy education 2
Dummy education 3
Dummy education 4
Age (ln) ++
Age squared (ln) ++
Ethnicity
Region West
Youngest child 0-4 years
Youngest child 4-12 years
Youngest child 12-18 years
Constant
- 0.710**
- 0.221**
- 0.040
0.069
10.229**
-1.375**
-0.706**
0.072**
-0.013*
-0.099**
-0.044
-17.202**
-0.950**
-0.508**
-0.100*
0.254**
18.974**
-2.737**
-0.487**
0.107**
-0.423**
-0.327**
-0.069**
-31.587**
rho (ρ)
sigma (σ)
lambda (λ= ρ*σ)
0.681**
0.366
0.249
0.784**
0.442
0.347
Log Likelihood
-9840.3
-16681.9
+ Category university is the reference category.
++ natural logarithm
** significant at 1%, * significant at 5%
Most of the coefficients for couples are significant and have the expected sign. In the wage
estimation for couples we see that rho significantly differs from 0. The coefficient for rho is positive
which means that unobservable characteristics have a positive effect on both wages as well as
participation.
5.2 Results parameters utility function
This section presents the estimation results of the parameters of the utility function. Table 5 shows
these results for singles. For single women, all coefficients are significant except for the quadratic
term for income. This does not apply for single men. The coefficients of income, leisure and higher
education are not significant at the 5% level. Furthermore, the interaction terms of children with
leisure are not significant. The latter result is not surprising given that single men with children are
rare in the sample.
15
The coefficients of the interaction terms of dummy variables with leisure are directly interpretable.
For example, single persons with low education have a greater preference for leisure. The same
holds for singles with a non-Western background. Singles in the Western region have a lower
preference for leisure. The coefficients for income, leisure and age are not directly interpretable.
For income and leisure, a quadratic term and an interaction term is included so that the marginal
utility of income and leisure is not constant and depends on the level of income and leisure.
However, it can be shown that leisure and income have a positive effect on the utility of individuals
and that marginal utility of income falls as income increases. This is intuitive. The model also
includes a quadratic term for age. The interpretation is that preferences for leisure decrease with
age (that is preference for income/work increases), but this relationship becomes positive for older
individuals (that is, a higher preference for leisure). As expected, single women with children have
a greater preference for leisure. This effect becomes smaller as children are older.
Table 5 shows that a dummy for participation is estimated as well. Initially, a model was estimated
without a dummy and this basic model strongly overpredicted the number of part-time jobs. This is
a well known issue by these types of labor supply models (see Van Soest for example). In order to
correct for this problem, researchers often include dummies which improve the predicted labor
supply distribution. The dummy for participation can be interpreted as follows:
•
Dummy represents fixed costs of participation (such as costs of childcare and travel costs)
•
Dummy corrects for the fact that small part-time jobs are rarely offered (correction for
supply side of labor)
•
Dummy displays search costs for workers and these workers have to search longer for
small part-time jobs
I have included a dummy for participation and the estimated coefficient is negative. In this case,
the interpretation is that the dummy represents fixed costs of participation.
Finally, table 5 shows that the variance of the random coefficients is significant for single men and
women. As previously stated, the random terms for leisure ensure that the coefficient of leisure
varies by individuals. Therefore, these models are often called random coefficients models. If the
variance is not significantly different from 0, this means that we have fixed parameters and
unobserved heterogeneity plays no role.
16
Table 5: estimation results parameters utility function, singles
Income (Y)
Leisure (H)
Income2
Leisure2
Income*Leisure
Men
(#3.276)
2.784
-3.258
-0.142
0.201
-0.251
Women
(#3.647)
10.234 **
46.322 **
0.426
-6.740 **
-1.905 **
H*Age
H*Age2
H*Educlow
H*Educhigh
H*Child0-4
H*Child4-12
H*Child12-18
H*ethnic
H*region
-2.000 *
0.500 **
1.317 **
-0.148
1.000
0.067
- 0.068
2.330 **
- 0.339 *
-9.676 **
2.382 **
4.179 **
-3.033 **
12.263 **
9.222 **
4.010 **
3.076 **
-1.660 **
Dummy participation
ln(σ)
- 2.032 **
0.994 *
-1.835 **
2.178 **
Log Likelihood
Pseudo R2
* p<0.10, **P<0.05
- 2.836.4
0.52
-4.607.0
0.29
An important consideration in the labor supply model above is that the quadratic utility function is
not automatically quasi-concave for all values of Y and H. In the discrete choice model, this is not a
problem as long the utility function is quasi-concave for the observed combinations of Y and H in
the sample. An important condition here is that the marginal utility of income is not negative. For
all observations, this condition is fulfilled.
Figure 1 and 2 show the actual and predicted distribution of working hours for single men and
women respectively. Both figures show that there is a good match between the actual distribution
and the predicted distribution.
Figure 1: Actual and predicted labor supply distribution, single men
80.0
72.4
72.4
70.0
60.0
50.0
40.0
30.0
20.0
14.3
14.4
8.0
10.0
0.6
0.0
0 hours
0.7
8 hours
1.8
1.6
2.8
7.8
3.2
16 hours
24 hours
Actual labor supply
Predicted labor supply
32 hours
40 hours
17
Figure 2: Actual and predicted labor supply distribution, single women
45
39.4
40
39.2
35
30
24.4
25
24.1
21.6
21.6
20
15
10.3
10
5
3.6
0.7
10.8
3.6
0.8
0
0 hours
8 hours
16 hours
Actual labor supply
24 hours
32 hours
40 hours
Predicted labor supply
In order to calculate elasticities, net wage is increased by 10% which results in an increase in
average working hours from 32.5 to 32.8. This amounts to an elasticity of 0.10 for single men. For
single women, the average working hours increase from 25.8 to 26.1 which leads to an elasticity of
0.15.
Table 6 shows the estimation results for couples. The structure of the model is as follows:
•
Alternatives labor supply men: 0, 30 and 40 hours
•
Alternatives labor supply women: 0, 10, 20, 30 and 40 hours
This combines to a total of 15 pairs of alternatives. The second column of table 6 shows the results
of the model in which couples jointly make a labor supply decision. Columns 3 and 4 include the
results of labor supply models where only one partner is flexible with respect to labor supply, while
the other partner keeps its labor supply fixed. Most coefficients are significant at 5% level. Only a
few coefficients for men are not significant. These are the dummies for high education, older
children (12-18 years), ethnicity and region. In addition, the signs for ethnicity (negative, so less
preference for leisure) and region West (positive, so higher preference for leisure) for both men
and women are not anticipated. I have no explanation for these results. For the remaining
variables all signs are significant and have the expected sign. The presence of children increases
the preference for leisure and this effect is stronger for women.
Initially, a basic model without dummies was estimated which again resulted in overprediction of
the number of small part-time jobs. Individuals with these small part-time jobs are mainly women.
Therefore only alternative specific dummies are added for women with small part-time jobs,
namely for 10 and 20 hours of work. The estimated coefficients for these dummies are significant.
Finally, the results show that the estimated (log) of the variance for the random coefficients for
leisure is significant for men and women.
18
Table 6: Estimation results parameters utility functions couples
Couples jointly
(# 14.184)
Couples, men
flexible
(# 14.184)
-7.308 **
-23.770 **
Income (Y)
Leisure men (Hm)
Leisure female (Hf)
Income2
Hm2
Hf2
Y*Hm
Y*Hf
Hm*Hf
-6.844 **
-5.177 **
13.061 **
1.176 **
1.555 **
-0.859 **
0.699 **
0.656 **
-1.834 **
Hm*Age
Hm*Age2
Hm*Educlow
Hm*Educhigh
Hm*child0-4
Hm*child4-12
Hm*child12-18
Hm*etnic
Hm*region
-2.760 **
0.666 **
0.121 *
-0.016
1.294 **
0.786 **
0.114
1.549 **
-0.108
Hf*Age
Hf*Age2
Hf*Educlow
Hf*Educhigh
Hf*child0-4
Hf*child4-12
Hf*child12-18
Hf*etnic
Hf*region
-6.172 **
1.546 **
0.926 **
-0.953 **
3.275 **
2.795 **
1.234 **
1.153 **
-0.317 **
Dummy 10 hours
Dummy 20 hours
-0.874 **
0.358 **
-1.996 **
-1.102 **
ln(σm)
ln(σf)
0.367 **
0.538 **
-1.897
Log Likelihood
Pseudo R2
* p<0.10, **P<0.05
-27534.5
0.29
-9150.6
0.64
1.061 **
3.524 **
Couples, women
flexible
(# 14.184)
-13.096 **
-21.533 **
1.032 **
2.656 **
1.451 **
2.703 **
-1.703 **
0.335 **
0.231 **
-0.020
0.060
-0.007
-0.145 **
1.154 **
-0.099 **
-6.735 **
1.771 **
1.731 **
-1.925 **
4.696 **
3.948 **
1.631 **
1.234 **
-0.832 **
-1.140 **
0.087 **
-5.280
-22127.1
0.13
Figure 3 shows the actual and predicted distribution of couples for the model where couples decide
cooperatively. Figure 3 shows that the model predicts the labor supply distribution well. To
determine the elasticities, net wages of men and women are increased by 10%. This results in an
elasticity of 0.20 for women, while the elasticity for men equals 0.07. Surprisingly, the elasticities
for women are very low compared to other studies. Van Soest (1995), for instance, found elasticity
for women (couples) of approximately 0.50. It is important to note that Van Soest uses data from
1987 and in this period the participation of women was low: only 42%. This may be an important
explanation for the relative high elasticity for women.
19
Figure 3: Actual and predicted labor supply distribution couples
30
27.2
26.5
25
22.8 22.8
20
15
11.5
12.5
11.4
11.5
10.3 9.8
10
5
2.6 2.1
0.3 0.4
3.1 3.4
2.3
1.11.5
1.1 1.1
1.5 1.5
1.8
0,20
hours
0,30
hours
0,40
hours
30,0
hours
0.7
1.1
2.7
1.7
1.9 1.7
0
0,00
hours
0,10
hours
30,10
hours
30,20
hours
Actual labor supply
30,30
hours
30,40
hours
40,00
hours
40,10
hours
40,20
hours
40,30
hours
40,40
hours
Predicted labor supply
The elasticities above are based on the expected value of labor supply in the baseline scenario en
the scenario in which wages are increased. Until now, the calibration method described by Creedy
and Kalb (2005) is not implemented yet. This means that the elasticities are based on uncalibrated
results. With uncalibrated probabilities we must restrict our attention to aggregated results only.
Calibration of the error terms (see section 3.1) however ensures that the actual choices of all
individuals obtain the highest utility. Hence, calibration guarantees that the labor supply model
perfectly predicts the labor supply distribution in the baseline scenario. Consequently, we are able
to focus on households into more detail, i.e. at the micro level. In this way, we can look beyond the
aggregated results and focus on several specific groups. The elasticity of 0.20 for women is an
average for the whole population. It is expected that part of the women that work full-time have a
negative wage elasticity, thus lowering average elasticity, while small part-timers are much more
elastic.
6. Policy simulation
The previous section showed that the labour supply model does a good job at predicting the labour
supply distribution in the Netherlands. However, the estimated elasiticities for women are rather
low compared to previous studies. The next step is to simulate some policy measures. In this
section the labour supply effects of tax credits for employees are presented as a first application of
the recently developed labor supply model. I focus on two important tax credits: a labour tax
credit for employees (in Dutch: arbeidskorting; AK) and a labour tax credit for employees, who are
second-earners or sole parents with young children (in Dutch: inkomensafhankelijke
combinatiekorting; IACK). Evers et al (2007) simulate some policy measures with a general
equilibrium model MIMIC, which is developed by the Netherlands Bureau for Economic Policy
20
Analysis (CPB) 15. They conclude for instance that the IACK stimulates labour supply of secondary
earners but at the expense of primary earners’ labor supply.
In the Netherlands, various tax credits exist that give tax payers a reduction on liability for taxes
and social security contributions. Employees for instance receive a general labor tax credit AK
which rises with income. Figure 4 shows the design of this tax credit AK. The maximum tax credit
is equal to € 1.431 and total budget amounts € 7.6 billion in 2005.
Figuur 4: Labor tax credit AK
1600
1400
1200
Tax Credit (AK)
1000
800
600
400
200
0
0
5000
10000
15000
20000
25000
30000
35000
40000
Income
For employees with (young) children, there is an extra tax credit: the IACK. Secondary earners, or
single parents, with a child younger than 12 years, are entitled to this tax credit. Figure 5 shows
the structure of the IACK in 2009. The IACK depends on the level of income: starting from an
individual income of € 4.368 (deflated to 2005 prices), the IACK increases with a rate of 3.8% until
the maximum of € 1.722 (deflated to 2005 prices) is reached. The fiscal loss due to the IACK is
approximately € 1.1 billion.
Figuur 5: Labor tax credit IACK
2000
1800
1600
Tax credit (IACK)
1400
1200
1000
800
600
400
200
0
0
5000
10000
15000
20000
25000
30000
35000
40000
Income
15
The CPB memorandum 143, Tax reform and the Dutch Labor Market: an applied general equilibrium
approach provides a nice description of this model.
21
Table 7 shows the first preliminary results of the recently developed labor supply model. Complete
abolishment of the tax credit for all employees (AK) would reduce labor supply of single men by
0.7% and single women by 1.1%. The drop in labor supply is higher for single women, which is
intuitive since the average elasticity is higher as well. For couples a similar story applies.
Surprisingly, the labor supply effect is smaller for women with a partner compared to single women
despite the fact that the elasticity is slightly higher. This is probably due to the fact that only 30%
of single women have children whereas 60% of cohabiting women have children. One would expect
that women with children are on average less elastic compared to women without children.
As a second application of the labor supply model, elimination of the tax credit IACK is simulated.
According to first preliminary results, the total labor supply effect (aggregated over the whole
population) of the IACK is negligible. The total sum of the tax credit IACK is modest (€ 1 billion)
compared to the tax credit AK (€ 7.6 billion) which explains why the labor supply effect of the tax
credit AK is much higher. Only single parents, and secondary earners, with young children receive
the tax credit IACK.
Table 6: Labor supply effects tax credits employees
Baseline scenario
Tax credit AK
Tax credit IACK
Single men
Labor supply
(average in hours)
Labor supply effect
(in %)
32.50
32.27
32.50
-0,7%
0.0%
Single women
Labor supply
(average in hours)
Labor supply effect
(in %)
25.78
25.51
25.77
-1.1%
0.0%
36.26
36.32
-0.2%
-0.0%
17.77
17.91
-0.8%
-0.1%
Couples, men
Labor supply
(average in hours)
Labor supply effect
(in %)
Couples, women
Labor supply
(average in hours)
Labor supply effect
(in %)
36.33
17.92
22
8. Conclusion
This paper presents a recently developed labor supply model for the Dutch tax benefit model
MICROS. The ultimate goal of this study is to develop a labor supply model that plays an important
role in the decision making process in the Netherlands. The labor supply model uses a discrete
choice framework and the estimates are based on cross section data from 2005. The model does a
good job at predicting the labor supply disttibution for single men, women and couples. First
preliminary results show, however, that elasticities are surprisingly low. That is, the labor supply
model estimates elasticities of 0.10 for single men and 0.15 for single women. For couples, the
elasticities are 0.07 for men and 0.20 for women. The low elasticities for men are in line with other
studies. However, most studies find higher elasticities for women. An explanation in favor of our
preliminary results is that other Dutch studies use older datasets. Over the years participation of
women increased and this in turn lowered their elasticities. On the other hand, the recently
developed labor supply model is still under construction and one needs to interpret these first
preliminary results with caution. In the near future, refinements of the labor supply model will take
place.
23
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