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IFO CONFERENCE ON
“SURVEY DATA IN ECONOMICS –
METHODOLOGY AND APPLICATIONS”
CESifo Conference Centre, Munich
14 – 15 October 2005
Labor supply model along the
intensive and extensive margin,
in regular and irregular
labor markets
Isilda Shima
Ifo Institute for Economic Research at the University of Munich e.V.
Poschingerstr. 5, 81679 Munich, Germany
Phone: +49 89 9224-0 Fax: +49 89 985 369
[email protected]
http://www.cesifo-group.de
9/19/2005
Labor supply model along the
intensive and extensive margin,
in regular and irregular
labor markets1
.
By
Isilda Shima
University of Turin
Abstract
The main purpose of the paper is to study the decision of the individual with regard to the participation
and the allocation of time in regular and irregular labor markets. The labor supply decision is analysed
along the extensive margin (participation decision in the labor market) and along the intensive margin
(hours of work on the job). Also the probability of participating in the respective labor markets is
studied. The basic model I refer to is the one developed by Strøm et al (2004), a labor supply model
when tax evasion is an option. This study reveals that at intensive margin the model achieves to capture
and predict better the level of irregular hours of work in comparison with the extensive margin. The
expected labor supply, predicted by using the estimated model at intensive margin, is closer to the
observed values compared to extensive margin model. The expected tax level evaded is predicted at a
higher level by the intensive margin model. These results will be compared with those attained by
estimating a labor supply model with the assumption of no irregular hours of work. The findings has
shown the relevance of studies of labor supply both at intensive and at extensive margin compared to a
discrete choice model of labor supply where tax evasion falsely is ignored. The results have important
policy implication for the reforms in the tax system and social welfare benefits.
1
I would like to thank Steinar Strøm, Alessandro Sembenelli for stationary support, useful critics and
valuable suggestions. I would also like to thank Steinar Strøm, for providing me with the survey data.
1
1- Introduction
In the literature, there have been several theoretical studies of tax evasion and
labour supply Allingham and Sandmo (1972), Andersen (1977), Isachsen and Strøm
(1980), Cowell (1985)), see also Isachsen , Klovland and Strøm (1982), Isachsen and
Strøm (1985) and Isachsen, Samuelson and Strøm (1985), as well as Lacroix and
Fortin (1992) and Lemieux, Fortin and Frechette (1994), Lacroix and Fortin Joubert
(2001) and Strøm, Jørgensen, Ognedal (2004). However, this is just a partial story
since the only message these studies reveal is that individuals may have an incentive
to work and provide irregular hours of work with the scope to minimize their tax
liabilities or to continue receiveing social welfare benefits.
On the other side the empirical literature on labor supply has emphasized two
margins of labor supply responses (see Heckman (1993)). Referring to Heckman
(1993), a crucial theoretical distinction with important empirical payoff, is the one
between labor supply decision at extensive margin (participation decision) and at
intensive margin (hours or weeks of work). The participation margin–the so-called
extensive margin–has been recognized as a potential resolution, as the variation in
the number of employees is the dominant source of fluctuations in total hours
worked (e.g., Coleman, 1984; Heckman, 1984).
However, these studies ignore the behavioural response to the respective transfer
and tax programs regarding the incomes generated by participating in irregular labor
market. Workers are heterogeneous in the subjective cost they face when operating in
the labor market, regular and irregular sector. Analytical and numerical investigations
suggest that interactions between regular and irregular activities can affect standard
results of policy interventions. Policies aiming at increasing individuals benefit of
participating in the regular sector are more desirable than deterrence policies (
Fugazzaa & Jacques, 2002).
2
Thus the scope of this paper is to combine these two fields of study into a
common one by analyzing the labor supply decision at intensive and extensive
margin, considering taxes, disposal income, non-labor income, including also the
option to not declare part of the labor income to the tax authorities.
Including the option of evasion to the labor supply studies, at extensive and
intensive margin, can make a difference in defining and predicting the individual
behavior and their
responses, participation and efforts in labor market. The
conclusions emerged from the study have important policy implications for the
reforms in the tax system, social welfare benefits and the design of an optimal tax
system.
In this study I try to analyze the decision of the individual in the labor market
and estimate the labor supply considering these two distinctions as well as including
also the option of working in the irregular labor market as an alternative way of
earning higher incomes. 2 The structure of the model used to study the labor supply is
important since it allows to distinguish between income and substitution effects in
case a new tax policy is introduced.
The model I use is based on Strøm et al (2004), a nested multinomial logit
model of labor supply when tax evasion is an option. By tax evasion I refer to legal
work whose income is not declared to the tax offices.
The data set allows for three different estimation strategies:
1-
an investigation at the intensive margin (IM) of labor supply when
tax evasion is an option. In this case I use all available information,
participation as well as hours of work, in the estimation of the
model.
2-
An investigation at the extensive margin (EM) of labor supply
when tax evasion is an option. In this case I use only the
participation information, the yes/no information in the estimation
of the model. The motivation in the rear of this approach is that
estimating a model using only the participation decision has been
2
A study of Webley& Cole & Eidjar regarding the tax paying behaviour, treats tax evasion as a
defective behaviour within a social dilemma, a conflict between the pursuit of collective outcomes and
their own individual outcomes. Thus tax system induce individuals to choose between co-operative
behaviour and defective behaviour. So it is relevant to define an appropriate tax system where this dual
behaviour is emphasised and taken into consideration.
3
the most common approach to a variety of problems in
microeconometrics. However, due to the structure of the model I
am able to recover all the parameters of the utility function. Hence,
the model can be used to predict hours of work even if it is
estimated on participation decision only. Thus the IM and EM
model can be confronted and compared how well they predict the
labor supply respectively with the observed hours.
3-
An investigation of labor supply when tax evasion is ignored. In
this case I use only the observed hours of work in the regular part
of the economy when estimating the model. The reason why, is
that, almost all the labor supply studies follow this last approach.
But in all countries tax evasion is an option. Unlike others I am
able to estimate a traditional labor supply model( a discrete choice
model, DCM ) on traditional data and compare estimates and
predictions from this model with a labor supply model when tax
evading activities are accounted for. The result is that IM performs
better than EM and DCM.
The tax policy reforms undertaken in Norway can help to understand and
evaluate the labor supply decision of the individuals in regular and irregular labor
market. The difficulty to estimate the labor supply decision in the presence of
nonlinear tax reform comes from the fact that individuals have different
preferences over leisure and disposal income (which can not be observed directly)
and that the budget set can be non-convex.
The Norwegian Income Tax System has continuously been reformed since
the late 1980s with the implication of less progressive taxes. In Appendix A we
show the income tax schedule in 1980, 1990 and 2000. Also in Norway, in 1992,
a broad tax reform was implemented with the purpose of reducing tax-induced
distortions by lowering the tax rates and broadening the tax base. This reform was
also a further step toward a more neutral tax system with respect to the type of
economic activity and the organizational and financial structure of such activity.
4
Moreover, the structure of the economy has changed toward a new one
where the opportunities to work in the shadow economy have been reduced.
There have been changes in the industrial sectors toward more firms with more
employees and less self employed, more government employees, lower
unemployment rates, higher income and higher wages in the regular economy.
Consequently, these changes have reduced the opportunities and the incentives to
evade taxes. During recent years the shadow economy in Norway has thus gone
through a decline, Shima (2005).
Still, the shadow economy has not vanished and it could be of importance
to account for the option of tax evasion when labor supply models are estimated
in general and in a particular economy, like the Norwegian economy.
The process of identifying the phenomenon of tax evasion in the labor market
would gain remarkably from these parallel studies. Independently from the
difficulties regarding the interpretation of the results, we can draw important lessons
about the tax system, the behaviour of individuals and the supply side of the labour
market, both the regular and irregular one.
The results obtained are important for policy implications, since
understanding better the mechanism of individual behaviour in labor market helps to
remove disincentives related to tax evasion and design of an optimal tax system.
Transforming the undeclared irregular work into a regular one helps to achieve full
employment, improve the quality and productivity at work and strengthen the social
cohesion.
2- Few words about labor supply models
There has been always a concern about the study of labor supply model and
individual behavior. The main studies are focused on studying the labor supply at
the extensive margin (hours of work) and at the intensive margin (participation).
Apart from the analysis of behavior their importance is related to the policy
implications, Blundell, Duncan and Meghir (1998), regarding the distortions in
the labor market and distributional issues.
5
Studies in labor supply and tax reform implications show that the effect of
taxes on hours of work in case of male are very week Mroz (1987). McCurdy
(1990) found weak responses in female labor supply, but his results where
contested by other studies where better estimation techniques were applied.
Different empirical studies, on European data, shows that males labor
supply is rather inelastic, while females labor supply is highly elastic with regards
to changes in wages, marginal taxes and non-labor income, Colombino and Del
Boca (1989). Almost the same results were found by Bourguignon and Magnac
(1990) studying the labor supply and income effects in France. In all these studies
the main focus has been on choice at the intensive margin. Studies of Moffitt R.
(1987) and Van Soest, Callan (1994), consider model of family labor supply
where the main advantage is allowing all kinds of non-linearities and nonconvexities in the budget set. Their studies reveal labor supply responses not only
for females but for males as well. In the model of Dagsvik and Strøm (2005) the
labor supply is analyzed when complicated budget constraints and restrictions on
hours of work are considered. In their model heterogeneity is allowed in the
opportunity sets as well as in preferences.
An important issue ignored to a great extent in empirical labor supply
models is the one related with the income generated by regular hours of work but
not declared to the tax authorities.
The focus of this paper will be on the relevance of this last argument. The
main purpose of the study will be the analysis of the labor supply and the
responses we get in the case when the issue of evasion is taken into consideration
in comparison with the model when this issue is ignored. The main purpose is to
understand the relevance of this matter in studying labor supply models.
3-Data description and summary statistics
The data I use have as the main source the survey conducted in 2003 by a
private Statistical Institution in Norway called MMI. This survey was also conducted
6
in 1980, 1989 and 2001. The individuals who participated in the survey replied to
questions which provide information about their personal characteristics and
economic variables basically gender, age, education, employment, hours of work,
marital status, social benefits and other sources of income, hourly wage rates, income
and taxes paid.
Table 1. Response rates, Appendix 1
Table 1 gives the response rates for the years 2001 and 2003. Respectively, the
response rates are fairly high for surveys of this type and they were particularly high
in 2003.
In addition, the participants in the survey were asked about their engagement
as well as their attitudes concerning non-reported income activities. They were also
asked if during the last 12 months they have ever evaded taxes or if they did not
report to the tax authorities some income from regular work. If the answer was yes
they where asked about the wage and number of hours undeclared to the tax
authorities.
Table 2 gives the summary statistics for the whole sample and Table 3 gives
summary statistics separately for evaders and non-evaders.
Table 2. Summary statistics: the whole sample in 2003. Appendix 1
Usually people are sceptical about answering questions regarding tax evasion and
undeclared hours of work. This problem may bias the responses of those who
participated in the survey. As a consequence it may bias the estimation results of
the model. In this survey, the response rates have been considerably high, which
can sustain the confirmation that the sample selected may give a good
representation of population characteristics (see Isachsen, Klovland and Strøm
(1982) and Goldstein, Hansen, Ognedal and Strøm (2003).
Table 3. Summary statistics: non-evaders and evaders in 2003. Appendix 1
It is, however, conceivable to belive that a substantial fraction of labor income in the
irregular labor market was under-declared in the survey.
The most important questions helpful to construct and estimate the model are
those regarding:
7
-
Gender
-
Age
-
Weekly hours of work in the regular economy
-
Hourly wage rate in main occupation
-
Occupation by industry
-
Non- labour income
-
Social acceptance related to not reporting income to tax authorities
-
How do they perceive the chance of being caught if they do not report parts of
their income to tax authorities
-
In the case of evasion being detected by tax authorities, how large do they
think the penalty tax rate will be
-
If, during the last 12 months, they have received compensation for work that
has not been reported or will not be reported to the tax authorities
-
If yes, how many hours of non-reported income activity have they conducted
during the last 12 months.
The questions mentioned above will be used to define the variables appearing in
the empirical model.
In Table 4 I report the replies of the respondents considering the decision whether to
evade taxes, and the perception of probability of being detected.
Table 4:How do people perceive the probability of being detected. Appendix 1.
So, I summarize the reply of the respondents considering the decision whether to
evade and the perception of probability of being detected. From table 4 it is shown
that:
-
Most people declared that they will probably not be caught and the perceived
probability that this event will happen is also low, respectively 52% among
the evaders and 40% for the whole sample.
-
The majority of the respondents are honest individuals and the fear of getting
caught may influence their decision not to evade.
8
-
Among evaders only one declared the highest probability of being definitely
caught and for the entire sample only 5% declared that they will definitely be
caught in case of evasion.
-
Comparing the percentage of individuals who declared definitely not be
caught, with those who declared to be definitely caught, the difference is
quite large ( 22% against 1%). This detail indicates that, among these two
polar events, most of the evaders assume that they will not be caught (giving
the highest probability to this event) against the event of being caught (giving
the lowest probability). Thus we can conclude that evaders give overweight to
the probability of not being caught.
In addition, since rational taxpayers may engage themselves in tax evasion by
underreporting their labor income they may, not only evade taxes but also, provide
some insurance against detection. As shown by Feinstein (1991) only a fraction of the
evaders get detected by the tax auditing.
However it has been difficult to obtain unambiguous results with regard to how
tax rates, probability of being caught through tax audits and penalty taxes would
affect individual behaviour.
Table 5 Social acceptance of tax evasion. Appendix 1
It is important to know the feeling among the tax evaders about the possibility
of detection and social acceptance. Table 5 reveals that the relationship between the
perception of the probability of being caught and the social acceptance of tax evasion
is such that the evaders, who give low weights( 1%) to the probability of being
caught, consider the tax evasion an acceptable behavior (57%). The majority of the
evaders consider tax evasion to be acceptable (75%).
An important variable which may influence the individuals decision about the
undeclared regular hours of work is the hourly wage. Therefore it is important to
observe the relationship between the hourly wage and those individuals who declared
to have evaded. In this survey individuals were asked about wages in the regular and
irregular labor market, and from their replies we observe the following:
9
Table 6 Hourly wage rates. NOK 2003. Appendix 1
We find that, among the evaders, the majority of the respondents are those with an
hourly wage (lower than 162 NOK per hour) below the level of average hourly wage
(166 NOK per hour), approximately 57%. The percentage of evaders, including also
the category of average hourly rate is around 70% This
exemplifies that the
phenomenon of tax evasion, not declaring part of the regular hours of work, is more
widely spread among individuals with hourly wage rate lower than the average. Also,
we find that, among honest individuals, the percentage of respondents increases with
the level of hourly wage rate. This indicates that for high hourly wage rates the
incentive not to declare regular hours of work diminishes. An explanation could be
that, if they get caught by the tax authorities, the opportunity cost would be higher,
the higher are the incomes not declared.
It is also important to observe what the survey demonstrates regarding the
relationship between the age and the behaviour towards evasion.
In table 7 I split the respondents into 4 groups of age: those with an age below 30,
those between 30s and 40s,those between 40s and 50s and those above 50.
It can easily be observed that the percentage of evaders decreases with the increase
of group age. The percentage of individuals in the group of below 30s, who declared
to have irregular hours of work in the labor market, is the highest, 15%. But among
the evaders we find that the group of those between 30s and 40s have the highest
percentage, 31 %.
Table 7 Age of the evaders. Appendix 1
The participation of the individuals below 30 in the labor market could be lower since
the starting age of entering in the labor market has shifted upward. This happens
because individuals invest more in education and instruction and as a consequence
they postpone the entry into the labor market. They may however find it profitable to
work a few hours of work in the irregular labor market.
In the second age category, those between 30 and 40, the participation in the
regular labor market is higher, but yet still we observe 31% as the largest group
among the evaders. The explanation could be that individuals at the ages 30-40s are
in the beginning of their career and the hourly wage is not very high. Therefore, they
are tempted not to declare part of their regular hours of work to tax authorities as an
10
opportunity to obtain higher incomes. As the work experience and qualification
increases with age, the individuals may have higher hourly wage rates and as
consequence higher generated labor income. We observe from the survey, table 6,
that the individuals get less inclined to evade taxes as their hourly wage increases.
Following the same reasoning we can conclude that when the age gets closer to the
retirement age the inclination to evade taxes decreases.
The choice made regarding the regular and irregular hours of work by gender
is demonstrated in the next table. Graphically also we can observe the main
differences of choices, in case of male and female.
Table 8, 9. Gender, regular and irregular hours.
Table 8 illustrate the distribution of hours of work per week among male and
female. It is shown that most of males and females declared to have full time jobs
and by gender there is almost no difference. They have a percentage of
approximately 50% demonstrating that the male and female generally prefer
having a full time job. Also it is shown that, among those who do not participate
in the labor market and have declared no hours of work, female have the highest
percentage of 32% compared to man of 25%. We can observe that for weekly
hours of work below the average of full time job the percentage of females is
higher compared to male, 78% versus 22%. This fact demonstrates a higher
preference among female for part-time jobs compared to male. As the weekly
hours of work increases and is above the full time job, the situation is reversed.
We find that for this category female percentage is quite low compared to male,
14% against 86%.
Graphically, it is shown this phenomenon, which is commonly found also in the
literature.
Table 9 furnish information and statistics about irregular hours of work by gender.
As we observe, most of the evaders, male and female declared to have irregular
hours of work for the low categories, but considering the difference by gender
male have a higher percentage compared to female. So we can draw the
conclusion that male participation and efforts in the labor market is higher
11
compared to female, respectively in regular and irregular labor market. What is
puzzling is the female response at the category of 600-799 hours per year. In
weekly bases this can be considered as aside job. So it may exist a low percentage
among female who decides to work part time and not declare it at all. This may
depend from marital status, level of income, social benefits and other factors
which I examine in the next tables, included in the appendix A.1. The distribution
of irregular hours of work by gender is also demonstrated graphically.
So far we have commented on some co-variation between observed
variables and the number of evaders. In the appendix A1.1 I have included
additional summery statistics related to other essential variables like occupational
status, working sector, level of income not declared to the tax authorities.
However, some of these variables may be correlated, and to find out how
economic variables and the observed ones affect individual behavior we need to
estimate a behavioral model.
4- Description of the Model
The basic idea behind the structure of the model is an application of the
utility maximization. Individuals consider after tax income as a good and hours
offered in the labor market as a bad. They face a market-determined wage, which
establishes the price at which they can exchange leisure for additional income. It
is expected that the individual reaches a higher level of utility by an increase of
disposal income and leisure. Thus to optimize the utility of an individual a trade
off between leisure and income is involved.
When we try to construct a model of labor supply we do not observe the
utility of an individual. We thus have to specify how preferences are distributed.
Usually the observed labor supply is assumed to correspond with the desired labor
supply. Actually the people are restricted in their choices, so it would be more
realistic to include in the labor supply studies the option of evasion and irregular
hours of work. This option may be considered as an alternative of compensation
12
to the restrictions in hours of work . Thus, it is assumed that preferred hours of
work are equal to actual hours of work, and the later includes the regular and
irregular hours of work.
The model I refer to is the one developed by Strøm et al (2004), a nested
multinomial logit model of labor supply when tax evasion is an option. Tax
evasion is characterized as the legal work whose income is not declared to the tax
offices.
I study quantitatively, at the intensive margin , the possibility of evading
and the number of hours supplied in labor markets, the regular and the irregular
one. I also study qualitatively, at the extensive margin, the decision of the
individual whether to evade during the last 12 months. The model can be used to
predict hours of work, even if it is only estimated on participation decisions.
Expected labor supply, predicted following the extensive and intensive
margin approach is compared with a discrete choice model of labor supply where
no irregular hours of work are observed.
First, individuals may respond along the extensive margin. That is, they can
decide whether or not to enter the labor force, regular and as well as irregular one.
Second, individuals can respond along the intensive margin. That is, they can vary
their hours or intensity of work on the job.
Thus, the basic assumption in this model is that the individual decides in two
stages:
In the first stage he decides to be honest or to be an evader, choosing the
approach with the highest utility. As preferences are not observable we can derive
the probabilities that individuals will pursue an evading or honest approach
depending on the expected values of maximum utility, Ben-Akiva and
Lerman(1985). Also, it is assumed that the probability of choosing an evading
approach depends on the individual’s perception of how socially acceptable tax
evading is and on the opportunity to evade taxes. The opportunity to evade taxes
is different across sectors. In previous studies, it has been revealed that the
construction sector is the one which mostly favours tax evasion. On the contrary,
13
the government sector is the one in which tax evading activities are the most
difficult to perform.
In the second stage, the individual decides how many hours to supply in
the regular and in the irregular labour market. Thus, being a tax evader implies
working in both markets, respectively in the regular and the irregular one. The
work in the second market consists of undeclared hours of work, and as a
consequence an undeclared part of labor income to the tax office3.
When the individual decides to follow an evading strategy, he has to
consider the risk of being caught. Thus, such a decision is considered to be a
decision under uncertainty. This decision under uncertainty is assumed to follow
the V-N-M (Von Neumann-Morgenstern) expected utility model, Von Neumann
and Morgenstern (1944), and Gul and Pesendorfer (2004).
The individual who decides to follow an honest approach works only in the regular
labor market.
The structure of the model I estimate is a conditional multinomial logit, since
we are dealing with a multiple choice problem, accordingly the decision is
conditional and varies over individuals and choices. Conditional multinomial logit
models have the feature that the predictors vary over choices( and possibly
individuals too) but the parameters do not.
The result at the intensive margin(IM) and extensive margin(EM) labor
supply model, when tax evasion is an option, can be compared with regard to the
prediction of expected labor supply following model (DCM) when tax evasion is
ignored.
Tax evasion is a risky activity and not easily observable. Thus, just a small
fraction of this activity is captured and detected by the tax authorities. Subsequently,
it is important to study the level of the phenomenon of tax evasion and
underreporting, quantitatively as well as qualitatively.
Summarizing, what was put in plain words the individual decide in two stages:
3
In the study of Webley& Cole & Eidjar(2001) tax evasion is considered to be a result of the
interaction of constraints and instigations, which can be both economic or psychological. They
concluded that the instigational factors operate in the early stage in the process of contemplating
breaking the rules and the constraining factors come into play at a later stage.
14
-
First the individual decides whether to be honest or an evader
-
Given the first decision, in the second stage he decides how many hours to
work in the regular and/or irregular labor market
Three different models will be estimated:
-
A labor supply model at the intensive margin or effort model that uses all the
observations, participation decisions as well as hours of work observed.
-
A labor supply model at the extensive margin or participation choice that uses
only the participation decision in the estimation of the model.
-
A discrete choice labor supply model assuming no irregular hours of work.
The structure of the model is such that also the extensive model can be used to
predict hours of work. These results will be compared with those attained in the
case that we estimate a labour supply model assuming, counterfactually, that there
are no irregular hours of work (DCM).
4.1- Intensive model of labour supply
Starting with the second stage, to generate the net income, I calculate individual gross
earnings assuming invariant gross hourly wage rates and I derive the net income by
applying the 2003 Norwegian tax and transfer system. Thus, the after tax wage
income of an honest individual is:
(4.1.1)
DiH
RiH I T ( RiH , I )
where i = 1,…. 2, n
and the utility of this honest individual is:
(4.1.2)
UiH =U(DiH,hiH,X)+İi
where i=1,2….,n
and:
15
-
RiH is gross annual wage income derived by multiplying hiH (annual hours
of work) with W (hourly wage rate in the formal market).4
-
I is non labor income.5
-
T(RiH , I) 6 is the step-wise tax function related to R and I. X is a vector
of socio-demographic characteristics,
-
n is the number of the alternatives of working hours.
U(DiH,hiH,X) is the deterministic part of the utility function and İi is be the random
part, assumed to be extreme value IID distributed with zero mean and a constant
variance across alternatives and individuals. This means that the cumulative density
of İi is given by F(İi )=exp(-exp(-İi)). Assuming that the individual chooses the
alternative with the largest utility across all the possible ones we can derive the
expected value of the maximum of the utility function, which we denote SH and it
has been demonstrated by Ben-Akiva and Lerman(1985) to be equal to:
n
(4.1.3) SH
E>maxi 1,2..n UiH @ P2 ln¦exp(ukH / P2 )
k 1
where P 2 is a constant and the marginal utility of income.
The deterministic part of the utility u kH = U(DkH,hkH,X) is observed and we know
the distribution of the remaining portion of the utility. Taking the derivatives of the
consumer surplus SH with respect to (ukH) we get the optimal choice probability
P(hiH / H) P(UiH maxk 1,nUkH) which is a multinomial logit conditional on the honest
strategy:
(4.1.4) P ( hiH / H )
wS H
wu iH
exp( u iH / P 2 )
n
¦ exp( u
kH
where 1=1,2..n
/ P2 )
k 1
4
Annual hours of work hiH are computed as the product of weekly hours of work with 52 week per
year.
5
Since in Norway personal income tax follows a dual approach, I- non labor income is taxed at a
rate of 28 per cent while labor income is taxed at a higher progressive rate, 2003 tax schedule.
6
The difficulty in estimating the labor supply decision in the presence of a nonlinear tax comes
from the fact that individuals have different preferences over leisure and disposable income
(which can not be observed directly) and that the budget set can be non-convex.
16
If the individual is an evader, his decision is taken under uncertainty following a VN-M (Von Neumann-Morgenstern) expected utility model. I will define a preference
relation over the first and second strategy( evading or not) and I will use this
preference to construct a utility function ( in case of detection or not). Then, I define
the expected utility of an evader as the sum of the utilities in case of detection and not
detection, as demonstrated below. First I describe the outcome if the individual is an
evader. There are two outcomes, one when he is not detected and one when he is
detected.
Dij,E,D RiH RjE I T(RiH RjE, I) S(RjE)
(4.1.5)
where i, j = 1,2, n
(if detected)
(4.1.6) Dij ,E , ND
RiH R jE I T ( RiH , I )
where i, j = 1,2,n
(if not detected)
and:
-
Dij,E,D is after tax and penalty rate income when the individual is an
evader, works hij annual hours, including hours hiH supplied in the regular
market and hjE supplied in the irregular market and detected by the tax
authorities.
-
ʌ(RjE) is the fine he has to pay if detected which depends on the income
evaded.
-
Dij,E,ND is after tax income when the individual evades, but he is not
detected.
-
RjE is gross annual wage income derived by multiplying hjE (annual hours
of work in the informal market) with WE (hourly wage rate in the irregular
market)
As previously mentioned, the decision taken under uncertainty concerning an event
implies that it may or may not happen. Most likely the probabilities of accruing of
these events are not precisely known. However, people can form a priori belief about
these probabilities.
17
In the model, the probability of being detected is denoted q and it is be based
on the respondents’ replies to question a29. The questions are given in the Appendix.
This question was used to structure variable q, the respondents perception
concerning the chance of being caught in case they do not report part of their income
to the tax authorities. Therefore, the utility function of an individual with undeclared
regular hours of work, UijE , following an evading approach, has two parts:
-the deterministic part (expected utility related to the lottery of tax evasion).
-the random term, with the same distribution as the random term in(1.2)
Thus, following the V-N-M expected utility model the utility of an evader will be
defined as:
(4.1.7) u ijE
q * u ( Dij , E , D , hiH h jE , X ) (1 q ) * u ( Dij , E , ND , hiH h jE , X ) H ij
where i,j=1,2..n
Continuing further we get that SE is given by:
(4.1.8) S E
E >max
i , j 1, 2 . n
U ijE
@
n
n
P 2 * ln ¦ ¦ exp( u ijE / P 2 )
k 1 r 1
where UijE q * u(Dij,E,D , hiH h jE , X ) (1 q) * u(Dij,E, ND , hiH h jE , X )
The conditional probability of working in the regular economy hiH hours and
in the irregular economy hiE hours, conditional on being a tax evader, can be derived
in the same way as we did previously with the honest individual:
(4.1.9)
P(hiH , h jE / E )
wS E
wuijE
exp(uijE / P 2 )
n
n
¦¦ exp(u
rkE
/ P2 )
k 1 r 1
According to Ben-Akiva and Lerman(1985) the probability of choosing an optimal
strategy can be evaluated by the expected consumer surpluses. Thus, P(H), the
probability of choosing the honest strategy is given by:
18
(4.1.10)
P( H )
exp(S H / P1 )
exp(S H / P1 ) exp(S E / P1 )
Note that the probability of being an evader is, P(E)=1-P(H) and P1 is a constant. If
P1 = P 2 the resulting model will be a multinomial logit model.
The unconditional probabilities are :
P(hiH , H ) P(hiH / H ) * P(H )
(4.1.11)
and
P(hiH , h jE , E) P(hiH , h jE / E) * P( E)
With P1 = P 2 , these unconditional probabilities are multinomial logit probabilities.
Considering the observations on the alternatives and choices made by the individuals,
their characteristics in each possible alternative, the parameters entering the
deterministic part of the utility function and the opportunity density can be estimated
by maximum likelihood. The likelihood expression is the joint probability of
individuals classified as honest with those who are classified as evaders, since in the
questionnaire were included questions to help distinguishing between the honest and
the evaders.
(4.1.12)
L
– P (h
S
SN H
iH
, H ) * – PS (hiH , h jE , E )
SN E
where NH is the number of honest individuals in the survey and NE is the
number of evaders.
I mentioned in the introduction that tax evasion is considered to be as a risky
activity, if detected is penalised by a fine, in addition to the stigma of reputation. So
it is important to bear in mind the individuals perception has about tax evasion, the
perception of detection, as well as the perception of acceptance of tax evasion by
the society. All these observations may influence the probability of choosing to
evade or not.
Since rational taxpayers may engage in tax evasion by underreporting their
income they may not only evade taxes but also provide some insurance against
19
detection. As shown by Feinstein (1991) only a fraction of the evaders get detected
by the tax auditing. Thus, it is important to know, what people think about the
possibility of detection and social acceptance. For this reason it is important to
include in the model a variable that reflects the perception of how socially
acceptable the individuals think tax evasion is.
It has been demonstrated in other studies that the opportunity to evade taxes
differs across sectors and jobs. It has been also shown that one of the sectors, where
tax evasion is widespread is the construction sector. The opposite is true if we
consider those who work in the government sector and police office.7
To integrate in the market these possible distinctions in tax evasion
opportunities we include in the model two dummy variables, one for those working in
the construction sector and one for those working in the government sector. In the
Appendix A1.1 I have constructed the summery statistics for the evaders by
occupational status and working sector.
Thus, the expected utility value of choosing a tax evasion strategy is influenced
by other important factors. These factors can capture the effects of social acceptance
and opportunity to evade on the choice probability of undertaking tax evading
activities. We denote this factor g(Z), or
g(Z)=exp(g0+g1Z1+g2Z2+g3Z3),
(4.1.13)
where
Z1=1 if the individual thinks that tax evasion is socially acceptable and 0
otherwise,
Z2=1 if the individual works in the construction sector and 0 otherwise,
Z3=1 if the individual is a government employee and 0 otherwise.
The g(Z) function is included in the model so that the value of evasion in the choice
probability is weighted by this function.
Thus we would have:
7
See Pestieau & Possen ( 1991) as well as Kolm&Larsen (2004) about the connection between
occupational choice and tax evasion.
20
(4.1.14)
P( H )
exp( S H / P1 )
exp( S H / P1 ) g ( Z ) * exp( S E / P1 )
Finally, the structure of the model I estimate is a conditional multinomial
logit, since we are dealing with a multiple choice problem, therefore the decision is
conditional and varies over individuals and choices.
4.2 -Extensive model of labour supply
The structure of the model based on participation decision at the regular and the
irregular labor market will be as follows:
The individual’s decision whether being an evader or not is captured by a dummy
variable8. The construction of this dummy variable is based on the responses given to
question a32. This question provides information about the fact of not declaring
regular hours of work and earned income to the tax authorities during last 12 months.
Compared to the previous model we have:
Pr(a32=1)=P(E)
(4.2.1)
and
Pr(a32=2)=P(H)=1-P(E)
(4.2.2)
following the same structure for the utility function and the optimal choice
probability we then have that the probability of being an evader is:
(4.2.3)
P(E)
ªn n
º
g(Z ) * «¦ ¦exp(ukrE / P1 )»
¬k 1 r 1
¼
n
ª
º
ªn n
º
«¦exp(ukH / P1 )» g(Z ) * «¦ ¦exp(ukrE / P1 )»
¬k 1
¼
¬k 1 r 1
¼
The probability of being honest is:
8
The dummy variable will take value 0 if taxes are evaded during the last 12 months and value the 1 if
he didn’t evade taxes during the last 12 months.
21
(4.2.4)
º
ªn
«¦exp(ukH / P1 )»
¼
¬k 1
P(H) 1 P(E)
n
ª
º
ªn n
º
«¦exp(ukH / P1 )» g(z) * «¦ ¦exp(ukrE / P1 )»
¬k 1
¼
¬k 1 r 1
¼
where :
g(Z)=exp(g0+g1Z1+g2Z2+g3Z3),
The likelihood expression in this case will be:
N
L
(4.2.5)
– P (E) P (H)
1 d
d
n
n
n 1
d 1 if a 32
d
1,
0 otherwise
Comparing the intensive and the extensive models of labor supply we observe
that, assuming µ1=µ2 , the same parameters appear in these models. The difference
between these models consists of the fact that in the intensive model the dependent
variable is based on alternatives of hours worked in both, the regular and the irregular
labor market. In the extensive model the dependent variable is based only on the
participation in respective labor markets. Thus, all the parameters of the utility
function are also estimated in this last model. Once estimated, this model can be
applied to yield the probability of working certain hours.
Both in the intensive and the extensive models of labour supply I use a log
transformation for the variables of
motivated
disposal income and leisure9. This is also
by the fact that in general log transformation works well in many
situations and it can help to make the data symmetric.
The deterministic part of the utility function of the honest individual is
9
Since different individuals have different hours of work, hourly wages and disposal income, the raw
data may have very large values or very small ones. Thus I Use log transformation of the data which
helps to squeeze and stretch the data. This will avoid problems like skewness , outliers and unequal
variation.
22
(4.2.6)
8760 hkH
D
ukH (D, h, X ) D0 * log( H ) (E0 E1 * X1 E2 * X 2 ) * log(
)
100000
8760
The deterministic part of the utility function of the evader is:
(4.2.7)
ukrE ( D, h, X )
8760 hkrH
D
)
q * ^ D 0 * log( ED ) (E0 E1 * X1 E 2 * X 2 ) * log(
100000
8760
`
8760 hkrH
D
)
(1 q) * ^ D 0 * log( END ) ( E 0 E1 * X 1 E 2 * X 2 ) * log(
100000
8760
where:
DH= disposable income when the individual has declared to be honest and works hkH
hours per week,
DED= disposable income if the individual is a detected evader and works hkrH hours.
DEND= disposable income in case the evader is not detected.
X1 = is a dummy variable, equals 1 if the individual is a woman and zero otherwise.
X2 = is the age (in years) of the respondents and we considered only those individuals
included in the category of age between 18 and 66 years old.
(q)= the transformed probability of being caught, where q is based on the replies of
the respondents.
They where asked how large they consider the chance (in percent) of being
caught, in case of not declaring the incomes to tax authorities. Thus, the probability
of detection is based on the individual's perception of detection probabilities, as
reported by the respondent.
The disposable income D has been calculated applying the stepwise taxfunction of 2003 which is given in details in Appendix 1. The fine, if tax evasion is
detected, is based on the respondents perception, as reported in the survey. Thus the
probability of being caught and the associated fines are subjective to the belief of
individuals. The hourly wage rate used to calculate gross incomes equals the ordinary
hourly wage rate reported by the respondent in the questionnaire. The survey encloses
information about the hourly wage rates of the irregular hours of work which are used
to generate not declared incomes. If annual hours of work are denoted by h, the
23
`
hours of leisure will be (8760-h).10
Hours worked in the regular sector are
observed in broad categories and I have used the midpoints (10, 25, 37.5) per week
with 50 hours a week as a maximum. Hours worked in the irregular economy are
reported as annual hours, and again in broad categories with midpoints
(10,25,37,75,150,250) and 700 as a maximum.
Referring to previous studies there exist a relation of substitutability between
hours of work in the regular market with those in the irregular market. The
marginal disutility of working in both markets is assumed equal. The hours of
work entering in the utility function are taken as the sum of irregular and regular
hours of work. In other studies it is assumed that the marginal disutility is not
equal since other factors like social stigma may increase the disutility of evading
and it would be higher in comparison with the case of no evasion (Fortin 2001).In
this model stigma effect is captured by the variable Z1 , used to weight the value
of tax evasion appearing in the probability function.
4.3- A discrete choice model (DCM) of labor supply
with no option of evasion
When we try to construct a model of labor supply we do not observe the utility of
an individual. We observe some characteristics and try to mach the unobservable
with what is observable by specifying a functional relationship.
In the DCM model the after-tax wage income is:
(4.3.1)
DiH
RiH I T (RiH, I ) where i = 1,…. 2, n
and the utility of the individual is be:
(4.3.2)
UiH =U(DiH,hiH,X)+İi where i=I,2….,n
and where:
10
8760= (365days*24hours – hours of work).
24
-
RiH is gross annual wage income derived by multiplying hiH (annual hours
of work) with WH (hourly wage rate in the regular market)
-
I is non labor income
-
T(RiH , I) is the step-wise tax function related to R and I.
UiH is the utility when the individual works hiH hours, X is a vector of sociodemographic characteristics, U(DiH,hiH,X) will be the deterministic part of the
utility function and İi will be the random part, assumed to be extreme value IID
distributed.
Wee can derive the expected value of the maximum of the utility function,
which we denote by SH like in (4.1.3):
n
(4.3.3)
SH
E>maxi 1,2..n UiH @ P2 ln¦exp(ukH / P2 )
k 1
where ukH=U(DkH,hkH,X).
Taking the derivatives of the consumer surplus SH with respect to (ukH) we get the
optimal choice probability P(hiH ) P(UiH
maxk 1,n UkH ) .
Thus, the conditional probability of choosing hiH hours is:
(4.3.4)
P(hiH )
wSH
wuiH
exp(uiH / P2 )
n
¦exp(u
kH
where 1=1,2..n
/ P2 )
k 1
The unobserved heterogeneity of the preferences is represented by the constant µ2.
The deterministic part of the utility function of the individual is:
(4.3.5)
ukH (D, h, X ) D0 * log(DH / 100000) (E0 E1 * X1 E2 * X 2 ) * log((8760 hkH ) / 8760)
where:
25
DHk= disposable income when the individual has declared to be honest and
works hkH hours.
The disposable income DHk has been calculated applying the stepwise tax-function of
2003 which is given in Appendix 1.
If hours of work are denoted by h, the hours of leisure will be (8760-h)11 annually.
Hours worked in the regular sector are observed in broad categories and we have
used the midpoints (10, 25, and 37.5) per week and with 50 hours a week as a
maximum.
X1 is a dummy variable, which equals 1 if the individual is a woman and zero
otherwise.
X2 is the age (in years) of the respondents (we consider only those individuals
included in the category of age between 20 and 60 years old).
5- The empirical results of intensive and extensive model of labor
supply compared with the DCM
5.1 Econometric specifications
One of the main problems we have to deal with, when trying to estimate
quantitatively and qualitatively the labor supply choice by an individual, is the
unobserved wages for the non-workers. This problem can be solved by following
Heckman procedure. To overcome the selectivity biased problem a wage equation
is defined as below , which will be estimated separately:
log w
:'*E H i
where : includes the explanatory variables, H is the error term which is normally
distributed with mean zero. The log (w) is assumed to vary across sectors and is
11
(8760-h) annual leisure= (365days*24hours – hours of work).
26
regressed on education and age. In the (Appendix 3) you will find the estimation
results and the graphical representation of the predicted wage.
Net income depends on labor supply, hourly wage rates, incomes generated from
other sources apart labor. To generate the individual net income, based on a nonlinear tax function including also non-labor income in the budget set, produces
non-linearity to the problem. The contribution of each individual to the likelihood
function is the probability that his observed choice of hours is an optimal utility
compared to other possible alternatives. As we mentioned previously from the
derivative of the consumer surplus we get the optimal choice which is a
multinomial logit.
Differenlty from Strøm et al (2004), which attempts to estimate a nested logit
model, I use a more general model. This general model can be achieved by
combining the multinomial logit model with the conditional one, so the
deterministic part of the utility function depends on individual characteristics that
are constant across choices, as gender, age, martial status and other characteristics
that differ across choices( and possible across individuals) like net income. The
nested logit model is mostly used for estimating choices over alternatives that can
be grouped together. Since in the model the tax evasion is considered as regular
hours of work not declared to the tax authorities it implies that these alternatives
of irregular hours of work are incorporated to the alternatives of regular hours of
work. Thus options of irregular hours of work go together with the regular hours
of work and can be classified as a nest12. So for simplicity I can generalize the
nested logit model and estimate it following a conditional multinomial logit
model in spite of a nested logit model which is computationally burdensome. In
the appendix I have included the scheme of the transformation of the Nested
Logit model to a generalized one.
The features mentioned above do favor the use of conditional multinomial logit
model but using these technique I failed to estimate the unobserved heterogeneity
12
In spite of considering 2 nests, 8 alternatives of irregular hours of work and 5 alternatives of
regular hours of work, I will consider 40 nests which are created as a combination of the initial 2
nests. This is demonstrated by the tree in the appendix 4.
27
of preferences in first and second stage respectively, P1 and P 2 , is assumed to
degenerate to a ratio P 2 / P1 = 1 in the case of the conditional multinomial logit.
5.2 Empirical results of EM, IM compared to DCM
Table 17, (Appendix 1.2) reports the estimation results of the intensive and
extensive model compared with the results of DCM. A full understanding of the
participation and hours of work decision including also the option of evasion
requires solving the problem of selection bias.
It is therefore important to deal with the problem of selection bias and correcting
for the missing wages of non-workers13 which I report in the appendix 3.
I observe that in the extensive and intensive margin approach the coefficients are
all significant expect age and dummy about working in the government sector. An
important distinction is that at the extensive margin the coefficient related to
woman and age is positive which means that the participation increases with age
and for women participation increases more than man. But in the intensive model
we find that the coefficient of age and woman are negative implying that if we
refer to efforts at work they decrease with age, and for women more than for man.
Getting closer to the retiring age they may prefer to work less both in the regular
and irregular labor market. Taking into consideration what was observed by the
survey regarding age and decision to evade these result seem logical.
The disposable income14 and hence taxes have a significant and positive impact
on choices. Thus the disposal income is one of the main determinants of the
behaviour towards tax evasion.
Concerning leisure, a positive and significant parameter it is found, at
extensive and intensive margin implying a positive correlation between this
variable and marginal utility of leisure.
13
I have corrected for selectivity bias.
Non linear tax schedules and transfer programs may create complicated functional relationships
involving wages, non labour income and labor supply in regular and irregular labor market. So it is
useful to distinguish marginal wages from average wages. The former are relevant to marginal
substitution decision and the latter are relevant to income effects Heckman (1993) .
14
28
Also perceived social acceptance of tax evasion has a significant impact,
such that the value of tax evasion increases with the perceived social acceptance
of tax evasion. Having more social support, in occurrence of evasion and hence,
finding a higher prevalence of evasion among colleagues, friends or the group to
whom they pertain to, induce individuals to have a more positive attitude toward
tax evasion. Thus, it is essential to bear in mind the individual’s perception about
tax evasion, the willingness to take risks, perception of possibility to evade,
perception of detection, perception of acceptance by the society of tax evasion
which influence and determine the probability of choosing to evade or not.
The dummy variables of working in the construction sector presented
significant coefficients both at the extensive margin and at the intensive margin
model15. The interpretation of this result is that the construction sector may have
the highest participation in the irregular labor market but exploring at the
intensive margin they do not provide the highest level of efforts and incomes in
the irregular labor market. As I concluded from summary statistics (see Appendix
1.2, Table 10&11) the sector with the highest level of income, generated by not
declaring part of the income from regular work, is the manufacturing sector.
On the subject of the dummy about the government sector it is difficult to
comment on it. At the extensive margin it has the expected sign but it is not
significant. At the intensive margin both the sign and the significance do not
satisfy the expectations. Thus the interpretation that the government sector is the
one which do not facilitate the process of tax evasion do not hold.
Table 18: Parameter Estimates following a IM, EM, DCM approach.
Appendix 1.2
15
The variable of the opportunity density of working in the construction sector includes also those
working in the manufacturing sector, since from the summery statistics was found also a high
percentage of evaders among those working in the manufacturing sector. They had also the highest
level of generated income from evasion.
29
5.3Predicted labor supply
Once I attain the estimation results they can be used to calculate and
predict the expected labor supply from the conditional probabilities of being an
honest or an evader combined with individual characteristics and actual rules of
the tax system. Thus, to recover the expected labor supply conditional that the
individual is an honest one, I have to calculate the utility, for each possible
combination of hours of work in the regular labor market by substituting the
estimations for each parameter into the formula 4.1.2. The following is a logit
transformation like 4.1.4 formula which provides the conditional probability of
being honest for each of the possible combinations. These probabilities are used
to compute the expected labor supply in the regular labor market conditional that
the individual decides to be an honest one. This is confirmed by the last formula
as follows:
1- E (YLH / H )
ª5
º
52 * «¦ P(hiH / H ) * hiH »
¬i 2
¼
where YL is the expected labor supply in a year.
I follow the same procedure to recover the expected regular labor supply
conditional that the individual is an evader. The utility of an evader is calculated
from the 4.2.6 formula which are used to compute the conditional probabilities of
being an evader like in 4.1.9 formula. These procedure is demonstrated by the
formula below:
2- E (YLH / E )
ª5 8
º
52 * «¦¦ P(hiH , h jE / E ) * hiH »
¬i 2 j 1
¼
The conditional probabilities like in 1.9 can also be used to calculate the expected
irregular labor supply conditional that the individual is an evader as follows16:
16
E (YLH )
E (YLH / H ) * P ( H ) E (YLH / E ) * P ( E )
30
5
3- E (YLE / E )
8
¦¦ P(h
iH
, h jE / E ) * h jE
i 1 j 1
Table 19 Predictions of labor supply. Appendix 1.2
In Table 19, E (YLH / H ) denotes the expected hours of work, given that the
individual has chosen an honest strategy, E (YLH / E ) is the expected hours of work
in the regular economy, given that the individual has chosen a tax evading strategy,
E (YLE / E ) is the expected hours of work in the irregular economy, given that the
individual has chosen a tax evading strategy, ELH is the unconditional expectation of
hours of work in the total economy, while ELE is the unconditional expectation of
hours of work in the irregular economy. Predictions are given in Table 19. The
comparison of the labour supply predicted it is presented in the graph6&7, Appendix
1.2.
The first block refers to the comparison of the E(YLH / H) respectively
observed, predicted by the extensive model (EM) and intensive model (IM). The
prediction of IM is much closer to the observed values. This is also factual for the
prediction of E (YLH / E ) in the second block and E (YLH ) in the third one.
In the 3d series I have included also the labor supply predicted if we would
assume that there is no option of evasion and the individual declares all the labor
incomes to the tax authorities. Thus, assuming wrongly that the individual do not
provide irregular hours of work we completely ignore the labor supply in the irregular
labor market and simultaneously the tax evaded. The prediction of labor supply,
similar to other studies, it is biased upward, relatively higher than the observed. In
addition, we ignore an important component, that it is captured by the intensive and
extensive margin model where the option of evasion is included.
In the graphic below I compare E (YLE ) (first block), hours of work in the irregular
economy predicted by EM and IM in confront to observed values. Also I compare
E (YLE )
E (YLE / E ) * P ( E )
- E(YLH) is the honest expected labor supply and E(YLE) is the evader expected labor supply.
31
E (YLE / E ) (second block) the expected hours of work in the irregular economy,
given that the individual has chosen a tax evading strategy.
It is demonstrated that the extensive model predicts the highest LE|E but since
the probability of being an honest individual following IM is higher than the one
predicted following the EM, the overall level of LE predicted by IM is the highest, as
it is shown from the first series.
In the EM the probabilities of participation are correctly predicted. This
follows directly from the estimation program and cannot be used to evaluate the
performance of the intensive model.
With the IM the estimation program does not imply that the participation
probabilities are the same as the observed fractions. I observe that IM predicts that 18
percent of the sample takes part in tax evading activities while only 11 percent is
observed to do so. On the other hand expected hours are fairly better predicted
compared to EM. In the EM the economic incentives play a more significant and
numerically important role than in the IM, where social acceptance is a key
explanatory variable, together with gender in the explanation of behavior. Besides, in
the IM marginal utility of leisure is numerically larger than appearing in EM.
Referring to DCM estimation results they are significant but in the vein of
what the literature sustains, such models, give biased upward results. This is also
our case, when we assume that the individual is an honest one, ignoring as outside
observer the option of tax evasion.
The expected labor supply, predicted excluding the option of evasion
provided such results which are higher than the observed ones, thus they are biased
upward. Comparing the results of IM, when tax evasion is an option, they are closer
to the observed ones, moreover, lower. Thus including into the model the alternative
that individual supplies work to irregular labor market may help to get a better
approximation of actual labor supply as well as to predict better the tax levels.
The IM may not replicate the real situation about the tax evasion and irregular
hour of work ,considering the peculiarity of this issue and the fail of the model to deal
with the unobserved heterogeneity, but it performances much better compared to
DCM.
32
The tax evasion is a risky activity, punished in case of detection.
Consequently, those who engage in recreation this dangerous game, as well as, do not
obey to the rules, hardly accept to fully report it.
Thus, from the survey the observed fraction of being an evader was calculated
to be 11 percent while from the intensive model the prediction of the probability of
being an evader and not declaring regular hours of work to the tax authorities was
calculated to be around 18 percent. Assuming that in the survey, the full reporting
about the actual level of tax evasion was partial, following this model, our estimates
may bring into light a result which is closer to the real tax evasion. Thus it is capable
to capture a fraction of the tax evasion which was not fully declared in the survey.
These results sustain the phenomenon of a higher level of undeclared regular
hours of work, higher undeclared labor incomes to the tax authorities and higher tax
evasion compared to what could be observed.
In case of the intensive model, which studies quantitatively this phenomenon,
the information provided is more substantial. Passing the first barrier, of accepting
that taxes have been evaded, the declaration of how many hours is and as
consequence more detailed information is provided. Even though it bears some
subjectivity, it still helps to get a more clear picture.
Thus, what was said above implies that the intensive model, which relies on
the responses, both at, participation and hours of work decision, has achieved to
visualize better the level of irregular hours of work compared to an extensive one and
what could be observed by the survey, taking into account the subjectivity of the
respondents in their replies.
The observed level of taxes and the predicted ones, based on the two model
approaches, the intensive and extensive one, are given in the table 19, Appendix 1.2.
Parallel to these results I have included the result we would get in case we
assume that all the individuals in the sample are honest and they do not participate in
the irregular labor market and declare all their regular hours of work to the tax
authorities.
Table 20 Prediction of tax levels. Appendix 1.2
TH denotes expected taxes paid by the honest individuals (first block) and TH|E
(second block) denotes the expected taxes paid by the tax evaders. T (third block) is
33
the total expected taxes in the population, which of course has to be between the two
former expectations. TE (forth block) is a hypothetical amount of expected taxes,
namely the amount of taxed paid by the tax evaders if all income, not only the regular
income, were reported to the tax authorities. TE-TH|E is the expected amount of taxes
evaded, which of course also is a hypothetical amount.
It is noticeable that the predicted level of taxation is lower than the observed
one. In the case of those individuals who appear to be honest but in fact has not
declared regular hours of work to the tax authorities, the level of tax they pay is lower
compared with the observed level of taxation. If the tax evaders had to report all
income we do not have any guarantee that he would have worked so many hours as
the sum of regular hours and irregular hours. Also the difference that exists between
the taxes evaded and the one paid in case of evasion and not detection is higher in IM
compared to EM. The predictions of higher E (YLH / H ) and E (YLH / E ) level, from
IM compared to EM, simultaneously with the predictions of higher E (YLE / E ) level,
from EM compared to IM, provides an overall effect of the predicted taxes evaded at
higher level, from IM against EM.
Accordingly, the expected labor supply it is better predicted by IM, and as
consequence the tax evaded it is better predicted following IM. This findings are
crucial for the reason that they highlight the importance of parallel studies at
intensive and extensive margin of the labor supply to predict the behavioral response
toward reforms, social policies, transfer programs of welfare system reforms.
DCM predicted a higher level of TH , compared to IM and EM, implying that
it predict a level of taxes higher than the actual one, discounting the tax level not
declared to the tax authorities. This result is very relevant for policy implications and
the performance of a reform in the tax system, which could give upward biased
predictions of tax revenues. The inclusion of the option of the evasion would assist
to provide a more realistic examination of the tax reform effects.
34
6. Conclusion
The main purpose of the paper has been to study the decision of the individuals
regarding their allocation of time in the regular and irregular labor market, based on
a IM and EM approach. The probability of participating in the respective labor
markets was also studied. The basic model I referred to was a labor supply model
when tax evasion is an option, developed by Strøm et al (2004).Following this model
I studied the decision of the individual with regards to the allocation of time in the
regular and irregular labor market qualitatively ( if he ever didn’t declare work in the
regular employment) by a EM model and quantitatively (if he undeclared regular
work how many hours where not declared) by a IM model.
The disposable income17 and hence taxes have a significant and positive impact
on choices. Thus the disposal income is one of the main determinants of the
behaviour towards tax evasion.
Related to leisure a positive and significant parameter it is found at extensive and
intensive margin implying a positive correlation between this variable and
marginal utility of leisure.
The dummy variables related to construction are significant both at the extensive
margin and at the intensive margin model. It is difficult to comment on the
dummy about the government sector. At the extensive margin it has the expected
sign but it is not significant. At the intensive margin both the sign and the
significance do not satisfy the expectations. Thus the conjectures that the
government sector is the one which do not facilitate the process of tax evasion do
not hold. Also perceived social acceptance of tax evasion has a significant impact,
such that the value of tax evasion increases with the perceived social acceptance
of tax evasion. Having more social support, in case of evasion and hence, finding
a higher prevalence of evasion among colleagues, friends or the group to whom
they pertain to, induce individuals to have a more positive attitude toward tax
evasion.
17
Non linear tax schedules and transfer programs may create complicated functional relationships
involving wages, non labour income and labor supply in regular and irregular labor market. So it is
useful to distinguish marginal wages from average wages. The former are relevant to marginal
substitution decision and the latter are relevant to income effects Heckman (1993) .
35
The IM could replicate a more realistic situation about the prediction of
expcted labor, mean tax and irregular hours of work. While considering the
peculiarity of this issue IM implied a higher level of tax evasion compared to EM and
DCM . Consequently, the expected labor supply and tax revenues are better predicted
by IM. These findings are crucial for the reason that they highlight the importance of
parallel studies at intensive and extensive margin to predict the behavioral response
toward reforms, social policies, transfer programs of welfare system reforms.
Thus the inclusion of option of evasion to the studies at extensive and
intensive margin would make the difference in sketching the optimal tax system.
The results obtained are important for policy implications. Understanding
better the mechanism of individual behaviour in labor market helps to remove
disincentives related to tax evasion as well as design social and economic policies
aiming at
increasing individuals benefits of participating in the regular sector.
Transforming the undeclared irregular work into a regular one may help to achieve
full employment, improve the quality and productivity at work and strengthen the
social cohesion.
36
Appendix 1
Table 1. Response rates
2003
2001
Asked to participate
1742
1690
Agreed to participate
86%
81%
Answer percentage
72%
58%
Response rate, percent of asked
62%
47%
Table 2. Summary statistics: the whole sample in 2003.
Number of observations
895
Number of non-evaders
797
Number of evaders
98
Percentage females in the sample
51.62%
Percentage who thinks that tax evasion is socially
accepted
Mean
St.D.
51.7 %
Minimum
Maximum
42.97
11.85
18
66
Hourly wage rate, NOK
166.55
72.71
423
510
Gross annual wage
income, NOK
Weekly hours worked
in the regular economy
391666
189966.5
50000
700000
37.6
9.69
15
60
Annual tax, NOK
100776
95541
0
618754
Perceived fine if
detected, per cent
26.8%
18.3
0%
50 %
Subjective probability
of detection
0 .129
0,050
0.0
0.25
Age
37
Table 3. Summary statistics: non-evaders and evaders in 2003
Non evaders
evaders
Age
43
40
Percentage females
54%
33 %
Weekly hours.
37
31.59
Annual hours in irregular market
73.24
Hourly wage rate, NOK
166.01
157.2
Annual gross wage income,
388627.5
356488
Annual gross income evaded
10485
Perceived fine if detected, %
27%
25%
Subjective probability of detection
0.133
0.10
Percentage who thinks that tax evasion is socially accepted
48%
76%
Table 4: How does people perceive the probability of being detected
Will
definitely Will probably not be
not be caught
caught
Might
Be
caught
Will
Will probably be definitely
caught
be caught
Total
q
0.05
0.1
0.15
0.2
0.25
evader
22
51
21
3
1
98
honest
63
303
284
94
45
789
Total
85
354
305
97
46
888
q- is the subjective probability of detection
38
Table 5 Social acceptance of tax evasion
Probability of
detection
Acceptable
Doubt of
acceptance
Not
acceptable
Uncertain
Total
0,05
21
1
0
0
22
0,1
43
5
0
3
51
0,15
8
12
1
0
21
0,2
2
1
0
0
3
0,25
1
0
0
0
1
Total
75
19
1
3
98
Table 6 Hourly wage rates. NOK 2003
A10- What is/was your average hourly pre-tax income from your main occupation
and evasion?
a10
a32
yes
no
total
percent
percent
Below 85 kr/hour
6
17
23
26%
7%
85-99 kr/hour
2
22
24
8%
2%
100-119 kr/hour
15
115
130
12%
18%
120-134 kr/hour
10
135
145
7%
12%
135-154 kr/hour
16
129
145
11%
19%
155-169 kr/hour
11
61
72
15%
13%
170-184 kr/hour
6
48
54
11%
7%
185-204 kr/hour
8
65
73
11%
10%
205-254 kr/hour
7
65
72
10%
8%
255-339 kr/hour
2
37
39
5%
2%
340-510 kr/hour
1
19
20
5%
1%
0
84
8
721
8
805
0%
10%
0%
100%
510+ kr/hour
total
39
Percentage of evaders per category
20%
18%
16%
14%
12%
10%
8%
6%
4%
2%
0%
1
2
3
4
5
6
7
8
9 10 11 12
Graph1
Table 7 Age of the evaders
Age of respondents
Evaders
Non evaders
Total in %
Below 30s
19
125
15%
30=<age<40
30
241
12%
40=<age<50
27
248
11%
age>=50
19
269
7%
Total
95
883
11%
Table 8 Gender and hours of work in regular sector
A8 and A1
no work
males females total
percent males percent females
136
169
305
45%
55%
less than 10 hrs
11
17
28
39%
61%
10-19 hrs
11
39
50
22%
78%
20-29 hrs
14
52
66
21%
79%
30-39 hrs
220
221
441
50%
50%
40-49 hrs
91
33
124
73%
27%
50-59 hrs
19
3
22
86%
14%
60 hrs +
total
7
509
1
8
535 1044
88%
49%
13%
51%
40
Table 8 illustrate the distribution of hours of work per week among male and
female.
graph2
Table 9 Gender and hours of work in irregular sector
A33 and A1
male female
total percent male
percent female
less than 10 hours
17
9
26
65%
35%
10-24 hours
16
12
28
57%
43%
25-49 hours
16
7
23
70%
30%
50-99 hours
10
2
12
83%
17%
100-199 hours
6
5
11
55%
45%
200-399 hours
4
0
4
100%
0%
600-799 hours
0
2
2
0%
100%
800-999 hours
1
0
1
100%
0%
70
37
107
65%
35%
total
A33- Approximately how many hours of non-reported income activities have you
engaged in during the last 12 months?
41
This table furnish information and statistics about irregular hours of work by
gender.
Graph3
Appendix A1.1
Table11
A13
A32
Yes
Primary sector
no Total1 Percent=yes/t1 Yes/t2
3
13
16
19%
4%
Construction
15
88
103
15%
18%
Manufacturing & Engin.
14
40
54
26%
17%
Consumer Goods
8
61
69
12%
10%
Transportation
8
63
71
11%
10%
Teaching/Education/Scientific research
6
67
73
8%
7%
Health
9 122
131
7%
11%
Banking/Finance
0
26
26
0%
0%
Lawyer, accountant, broker
0
10
10
0%
0%
Service sector, other
7
45
52
13%
8%
National security, police, prison service
1
18
19
5%
1%
Public administration
2
54
56
4%
2%
10
85
95
11%
12%
1
3
4
25%
1%
84 695
779
11%
100%
Other occupation
No occupation
Total2
42
A13- Occupation by industry.
A32- Have you during the last 12 months had work for which the income has not been or
will not be reported to the tax authorities?
Table 12
A13
Nr obs with
RE
Mean RE St.dv
Min
max
Total nr
of obs
Primary sector
3
1588
1046
430
2465
16
19%
Construction
15
7847
11291
430
43500
103
15%
Manufacturing & Engin.
13
17321
24419
430
86100
54
26%
Consumer Goods
8
13293
17380
430
53100
69
12%
Transportation
Teaching/Education/
Scientific research
7
4918
5631
1100 17250
71
11%
6
3171
2407
0
6450
73
8%
Health
9
4160
5283
430
16500
131
7%
Banking/Finance
26
0%
Lawyer, accountant, broker
10
0%
Service sector, other
National security, police,
prison service
7
8424
1
1950
Public administration
2
2340
Other occupation
10
15076
No occupation
1
7215
total
11391
430
30100
52
13%
1950
1950
19
5%
2701
430
4250
56
4%
14753
731
43050
95
11%
7215
7215
4
25%
695
779
779
11%
84
RE-incomes generated from irregular hours of work by working sector.
If we refer to the participation decision we find the higher level among those
working in manufacturing sector and construction sector. Referring to hours of
work and incomes generated from irregular hours of work we find the highest
level among those working in manufacturing, consumer goods and to the category
of other sectors. The lowest level is among national security and public
administration. Regarding those included to the category of no occupation we
don’t have a good representative rate to derive to certain conclusion. So it would
be important to see the relation between the occupational status and tax evasion.
43
A6- Education and work for which the income has not been or will not be
reported to the tax authorities during the last 12 months.
Table 13
A6
A32
6 years
+ 3 years
+ 6 years
University
total
yes
8
16
56
29
109
no
total
97
171
302
381
951
percent
105
187
358
410
1060
percent
8%
9%
19%
8%
11%
7%
15%
51%
27%
100%
The table shows that among the evaders the highest representation is from those
individuals who hold a high school diploma or are not graduated. Most probably
have not very qualified jobs. They mostly work in the service sector or other
sectors which do not require a high qualification and the hourly wage rate may be
low. Those who have attained the diploma university has the opportunity to find a
well paid job and as we showed previously, in table 6, the numbers of evaders
diminishes as the hourly wage increases.
A7 – occupational status
Table 14
yes
no
Total
Percent
Salaried worker
Self-employed
Pupil/student/apprentice
Unemployed
67
8
13
1
583
47
67
29
650
55
80
30
18%
19%
10%
3%
61%
7%
12%
1%
Pensioner
On social security
4
10
129
71
133
81
3%
12%
4%
9%
2
4
109
9
17
952
11
21
1061
18%
19%
10%
2%
4%
100%
Married without income
Other
Total
The higher number among evaders comes from salaried job. This fact is important
as it emphasize the nature of evasion. The behavioural of an employee to not
declare part of irregular hours of work should be sustained also by the other side
of the market, the employer.
The second place goes to the Pupil/student/apprentice which is in line with the
finds we had about age and education.
We can conclude, by considering the number of evaders in each occupational
status, that the higher percentage is among self-employed. This group has higher
44
probability to evade and not declare part of their work and income to tax
authorities as long as they are the actors in both supply and demand side of labor
market.
A19 - Do you receive other than work related income, such as social security,
retirement pension, interest, stock profits or other types of income? If so,
approximately how much per year?
Table 15
A19 A32
below 8000 kr
8-17000 kr
17-35000 kr
35-70000 kr
70-100000 kr
100-140000 kr
140-170000 kr
170-260000 kr
over 260000 kr
No other income
Total
yes
11
8
12
11
2
5
1
3
1
53
107
no total
Percent
121
132
60
68
62
74
63
74
43
45
41
46
25
26
23
26
24
25
438
491
900
1007
8%
12%
16%
15%
4%
11%
4%
12%
4%
11%
11%
10%
7%
11%
10%
2%
5%
1%
3%
1%
50%
100%
The relationship between the participation in the irregular labor market and
incomes other than work it is increasing up to 35000 kr and then it is
heterogeneous. The increasing participation in the irregular labor market with the
increase of incomes other than labor income it is more common among low
income earners and they may choose to receive social security, retirement pension
and other transfer income combined with the incomes received from irregular
hours of work up to a certain level, in our case up to 35.000 kr. This result it is
very important for policy implications. The design of the tax system should be
such that it can induce these low income workers to shift from irregular to regular
labor market.
45
Table 16: Wages by gender ( shiko nese duhet te shtosh dhe percent)
Category
Hourly
Males Females
Total
wage(NOK)
1
42.5
5
10
15
2
92
5
15
20
3
109.5
36
88
124
4
127
52
88
140
5
144.5
71
71
142
6
162
47
25
72
7
177
28
26
54
8
194.5
46
27
73
9
229.5
46
22
68
10
287
28
11
39
11
425
16
4
20
12
510
7
0
7
Hourly wage rate by gender
160
140
120
Total
100
80
male
60
40
female
woman
20
0
Categories of hourly wage rate
Graph 4
46
From the table 16 and the graph 4 it can be observed that those hourly wage rates
below the mean level the percentage of female is higher than the percentage of
males. For the category of hourly wages above the mean level the opposite is true,
confirming what is highly sustained also from other studies.
A35- Approximately how much non-reported income had you accumulated at the
last tax evasion?
Table 17
Categories of income
below 10000 kr
10-15000 kr
15-30000
30-70000
70-100000
140-170000
Total
Evaders
Percent
66
13
17
8
2
1
107
62%
12%
16%
7%
2%
1%
100%
Level of income not declared to the tax authorities
70%
60%
50%
40%
non-regular income
30%
20%
10%
0%
1
2
3
4
5
6
Graph 5
47
Table1 818 Parameter Estimates following a IM, EM and DCM approach
Variable
Dependent
variable:
Parameter
Parameter
Parameter values of
Values of EM
values of IM
DCIM
Participation
Hours of work
Hours of work
D
(disposal income)
0.784
(0.187)
0.591
(0.233)
6.728 (0 .615)
B1
(dummy woman)
7.703
(2.606)
-6.000
(1.668)
1.887
(0.474)
B2
(age)
0.121
(0.078)
6.871
(3.368)
-1.449
(0.251)
1.242
(0.275)
-0.077
(0.054)
11.267
(2.459)
-3.117
(1.000)
0.623
(0.334)
-0.0182
(0.0099)
-2.531
(0.2674)
0.973
(0.323)
-0.285
(0.678)
-214
0.30
0.942
(0. 468)
0.968
(0.751)
-2548
0.14
-1158.0428
0.277
895
895
895
B0
( leisure )
(constant )
Z1(dummy accept
evasion)
Z2(dummy construct)
Z3 (dummy govern)
Log likelihood
McFadden ȡ2
Nr obs.
Standard errors in brackets.
18
DCEM (Discrete choice at extensive margin)
DCIM (Discrete choice at extensive margin)
48
Table 19 Predictions of labor supply
Variables
P(H)
P(E)
LH/H
LH/E
LE/E
LH
LE
Observed values(per year)
0.89
0.11
1572
1715
74
1586
10
Labor supply,EM( per year)
0.89
0.11
1390
1071
281
1272
31
Labor supply,IM ( per year)
0.82
0.18
1451
1435
265
1448
47
Labor supply DCIM( year)
2504
Graph 6
Predicted labor supply comparision
3000
2500
2000
1500
1000
500
0
1
2
3
4
Observed LH|H
EM prediction LH|H
IM prediction LH|H
DCIM prediction
Table 20 Prediction of tax levels
Variables
TH
TH/E
T
TE- TH/E
Observed Level of taxes
102402
87170
94786
4028
Predicted taxes EM
61685
41053
50287
12939
Predicted taxes IM
65396
63565
65067
15391
Honest intensive
139550
49
Graph 7
300
250
200
150
100
50
0
1
2
Observed
EM prediction
IM prediction
Graph 8
Comparision of Tax predicted
140000
120000
100000
80000
60000
40000
20000
0
1
2
3
4
Observed
EM prediction
IM prediction
DCIM prediction
Appendix 2
Tax functions 1980, 1990 and 2003.
The tax function is a step-wise linear function. If the marginal tax rates are uniformly
increasing with income, then the tax function has a strict progressive structure.
Let T denote the amount of taxes paid and let Y denote wage income. Let subscript i
denote the tax bracket i and let Yi denote the lower bound in the tax bracket and let
50
Yi+1 denote the upper bound. Ti is the amount of taxes paid when wage income Y is
within these bounds.
Tax function 1980.
Wage income Y
Yd9000
9000dYd10000
10000dYd11250
11250dYd16000
16000dYd17500
17500dYd31000
31000dYd35800
35800dYd44800
44800dYd60800
60800dYd70800
70800dYd80800
80800dYd90800
90800dYd107800
107800dYd137800
137800dYd182400
182400dYd187800
187800dYd287800
287800dY
Tax T
0
0.524Y-4680
0.513Y-4670
0.313Y-2357
0.285Y-1918
0.296Y-2110
0.324Y-2959
0.384Y-5107
0.434Y-7347
0.484Y-10387
0.544Y-14635
0.604Y-19483
0.654Y-24023
0.704Y-31723
0.744Y-37235
0.694Y-46355
0.734Y-53867
0.754Y-59623
Tax function. 1990.
Wage income Y
Yd27856
27856dYd 30057
30057dYd72718
72718dYd153775
15377dYd199152
199152dYd258393
258393dY
Tax T
0.078
0.338Y-7243
0.3042Y – 6227
0.338Y – 8684
0.438Y – 24062
0.608Y – 57918
0.693Y-79881
A1Tax rule 2003
Tax function 2003. Amounts are in NOK.
Income Y
0 – 23 000
23 000 – 39 091
39 091 – 203 356
203 356 – 320 000
320 000 – 830 000
830 000 –
Tax
0
0.078Y
0.2936˜Y – 8 428
0.358˜Y – 21 524
0.493˜Y – 64 724
0.553˜Y – 114 524
51
Appendix 3
Heckman estimation results
Variables
Education
Age
Regression equation
Selection
Log(w)
equation
0.13
(0.015)
0.009
(0.001)
0.28
(0.057)
-0.0093
(0.004)
-0.0476
(0.042)
-0.68
(0.109)
1.786
(0.031)
Marital status
gender
4.265
(0.082)
895
0.38
(0.011)
-0.714
(0.055)
constant
Nr of observations
Sigma
rho
* (standard errors in brackets)
Graphical representation of the wage predicted based on Heckman
estimation results.
.02
.01
Density
.015
.005
100
150
200
0
250
wagen1
52
Appendix 3
Nested logit model
A1 A2 A3 A4 A5
A1 A2 A3 A4 A5
A1 A2 A3 A4 A5
B1 B2 B3 B4 B5 B6 B7 B8
A1 A2 A3 A4 A5
A1 A2 A3 A4 A5 A1 A2 A3 A4 A5
A1 A2 A3 A4 A5
A1 A2 A3 A4 A5 A1 A2 A3 A4 A5
Generalized nested logit model
C1
A1
B1
C2
A1
C3
B2 A1
C4
C5
..............................C40
B3 ........................................................................A5
B7 A5
B8
53
Appendix 3
The last line gives the McFadden ȡ2 which is given by:
U 2 =1-
logL
1
N * log( )
A
where:
LogL is the log likelihood reported in the second line from below in the table.
N is the number f observations=895
A is the number of alternatives=40
The calculated ȡ2 indicates that the random elements are dominating behavior in
the both models. When the ȡ2 = 0, one cannot reject the hypothesis that all
choices are made at pure random and when ȡ2 = 1, the observed covariates
explain all the variations in the observed behavior).
References
Allingham, M.G. and A. Sandmo (1972): Income Tax Evasion: A
Theoretical Analysis, Journal of Public Economics, 1, 323-338.
Ben-Akiva, M. and S. Lerman(1985): Disaggregate Travel and Mobility
Choice Models and Measures of Accessibility. In D. Henscher and P.
Stopher (eds): Behavioral Travel Modelling. Croom Helm, London.
Blundell.R;Duncan A.;Meghir C.(1998):Estimating labor supply responses
using tax reforms Econometrica Vol 66, No.4 (Jul.,1998), 827-861.
Burtless,G and J.Hausman 1978: The effect of taxation on labor supply:
Evaluating the Gery income Maintenance Experiment. Journal of Political
Economy 86 (December): 1103-30.
Cowell, F. A. (1991). Tax-evasion experiments: an economist’s view. In
P. Webley, H. Robben, H. El.ers, and K. Hessing (Eds.), Tax Evasion:
An Experimental Approach. Cambridge: Cambridge University Press.
54
Cowell, Frank A. (1990), Cheating the Government. Cambridge, Mass.: MIT
Press.
Cowell, Frank A. (March 2003), “Sticks and carrots,” Discussion Paper No.
DARP 68, London School of Economics.
Dagsvik, J. and S. Strøm (2005): Sectoral choice, labor supply, choice
restrictions and functional form, forthcoming in Journal of Applied
Econometrics
Gul F. and Pesendorfer W. Pesendorfer “Random expected Utility” mimeo
2004.
Fugazza M, Jacques J-F, 2003 : Labor market institutions, taxation and the
underground economy, Journal of Public Economics 88 (2003) 395– 418.
Hausman J. :Labor supply; 1981. In How taxes affect economic behavior,
ed H.Aaron and J.Pechman. Washington: Brookings.
Hausman J.:The econometrics of non-linear budget sets. Econometrica 53,
1255-82.
Hausman J, McFadden D,(1984): Specification test for Multinomial Logit
Model. Econometrica, Vol.52, No.5 1219-1240.
Cowell, F. A. (1985) Tax Evasion with Labour Income, Journal of Public
Economics, 26,19-35.
Dagsvik, J. and S. Strøm (2005): Sectoral choice, labor supply, choice
restrictions and functional form, forthcoming in Journal of Applied
Econometrics
Fortin, Joubert Lacroix (2001): Labor supply in the underground economy,
taxation
tax enforcement policies. Conference EALE 2004.
Isachsen, A. J. and S. Strøm (1980): The Hidden Economy: The Labor
Market and Tax Evasion, Scandinavian Journal of Economics, 82, 304-11.
Isachsen, A. J. and S. Strøm (1985): The Size and Growth of the Hidden
Economy in Norway, Review of Income and Wealth, 31, 21-38
Isachsen, A. J. Samuelson, S.O. and S. Strøm (1985): The Behavior of Tax
Evaders, in W. Gaertner and A. Wenig (eds): The Economics of the Shadow
Economy, Springer-Verlag, Berlin.
Lacroix, G. and Fortin, B. (1992): Utility-based estimation of labour supply
55
functions in the regular and the irregular sectors, Economic Journal, 102,
1407-1422.
Lemieux, T., Fortin, B. and Frechette, P. (1994): The effect of taxes on
labor supply in the underground economy, American Economic Review, 84,
231-254.
Meyer, Bruce D. and Rosenbaum, Dan T. “Welfare, the Earned Income Tax
Credit, and the Labor Supply of Single Mothers.” National Bureau of Economic
Research (Cambridge, MA) Working Paper Number 7363, 1999.
McFadden, D. (1978): Modeling the choice of residential location, in A.
Karlqvist, L. Lundqvist, F. Snickars and J. Weibull, eds, Spatial Interaction
Theory and Planning Models, North-Holland, Amsterdam, 75-96.
Moffitt R. (1987): The econometrics of Piecewise-linear budget constraints.
Journal of business and economic statistics 51 (April) 243-48.
Strøm S. , Jørgensen, O and Ognedal, T. (2004) Labor supply when tax evasion is
an option. Manuscript.
Webely, P & Cole, M & Eidjar O-P (2001): The prediction of self-reported
and hypothetical tax-evasion: Evidence from England, France and Norway.
Journal of Economic Psychology 22 (2001) 141-155.
Von Neumann, J. and Morgenstern, O. (1944), Theory of Games and
Economic Behavior, Princeton University Press.
56