PROOF COVER SHEET
Journal acronym: CIRA
Author(s): Basil Dalamagas
Article title: A macroeconomic approach to the income-tax work-effort relationship
Article no: 580269
Enclosures: 1) Query sheet
2) Article proofs
Dear Author,
1. Please check these proofs carefully. It is the responsibility of the corresponding author to check
these and approve or amend them. A second proof is not normally provided. Taylor & Francis cannot be held responsible for uncorrected errors, even if introduced during the production process.
Once your corrections have been added to the article, it will be considered ready for publication.
For detailed guidance on how to check your proofs, please see
http://journalauthors.tandf.co.uk/production/checkingproofs.asp
2. Please review the table of contributors below and conﬁrm that the ﬁrst and last names are
structured correctly and that the authors are listed in the correct order of contribution. This
check is to ensure that your name will appear correctly online and when the article is indexed.
Sequence
1
2
Preﬁx
Given name(s)
Surname
Basil
Stelios
Dalamagas
Kotsios
Sufﬁx
Queries are marked in the margins of the proofs. Unless advised otherwise, submit all corrections
and answers to the queries using the CATS online correction form, and then press the “Submit All
Corrections” button.
AUTHOR QUERIES
General query: You have warranted that you have secured the necessary written permission from
the appropriate copyright owner for the reproduction of any text, illustration, or other material in
your article. (Please see http://journalauthors.tandf.co.uk/preparation/permission.asp.) Please check
that any required acknowledgements have been included to reﬂect this
AQ1
Blubdell and MaCurdy (1999) is not in the References.
AQ2
Please check: cF in text but cf in equation.
AQ3
OECD Economic Surveys, UK (1995, 1998, 2009) are not in the References.
AQ4
Year required. Reference not cited in the text.
AQ5
Publisher location required. Cambridge?
QA: MM
International Review of Applied EconomicsAquatic Insects
Vol. X, No. X, XXXX 2011, XXX–XXX
A macroeconomic approach to the income-tax work-effort
relationship
Basil Dalamagas* and Stelios Kotsios
University of Athens, Department of Economics, PO Box 8444, 10010, Athens, Greece
(Received 26 January 2011; ﬁnal version received 12 February 2011)
5
In this paper, we analyse the dynamic relationship between hours worked per
employee (per self-employed) and marginal income tax-rate shocks in terms of
both a comparative-dynamics model and a stochastic general equilibrium econometric model. The econometric model is estimated for Germany, UK and USA
over the post-1960 period using the GMM estimation technique. Estimates in
both models show that increases in the marginal income-tax rate exert negative
effects on hours worked by both employees and the self-employed, but the
response of the employees who are subject to tax withholding is stronger than
the response of the self-employed.
10
Keywords: hours worked per employee and self-employed; tax withholding;
15
incentive to work; labour supply; marginal income tax rate.
JEL Classiﬁcations: E1; E6
20
1. Introduction
A classic challenge facing macroeconomists is to explain observed variations in
employment attributable to tax-induced income changes. A number of research programmes have tried to explore the market forces that could potentially inﬂuence the
income-tax work-effort relationship, with the majority of the relative studies lending
support to the Hicksian theoretical framework of the income-substitution effects
(upward or downward sloping labour supply curve). The picture that emerges from
existing literature does not seem to be a coherent one (for a summary of the
opposing views, see Myles 1995). A possible reason may be that differences in the
response of working time to tax-induced income changes are likely to be linked not
only to the size of the tax liability or to the characteristics of the labour market but
also to other factors that have not been adequately explored so far. Some of these
factors, on which the present study will focus, are described below.
Tax withholding. Tax withholding provisions are likely to affect incentives to
work, as the burden from the personal income tax withheld may not easily be
felt and thus it may be less damaging to work effort than the burden from the
same tax paid by direct assessment.
*Corresponding author. Email: [email protected]
ISSN 0269-2171 print/ISSN 1465-3486 online
Ó 2011 Taylor & Francis
DOI: 10.1080/02692171.2011.580269
http://www.informaworld.com
25
30
35
QA: MM
2
5
10
15
20
25
30
35
40
45
50
B. Dalamagas and S. Kotsios
The distinction between short-run and long-run effects. A tax-induced decline
in work effort tends to be smaller in the short run than in the long run. Since
income commitments are more rigid than leisure commitments, work effort
may even increase at ﬁrst and decrease later. On the other hand, in the long
run, aspiration levels in terms of goods and/or leisure may rise, as new consumption goods become available and households may be willing to surrender more leisure, unless the new goods are complementary to leisure.
The secular rise in leisure. The observed long run increase in leisure may not
have been a simple expression of individual choices. Instead, it may have
been the product of a complex set of social forces, such as the rise of mass
education and the strength of unionism.
The proportion of workers to the total labour force which varies across countries and over time.
The distinction between employees and the self-employed may be of crucial importance since employees are not free to adjust their supply of effort (working time);1
this may be a key factor in determining the response of hours worked to changes in
personal income tax rates. Recipients of lower wages are typically subject to contracts and may have to choose between working a given number of hours or not at
all. In this case, income tax leaves hours worked more or less unaffected. This is
taken up in Section 4 by drawing a line between employees and overtime for an
employee. On the other hand, households commanding high salaries tend to be selfemployed, employers or in supervisory positions and, hence, less subject to work
discipline. However, they may be motivated by non-pecuniary factors, so that their
supply of effort is relatively inelastic to income tax changes. Farmers form a speciﬁc category of self-employed with a working time schedule being determined largely irrespective of the income tax structure. Lastly, some income recipients (e.g.
the executive, who sets his own wage rate) may be able to recover income tax by
demanding an increased wage rate. In these cases, the response of hours worked to
income tax changes is negligible.2
Since the present study will focus on exploring the validity of the above propositions, the aim will be to substantiate (or invalidate) the argument that tax withholding, the proportion of employees in the total labour force and the remaining
factors play an important (and thus far largely neglected) role in determining the
shape of the supply curve of labour. To this end, we modify the standard general
equilibrium model to distinguish between two groups of labour. The ﬁrst group
encompasses all employees. The term ‘employees’ covers a wide range of working
people (in manufacturing, retail and wholesale establishments, ﬁnancial institutions,
the public sector and so on) who bear two common features. First, they are subject
to the provisions of labour legislation and to contracts that do not allow deviations
from the prevailing working time pattern. In this case, changes in marginal tax rates
may inﬂuence solely overwork and the working scheme of part-time employees, of
(married) women, of newcomers to the labour force and so on. Second, a portion of
their wage, corresponding to their personal income tax liability, is retained by their
employers who refund it to the tax collection agency on a monthly basis (tax withholding).
The second group of the labour force contains the remaining part, the so-called
self-employed. In the present context, the term ‘self-employed’ denotes a large
number of income recipients (e.g. employers, managers, farmers, freelancers, prop-
QA: MM
International Review of Applied Economics
AQ1
3
erty owners) who are free to adjust their hours of work. They are also not subject
to the tax withholding provisions, as their tax liability is assessed each year on
income accrued in the previous year.
Our analysis has two novel features. First, the labour force is not treated as a
homogeneous group of workers subject to the same tax rules, as is the underlying
assumption in all previous studies (see, for example, Yuan and Li 2000; Pisauro
1991; Barzel and McDonald 1973; Aronsson et al. 2002). Tax collection regulations
differ between employees and the self-employed and the ratio of employees to the
self-employed varies widely across countries and over time; as a result, the response
of employees to changes in income tax rates may not be in the same direction or of
the same magnitude as the response of the self-employed. Therefore, policy prescriptions for tax reform, in order to encourage incentives to work, may prove to be
inefﬁcient if they are based on the average response of the total labour force. Analogous reasoning applies to all of the previous studies (see, for example,
Klevmarken 2000; Belﬁeld and Heywood 2001; Blomquist 1983; Pencavel 1986)
which divide the labour force into groups of workers (unionized or not, male or
female, high- or low-skilled, white or other races, and so on), as no account is
taken of whether each group contains employees and/or self-employed.
Second, we extend our analysis beyond the limits set out by the micro econometric framework. There is a voluminous literature on labour supply based on
micro data; a summary of this literature is given by Blubdell and MaCurdy (1999;
Handbook of labor economics). It is argued that access to micro data is vital for
our understanding of the economic incentives behind the decision to supply work
hours. For instance, only micro data allow us to capture the (often complicated)
inﬂuences that taxes and transfers may have on the choice sets and to use this information in the estimation. Notwithstanding the validity of these arguments, it seems
equally defensible to examine the reaction of large working groups to tax rate
changes by using a macroeconomic approach, which provides an interesting alternative to the micro econometric research.
Different kinds of models have come under the heading of the income
tax-working time relationship. However, existing literature leads to surprisingly different conclusions as to the effects of tax rate changes on working schedules. See,
for example, Yellen (1984), Johnson and Layard (1986), Weiss (1980), Pisauro
(1991), Fiorito and Padrini (2001), Aronsson et al. (2002).
This paper extends the analysis of income taxation and working time patterns to
a dynamic general equilibrium framework. In this context, two approaches are
employed. The ﬁrst approach is a comparative dynamics method of analysis that
uses a simple Cobb-Douglas single-sector model with an equally simple government sector to provide numerical illustration of the effects of personal income taxation on work effort. In the second approach, the parameters of a more complex
general equilibrium model with a CES production function are estimated econometrically for three industrialized countries (USA, the UK and Germany) and the relative coefﬁcient values are used to carry out policy simulations and to evaluate the
response of hours worked to changes in the marginal income tax-rate. In both
approaches we ﬁnd that tax withholding affects taxpayers’ labour supply decisions
in the sense that incremental tax-rate increases reduce the working time of employees at a higher rate than hours worked by the self-employed.
The paper is organized as follows. The essential features of the comparative
dynamics model, accompanied by the numerical speciﬁcation of the parameters, the
5
10
15
20
25
30
35
40
45
50
QA: MM
4
5
10
15
20
B. Dalamagas and S. Kotsios
estimation results and inferences are presented in Section 2. Section 3 describes the
theoretical foundation of the econometric model and speciﬁes the propositions and
hypotheses to be tested. Section 4 assesses the effect of marginal income tax rate
changes on working hours, by utilizing standard simulation techniques. Conclusions
and a critical view of the assumptions are undertaken in Section 5.
2. The comparative dynamics model
Typical of most of the work on the response of working time to tax-rate changes is
the adoption of a simple neo-classical single-sector growth model with an exogenously growing labour supply, ﬁxed savings ratios and zero depreciation of capital.
The government ﬁnances a given path of government expenditures using a combination of proportional taxes at different rates on the income of employees, on the
earnings of the self-employed and on capital income. The crucial assumption is that
employees – but not the self-employed – are subject to tax withholding. The exercise to be conducted is to estimate the response of hours worked both by employees
and the self-employed to changes in the personal income tax rate.
The economy is assumed to move along an arbitrary growth path indicated by
the initial stocks of capital and labour, the savings behaviour and the government’s
activities. The time path of per-capita government revenue, T, is given by
T ¼ sWe he þ sf Wf hf þ sr rK
25
30
ð1Þ
where s is the tax rate on employees’ income, sf is the effective tax rate on the
earnings of the self-employed and sr is the tax rate on capital income; we ðwf ; rÞ is
the hourly employee’s wage rate (hourly earnings of the self-employed, rental rate),
he ðhf Þ is the annual hours of work per employee (self-employed) and k is the capital-labour ratio. All variables are time dependent but the time subscript will be suppressed except where needed for clariﬁcation.
The statutory tax rate, s, is the same for both employees and the self-employed;
however, s applies to the employee’s current income, whereas the current tax liability of the self-employed is calculated by applying the statutory tax rate to his previous-year income, given that the self-employed is not subject to tax withholding.
The postponement of his tax payment is expected to generate an interest gain, with
his effective or actual current tax obligation being deﬁned as
sf Wf hf ¼ ð1 iÞsWf ;t1 hf ;t1
ð2Þ
35
where i is the interest rate. Therefore, the effective tax rate for the self-employed is
given by:
ð1 iÞsWf ;t1hf ;t1
sf ¼
ð3Þ
Wf hf
40
Per capita output is given by
y ¼ Ak a h1a ¼ f ðk; hÞ
45
ð4Þ
where h is the weighted average of the annual hours of work, h ¼ phe þ ð1 pÞhf ,
with p standing for the probability of being an employee.
Given the savings ratios out of employees, se, of the self-employed, sf, and of
capital, sr, and using the competitive rental and wage rates from the marginal
QA: MM
International Review of Applied Economics
5
productivity conditions, per capita accumulation can be represented by the differential equation:
k ¼ ðse þ sf Þ½f ðk; hÞ sWe he sf Wf hf þ ½sr ðse þ sf Þð1 þ sr Þrk se Wf hf
sf We he nk
¼ gðk; s; tÞ
ð5Þ
5
where n is the rate of growth of the labour force.
Equation (5) is a non-linear differential equation in k. For given paths of sr, of
the savings ratios and of the annual per capita incomes of both employees and the
self-employed, as well as for an initial value of k(0), equation (5) determines the
path of accumulation of per capita capital for any arbitrary path of s the government might choose.
To determine the path of k, ð~k ¼ @k
@sÞ from equation (5) and to show how this
path is inﬂuenced by changes in s, we follow a process similar to that described by
Boadway (1979), who utilizes a proposition from the theory of differential equations to ﬁnd that
~kðtÞ ¼ gs ðegkt 1Þ
gk
The derivatives of g with respect to s and k are calculated from equation (5).
From the path of k, one can then determine the values of hours worked by employees and the self-employed over time (details on request).
~e
h
a
1 p k~
1
1 p sf ð1 þ sÞ
1þ
x 1þ
x
¼
k 1þs
p
p
sð1 þ sf Þ
he rð1 aÞ
10
15
20
h
where x ¼ hfe and r is the local elasticity of substitution.
Following a similar process, we can derive the expression for the path of hours
~h
worked by the self-employed, hff .
To get an idea of the importance of the time dimension in the long-run response of
working time to tax withholding, we will use the following numerical example. The
economy is assumed to start in a steady state with the following parameter values:
se ¼ 0:10;
a ¼ 0:35;
sf ¼ 0:20;
p ¼ 0:40;
sr ¼ 0:70;
r ¼ 1;
sr ¼ 0:25;
s ¼ 0:15;
25
sf ¼ 0:12;
x ¼ 1:20
30
The computations were done by employing a discrete time analogue of the
model and using time periods of 0.05 years. The values of r and n used were
0.0015, which correspond to roughly 0.03 on an annual basis. ~
~ ~
h
Table 1 shows the time paths of the variables kk ; hhee and hff resulting from an
increase in the tax rate, s, ﬁrst on the employee’s income and then on the earnings
of the self-employed.
As becomes evident from Table 1, an incremental increase in the rate of
personal income taxation reduces hours worked by both employees and the
self-employed in the long-run. However, the working time of employees, who are
subject to tax withholding, declines throughout the time period examined at a much
higher rate than the working time of the self-employed, who are free of any tax
35
40
Time path of capital
0
0.0040
0.0080
0.0120
0.0159
0.0199
0.0238
0.0277
0.0316
0.0354
0.0393
0.0431
0.0469
0.0507
0.0545
0.0582
0.0620
0.0657
0.0694
0.0731
0.0768
0.3210
0.5218
0.7261
0.8498
Period
0
5
10
15
20
25
30
35
40
45
50
55
60
65
70
75
80
85
90
95
100
500
1000
2000
5000
Time path of the working pattern per self-employed
1.027
1.029
1.030
1.032
1.034
1.035
1.037
1.038
1.040
1.042
1.043
1.045
1.046
1.048
1.049
1.051
1.053
1.054
1.056
1.057
1.059
1.159
1.241
1.325
1.375
Time path of the working pattern per employee
2.482
2.485
2.487
2.490
2.493
2.495
2.498
2.500
2.502
2.505
2.507
2.510
2.512
2.515
2.517
2.519
2.522
2.524
2.527
2.529
2.531
2.687
2.815
2.945
3.024
6
Table 1. Time path of the working pattern per employee and per self-employed.
QA: MM
B. Dalamagas and S. Kotsios
QA: MM
International Review of Applied Economics
7
withholding constraints. This simulation was performed for a wide variety of realistic parameter values and the same order of magnitude resulted for the reduction of
hours worked by employees and the self-employed.
Thus, tax withholding appears to be of crucial importance in formulating individual choices, with the data providing evidence that this particular tax provision
constitutes a major disincentive to work effort. Moreover, such a ﬁnding seems to
be inconsistent with the prevailing view, according to which income taxes withheld
are noticed less and hence they are less damaging to work effort than income taxes
paid by direct assessment.
However, the results of the present section should be interpreted with caution. It
would be premature to derive policy prescriptions from inferences based on the
analysis of the effects of income taxation on the growth path of an economy
between two arbitrary points of time in a simpliﬁed model, the parameters of which
have been selected to correspond to those used in the conventional steady-state
numerical examples.
To enhance understanding of the workings of the real-world economies in the
presence of tax withholding provisions and to model the response of employees and
the self-employed to income tax-rate changes, we will consider the case of obtaining empirical results based on a more sophisticated general equilibrium setting that
describes taxpayers’ behaviour in three advanced countries (the USA, the UK,
Germany).
3. The general equilibrium econometric model
3.1. Households
Consider a two-group economy, in which the ﬁrst group consists of employees and
the second group is made of the self-employed. Households in both groups derive
income from providing capital and labour services to ﬁrms. The fundamental uncertainty in the present analysis is, ex hypothesi, an exogenous shock to marginal
income tax rates.
The aim of the present study is to quantify the response of working time of both
the average employee and the average self-employed to changes in the marginal rate
of the personal income tax. The economy is assumed to be populated by a continuum of identical inﬁnitely lived households. Each household is thought of as a very
large extended family that contains a continuum of members. Members in each family perfectly insure each other against income variations, which are due either to the
employment status (employees or self-employed) of the members or to changes in
their employment status. The social planner evaluates streams of consumption services (ct) and employment (hours of work, ht), according to the objective
function:
E0
1
X
bt U ðct ;ht Þ;
0<b<1
ð6aÞ
t¼0
with preferences of the representative household specified as
h1þr
U ðct ; ht Þ ¼ U ðct Þ Gðht Þ ¼ log ct n t
; r P 0; n > 0
1þr
ð6bÞ
5
10
15
20
25
30
35
40
QA: MM
8
B. Dalamagas and S. Kotsios
where b is the discount factor, r denotes the inverse of the inter-temporal elasticity
of substitution for labour supply, and both U and G represent increasing and concave functions in their respective argument.
The representative household can be thought of as consisting of a very large
number of members who pool their income and, thus, provide each other with complete insurance against income losses or against changes in occupational status.
Alternatively, the representative household’s consumption may be given by
5
10
C ¼ pce þ ð1 pÞcf ;
AQ2
15
06p61
ð7Þ
where ce is the average consumption per employee, cF is the average consumption
per self-employed and p is the probability of being an employee.
Substituting equation (7) into the utility function, equations (6a,b), permits the
transformation of the so far exogenously treated occupational status, as indicated by
p, into a choice variable for the household.
The joint budget constraint faced by both types of households is:
ct þ it ¼ pt we;t he;t ð1 sÞ þ ð1 pt Þ wf ;t hf ;t ð1 rt Þðst1 wf ;t1 hf ;t1 Þ þ rt kt þ ðnwÞt
ð8Þ
20
25
where it is investment, we;t ðwf ;t Þ is the hourly wage rate (earnings) for employees
(self-employed), st is the average (personal) income tax rate, rt is the interest rate,
(nw)t is the non-wage income and kt is capital. The law of motion for the capital
stock is given by
Ktþ1 ¼ ð1 dÞkt þ it ; k0
ð9Þ
givenwhere d2 (0,1) is the capital depreciation rate.
30
3.2. Firms
There is a continuum of identical competitive ﬁrms in the economy, with the total
number normalized to one. Each ﬁrm produces output yt according to a constant
elasticity of substitution (CES) technology
yt ¼ Akta ½pt ðebc t he;t Þq þ ð1 pt Þðebf t hf ;t Þq 35
40
1a
q
ð10Þ
where q 6 1, pt is the share parameter (probability of being an employee), A is a
neutral productivity term, and ebe t ðebf t Þ are factor augmenting productivity terms.
Given the prices of output and factor rewards, the ﬁrm’s problem is to choose
the amount of both capital and labour services that maximize the present value of
proﬁts, subject to constraint (10). From the maximization process, the wages of
employees, the earnings of the self-employed and the return on capital are then
derived.
3.3. Government
The role of the public sector in our model is to collect taxes and spend the revenues
on government purchases. Government spending, gt, is given by:
QA: MM
International Review of Applied Economics
gt ¼ j0 þ j1gt1 þ j2yt
9
ð11Þ
The government ﬁnances its expenditure by personal income taxes, Ty,t, and
other direct and indirect taxes, Tt. The excess of government spending over tax
revenue is ﬁnanced by issuing government bonds, Bt ð¼ Bt Bt1 Þ with Bt
standing for the public debt). Thus, the government budget constraint in period
t is
5
10
_
gt ¼ Ty;t þ Tt þ Bt
The progressive element of the personal income tax is captured by the following
tax revenue function:
Ty;t ¼ hðTBÞct
15
ð12Þ
where (TB)t is the tax base which is given by
20
ðTBÞt ¼ pt We;t he;t þ ð1 pt Þwf ;t1 hf ;t1
In equation (12), the parameter c measures the elasticity of the income tax revenue with respect to the tax base, i.e. the degree of personal income-tax progressivity. The tax is progressive, regressive or proportional, depending on whether c > 1,
c < 1, or c = 1, respectively.
The average tax rate, st , is given by
st ¼
25
Ty;t
hðTBÞct
¼
¼ hðTBÞc1
t
ðTBÞt
ðTBÞt
30
whereas the marginal tax rate, st, is estimated as follows:
st ¼
@Ty;t
¼ chðTBÞc1
¼ cs
t
@ðTBÞt
or
st ¼
st
c
ð13Þ
35
Since the marginal tax rates are widely used in literature for tracing the sensitivity of hours worked to a tax reform (see, however, Fiorito and Pedrini 2001, for a
different view), the average tax rate in the household budget constraint (8) will be
replaced, in what follows, by its equivalent in equation (13).
We close our model with the National Accounts identity
40
QA: MM
10
B. Dalamagas and S. Kotsios
yt ¼ ct þ it þ gt
5
ð14Þ
3.4. Solving the household’s optimization problem
The household, i.e. the average employee and the average self-employed, faces the
problem of maximizing the expected discounted utility, equation (6a), subject to the
budget constraint (8). From the ﬁrst-order conditions we can then derive after
appropriate manipulations (which are available on request) the employment equations for employers (he,t) and the self-employed (hf,t):
2
3a1
a2
st
ð1
aÞy
ð1
Þ
t
1 pt
6
c 7
p
1
þ
x
ð15Þ
he;t ¼ a0 4
5
t
t
wT
pt
ct ð1 þ wfT;t Þ
c;t
10
where
1
1þr
wTf;t wf ;t
1
1
r
; a2 ¼ and T ¼
; a1 ¼
xt
a0 ¼
n
1þr
1þr
wc;t wc;t
15
hf ;t
3b1
2
b2
st
pt
6ð1 aÞyt f1 ð1 rt Þcpt lt mt g7
1
¼ b0 4
x
5 ð1 pt Þ 1 þ
wT
1 pt t
ct ð1 þ wTc;t Þ
ð16Þ
f ;t
where
1
1þr
wTc;t wc;t 1
1
1
r
; b2 ¼ and T ¼
; b1 ¼
x
b0 ¼
n
1þr
1þr
wf ;t wf ;t t
20
pt ¼
25
30
st
wf ;t
hf ;t
; lt ¼
; mt ¼
st1
wf ;t1
hf ;t1
The coefﬁcient values of the constrained estimation of the model (a0 = b0,
a1 = b1, a2 = b2) will be used throughout the econometric analysis, as these values
were found to be closely related to the coefﬁcient values of the unconstrained estimation (a0 – b0, a1 – b1, a2 – b2).
4. Estimating the general equilibrium model
In carrying out the estimation process, equations (9) to (16) have been used in the
GMM (Generalized Method of Moments) to obtain the estimates of the parameters
in the sample countries. To obtain GMM estimates, we have written the moment
QA: MM
International Review of Applied Economics
11
conditions as orthogonality conditions between the above nine expressions, including the corresponding parameters, and a set of instrumental variables (details
available on request).
Sources and deﬁnitions for all variables are reported in the Appendix. It should
be stressed that data series on hours worked by employees had to be modiﬁed to
account for the fact that employees are subject to contracts that do not permit deviations from the prevailing working time pattern. To this end, annual hours of work
in the labour supply function for employees are redeﬁned to represent the difference
between the actual hours of work per worker in manufacturing – as given by the
OECD Labor Force Statistics – and the statutory hours of work – as given by the
Main Economic Indicators of OECD and the Data Stream. Such a difference may
be considered to reﬂect the working time pattern over and beyond the ofﬁcial contracts (overtime, part-time work, occasional employment and so on). The application
of the GMM requires that each equation includes only stationary variables. Thus,
before estimating the model, the order of integration of the variables has to be
established. To assess their time-series properties, we carried out the
Kwiatkowski-Phillips-Schmidt-Shin (KPSS) test. Table 2 reports the results from
this test to determine the integrated processes of each individual series.
The results suggest that, while the unit root hypothesis cannot be rejected for
the levels of each of the variables (yt, kt, he,t, hf,t) in the production function, the
corresponding ﬁrst-differenced series are stationary. The same was shown to be true
with respect to the equations for consumption, capital, government expenditure, tax
revenue and employment. It was only with the interest rate equation that the test
statistics for the interest rate and the output–capital ratio showed that the null
hypothesis can be rejected in favour of the hypothesis that the series are I(0) at least
at the 5% level.
Investigation of the univariate stationary properties of the series is only
necessary, but not sufﬁcient, for adequately specifying the model. In addition, the
number of common trends in the multivariate representations must be examined.
Experimentation with the tests of Johansen and Juselius suggested the existence of
at least one cointegrated vector in all countries at the 1% or 5% level.
Table 2. KPSS test-results.
Variable
UK
USA
Capital–labour ratio, k
Per capita output, y
Ratio of employees to working population, p
Annual hours of work per employee, he
Annual hours of work per self-employed, hf
Dk
Dy
Dhe
Dhf
0.79
0.83
0.57⁄⁄
0.80
0.94⁄⁄
0.58⁄⁄
0.51
0.67⁄⁄
0.42⁄
0.76
0.78
0.48⁄⁄
0.89
0.82
0.70⁄⁄
0.68⁄⁄
0.56⁄⁄
0.71⁄⁄
Germany
0.85
0.77
0.36⁄
0.84
0.91
0.62⁄⁄
0.49⁄⁄
0.39⁄
0.48⁄⁄
A-Note: ⁄and ⁄⁄indicate signiﬁcance at the 95% and 99% critical levels, respectively. The null hypothesis is that the variable considered is stationary. The asymptotic critical values are 0.739 (1% level) and
0.463 (5% level).
5
10
15
20
25
30
Capital depreciation rate, d
Capital share of output, a
Discount factor, b
Govern. spending equation
(33) J0, constant term
J1, coefﬁcient on lagged g
J2, coefﬁcient on income
Tax revenue function (34)
log h, constant term
c, tax-to-income elasticity
Production function (29)
log A, neutral productiv.
term
q, inverse of elastic. of
subs t.
be, employee’s productivity
Employment equations
(47),(48) a0 = b0,
constant terms
a1 = b1, coef. on income/
cons.
a2 = b2, coef. on
employees/self-employed
Employment
Dummy1
Dummy2
Capital utilisation rate
Real unit labour cost
Unionization rate
0.77 (0.06)
0.04 (0.01)
2.3 (0.62)
0.55 (0.06)
4.5 (2.1)
0.13 (0.05)
0.02 (0.003)
3.6 (0.83)
0.13 (0.06)
1.34 (0.28)
–
–
–
–
–
–
0.91 (0.16)
0.004 (0.03)
4.6 (1.67)
1.3 (0.07)
2.4 (0.45)
0.29 (0.12)
0.01 (0.007)
8.1 (1.68)
0.26 (0.14)
0.51 (0.14)
–
–
–
–
–
–
0.02 (0.006)
0.03 (0.003)
0.26 (0.08)
0.213 (0.02)
0.91 (0.32)
0.99 (0.43)
916.3 (934)
175 (86.6)
UK
–
–
–
–
–
–
0.18 (0.07)
184.3(85.6)
–
–
14.2 (18.7)
64.3 (28.2)
63.5 (5.3)
0.54 (0.23)
0.23 (0.08)
0.016 (0.009)
6.7 (1.91)
0.002 (0.003)
7.7 (1.62)
0.81 (0.24)
0.39 (0.16)
1.5 (0.19)
2.7 (0.62)
0.85 (0.34)
0.014 (0.009)
5.2 (2.15)
0.02 (0.004)
0.27 (0.08)
0.93 (0.27)
865 (632)
Germany
0.83 (0.27)
1.8 (0.83)
1.8 (0.28)
0.46 (0.13)
0.06 (0.02)
10.3 (16.7)
0.05 (0.002)
0.19 (0.02)
0.99 (0.33)
2592 (1238)
USA
USA
–
1.8 (1.2)
3.9 (1.4)
–
–
230.1 (96.5)
0.87 (0.34)
0.15 (0.05)
0.031 (0.01)
4.7 (0.14)
0.28 (0.11)
0.64 (0.18)
3.9 (1.8)
0.79 (0.18)
0.05 (0.01)
2.9 (0.95)
(Continued)
–
3.9 (1.3)
–
–
–
–
0.25 (0.12)
0.53 (0.21)
0.012 (0.005)
6.87 (2.34)
0.68 (0.31)
1.6 (0.68)
2.3 (0.48)
0.54 (0.24)
0.08 (0.03)
12.4 (10.5)
0.03 (0.006)
0.04 (0.003)
0.257 (0.08)
0.27 (0.11)
0.99 (0.49)
0.98 (0.41)
189 (82.9)
2168 (1087)
UK
General equilibrium model with country-speciﬁc variables
12
Germany
Standard general equilibrium model
Table 3. Parameter estimates of the general equilibrium model.
QA: MM
B. Dalamagas and S. Kotsios
UK
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
USA
Standard general equilibrium model
Germany
Note: Standard errors in parentheses.
Replacement ratio
Unemployment growth
Employment deviation
ht–1
Reuniﬁcation
Table 3. (Continued)
–
–
–
–
0.65 (3.9)
Germany
63.4 (42.7)
–
–
–
–
UK
–
304.5 (108.1)
14.1 (8.7)
0.58 (0.21)
–
USA
General equilibrium model with country-speciﬁc variables
QA: MM
International Review of Applied Economics
13
QA: MM
14
5
10
15
20
25
30
35
40
45
50
B. Dalamagas and S. Kotsios
In estimating the model, we applied the estimation technique adopted by
Mankiw et al. (1985), who rely heavily on Hansen and Singleton’s (1982) method
of manipulating the general case of non-linear rational expectations models.
Model parameter estimates and standard errors for the sample countries are
reported in Table 3.
An objection that one might raise to the estimates of the standard general equilibrium model of Table 3 (ﬁrst four columns) is that they are likely to warrant a
limited degree of conﬁdence if there are additional determinants of employment not
accounted for by equations (9) to (16). This may be the case when one considers
the possibility of expanding the initial data set along the lines suggested by OECD
(OECD’s Economic Surveys, various issues). These surveys point to a number of
institutional reforms and revisions in economic policy, which occurred during the
period examined in the three countries (country-speciﬁc variables) and may have
potentially inﬂuenced labour supply.3
The country-speciﬁc variables were added to the list of the RHS variables of
equations (15) and (16), as additional explanatory factors of hours worked per
employee and per self-employed. The augmented employment relationships, in conjunction with the remaining equations of the model, were again used in GMM to
get new estimates of the parameters. The results are presented in Table 3 (last four
columns). The revised estimates will be employed to examine the dynamic response
of working time to marginal tax-rate changes.
To this end, dynamic simulations of the model are carried out over the sample
period. Using exogenous time series but only the starting values of the endogenous
variables, the model generated historically simulated values for hours worked. We
found that these values were close to average historical values, as indicated by the
low values of the RMSE test (between 1.2% and 4.3%) for the equations considered. Thus, the model appears to track hours worked closely and provides as a basis
run a good representation of the behaviour of the three economies in a disturbed
sample period.
Next, we carried out dynamic stochastic simulations to generate the time path of
working time and conduct policy experiments in order to investigate how the model
as a whole behaves in response to exogenous shocks to tax-rate adjustments. The
dynamic simulations for each country were then compared with the control solution
and the dynamic responses of each economy to tax-rate shocks were examined. In
Table 4, we present average (over the sample period) estimates of the dynamic
responses of hours worked to a permanent one standard-deviation shock to marginal
tax rates.
The general observation to be made from Table 4 is that the results are not
at odds with those of the comparative dynamics analysis of the previous section, but they carry superior information. They provide us with numerical estimates of the effects of a one standard-deviation shock to tax rates on hours
worked.
In all of the sample countries, changes in working patterns move in the opposite
direction to tax-rate changes. Thus, a persistent increase in the marginal tax-rate
(from 29.6% to 36.6%) in the US leads to a 2.7% decrease in annual hours worked
per self-employed. The corresponding reductions are roughly 2.1% in the UK and
1.9% in Germany. On the contrary, a one-standard-deviation rise in marginal tax
rates results in an 8% decrease in annual hours worked per employee in the US
(6% decrease in the UK, 7.2% decrease in Germany).
1987
2099
1951
1843
1973
1795
Dynamic simulations
2212
2302
2364
Control solution
2171
2253
2301
Dynamic simulations
Hours worked per self-employed
Note: All numbers represent average values of hours worked and tax rates over the sample period.
Germany
UK
USA
Control solution
Hours worked per employee
Table 4. Dynamic effects of marginal tax rate changes on work effort.
0.068
0.124
0.296
Control solution
0.080
0.154
0.366
Dynamic simulations
Marginal (personal income) tax rate
QA: MM
International Review of Applied Economics
15
QA: MM
16
5
10
15
20
25
B. Dalamagas and S. Kotsios
In general, inspection of Tables 3 and 4 indicates that:
The tax-induced decline in work effort is smaller in the short run than in the long
run, even though the rate of decline is not signiﬁcantly high.
The secular rise in leisure seems to be – at least in part – an expression
of individual choices as a lot of institutional and legal factors, capable of
affecting labour supply, have been taken into consideration in the econometric
analysis.
Even though in most cases employees are not free to adjust their working patterns,
tax withholding – and hence directly observable cuts in take-home pay – make their
supply of effort (especially overwork and part-time work) more elastic to income
tax changes than is the case with hours worked by the self-employed.
5. Concluding remarks
In this paper, we argue that an analytical approach to the tax–employment relationship that takes into account the distinction between employees and the selfemployed helps to generate important insights. To substantiate this argument, we
constructed both a comparative dynamics model and a stochastic general equilibrium model in which employees and the self-employed enter as separate factors into
the production process. The econometric model was estimated and tested for three
industrialized countries over the period 1960–2007. The main points from these
models can be summarized as follows. Increases in the marginal income tax rate
exert negative effects on working hours either per employee or per self-employed,
but the response of employees, who are subject to tax withholding, is stronger than
the response of the self-employed, whose current-year tax will be paid in the course
of the next year.
Notes
30
35
40
45
1. For the sake of simplicity, the terms ‘work effort’ and ‘working time’ are used
interchangeably in the present text to indicate weekly hours of work. In the real
world, employees subject to contracts cannot vary working time, but they can
vary effort, unless they are perfectly monitored.
2. As becomes evident from the above, our analysis will focus on the effects of an
income tax on hours worked and no attempt will be made to examine the effects
of the employee social security contributions. The underlying reasoning is that
the response of working hours to increases in social security contributions is
expected to be substantially milder than that of an income-tax increase, because
of the redistributive or reciprocal nature of the former, as well as of the incometax progressivity.
3. In Germany: the unemployment rate – to account for the global reductions of
working time in the 1980s and 1990s to reduce unemployment – together with
unionization, capital utilization, real unit labour costs – which accompanied the
reduction in ofﬁcial weekly working hours in the period 1984–1994 – and a
dummy variable to control for the effects of reuniﬁcation. Efforts to econometrically estimate relationships between variables such as employment rates and real
wages for Germany over a period covering both the pre- and the post-uniﬁcation
years is expected to meet serious problems, because of the different experiences
QA: MM
International Review of Applied Economics
AQ3
17
of the two parts of this country. To cope with this problem, we ran two separate
regressions for the equations of our model. The ﬁrst set of GMM estimates used
data solely for West Germany over the period 1960–1990; the second set was
based on combined data for both West Germany up to 1990 and the reuniﬁed
Germany over the period 1991–2007, with a dummy variable to capture the
effects of reuniﬁcation. Both sets of GMM estimates gave parameter values of
the same sign and the same order of magnitude for the crucial variables of the
model. Table 3 displays the estimates of the second set, which refers to the entire
period 1960–2007.
In the UK: the ratio of unionized workers to their total number – to account for
the strength of labour unions – the net replacement ratio – to catch the disincentive effects on hours worked – and two dummy variables: the ﬁrst for the period
1999–2003 (to account for the effects of the Working Time Directive on hours
worked) and the second for the period 1980–2004 (to account for the impact of
all the reforms made to improve work incentives).
In particular, the second dummy variable was introduced to account for the fact
that the UK launched several initiatives in the period 1980–2004 to increase
labour market attachment of the unemployed. A series of employment laws
reduced employees’, and especially unions’ bargaining power. Wage Councils
were largely abolished, welfare beneﬁts reduced and eligibility tightened. The
most important of these initiatives, which cannot be captured by the tax variable,
are the following.In the early 1980s, marginal withdrawal rates could exceed
100%, creating strong disincentives to work. This anomaly was tackled in 1988
by calculating entitlement on net rather than gross income.
The November 1994 budget introduced changes to employers’ national insurance
contributions (NICs) to favour employment of the part time, the low paid and
the long-term unemployed. The same budget introduced: (i) nationwide extension
of the ‘workwise’ and ‘1-2-1’ schemes; (ii) extension of the ‘Community Action’
scheme; (iii) extension of the ‘Work Trials’ scheme; (iv) nationwide availability
of the ‘Jobﬁnders Grant’.
In 1995, Family Credit and the Disability Working Allowance offered an extra
UK£10 a week to claimants working for more than 30 hours a week.
In 1995, Invalidity Beneﬁt was replaced by Incapacity Beneﬁt, which applied a
tougher medical test to assess incapacity and eligibility for beneﬁt.
In 1996, the means-tested component of the Jobseekers’s Allowance (JSA)
replaced ‘Income Support’ as a safety-net beneﬁt with a marginal withdrawal
rate of 100%. To counter the disincentive to work, a ‘back-to-work bonus’ was
introduced.In the period 1998–2001, the UK initiated important active labour
market programmes to reduce unemployment and inactivity. They are welfare-towork programmes under the umbrella of the ‘New Deal’, which gives special
attention to disadvantaged groups (young people, the long-term unemployed,
lone parents, disabled people).
The Working Families Tax Credit (WFTC) was introduced in 1999 to provide
in-work ﬁnancial support for families with children, in order to address the issue
of workless households.
In 2003, the government combined several parts of the tax and beneﬁt system
that supported families, including the WFTC, and replaced them with the Child
Tax Credit and the Working Tax Credit.For a detailed discussion of the above
measures, see OECD Economic Surveys, UK (1995, 1998, 2009).
5
10
15
20
25
30
35
40
45
50
QA: MM
18
5
10
B. Dalamagas and S. Kotsios
In the US: employment growth, deviations of employment from trend and a
lagged dependent variable – to capture cyclical inﬂuences – as well as a dummy
variable for the period 1996–2003 to capture the effects of the 1996 Welfare
Reform Bill and the 1998 reauthorization of Head Start by the Congress
(because poor families with children are now better able to work since young
children are at publicly funded schools, rather than privately funded daycare).
References
Aronsson, T., K. Lofgren, and T. Sjogren. 2002. Wage setting and tax progressivity in
dynamic general equilibrium. Oxford Economic Papers 54: 490–504.
Barzel, Y., and R. McDonald. 1973. Assets, subsistence and the supply curve of labor. The
American Economic Review 63: 621–33.
15
Belﬁeld, C., and J. Heywood. 2001. Unionization and the pattern of non-union wages: Evidence for the UK. Oxford Bulletin of Economics and Statistics 63: 577–98.
Bender, K., Donohue, S., and Heywood, J. Job satisfaction and gender segregation. Oxford
AQ4
Economic Papers 57: 479–96.
Bhattarai, K. 2007. Welfare impacts of equal-yield tax reforms in the UK economy. Applied
20
Economics 39: 1545–63.
Blomquist, S. 1983. The effect of income taxation on the labor supply of married men in
Sweden. Journal of Public Economics 22: 169–97.
Boadway, R. 1979. Long-run tax incidence. A comparative dynamic approach. Review of
Economic Studies 46: 505–11.
25
Chung-cheng Lin. 2003. A backward-bending labor supply curve without an income effect.
Oxford Economic Papers 55: 336–43.
Devereux, M., C. Allen, and B. Lapham. 1996. Monopolistic competition, increasing returns
and the effects of government spending. Journal of Money, Credit and Banking 28:
233–254.
30
Dickinson, D. 1999. An experimental examination of labor supply and work intensities.
Journal of Labor Economics 17: 638–70.
Evans, C.L. 1992. Productivity shocks and real business cycles. Journal of Monetary Economics 29: 191–208.
Fiorito, R., and F. Padrini. 2001. Distortionary taxation and labor market performance.
35
Oxford Bulletin of Economics and Statistics 63: 173–96.
Gilbert, F., and R. Phouts. 1958. A theory of the responsiveness of hours of work to changes
in the wage rate. Review of Economics and Statistics 40: 116–21.
Hanoch, G. 1965. The backward-bending supply of labor. Journal of Political Economy 73:
636–42.
40
Hansen, P., and K. Singleton. 1982. General instrumental variables estimation of non-linear
rational expectations models. Econometrica 50: 1269–86.
Johnson, G.E., and P. Layard. 1986. The natural rate of unemployment: Explanation and policy. In Handbook in labor economics, Vol. II, ed. O. Ashenfelter, and R. Layard, 921–
99. Amsterdam: Elsevier Science Publishers.
45
Klevmarken, A. 2000. Did the tax cuts increase hours of work? A statistical analysis of a
natural experiment. Kyklos 53: 337–62.
Langot, F. 1996. Do we need a hysteresis model to explain the unemployment persistence?
Annales d’ Economie et de Statistique 44: 30–57.
Mankiw, G., J. Rotemberg, and L. Summers. 1985. Intertemporal substitution in macroeco50
nomics. Quarterly Journal of Economics 100: 225–51.
Menezes, C., and H. Wang. 2005. Duality and the Slutsky income and substitution effects of
increases in wage rate uncertainty. Oxford Economic Papers 57: 545–57.
Merz, M. 1995. Search in the labor market and the real business cycle. Journal of Monetary
Economics 36: 269–300.
55 AQ5 Myles, G.D. 1995. Public economics. Cambridge University Press.
Nickolson, W. 1998. Microeconomic theory. FloridaUSA: The Dryden Press, Harcourt Brace
College Publishers.
Pencavel, J. 1986. Labor supply of men: A survey. In Handbook of labor economics, ed.
O. Ashenfelter, and R. Layard. Amsterdam: North-Holland.
QA: MM
International Review of Applied Economics
19
Rerroni, C. 1995. Assessing the dynamic efﬁciency gains of tax reform when human capital
is endogenous. International Economic Review 36: 907–25.
Pisauro, G. 1991. The effect of taxes on labor in efﬁciency wage models. Journal of Public
Economics 46: 329–45.
Weiss, A. 1980. Job queues and layoffs in labor market with ﬂexible wages. Journal of
Political Economy 88: 526–38.
Yellen, J.L. 1984. Efﬁciency wage models of unemployment. American Economic Review
74: 200–05.
Yuan, M., and W. Li. 2000. Dynamic employment and hours effects of government spending
shocks. Journal of Economic Dynamics and Control 24: 1233–66.
5
10
15
Appendix. Descriptions and sources
The time series include Gross Domestic Product at market prices, private consumption expenditure, private capital stock, government consumption expenditure, personal income tax revenue, public debt, private investment, annual compensation of
employees (excluding social security contributions) and the operating surplus of the
private, unincorporated sector. All the above variables are deﬂated by the GDP
deﬂator and expressed in per capita terms. Per capita values are obtained by dividing each of these variables by the population deﬁned as the total number of
employees and the self-employed.
The remaining time-series used include the total number of the self-employed,
the total number of employees, the lending rate and the weekly hours of work per
worker in manufacturing. The annual hours of work of the self-employed are indirectly derived from the production function, as described in Section 3.4.
The hourly wage rate is estimated as the ratio of the annual compensation of
employees to the product of three arguments: weekly hours of work per worker in
manufacturing, total number of employees and the number of working weeks per
year (48). The hourly earnings of the self-employed are estimated as the ratio of the
operating surplus of the private unincorporated sector to the product of two elements: annual hours of work of the self-employed and their total number.
Non-wage income includes such elements as government transfer payments to
households, interest payments on public debt to domestic government-bond holders
and interest receipts from private deposits with domestic ﬁnancial institutions.
Most of the aforementioned annual data are provided by Data Stream. For some
data, however, it was necessary to use additional sources: Flows and Stocks of
OECD Countries, OECD, for the capital stock, National Income Accounts of OECD
Countries, OECD, for the operating surplus of private unincorporated sector, and
Labour Force Statistics, OECD, in conjunction with the Main Economic Indicators,
OECD, for hours worked per worker in manufacturing. Missing observations in
some of the years were approximated by using interpolation techniques.
20
25
30
35
40
45