Regression‐Kink Approach for Wage Effect on Male Work Hours
| Published date | 01 June 2016 |
| DOI | http://doi.org/10.1111/obes.12112 |
| Date | 01 June 2016 |
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©2015 The Department of Economics, University of Oxford and JohnWiley & Sons Ltd.
OXFORD BULLETIN OF ECONOMICSAND STATISTICS, 78, 3 (2016) 0305–9049
doi: 10.1111/obes.12112
Regression-KinkApproach for Wage Effect on Male
Work Hours*
Young-sook Kim† and Myoung-jae Lee‡
†Korean Women’s Development Institute, Seoul 122-707, South Korea
(e-mail: youngkim@kwdimail.re.kr)
‡Department of Economics, Korea University, Seoul 136-701, South Korea
(e-mail: myoungjae@korea.ac.kr)
Abstract
In finding the effect of after-tax wage rate on work hours, the main difficulty is the endo-
geneity of after-tax wage rate that equals ‘one minus average tax rate’times wage rate. To
overcome this endogeneity problem, we take advantage of jumps in the marginal income
tax rate, which is a regression discontinuity (RD) idea. This RD, in turn, makes the aver-
age income tax rate ‘kink-continuous’, which is a regression kink (RK) idea. We provide
a simple economic model resulting in the RD and RK features, explain how to implement
RK in practice, and then apply our methods to Korean male data. Our main RK-based
labour supply elasticity estimate 7.16% turned out to be insignificant with t-value 1.52,
but it is much larger than most estimates in the literature. This maybe attributed to, among
other things, the facts that the RK instrument is unique, that RK identifies only the local
elasticity at the kink point and that RK requires large data as regression derivatives are
estimated.
I. Introduction
In economics, effects of after-tax wage rate on work hours are of considerable interest,
as reviewed in Hausman (1981, 1985), Blundell and MaCurdy (1999), Keane (2011) and
Cahuc, Carcillo and Zylberberg (2014). For instance, if the elasticity of work hours with
respect to after-tax wage is large, a tax rate hike intended to increase tax revenuemay result
in a large decrease in work hours, which in turn may reduce the tax revenue. In a static
framework, a frequently used model for the elasticity is, for a parameter
w,
ln(work hours) =
w×ln(after-tax wage) +‘other regressors’ + error (1)
which also arises in dynamic optimization frameworks; often the level variables without
logarithm are also used.
JEL Classification numbers: C31, C34, C36, J22, H24.
*The authors are grateful to the Editor and anonymous reviewers for their detailed comments. The research of
Myoung-jae Lee has been supported by the National Research Foundation of Korea Grant, funded by the Korean
Government (NRF-2014S1A2A2027803).
RK for wage effect on male work hours 425
Despite the popularity, equation (1) has well-known endogeneity problems of after-tax
wage due to a couple of reasons. First, the simultaneity of work hours and after-tax wage
holds, as work hours determine labour income. Second, there may be common factors
affecting both after-tax wage and the model error term; e.g. taste for work may lurk in
the model error term that is related to work hours and wage. Third, the true wage may
be measured with an error, and the measurement error appears in the model error term to
make the reported after-tax wage endogenous.Yet another problem of equation (1) is that
there exist multiple, not a single, tax rates due to progressive tax, in which the marginal
tax rate is endogenously determined by income.
Toavoid the endogeneity problems, usually instruments are used for after-tax wage, but
convincing instruments are rare because it is hard to justify excluding those instruments
from the work hour equation. In this paper, we take advantageof an exogenous variation in
after-tax wage due to a marginal tax rate change as income passes a threshold in the income
tax schedule. This is a regression discontinuity (RD) idea. Even if a person can control
his/her own income to manipulate the marginal tax rate, so long as such a manipulation
cannot be done perfectly so that there remains some randomness, RD gives a ‘threshold
randomization’ (Lee and Lemieux, 2010).
In addition to using RD, we will use the lagged after-tax wage instead of the current
after-tax wage, which avoids the simultaneity problem. One way to view this approach is
to think of the lagged after-tax wage as a predictor for the current after-tax wage so that,
for a parameter ,
ln(after-tax wage) =×ln( lagged after-tax wage)+‘prediction error’. (2)
Substituting this into equation (1) gives, with w≡
w,
ln(work hours) =w×ln(lagged after-tax wage) +‘other regressors’ + error. (3)
In most developed countries, the exact current income tax is not known until the following
year when the income tax return is filed, and the income tax currently withheld in the
payroll is based on the last year’s income. This means that there is uncertainty in the
current after-tax wage, and thus individuals may determine their work hours based on
the lagged after-tax wage, instead of the current one; i.e. we may take equation (3) as a
data-generating process (DGP) instead of equation (1).
In the literature, many studies assume a constant tax rate, in which case marginal tax
rate equals average tax rate. But in reality, a progressivetax system holds in most developed
countries, and this raises the question of which tax rate to use in equations (1) or (3). One
approach for progressive tax is considering explicitly the nonlinear budget constraint due
to the progressive tax and modeling the choice of tax rate (e.g. Burtless and Hausman,
1978; Wales and Woodland, 1979). This is a ‘global’ approach, whereas our approach is
‘local’ around an income threshold in the income tax schedule.
In our local approach, we use average tax rate instead of marginal tax rate for two
reasons. One is that marginal rate is not easily observed but the average rate is, whichis the
case in our data. The other is that, if one chooses work hours based on the lagged after-tax
wage, then the tax rate in his/her mind is likely the average tax rate (e.g. ‘I lost 30% of
my income to tax’), not the marginal rate. Using average tax rate requires modifying the
RD idea: since average rate is an integral of marginal rate, averagerate gives a ‘regression
©2015 The Department of Economics, University of Oxford and JohnWiley & Sons Ltd
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