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Despite a large literature estimating the
effects of income taxation on the labour decisions of young and middle-aged
workers, little is known about the extent to which older workers respond to
changes in their income taxes. This paper explores this unresolved empirical
issue, using longitudinal administrative data on more than one million
individuals from Canada and exploiting a recent tax reform in the empirical identification
strategy that explicitly targeted older couples. Specifically, this paper makes
two contributions. First, older workers are shown to respond meaningfully to
changes in their income taxes; however, in contrast with standard predictions,
they are responsive to the average—not the marginal—tax rate. The compensated elasticities of labour income with respect
to the average and marginal net-of-tax shares are estimated to be 0.421 and -0.112 conditional on being employed, respectively, of which only the former is statistically significant. In addition, each 1% increase in total after-tax income reduces the likelihood of being employed by 1.6 to 2.3 percentage points. Second, changes in individuals’ taxes have spillover effects on the
employment and labour income decisions of their spouses, although the income
pooling prediction of the unitary model is rejected empirically. These findings
offer new insight into the “black box” of intra-household labour supply and
inform the optimal designs of income tax and retirement income systems.
Keywords:
labour income, pension, effective tax rate, income
splitting, unitary model, instrumental variables.
Executive summary
Using longitudinal administrative tax data
on more than one million individuals and their spouses in Canada, this paper
assesses the extent to which older workers respond to changes in their income
taxes. In particular, the primary findings from this paper are as follows:
The compensated elasticity of taxable labour
income with respect to the average net-of-tax share (one minus the tax
rate) is 0.421, conditional on being employed. Therefore, a 10% increase in the
average net-of-tax share leads to a 4.21% increase in the labour income of
older workers.
Changes in tax liabilities also have large
effects on individuals’ labour market participation decisions. The analysis
suggests that each 1% increase in total after-tax income reduces the likelihood
that individuals are employed by 1.6 to 2.3 percentage points.
In addition, changes in individuals’ tax
rates and tax liabilities can have spillover effects on the employment and
labour income decisions of their spouses. The findings from this
intra-household analysis indicate the following:
Each 10% change in individuals’ total after-tax
income is estimated to induce spouses to reduce their labour earnings by 0.76%
to 1.17% conditional on being employed, and to become 1.7 to 1.8 percentage
points less likely to be employed.
Each 10% change in individuals’ labour income
following a tax reform is estimated to induce spouses to reduce their labour
earnings by approximately 15%.
Taken together, the results of this paper suggest
that the employment and labour income decisions of older workers respond
meaningfully to changes in both their own income taxes and the income taxes of
their spouses. These findings offer new insight into intra-household labour
supply, and inform the optimal designs of income tax and retirement income
systems.
1 Introduction
The aging of workforces and increasing life
expectancies pose significant challenges for economic growth, national savings,
and the solvency of public pension systems in many countries (Organisation for
Economic Co-operation and Development [OECD] 2014). To address these concerns,
governments have been increasing retirement ages and strengthening work
incentives in order to raise employment rates among older workers and improve the
sustainability of their pension systems (OECD 2012). These initiatives are
motivated by a large literature that finds individuals’ pension receipts or
decisions to retire are responsive to the retirement incentives that public
pension plans create (Baker and Benjamin 1999; Feldstein and Liebman 2002;
Baker, Gruber and Milligan 2003; French and Jones 2012). In contrast to these
pension reforms, the tax codes of many countries offer age-related deductions
and reduced taxation of public pension income (OECD 2011), which lower the
effective tax rates of older workers and create ambiguous labour supply
incentives. Yet the extent to which older workers respond to income taxes, so
that the tax code is a viable policy lever for influencing labour supply, has not
received considerable attention in empirical research (Schmidt and Sevak 2009;
Alpert and Powell 2014). A better understanding of the extent to which
older workers respond to changes in their income taxes would inform the optimal
designs of income tax and retirement income systems.
Using administrative data on more than
one million taxfilers from Canada, this paper provides new insight into this
unresolved issue by estimating employment and labour income responses to
policy-induced changes in income tax rates among older workers. Specifically,
this paper makes two key contributions. First, it credibly estimates whether
older workers respond to exogenous changes in their effective net-of-tax
shares.Note
The empirical identification strategy exploits a recent tax reform that
targeted individuals near or of retirement age, making Canada an ideal setting
to study this issue empirically. On January 1, 2007, the federal government
implemented pension income splitting, which permits couples to notionally “split”
private pension income for tax purposes. The unit of taxation in Canada is the
individual, but the income tax system recognizes individuals’ reduced ability
to pay taxes when they have dependent spouses. Due to the reform, pension
recipients can now transfer up to half of this income to their spouses to
reduce household tax liabilities. When income is split, the effective tax rate
of each individual may either decrease or increase depending on whether that
individual sends or receives income, respectively. The reform also had
different effects on tax liabilities depending on the pensioners’ age and
whether the pension income derives from an employer-sponsored pension plan
(EPP), which creates several margins of variation in effective income tax rates
to be exploited empirically. Instrumental variables (IV) are constructed for
individuals’ net-of-tax shares that vary over time due solely to this reform, following
Auten and Carroll (1999) and Gruber and Saez (2002).
The results show that compensated changes
in income tax rates induce large labour income responses conditional on being
employed (the intensive margin). However, in contrast with standard
predictions, older workers are responsive to the average—not the marginal—tax rate. The compensated elasticities of labour income with respect
to the average and marginal net-of-tax shares are 0.421 and -0.112,
respectively, of which only the former is statistically significant.Note
These findings support the “schmeduling” hypothesis of Liebman and Zeckhauser
(2004), which posits that individuals use the average price as a proxy for the
marginal price when nonlinear price schedules are so complex that knowing what
marginal price is actually faced is difficult.Note In
addition, individuals exhibit large participation responses to changes in total
tax liabilities (the extensive margin). For each 1% exogenous change in total
after-tax income, individuals are estimated to become 1.6 to 2.3 percentage
points less likely to be employed, on average.
The second contribution of this paper is to
test for spillover effects of changes in tax rates across spouses—an important issue among older couples whose retirement decisions
could be codependent (Gustman and Steinmeier 2004, 2009; Banks, Blundell and
Rivas 2010). In a model of taxable labour income augmented to include intra-household
decisions, it is shown that the effect of a tax reform across spouses can be
decomposed into 1) a cross-spouse income effect, owing to the change in
household disposable income; and 2) a cross-spouse labour effect. Then, the
extent to which each of these effects matters for determining employment and
labour income decisions is examined separately. These results indicate that
each 1% change in individuals’ total after-tax income induces spouses to reduce
their labour earnings by 0.076% to 0.117% conditional on being employed, and
also reduces the likelihood of being employed by an average of 1.7 to 1.8 percentage points. Hence, there are large cross-spouse effects of changes in
income taxes along both the intensive and extensive margins. However, in
contrast with the income-pooling prediction of the unitary model of labour
supply, individuals appear to be slightly more responsive along the extensive
margin to changes in their own after-tax income than to the after-tax income of
their spouses.
Overall, the results indicate that the tax
code is a viable policy lever for influencing the employment and labour income
decisions of older workers. These findings relate to several interconnected
literatures. While many studies estimate the elasticity of taxable income with
respect to the marginal net-of-tax share, that research has produced a range of
empirical results owing to the diversity of tax reforms analyzed and model
specifications used (Gruber and Saez 2002).Note Of direct
relevance to this paper are previous studies that estimate the elasticity of
taxable labour or wage income to the marginal net-of-tax share (Moffitt and
Wilhelm 1998; Saez 2003; Bloomquist and Selin 2010; Bosch and van der Klaauw
2012; Kleven and Schultz 2014). This work tends to find lower elasticities
than the taxable income literature, perhaps owing to inflexible labour
contracts or work preferences.Note
Another explanation for the low tax responsiveness typically observed in this literature is that individuals use the average tax rate as a proxy for the marginal tax rate given the complexity of nonlinear income tax schedules. While this schmeduling hypothesis has been tested in other contexts—for example, Ito (2014) finds evidence of this behaviour in electricity consumption—this paper is the first to show that schmeduling occurs with respect to income taxes using a quasi-experimental design. The only other study that addresses this issue is that of de Bartolome (1995), who conducts a controlled experiment and shows that there are as many individuals who use the average tax rate as if it were the marginal tax rate as there are individuals who correctly use the marginal tax rate. Hence, this paper's findings contribute to the wider issue of tax salience (Feldman and Katuščák 2006; Chetty, Looney and Kroft 2009; Finkelstein 2009; Chetty and Saez 2013; Taubinsky and Rees-Jones 2015; Feldman, Katuščák and Kawano 2016).
This paper is also among the first to
estimate intra-household labour supply decisions using a reduced-form
experimental design that exploits a tax reform in the identification. Previous
studies tend to estimate cross-spouse effects structurally (Gustman and
Steinmeier 2004, 2009; Banks, Blundell and Rivas 2010; Laitner and Silverman 2012;
Michaud and Vermeulen 2011; Van Soest and Vonkova 2014). Two notable exceptions
are the following: 1) Yamada (2011), who shows that the hours worked of married
women responded significantly to a series of Japanese tax reforms during the
1990s, although that analysis assumed labour supply decisions within couples
are determined sequentially for identification; and 2) Kabátek, Van Soest, and
Stancanelli (2014), who estimate the effects of a tax reform on intra-household
labour supply and domestic work decisions among couples in France, where the
unit of taxation is the couple. Using a random coefficients model, the study
concludes that spouses’ labour market and housework hours are both responsive
to changes in the tax code.Note In
contrast, the intra-household model of taxable labour income developed in
Section 2 of this paper shows that, when the unit of taxation is the
individual, a tax reform can be exploited to credibly estimate intra-household
labour supply decisions using an IV approach, which offers a novel contribution
to this literature.
The paper proceeds as follows. The next
section presents a unitary model of taxable labour income to provide a
framework for the empirical analysis. Section 3 describes the data, sample
selection, and empirical methodology, including key features of the tax reform
to be exploited in the identification and how the predicted tax measures are
constructed. Sections 4 and 5 assess the effects of income tax changes on
individuals’ labour income and cross-spouse effects, respectively. Section 6
concludes.
2 Theoretical
framework
This section presents a stylized model of
taxable labour income (Gruber and Saez 2002; Kleven and Schultz 2014) and
derives comparative statics to provide a framework for interpreting the
empirical results. More precisely, the model is extended to a setting with
intra-household labour supply (Chiappori 1988). This yields predictions of how
individuals should respond to changes in their own tax rates relative to
changes in the tax rates of their spouses, and validates an IV approach used in
Section 5 to estimate cross-spouse labour effects.
2.1 Setup
In the intra-household
model, a single economic agent maximizes a weighted average of utilities for
individual and spouse , , by choosing consumption and
taxable labour incomes and conditional on vectors of personal traits and . The parameter is
the weight factor.Note
This setup implicitly assumes that and depend on such factors as hours worked,
effort, or tax sheltering, and that these activities are separable from
consumption in the utility function (Kleven and Schultz 2014). The agent
chooses the bundle subject to the budget constraint , where is
the marginal tax rate and is
virtual income for each .
The following standard assumptions on the
agent’s utility function are imposed. For each : 1) and , more consumption but less work is desired; 2) and , there are diminishing returns to consumption and increasing
marginal costs of labour supply; and 3) , the marginal utility of consumption is decreasing in the
labour income requirements to achieve this consumption. On the assumption that
leisure is (weakly) complementary across spouses, for each subject to , the following conditions are also assumed: 4) ; 5) ; and 6) .
2.2 The
intensive margin
Conditional on participating in the labour
market, the optimal taxable labour income (for a given ) is implicitly solved for by
the first-order condition:
To find the individual’s labour income
responses to changes in the own net-of-tax share and the net-of-tax share of
the spouse, totally differentiate Equation (1) with respect to and
and evaluate at to obtain:
where , , and are constants that depend
entirely on the model’s parameters and second-order partial derivatives of
utility (see the Appendix for derivations). Equation (2) shows that the
individual’s response to a change in the own tax rate depends on: 1) a
substitution (price) effect, evaluated relative to a weighted average of the
marginal utilities of consumption for both spouses, ; 2) an income effect, expressed as the sum of the
infra-marginal effect of the reform relative to and the change in virtual
income, ; and 3) a cross-spouse labour income response, . This expression forms the basis for the estimating equation of
individuals’ responsiveness to changes in taxes carried out in Section 4.
Further, Equation (3) shows that a change
in the spouse’s tax liability only has income and cross-spouse labour effects
on the income adjustment of the individual. In this case, the income effect is
expressed as the sum of an infra-marginal effect relative to and the change in virtual
income, . The lack of direct price effect arises because, despite the joint
optimization, the spouse’s tax rate is only levied on spousal labour income; a
small deviation in does not affect the
marginal value of an extra $1 earned by the individual.Note
Hence, combining Equations (2) and (3), exogenous variation in the
net-of-tax share of the spouse, , is a valid excluded instrument for to estimate how a change
in the taxable labour income of the spouse directly affects the taxable labour
income of the individual, . The tests of cross-spouse income and labour effects are
performed in Section 5, using these model implications to guide the analysis.
2.3 The extensive
margin
The labour market participation decision
depends on the utility gain from working relative to the cost. Suppose the
utility cost of supplying labour is for each . As in Alpert and Powell (2014), the agent solves the following
maximization problem:
where is
an indicator function, and for each is the solution to the
intensive-margin optimization problem outlined above. The participation
decision only depends on the effect of total after-tax income on consumption—an income effect. To see this, notice that a tax reform that is
revenue-neutral for the agent has no effect on
participation. For a decrease in the total tax liability of either the
individual or spouse, the benefit of working increases, in turn raising the
likelihood that the individual is employed.
3 Data
and empirical methodology
This section first describes the dataset
and sample selection used. Then, a brief overview of Canada’s income tax system
is provided, including details of the tax reform exploited in the empirical
analysis. This section concludes by presenting the estimating equations derived
from the theoretical framework and outlining how the predicted tax measures
were constructed.
3.1 Data
and sample selection
The Longitudinal Administrative Databank
(LAD) is used to carry out this study. The LAD is a panel dataset comprising a
20% nationally representative subset of the T1 Family File (T1FF). Importantly,
the T1FF is a yearly cross-sectional dataset of taxfilers and their families
based on records from Canada’s central tax authorities. While individuals file
tax returns independently in Canada, census families (both legal and common-law)
were created in the T1FF based on the spousal social insurance number listed on
each individual’s tax form or by matching based on name, address, age, sex, and
marital status. Therefore, the LAD provides data on both individuals and their
spouses, which is needed to carry out this intra-household analysis.Note
Since the LAD does not contain information on individuals’ tax rates, these
measures were constructed using Milligan’s (2012) Canadian Tax and Credit
Simulator (CTaCS) along with the wide scope of information available in the
data to accurately predict tax liabilities.
The following sample restrictions are
imposed. First, individuals were included in the sample only if they were
observed filing taxes in every year from 2005 to 2008, a time period that
encompasses the relevant tax reform. This restriction is needed for the
analysis to control for fixed effects in the empirical analysis; approximately
90% of taxfilers meet this requirement. Second, both individuals and their
spouses must have been 55 years of age or older in 2008 (the last year of data
used), so that the analysis centers on older workers. Third, individuals and
their spouses must have been 54 years of age or younger in at least one year
from 1991 to 2006, for methodological reasons discussed below.
Table 1 presents descriptive statistics for
this sample. Individuals are 60 years old on average, of whom approximately
half are male and 6.1% are immigrants. Importantly, more than half of
individuals and their spouses were employed in 2006 (62.9% and 62.6%,
respectively), and many couples consisted of at least one pensioner (44.2%),
which means there is a large share of households whose labour decisions were
potentially affected by the tax reform. Total after-tax labour income in 2006
averaged $38,650 and $38,100 for individuals and their spouses, respectively,
and the corresponding marginal tax rates with respect to labour income were
24.1% and 20.5%.
Table 1
Descriptive statistics Table summary
This table displays the results of Descriptive statistics. The information is grouped by Statistic (appearing as row headers), Median and Average, calculated using years, percent and nominal dollars units of measure (appearing as column headers).
Statistic
Median
Average
years
Demographics
Individual's age
60.0
60.3
Spouse's age
60.0
60.3
percent
Female
Note ...: not applicable
49.8
Male
Note ...: not applicable
50.2
Married
Note ...: not applicable
100.0
Immigrant
Note ...: not applicable
6.1
Non-pension income
Individual has labour income
Note ...: not applicable
62.9
Spouse has labour income
Note ...: not applicable
62.6
Family has capital gains
Note ...: not applicable
26.8
Family has investment income
Note ...: not applicable
62.5
Family has Employment Insurance income
Note ...: not applicable
12.5
Family has social assistance income
Note ...: not applicable
1.8
Pension income
Individual has private pension income
Note ...: not applicable
28.4
Spouse has private pension income
Note ...: not applicable
28.2
Family has private pension income
Note ...: not applicable
44.2
nominal dollars
Earnings
Individual's labour income
10,000
27,500
Spouse's labour income
9,750
26,950
Individual's total after-tax income
28,950
38,650
Spouse's total after-tax income
28,700
38,100
percent
Allowances
Family has disability allowances
Note ...: not applicable
3.9
Family has medical expense allowances
Note ...: not applicable
42.5
Marginal tax rates
Individual's marginal tax rate
26.7
24.1
Spouse's marginal tax rate
19.2
20.5
Average tax rates
Individual's average tax rate
18.2
14.8
Spouse's average tax rate
14.7
14.3
... not applicable Notes: These descriptive statistics pertain to the relevant sample of individuals and their spouses in 2006, the year prior to the introduction of pension income splitting. The earnings values are rounded to the nearest $50. The number of observations in the sample is 527,286. Source: Statistics Canada, Longitudinal Administrative Databank.
3.2 Pension
income splitting reform
Personal income tax in Canada is calculated
based on a measure of taxable income (net of permitted deductions), then tax
credits are applied to determine the net amount of income tax payable. While
the unit of taxation is the individual, the personal income tax system
recognizes taxpayers’ reduced ability to pay taxes when individuals have
dependent spouses and in certain cases when taxpayers support other dependent
relatives (e.g., parents or grandparents). This recognition is generally
provided in the form of additional tax credits and through permitting the
transfer of certain dependents’ unused portion of personal tax credits to the
taxpayers.
Taxes are determined at the federal and
provincial levels, with the federal and provincial governments each applying
separate tax rates to a uniform measure of taxable income and each applying
separate tax credits to determine the net amount of federal and provincial tax
owing.Note
At the federal level, taxable income in 2006 was divided into four
brackets: 1) the first $36,378 of income; 2) from $36,379 to $72,756; 3) from
$72,757 to $118,285; and 4) over $118,285. The income tax rates for these
brackets were 15.25%, 22%, 26%, and 29%, respectively, and the federal basic
exemption was $9,039. At the provincial level, there is significant
heterogeneity in income tax structures and rates. For example, Alberta levied
provincial taxes using the same bracket structure as the federal level, whereas
Nova Scotia, Ontario, and British Columbia had eight brackets; basic exemptions
ranged from $7,231 in Nova Scotia to $14,799 in Alberta. Given the plethora of
factors that affect taxable income, some researchers regard the Income Tax Act as one of Canada’s most
complex pieces of legislation (Wolfson et al. 2016).
On January 1, 2007, the federal government
implemented pension income splitting, which permits individuals to notionally
“split” private pension income with their spouses. In particular, pension
recipients with high income (the “pensioners”) may allocate up to 50% of their eligible
pension income to their spouses (the “transferees”) to reduce household tax
liabilities. To qualify, the pension income must satisfy certain criteria. If a
pensioner is 65 years of age or older, eligible pension income includes lifetime
annuity payments under employer-sponsored
pension plans (EPPs), registered retirement savings
plans, and payments out of Registered Retirement Income Funds. However, if a
pensioner is less than 65 years old, eligible pension income only includes lifetime
annuity payments from EPPs and certain payments received as a result of the
death of a spouse.
3.3 Empirical
model
The objective of this study is to estimate
both individual and cross-spouse responses to changes in tax rates. The
empirical model extends the work of Gruber and Saez (2002), Gelber (2014), and
the related literature by expressing the change in the individual’s log of
labour income to the changes in the individual’s log of the net-of-tax share
and log of total after-tax income, as well as the direct adjustment to the
spouse’s log of labour income. The baseline estimating equation for the
intensive-margin analysis, derived from Equation (2), is as follows:
where is total pre-tax income and is
tax liability for each at
time ; is
the marginal tax rate with respect to labour income; is a
set of observed covariates; is
the statistical residual; and is
the difference operator, . Thus, measures the change in the log of the
net-of-tax share, and measures the change in the log of total
after-tax income. The regression parameters of interest are: 1) , the substitution response to a marginal
deviation in the price of labour; and 2) , the income effect of the change in total
after-tax income. The model predicts that and .
Implicit in Equation (5) is the fact that tax liability is a function of the income and personal
characteristics of both the individual and spouse (which affect taxable income
through various allowances), as well as a vector of tax parameters. Formally, subject to and is
the set of relevant tax parameters at time . As is common in the elasticity of taxable
income literature, lagged labour income, , is controlled for flexibly in order to
account for mean-reversion bias and potential changes in income inequality
around the time of the tax reform (Auten and Carroll 1999; Gruber and Saez
2002; Saez, Slemrod and Giertz 2012; Gelber 2014; Kleven and Schultz 2014).
Specifically, is
set to be a 10-piece spline based on percentiles. Most
of the literature cited above estimates tax elasticities using policy-induced
variation in marginal income tax schedules over time. That approach assumes
individuals at one point in the income distribution are a reasonable control
group for individuals at the other points in the distribution, which makes
controlling for mean-reversion and a changing income distribution especially
important. Yet including controls that are too flexible invariably absorbs much
of the tax rate variation created by the reform that is useful in the
identification. This issue is less of a concern in this analysis because
variation in effective tax rates brought on by the introduction of a new tax
allowance is exploited. The pension income splitting reform affected
individuals differently across multiple dimensions including, but not limited
to, the income distribution. This analysis will show how the results change as
lagged income becomes controlled for.
Based on Equation (4), the extensive-margin
analysis relates the change in labour market participation to the change in the
log of total after-tax income, as well as the change in spousal labour market
participation. Specifically, the estimating equation is:
where these variables are defined above.
The expectation is that an increase in the after-tax income of the individual
makes leisure more affordable and reduces the incidence of being employed, . While mean-reversion and distributional changes in income are
less of an issue in the extensive-margin analysis, a 10-piece spline for lagged
labour income is still included, as described in the Table 2 notes.
An implicit assumption of the empirical
model is that hourly wages are uncorrelated with the change in taxes, so that
the full burden of an income tax reform operates through its effect on time
spent working. As in Gelber (2014), this analysis partly addresses concerns
regarding this assumption by controlling for an array of job-specific
characteristics in the intensive-margin analysis, including indicators for
union status, EPP coverage, and sector of employment, although excluding these
variables would have no qualitative effect on the results.
3.4 Instruments
The instruments for the changes in the
net-of-tax shares and total after-tax income are predicted tax measures,
calculated by estimating how tax liabilities would have changed due to the
reform holding everything else constant. Denote as the parameter
governing pension income splitting and
as the vector of all
other tax parameters. In addition, for each , denote as the pre-reform total
income ( ) net of a predicted
amount that would have been split ( ) in this period had this
practice been permissible, where if individual is the transferee and if is the pensioner. In
other words, ( ) is the predicted change
in total income around the introduction of pension income splitting resulting
exclusively from this tax reform; the process for calculating is described below. Taken
together, the instruments for the changes in the marginal net-of-tax share and
total after-tax income are:
where . Equations (7) and (8) show that the only factor for each
instrument that changes within individuals over time is due to pension income
splitting, namely as a result of the reform’s introduction ( ) and the amount of
pension income predicted to be sent or received resulting from the reform ( ). The variation across
individuals comes from the differential effects of the reform on transferees
versus pensioners, age groups, and whether the pension income is derived from
EPPs. Exploiting policy-induced variation in net-of-tax shares is necessary to estimate
the elasticity of taxable labour income consistently because of tax
progressivity. Since the marginal tax rate increases with income, the ordinary
least squares (OLS) estimator is biased downwards. Figure 1 shows this downward
bias, as well as a reduced-form look at how the instrument overcomes this
problem.
The process for predicting the amount of
pension income split ( ) is based on two
assumptions. First, although eligibility to split pension income depends on
whether this income is derived from EPPs, the tax data do not reveal such
information. To address this issue, sources of pension income are inferred
using the longitudinal component of the data: workers who were observed with a
positive EPP contribution from 1991 to 2006 at least once during normal working
years (defined here as 54 years of age or younger) are assumed to draw all
their pension income from an EPP.Note
All other pension recipients are assumed to be drawing from other private
savings accounts and are, therefore, subject to the age restriction for
splitting.Note
Second, it is assumed that the person in each family with the highest pension
income always transfers 50% of this income in order to predict changes in taxes
resulting from the reform. Splitting a lesser amount may be optimal in
practice, especially when spouses’ incomes are similar. However, predicting
splitting using an optimization approach is difficult to implement in practice,
and would require a strong assumption that all taxfilers are sufficiently
knowledgeable about the tax system to optimize correctly. Imposing that 50% is
always transferred avoids any behavioural assumptions and is correlated with
the reform’s true effect since this method is strictly based on a maximum
eligibility rule.Note
Description for Figure 1
The title of Figure 1 is “Graphical inspection of the net-of-tax shares, actual and instruments.”
This figure contains two charts (Panels A and B), which are described below.
Chart title: Panel A: Marginal net-of-tax share
This chart is a combination of a scatter plot and a line chart.
The vertical axis (y-axis) title is “percentage change in labour income.”
The axis graduation begins at -100 and ends at 100, with tick marks at every 50 units.
The horizontal axis (x-axis) title is “Percentage change in the marginal net-of-tax share.”
The axis graduation begins at -50 and ends at 50, with tick marks at every 25 units.
There are two series in this chart: one is called “Actual” and the other, “Predicted.”
Chart title: Panel B: Average net-of-tax share
This chart is a combination of a scatter plot and a line chart.
The vertical axis (y-axis) title is “percentage change in labour income.”
The axis graduation begins at -100 and ends at 100, with tick marks at every 50 units.
The horizontal axis (x-axis) title is “Percentage change in the average net-of-tax share.”
The axis graduation begins at -20 and ends at 20, with tick marks at every 10 units.
There are two series in this chart: one is called “Actual” and the other, “Predicted.”
Notes: The relationship between labour income and the marginal (Panel A) and average (Panel B) net-of-tax shares are shown. Each dot corresponds to a unique observation, reflecting the individual’s percentage changes in labour income and actual net-of-tax share. The kernel-weighted local polynomial smoothing of these relationships are also shown, for both the actual and predicted net-of-tax shares.
To illustrate the actual and predicted
variations in the net-of-tax shares and total after-tax income due to
splitting, Charts 1 and 2 show the distributions of individuals who experienced
different changes in each variable among couples with at least one pensioner,
based on whether the individual was predicted to be the transferee or
pensioner. These charts illustrate that there are large shares of individuals
who experienced both decreases and increases in the tax measures owing to the
tax reform. On balance, the instruments reasonably approximate the actual
changes in taxes around the time that pension income splitting was introduced.
However, the mass of individuals who experienced no change in each instrument
is disproportionately large relative to the corresponding actual variable given
that no splitting is predicted to occur if: 1) individuals and spouses have
equal pension incomes; or 2) the age and EPP requirements for splitting
eligibility are not met. The predicted after-tax income is shown to be non-decreasing
for transferees and non-increasing for pensioners, which occurs by design. As a
result, the marginal and average net-of-tax shares tend to decrease by a lesser
amount than the actual declines in these variables for transferees, while the opposite
is true for pensioners.
Data table for Chart 1
Data table for Chart 1
Table summary
This table displays the results of Data table for Chart 1 Less than -15.00, -15.00 to -5.01, -5.00 to -0.01, 0.00, 0.01 to 5.00, 5.01 to 15.00 and Greater than 15.00 (appearing as column headers).
Less than -15.00
-15.00 to -5.01
-5.00 to -0.01
0.00
0.01 to 5.00
5.01 to 15.00
Greater than 15.00
Marginal net-of-tax share
Actual
26.42
21.00
11.63
3.07
25.81
6.57
5.50
Predicted
11.86
25.54
16.27
26.52
15.78
3.43
0.60
Average net-of-tax share
Actual
21.56
19.30
21.62
3.14
24.19
8.00
2.19
Predicted
6.63
20.71
40.90
7.08
22.93
0.92
0.83
Total after-tax income
Actual
10.81
5.32
5.15
0.10
11.42
14.11
53.09
Predicted
0.00
0.00
0.00
3.73
7.03
13.40
75.85
Notes: This chart shows the percentage of individuals who experienced different signs and magnitudes of change in the actual and predicted tax variables from 2006 to 2007. The results are conditional on individuals who are predicted to be transferees. Source: Statistics Canada, Longitudinal Administrative Databank.
Data table for Chart 2
Data table for Chart 2
Table summary
This table displays the results of Data table for Chart 2 Less than -15.00, -15.00 to -5.01, -5.00 to -0.01, 0.00, 0.01 to 5.00, 5.01 to 15.00 and Greater than 15.00 (appearing as column headers).
Less than -15.00
-15.00 to -5.01
-5.00 to -0.01
0.00
0.01 to 5.00
5.01 to 15.00
Greater than 15.00
Marginal net-of-tax share
Actual
3.83
7.00
15.89
1.12
26.57
20.01
25.57
Predicted
0.70
4.18
17.50
22.01
22.36
25.65
7.60
Average net-of-tax share
Actual
0.90
5.16
17.05
0.92
34.52
26.48
14.96
Predicted
0.04
0.08
17.08
4.50
50.74
27.19
0.38
Total after-tax income
Actual
36.60
13.67
9.22
0.06
15.00
12.30
13.15
Predicted
72.85
15.63
8.25
3.26
0.00
0.00
0.00
Notes: This chart shows the percentage of individuals who experienced different signs and magnitudes of change in the actual and predicted tax variables from 2006 to 2007. The results are conditional on individuals who are predicted to be pensioners. Source: Statistics Canada, Longitudinal Administrative Databank.
4 Labour
income responses to tax rates
The regression estimates of individuals’
labour income responses to changes in their net-of-tax shares and total
after-tax income are presented in this section, based on empirical model
specifications derived from Equations (2) and (4) of the theoretical framework.
To estimate these responses consistently, the predicted tax measures defined in
Equations (7) and (8) are used as instruments in a two-stage least squares
(2SLS) approach.
4.1 Primary
results
In Table 2, the first-stage effects of the
instruments for the marginal net-of-tax share and total after-tax income on the
endogenous regressors in Equations (5) and (6) are shown, for both the
intensive-margin analysis in Panel A and the extensive-margin analysis in Panel B. As expected, these results indicate that the instruments are strong
predictors of the true variation in taxes around the time of the pension income
splitting reform, with large F-statistics for the tests of excluded instruments.
Each regression controls for many observed characteristics across both
individuals and their spouses, including age and spousal age fixed effects,
sex, marital status, immigrant status, and province of residence; log values of
family income from capital gains, investments, Employment Insurance, and social
assistance; and log values of family tax allowances for disability and medical
expenses. In addition, several job characteristics of the individual are
controlled for in the intensive-margin analysis: indicators of union status,
EPP coverage status, and sector of employment based on the 2-digit North
American Industrial Classification System (NAICS) code. Throughout the
analysis, standard errors are always clustered by individual.
Table 2
First-stage inspection of the instruments Table summary
This table displays the results of First-stage inspection of the instruments Uncompensated effect, Compensated effect, Income effect, Marginal net-of-tax share and Total after-tax income, calculated using estimates units of measure (appearing as column headers).
Notes: The following control variables are included in the extensive-margin analysis: cohort fixed effects for both the individual and spouse; sex, marital status, immigrant status, and the province of residence of the individual; log values of family income from capital gains, investments, Employment Insurance, and social assistance; and log values of family tax allowances for disability and medical expenses. In addition to these variables, the intensive-margin analysis also controls for the following job-related factors of the individual: union status, employer-sponsored pension plan coverage status, and sector of employment using the two-digit North American Industrial Classification System (NAICS) code. A 10-piece spline in the one-period lagged value of the log of labour income is also always included in the regressions. Standard errors are clustered by individual. The bottom column headers show the dependent variable used in each regression. The number of observations is 178,064 for the intensive-margin analysis and 527,286 for the extensive-margin analysis. Source: Statistics Canada, Longitudinal Administrative Databank.
The second-stage regression results for the
intensive-margin analysis are shown in Table 3 using both OLS and IV
(reduced-form and 2SLS) estimators. The downward bias of the OLS estimator for
the marginal net-of-tax share caused by tax progressivity is apparent. In
addition, there is significant upward bias in the OLS estimates of the effects
of total after-tax income on labour earnings, which arises because individuals
with higher labour earnings are more likely to also have higher total income.
The predicted measure of total after-tax income effectively and consistently
corrects for this bias. Along the intensive margin, in Panels A and B of Table 3, the uncompensated regression estimates—not instrumenting for using the corresponding
predicted variable—suggest that individuals respond meaningfully to changes in their
marginal net-of-tax shares. Specifically, each 1% increase in the net-of-tax
share appears to induce a 1.004% to 1.036% increase in labour income, on
average, depending on whether the lagged labour income controls are included.
However, controlling for income effects of the tax reform by instrumenting for
the change in total after-tax income using absorbs
this effect—a finding that is consistent with previous studies. Hence, these
results ultimately indicate that individuals’ labour income decisions are
unresponsive to exogenous changes in their marginal tax rates.
Table 3
Intensive margin—Labour income responses to changes in the marginal net-of-tax share and total after-tax income Table summary
This table displays the results of Intensive margin—Labour income responses to changes in the marginal net-of-tax share and total after-tax income Ordinary least squares, Instrumental variables, Reduced form and Two-stage least squares, calculated using coefficient estimates units of measure (appearing as column headers).
Notes: The dependent variable is the log value of labour income. The reduced-form model directly estimates how the predicted tax variables affect labour income. The covariates listed in the notes of Table 2 and a spousal variable for the log of labour income are included in every regression. Standard errors are clustered by individual. The number of observations is 178,064. Source: Statistics Canada, Longitudinal Administrative Databank.
In contrast, Table 4
shows that each 1% increase in total after-tax income reduces the likelihood
that individuals are employed by 1.6 percentage points, on average. This
finding indicates that older individuals do respond to tax incentives along the
extensive margin. Since the probability that individuals are employed in the
pre-reform period is 62.9%, as shown in Table 1, the implied elasticity of
employment to total after-tax income is . As the model predicts, the change in
after-tax income is the only relevant factor in explaining labour market
participation, whereas the marginal net-of-tax share is statistically
insignificant in the preferred model specification that controls for lagged
labour income.
Table 4
Extensive margin—Employment responses to changes in the marginal net-of-tax share and total after-tax income Table summary
This table displays the results of Extensive margin—Employment responses to changes in the marginal net-of-tax share and total after-tax income Ordinary least squares, Instrumental variables, Reduced form and Two-stage least squares, calculated using coefficient estimates units of measure (appearing as column headers).
Notes: The dependent variable is an indicator of whether the individual was employed in the reference year. The reduced-form model directly estimates how the predicted tax variables affect employment. The covariates listed in the notes of Table 2 and an indicator variable for whether the spouse was employed are included in every regression. Standard errors are clustered by individual. The number of observations is 527,286. Source: Statistics Canada, Longitudinal Administrative Databank.
4.2 Average
versus marginal net-of-tax shares
There are several reasons why workers’
labour income may be unresponsive to a change in the marginal price of labour
especially in the short run, such as inflexible employment contracts or work
preferences. Since the demand for work diminishes as workers age, and
retirement or partial retirement become viable substitutes for labour market
participation, the ex ante
expectation is for older workers to be at least as responsive as young and
middle-aged workers to changes in tax rates. However, under-responsiveness may
stem from behavioural factors including an imperfect understanding of the tax
system. As Milligan (2009) shows, marginal income tax schedules in Canada are
complex functions of taxfilers’ province of residence, demographics, sources of
income, and a plethora of other factors determined at the federal and
provincial levels. For this reason, individuals may struggle to know their
true marginal tax rates at the time of making labour decisions, especially when
some sources of income are uncertain.
Liebman and Zeckhauser (2004) have posited
that, when nonlinear price schedules are complex and knowing what marginal
price is actually faced is difficult, individuals may use the average price as
a proxy to help guide their decision-making. Figure 2 plots the typical
marginal and average income tax schedules for the sample of individuals
included in this study over a range of labour income from $0 to $60,000. The
marginal tax rate exceeds the average tax rate due to progressivity, and the
marginal tax rate has clear discontinuities at various points where specific
features of the tax code and social programs start or stop taking effect,
whereas the average tax rate is a smooth function of labour income.
Description for Figure 2
The title of Figure 2 is “Marginal and average tax rate schedules, illustrated.”
This figure is a line chart.
The vertical axis (y-axis) title is “percent.”
The axis graduation begins at 0 and ends at 40, with tick marks at every 10 units.
The horizontal axis (x-axis) title is “Labour income (dollars).”
The axis graduation begins at 0 and ends at 60,000, with tick marks at every 20,000.
There are two series in this chart: one is called “Marginal tax rate” and the other, “Average tax rate.”
There are two vertical broken lines in the chart, extending from the x-axis to the last graduation in the y-axis.
The first one, located at $3,500 on the x-axis, is called “CPP/QPP basic exemption.
The second one, starting at $9,039 on the x-axis, is called “Federal basic exemption.”
The third one, starting at $36,378 on the x-axis, is called “Second federal tax bracket.”
The fourth one, starting at $42,100 on the x-axis, is called “CPP/QPP YMPE” (Canada Pension Plan and Quebec Pension Plan Year’s Maximum Pensionable Earnings).
Notes: The marginal and average tax rate schedules are shown for the relevant sample of taxfilers, among those earning from $1 to $60,000 in 2006. Individuals were binned according to income in $250 increments and the average values of the tax rates within each bin are shown. Several income thresholds are illustrated: the point where the Canada Pension Plan and Quebec Pension Plan (CPP/QPP) social program contributions begin ($3,500 in 2006); the federal basic income tax exemption ($9,039 in 2006); the start of the second federal income-tax bracket ($36,378 in 2006); and the CPP/QPP Year’s Maximum Pensionable Earnings threshold ($42,100 in 2006) at which point the CPP/QPP marginal contribution rate falls to zero. These program features result in clear discontinuities in effective marginal tax rates, whereas average effective tax rates remain smooth through the income thresholds.
To determine whether individuals are more
responsive to the average or marginal net-of-tax share along the intensive
margin, the approach from Ito (2014) is used of performing an encompassing test
of these alternative price measures. For each , denote as the average net-of-tax
share for individual at time . The change in the log of the average net-of-tax share is , and the instrument for this endogenous regressor is given by:
The estimating equation assesses the extent
to which average and marginal net-of-tax shares independently affect labour
income. Specifically, the statistical model for the intensive-margin analysis
is given by:
Note that , and are separately identified
in this environment because of tax progressivity and the fact that both and are varying exogenously
in the instruments due to the tax reform, as shown graphically in Figure 3 and
derived formally in the Appendix. To the extent that individuals understand the
income tax schedule and the lack of response to the marginal net-of-tax share
correctly indicates that labour income is unresponsive to changes in tax rates,
the expectation is that . In contrast, the schmeduling hypothesis predicts that and .
For expositional purposes, an encompassing
test is also performed for the extensive-margin analysis. The corresponding
statistical model in this case is the following:
The encompassing test of an
extensive-margin response serves as a useful placebo test of whether
individuals may respond to changes in their average tax rates as a proxy for
their marginal rates, or whether this is simply due to an income effect of the
tax reform given that and are correlated. Since the
theoretical framework predicts that individuals only respond meaningfully to
changes in their total after-tax income along the extensive margin, the expectation
is that and . In contrast, if captures an income
effect, the likely outcome in this case is and .
The results from Equation (10) are shown
in Panel A of Table 5. These findings indicate that individuals are very
responsive to contemporaneous changes in their average—not their marginal—tax rates. For each 1% increase in the average net-of-tax share,
labour income is estimated to increase by approximately 0.421% in the preferred
model specification. In contrast, the marginal net-of-tax share and total
after-tax income continue to be insignificant determinants of labour earnings,
consistent with the previous section’s findings. Ito (2014) posits for the case
of domestic electricity consumption that individuals may initially respond to
the average price, but then start to use the lagged marginal price as this
information becomes available over time. In this setting, Table 5 finds no
evidence of a delayed responsiveness in to either the marginal or
average net-of-tax share, although an increase in total after-tax income does
(weakly) induce a reduction in labour earnings in the next period, which is consistent
with the initial expectation that from the previous
section.
Description for Figure 3
The title of Figure 3 is “The relationship between the changes in the actual and predicted tax variables.”
This figure contains four charts: two charts in Panel A two charts in Panel B, which are described below.
Panel title: Panel A: Marginal net-of-tax share versus average net-of-tax share
Chart title: Actual
This chart is a combination of a scatter plot and a line chart.
The vertical axis (y-axis) title is “percentage change in the average net-of-tax share.”
The axis graduation begins at -50 and ends at 50, with tick marks at every 25 units.
The horizontal axis (x-axis) title is “Percentage change in the marginal net-of-tax share.”
The axis graduation begins at -50 and ends at 50, with tick marks at every 25 units.
The chart contains a diagonal line extending from -50 to 50 on the x-axis.
Chart title: Predicted
This chart is a combination of a scatter plot and a line chart.
The vertical axis (y-axis) title is “percentage change in the predicted average net-of-tax share.”
The axis graduation begins at -20 and ends at 20, with tick marks at every 10 units.
The horizontal axis (x-axis) title is “Percentage change in the predicted marginal net-of-tax share.”
The axis graduation begins at -20 and ends at 20, with tick marks at every 10 units.
The chart contains a diagonal line extending from -20 to 20 on the x-axis.
Panel title: Panel B: Average net-of-tax share versus total after-tax income
Chart title: Actual
This chart is a combination of a scatter plot and a line chart.
The vertical axis (y-axis) title is “percentage change in the total after-tax income.”
The axis graduation begins at -75 and ends at 75, with tick marks at every 25 units.
The horizontal axis (x-axis) title is “Percentage change in the average net-of-tax share.”
The axis graduation begins at -15 and ends at 15, with tick marks at every 5 units.
The chart contains a curved line extending from -15 to 15 on the x-axis.
Chart title: Predicted
This chart is a combination of a scatter plot and a line chart.
The vertical axis (y-axis) title is “percentage change in the predicted total after-tax income.”
The axis graduation begins at -20 and ends at 20, with tick marks at every 10 units.
The horizontal axis (x-axis) title is “Percentage change in the predicted average net-of-tax share.”
The axis graduation begins at -5.0 and ends at 5.0, with tick marks at every 2.5 units.
The chart contains a curved line extending from -5.0 to 5.0 on the x-axis.
Notes: The relationship between the change in the marginal net-of-tax share relative to the change in the average net-of-tax share (Panel A) and between the change in the average net-of-tax share relative to the change in total after-tax income (Panel B) are shown, for both the actual and predicted tax variables. Each dot corresponds to a unique observation. The kernel-weighted local polynomial smoothing of these relationships are also shown. The predicted measures maintain the same basic relationships as the actual measures, but are less noisy.
Panel B of Table 5 shows the results from
the extensive-margin analysis of Equation (11). Notably, in the preferred model
specification that controls for income effects of the tax reform, changes in
the marginal and average net-of-tax shares are both insignificant predictors of
contemporaneous changes in labour market participation, as expected. This provides
additional support for the notion that individuals respond to changes in their
average tax rates along the intensive margin as a proxy for their marginal
rates and not simply because of income effects resulting from the reform. The results
for an initial response also continue to indicate that each 1% increase in
total after-tax income reduces the likelihood of being employed, in this case
by an average of 1.5 percentage points, the implied elasticity being
-0.024%. However, the assessment of a delayed response shows that increases in
the average net-of-tax share and total after-tax income both reduce the
likelihood that individuals are employed in the next period, suggesting that
individuals may use the average tax rate as a measure of the reform’s income
effect in a lagged context. This finding partly supports modelling employment
as a function of the average net-of-tax share, which is an approach that has
been used in related studies (Eissa and Hoynes 2004; Gelber and Mitchell 2012).
Table 5
Encompassing tests—Labour income and employment responses to changes in the marginal versus average net-of-tax shares Table summary
This table displays the results of Encompassing tests—Labour income and employment responses to changes in the marginal versus average
net-of-tax shares Initial timing of response, net-of-tax shares, Delayed timing of response, net-of-tax shares, Marginal, Average and Marginal and average, calculated using coefficient estimates units of measure (appearing as column headers).
Notes: The covariates listed in the notes of Tables 2, 3 and 4 are included in every regression. Standard errors are clustered by individual. The number of observations is 178,064 for the intensive-margin analysis and 527,286 for the extensive-margin analysis. Source: Statistics Canada, Longitudinal Administrative Databank.
5 Intra-household
effects
The extent to which changes in the tax
liabilities of spouses have spillover effects on the employment and labour
income decisions of individuals is investigated in this section. More
precisely, based on the comparative statics of Equations (2) and (3) derived in
the theoretical framework, this section estimates whether individuals respond
directly to: 1) changes in their spouses’ total after-tax income, which affect
the household budget set (a cross-spouse income effect); and 2) changes in
their spouses’ employment and labour income decisions (a cross-spouse labour
effect). This analysis is important because the labour supply decisions of
older workers may be codependent, and the pension income splitting reform is
known to have had different effects on the tax liabilities of individuals and
spouses.
5.1 Test
of cross-spouse income effects
This analysis estimates whether individuals
respond equally to changes in their own total after-tax income and to the
after-tax income of their spouses, as predicted by the unitary model. To this
end, variants of Equations (5) and (6) are estimated, given by:
Intuitively, the test for a cross-spouse
income effect is carried out by directly inserting the variable for the change
in the spouse's log of total after-tax income into the estimating equation to
determine its significance. As before, to credibly identify the effects of the
endogenous regressors, the instruments , and are used in a 2SLS
approach. While pension income splitting mechanically shifts the total
after-tax incomes of individuals and spouses in opposite directions, these
effects are separately identified within couples since the percentage changes
in total after-tax income depend on the initial (pre-reform) levels of pension
and total income. Note that the average rather than the marginal net-of-tax
share is used in Equation (12) based on the results in the previous section.
The unitary model predicts that individuals respond equally to changes in their
own as well as their spouses’ tax liabilities, hence the expectation is that from Equation (12), and from Equation (13).
The results of this analysis are shown in
Table 6 based on the OLS and IV (reduced-form and 2SLS) estimators. Notice that
this analysis is carried out separately across individuals (Panel A) and their
spouses (Panel B), where “individuals” are the taxfilers observed in the data
and “spouses” are the taxfilers matched to those individuals with whom they are
married or in a common-law relationship. Since the unit of taxation in Canada
is the individual, and taxfilers are randomly selected into the LAD dataset,
individuals and spouses should exhibit roughly symmetric cross-spouse responses
to the tax reform despite the fact that the reform is known to have had
opposite effects on each spouse's total after-tax income, as shown in Charts 1
and 2.
Table 6
Tests of cross-spouse income effects Table summary
This table displays the results of Tests of cross-spouse income effects Ordinary least squares, Instrumental variables, Reduced form and Two-stage least squares, calculated using coefficient estimates units of measure (appearing as column headers).
Ordinary least squares
Instrumental variables
Reduced form
Two-stage least squares
coefficient estimates
Panel A: Responses of individuals to changes in the couples' total after-tax incomes
Notes: The covariates listed in the notes of Tables 2, 3 and 4 are included in every regression, as well as a 10-piece spline in the one-period lagged value of the log of the spouse's labour income. Standard errors are clustered by individual. The number of observations is 178,064 for the intensive-margin analysis and 527,286 for the extensive-margin analysis. Source: Statistics Canada, Longitudinal Administrative Databank.
The findings indicate, first, that
individuals’ and spouses’ labour incomes respond meaningfully to exogenous
changes in their own average net-of-tax shares, but not to changes in their own
total after-tax incomes, consistent with the results presented in Section 4. In
addition, large cross-spouse responses are observed: each 1% increase in total
after-tax income leads to a decrease in the other spouse’s labour earnings of
approximately 0.076% to 0.117% on average. Hence, older workers’
intensive-margin decisions are influenced by changes in their own average tax
rates, and by changes in disposable income at the household level brought on by
their spouses. These results are quite robust given that they are qualitatively
similar across panels, as expected.
Table 6 also shows that there are large
cross-spouse effects of a tax reform along the extensive margin. For
individuals, a 1% increase in their own and their spouses’ total after-tax
incomes reduces the likelihood of being employed by 2.3 and 1.8 percentage
points; implied elasticities are -0.037 and -0.029, respectively. These
findings are again similar for spouses. Importantly, while the own elasticity
is only approximately 20% larger than the cross-spouse elasticity for both
individuals and spouses, a test of equality rejects that they are equal (p=0.014
in Panel A, and p=0.022 in Panel B). As a result, the prediction of income
pooling based on the unitary model is rejected (this finding is consistent with
that of Gelber [2014]), although it is interesting to note that the own and
cross-spouse elasticities are at least qualitatively similar.
5.2 Test
of cross-spouse labour effects
The comparative statics in Subsection 2.2
show that a spouse’s marginal net-of-tax share is a valid excluded instrument
for estimating how a change in the labour income of the spouse affects an
individual’s employment and labour income decisions, provided that the spouse’s
tax rate varies exogenously. This is true because the marginal income tax rate
of each spouse is only levied on that spouse’s income, since the unit of
taxation in Canada is the individual. With this in mind, the following variants
of Equations (5) and (6) are estimated:
To obtain causal estimates of the effects
of interest, namely and , the change in the spouse’s predicted net-of-tax share is used
as the instrumental variable for in a 2SLS approach. While
the theory indicates that the marginal tax rate should be used, the
encompassing test of Subsection 4.2 suggests the average tax rate should be
used in its place. Thus, the results will be shown using both and as the excluded
instrument, although the results do not differ meaningfully in either case.
Based on the model, the expectation is that individuals compensate for an
exogenous decline in their spouses’ labour income by working more, and vice
versa, such that .
Several features of these model
specifications are important to mention. In Equation (14), the preferred
specification uses the average net-of-tax share, although the marginal tax rate
is used when is
used as the excluded instrument. As before, this analysis conditions on
observations where both individuals and their spouses have strictly positive
labour income. In Equation (15), the parameter captures
the effect of a change in the labour income of the spouse on the individual’s
labour market participation, and is conditional on the spouse being employed.
This restriction is necessary to ensure the spouse’s net-of-tax share is a
valid excluded instrument based on the prediction from the theoretical
framework. Lastly, as in Subsection 5.1, the analysis is repeated to
assess whether there is symmetry of the findings across individuals and
spouses, in this case using as the excluded
instrument.
The results of this analysis are shown in
Table 7, for both individuals (Panel A) and spouses (Panel B). In both cases,
the OLS regressions indicate that there is a significant positive correlation
between the labour incomes of individuals and their spouses, which likely occurs
as a result of positive assortative matching. In contrast, the intensive-margin
2SLS regressions indicate that each 1% change in one spouse’s labour income
induces the other spouse to reduce their labour income by approximately 1.008%
to 1.567%, a finding that is quite robust both across spouses and the choice of
excluded instrument. The sign and magnitude of this result are both consistent
with expectations from the model. Moreover, the extensive-margin analysis
indicates that there are large cross-spouse income effects of a tax reform on
the labour market participation decisions of individuals—the implied elasticity of employment to the spouse’s labour income
is approximately -0.636% to -0.196%.
Table 7
Tests of cross-spouse labour effects Table summary
This table displays the results of Tests of cross-spouse labour effects. The information is grouped by Excluded instrument (appearing as row headers), Ordinary least squares, Two-stage least squares, Marginal net-of-tax share and Average net-of-tax share, calculated using coefficient estimates units of measure (appearing as column headers).
Excluded instrument
Ordinary least squares
Two-stage least squares
Marginal net-of-tax share
Average net-of-tax share
coefficient estimates
Panel A: Responses of individuals to changes in spouses' labour income
Notes: The covariates listed in the notes of Tables 2, 3 and 4 are included in every regression, as well as a 10-piece spline in the one-period lagged value of the log of the spouse's labour income. For the two-stage least squares regressions, the estimates in the second column have been derived using the marginal net-of-tax share as the excluded instrument, and the estimates in the third column have been derived using the average net-of-tax share. Standard errors are clustered by individual. The number of observations is 178,064 for the intensive-margin analysis, and the numbers of observations are 259,915 and 265,470 for the extensive-margin analyses in Panels A and B, respectively. In Panel A, the F-statistics of excluded instruments from the first-stage instrumental variables regressions are: 1) 111.51 and 210.34 for the intensive margin using the marginal and average net-of-tax shares as excluded instruments, respectively; and 2) 198.43 and 503.07 for the extensive margin using the marginal and average net-of-tax shares. The corresponding F-statistics in Panel B are 1) 157.19 and 40.72 for the intensive margin using the marginal and average net-of-tax shares; and 2) 343.52 and 142.33 for the extensive margin using the marginal and average net-of-tax shares. Source: Statistics Canada, Longitudinal Administrative Databank.
Lastly, Table 8 carries out the tests of
cross-spouse income and labour effects for various subsamples to test for
heterogeneity by sex, income, and family composition. Several findings are
noteworthy. In the intensive-margin analysis of Panel A, men appear more responsive
than women to changes in their tax rates and the tax liabilities of their
spouses, whereas women respond more to changes in the labour income of their
spouses. Tax responses are also robust across income groups and appear to be
primarily driven by the middle of the income distribution, whereas cross-spouse
labour responses are the largest among high-income households. Couples without children
residing in the household are the most responsive to changes in their average
tax rates, whereas those with children exhibit the largest cross-spouse income
and labour effects. This finding may arise because households without children
are less financially constrained and are, therefore, able to adjust their
labour supply in response to price incentives, whereas those with children make
labour decisions in a manner that is most consistent with the model.
Along the extensive margin shown in Panel B, the results continue to indicate that women are more responsive than men to
cross-spouse labour effects. In this case, however, income effects of a tax
reform have the largest effect on the labour market participation of older
workers from high-income households, which may arise because these workers are
the most likely to be able to afford to retire early. The results are also
similar across couples with and without children. Overall, the results of this
heterogeneity analysis are generally consistent with the primary findings, and
are quite robust and symmetric across both individuals and spouses.
Table 8
Heterogeneous responses Table summary
This table displays the results of Heterogeneous responses. The information is grouped by Endogenous regressor (appearing as row headers), Individuals' cross-spouse effect on, Spouses' cross-spouse effect on, Income, Labour, Individual's average net-of-tax share, Individual's total after-tax income, Spouse's total after-tax income, Spouse's labour income, Spouse's average net-of-tax share and Individual's labour income, calculated using coefficient estimates units of measure (appearing as column headers).
Notes: The covariates listed in the notes of Tables 2, 3 and 4 are included in every regression, as well as a 10-piece spline in the one-period lagged value of the log of the spouse's labour income. Standard errors are clustered by individual. The bottom column headers show the endogenous regressors being instrumented. The number of observations is 178,064 for the intensive-margin analysis and 527,286 for the extensive-margin analysis. Source: Statistics Canada, Longitudinal Administrative Databank.
6 Conclusion
This paper assesses the extent to which the
labour decisions of older workers respond to policy-induced variation in
effective income tax rates, in Canada. To credibly identify these effects, the
analysis exploits exogenous variation in tax rates following a recent reform
that reduced the income tax liabilities of older couples by permitting
pensioners to split this income with their spouses, using an instrumental
variables design. The results show that older workers are very responsive to
changes in taxes in terms of both their employment and labour income
adjustments. However, in contrast with standard predictions, workers respond to
changes in their average—not their marginal—tax rates. The compensated elasticities of taxable labour income
with respect to the average and marginal net-of-tax shares are estimated to be
0.421 and -0.112, respectively, of which only the former is statistically
significant.
An explanation for this result is that the
individuals use the average price of labour as a proxy for the marginal price
given that the income tax schedule in Canada is complex and may be difficult to
understand (Liebman and Zeckhauser 2004). Given that the marginal tax rate
generally exceeds the average tax rate due to progressivity, this finding
suggests that workers oversupply labour at older ages because of tax illiteracy
as they are not taking their true marginal costs of working into account properly.
This finding also raises questions about the extent to which the weak
responsiveness to income taxes found in related studies of young and
middle-aged workers can also be explained by low tax salience, this being an
important issue for future research.
In addition, individuals appear responsive
to variation in household income resulting from changes in the tax liabilities
and earnings of their spouses following a tax reform. This result is sensible
in the context of this study given that income splitting necessarily involves
some collaboration and tax planning between spouses. While the test of
cross-spouse income effects rejects the income pooling prediction of the unitary
model of labour supply, individuals and spouses nonetheless still take changes
in each other’s incomes into account when making their own employment
decisions, which is qualitatively consistent with expectations. These findings
provide new insight into intra-household labour supply.
Appendix
Derivations
of and
The optimal levels of income are given by:
where . Given , the first-order condition to this optimization problem with
respect to is:
To derive the effect of a change in the
marginal net-of-tax share on the taxable labour income of the individual,
totally differentiate Equation (17) with respect to and evaluate at per the envelope
condition, then solve for to obtain:
and,
denote , , and . Based on the assumptions imposed on the
utility function, , , and . Substituting these terms into Equation
(18) gives Equation (2), as desired.
To solve for Equation (3), totally differentiate
Equation (17) with respect to and solve for . The derivation is the same as above, except that the first
term on the right-hand side of Equation (18) is not present.
Separately
identifying , and
The predicted marginal tax rate, , is separately identified from the other two predicted tax
variables given the nonlinearity (convexity) of the tax schedule, due to
progressivity. For the remaining two variables, note that the percentage change
in the predicted total after-tax income, , can be expressed algebraically as follows:
The percentage change in the predicted
average net-of-tax share, , is expressed algebraically as follows:
Hence, on average. These two
predicted variables are separately identified in this environment, as desired.
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