A Structural Model of Tax Progressivity and
Self-Employment
Jean-Francois Wen and Daniel V. Gordon
Department of Economics
University of Calgary
Calgary, Alberta
T2N 1N4
PRELIMINARY
March 8, 2010
Abstract
We extend the theoretical model of Rees and Shah (1986) to incorporate
the e¤ects of progressive taxation, as arguments in the individual’s utility
choice model between self-employment and paid employment. Measures of
the degree of progressivity in the tax and transfer system are constructed
from the concept of tax convexity (Gentry and Hubbard, 2000, 2004). The
earnings equations are corrected for self-selection bias and are combined
with the Canadian Tax and Credit Simulator (Milligan, 2007) to calculate
tax di¤erentials. The structural model includes both the predicted net-of-tax
earnings and the tax convexity variables in the self-employment/employed
labor choice decision. The model is estimated using data spanning 19992005 from Statistics Canada’s Survey of Labour and Income Dynamics. The
principal …ndings are that upside tax convexity has a negative e¤ect on the
probability of self-employment, while downside tax convexity has a positive
e¤ect on self-employment, both with high levels of statistical signi…cance.
We use the model to estimate the e¤ects of federal tax rate reductions in
2001 on the rate of self-employment in Canada.
1
Introduction
Entrepreneurship is regarded as vital for generating employment and innovation. It is, however, a risky occupation with high potential returns
and high failure rates. Since the income tax system alters the relationship
between risk and reward, its design may be an important determinant of
entrepreurial activity. The impact of a proportional income tax with loss
o¤set provisions is theoretically to increase risk-taking by risk averse individuals (Domar and Musgrave, 1944). Similarly, a revenue compensated
increase in the rate of a linear progressive income tax can raise the share of
the workforce engaged in entrepreneurship.1
A plausible view, however, is that progressivity achieved with a rising
marginal tax rate schedule is likely to discourage entrepreneurship because
the higher tax rates penalize success by more than the lower tax rates provide
relief against poor returns. One way to examine this hypothesis empirically
is to estimate the e¤ects of the tax and transfer system on the occupational
choice between self-employment and employed labor. Self-employment is
frequently used as a proxy for entrepreneurship in empirical studies. Hence,
we develop a structural model of earnings and tax di¤erentials in a random
utility model of a discrete occupational choice. Of particular interest are
the “tax convexity” variables measuring the asymmetric …scal treatment of
upside and downside income risks as a result of tax progressivity (Gentry and
Hubbard, 2000, 2004). The idea is that uncertainty about prospects obliges
entrepreneurs to consider income scenarios spanning di¤erent segments of
the tax schedule. This is a potentially important interaction between tax
policy and entrepreneurship. The degree of tax convexity is a¤ected not
only by marginal income tax rates and thresholds, but also by payroll taxes,
tax credits and their clawbacks, loss o¤set provisions, and numerous other
tax and transfer considerations.2
1
Increasing linear progressivity positively impacts entrepreneurship, innovation, and
growth in Garcia-Penalosa and Wen (2008). In Kanbur (1981) the e¤ect on entrepreneurship is ambiguous due to the general equilibrium e¤ects on …rm sizes and wages.
2
Blanch‡ower and Oswald (1998) tabulate the answers to a pertinent question asked
in the 1987 National Survey of the Self-Employed in the United Kingdom. 139 individuals
who said they were “seriously intending”to become self-employed in the next few months
1
Tax convexity is measured by Gentry and Hubbard as the spread in the
e¤ective marginal (or average) tax rates for successful and unsuccessful selfemployment outcomes, de…ned relative to the ability of each individual. It
is clear why high tax rates in the event of success may discourage entrepreneurial risk-taking. It is less evident why low tax rates in the case of failure
should discourage self-employment. Gentry and Hubbard provide two illustrations of why both the upside and downside components of tax convexity
may be negatively correlated with self-employment rates. First, the value
of loss o¤sets, in the event of failure, increases with the tax rate. Hence,
an entrepreneur with negative pro…ts can bene…t from a high tax rate in
the lowest bracket. Second, since the alternative to self-employment is to
work for wages, a comparatively high tax rate in the bracket encompassing
wage earnings reduces the opportunity cost of self-employment, and most
wage earners face marginal tax rates that are below the top rate. In both of
these examples, small tax rates in the middle to lower tax brackets discourage self-employment. Although these examples show the potential relevance
of Gentry and Hubbard’s tax convexity variable as a negative correlate of
self-employment rates, the approach depends on particular con…gurations
of self-employment and wage employment earnings. Loss o¤setting, for example, is not relevant to an entrepreneur earning low but positive pro…ts.
A more straightforward way to assess the impact of tax progressivity is to
calculate the expected value of the tax liability of an entrepreneur facing a
distribution of possible returns and to compare this burden with the same
individual’s predicted tax liability. If high marginal tax rates on successful entrepreneurs penalize success more than low marginal tax rates provide insurance against failure, then the expected tax liability will exceed
the predicted tax liability and self-employment is discouraged. This idea is
implemented in our empirical work using proxies for the potential income
were asked to select one of 20 possible answers to the question, “What was your biggest
concern with becoming self-employed?” Interestingly, the answers “Understanding tax”
and “No guaranteed income” were tied at 14.4 percent as the second mostly frequently
cited responses, after “Where to get …nance” at 20.1 percent. This suggests to us that
individuals are aware that the decision to become self-employed has potentially important
tax implications and that income risk is also a factor.
2
shocks. We also generalize the approach by measuring tax convexity separately for upside and downside income realizations relative to the predicted
self-employment income. We expect upside tax convexity to discourage risktaking via the penalty on success, and downside tax convexity to encourage
risk-taking via the social insurance e¤ect arising from lower marginal tax
rates and income support programs.3 The overall e¤ect of tax progressivity
on self-employment rates is the sum of the upside and downside tax convexity e¤ects. We calibrate the person-speci…c upside and downside income
realizations (relative to the individual’s expected income) using both an ad
hoc method and a more principled procedure that uses the the predicted
residuals from the econometric earnings equations to determine the spread
of the upside and downside income shocks.
Our model is estimated using a longitudinal panel dataset with 157,310
observations for Canada spanning the available years 1999 to 2005. The
Canadian Tax and Credit Simulator (CTaCS) developed by Milligan (2007)
is used to calculate the total federal and provincial tax and transfer implications of the employment/self-employment choice for each individual in our
data. The tax parameters include income taxes, payroll taxes, and money
transfers and their clawbacks. Previous work on the e¤ects of tax convexity on occupational choice has focused exclusively on the United States.
The income tax system in Canada di¤ers in important respects from the
U.S. tax system. The personal and corporate income tax systems are integrated in Canada for incorporated businesses earning up to $300,000. This
is achieved with a personal dividend tax credit that o¤sets corporate taxes.4
In contrast, in the U.S. the tax structure provides an incentive to shift labor
income to corporate income when income realizations are large.5 There exists a $500,000 lifetime capital gains exemption on small business shares in
Canada, which has no equivalent in the U.S. Marginal tax rates are higher in
Canada and the rates apply to individual taxpayers, rather than to married
3
In contrast, Gentry and Hubbard (2000) hypothesize that downside tax convexity
should discourage entrepreneurship, for reasons discussed above.
4
The integration arises only if the corporation pays dividends.
5
See Cullen and Gordon (2007) for the impact of this tax feature on self-employment.
3
couples as in the U.S. These and other comparative features of the Canadian
tax system provide an alternative …scal setting to explore the e¤ects of tax
progressivity on self-employment. A noteable feature of our sample period
is the major tax reform in Canada in 2001. Marginal income tax rates were
reduced for the middle and bottom income brackets and the surtax was eliminated. The corporate tax rate on small business income between $200,000
and $300,000 earned by a Canadian-controlled private corporation was cut
from 28 to 21 percent (phased in over …ve years) and the capital gains inclusion rate for individuals and corporations was cut from three-quarters
to one-half. These reforms decreased the degree of upside tax convexity
at the median self-employment income in Canada and the federal government asserted that the new measures would promote entrepreneurship and
growth.
Cross-sectional studies of self-employment generally take the form of either reduced-form or structural models.6 Reduced-form models specify the
self-employment choice as a function of variables thought to determine labor
market outcomes, such as education, labor market experience, age, job stability, capital, occupational status, unemployment, location, marital status,
spouse’s educational attainment, spouse’s employment status, the number of
children and health, and marginal or average tax rates. This is the method
used by Long (1982), Schuetze (2000), Gentry and Hubbard (2000), and
Hansson (2006) to examine income tax e¤ects. A less common approach utilizes structural models derived formally from the self-employment decision
as a function of the earnings di¤erential between self-employment and wage
work.7 Only the studies by Bruce (2000), Parker (2003), and Fossen (2007)
estimate structural models containing earnings equations and net-of-tax income di¤erentials in place of gross earnings di¤erentials as determinants
of self-employment. These studies do not, however, include tax convexity
as a determinant of self-employment. As shown by Gentry and Hubbard
6
Le (1999) provides a useful survey of studies on self-employment.
Early examples of this approach can be found in Rees and Shah (1986) for the UK
labour market, de Wit and van Winden (1989) for the Dutch labour market and Bernhardt
(1994) for the Canadian labor market.
7
4
(2000), the omission of tax convexity considerations may be important for
understanding how taxation a¤ects occupational choice.
In this paper, we extend the theoretical model of Rees and Shah (1986)
to include the e¤ects of tax progressivity. We then estimate a reduced-form
equation in order to control for sample-selection bias in the estimated earnings equations and we use the corrected predicted earnings together with
CTaCS to obtain net-of-tax income di¤erentials between self-employment
and paid employment, and to construct tax convexity measures. These
are used as explanatory variables in the structural probit equation for selfemployment.8 We …nd that upside tax convexity is negatively related to
the rate of self-employment and, conversely, downside tax convexity is positively related to self-employment, both with high statistical signi…cance.
Hence, the overall impact of tax progressivity depends on the balance between these e¤ects. These results corroborate some of the …nding of Gentry
and Hubbard (2000) for the U.S., which is one of the few studies …nding a
negative correlation between income tax rates and self-employment.9 Relatedly, Stabile (2004) and Folster (2002) …nd that self-employment increased
after changes in legislation which exempted self-employment from certain
payroll taxes. Most of the earlier studies conclude, on the contrary, that
higher tax rates increase the level of self-employment, which is attributed to
the opportunities provided by self-employment for tax avoidance or tax evasion (e.g. Long, 1982, Blau, 1987, Parker, 1996, Bruce, 2000, and Schuetze,
2000).
The paper is organized as follows. Section 2 describes the random utility model of a discrete occupational choice between self-employment and
salaried work. Section 3 describes the data and speci…es the econometric
equations, the identi…cation techniques and self-selection issues. Section 4
presents the empirical results. Section 5 illustrates the usefulness of the estimated model by using it to analyze the 2001 federal income tax reform in
8
We focus on the rate of self-employment, as in Rees and Shah (1986), rather than
on the transitions between wage work and self-employment, in contrast with Gentry and
Hubbard (2000), Fossen (2007), Hansson (2006) and Bruce (2000).
9
Other exceptions include Folster (2002), Bruce and Mohsin (2006), Hansson (2006),
and Fossen (2007).
5
Canada. Section 6 concludes.
2
A Model of Occupational Choice
A simple model is used to illustrate the theoretical e¤ects of taxation on
occupational choice between self-employment (S) and employment for …xed
pay (E). Denote individual i’s before-tax income in occupation j 2 fS; Eg
by yji and after-tax income by xij . Represent income tax progressivity using
the function (Musgrave and Thin, 1948, and Benabou, 2000):
xij = yji
where
1
yb
(1)
and yb are parameters of the tax system. At the income level yb the
taxpayer’s tax liability is zero. The term 1
is the elasticity of after-tax
income with respect to before-tax income; hence,
can be interpreted as
the semi-elasticity of the average tax rate with before-tax income.10 The
larger is
the greater is the marginal progressivity of the income tax. The
expression “tax convexity” conveys the notion that the slope of a graph
of the average tax rate against the logarithm of income is positive, if the
marginal tax schedule is rising, and in practice the graph may be upward
bending.11
Utility is assumed to depend on after-tax income (consumption) and on
an hedonic index Qij of non-pecuniary job characteristics associated with
occupations S and E. The index is composed as follows:
Qij =
X
i
n qnj
(2)
n
10
In familiar notation, write 1
= d ln x d ln y which in turn equals d ln[y(1 s)]
d ln y, where s is the individual’s average tax rate (i.e. the share of income paid in taxes).
Express this as 1
1 + d ln(1 s) d ln y and use the approximation ln(1 s)
s
for small s to obtain
ds d ln y as required.
11
We follow Gentry and Hubbard’s use of the expression “tax convexity” even though
this may be somewhat confusing since tax progressivity need not imply convexity in the
average or marginal tax schedules; rather, more progressivity implies a steeper tax schedule.
6
where qnj is the measure of a non-pecuniary job characteristic in occupation
j and
i
n
is its utility weight. As in Rees and Shah (1986), let the utility
function be
bi
uij = U (xij ; Qij ) = xij
exp di Qij
(3)
where di and bi are preference parameters; risk aversion is decreasing with
bi and non-pecuniary considerations increase with di .
Before-tax income is assumed to be lognormally distributed:
yji
i
j;
LN (
i
j ):
Substituting (1) for xij into (3) gives
uij = yji
(1
)bi
yb
bi
exp di Qij :
(4)
An individual i chooses the occupation j 2 fS; Eg that maximizes expected
utility E(uij ).
Since yji is lognormal, yji
is
E
h
yji
(1
)bi
i
(1
)bi
is also lognormal and its expected value
)bi
= exp (1
i
j
+
1
(1
2
)bi
i 2
j
(Aitchison and Brown, 1966, Theorem 2.1). Thus maximizing expected
utility in (4) is equivalent to maximizing the following utility index:
Vji (Qij ; y ij ; cij ) = (1
where y ij
1
(1
2
) ln y ij
E(yji ) = exp
i
j
+ 12 (
di Qij
; (5)
bi
q
is the mean of yji and cij = exp( ij )2
)(1 bi (1
i )2
j
is the coe¢ cient of variation.
)) ln 1 + (cij )2 +
Expected utility is higher with self-employment compared with paid employment if C
i
VSi (QiS ; y iS ; ciS )
VEi (QiE ; y iE ; ciE )
7
0. Using (5), C
i
0
1
is equivalent to
(1
) ln
The term (1
y iS
y iE
1
(1
2
bi (1
)) ln
1 + (ciS )2
(1 + (ciE )2
+
di
QiS
bi
QiE
0:
(6)
) appears twice on the left-hand side of (6). First, its appear-
ance as a multiplicative factor indicates that greater tax progressivity (higher
) reduces the relative importance of …nancial di¤erences, both reward and
risk, in determining occupational choice. The second appearance of the tax
term is less familiar. To better understand this e¤ect, suppose individuals
are risk-neutral, so bi = 1. In that case, the term,
reduces to
ln
1 + (ciS )2
1 + (ciE )2
:
(1
bi (1
)) ln ( )
(7)
We would normally expect ciS > ciE , as self-employment is loosely associated
with entrepreneurial risk-taking.12 Assuming this to be the case, (7) shows
another distinct way in which tax progressivity discourages self-employment.
This e¤ects arises because income realizations above a self-employed individual’s expected income increase the tax liability by more than income
realizations of similar magnitudes, but below the mean, decrease the tax
liability. In the econometric model, proxies are constructed to represent
the term (7) for each individual, based on the predicted changes in tax liabilities associated with self-employment income shocks above and below
the expected income, referring to these as taxconvexU and taxconvexD, respectively. The expected signs of the regression coe¢ cients are negative for
taxconvexU and positive for taxconvexD.
The term (1
) ln y iS =y iE in (6) can be interpreted as the percentage
change in expected after-tax income that results from switching occupations
from employment to self-employment. In the econometric model this variable is called NetIncdif. Hence, we would expect the estimated coe¢ cient
on NetIncdif to be positive.
We do not observe the individual’s degree of risk aversion, which is de12
In our data (over the whole sample) the coe¢ cient of variation is 0.946 for selfemployment and 0.562 for paid employment.
8
termined by bi ; the coe¢ cient of variation of i’s income distribution in occupation j; and the non-pecuniary aspects embodied in the hedonic indexes
and di . The unobservable characteristics will be proxied with observable
variables believed to a¤ect occupational choice.
Finally, note that self-employment and paid employment determine an
individual’s labor earnings, but the total tax liability depends also on investment income, alimony payments, and so on. In other words, total income
is
yji = eij + ai ;
(8)
where eij is labor earnings of i in occupation j, and ai is i’s non-labor income.
We take ai as exogenous when calculating an individual’s tax liability but
we predict eij with econometric equations.
3
Data and Econometric Issues
The empirical work uses Statistics Canada’s Survey of labor and Income Dynamics (SLID) public use Microdata. SLID is a longitudinal study designed
to capture changes in the economic well-being of individuals and families
over time and the determinants of labor market income. In a given year, the
sample is composed of two panels. A panel is surveyed for six consecutive
years and a new panel is introduced every three years. Thus two panels
are always overlapping. Each panel includes roughly 15,000 households.
Households are interviewed up to twelve times over a six-year period. Every
January interviewers collect information regarding respondents’labor market experiences during the previous calendar year. In May, information on
income is collected from the same households.13 Interviews are conducted
over the telephone with the assistance of a computer to minimize errors.
13
These interviews are conducted in May after households have completed their tax
returns. Households have the option of granting Statistics Canada permission to use their
T1 tax form information rather than spend the time detailing this information to Statistics
Canada. Over 80% of households choose this option. Scripts were read from the computer
screen and data was entered into the database. The computer noti…ed the interviewer of
discrepancies so that they could be remedied before the interview was completed, reducing
measurement error.
9
The sample frame for the survey covers all individuals in Canada.14 The
data used in this research covers the …ve year period 1999-2005 for a total
of 157,310 observations of which 9,805 are de…ned as self-employed.
The key variable of interest in our analysis is employment status. We de…ne persons to be self-employed if they report their major source of earnings
to be from self-employed work and they also report no farm income. Person
are de…ned to be employed if they report their major source of earnings to be
from wages and salary and they also report no farm income. Thus, we construct a binary dependent variable equal to one if a person is self-employed
and equal to zero when a person is employed as de…ned above.15
The SLID Person File is used to download all variables associated with
the individual and this is then linked to the SLID Economic Family File to
collect household information. The variables obtained from SLID and used
in the empirical work are de…ned in Table 1. The …rst column in Table 1
lists the variables as named in SLID and the second column de…nes the variables for use in this study. The main earnings variable (earng42) measures
salaries, wages and self-employed income. Two variables that characterize the …nancial status of individuals and are assumed to impact the selfemployment choice are investment income (inva27) and taxable capital gains
(capgn27).16 We specify a number of control variables describing individual
characteristics believed to a¤ect labor market outcomes such as age, gender, education, health, marital status, parenthood, and immigration status.
To account for labor market conditions we control for unemployment spells
(wksuem28) and industry of employment (white collar, blue collar, and service). Finally, we control for geographic di¤erences by including a set of
provincial dummy variables and where appropriate yearly dummy variables
to account for possible distributional shifts each year.
14
Residents of the Yukon, the Northwest Territories and Nunavut, as well as, residents
of institutions and persons living on native reservations, which constitute less than 3% of
the population, are not included.
15
For the data used here, the yearly percentage self-employed in Canada is: 6.18, 5.66,
5.17, 6.55, 7.08, 5.95 and 6.42 for the years 1999-20005, respectively.
16
Blanch‡ower and Oswald, A. (1998) …nd evidence that …nancial constraints are an
important deterrent to self-employment.
10
Table 2 shows summary statistics by employment classi…cation for the
combined seven years. The data show an interesting statistical picture of
the self-employed versus employed. On average the self-employed have lower
earnings and a greater variation in earnings compared to the employed. This
is consistent with the general notion that self-employed work is more risky.
As well, the self-employed show both higher average levels of investment
income and capital gains, are slightly less educated, moderately older and
more likely to be married and have children.
We need to estimate the earnings functions for employed and self-employed
workers. In general, the expected earnings equation can be written as,
ln earnings j = Z
j
+ "j
(9)
for j = employed (E) and self-employed (S). Z is a vector of variables common to both equations and de…nes those variables thought to in‡uence earnings. A problem with a least squares estimation of equation (9) is the possibility of omitted variable bias caused by self-selection into employed/selfemployed classi…cations. We follow the standard Heckman procedure to correct for omitted variable bias by estimating, for each year, a reduced form
probit speci…ed over the choice between employed and self-employed. From
these equations the inverse Mills ratios are calculated for the self-employed
and employed individuals and included in the appropriate earnings equation.17 The corrected earnings function is …rst estimated using data only for
employed individuals and then used to generate predicted employed earnings for each individual in the data set, both self-employed and employed.
This operation is repeated by estimating the earnings equation using only
self-employed data and then predicting expected self-employed earnings for
each individual in the data set. What we obtain from this exercise is the predicted earnings for an individual if that person had chosen self-employment
or alternatively paid employment. Next the predicted earnings for self17
Under the assumption of normality of the error structure the inverse Mills variable
is the ratio of the normal density (') to the cumulative normal density ( ). For the
self-employed the inverse Mills ratio is de…ned as '( )= ( ) and for employed labor it
is de…ned as '( )= (1
( )) (Lee, 1978).
11
employment and paid employment for each individual, together with their
…nancial and personal characteristics, are used in the CTaCS simulator to
generate tax liabilities from each occupational choice. Finally, the predicted
income (i.e. predicted earnings plus the non-labor income reported in the
data) and tax liabilities from each occupation are used to calculate the logarithmic net-of-tax income di¤erence (NetIncdif) between self-employment
and paid employment.
We are particularly interested in measuring the impact of tax progressivity—
i.e. the convexity of the tax system— on the decision for self-employment.
We measure the responses of individuals to the portion of the tax schedule
applicable to income greater than their expected self-employment income,
and to the portion of the tax schedule applicable to incomes below their
expected income from self-employment. The …rst approach to constructing such variables follows one of the methods used by Gentry and Hubbard (2000) (hereafter identi…ed as GH), whereby we double the predicted
self-employment earnings and use the CTaCS simulator to generate “upside” tax liabilities. We use this to construct upside tax convexity as the
log ratio of upside tax liabilities to the tax liabilities occuring when selfemployment earnings are at their predicted level, de…ning this variable as
(taxconvexUGH ). The measure of “downside” tax convexity is calculated
as the log ratio of tax liabilities with predicted self-employment income to
tax liabilities with half the predicted self-employment income, de…ning this
variable as (taxconvexDGH ).18
The second approach to tax convexity relies on the data to provide
a more empirically justi…ed measure of tax response (hereafter identi…ed as
PR). We do this by recovering the non-robust predicted residuals from the
self-employed earnings function applied to the complete sample (both employed and self-employed individuals). In other words, for each individual
we have the predicted residual conditional on self-employed income. This
18
In addition to this ad hoc approach to calculating tax convexity, Gentry and Hubbard
(2000) also use a statistically-based procedure, whereby the income shocks are based on
the instability of self-employment earnings observed in the data. They …nd similar results
in each case.
12
error is doubled to represent two standard deviations above the mean and
added to individual predicted self-employed earnings and the corresponding
tax liabilities are computed with CTaCS. We then calculate the log ratio
of tax liabilities at the “upside” error-adjusted self-employed earnings to
the tax liabilities at predicted self-employed earnings, de…ning this variable taxconvexUPR . The corresponding “downside”shocks to self-employed
earnings are calculated by subtracting two standard deviations of the predicted error from individual predicted self-employed earnings. Tax liabilities
are then generated with the CTaCS simulator and we calculate the log ratio of tax liabilities with actual self-employed earnings to the tax liabilities
from downside error-adjusted self-employed earnings, de…ning this variable
taxconvexDPR .19
Using these generated variables the structural probit equation for occupational choice (C) is written as,
C = Z +X +
I
NetIncdif +
TU
taxconvexU i +
TD
taxconvexD i + +"C
(10)
where i = GH or P R. The vector Z is as de…ned earlier. The vector X
includes investment income, taxable capital gains, and the number of children in the household. "C is assumed to be iid and asymptotically normally
distributed.
Additional dummy variables are added to equation (10) to account
for provincial and yearly changes. The provincial dummies control for differences in economic development across provinces. The yearly dummies
account for distributional changes across years and for the stock market
decline in the technology sector in 2001.
19
We also tested a speci…cation of tax convexity in which we do not take the logarithm of
the tax liabilities ratio and we found qualitatively similar results to the logarithmic form.
We prefer the latter formulation because it has a natural interpretation as the percentage
change in tax liability as a result of an income shock.
13
4
Empirical Results
This section presents the results obtained from estimating the three econometric models described above: the reduced form probit and the self-employed
and employed earnings functions for each year, and the structural probit for
the combined seven years of data.20 The results of the maximum likelihood estimation for the reduced form probit for 1999 to 2005 are reported
in Table 3. Keep in mind that the purpose of the reduced form probit is
to allow measurement of the inverse Mills ratios that allow correction for
the omitted variable problem in the earnings equations for self-employed
and employed. Consequently, to justify the reduced form equations it is
necessary that they be econometrically identi…ed and the estimation procedure must produce consistent estimates. For identi…cation we maintain
the assumption of normality of the population error terms. We default to
the large number of observations used in estimation and the central limit
theorem to support this assumption. This assumption is consistent with
standard work in this area. However, normality is not enough to support
identi…cation without at least one identifying variable in the reduced form
estimation relative to the earnings equation. The reduced form equations
have three identifying variables: inva27 (investment income), capgn27 (capital gains) and kids (number of children in the household). These variables
proxy for risk in the self-employed decision but are assumed not to have
a determining impact on earnings. The investment variable is statistically
important at less than the 10% level in six of the seven years, the capital
gains variable is statistically unimportant in all years but 1999,21 and the
number of kids variable is signi…cant at standard p-values in all but one year
(2001).22
For parameter consistency we argue that all right-hand-side variables in
20
The strategy for econometric model building, speci…cation and validation was based
on data for 1999. The models were then applied directly to each additional year.
21
Although statistically insigni…cant the capital gains variable is not dropped from the
model, beecause it serves a purpose as a control variable to reduce the variance.
22
Rees and Shah (1986) make a similar argument for identi…cation using a ‘child’variable
for identi…cation. However, this variable is statistically insigni…cant in their estimation
and brings into question the identi…cation of their reduced form equation.
14
the reduced form probits maintain the restriction that the expected value
of the error term conditional on right-hand-side variables is zero. In other
words, the right-hand-side variables can be treated as exogenous variables
in estimation. As our regressors represent individual characteristics, past
choices in occupation and geographical location, this assumption appears to
be reasonable. Therefore, we conclude that in each year the probit equation
is well speci…ed, identi…ed and econometrically reasonable, and we proceed
to calculate the inverse Mills ratios for each earnings equation for each year.
The maximum likelihood robust estimates for the self-employed earnings
equation are reported in Table 4 and for the employed earnings equation in
Table 5.23 The base reference individual is a non-immigrant, white collar,
single female with no kids, in good health, and resident in Ontario. Comparing Tables 4 and 5 we observe a better …t to the data for the employed
earnings equation compared to the self-employed earnings equation. For
each year the estimated employed earnings equation shows almost all coef…cients with p-values of 1% or less. On the other hand, the self-employed
equations report p-values for 15 out of 77 coe¢ cients greater than 10%.
This likely re‡ects the risk involved in this type of activity, the heterogeneity of the self-employed and the number of observations used in estimating
the di¤erent earnings equations; approximately 1,300 observations per year
for self-employed compared to approximately 22,000 per year for employed.
Nevertheless, over 80% of the coe¢ cients in the self-employed earnings equations are statistically accurate at less than the 10% level and, what is more,
a null hypothesis that all coe¢ cients except the intercept term are zero can
be easily rejected. In support of the estimated results it is also worth noting that except for one occasion there are no sign changes in coe¢ cients
across the di¤erent years for both self-employed and employed equations.
The exception is the age-squared variable in 2005 for the self-employed.
The estimated earnings coe¢ cients for the employed tell a consistent
23
The error structure in the earnings equations are corrected for possible heteroscedasticity but as described by Amemiya (1984) this does not account for possible heteroscedasticity introduced by the fact that the inverse Mills ratios are generated variables. However,
this problem does not cause inconsistency in the parameter estimates and consistency is
required here.
15
story with the literature. Earnings increase with years of schooling and
with the male and married indicators, are less for immigrants and (although
not reported) Ontario o¤ers the highest earnings levels relative to the other
provinces. Note that blue collar and service workers show negative earnings
relative to white collar workers. The results for the self-employed are similar
except for two interesting cases. It is true that the male/female ratio among
the self employed is higher than for the employed but in terms of earnings,
males show no dominance in earning potential relative to females. (The
male dummy is statistically signi…cant in only three of the seven years at
less than the 5% level.) This contrasts sharply with the earnings equation for
the employed; here male dominance in earning potential is strikingly clear
for each year in the data. The second case is the married indicator, which
is strongly positively correlated with earnings in the employed equation for
all years. On the other hand, for the self-employed the married indicators
are negatively correlated with earnings for each year in the data set and
statistically signi…cant at the 5% level in six of the seven years.
It is also interesting to compare the inverse Mills ratio for each equation.
The results show a very strong positive bias for those individuals who have
chosen either self-employment or employed labor.24 Importantly, a Wald test
of independence between the reduced form probit and the wage equation is
soundly rejected for each year for each set of equations. We interpret these
results to indicate that self-selection is important in employment classi…cation and that the correction for omitted variable is necessary for consistent
results in the earnings equations.
The next challenge is to model and estimate the structural probit equation for employment classi…cation. We estimate two forms of the structural
probit. The …rst is based on the GH tax convexity speci…cation and the
second is based on the PR tax convexity speci…cation. The estimated earnings equations are used to predict the earnings for each individual for each
employment classi…cation and then combined with personal and …nancial
information, and entered in the CTaCS simulator to generate the individual
tax implications of each scenario. From the predicted earnings and corre24
Note the inverse Mills ratio for the self-employed is negative; see footnote 17.
16
sponding tax liabilities for each individual the net income di¤erence from
employment classi…cation is calculated and the log transform of this ratio
is de…ned as NetIncdif. We expect a positive coe¢ cient for this variable
in the structural probit indicating larger predicted net income di¤erences
in self-employment increase the probability of self-employment. The upside
tax convexity variable is expected to be negative in the structural probit
and indicates that as tax progressivity in the upper tax brackets increases
the probability of self-employment decreases. The downside convex variable
is expected to have a positive coe¢ cient in the structural probit re‡ecting
lower taxes paid as a percentage of lower earnings, as a result of tax progressivity in the lower tax brackets. Provincial and yearly dummies are also
added to the structural equation.
The results of the structural model are reported in Table 6. Columns 2
and 3 report estimated coe¢ cients and p-values, respectively for the structural probit using the GH tax convexity formulation and columns 4 and 5
report the corresponding estimated coe¢ cients and p-values, respectively for
the structural probit using the PR tax convexity formulation. Over, 150,000
observations are used in estimation for each structural equation. The reference person is a single non-immigrant female with no kids in good health
working in the service industry in Ontario in 1999. For both consistency and
e¢ ciency in estimating the parameter values, the maximum likelihood estimator is augmented by bootstrapping the standard errors. One thousand
replications are used in the bootstrap results. The bootstrap is necessary
because of the generated nature of the NetIncdif and tax convexity variables.
For both the GH and PR equations, we observe a strong positive relationship of the probability of self-employment with investment income (inva27),
age (ecage26), and the indicator variables health, male, married, immigrant,
and blue collar (blucol) and service occupations. In contrast, the number
of weeks unemployed (wksuem28) is negatively correlated with the probability of self-employment. Interestingly, years of education (yrschl18) o¤ers
no strong incentive for self-employment in the GH equation but is negatively correlated in the PR equation. Children in the household (kids) has
an important positive impact in the GH equation but no impact in the PR
17
equation.
For the provincial dummies, only British Columbia (bc) shows a statistically positive coe¢ cient relative to Ontario and indicates that bc has a larger
representation of the population self-employed. In fact, summary statistics
show British Columbia with the highest rate of self-employment participation with 7.04% compared to Ontario with 5.45%. The 2001 year dummy
clearly picks up the substantial decline in the probability of self-employment
with stock market problems in that year.
Perhaps the most interesting results are for the net income and tax convexity variables reported near the bottom of Table 6. We observe for both
the GH and PR speci…cations that the net income and tax convexity variables are consistent with sign expectations. The coe¢ cients for NetIncdif
and taxconvexD are positive with small p-values.25 The taxconvexU coe¢ cients are negative and again with very small p-values. It is interesting to
note that for either the GH or PR speci…cation the magnitude of the coe¢ cient on the upside tax convexity variable is considerably large than on the
downside. These results suggest overall that tax progressivity in‡uences the
occupational choice between self-employment and paid employment in ways
consistent with the theory. In further empirical work described below, we
report only the PR speci…cation of the structural probit.
Measures of robustness in the structural regression results are provided
in Tables 7 and 8. In Table 7, the structural probit equation based on the
PR speci…cation is taken to the yearly data and the table reports coe¢ cient
results only for the net income and tax convexity variables. Only the taxconvexU coe¢ cient maintains the expected sign for each year of the data
although it is statistically zero in year 2003. In addition, the NetIncdif and
taxconvexD coe¢ cients measure large p-values in a number of years. Note
particularly year 2003 which reports no statistical signi…cance across all
three coe¢ cients even though the data set contains over 25,000 observations
25
The …nding that net income is an important determinant of the selfemployment/employment choice stands in sharp contrast to the statistical results of Parker
(2003), who concludes from examining U.K. data, that the choice of self-employment is
unrelated to pecuniary considerations.
18
for that year. Table 8 reports the same net income and tax coe¢ cients except for this table we run the model on yearly cumulative data totals. Note
the size of the observations listed at the bottom of each row. This table
shows that all coe¢ cients over cumulative totals have the expected signs.
Now all coe¢ cients in each cumulative period reported in the table have
reasonable p-values except NetIncdif in cumulative years 1999-00, 1999-01
and 1999-02. Based on the empirical results, we argue that the full structural probit model is econometrically reasonable and we proceed to evaluate
probability simulations for di¤erent hypothetical policy scenarios.
5
Policy Application
Finally, we use the model to calculate the change in the probability of selfemployment, resulting from the personal income tax reforms of the federal
government in Canada announced in 2000 and implemented in 2001, and
we compare this to a counterfactual case of no tax reform.26 Speci…cally,
we compare the probability of self-employment under the 1999 and 2001 tax
schedules. The application serves, …rst, to give a sense of the magnitudes of
the self-employment probabilities implied by the estimated coe¢ cients of the
model, and, second, to show how changes in the di¤erent tax brackets a¤ect
self-employment via Netincdif and the upside and downside tax convexity
variables. The analysis yields fresh insights on how to design tax policy to
encourage self-employment.
Table 9 describes the federal marginal personal income tax schedules in
1999 and 2001. In addition, tax brackets became fully indexed in 2001 (after
no changes in the tax brackets during the previous …ve years) and the federal
surtax was eliminated.
26
We ignore changes in the corporation income tax to focus on personal income taxes.
The proportion of incorporated self-employed individuals in our data is small.
19
Table 9: Federal Personal Income Tax Schedules in 1999 and 2001
1999
2001
Tax bracket
Tax rate
Tax bracket
Tax rate
y
17%
y
16%
$29; 590 < y < $59; 180
26%
$30; 755 < y < $61; 510
22%
$59; 180
29%
$61; 510
26%
29%
y
y
$29; 590
y < $100; 000
$100; 000
$30; 755
y < $100; 000
$100; 000
29%
It will be useful to decompose the move from the 1999 tax system to the
2001 tax system into three steps, indicated in Table 10. In “Tax Scenario 1”
the only change is the tax rate in the …rst bracket, reduced from 17 percent
in 1999 to 16 percent in 2001, holding the other parameters of the tax system
constant at the 1999 levels. “Tax Scenario 2” changes only the second tax
bracket, from a tax rate of 26 percent in 1999 to 22 percent in 2001, again
holding the other tax parameters at their 1999 levels. In “Tax Scenario 3”
only the third marginal tax rate is changed, from 29 percent to 26 percent
on income between about $60,000 to $100,000, the other tax parameters
remaining at the 1999 levels. This decomposition of the tax reform enables
us to better understand the e¤ects arising from changes in dii¤erent parts
of the tax schedule.
Table 10: Scenarios o¤ Federal Personal Income Tax Schedules
Tax bracket
Scenario 1
Scenario 2
Scenario 3
y
16%
17%
17%
$29; 590 < y < $59; 180
26%
22%
26%
$59; 180
29%
29%
26%
29%
29%
29%
y
$29; 590
y < $100; 000
$100; 000
We simulate the average probability of self-employment for two broad
classes of individuals (with sample sizes of about 1,000). The …rst is workers who are male, white collar, non-immigrant, in good health, married, and
with all other variables set at the 2001 levels in Ontario; the average predicted self-employment income for the group is $63,639. The second group
has the same characteristics as the …rst, except that the occupations are blue
collar; their average predicted income for this group is $48,803. Table 11 re20
ports the simulated values of the average probability of self-employment for
the white collar group in 1999, 2001, and for each of the three Tax Scenarios. According to the simulated model, the 2001 tax reforms would increase
self-employment rates among the designated white collar group by 1.1 percent. Most of the increase stems from Tax Scenario 2, where the second
marginal tax rate is changed by four percentage points. Table 12 shows the
simulated values for the blue collar group, where the average probability of
self-employment rises by 0.6 percent. In each case the e¤ect of the tax reform
on self-employment rates is very modest. This relatively small impact of the
tax reform on self-employment is in part due to the fact that the changes in
the marginal income tax rates are not particularly large, amounting to less
than $1,000 for most individuals; it would be surprising if such changes in tax
liabilities would have a large e¤ect on occupational choices. However, part of
the reason for the modest change can be ascertained from examining closely
the impact of the tax reforms on the NetIncdif, taxconvexU and taxconvexD
variables in the model. Hence, Table 13 provides a simulation of the probit
equation for a single individual, who is male, blue collar, non-immigrant,
healthy, married, and has all other characteristics at 2001 levels in Ontario,
His whose predicted self-employment income is $58,861 and his residual from
the income equation, used in the calculation of taxconvexU, is set at approximately the average for indnividuals with his characteristics, i.e. $10,000.
The table shows the values of the key tax variables in 1999, 2001, and in
the case of Tax Scenario 3; the table also shows the marginal coe¢ cients for
the three tax variables. The marginal coe¢ cient multiplied by the change
in the associated tax variable gives the contribution of the tax variable on
the self-employment probability. Looking …rst at Tax Scenario 3 we see that
the cut in the third marginal tax rate from 29 percent to 26 percent reduces
upside tax convexity, as expected, which gives a boost to self-employment.
However, we also see that the gap between after-tax self-employment income and after-tax employment income widens— i.e. NetIncdi¤ becomes
more negative— which mitigates against self-employment. This is a consequence of the fact that predicted (and actual) self-employment income is
systematically less than predicted employment income for most individuals.
21
Thus middle income tax cuts tend to discourage self-employment insofar as
wage earners usually bene…t by more than self-employed workers do. Overall, for the individual simulated in Table 13, the 2001 tax reform reduced his
likelihood of self-employment from 8.533 percen tin 1999 to 8.492 percent in
2001. Of course, the tax reforms could enhance entrepreneurship in other
ways besides occupational choice, such as increased investment in capital,
or more hours spent working.
What lessons can be learned from the simulations of the model? Tax
reforms designed to increase average rates of self-employment are unlikely
to have much impact, given that the tax schedule creates counter-balancing
incentives for self-employment via the three tax variables, NetIncdi¤, taxconvexU and taxconvexD. The reform with the most impact on average
self-employment rates is a cut in the marginal tax rate faced by the average
self-employed income, while not cutting the marginal rate faced by wage
workers, whose incomes tend to be somewhat higher than self-employed incomes. This explains the relative success of Tax Scenario 2 in promoting
self-employment. More generally, however, tax reforms may be better aimed
at targeting the low frequency, but potentially highly innovative, upper income earners, via cuts in the top marginal tax rate, rather than attempting
to raise the overall rate of self-employment.
6
Conclusions
This paper makes two basic contributions. First, we develop a theoretical
utility choice model that de…nes the causal variables of choice, including tax
progressivity, in the decision to become self-employed. Second, the theoretical model guides the speci…cation of a structural probit model of the choice of
self-employment. The structural model requires generated variables de…ning
earnings and tax liabilities for each individual, in each employment classi…cation. We do this using earnings equations for both the self-employed and
employed. These equations are corrected for sample selection bias and used
to predict earnings for each individual if they had chosen either employment or self-employment. Tax implications of the predicted earnings are
22
calculated using the CTaCS tax simulator. From this information we derive
the net-of-tax income di¤erences from the employment classi…cations and
tax convexity variables measuring tax progressivity. These generated variables are included in the structural probit model of self-employment. The
results show that expectations of higher net-of-tax income di¤erences between self-employment and employment increase the probability of choosing
self-employment. Our major …nding is that tax progressivity matters in the
self-employment choice via the tax convexity variables. In particular, we …nd
strong statistical support for the conclusion that the “penalty on success”
via progressive marginal tax rates in the upper tax brackets is a deterrent
to self-employment, while the “social insurance” e¤ect of progressivity in
the lower brackets is an inducement to self-employment. The usefulness of
a structural model for predicting changes in self-employment rates for hypothetical tax reforms is illustrated with an example of a major tax reform
implemented in Canada. The simulation suggests that tax reforms are unlikely to increase self-employment rates much, unless they manage to lower
the marginal tax rate faced by self-employed workers, while not reducing the
marginal tax rate faced by most wage earners, given that paid employment
is on average more lucrative than self-employment for any given person.
This e¤ect corresponds roughly to the reduction in Canada in 2001 of the
tax rate applicable to incomes between about $30,000 and $60,000 from 26
percent to 22 percent. A useful extension to the model would be to allow
for endogenous hours of work in paid- and self-employment, which is information that is available in the SLID data. In this way, taxation can impact
self-employment not only via the extensive margin, but also through the
intensive margin.
23
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26
Table 1: Variable Definitions
Variable
Self-employed
earng42
inva27
capgn27
yrschl18
ecage26
age2
health
male
married
kids
immigrant
wksuem28
blucol
whtcol
service
newfoundland
pei
novascotia
newbrunswick
quebec
ontario
manitoba
saskatchewan
alberta
bc
Definition
Takes value 1 if major source of income
from self-employed earnings and no farm
earnings. Takes value 0 if major source of
income from wages and salaries and no
farm earnings.
Salaries, wages and self employed earnings
Investment income
Capital gains
Years of schooling
Age
Age squared
Takes value 1 if disabled 0 otherwise
Takes value 1 if male 0 otherwise
Takes value 1 if married 0 otherwise
Number of children in household
Takes value 1 if immigrant 0 otherwise
Weeks unemployed
Blue collar employee
White collar employee
Service employee
Newfoundland
Prince Edward Island
Nova Scotia
New Brunswick
Quebec
Ontario
Manitoba
Saskatchewan
Alberta
British Columbia
Table 2: Summary Statistics: 1999-2005
earng42
inva27
capgn27
yrschl18
ecage26
Health
Male
Married
Kids
immigrant
wksuem28
whtcol
Blucol
Service
Obs.
Self-Employed
Mean
Std. Dev.
32875.43
42570.13
1562.67
7112.22
696.99
6722.84
13.59
3.36
44.06
10.22
0.16
0.36
0.63
0.48
0.79
0.41
0.96
1.10
0.08
0.28
0.39
3.01
0.45
0.49
0.31
0.46
0.23
0.42
9,805
Employed
Mean
38043.48
962.65
432.35
13.74
39.78
0.14
0.54
0.68
0.92
0.06
1.13
0.51
0.27
0.21
147,505
Std. Dev.
26288.21
5192.81
5342.68
2.97
11.29
0.34
0.49
0.47
1.05
0.24
4.76
0.49
0.44
0.41
Table 3: Maximum Likelihood Estimates of
Reduced Form Probit by Year a)
1999
2000
2001
2002
2003
2004
2005
0.005
(0.002)b)
0.003
(0.103)
-0.005
(0.347)
0.488
(0.000)
-0.039
(0.001)
-0.029
(0.000)
0.015
(0.715)
0.173
(0.000)
0.150
(0.000)
0.038
(0.000)
-0.022
(0.661)
0.067
(0.068)
0.196
(0.000)
-3.059
(0.000)
0.004
(0.067)
0.002
(0.208)
-0.002
(0.641)
0.516
(0.000)
-0.039
(0.001)
-0.015
(0.001)
-0.015
(0.718)
0.212
(0.000)
0.122
()0.001
0.039
(0.006)
-0.002
(0.977)
0.032
(0.404)
0.201
(0.000)
-3.23
(0.000)
0.004
(0.051)
0.000
(0.949)
-0.001
(0.791)
0.579
(0.000)
-0.049
(0.000)
-0.01
(0.001)
0.005
(0.901)
0.214
(0.000)
0.139
(0.000)
0.013
(0.387)
-0.002
(0.971)
0.077
(0.057)
0.265
(0.000)
-3.398
(0.000)
0.008
(0.000)
-0.000
(0.946 )
0.004
(0.469)
0.422
(0.000)
-0.033
(0.003)
-0.030
(0.000)
0.003
(0.940)
0.201
(0.000)
0.154
(0.000)
0.038
(0.006)
0.102
(0.040)
0.067
(0.067)
0.222
(0.000)
-3.015
(0.000)
0.005
(0.000)
0.002
(0.319)
0.009
(0.027)
0.427
(0.000)
-0.032
(0.001)
-0.012
(0.001)
-0.009
(0.755)
0.166
(0.000)
0.138
(0.000)
0.030
(0.011)
0.068
(0.117)
0.116
(0.000)
0.201
(0.000)
-3.039
(0.000)
0.003
(0.225)
0.002
(0.199)
0.000
(0.973)
0.282
(0.003)
-0.018
(0.109)
-0.024
(0.000)
-0.041
(0.300)
0.123
(0.000)
0.125
(0.001)
0.027
(0.079)
0.169
(0.002)
0.103
(0.008)
0.117
(0.003)
-2.596
(0.000)
0.004
(0.038)
0.000
(0.936)
0.008
(0.119)
0.163
(0.060)
-0.002
(0.837)
-0.017
(0.001)
0.033
(0.340)
0.162
(0.000)
0.113
(0.001)
0.032
(0.029)
0.089
(0.078)
0.123
(0.001)
0.119
(0.002)
-2.549
(0.000)
SE c)
1,479
1,267
1,118
1,466
1,989
1,203
E
22,472
21,136
20,506
20,923
26,087
19,008
a)
Provincial dummy variables are included in each equation but not reported.
b)
p-value in parentheses with robust standard errors.
c)
SE is Self-employed and E is employed observations
1,415
20,587
inva27
capgn27
yrschl18
ecage26
age2
wksuem28
health
male
married
kids
immigrant
blucol
service
constant
Obs.
Table 4: Maximum Likelihood Estimates of
Heckman Wage Equation by Year a): Self-Employed
1999
2000
2001
2002
2003
2004
2005
0.068
(0.000)b)
-0.245
(0.298)
0.011
(0.692)
0.039
(0.001)
-0.259
(0.008)
0.245
(0.001)
-0.292
(0.001)
-0.077
(0.512)
-0.398
(0.000)
-0.815
(0.000)
6.781
(0.000)
0.079
(0.000)
-0.691
(0.003)
0.052
(0.056)
0.025
(0.006)
-0.179
(0.094)
0.049
(0.536)
-0.251
(0.008)
-0.146
(0.28)
-0.343
(0.000)
-0.898
(0.000)
8.099
(0.000)
0.075
(0.000)
-0.642
(0.015)
0.053
(0.080)
0.029
(0.012)
-0.189
(0.077)
0.123
(0.163)
-0.127
(0.156)
-0.239
(0.055)
-0.392
(0.000)
-0.918
(0.000)
7.387
(0.000)
0.063
(0.000)
-0.908
(0.000)
0.081
(0.002)
0.041
(0.001)
-0.160
(0.056)
0.021
(0.786)
-0.158
(0.057)
-0.316
(0.004)
-0.444
(0.000)
-0.942
(0.000)
8.406
(0.000)
0.065
(0.000)
-0.657
(0.000)
0.057
(0.007)
0.009
(0.259)
-0.095
(0.202)
0.119
(0.064)
-0.146
(0.030)
-0.320
(0.001)
-0.519
(0.000)
-0.986
(0.000)
7.362
(0.000)
0.051
(0.000)
-0.235
(0.271)
0.011
(0.659)
0.037
(0.001)
-0.125
(0.210)
0.199
(0.012)
-0.187
(0.029)
-0.537
(0.000)
-0.399
(0.000)
-0.751
(0.000)
6.698
(0.000)
0.046
(0.000)
-0.025
(0.900)
-0.014
(0.537)
0.017
(0.102)
-0.238
(0.003)
0.158
(0.029)
-0.227
(0.003)
-0.549
(0.000)
-0.396
(0.000)
-0.612
(0.000)
6.536
(0.000)
0.000
0.000
0.000
0.000
0.000
0.000
1,479
1,267
1,118
1,466
1,989
1,203
-2.192
-2.584
-3.331
-2.022
-2.664
-3.507
(0.000)
(0.000)
(0.000)
(0.000)
(0.000)
(0.000)
rho testd)
401.05
520.35
252.76
372.72
404.18
242.05
(0.000)
(0.000)
(0.000)
(0.000)
(0.000)
(0.000)
iterationse)
8
7
12
5
9
7
a)
Provincial dummy variables are included in each equation but not reported.
b)
p-values in parentheses with robust standard errors.
c)
p-value on a Wald test that all coefficients except the constant are equal to zero
d)
Wald test of independence between the reduced form probit and wage equation.
e)
Number of iterations until convergence.
0.000
1,412
-1.875
(0.010)
288.46
(0.000)
5
yrschl18
ecage26
age2
wksuem28
health
male
married
immigrant
blucol
service
constant
null testc)
Obs.
Mills
Table 5: Maximum Likelihood Estimates of
Heckman Wage Equation by Year a): Employed
1999
2000
2001
2002
2003
2004
2005
0.044
(0.000)b)
0.982
(0.000)
-0.103
(0.000)
-0.031
(0.000)
-0.073
(0.000)
0.422
(0.000)
0.068
(0.000)
-0.087
(0.000)
-0.130
(0.000)
-0.449
(0.000)
0.570
(0.000)
0.047
(0.000)
1.009
(0.000)
-0.106
(0.000)
-0.028
(0.000)
-0.068
(0.000)
0.427
(0.000)
0.067
(0.000)
-0.059
(0.000)
-0.125
(0.000)
-0.466
(0.000)
0.498
(0.000)
0.049
(0.000)
0.968
(0.000)
-0.102
(0.000)
-0.034
(0.000)
-0.086
(0.000)
0.414
(0.000)
0.074
(0.000)
-0.062
(0.001)
-0.119
(0.000)
-0.455
(0.000)
0.592
(0.000)
0.047
(0.000)
0.948
(0.000)
-0.099
(0.000)
-0.036
(0.000)
-0.056
(0.000)
0.427
(0.000)
0.0542
(0.000)
-0.074
(0.000)
-0.149
(0.000)
-0.458
(0.000)
0.701
(0.000)
0.049
(0.000)
1.006
(0.000)
-0.105
(0.000)
-0.030
(0.000)
-0.079
(0.000)
0.413
(0.000)
0.052
(0.000)
-0.128
(0.000)
-0.159
(0.000)
-0.474
(0.000)
0.576
(0.000)
0.051
(0.000)
1.025
(0.000)
-0.108
(0.000)
-0.035
(0.000)
-0.094
(0.000)
0.404
(0.000)
0.057
(0.000)
-0.111
(0.000)
-0.110
(0.000)
-0.452
(0.000)
0.523
(0.000)
0.053
(0.000)
0.931
(0.000)
-0.097
(0.000)
-0.032
(0.000)
-0.075
(0.000)
0.399
(0.000)
0.048
(0.000)
-0.09
(0.000)
-0.128
(0.000)
-0.469
(0.000)
0.725
(0.000)
0.000
0.000
0.000
0.000
0.000
0.000
22,472
21,136
20,506
20,923
26,087
19,008
1.410
1.642
1.813
1.274
1.333
1.349
(0.000)
(0.000)
(0.000)
(0.000)
(0.000)
(0.001)
rho testd)
42.75
44.25
30.39
33.34
41.19
32.80
(0.000)
(0.000)
(0.000)
(0.000)
(0.000)
(0.000)
6
9
6
6
6
6
iterationse)
a)
Provincial dummy variables are included in each equation but not reported.
b)
p-values in parentheses with robust standard errors.
c)
p-value on a Wald test that all coefficients except the constant are equal to zero.
d)
Wald test of independence between the reduced form probit and wage equation.
e)
Number of iterations until convergence.
0.000
20,587
2.237
(0.000)
42.89
(0.000)
7
yrschl18
ecage26
age2
wksuem28
health
male
married
immigrant
blucol
service
constant
null testc)
Obs.
Mills
Table 6 Maximum Likelihood Estimation a) of
Structural Probit: 1999-2005
Variable
Coefficient
GHb)
p-value
Coefficient
PR c)
inva27
4.15E-06
0.000
2.11E-06
capgn27
1.10E-06
0.143
1.37E-07
yrschl18
0.001
0.683
-0.013
ecage26
0.049
0.000
0.053
age2
-0.039
0.000
-0.04
health
0.041
0.006
0.116
male
0.177
0.000
0.098
married
0.146
0.000
0.161
kids
0.025
0.000
0.003
immigrant
0.069
0.001
0.125
wksuem28
-0.022
0.000
-0.027
blucol
0.091
0.000
0.148
service
0.198
0.000
0.315
newfoundland
-0.144
0.000
-0.168
pei
0.028
0.378
-0.005
novascotia
-0.069
0.003
-0.064
newbrunswick
-0.085
0.001
-0.027
quebec
-0.042
0.007
-0.078
manitoba
-0.028
0.220
-0.024
saskatchewan
-0.001
0.993
-0.038
alberta
-0.031
0.108
-0.041
bc
0.086
0.000
0.107
D00
-0.041
0.040
-0.056
D01
-0.085
0.000
-0.111
D02
0.019
0.336
-0.028
D03
0.059
0.001
0.001
D04
-0.020
0.331
-0.042
D05
0.003
0.896
-0.056
NetIncdif
0.049
0.039
0.043
taxconvexUi d)
-0.184
0.000
-1.029
taxconvexDi e)
0.043
0.000
0.076
Constant
-2.969
0.000
-2.662
Observations
150,797
151,572
a)
Bootstrapped standard errors (1,000 replications)
b)
Gentry and Hubbard (2001) (GH) procedure for tax convexity
c)
Predicted residual (PR) procedure for tax convexity
d)
taxconvexUi for i either GH (column 2) or PR (column 4)
e)
taxconvexDi for i either GH (column 2) or PR (column 4)
p-value
0.011
0.864
0.000
0.000
0.000
0.000
0.000
0.000
0.583
0.000
0.000
0.000
0.000
0.000
0.879
0.007
0.267
0.000
0.276
0.088
0.035
0.000
0.006
0.000
0.161
0.947
0.041
0.005
0.038
0.000
0.008
0.000
Table 7: Robustness Check for Structural Probit
Net Income and Tax Convex Variables by Year
1999
2000
2001
2002
2003
2004
2005
0.375
(0.002)a)
-1.732
(0.000)
0.128
(0.024)
0.379
(0.006)
-1.546
(0.000)
-0.126
(0.094)
0.654
(0.000)
-1.775
(0.000)
0.116
(0.107)
0.468
(0.001)
-1.997
(0.000)
0.170
(0.014)
0.048
(0.200)
-0.0004
(0.996)
0.014
(0.679)
-0.059
(0.701)
-1.408
(0.048)
-0.088
(0.718)
-0.005
(0.972)
-1.193
(0.000)
-0.006
(0.961)
Obs.
21,753
21,263
20,446
a)
p-values based on robust Standard Errors
21,460
25,407
19,203
21,265
NetIncdif
taxconvexUPR
taxconvexDPR
Table 8: Robustness Check for Structural Probit
Net Income and Tax Convex Variables Cumulative Data
1999
1999-00
1999-01
1999-02
1999-03
1999-04
1999-05
0.375
(0.002)a)
-1.732
(0.000)
0.128
(0.024)
0.045
(0.434)
-1.560
(0.000)
0.129
(0.005)
0.072
(0.166)
-1.597
(0.000)
0.127
(0.001)
0.012
(0.774)
-1.65
(0.000)
0.138
(0.000)
0.104
(0.000)
-0.961
(0.000)
0.086
(0.000)
0.084
(0.000)
-1.009
(0.000)
0.074
(0.015)
0.043
(0.045)
-1.029
(0.000)
0.076
(0.011)
Obs.
21,753
43,016
63,462
p-values based on robust Standard Errors
84,922
110,329
129,532
150,797
NetIncdif
taxconvexUPR
taxconvexDPR
a)
Table 11: Average Probability of Self-Employment for White Collar
1999
2001
Tax Scenario 1
Tax Scenario 2
Tax Scenario 3
7.061
7.138
7.055
7.159
7.062
Table 12: Average Probability of Self-Employment for Blue Collar
1999
2001
Tax Scenario 1
Tax Scenario 2
Tax Scenario 3
7.421
7.465
7.445
7.460
7.421