Appendix 2: Analytical framework (Not intended for publication)
In this appendix we present a simple model that shows the effects of tax progressivity on selfemployment. We assume that there are two groups of individuals: the self-employed and
workers. Empirical stylized facts show that the majority of the self-employed do not hire workers
(i.e. own account self-employment).1 Thus as in Parker (1999), we assume that the selfemployed (entrepreneurs) work for themselves but they do not hire workers. Entrepreneurial
activity is a risky occupation. Thus as in Gentry and Hubbard (2000) we assume that it can yield
a return, YE, if successful or zero otherwise. Working for others, on the other hand, yields a
riskless income YW (which is the wage rate). Thus individuals choose between a safe job and a
risky one based on the return from the two occupations. Suppose we denote the probability of
success in entrepreneurial activity by , then the pre-tax expected return from self-employment
would be YE. We assume that YW < YE.2 Let v denote the proportion of the labour force that
chooses self-employment.3 Obviously the returns in the two occupations depend on the number
of individuals working in the two jobs. In particular the derivative of the income levels with
respect to v are given by YE’(v) < 0 and YW’(v) > 0. That is the higher the proportion of the labor
force in the self-employment sector, the lower will be the return from self-employment.
However, as more and more people choose the self-employment sector, the income of workers in
the safe job sector increases.
1
See Kamhi and Leung (2005) for a detailed analysis of self-employment and its various components in Canada.
See Pestieau and Possen (1991) for a somewhat similar assumption. This implies that the expected income from
self-employment is higher than the wage income. Otherwise individuals will choose only the safe job.
3
This is similar to the measure of entrepreneurship commonly used in the empirical literature.
2
1
In Canada, as in many other countries, income from self-employment is taxed as any
ordinary personal income at the applicable personal income tax rates after deductions for
business expenses. As extensively discussed in the literature, there is a greater tax evasion
opportunity for the self-employed than for workers. Thus as in Pestieau and Possen (1991) we
assume that it is difficult to evade taxes in the safe job but there is a tax evasion opportunity in
the self-employed sector. Following Feldstein (1969) and Kanbur (1982), we also assume that
the tax structure is progressive and for the employees it is given as


TW  YW 1  (1   )YW 1 ,
(1)
where 0 <   1. TW and YW denote the tax liability and the before-tax income level of employees,
respectively.  > 0 is the coefficient of residual income progression (RIP) and it denotes the
degree of tax progressivity.4 RIP is simply the ratio of one minus the marginal tax rate (MTR) to
one minus the average tax rate (ATR).5 See Musgrave and Musgrave (1989) and Dahlby (2008)
for a discussion of alternative measures of tax progressivity. The above tax structure has the
following properties. If  = 1, the tax structure is proportional with a marginal tax rate . While
 >1 shows that the tax schedule is regressive. Notice that both the marginal and average tax rate
rise with income when  < 1 and a lower value for  implies a more progressive tax structure.
As it will be clear later, the above tax formulation is useful to investigate the impact of changes
in tax progressiveness (as measured by ) on self-employment.
When the self-employed evade taxes, there is a probability of detection through auditing.
Let the probability of detection be denoted by p. Denote also the share of income that the selfemployed conceal from taxation by  where 0  1. The rate of tax evasion  is assumed to be
4
The coefficient of residual income progression is also the elasticity of after-tax income to the before-tax income.
5
For our tax schedule, MTR  1   (1   )YW

 1
 and ATR  1  (1   )Y 
 1
W
2
exogenous. Thus the tax liability of successful entrepreneurs who earn the higher income YE and
get away with the evasion is given by


TE  (1   )YE 1  (1   )(1   )  1YE 1 .
(2a)
However, if caught through auditing, tax evaders pay the full tax and a certain percent of
the amount of tax evaded as penalty (see Yitzhaki, 1974). Let  > 0 denote the penalty rate. The
tax liability of the self-employed that evade taxes and are caught through auditing is given by


TE  YE 1  (1   )YE 1  X ,
 

(2b)


where X  YE 1  (1   )YE 1  (1   )YE 1  (1   )(1   )  1YE 1 >0.
Note that TE is tax liability for those who evade taxes and X is the amount of tax liability that is
evaded. In the absence of tax evasion (i.e.,  = 0), X will be reduced to zero.
To obtain analytically tractable results, following Gentry and Hubbard (2000), we assume
that individuals are risk neutral.6 For risk neutral individuals, the occupational choice simply
depends on the after-tax returns from the two jobs. Equilibrium in occupational choice requires
that the expected after-tax income from self-employment must be equal to the after-tax return
from the safe job (employment); see Evans and Jovanovic (1989). Thus in this case, for the two
occupations to exist together the following condition must be satisfied:
 (1  p  p ) X   (1   )(YE (v))   (1   )(YW (v))  ,
(3)
where the variables are as defined before.
6
This is assumption is important to obtain analytically tractable relationship between the self-employment rate and
tax progressivity. This helps us to focus on tax progressivityrather than risk aversion  as the determinant of
occupational choice. Previous studies such as Pestieau and Possen (1991) focused on risk aversion as the prime
factor for occupational choice.
3
The left-hand side of Eq. (3) shows the after-tax expected return from self-employment.
This includes the expected benefit from tax evasion which is the first term in the left-hand side.
For tax evasion to be attractive this term should be positive. Otherwise, the self-employed would
not evade taxes. In our analysis we assume that the expected benefit from tax evasion is
positive.7 The right-hand side of the above equation on the other hand shows the after–tax return
from employment. For a given , we are interested to know how changes in tax progressivity ()
affect the self-employment rate (v). 8 Thus totally differentiating Eq. (3) with respect to v and 
and noting that the income levels depend on v one would obtain:
dv

,

d  (1  p  p ) XYE1YE ' (v)  YE 1YE ' (v)  (1   ) YW  1YW ' (v)
(4)
where,




   1  p  p  X ln YW  (1   ) YE  ((1   )YE )  ln YE  (1   )(1   )  YE ln( 1   ) >0,
   (1   )YE ln( YE / YW ) >0,
While the denominator in Eq. (4) is negative, the sign of the numerator is ambiguous.
Thus the effect of tax progressivity on self-employment is not clear from Eq. (4). In the absence
of tax evasion opportunity (i.e.  = 0), X and  will reduce to zero.9 In this case, dv/d will be
positive implying that an increase in tax progressivity (i.e., lower ) discourages selfemployment. That is the greater the tax progressivity, the lower the rate of self-employment.
Thus, as Gentry and Hubbard (2000) explain, the progressive income tax has a detrimental effect
on entrepreneurship and can be viewed as a “success tax”. The reason for this is straightforward.
This implies that the exogenous penalty rate < (1-p)/p. If  = (1-p)/p, there will be no benefit from tax evasion.
For a somewhat similar exercise in a different context, see Kanbur (1982).
9
This is also true at the prohibitively high penalty rate  = (1-p)/p.
7
8
4
When the tax structure becomes more progressive the government claims a higher share of the
return from successful entrepreneurs (which assume the risk of earning a very low income if not
successful). This discourages the risk taking behaviour of the self-employed as the government
shares the reward but not the loss from the risky activity.
In the presence of tax evasion opportunity, however, the relationship between tax
progressivity and self-employment becomes more complicated. In fact, the sign of dv/d
generally depends on the relative strength of the adverse impact of the “success tax” denoted by
 and the tax evasion opportunity given by .10 Eq. (4) shows that if  > , dv/d will be
positive and it implies that the tax evasion opportunity is lower than the detrimental effects of the
“success tax”. Thus greater tax progressivity discourages self-employment. However if  < ,
then it implies that the benefit of tax evasion opportunity outweighs the adverse impact of taxing
success at a progressive rate. In this case self-employment becomes more attractive as tax
progressivity increases. That is, greater tax progressivity encourages self-employment.11
In summary, the above simple model shows that in the presence of tax evasion
opportunity, the impact of tax progressivity on self-employment is ambiguous. It all depends on
the relative strength of the detrimental negative effects of the “success tax” and the positive
effect of the tax evasion opportunity. Other things remaining constant, if the tax evasion
opportunity from being a self-employed is stronger than the adverse impact of taxing success at a
progressive rate, an increase in tax progressivity raises self-employment rate. On the other hand,
if the tax evasion opportunity is lower (say because of a high level of tax enforcement, penalty,
higher frequency of auditing, etc.) then higher tax progressivity acts as a tax on successful
Notice that  is equal to zero if YE =YW. If the self-employed succeed and earn the higher income (which we have
assumed is greater than the income from the safe job) then  becomes positive.
11
See also Parker (2003) on the impact of tax evasion opportunity on occupational choice.
10
5
entrepreneurs and discourages self-employment. Thus, the impact of tax progressivity on selfemployment is generally an empirical issue. Consequently, in our paper we explore this issue
empirically using aggregate panel data from 10 Canadian provinces over the period 1979 to
2006.
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