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Shades of Grey: Business Compliance with Fiscal
and Labour Regulations1
Katherine Cuff
McMaster University, 1280 Main St. W., Hamilton, On, Canada, L8S 4M4
Steeve Mongrain
Simon Fraser University, 8888 University Dr., Burnaby, BC, Canada, V5A 1S6
Joanne Roberts
Yale-NUS College, 16 College Ave W, Singapore, 138527
June 19, 2018
1All authors are grateful to the Social Sciences and Humanities Research Council of
Canada for financial support and for comments received by participants of the CPEG con-
ference in Montreal, the CEA meetings in Montreal, and the IIPF Congress in Taormina.
We also thank seminar attendees at Aix-Marseille University, the Max Planck Institute in
Munich, and the State University of New York at Buffalo. The usual disclaimer applies.
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Abstract
Firms face many fiscal and labour regulations, but they may evade these legal require-
ments in many different ways. We develop a model that captures these two types of
evasion firms decisions and unlike existing literature assume firms can evade labour
regulations independently from fiscal responsibilities. We characterize firms’ entry
and evasion behaviour and find that the design of the tax system and firm entry
generate both positive and negative correlations between evasion decisions, consis-
tent with what is observed empirically. We then derive the government’s optimal tax
policies and find a profit tax system with no payroll taxes, which is optimal in the ab-
sence of any evasive behaviour, is no longer desirable when such evasion is considered.
There can be a role for both positive payroll taxes and less than full deductibility of
input costs in the optimal corporate income tax system.
Key Words: Informal Labour Market; Labour Regulation; Tax Evasion; Payroll
taxes; Corporate Income Taxes
JEL: H32, H26, K42
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1 Introduction
Government impose many different forms of labour regulations and taxes on busi-
nesses. Labour regulations stipulate that firms must pay payroll taxes, make social
security contributions, meet health and safety standards in the workplace, and com-
ply with employment standards, including general holidays, vacations, working hours
and minimum wages. Business tax laws require firms to collect sales taxes on goods
sold, and pay taxes on their income or profits. Empirically it has been documented
that businesses may evade some government regulations while complying with oth-
ers. Termed ‘partial compliance’, Kumler, Verhoogen, and Fŕıas (2015) document
that formally registered firms in Mexico evade social security contributions and Car-
rillo, Pomeranz, and Singhal (2017) show that there is widespread misreporting of
both revenues and costs by formal firms in Ecuador. The process of formalization it-
self can require registration at different levels of government agencies for tax purposes
and for a given number of paid workers there is variation in the percentage of firms
registering with the different agencies (De Mel, McKenzie and Woodruff, 2013). The
existence of different margins along which firms can choose to evade or not comply
with government regulations can result in increased enforcement along one margin
changing firms’ evasive behaviour along another margin (Carrillo, Pomeranz, and
Singhal, 2017). Understanding firm behaviour when they can make evasion decisions
along various margins is crucial to the design of an efficient and effective tax system.
Despite this empirical evidence of firms responding differentially to government
labour regulations and tax laws, much of the theoretical literature on firms’ evasion
decisions has either focused solely on the evasion of business taxes1 or the joint deci-
sion of firms to evade all or none of the government mandated activities.2 This latter
1The corporate tax evasion literature such as in Marrelli and Martina (1988), Crocker and Slemrod
(2005) or Chen and Chu (2005) to mention a few, is not really concerned with labour regulations.
Likewise, Bayer and Cowell (2009), de Paula and Scheinkman (2010) or Lipatov (2012) are also only
interested in corporate or sales tax evasion.2Rauch (1991), Fortin, Marceau and Savard (1997), Fugazza and Jacques (2003), and de Paula
and Scheinkman (2011) all model the choices of entrepreneurs to operate either in the formal (where
all regulations are respected) or the informal sector (where all regulations are evaded) based on
factors like scale economies, wage regulations and taxes. Cuff, Marceau, Mongrain and Roberts
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approach includes the large literature on the formal versus the informal sector.3 By
either ignoring the labour market regulation evasion decision or assuming tax eva-
sion implies labour regulation evasion, existing models cannot capture these empirical
observations and potentially lead to misguided policy prescriptions.
In this paper, we allow firms to decide whether to evade labour regulation indepen-
dently from their decision to evade business income taxes and analyze optimal gov-
ernment policy given firms’ evasion decisions. Examining these two evasion decisions
independently is of practical relevance and critical to understanding how government
should optimally structure business taxes. Our paper contributes to a small literature
that attempts to model labour market regulation evasion decisions separately from
income tax evasion decisions.4 Tonin (2011) considers minimum wage evasion, but
only to the extent it influences personal income tax evasion and Madzharova (2013)
illustrates that the deductibility of wages in light of a lowered corporate tax can give
an incentive to under-report wages (and pay less payroll taxes) and thereby shift
income from the payroll tax base to the corporate tax base.
Our paper also complements a recent paper by Ulyssea (2018) who incorporates an
extensive and intensive margin for firms’ labour market regulation evasive behaviour.
Firms choose whether to become a formal or informal firm where informality is defined
by the evasion of all income taxes and the hiring of all workers informally. Formal
firms who pay all of their income taxes can choose to hire some share of their workers
informally. Consequently, there is only an extensive margin with respect to income
tax evasion. Whereas, in our paper, we allow for both an extensive and intensive
decision for a firms’ income tax evasion decision, thereby capturing the reality that
some firms can avoid or evade some of their income tax liability, and allow for only
an extensive margin for a firms’ labour market regulation evasion behaviour. We also
(2011), Djajic (1997), and Epstein and Heizler (2007) assume the decision to evade one type of
regulation implies evading all other regulations.3Kanbur and Keen (2014) formalize the idea that the informal sector is heterogenous, but they
do not look at the interaction between labour and fiscal policies.4There is also a literature looking at personal tax evasion where taxpayers can evade taxes using
different means. Alm (1988), Cremer and Gahvari (1994) and Martinez-Vazques and Rider (2005)
examine the substitutability of different forms of evasion/avoidance and highlight how it makes the
comparative statics and characterization of the optimal policies non-trivial.
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characterize optimal policy in this environment.
We adopt a simple model in which a set of heterogenous entrepreneurs decide
whether to start up a firm or not. Each active firm opens a position, hires a single
worker, and produces output according to a linear production technology. Firms differ
in the output they produce. Firms decide whether to evade labour market regulations
and whether to evade some or all of their corporate taxes liability. Labour market
regulations are comprised of a payroll tax and other employment standards. A firm
choosing to evade such labour regulations by hiring a worker informally benefits in
two ways. First, the firm does not pay payroll taxes. Second, opening an informal
position can be less costly. Costs attached with opening a position is common in the
labour search theory and, as in Ulyssea (2010), we assume that opening a position
when respecting labour regulation is more costly and further we assume that the costs
differ across firms.
Our model predicts that low productive firms are more likely to evade all of their
income tax liability, and more productive firms, who are more likely to pay a higher
portion of their tax liability, evade more in absolute terms. This is consistent with
the empirical literature.5 More interestingly, we find that entry decisions and policy
design can create a positive correlation between labour market and corporate tax
compliance decisions for more productive firms and potentially a negative correlation
for firms with lower productivity. Something that cannot arise in most standard firm
evasion models by construction.
Entry decisions generate a positive correlation by selecting into the market a
disproportional amount of firms who engage in both types of evasion activities. Low
productive firms are more likely to evade corporate taxes and often the only way
these less productive firms find it profitable to enter the market is by avoiding labour
regulations. Whereas a policy of income tax credits for formal labour costs can
generate complementarity or substitutability between the two evasion activities. High
productive firms who pay corporate taxes have a greater incentive to hire workers
formally when they can deduct wages and payroll taxes from their taxable income. For
5Almeida and Carneiro (2006), Dabla-Norris, et al. (2008) and de Paula and Scheinkman (2011)
show that informal firms are less productive, while Nyland, Smyth and Zhu (2006) provide evidence
that more productive firms evade more in absolute terms.
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these firms, joint compliance is beneficial, and so evasion decisions are complementary.
For low productive firms who do not pay any corporate taxes, any new taxable income
must be hidden appropriately and complying with labour regulation is a way for these
firms to reduce the amount of taxable income they must conceal. The two evasion
activities are then substitutes for one another.
To discuss optimal policy, we assume the government maximizes a social welfare
function which is a weighted sum of total surplus and tax revenue, as in standard
economic theory and which is commonly used in externality models.6 The govern-
ment’s policy instruments include: a corporate tax rate, a payroll tax, and the share
of deductible labour costs. Under full cost deductibility, the tax system replicates
a pure profit tax. Without cost deductibility, the corporate tax is equivalent to a
turnover tax that does not grant tax credit for labour related costs. In between, are
tax systems that relies more or less on corporate income tax versus output taxes.
When firms cannot evade either labour regulation or corporate taxes, a pure profit
tax with no payroll tax is optimal. However, when corporate tax evasion is possible,
a pure profit tax may no longer be desirable and the optimal tax system may feature
positive payroll taxes and less than full deductibility of input costs. We make a dis-
tinction between the case where labour regulation evasion is possible relative to the
case where it is not.
The setting where labour regulations cannot be evaded is similar to Best et al.
(2015) with one important difference. In their paper, firms can only evade taxes by
over reporting costs making turnover taxes evasion proof. Therefore, turnover taxes
can rise additional revenues without facing the threat of evasion in their paper. In our
paper, firms can evade taxes by under reporting revenue as well as costs, meaning firms
can evade both profit and turnover taxes. Without the possibility of labour regulation
evasion, payroll taxes in our context are evasion proof but affect both the entry
decision and income tax evasion decisions of the firm. Consequently, the government
will trade-off the revenue raised by the payroll tax with the subsequently social cost
of increased income tax evasion and reduction in firm entry. The government may
also wish to offer less than full cost deduction because it increases the cost of evasion
by increasing taxable income. With higher taxable income, firms must be more
creative to evade the same share of revenue. When both forms of evasion are possible,
6See, for example, Petrakis and Xepapadeas (2003), and Schoonbeek and de Vries (2009).
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the interaction between the three policy instrument become richer. Allowing more
generous tax credits by relying less on sales taxes increases the incentive to comply
with labour regulation. Payroll taxes can now be evaded, but only by firms with
informal employment status. This result is consistent with some evidence that OECD
countries with a larger share of underground economy tend to rely more on sales taxes
than corporate income tax to generate revenue as shown in Figure 1.
Figure 1: Ratio of tax revenue from sales to corporate income taxes and share of un-
derground economy using data from El-Sibaie (2017) and Buehn & Schneider (2012).
The remainder of the paper is as follows. In the next section, we describe the
model in detail. In Section 3, we characterize the firms’ optimal entry and evasion
decisions given government policies and consider the government’s problem in Section
4. As a benchmark, we characterize the government’s optimal policies when firms are
unable to evade either labour market regulations or corporate taxes and then consider
optimal policies when firms can only evade corporate income taxes and when firms
can evade along both dimensions. We illustrate the optimal policies with numerical
simulations. Finally, we conclude in Section 5. When not stated, proofs can be found
in the Appendix.
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2 The Model
The economy is composed of three types of agents: entrepreneurs, workers, and a
government. There exists a unitary mass of risk neutral entrepreneurs characterized
by a pair of technological parameters {θ, λ} independently and uniformly distributedover the unit interval. Specifically, θ reflects productivity, while λ represents some
specific costs associated with labour market evasive behaviour described further be-
low. Each entrepreneur chooses whether to be active or not. We refer to this choice
as the entry decision. Inactive entrepreneurs earn a payoff normalized to zero. Active
entrepreneurs (referred to as firms) open a position, employ exactly one worker, and
produce output. The price of output is normalized to one. Each firm generates 1 + θ
in revenue. Differences in technology or managerial talent can motivate differences in
revenue or productivity.
Active entrepreneurs decide whether to open their position in accordance with
labour regulations, which we call a formal position, or without respecting such regu-
lations, referred to as an informal position. We normalize the cost of opening a formal
position to one. Only a proportion µ ∈ [0, 1] of the total cost of opening a formalposition is both monetary and observable to the government whereas the rest is as-
sumed to be either non-monetary or non-observable. The cost of opening an informal
position is 1−λ, where λ is heterogenous across entrepreneurs and is not observed bythe government. The cost differential between opening a formal position and opening
an informal position is simply λ. Differences in opening costs could reflect differences
in production technologies. For example, some production methods involve greater
risk, such as in the construction or food processing sectors, and conforming to safety
standards is more costly. Heterogeneity could also reflect seasonality in production
such as in the agricultural or fishing industries. Opening a position that abides by
the labour market regulations for a short amount of time may impose excessive costs
that could be avoided by not respecting labour regulations. The cost heterogeneity
could also come from differences in local or sectoral specific regulations (Al-Ubaydli
and McLaughlin, 2015).
There is a mass greater than one of homogenous workers. Each worker can supply
one unit of labour at an opportunity cost of w (home production or disutility of
labour). Unemployed workers are assumed to earn no income and receive no disutility.
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When opening a position, firms post wages. All firms with an open position are
matched with a worker with probability one. Because of the absence of search frictions
and given inelastic labour supply, all firms will post wage w which is just sufficient
to attract a worker. Firms with a formal position pay wage w to workers and pay a
unit payroll tax τ to the government. Firms with informal positions pay wage w, but
do not pay any payroll taxes.
Informal employment can be concealed from the government at some cost c` > 0.
One interpretation of this cost is as a limiting case of the concealment technology used
in Cremer and Gahvari (1994) where paying c` guarantees non-detection in the case
of an audit. We view any concealment effort as an unproductive activity generating
no social benefit apart for allowing firms to employ a worker informally.7 We could
also re-interpret the concealment cost as a loss in productivity associated with hiring
a worker informally. In addition, firms employing a worker informally may impose
an external cost x ≥ 0 to society, such as unsafe working conditions or lower qualityproduction standard.
Firms with a formal position may claim a deduction for their input costs. Let
δ ∈ [0, 1] be the fraction of observable input costs that can be deducted from thefirm’s taxable income. This includes the amount of observable costs of opening the
formal position, the wage paid, and the payroll tax, i.e., µ+ w + τ . Let the variable
β ∈ {0, 1} indicate whether a firm hires its worker informally or not. That is, β = 1denotes a firm that is choosing to evade the labour market regulations and employ
its worker informally, and β = 0 denotes a firm choosing not to evade the labour
market regulations and employ its worker formally. Using this indicator variable, we
can write any firm’s total taxable income as
π(β; θ) = 1 + θ − δ(1− β)[µ+ w + τ ]. (1)
All firms are subject to a corporate income tax at rate t and pay tax on the amount
of taxable income they report to the tax authority. More productive firms have higher
taxable income as shown by (1). By choosing both the corporate income tax, t, and
7Alternatively, one could interpret c` as the expected fine for employing a worker informally. Since
entrepreneurs are risk neutral, both interpretations lead to the same behaviour. Fines, however, may
generate additional government revenue which would reduce the social costs of informality.
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the deduction rate for observable input costs, δ, for formal firms, the government is
effectively selecting an output tax on informal firms and both a profit and output tax
on formal firms where δ determines the relative size of the output and profit taxes
for the formal firms.8 When δ = 1, firms with formal positions are only subject to a
pure profit tax. Alternatively, when δ = 0 formal firms are only subject to an output
tax. All firms with informal workers only face an output tax regardless of δ as none
of these firms can claim deductions for their input costs.
Firms choose what proportion α of their taxable income to conceal from the
authorities, or equivalently, how much taxable income to report, (1−α)π(β; θ). Firmsonly pay corporate tax on the amount of reported taxable income, but it is costly to
conceal taxable income. A firm who conceals an amount απ(β; θ) of taxable income
from the tax authority incurs a cost
C(απ(β; θ)
)= ct
[απ(β; θ)
]1+ρ1 + ρ
, (2)
where ρ > 0 and ct > 0 is common to all firms. Concealment cost are frequently
assumed in the literature on evasion, e.g., Cremer and Gahvari (1994), Hindriks, Keen
and Muthoo (1999), Slemrod (2001) or Kanbur and Keen (2014). As usually done,
we assume that the cost of concealing taxable income is increasing at an increasing
rate in the total amount concealed, that is,
C ′(·) = ct[απ(β; θ)
]ρ> 0, C ′′(·) = ρct
[απ(β; θ)
]ρ−1> 0. (3)
We view concealment efforts as social waste and we are agnostic as to the means
by which firms reduce their tax liabilities.9 Firms could omit to declare part or all
8To see this, let R be firm revenue (with output price normalized to unity) and C total (observ-
able) input costs. Denote tP a tax levied on profits R− C, and tT an output tax levied on R. The
corporate income tax rate t is levied on the income tax base R − δ(1 − β)C where δ ∈ [0, 1] and
raises revenue tR− tδ(1− β)C. The same tax revenue can be raised by levying both an output and
profit tax, (tT + tP )R − tPC, provided tP = tδ(1 − β) and tT = t(1 − δ(1 − β)). Therefore, the
government’s choice of a corporate income tax rate and a income deduction rate {t, δ} is equivalent
to choosing an output tax of t on informal firms and both a profit tax of tδ and an output tax of
t(1− δ) on formal firms.9Like for the case of c`, concealment costs could be interpreted as expected sanctions. To match
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of the income generated, they could falsely claim deductions, they could use illegal
tax shelters or any combination of those means. In fact, the model can accommodate
aggressive tax avoidance where the “letter” of the law is respected but not the “spirit”
of the law. Allowing for such level of generality implies that a firm who pays no taxes
can either be a truly informal (ghost) firm or simply a firm who reports no taxable
income (see e.g., Kanbur and Keen (2014)).
The government maximizes social welfare denoted by Ω = (1 + m)TR + PS +
WS −X, where m ≥ 0 is the constant marginal benefit of public spending,10 TR istax revenue, PS is producers’ surplus, WS is workers’ surplus, and X is the sum of
all external costs x. The government’s set of fiscal policies includes a corporate tax
rate t, a payroll tax τ , and an input cost deduction rate δ ∈ [0, 1]. Since the marginalbenefit of public spending m is assumed to be constant, full expropriation would be
optimal if lump sum taxes were available. With distortionary taxes this is not the
case.
Equilibrium behaviours are defined as the solution to the following sequential
game. Government announce policies {t, τ, δ}. Given these policies, entrepreneursdecide whether or not to enter the market and start a firm. All active entrepreneurs
open a position formally or informally and post the associated wage w. All open
position are filled and unmatched workers remained unemployed. Production takes
place and firms decide the proportion of taxable income to declare.
3 Positive Analysis
In this section, we solve the latter part of the game taking government policies as
given. Entrepreneurs anticipate their optimal evasion decisions when choosing to
the assumption regarding the curvature of the cost function, penalties or audit probability would
need to be convex in amount evaded. There are justifications for both. Additional criminal sanctions
apply for more serious cases of tax evasion, and as pointed out in Hoopes, Mescall and Pittman (2012)
larger firms in terms of asset holdings face higher probability of audits.10Alternatively, one could interpret m as a constant marginal cost of public funds.
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be active or not. Therefore, we first characterize a firm’s optimal evasion decisions
assuming the entrepreneur is active and then determine the entrepreneur’s optimal
entry decision.
3.1 Evasion Decisions
An active entrepreneur, or firm, with technology parameters {θ, λ} faces the followingmaximization problem:
maxα∈[0,1],β∈{0,1}
(1− β)[1 + θ − (1 + w + τ)− (1− α)t
[1 + θ − δ(µ+ w + τ)
]]+ β
[1 + θ − (1− λ+ w)− (1− α)t(1 + θ)− c`
]− C
(απ(β; θ)
)
The optimal tax evasion decisions of a firm with parameters {θ, λ} given somelabour regulation evasion decision β ∈ {0, 1} is given by Lemma 1.
Lemma 1: Firms with θ > θ̄(β) conceal only a fraction of their taxable income
α(β; θ) =
(t
ct
) 1ρ[
1 + θ − δ(1− β)(µ+ w + τ)]−1∈ (0, 1). (4)
Firms with θ ≤ θ̄(β) conceal all of their taxable income, so α(β; θ) = 1, where
θ̄(β) =
(t
ct
) 1ρ
+ δ(1− β)(µ+ w + τ)− 1. (5)
Firms will never optimally pay all of their corporate taxes since the marginal con-
cealment cost is zero when α = 0 and the marginal benefit which is given by the
income tax rate t is positive. Therefore, α(β; θ) > 0 for all active firms. For some
firms however, the marginal cost of concealment is so low when they evade all of their
taxable income that they optimally do so, that is, α = 1. These firms may simply
not file a tax report or file a tax report but find a way to bring their reported taxable
income down to zero, perhaps through creative accounting.
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A higher corporate tax rate increases tax evasion both along the intensive and
the extensive margin. Firms who report positive taxable income conceal a higher
proportion of their taxable income because the marginal benefit of doing so increases,
and the number of firms evading all of their corporate taxes also increases because
the total benefit increases.11 The effect of a change in either the deduction or payroll
tax rate on the corporate tax evasion decision is more subtle and depends on whether
the firm is complying with the labour market regulations.
If a firm chooses not to evade labour market regulations (β = 0), then both of
these policies affect the corporate tax evasion decision by influencing a firm’s taxable
income and therefore a firm’s marginal concealment costs. The intuition is as follows.
A higher deduction rate or a higher payroll tax lowers taxable income. The effect
this lower taxable income has on a firm’s decision depends on whether the firm is
paying any corporate taxes or not. Firms who conceal all of their taxable income
mechanically evade less in absolute value when taxable income decreases. These
firms are not adjusting the proportion of taxable income they evade; they are choosing
α = 1. However, with lower taxable income they need to evade less. For firms who are
paying some corporate taxes, a lower taxable income implies a lower marginal cost of
concealment. These firms may then take advantage of this lower marginal concealment
cost to evade a higher proportion of their smaller taxable income. Therefore, a change
in either the deduction rate or the payroll tax can have a different effect on firms
depending on whether or not the firm is paying any income taxes. On the other
hand, if a firm is evading labour market regulations (β = 1), neither the deduction
rate nor the payroll tax affects the firms’ corporate tax evasion decision.
We can now turn to characterizing the firms decision whether or not to comply
with labour regulations. Define the net profits of a firm hiring a worker informally by
Π(1; θ, λ) ≡[θ + λ− w −
(1− α(1; θ)
)t(1 + θ)− c`
]− C
(α(1; θ)π(1; θ)
), (6)
where α(1; θ) is given by (4) for θ > θ̄(1) and equal to one otherwise. Similarly, define
11This is consistent with many studies in the tax evasion literature that show an increase in tax
rates leads to an increase in size of the informal sector. See, for example, Clotfelter (1983), Fugazza
and Jacques (2003), Enste (2010) and Wiseman (2013).
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the net profits of a firm hiring a worker formally by
Π(0; θ) ≡[θ−w− τ −
(1−α(0; θ)
)t[1 + θ− δ(µ+w+ τ)
]]−C
(α(0; θ))π(0; θ)
), (7)
where α(0; θ) is given by (4) for θ > θ̄(0) and equal to one otherwise.
Labour Regulation Evasion: A firm with parameters {θ, λ} evades labour marketregulations if and only if Π(1; θ, λ) ≥ Π(0; θ).
The benefit of evading labour regulations is simply the reduction in costs associated
with hiring and employing a worker informally relative to doing so formally, that is,
λ + τ . The various costs of evading labour regulation are more complex. There is
obviously the direct concealment cost of employing a worker informally, c`, but there
are also fiscal consequences. Evading labour regulation deprives a firm from claiming
the corporate tax deduction. Ceteris paribus, taxable income for a firm employing
its worker informally is higher (for a given θ). A constrained firm who evades all
corporate taxes automatically faces higher taxable income. Obviously, such a firm
pays no taxes, but must still spend more on concealing its evasion behaviour. On the
other hand, an unconstrained firm who only evades a fraction of its taxable income
is able to adjust. As taxable income goes up, the firm reacts by evading a smaller
proportion of its taxable income to save on concealment costs.
Using Lemma 1 and the labour regulation evasion decision, we define λ̄ ≡ c` − τas the difference in employment costs between a firm that evades labour regulations
and a firm that does not and we can then state Proposition 1 as follows:
Proposition 1: A firm with parameters {θ, λ} makes the following evasion decisions:
• A firm with θ ≤ θ̄(1) conceals all of its taxable income, α(β; θ) = 1. It alsoevades labour market regulations (β = 1) if and only if λ ≥ λ̄s(θ), where
λ̄s(θ) = λ̄+ct
1 + ρ
[[1 + θ
]1+ρ − [1 + θ − δ(µ+ w + τ)]1+ρ]. (8)• A firm with θ ∈ [θ̄(1), θ̄(0)] evades labour market regulations (β = 1) if and
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only if λ > λ̄m(θ), where
λ̄m(θ) = λ̄+t
[1+θ−
(t
ct
) 1ρ]
+ct
1 + ρ
[(t
ct
) 1+ρρ
−[1+θ−δ(µ+w+τ)
]1+ρ]. (9)
If the firm evades labour market regulation, it conceals a proportion α(1; θ) ∈(0, 1) of its taxable income. If the firm complies with labour market regulations,
it conceals all of its taxable income.
• A firm with θ > θ̄(0) conceals a share α(β; θ) ∈ (0, 1) of its taxable income andevades labour market regulations (β = 1) if and only if λ > λ̄h, where
λ̄h = λ̄+ δt[µ+ w + τ ]. (10)
Figure 2 illustrates the optimal evasion decisions α and β for firms as a function
of θ and λ as described in Proposition 1. We can now clearly identify four types
of firms in this economy. In the top left corner of Figure 2, firms operate without
paying any corporate taxes and do not respect the labour regulations; we refer to
these firms as true informal firms or shadow firms. Shadow firms are low produc-
tivity firms with high cost savings to operating informally. At the other end of the
spectrum in the bottom right corner, firms are paying some corporate taxes, and are
respecting the labour regulations; these are referred as lawful firms, although they
may engage in some tax evasion or avoidance activity. In the bottom left corner,
firms evade all corporate taxes, but respect labour regulations. These firms cannot
be considered informal firms since they hire their workers formally. However, these
firms are generating low enough revenue so they are able to produce zero taxable
income via evasion or avoidance activities. We call those firms aggressive tax evaders
(ATE). Finally, in the top right corner, firms are paying some corporate taxes, but
hire workers informally. Those are the firms with illegal labour practices (ILP).
Proposition 1 reveals some simple patterns. First, less productive firms (low θ)
conceal a higher proportion of their taxable income and are more likely to conceal
all their income. This is consistent with empirical evidence in Almeida and Carneiro
(2006), Dabla-Norris et al. (2008) and de Paula and Scheinkman (2011). Second,
among firms who fully evade their corporate tax liability, shadow and ATE, the more
productive firms evade more in absolute value. These firms mechanically evade more
as taxable income grows. Third, there can be both formal and informal firms with
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the same productivity. Firms with a lower cost of opening an informal position
(high λ) are more likely to hire their worker informally. Proposition 1 also illustrates
the interaction between the two types of evasion decisions, and how the relationship
between these two decisions depends on the design of the tax system, specifically
on the deductibility of labor costs. As a source of comparison, we consider the case
with no deduction (δ = 0), as would be the case for an output tax for all firms, as
summarized in Result 1 below.
(((((
�����
��
λ
θ
1
10
0 θ̄(1) θ̄(0)
λ̄
λ̄h
λ̄m(θ)λ̄s(θ)
α = 1
β = 0
α = 1
β = 1
α(1; θ) ∈ (0, 1)β = 0
α(0; θ) ∈ (0, 1)β = 1
Figure 2: Optimal Evasion Decisions
Result 1: Without a tax deduction on input costs:
(a) Firms with θ ≤ θ̄(1) ≡[t/ct] 1ρ − 1 conceal all of their taxable income and firms
with θ > θ̄(1) conceal a portion α(θ) of their taxable income where
α(θ) =
[t
ct
] 1ρ
(1 + θ)−1 with α′(θ) < 0.
(b) Firms abide by labour regulations if and only if λ ≤ λ̄ ≡ c` − τ .
Figure 3 below shows the evasion decisions without a tax deduction on input costs.
Both evasion decisions are completely independent. Overall, a total of λ̄ firms evade
labour regulations, and a total of θ̄ firms pay no corporate taxes. The same four types
of firms can be identified as in Figure 2.
14
-
λ
θ
1
10
0 θ̄(1)
λ̄
α = 1
β = 0
α = 1
β = 1
1 > α(θ) > 0
β = 0
1 > α(θ) > 0
β = 1
Figure 3: Optimal Evasion Decisions, δ = 0
By comparing Figures 2 and 3, we can highlight the important role deductions play
in determining the interactions between these two types of firm evasion behaviour.
Without a deduction, a firm’s corporate tax evasion decision depends only on the
firm’s productivity θ and the firm’s labour market regulation evasion decision depends
only on the value of λ. With a positive deduction, the two fiscal evasion decisions
are no longer independent and both decisions can depend on both the values of θ
and λ. Take the example of a firm with λ ∈ [λ̄, λ̄h]. If the firm productivity level(θ) is low enough, it would prefer to hire a worker informally. At higher productivity
levels, taxable income is higher. At some point (given by λ̄s(θ) in Figure 2), the firm
would prefer to hire a worker formally, so as to reduce its cost of concealing income.
As an another interesting example, take a firm with productivity θ ∈ [θ̄(1), θ̄(0)]. Forsmall differences in the cost of opening a position in the formal versus the informal
sector, firms will respect labour regulations. By benefiting from a low taxable income,
the firm finds ways to fully evade its fiscal responsibility, by reporting zero taxable
income for example. However, if λ is sufficiently large, the benefit of hiring a worker
informally outweighs the costs, and the firm will do so. This creates a sharp increase
in taxable income, and the firm now finds it too costly to fully evade corporate taxes.
Finally, note that, quite naturally, Figure 2 converges to Figure 3 as δ → 0. Theslope of λ̄s(θ) becomes zero, θ̄(0) converges to θ̄(1), and both λ̄h and λ̄s(θ) converge
to λ̄.
15
-
There are four important implications of a positive labour cost deduction:
1. There will be more aggressive tax evaders (ATE). The increase in the total
number of firms fully evading corporate taxes comes solely from those firms
hiring workers formally. The deduction reduces taxable income and therefore,
the cost of concealing income. This gives additional room for corporate tax
evasion.
2. Among shadow firms and ATE, more productive firms evade more and are
more likely be an ATE. For these firms, evasion decisions are substitutes as
in Madzharova (2011). More productive firms mechanically evade more be-
cause α is constrained to one. At the same time, these firms have more income
to conceal and so gain more by hiring workers formally to benefit from the
deduction.
3. Among lawful and ILP firms, more productive firms pay a larger fraction of
their taxable income and are more likely to be lawful. For these firms, com-
pliance decisions are complementary. Because these firms are able to make
an unconstrained decision, paying a higher proportion of their corporate taxes
raises the gain from hiring a worker formally.
4. There will be fewer shadow firms. This is a direct consequence of having the
deduction which increases the benefit of hiring a worker formally to either reduce
the corporate tax liability or reduce the cost of concealing income, as noted in
the previous two points.
3.2 Entry Decision
When an entrepreneur of type {θ, λ} decides to enter the market, it perfectly an-ticipates its future evasion decisions. From Proposition 1, we can derive the entry
decision of a given entrepreneur.
Entry Decisions: An entrepreneur who hires a worker formally is active if and only
if Π(0; θ) ≥ 0, while an entrepreneur who hires a worker informally is active if andonly if Π(1; θ, λ) ≥ 0.
To illustrate entrepreneurs’ joint entry and evasion decisions, we define zero-profit
isoprofit curves in Lemma 2 and show these curves when all types of evasion decisions
16
-
are observed in Figure 4. The shape and slope of the curves defined in Lemma 2 are
derived in the appendix.
Lemma 2: The zero-profit isoprofit curve for firms employing workers formally is
given by Π(0; θ̂(0)
)= 0 which implicitly defines θ̂(0). The zero-profit isoprofit curve
for firms with workers employed informally is given by Π(1; θ̂(1, λ), λ
)= 0 which
implicitly defines θ̂(1;λ).
λ
θ
1
10
0 θ̄(1) θ̄(0)
λ̄
λ̄h........................................
...................................
................
................
..................
...................
.....................
......................
........................
.........................
Active
Inactive
λ
θ
1
10
0 θ̂(0)
θ̂(1; 1)
θ̂(1;λ)
λ̄
Figure 4: Optimal Entry Decision
Entry decisions have no direct impact on evasion decisions, but rather affect the
distribution of active firms via a selection effect. This selection effect arises from
the following: the entry decisions for entrepreneurs who hire workers formally is
independent of λ, but entrepreneurs who hire workers informally are more likely to
be active when λ is large. Shadow firms and ATE who fully evade corporate taxes are
the low profitability firms, so are more likely to be “the marginal firm”, that is, just
on the margin of choosing to be inactive. At the same time, entrepreneurs with low
costs of opening an informal position are more likely to evade labour regulations and,
because of these large cost savings, are also more likely to be active. Low profitability
entrepreneurs who respect labour market regulations are simply chased out of the
market. The market is then over populated by shadow firms because it is the only
way to be profitable.
17
-
4 Normative Analysis
We begin by characterizing the government’s optimal tax polices in a benchmark
case with no evasion opportunities to gain some insight into the optimal tax policies.
We then characterize the optimal policies when firms can chose to evade corporate
taxes, and then characterize the optimal policies in the general case with both types
of evasion activities.
4.1 No Concealment Opportunities
In this case, firms cannot evade either labour regulations or corporate taxes, so α =
β = 0 for all firms. The only decision an entrepreneur makes is whether to be active
or not. From Lemma 2, we know that a firm enters if and only if θ ≥ θ̂(0), where:
θ̂(0) =t+ w + τ
1− t− t
1− tδ[µ+ w + τ ] ≥ w. (11)
Without taxes θ̂(0) = w and entry is efficient. Taxes distort the entry decision of
firms. An increase in either corporate taxes or payroll taxes reduces the number
of active firms. More generous corporate tax deduction, δ, has the opposite effect.
Firms’ entry decisions are illustrated in Figure 5.
λ
θ
1
10
0 w θ̂(0)
Inactive Active
Figure 5: Entry Decision; No Evasion Opportunities
18
-
The government’s problem is to maximize private surplus (entrepreneurs and
workers) plus tax revenue adjusted for the marginal benefit of public spending, tak-
ing into account the entry decisions of firms. The government’s objective func-
tion is then Ω(t, δ, τ) = (1 + m)TR + WS + PS where tax revenues are TR =∫ 1θ̂(0)
[t(1 + θ− δ(µ+w+ τ)
)+ τ]dθ, private surplus is WS =
∫ 1θ̂(0)
wdθ and producer
surplus is PS =∫ 1θ̂(0)
[1 + θ − 1− w
]dθ − TR.
Define
ωF (θ; t, τ, δ) = θ +m[t(1 + θ) + τ − δt(µ+ w + τ)
], (12)
as the net social surplus generated by a fully complying firm with productivity θ.
Wages don’t enter directly because it is just a transfer from producers to workers.
Taxes are also a transfer, but are better served in the government’s hands by a factor
m. The government’s problem can then be written as:
maxt,δ,τ
∫ 1θ̂(0)
ωF (θ; t, τ, δ)dθ,
subject to t ∈ [0, 1], δ ∈ [0, 1] and τ ≥ 0.
Proposition 2: Without evasion opportunities, a pure profit tax is optimal. The
corporate tax system features full cost deductibility and no payroll taxes. Corporate
tax rate t(m) is positive only if m > (1−u)w∫ 1w[1+θ−µ−w]dθ
, and is then implicitly given by:
m
∫ 1θ̂(0)
[1 + θ − (µ+ w)]dθ = ωF(θ̂(0)
)∂θ̂(0)∂t
, (13)
for θ̂(0) = w + (1− µ) t(m)1−t(m) .
The left hand side of equation (13) represents the marginal benefit of taxation, while
the right hand side represents the social loss due to the reduction in economic activity.
We can make three observations. First, with a sufficiently low marginal benefit of
public spending m, the optimal corporate tax rate would be zero. Even at low tax
rates, entry is quite responsive to taxation requiring a sufficiently high social benefit
to make taxation desirable. Second, when the full cost of opening a position can be
deducted (µ = 1), a pure profit tax (δ = 1) does not distort entry because it simply
shrinks profits proportionally, and so the tax is neutral (i.e., firms enter if θ ≥ w). Insuch a case, a 100% tax rate is optimal. When µ < 1, even a pure profit tax distorts
entry.12 More generally, as µ increases, the corporate tax base elasticity increases.
12Efficient entry could still be obtained in this case if either δ and τ were unrestricted, and would
require subsidizing input costs.
19
-
Third, when m→∞, the government maximizes tax revenue.
The optimal tax system features full costs deductibility and no payroll taxes.
Allowing for full deductibility is a way to minimize the elasticity of the tax base
with respect to the corporate tax rate. As for the absence of payroll taxes, firm
heterogeneity is the key factor. With heterogeneity, the corporate tax liability is
increasing in productivity and corporate tax revenues are determined by the average
productivity of active firms, which is naturally higher than the productivity of the
marginal one. With a payroll tax, however, the government collects the same amount
of payroll tax revenue from every firms. The distinction between marginal and average
productivity is not important. The net benefit of corporate taxation depends on the
full distribution of active firms’ productivities. If all firms had the same productivity,
then the net benefit from increasing either form of taxes (income or payroll) would be
the same. With heterogenous firms, however, a corporate tax generates more revenue
from supra-marginal firm, and still influences entry only at the margin. Therefore, a
corporate income tax is preferable to a payroll tax.
Figure 6: Optimal Corporate Tax Rate; No Evasion
Figure 6 shows two optimal corporate tax schedules to illustrate the above results. In
both cases, the wage is set at w = 0.25. The blue curve, which serves as a benchmark,
assumes µ = 0.5, while the green curve looks at an extreme case where µ = 0.9. In
both cases, as the marginal benefit of public spending, m, increases the government
optimally increases its corporate tax rate. When µ = 0.5, the optimal tax rate is
20
-
positive for values of m above 0.19 and the optimal tax rate can be as high as 25%
for high values of the marginal benefit of public spending such as m = 1. When
m = 0.5, the optimal tax rate is 17.4%, and 64.5% of all entrepreneurs are active.
The green curve illustrates what happens when the share of the costs of opening a
formal position becomes quite large. As discussed above, as µ gets larger the elasticity
of the corporate tax base gets smaller. Consequently, the optimal tax rate for a given
marginal benefit of public spending is higher - the green curve lies everywhere above
the blue curve. An increase in µ shifts the optimal tax schedule upward because it
lowers the corporate tax base elasticity.
4.2 Corporate Tax Evasion Only
We now consider the situation where firms are unable to evade labour market reg-
ulation, but firms can decide how much taxable income to conceal from the tax
authorities. From Lemma 1, we know that firms with θ < θ̄(0) evade all corporate
taxes (α = 1). To match reality, we assume concealment costs are sufficiently small
so that some firms full evade corporate taxes.
Condition 1: Some firms fully evade corporate taxes if and only if
ct <t(
1− t1+ρ
)ρ[1− δu+ (1− δ)(w + τ)]ρ
. (14)
Given Condition 1, the entry decision θ̂(0) is now implicitly defined by
θ̂(0)− w − τ − ct1 + ρ
[1 + θ̂(0)− δ(µ+ w + τ)
]1+ρ= 0 (15)
Social welfare generated by an active firm is now denoted by ω̄F(θ, α(θ)
)and given
by
ω̄F(θ, α(0, θ)
)=ωF (θ)−mtα(0, θ)
[1 + θ − δ(µ+ w + τ)
]− ct
α(0, θ)1+ρ
1 + ρ
[1 + θ − δ(µ+ w + τ)
]1+ρ(16)
A firm generates the same social benefit as before less the social value of the corpo-
rate taxes evaded and the concealment costs incurred by firms from evading those
corporate taxes. The government’s problem is
maxt,δ,τ
∫ 1θ̂(0)
ω̄F(θ, α(0, θ)
)dθ, (17)
21
-
subject to t ∈ [0, 1], δ ∈ [0, 1], and τ ≥ 0, and where α(θ) = 1 when θ < θ̄(0).
Proposition 3: When only corporate tax evasion is possible, optimal policy may
include a corporate tax with less than full cost deductibility and a positive payroll
tax rate. The following conditions are necessary and sufficient for δ < 1 and τ > 0,
respectively:
mt
∫ 1θ̄(0)
dθ −∫ θ̄(0)θ̂(0)
ct[1 + θ − (µ+ w + τ)
]ρdθ >
[(w + τ) +mτ
]∂θ̂(0)∂δ
, (18)
(1− δt)m∫ 1θ̄(0)
dθ +m
∫ θ̄(0)θ̂(0)
dθ + δct
∫ θ̄(0)θ̂(0)
[1 + θ − δ(µ+ w)
]ρdθ > w
∂θ̂(0)
∂τ, (19)
and the optimal corporate tax rate is then implicitly given by:
m
∫ 1θ̄(0)
[1− α(θ)][1 + θ − δ(µ+ w + τ)]dθ = 1 +mρ
∫ 1θ̄(0)
[t
ct
] 1ρ
dθ. (20)
When corporate tax evasion is possible, governments may no longer rely solely on a
pure profit tax. Payroll tax could be positive and less than full deductibility of costs
could be implemented.
Equation (19) determines if payroll taxes are desirable. On the left hand side are
the benefits generated by the payroll taxes. For each additional tax dollar imposed,
the government collects 1 − δt from firms who pay some corporate income tax andthe full dollar from firms who evade all fiscal responsibility. In addition to the fiscal
benefit, payroll taxes decrease taxable income for all firms. With the Cobb-Douglas
concealment costs, this has no impact on firms who pay some corporate income taxes.
Firms simply evade a larger fraction of a smaller taxable income and α(0; θ)π(0; θ)
remains constant. However, for firms who fully evade corporate income taxes smaller
taxable income imply less spending on concealment activities and a social benefit
given by the last term on the left hand side of (19). On the right hand side of (19) is
the cost associated with increasing payroll taxes. Even if the marginal firm pays no
corporate income tax, it pays payroll taxes. As a consequence, increasing τ reduces
the number of active firms. The marginal firm makes zero profits, but generates a
value added equivalent to w+τ . In addition, losing a firm means a fiscal shortcoming,
which has a social cost of mτ . As a consequence, the cost of losing a firm when τ = 0
is simply w.
The corporate tax system may also allow for less than full cost deductibility.
Allowing for less than full cost deductibility generates a fiscal benefit in the form of
22
-
lower tax credits as given by the first term on the left-hand side of equation (18).
Since only tax paying firms receive tax credits, firms who pay no corporate income
tax generate no fiscal benefit. (The government cannot draw blood from a stone.) At
the same time, reducing δ results in lower taxable income for all firms. Tax paying
firms fully adjust, but firms who pay no corporate income tax cannot. This leads to
an increase in the social cost of concealment activities instead of a reduction as for
the case of payroll taxes as given by the second term on the left-hand side of (18).
Similar to payroll taxes, the right-hand side of (18) shows that a reduction in δ also
reduces entry and losing a firm imposes a social cost of (w + τ) +mτ .
When unavoidable, payroll taxes act as turnover taxes considered in Best et al.
(2015). In our paper however, turnover or sales taxes can be evaded in the same way as
corporate income taxes. Rewriting taxable income as δ(1+θ)+(1−δ)(1+θ−µ−w−τ)stresses that a reduction in δ is equivalent to a shift toward turnover or sales taxes.
Even if firms can avoid both forms of taxation by underreporting income, turnover
taxes increase taxable income. Given that tax paying firms adjust their evasion
strategies to keep α(0; θ)π(0; θ) constant, additional revenue can be generated. This
is a different mechanism as proposed in Best et al. (2015).
Increasing corporate taxes no longer reduces the number of active firms since
the marginal firm in the market pays no taxes. What now becomes important is
how corporate tax affects tax evasion decisions both on the extensive (number of
firms fully evading corporate taxes) and the intensive margin (proportion of taxable
income evaded by tax paying firms). Increasing the corporate tax rate does not
change the evasion decisions of shadow firms and aggressive tax evaders: they pay no
taxes anyway. Nor does raising taxes lower total economic activity, since the marginal
firm pays no tax. The corporate income tax is still distortionary because it promotes
tax evasion. The optimal corporate tax rate balances the additional benefits from
increased tax revenue with the cost imposed by increased evasion activities and will
be positive as long as m > 0.
The following simulation describes an optimal tax system with both a payroll tax
and less than full deduction. We simulate a case where evading corporate taxes is
relatively cheap, making the corporate tax a weak fiscal instrument. We fix the wage
to w = 0.25 and the marginal benefit of public spending to m = 0.5. We set µ to half,
ρ = 5 and ct = 1. The optimal tax system features less than full cost deductibility
with δ = 0.83, and a positive payroll tax at τ = 0.04. The payroll tax is equivalent
to an average tax rate of 10% on firms’ profits and a rate of 5.3% on the profits of
23
-
the most productive firm. Less productive firms face higher effective rates because
of the lump sum nature of the payroll tax. The corporate tax rate is 11.5%. In
this simulation θ̂(0) is equal to θ̄(0), so only the marginal firm fully evades corporate
taxes.
Table 1 below compares the optimal tax regimes with and without corporate
income tax evasion. First note that with income tax evasion, additional entrepreneurs
start a firm. Evading part of their corporate tax liability allows some marginal firms
to make positive profits and be active. The second important difference is with the
effective corporate tax rate on total profits. To compare tax rates on profits, we
assumed that (1 − µ) is a monetary cost that is not observable by the government.Actual operating profits are then θ−w− τ .13 Even without tax evasion, effective taxrates are higher than the nominal corporate tax rate because of the non-observable
opening costs that are exempt from tax credit calculations. The average firm pays
up to 37.6% taxes on their actual profits. Effective tax rates decline with a firm’s
revenue, as the fraction of costs that are ineligible for a tax refund acts as a lump
sum tax. The most productive firm faces an effective tax rate 8.5 percentage points
lower. In our simulation, the presence of tax evasion further shifts the burden of
taxation on to low productivity firms. The design of the tax system now favours high
productivity firms.
m = 0.5
With
Without
t τ δ
17.4% 0 1 64.5%
firms
active effective tax rates
top average
29.1% 37.6%
11.5% 0.04 0.83 69.8% 38.5%25.9%
Table 1: Optimal Policies without and with Corporate Income Tax Evasion
13If 1 − µ was assumed to be non-monetary, then actual profits would be larger and all effective
tax rates would be lower.
24
-
4.3 Labour Market Regulation and Corporate Tax Evasion
We now characterize the optimal policies without any restrictions on evasion decisions.
In this case, Condition 1 still applies so some firms evade all their fiscal responsibility.
Entry decision for firms with formal employment status θ̂(0) is defined as in the
previous section. Firms with informal employment status enter if θ > θ̂(1, λ) where
the cut off is implicitly defined by:
θ̂(1, λ) + λ− w − c` −ct
1 + ρ
[1 + θ̂(1, λ)
]1+ρ= 0. (21)
Government policies now affect the decision of a firm to become formal/informal, in
addition to the decision to entry or not and the amount of income tax to evade.
There are two social costs associated with an informal position. The concealment
costs c` and the external cost x. There are also benefits associated with an informal
position. Opening an informal position is less costly by 1−λ and so the largest socialcost saving is one. There is also a maximal fiscal benefit of m(µ+w) associated with
an informal position since no tax credits are given in this case. In what follows, we
assume that a formal position is socially desirable to an informal one as stated in
Condition 2.
Condition 2: A formal position yields higher social surplus than an informal position
when:
c` + x > 1 +m(µ+ w). (22)
The government’s problem is to maximize Ω(t, δ, τ), subject to t ∈ [0, 1], δ ∈ [0, 1],and τ ≥ 0, where Ω(t, δ, τ) can be found in the proof of Proposition 4. The main twocomponents of the aggregate welfare are the net social welfare generated by active
firms with formal employment ω̄F(θ, α(0, θ)
), defined as before, and the net social
welfare generated by active firms with informal employment ω̄I(θ, λ), defined as
ω̄I(θ, λ, α(θ)
)=θ + λ− c` − x+mt
[1− α(1, θ)
](1 + θ)
− ctα(1, θ)1+ρ
1 + ρ
[1 + θ
]1+ρ. (23)
Total welfare aggregates these net social welfare over the number of each type of firm
according to the firms’ optimal entry and evasion decisions as illustrated in Figure 3.
We characterize the optimal policies in the following Proposition.
25
-
Proposition 4: With both types of evasion, the optimal policy may include a cor-
porate tax with less than full cost deductibility and a positive payroll tax rate. Con-
ditions (44) and (46) are necessary and sufficient for δ < 1 and τ > 0 respectively
and the optimal corporate tax rate is given by equation (42). All expressions can be
found in the appendix.
Accounting for labour regulation evasion changes trades off three different way:
i) costs and benefits of increasing payroll taxes or lowering tax credits applies only
to firms with formal employment status; ii) payroll taxes promote informality, while
tax credit encourage formality; iii) higher corporate income taxes makes tax credits
more valuable and promote formality. Because of the second point, payroll taxes or
restricted tax credits may well be part of an optimal tax system, but it is less likely
when the social costs of informality are high. Because of the last point, the optimal
corporate tax rate tends to be higher.
We start with the payroll tax. All trade offs between payroll and corporate income
taxes described in Proposition 3 are still there, but only applies to firms with formal
employment status. Payroll taxes can still collect tax revenue from firms who are
not paying any income taxes, but only from the ones with formal position. Shadow
firms are able to evade all fiscal responsibility. Payroll tax revenues on the left hand
side of equation (46) is restricted to labour regulation compliers only. Payroll taxes
still restrict entry, but again only for firms with formal employment status. Finally,
payroll taxes reduce taxable income for labour regulation abiding firms exclusively.
As a consequence, labour regulation evasion reduces the existing benefits and existing
costs in a proportional way. Employment informality adds one more cost however.
Payroll taxes encourage opening informal positions, which imposes social costs. If
these social costs c` and x are important, the payroll tax becomes much less attractive.
This effect is described by the last three term in equation (46) in the appendix.
The same apply to reducing tax credits. Only firms with formal employment
status are relevant when accounting for the diverse benefits and costs of lowering
δ. Similarly to payroll taxes, restricting tax credits makes formal employment less
attractive, so it promote informality.
We now address the question as to why corporate taxes should be higher. There
are three reasons. First, firms with informal employment status do not benefit from
deductions, so they have higher taxable income, and the benefit of increasing taxes
will be higher. Second, there are fewer firms fully evading taxes since θ̄(1) < θ̄(0),
that is, it is more costly to evade taxes for firms with informal employment because
26
-
of the additional taxable income. Again, higher benefit of taxing leads to higher
taxes. The third reason is more complicated. Firms must pay concealment costs
when evading taxes, so lowering taxable income is desirable. One way to do it is by
hiring workers formally. Higher corporate tax rates encourages firms to open formal
positions by making cost deductions more profitable. Higher corporate taxes are a
way to enforce labour regulation and reduce social cost.
5 Conclusion
In this paper, we have modelled the entry and evasion decisions of firms when labour
regulation evasion and corporate tax evasion decisions are independent of one another
and characterized optimal government policy given the firms’ decisions. Our two most
important findings are: 1) entry decisions and policy design can create a positive cor-
relation between labour market and corporate tax compliance decisions for firms with
high productivities, but a potentially negative correlation for less productive firms,
and 2) pure profit taxes without payroll taxation, which is optimal when abstracting
for the possibility of corporate tax evasion, is no longer optimal when such activity
is accounted for.
We first characterize a firm’s optimal evasion decisions and, given their evasion
decisions, their optimal entry decision. We find that a firm’s evasion decisions are a
function of the firm’s productivity and entry costs. On the surface, less productive
firms evade a higher proportion of their taxable income and are more likely to evade
all their income. More deeply, the presence of deductions can cause spillover effects
between the two evasion decisions. When there is no deduction available, the tax eva-
sion decision only depends on a firm’s productivity and the labour regulation evasion
decision only depends on a firm’s cost of opening an informal position. When there
is a positive deduction, the two evasion decisions can depend on both productivity
and opening costs: deductions create an interaction between the evasion decisions
that can be either complementary or substitutable. More productive firms who pay
more corporate taxes will adhere to labour regulation if they can deduct wages and
payroll taxes and less productive firms who are more likely to evade all tax liability
will adhere to labour regulations when deductions are possible to decrease their con-
cealment costs. We find that these results are consistent with much of the findings
in the empirical literature and they also add nuanced insights.
27
-
To analyze the implications for optimal policy, we characterize the optimal policy
when evasion is not possible, when only corporate tax evasion is possible, and when
both forms of evasion are possible. With no evasion opportunities, the optimal policy
is a pure profit tax with full cost deductibility and no payroll taxes. When only
corporate tax evasion is possible, and conditioning on the requirement that some firms
fully evade corporate taxes, the optimal policy may include a corporate tax with less
than full cost deductibility and a positive payroll tax. This change in optimal policy
occurs because policy must now take into account the evasion decision of the firm:
it must balance the benefits from increased tax revenue against the costs of evasion.
Since increasing the corporate tax leads to more corporate tax evasion, a corporate
tax is no longer superior to a payroll tax. However, a payroll tax affects entry into the
market. That being said, a higher payroll tax may be preferable to a lower deduction
to raise tax revenue because an increase in payroll taxes reduces taxable income and
reduces concealment costs when compared to a decrease in deductions.
Lastly, when both labour market evasion and corporate tax evasion are possible,
we find that the optimal policy may include a corporate tax with less than full cost
deductibility and a positive payroll tax. Different from the previous case where there
was only one type of evasion possible, this optimal policy may now feature a higher
corporate tax rate. We consider the social costs of informality. Due to the different
evasion decisions by firms with differing productivities, a payroll tax is more attractive
than a decrease in the deduction as a means of raising tax revenue: small shadow
firms will have an incentive to become formal firms. For informal firms paying some
corporate taxes, they are not able to claim deductions nor do they pay payroll taxes.
By increasing corporate taxes, this has a negative impact on the informal firms. To
mitigate the negative effect, an informal firm may become a formal firm. They will
only become a formal firm if the benefits of doing so are greater than their costs, that
is, the payroll tax must be low enough and the deduction must be high enough to
offset the cost of a formal position.
This model shows that when a firm’s evasion decisions are modelled indepen-
dently, this has an important effect on optimal policy. In order to understand how
government should structure optimal policy, we have highlighted the importance of
considering these different firm evasion decisions to assess the complex interaction
between government policy and evasion decisions.
28
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A Appendix
Proof of Lemma 1 The choice of α is only relevant for π(β; θ) > 0. Assume this
is the case. Note t − C ′(απ(β; θ)) is decreasing with α since C ′′(απ(β; θ)) > 0. Ift−C ′(π(β; θ)) < 0, then the solution is interior and using (1) and (3), α(β; θ) is givenby (4). If t− C ′(π(β; θ)) ≥ 0, or equivalently using (1) and (3),
t− ct[1 + θ − δ(1− β)(µ+ w + τ)
]ρ≥ 0, (24)
then α(β; θ) = 1. Define θ̄(β) as the value of θ such that (24) is given by (5). Firms
with θ ≤ θ̄(β) conceal all of their income, α = 1. Firms with θ > θ̄(β) conceal only afraction of their income, α(β; θ) ∈ (0, 1).
Proof of Proposition 1: Consider a firm with θ ≤ θ̄(1) < θ̄(0). Such a firm evadesall of its corporate taxes, regardless of its labour regulation evasion decision. This
type of firm will evade the labour regulations iif λ ≥ λ̄s(θ) where using (7) and (6),λ̄s(θ) is given by (8).
Next, consider a firm with θ ∈ [θ̄(1), θ̄(0)]. Such a firm evades all of its corporatetaxes if it does not evade the labour regulations, but only conceals a portion of its
income if it evades labour regulations. Comparing (7) with (6) and using the first
order condition on the choice of α, such a firm evade labour regulations iif λ ≥ λ̄m(θ)where λ̄m(θ) is given by (9).
Finally, consider a firm with θ > θ̄(0). This type of firm only conceal a portion
of its income, regardless of its labour regulation evasion decision. Comparing (7) and
(6), this type of firm evade labour regulations iif λ ≥ λ̄h(θ) where
λ̄h(θ) =λ̄+[1− α(0; θ)
]t[1 + θ − δ(µ+ w + τ)
]−[1− α(1; θ)
]t[1 + θ]
+ ct
[α(0; θ)
[1 + θ − δ(µ+ w + τ)
]]1+ρ − [α(1; θ)[1 + θ]]1+ρ1 + ρ
. (25)
Substituting in the expressions for α(0; θ) and α(1; θ) using (4), we can rewrite (25)
as λ̄h(θ) ≡ λ̄h where λ̄h is given by (10). From (8), (9), and (10), the effect of θ on thedifferent cutoffs λ are as follows: ∂λ̄s(θ)/∂θ = ct
[(1+θ)ρ− [1+θ−δ(µ+w+τ)]ρ
]≥ 0,
∂λ̄m(θ)/∂θ = t− ct[1 + θ− δ(µ+w + τ)
]ρ> 0 and ∂λ̄h/∂θ = 0. As shown in Figure
1, λs(θ) is steeper than λm(θ).
Proof of Lemma 2: Equating (7) to zero and using (2), the zero iso-profit curve
33
-
for a firm with a formal position is given by:
θ̂(0) =w + τ + [1− α(0; θ̂(0)
)]t[1 + θ̂(0)− δ(µ+ w + τ)]
+ α(0; θ̂(0)
)1+ρ ct1 + ρ
[1 + θ̂(0)− δ(µ+ w + τ)]1+ρ, (26)
which implicitly defines θ̂(0). Similarly, using (6) we find that the zero iso-profit curve
for firms with informal positions:
θ̂(1;λ) =d+ c` − λ+[1− α
(1; θ̂(1;λ)
)]t[1 + θ̂(1;λ)
]+ α
(1; θ̂(1;λ)
)1+ρ ct1 + ρ
[1 + θ̂(1;λ)
]1+ρ, (27)
which implicitly defines θ̂(1;λ). Define θ̂(1; 1) as the productivity level where θ̂(1;λ)
is evaluated at λ = 1. Consider first a firm who optimally chooses α = β = 1. Using
(6), the slope of the zero iso-profit curve in {θ, λ} space is given by:
∂θ̂(1;λ)
∂λ
∣∣∣∣Π
=−1
1− ct[1 + θ̂(1;λ)
]ρ < 0. (28)The slope of the zero iso-profit curve depends on λ where ∂
2θ̂(1;λ)∂λ2
∣∣Π̄
= ρctθρ−1 > 0.
Therefore, the zero iso-profit curve is convex for a firm that conceals all of its income
and evades the labour regulations. Now consider a firm who conceals only a fraction
of its income and evades the labour regulations. Using (6) and the expression for
α(1; θ) from (4), the slope of the zero iso-profit curve in {θ, λ} space is given by:
∂θ̂(1;λ)
∂λ
∣∣∣∣Π
=−1
1− t< 0. (29)
Finally consider a firm who is optimally abides by the labour regulations, β = 0.
For any α(0; θ) ∈ (0, 1], the zero iso-profit curve will be a vertical line since maximizedprofits are independent of λ.
Proof of Proposition 2: The first-order condition on t is given by:
m
∫ 1θ̂(·)
[1 + θ − δ(µ+ w + τ)]dθ ≤ ωF(θ̂(·))∂θ̂(·)∂t
, (30)
where t = 0 if the condition above is satisfied with strict inequality. Since 1 + θ −δ(µ+w+τ) is increasing in θ, and is equal to 1+w+τ
1−t −δt
1−t(µ+w+τ) when evaluated
34
-
at θ̂(·), we can infer that:
m
∫ 1θ̂(·)
[1 + w + τ
1− t− δ t
1− t(µ+ w + τ)
]dθ < ωF
(θ̂(·))∂θ̂(·)∂t
. (31)
Using the appropriate derivative for θ̂(·) we can show that:
ωF(θ̂(·))> m(1− t)
∫ 1θ̂(·)
dθ. (32)
The first order condition on δ is given by:
ωF(θ̂(·))≥ m(1− t)
∫ 1θ̂(·)
dθ. (33)
Given equation (32), equation (33) must be satisfied with strict inequality, so δ = 1.
Using the similar steps as above, we can show that τ = 0.
Proof of Condition 1: Some active firms fully evade corporate taxes iff Π(θ̄(0)
)> 0,
which is the case if[t
ct
] 1ρ
−[(1 + w + τ)− δ(µ+ w + τ)
]>
ct1 + ρ
[t
ct
] 1+ρρ
(34)
or, equivalently
ct <t(
1− t1+ρ
)ρ[1− δu+ (1− δ)(w + τ)]ρ
. (35)
Proof of Proposition 3: Entry cutoff θ̂(0) varies with policy parameters in the
following way:
∂θ̂(0)
∂t= 0;
∂θ̂(0)
∂τ=
1− δct[1 + θ̂(0)− δ(µ+ w + τ)
]ρΠθ(0; θ̂(0)
) > 0;∂θ̂(0)
∂δ= −(µ+ w + τ)
ct[1 + θ̂(0)− δ(µ+ w + τ)
]ρΠθ(0; θ̂(0)
) < 0.Note that Πθ
(0; θ̂(0)
)= 1− ct
[1 + θ̂(0)− δ(µ+w + τ)
]ρ ≥ (1− t), with the equalityholding when θ̂(0) = θ̄(0). The first-order condition on t for an interior solution is
given by:
m
1 +m
∫ 1θ̄(0)
[1− α(θ)][1 + θ − δ(µ+ w + τ)]dθ = 1ρ
∫ 1θ̄(0)
[t
ct
] 1ρ
dθ. (36)
35
-
There exist an interior solution to the equation above since ∂α(θ)∂t
= 0 when t = 0, and
since α = 1 for all firm when t→ 1.
The first-order condition on δ is given by:[θ̂(0) +mτ − ct
[1 + θ̂(0)− δ(µ+ w + τ)
]1+ρ1 + ρ
]ct[1 + θ̂(0)− δ(µ+ w + τ)
]ρΠθ(0; θ̂(0)
)+ct
∫ θ̄(0)θ̂(0)
[1 + θ − δ(µ+ w + τ)
]ρdθ −mt
∫ 1θ̄(0)
dθ ≥ 0, (37)
where δ = 1 if the equation above is satisfied with strict inequality. There exist an
interior solution where δ < 1 if and only if
mt
∫ 1θ̄(0)
dθ −∫ θ̄(0)θ̂(0)
ct[1 + θ − (µ+ w + τ)
]ρdθ >
[(w + τ) +mτ
] ct[1 + θ̂(0)− (µ+ w + τ)]ρ1− ct
[1 + θ̂(0)− (µ+ w + τ)
]ρ . (38)The first-order condition on τ is given by:
(1− δt)m∫ 1θ̄(0)
dθ +m
∫ θ̄(0)θ̂(0)
dθ + δct
∫ θ̄(0)θ̂(0)
[1 + θ − δ(µ+ w + τ)
]ρdθ ≤
[(w + τ) +mτ
]1− δct[1 + θ̂(0)− δ(µ+ w + τ)]ρΠθ(0; θ̂(0)
) , (39)where τ = 0 if the equation can only be satisfied with inequality. There exist an
interior solution where τ > 0 if and only if:
(1− δt)m∫ 1θ̄(0)
dθ +m
∫ θ̄(0)θ̂(0)
dθ + δct
∫ θ̄(0)θ̂(0)
[1 + θ − δ(µ+ w)
]ρdθ >
w1− δct
[1 + θ̂(0)− δ(µ+ w)
]ρ1− ct
[1 + θ̂(0)− δ(µ+ w)
]ρ . (40)
Proof of Proposition 4: The government maximize Ω(t, δ, τ), subject to t ∈ [0, 1],
36
-
δ ∈ [0, 1] and τ ≥ 0, where Ω(t, δ, τ) is given by the expression below∫ λ̄h0
∫ 1θ̄(0)
ω̄F(θ, α(0, θ)
)dθdλ+
∫ θ̄(0)θ̄(1)
∫ λ̄m(θ)0
ω̄F(θ, α = 1
)dλdθ
+
∫ θ̄(1)θ̂(0)
∫ λ̄s(θ)0
ω̄F(θ, α = 1
)dλdθ +
∫ 1λ̃
∫ θ̂(0)θ̂(1,λ)
ω̄I(θ, λ, α = 1
)dθdλ
+
∫ θ̄(1)θ̂(0)
∫ 1λ̄s(θ)
ω̄I(θ, λ, α = 1
)dλdθ +
∫ θ̄(0)θ̄(1)
∫ 1λ̄m(θ)
ω̄I(θ, λ, α(1, θ)
)dλdθ
+
∫ 1λ̄h
∫ 1θ̄(0)
ω̄I(θ, λ, α(1, θ)
)dθdλ, (41)
where λ̃ is defined by θ̂(1, λ̃) = θ̂(0). Note that λ̃ is independent of t. Since α(0, θ)[1+
θ − δ(µ + w + τ)]
= α(1, θ)[1 + θ
], and using the definition of λ̄m(θ), the first order
conditions with respect to tax rate t is given by:
m
∫ λ̄h0
∫ 1θ̄(0)
[1− α(0, θ)
][1 + θ − δ(µ+ w + τ)
]dθdλ+m
∫ 1λ̄h
∫ 1θ̄(0)
[1− α(1, θ)
][1 + θ
]dλdθ
+m
∫ θ̄(0)θ̄(1)
∫ 1λ̄m(θ)
[1− α(1, θ)
][1 + θ
]dθdλ+
∫ 1θ̄(0)
[ω̄F(θ, α(0, θ)
)− ω̄I
(θ, λ̄h, α(1, θ)
)]∂λ̄h∂t
dθ
+
∫ θ̄(0)θ̄(1)
[ω̄F(θ, α = 1
)− ω̄I
(θ, λ̄m(θ), α(1, θ)
)]∂λ̄m(θ)∂t
dθ =
1 +m
ρ
∫ θ̄(0)θ̄(1)
∫ 1λ̄m(θ)
[t
ct
] 1ρ
dλdθ +1 +m
ρ
∫ 1θ̄(0)
[t
ct
] 1ρ
dθ. (42)
Since the left had side is equal to 0 at t = 0, it implies that t > 0, for all m ≥ 0provided that ω̄F
(θ, α)> ω̄I
(θ, λ, α
). Since α = 1 when t→ 1, then t < 1. The first
order condition with respect δ is given by:
−mt∫ λ̄h
0
∫ 1θ̄(0)
dθdλ+ ct
∫ θ̄(0)θ̄(1)
∫ λ̄m(θ)0
[1 + θ − δ(µ+ w + τ)
]ρdλdθ
+ ct
∫ θ̄(1)θ̂(0)
∫ λ̄s(θ)0
[1 + θ − δ(µ+ w + τ)
]ρdλdθ +
∫ 1θ̄(0)
[ω̄F(θ, α(0, θ)
)− ω̄I
(θ, λ̄h, α(1, θ)
)]µ+ w + τ
∂λ̄h
∂δdθ
−∫ λ̃
0
ω̄F(θ̂(0), α = 1
)µ+ w + τ
∂θ̂(0)
∂δdλ+
∫ θ̄(0)θ̄(1)
[ω̄F(θ, α = 1
)− ω̄I
(θ, λ̄m(θ), α(1, θ)
)]µ+ w + τ
∂λ̄m(θ)
∂δdθ
+
∫ θ̄(1)θ̂(0)
[ω̄F(θ, α = 1
)− ω̄I
(θ, λ̄s(θ), α = 1
)]µ+ w + τ
∂λ̄s(θ)
∂δdθ ≥ 0 (43)
37
-
For δ to be smaller than one requires that the following condition be satisfied:
mt
∫ λ̄h0
∫ 1θ̄(0)
dθdλ− ct∫ θ̄(1)θ̂(0)
∫ λ̄s(θ)0
[1 + θ − (µ+ w + τ)
]ρdλdθ
−ct∫ θ̄(0)θ̄(1)
∫ λ̄m(θ)0
[1 + θ − (µ+ w + τ)
]ρdλdθ >∫ λ̃
0
[(w + τ) +mτ
] ct[1 + θ̂(0)− (µ+ w + τ)]ρ1− ct
[1 + θ̂(0)− (µ+ w + τ)
]ρdλ+t
∫ 1θ̄(0)
[ω̄F(θ, α(0, θ)
)− ω̄I
(θ, λ̄h, α(1, θ)
)]dθ
+ct
∫ θ̄(0)θ̄(1)
[ω̄F(θ, α = 1
)− ω̄I
(θ, λ̄m(θ), α(1, θ)
)][1 + θ − µ− w
]ρdθ
+ct
∫ θ̄(1)θ̂(0)
[ω̄F(θ, α = 1
)− ω̄I
(θ, λ̄s(θ), α = 1
)][1 + θ − µ− w
]ρdθ. (44)
The first order condition with respect τ is given by:
m(1− δt)∫ λ̄h
0
∫ 1θ̄(0)
dθdλ+m
∫ θ̄(0)θ̄(1)
∫ λ̄m(θ)0
dλdθ +m
∫ θ̄(1)θ̂(0)
∫ λ̄s(θ)0
dλdθ
+ δct
∫ θ̄(0)θ̄(1)
∫ λ̄m(θ)0
[1 + θ − δ(µ+ w + τ)
]ρdλdθ + δct
∫ θ̄(1)θ̂(0)
∫ λ̄s(θ)0
[1 + θ − δ(µ+ w + τ)
]ρdλdθ
−∫ λ̃
0
ω̄F(θ̂(0), α = 1
)∂θ̂(0)∂τ
dλ+
∫ 1θ̄(0)
[ω̄F(θ, α(0, θ)
)− ω̄I
(θ, λ̄h, α(1, θ)
)]∂λ̄h∂τ
dθ
+
∫ θ̄(0)θ̄(1)
[ω̄F(θ, α = 1
)− ω̄I
(θ, λ̄m(θ), α(1, θ)
)]∂λ̄m(θ)∂τ
dθ
+
∫ θ̄(1)θ̂(0)
[ω̄F(θ, α = 1
)− ω̄I
(θ, λ̄s(θ), α = 1
)]∂λ̄s(θ)∂τ
dθ ≥ 0. (45)
38
-
If the following condition is satisfied, τ is positive:
m(1− δt)∫ λ̄h
0
∫ 1θ̄(0)
dθdλ+m
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