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.

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

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

1

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.

2

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.

3

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).

4

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.

5

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.

6

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.

7

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

8

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.

9

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.

10

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).

11

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

12

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

13

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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32

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