Informal production, technology and capital subsidies: A challenge for

economic policy

Francesco Busato, Dept. of Economic and Legal Studies, University of Naples Parthenope, Italy.

Bruno Chiarini, Dept. of Economic and Legal Studies, University of Naples Parthenope, Italy.

Elisabetta Marzano, Dept. of Economic and Legal Studies, University of Naples Parthenope, Italy and CESIfo.

Date: March 23 2018

Abstract

Informal firms play a crucial role in developing economies as well as in many industrialized countries such as

Italy, Greece and Spain where substantial areas and regions are less developed and where firms are small and

lack the necessary scale to produce efficiently. The cost advantages that unregistered firms gain by evading taxes

may not offset their low productivity and small scale. In such circumstances, where access to public goods and

other benefits of official status are considerable, firms may choose to operate simultaneously in official and

unofficial sectors. With this aim, we represent a specific technological advantage (aggregate capital externality)

of moonlighting firms over ghost firms that we believe is intuitively plausible and squares with common

knowledge. Our model shows that as long as a firm’s efficiency increases, the share of unreported production

shrinks. We then consider the challenging implications of this framework for fiscal policies designed to support

firms, i.e. tax allowances and capital subsidies.

Keywords: formal and informal sectors; firm size; capital investment; state aid, tax exemptions.

JEL classification: O17, E26, E22, H25.

1. Introduction

The authors acknowledge financial support from University of Naples Parthenope (finanziamento ricerca individuale di Ateneo, 2015-2017). Corresponding author: Elisabetta Marzano, DISEG, Università Parthenope, Via generale Parisi 13, V piano, 80132 Napoli, Italy.

1

Underground activities occur in most countries, and there are significant indications that such

phenomena are widespread. At the end of the 2000s the estimated average size of the underground

sector, as a percentage of total GDP, was about 14 percent in the 21 OECD countries, with all the major

European countries reporting a size of the hidden economy well over 10% of total production and Italy

in excess of 20% (Buhen and Schneider, 2012).1 This notable size of underground production (hence of

tax evasion) necessarily affects the structure of firms, requiring a particular size and technology that

allows the companies involved to thrive, with benefits that outweigh the costs related to operating in an

inefficient context.

The aim of this paper is twofold. First, we intend to contribute, in a positive approach, to explain the

convenience of staying underground by modeling the technology of a firm that operates in the shadow

economy. Our assumption about the technological structure is able to capture an important stylized

fact, confirmed in countries where the shadow economy has a persistent share, namely the link between

firm size and technological efficiency, on the one hand, and tax compliance, on the other. Second,

within this productive framework and in view of the widespread use of policies to support the

productive system in the EU and especially in Italy, the paper shows how this fiscal policy may

exacerbate the phenomenon of the underground economy.

The model presented in this paper focuses on moonlighting firms, by which we mean firms that operate

simultaneously in the official and unofficial sectors, using the same stock of capital while evading

taxation for the activities that are undertaken underground. Such firms are able to evade taxation, like

those that operate only in the underground economy, but in addition, they can exploit

technological/institutional advantages conferred by their "above-ground" activities.

Our analysis focuses on the Italian economy due to its sizeable underground sector and the high

percentage of “moonlighters” which operate in the unofficial sector. Furthermore, Italian governments

have repeatedly supported firms (especially small and medium-sized enterprises) with a plethora of

investment subsidies and tax allowances. However, we believe that the theoretical scheme and its

predictions may be applied, without loss of generality, to other countries with substantial hidden

sectors.

Our analysis yields two main results. First, the model shows that firm size, technology and informality

are deeply connected. Technology matters (what we call moonlighting and the total factor productivity

1 The Italian National Institute of Statistics reports for 2013 an underground share of about 13% of GDP.2

effect, discussed below) for determining firm size and how to allocate resources between official and

unofficial production, hence the size of reported revenues.

Second, the paper discusses selected fiscal policy measures. In particular, we show that investment

subsidies promote tax evasion: subsidies induce firms to increase their capital stock (a level effect), but

also produce a reduction in the share of capital used in official activity (a composition effect). An

investment subsidy policy is a non-excludable public good that opens room for free-riding (tax evasion,

in other words). In this context the Government is unable, because of (un-modeled) monitoring costs, to

distinguish between regular and moonlighting firms. Firms therefore have an incentive to declare a

sufficiently small amount of revenue to be eligible for the subsidy, while investing relatively more in

the underground economy and ”pocketing the tax wedge”. In addition, the tax-enforcement system

plays a major role in determining both firm size, affecting aggregate capital stock, and tax evasion.

The paper is structured as follows. Section 2 provides some stylized facts and further motivations for

the paper. Section 3 explains the firm’s maximization problem and characterizes the long-run

equilibrium. In Section 4 the relationship between firm size, TFP and informality is discussed, whereas

in Section 5 the main results of fiscal policy effects are reported. Finally, in Section 6 we make some

concluding remarks.

2. Selected stylized facts

This section briefly presents empirical evidence supporting the claim that production structure, tax

evasion and industrial policies are intertwined. It focuses on firm size distribution, revenue

underreporting, and tax evasion schemes (partial evasion vs. full evasion).

With regard to firm size distribution, Table 1 shows that about 90 percent of firms are “small”, having

up to nine employees.2

Table 1: Number of Italian firms by firm size, year 2013

No. of employees Total firms (%)

0-9 4,094,444 (95.27)

10-19 127,998 (2.98)

20-49 50,760 (1.18)

50-249 20,897 (0.49)2Farrel (2004), La Porta and Shleifer (2008), and Dabla-Norris et al. (2008), amongst others, find that informality in developing countries is associated with smaller and less productive firms.

3

above 250 3,383 (0.08)

Total firms 4,297,482

Source: ISTAT, and the authors' calculations

Significant under-reporting of revenues is concentrated in the sector of smaller firms (micro, small and

medium size). This is the consequence of so-called "Sector Studies" (Studi di Settore) implemented by

the Italian Revenue Service (IRS), a mechanism that sets a revenue threshold below which firms are

allowed to keep a simplified bookkeeping system (Convenevole and Perinetti, 2008; Santoro, 2008,

2016; Chiarini and Monteleone 2016). According to IRS data (2013) more than 3.6 million taxpayers

complied with the presumptive index set by Sector Studies, and the average size of declared revenues

was considerably below the threshold (about 200,000 euros). Evidence provided by Ercoli (2005) confirms the occurrence of a threshold effect, driving firms to remain relatively small in order to stick

below the threshold allowing the simplified bookkeeping system. This enhances the opportunity of

successful tax evasion, since it reduces the effectiveness of fiscal controls. Ercoli's data also suggest

that small firms are mostly involved in tax evasion through underreporting of revenues, whereas large

firms mainly evade taxes by inflating costs.3

Finally, evidence suggests that tax evasion is not a discrete choice (i.e. either evading or not evading),

but firms choose typically to partially evade taxes. A Censis study (2005) confirms that most firms are

only partial tax evaders, while firms completely unknown to the fiscal authorities are a residual share

(see Table 2).4

3 This is also confirmed by Di Nicola and Santoro (2000) who show that tax evasion is very widespread among small firms and new firms, especially those located in the south of Italy. The strategic aspects of small firms that evade part of their turnover, and their interconnections with Sector Studies were investigated in Chiarini and Monteleone (2016).4The survey carried out by Censis (Centre for Social Studies) is based on qualitative methodology, i.e. interviews with key informants (managers, union representatives, public officers and so on). Hibbs and Piculescu (2010), using data from the World Bank, point out that managers of more than 60% of the 3,818 enterprises interviewed, distributed over 54 countries, are used to operating both in the official and unofficial sector.

4

Table 2: Irregular firms as a percentage of total firms (2005)

Irregular firms North-West North-East Center South Italy

Full tax evasion (1) 5.8 4.9 6.8 16.8 9.7

Underreporting (2) 29.7 31.3 41.7 59.9 43.4

Total irregular firms (1+2) 35.5 36.2 48.5 76.7 53.1

Source: Authors' calculation from Censis (2005).

These firms, using their “regular side”, can compete for fiscal benefits, such as tax relief policies for

investment expenditure or tax allowances. This is likely, since an important share of state aid policies

typically target small and medium-size enterprises. 5

While the justification for state aid policies has often been discussed, typically to improve social and

regional cohesion to promote growth, their implications in contexts with a strong unofficial economy

are, to the best of our knowledge, unexplored.6 The data support the existence of interactions between

aid policies and the underground economy; Marzano (2005) confirms such evidence, reporting data on

investment incentives and numbers of irregular workers for the 20 Italian regions, and suggesting that

there is a positive correlation between the two measures.

Thus, against the general background used to study capital subsidies, the paper discusses possible

interactions between state aid, and especially tax benefits and capital subsidies, in the presence of tax

evasion and the underground economy, focusing on the productive activity of firms operating

simultaneously in both the official and unofficial sector. In the following sections we present a model 5 See, amongst others Carmignani and D’Ignazio (2011). In recent years we have seen the proliferation of a

myriad of calls primarily for startup and innovation in micro enterprises and SMEs, particularly with European,

regional and local funds. See Perotti and Teoldi (2014). See also Giavazzi et al. (2012) for an attempt to survey

the total expenditure on subsidies to enterprises.

6 In 2011, the public contribution to the production of enterprises amounted to 16.7 billion euros, the contribution to firms’ investments reached 14.7 billion and other transfers to firms 2.7 billion. The evidence also shows that investment incentives have generally had very modest additional effects. See amongst others, Cannari and Chiri (2001), Pellegrini and Carlucci (2003), Giavazzi et al. (2012), and the literature quoted therein.

5

which is able to explain such facts and to discuss selected policies.

3. The Model

3.1 Moonlighting production structure

Suppose there exists a continuum of firms, uniformly distributed over the unit interval. A representative

firm produces output using physical capital and choosing its allocation between regularly

produced output YR (with capital share ) share and underground-produced output YU (with capital

share 1-).

(1)

This scheme defines the case of “moonlighting production”, where part of the firm operates "above

ground", while the other underground (we provide more details below, where the evasion mechanism is

presented). The regular economy offers benefits (e.g. credit, banking services; public sector services,

such as loans and capital subsidies; marketing and advertising services; trademarks) which, once

obtained through the above-ground part, could be used to support unofficial activities as well.

Assume, next, that services from participation in the official market are proportional to firm size and

that there exists an external effect generated by underreporting, which we call the moonlighting effect.

It is modeled as a total capital externality, allowing total factor productivity (TFP) to be endogenous.

Total production is defined as follows:

(2)

where a is the capital elasticity, is the size of the moonlighting effect, B is the exogenous TFP, and

B’ is the endogenous TFP. The quantity of total capital enhances the productivity of unofficial

production; the moonlighting effect acts as trading inside two plants of the same firm. In this model,

choosing to allocate a share of total capital to the official economy, , entails a cost in terms of

6

a

aaURMOONL

KB

KBKBYYY

'

1'

0

taxation, but involves a benefit in terms of an external effect going from official to unofficial

production, i.e. , is an externality-producing activity.7

The firm’s task is to choose its optimal size, K, by allocating resources across sectors. Comparing a

ghost (fully underground) with a moonlighting firm, the latter experiences:

i) a reduced risk of being audited, given the use of official production as a convenient screen

to fiscal audits;

ii) a weaker constraint to size expansion, given the additional official production;

iii) benefits from several services available only in official markets.

It is often assumed that firms operating in the underground economy are less efficient than regular

ones.8 Although this is plausible, the model suggests that firms operating simultaneously in the official

and unofficial sectors (moonlighters) might overcome some of the shortcomings of fully underground

production (ghost).

A distinctive characteristic of our model is that services available on official markets are freely

available also for unofficial activities. At the same time firms benefit from participation in the official

market: access to credit, banking services; public sector services, such as loans and capital subsidies;

marketing and advertising services; trademarks. Overall, these opportunities linked to the "market" and

to "regulation" can explain the spread of moonlighting and also suggest that this model of production

can be particularly attractive.

When a firm engages in moonlighting, it exchanges a share of the exogenous TFP (B) for an

endogenous one ( ). In order to ensure the advantage of moonlighting technology, a sufficient

condition is that Y(ghost)<Y(moonl) for a given capital stock, which reads as follows:

7In a different framework, Hibbs and Piculescu (2010) allow "B" to denote the productive value of institutional services available only to official activity. Here we claim it is more plausible that some of those services can be used surreptitiously to enhance unofficial production (through the moonlighting effect) without the enforcement authorities catching on, whereas totally unofficial ( "ghost" ) firms do not have access to this profit-enhancing externality.8Typical explanations include lower entrepreneurial ability, difficulty in getting financial support and high transaction costs due to the need to locate trustworthy trading partners. See Anderberg et al. (2003); Loayza (1994).

7

0

aK

(3)

Condition 1 below suggests that the size of the externality should be sufficiently low as to ensure that

returns to scale are not increasing at the firm level:

Condition 1

The restriction on the size of the moonlighting effect and hence the exclusion of any sort of

increasing returns of scale is a necessary assumption to allow the moonlighting firm to choose a finite

optimal scale for its capital stock, capturing the positive interaction between official and underground

production.9

3.2 The tax evasion model

The official economy confers benefits from several services supplied both by the government and by

the private market. However, engagement in the official economy necessarily involves tax liabilities.

That said, tax evasion is a risky activity and, at least for the wholly underground ghost firms, it

prevents them from gaining access to benefits available in the official economy.

For a given triplet of tax-enforcement parameters ( ), i.e., a proportional sales tax rate, , a fixed

and exogenous probability of being detected and fined, , and a fixed surcharge s>1 for income

(discovered by the authorities) to be concealed, the expected after-tax production is:

(4)

where the second term in equation (4) stands for the expected return of tax evasion, and is given by:

9In the appendix it is shown that a sufficient condition to allow saddle path stability is:

.8

aaa

BK

11

aa

10

aaaa 11 2

s,,

UYsY 11

In this economy two extreme scenarios of full compliance and total evasion occur, respectively, when

and, in the case of confiscatory taxation, . In the former case, no positive returns arise

from tax evasion, as is clear from Eq. 4, whereas in the latter situation no positive after-tax returns

occur in official production.

More realistically, we are interested in studying the implications of tax evasion and assume that

Condition 2 is fulfilled in the remainder of the paper:

Condition 2

This condition ensures that firms would have an incentive to produce both officially and unofficially.10

The optimal capital allocation depends on technological ( ) and institutional ( )

parameters.11

3.3 Value of the firm

At time zero the firm is endowed with a given positive amount of capital , and with an

intertemporally fixed flow of a non-capital resource (i.e. labor), which are normalized to unity.10In this paper we use a simple tax evasion model, without size-specific auditing probabilities. There are many issues, concerning the penalty rate, the possibility of detection and audit, that we cannot discuss here. See, among others, the survey of Andreoni, Erald and Feinstein (1998), Slemrod and Yitzhaki (2002), Bayer (2006) and Sandmo (2006). Both the empirical and theoretical literature usually consider taxation and regulation as the main causes of the existence of the underground sector (see Thomas, 1992; Tanzi, 1980; Dallago, 1990). Analysis of tax evasion, starting from Allingham and Sandmo (1972) and Yitzhaki (1974), focuses on the structure of marginal taxation, and/or the consequences for private/social welfare, without investigating the link between tax evasion and technology (see Cowell, 1990; Trandel and Snow, 1999, for surveys on tax evasion, and Alm, 1985 for the welfare effects of evasion). On the other hand, when focusing on the technology of underground activities, the literature very often concentrates on labor inputs, neglecting capital utilization (see Portes, Castells and Benton, 1989; Boeri and Garibaldi, 2001; Busato and Chiarini, 2004; Busato, Chiarini and Rey, 2012).11We do not consider the effect of corruption and bribery, which are additional costs for firms operating in the underground economy. This issue is well addressed in Hibbs and Piculescu (2010).

9

1s y probabilitith w -1y probabilit with

s

0 1

0s-1 ;10

,, aB s,,

0K

Each instant a firm maximizes the inter-temporal cash-flow function, choosing how many resources to

allocate to official production, and how much revenue to invest, I. Therefore, the output level of

the evading firm may depend on its evasion behavior. Investing is a costly process for firms; the

standard assumption adopted herein is that adjustment costs are a convex function of the rate of change

of the capital stock:

(5)

In addition, we assume that investments are encouraged by government, which provides a capital

contribution proportional to total investment, , to firms which are willing to increase their capital

stock. We assume that government is neither able to know whether new capital will be employed in

official or unofficial production, nor has accountability tools at its disposal enforcing the firm to

declare only the capital officially employed.12

The value of the firm is the expected present value of its revenues net of expenditures on capital input

and costs incurred by adjusting its capital input. The representative firm maximizes expected cash flow

V subject to a constraint set:

12This assumption, along with Condition 1 in the main text, is a strong incentive toward underground production. A different situation would occur if the fiscal authorities were more effective in allowing incentives to capital than in detecting tax evasion. In this case the rational agent would choose to produce irregularly, YU >0, but

seeks incentives only on the regular share of its investment, . This hypothesis complicates the analysis considerably, generating unstable and oscillating equilibria.

10

.1 ; bIIC b

I

MaxI , μ

V=∫t=0

∞

e−rt Π dt (6 )

s .toΠ= (1−τ ) B (μK )a+(1− ρτ s ) (1−μ )a K a (1+σ )−rK−I−I b+αI K̇=I−δK 0≤μ≤1 K̄0>0 limt→∞

e−rt φ0 K=0

α , τ∈ (0,1 ) ;s≥1 ; ρs<1 ;0<σ<1−aa

The quantity represents the firm's expected revenues, net

of taxation, I is the amount of gross investment, and is the physical depreciation rate of capital. The

amount denotes an investment allowance, where falls in the (0,1) interval. It represents

several different types of state aid, such as grants to firms investing in less developed areas (regional

aid), loans to small and medium-sized enterprises (SME aid), and other facilities for specific sectors

(sector aid).

Defining and Lagrange multipliers and the current value Hamiltonian H , manipulation of the

first order conditions leads to the following conditions characterizing optimal capital accumulation and

tax evasion:13

13The optimization problem is well defined, i.e. the objective function is concave:

.

11

rKKsKB aaa 1111

I

10 , 2

0,, 222222 IK

{I=[ (φ0−1+α )/b ]1/ (b−1 ) (7 ) ¿ {a (1−τ )B (μ )a−1 K a−(1−ρτ s ) (1−μ )a−1 K a (1+σ )=0 (8 )¿ {φ̇0=(r+δ )φ0−[ (1−τ )aB μa (K )a−1+a (1+σ ) (1−ρτ s ) (1−μ )a K a (1+σ )−1 ] (9 )¿ ¿¿¿

Proposition 1 below proves that the model has an interior solution.

Proposition 1 For firms with moonlighting technology it is not worth either becoming completely

regular ( ) nor turning into a ghost firm ( ) : i.e. the model does not admit corner solutions.

Proof : as well as are the basis of a negative power in Eq. 8, such that to have a finite

solution they must necessarily lie in the open interval (0,1).

The investment function (Eq. 7) suggests that for a given level of fiscal allowances, , investment is

increasing in , and gross investment is zero when the marginal value of capital is just equal to the

market price of capital, normalized to 1 , net of fiscal allowances. Fiscal incentives for capital

accumulation clearly increase investment.

Eq. 8 ensures the optimal allocation of capital between visible (official) and underground (unofficial)

production: the marginal effect of a capital reallocation on the net-of-tax revenues in the two sectors

must be equal.

3.4 The steady state

3.4.1 Qualitative analysis

Imposing certainty equivalence, and steady state conditions on the system ( ) we obtain

the following equilibrium conditions:

12

1 0

1

0

0;00 K

(11)

The first equation suggests that in equilibrium (i.e. in the long run) the shadow price of capital is the

discounted value of the net-of-tax marginal productivity of capital; the second condition states that the

stock of capital is stable when investment is just equal to physical depreciation of capital; finally, the

last relation expresses the optimal allocation of the capital stock between official and unofficial

production. It should be stressed that the long-run equilibrium can only be described in a three-

dimensional space, and given the non-linearity of the involved relationships, we are compelled to use

calibration and simulate the system in order to describe the nature of the steady state.

Proposition 2 In the long run, the dynamic System 11 admits a unique steady state.

Proof APPENDIX

Proposition 3 The steady state of the dynamic System 11\ is always a saddle path.

Proof APPENDIX

3.4.2 Model parameterization

The model depends on five parameters. We calibrate these parameters for Italy, a country with a large-

scale underground production and a high proportion of small firms which simultaneously produce

officially and unofficially. Italian governments have repeatedly supported these firms with capital

subsidies and tax allowances.14

14For the size of the underground economy, see ISTAT (2015). An outline of the state aid to firms in Italy may 13

11

1

11

1

0

1110

111

11

11111

aaa

aaa

aaaa

BsK

BsK

KI

KsaKaBr

The capital elasticity α , consistent with the calculations of the capital income share from the national

accounts, is set at the value 0.3; the exogenous cost of capital (the real interest rate), r , is set at 0.025;

the rate of physical depreciation of capital, , is calibrated to 0.125. Next, the tax rate, , is set at 0.4,

which is the average between the IRES (Imposta redditi società, a kind of taxation on company profits)

and the effective average taxation, as calculated by Chiarini et al. (2008); the tax surcharge applied to

firms caught evading taxes, s, following Italian civil law, is set at 1.3. The probability that a firm is

discovered and convicted of tax evasion, , is set at a very low value, 0.05, to give an idea of low

enforcement, which intuitively corresponds to actual conditions in Italy. This is particularly true for

small firms since, according to Ercoli (2005), most of the inspections target large firms. The size of the

subsidy for capital accumulation, , is set at 14% in the baseline calibration.15

Eventually, technological parameters B and are jointly calibrated to obtain an average evasion

consistent with Italian data. The moonlighting effect must also be consistent with Condition 1 defined

above, and with the model saddle path condition, outlined in the Appendix. As the maximum value for

this parameter is 1.6, we set it at an intermediate level of 1, such that the total capital externality is 0.3.

Finally, given data reported by the Revenue Agency on tax gaps, a plausible figure for tax evasion is

20%; accordingly, we set the exogenous total factor productivity, B, to a value of 10 and the size of the

adjustment costs to 1.1.16

Given this set of parameters, the solution of the dynamic system identifies a single long-run

be found in Bosco (2002) and Ministero delle Attività Produttive (2005) and Giavazzi et al. (2012).

15Calibration of the fiscal parameters and was chosen starting from the analysis of the Italian firm fiscal regimes addressed in Bontempi et al. (2001). In particular, incentives to investment identified as Credito di Imposta range from an average level of 0.14 for the Center-North regions, to 0.65 for the least developed region (Calabria). Finally, the calibration for the penalty, s, is discussed in Busato and Chiarini (2004).16We simulate the outcomes for different values of B in Section 3.4.4.

14

1.1125.03.03.105.0025.0140.01014.0basrB

benchmark the :nCalibratio Model

equilibrium, given by the equilibrium vector:

with a benchmark capital size equal to 18, and a share of aggregate capital deployed in the official

production amounting to 79%.

3.4.3 Steady State Relations and

The three steady state relations expressed by System 11 can be represented in the space . In

order to provide more insights into the local dynamics around the steady state, we prefer to represent

them in two bi-dimensional graphs as in Figure 1.17 The left-hand panel in the Figure displays the two

steady state relations (the shadow price of capital) and (the stock of capital), which are

standard in the literature on optimal investment.

17As stated above, we have a nonlinear system described in a three-dimensional space. In order to find the steady state characteristics we must calibrate and simulate the system.

15

79.0;18 ** K

0;K K,

,; 0K

00 0K

FIG. 1: Points on locus are characterized, for each level of K , by a higher than the

equilibrium level. Given the dynamic expressed in Eq. 9 it implies a growth in the shadow price of

capital (arrows pointing up). Similarly, when considering points above , we register for each K

a higher than the equilibrium level. Given the investment function, Eq.7, and the dynamic expressed

in Eq. 10, it implies a growth of capital stock (arrows pointing right).

The right-hand panel in Figure 1 represents, in the space , the relationship between the official

capital share and the total stock of capital K , defined by the last equation of System 11: for each

level of identified by the solution of System 11, a unique cash-flow maximizing value of is

identified. The locus is decreasing: given the nature of the moonlighting effect, the larger the

amount of total capital, the more benefit is obtained in shifting it to underground production (i.e.

16

00 0

0K

0

K,

K

K

drops).

The left-hand panel in Figure 1 also displays the local dynamics: the stability arrows show that there is

a single stable arm which leads the firm toward the long-run equilibrium, consistent with the standard

literature. When the capital stock dimension is lower than the optimal level, given Eq. 8, the official

capital share, , is higher than optimal (see also the right-hand panel in Figure 1). During the process

of capital accumulation, the firm also shifts capital into underground technology (i.e. drops). This

allocating process lasts until the marginal productivity is equal across sectors (official and unofficial

sectors, see. Eq. 8). An analogous symmetric process applies when the capital dimension is higher than

the optimal level and the firm operates on the lower and right-hand side of the stable arm. The gradual

character of the optimal adjustment along the saddle-path derives from the assumption of strictly

convex adjustment costs, which can be plausibly assumed to be higher in small inefficient firms

compared to large firms.18

4 Exogenous TFP, firm size and informality

Parameter B denotes, in Eq. 2, the exogenous component of total factor productivity (TFP) in

moonlighting technology, and it impacts the relationship between firm size (K) and underground

activity (µ). In other words, we show that the more efficient is official production in terms of TFP, the

larger is firm size and the less it is worth exploiting moonlighting technology. Therefore, an inefficient

firm is expected to be smaller and more prone to engage in underground activities compared to an

efficient one.

Changes in this technological parameter generate considerable differences with the baseline calibration,

both in terms of optimal capital dimension and official capital share. Figure 2 shows the pattern of

steady state capital size and its official allocation, calculated by numerically solving System 11, for a

set of possible parameterizations of the exogenous TFP. To be exact, we get the pattern of the steady

state capital size (as well as ) changing B in the interval (0,100), keeping all the remaining

parameters unaltered at their benchmark.

18Of course, every path other than the saddle path takes the firm far from the long-run equilibrium to areas in which the transversality condition (see Eq. 6) no longer applies.

17

FIG. 2: The effect of exogenous TFP (B) on optimal capital stock (K*) and official capital share (

*).

As long as the exogenous TFP rises, there is a corresponding increase in capital stock, i.e. firm size. On

the other hand, a larger TFP also implies that capital is increasingly allocated in regular production, i.e.

rises, and the pattern displayed in the right-hand panel of Figure 2 shows a convex relationship,

slowly approaching unity as TFP tends to become very large.

These simulations suggest a strong and direct relationship between the exogenous TFP (measuring the

degree of efficiency of the technology and driving firm size), and the choice to operate regularly. This

is consistent with the presented evidence and with the literature.

Two further points are worth emphasizing before proceeding. First, in contrast with the standard view 18

of the role of unofficial firms in development, the model suggests that for small and poorly efficient

firms it is worth declaring some of their revenues, i.e. is always above zero, but the visible

production is considerably lower than total production. Next, as long as TFP and firm size rise, the

share of capital allocated to official production tends to one: a process of technological growth should

be able to promote compliance.

5. Policy implications

This section presents the effects of selected fiscal policy simulations perturbing the enforcement

parameter space and the subsidy policy . In particular, we consider how different values

affect the size of the moonlighting firm, and the allocation of the total capital stock between the two

productions. Parameter can also be broadly considered a policy instrument, in the sense that the

possibility for the moonlighting firm to exploit the external effect of the aggregate capital is supposed

to be a function of the institutional and social framework in which firms operate.

We simulated the reaction functions of the long-run values of capital stock, capital allocation and total

production (see Figure 3) to policy changes (different sizes of each single fiscal policy parameter).

Each graph in the top panel shows, respectively, the effects of a variation in tax rate (first column),

capital subsidy (second column), expected penalty (third column) and moonlighting effect (fourth

column) on the size of total capital stock, while in the middle and bottom rows the reaction functions

for the officially deployed capital, ( ), and total production are displayed. The reaction functions are

always monotone, though nonlinear, and discussed separately below.

19

s,,

FIG.3: reaction of the equilibrium capital stock (K*, top row), equilibrium capital allocation ( * ,

middle row) and total production (Y*, bottom row) to: taxation (column 1); investment subsidy

incentives (column 2); expected penalties for discovered tax evasion (column 3); moonlighting effect

(column 4).

Taxation is the only policy capable of generating a positive co-movement between total capital and

official capital share. For instance, starting from the baseline value of taxation, 0.4, a fall in the tax rate

generates increases in the total capital stock as well as its officially deployed share. The tax reduction

increases the net-of-tax marginal revenue of capital; this occurs in more marked fashion in officially

produced output due to Condition 2.19 The fall in the taxation ratio, , alters the

equilibrium relationship between K and expressed in Eq. 8. Hence, a tax cut (rise), ceteris

19Given Condition 2 in the main text, a fall in the tax rate necessarily causes, in the steady state solution (11), a

fall in the taxation ratio 20

11 s

11 s

paribus, induces the moonlighting firm to engage in more (less) official production.

Consider, next, investment subsidies (second column). Increasing subsidies to capital accumulation

pushes up the equilibrium level of the capital stock, as we would intuitively expect, but also generates a

marginal reduction in the official capital share. The stronger incentive to capital accumulation reduces

its cost, such that there is an immediate effect on investment. The rise in capital stock alters equilibrium

marginal productivity (Eq. 8), such that as long as net investment is positive, the firm also reallocates

capital between the official and unofficial sectors. The important point is that, contrary to the

presumption that subsidies may also be useful for pushing firms to operate above ground, in the

presence of moonlighting technology, they incentivize the allocation of raised capital to the unofficial

economy overall.

This marginal increase does not bring firms out of informality, nor is it able to push up their total

factor productivity. Although the stock of capital rises with an increase in subsidies, in relative terms,

and consistently with empirical evidence, our firm still stays "informal", and remains inefficient and

small.20

The third column in Figure 3 presents the impact of a stricter enforcement policy, as simulated by a

larger value of , i.e. the expected penalty for discovered underground production. The graph

confirms that increasing enforcement effectiveness lowers the share of capital allocated to unofficial

production. However, there is also a negative effect on total capital, as well as total production. This

evidence, associated to the strong and positive effects of a tax cut, seriously depreciates the role of

enforcement in fighting tax evasion.

Finally, we examine the impact of the external effect, . With regard to the literature on the

relationship between underground production, firm size and development, this is the new technological

element which characterizes our firms, exploiting the nexus of operating across official and unofficial

productions. The moonlighting effect, proposed in this paper, shows how the evader and the regular

entrepreneur are intertwined, and how great is the advantage of operating together through the

economy as a result of transparent support of official activity for unofficial production. This insight

follows directly from the model and, as stressed above, it is supported by empirical evidence, emerging

from several surveys, on the characteristics of firms that operate in the underground sector. Intuitively, 20See Figure 2 for the relationship between TFP and firm size, and data in Table 1 to assess how large the number of small firms is.

21

s

a large (small) value for implies that the moonlighting firm strongly (weakly) benefits from the

simultaneity of its two productions. For instance, a larger value of compared to the benchmark (

=1) triggers an investment process and a drop in the officially deployed share of capital. While

approaches the threshold excluding increasing returns of scale, the solution converges toward a ghost

firm, i.e. , while size is no longer determinate. 21

Two main implications are worth stressing when focusing on policies against tax evasion. First, a trade-

off arises when a stricter penalty is enforced: in this situation, as shown clearly by the third column of

Figure 3, the rise in official capital is associated with a decline in total production. Secondly, tax

evasion, as proxied by the official share , seems to display a hard core which is, for plausible fiscal

policy parameters, around 20%. This proportion is barely affected either by a rise in expected penalty

and/or by larger capital subsidies, whereas tax evasion is appreciably affected, under moonlighting

technology, by the size of the externality effect, , and tax rate, .

In evaluating industrial policies, such as state aid, we conclude that the fiscal authorities should be very

careful when planning policies to support investment, especially in developing areas where the

underground economy is sizeable, because of their perverse effects. The rationale of the state aid is to

address various market failures (externalities, merit or public goods and so on) or may be justified

based on equity arguments, to improve social and regional cohesion, in order, for instance, to promote

growth. Figure 3 shows that capital subsidies (grants, tax exemption, equity participation, soft loans, etc.) have a deep impact on capital accumulation, but they also produce a reduction in the honest use

of capital. In designing policy subsidies to the stock of capital, what should be taken into account is the

nature of the firm, and, in particular, whether in the sector, and also in the area where the firm operates,

a large part of output is unreported. This is an aspect that the literature on incentives to firms has

totally neglected (see also Giavazzi’s recent report commissioned by the Italian government).

As incentives to investment in the presence of moonlighters always produce incentives to go

underground, it may be argued there is the risk that this policy proves, via underground activities, to be

21Graphically, the locus would have the usual increasing shape, but we would also observe an

increasing locus situated above such that no equilibrium could be found.22

0

0K

00 0K

what is known as a time-inconsistent policy. If government policies support moonlighting firms, the

latter will not find it worth increasing their reported capital, given that they already enjoy fiscal

incentives. Moreover, as we showed in Section 3, technology (i.e. the TFP effect) matters for

determining the extent of the declared production. Granting subsidies might have the side-effect of

lowering the profitability to invest in TFP-enhancing activities, which are a powerful mechanism to

attain more official production. Therefore, the government would be forced to subsidize capital

accumulation for longer than expected, without having any considerable impact on tax evasion.

Policy strategies targeting growth in developed countries such as Italy need to focus on a much more

complex firm structure than the typical informal (ghost) firm which characterizes developing countries.

Lack of access to finance and the other benefits of official status are a serious obstacle to doing

business. Moreover, and paradoxically, remaining unregistered means giving up the possibility of

enjoying government policies, such as subsidies, designed precisely to eliminate or reduce informal

activities.

6. Conclusions

In this paper we investigated the effects of selected fiscal policies, some of them broadly included

among state aid policies, in a context in which underground production is feasible.

The innovation of the paper is twofold. First, we represented a specific technological advantage

(aggregate capital externality) of moonlighting firms over ghost firms that we believe is intuitively

plausible and squares with common knowledge. Informal firms play a crucial role in developing

economies as well as in many industrialized countries such as Italy, Greece, and Spain, where

substantial areas and regions are less developed and where firms are small and lack the necessary scale

to produce efficiently. The cost advantages that the unregistered firms gain by avoiding taxes may not

offset their low productivity and small scale. In such circumstances, where access to public goods and

other benefits of official status are important, firms may choose to operate simultaneously in official

and unofficial sectors. Second, we considered the implication of this framework for two commonly

used modes of fiscal policy designed to increase investment and the capital density of production (and,

hence, ultimately labor productivity and standards of living), i.e. tax allowances and capital subsidies.

In this regard, we set out an optimal investment model in which a representative firm maximizes its

23

expected cash flow by choosing an optimal combination of capital stock and its allocation between

official and unofficial production. Among our results we considered the troubling aspects of capital

subsidies. In the context of moonlighting firms, government fiscal support of private investment

spending yields an incentive not only to increase capital accumulation but also for its underground use.

The calibrated model provided evidence of a persistence in tax evasion which cannot be easily reduced

below a threshold of about 20% without drastic policies, such as very large tax cuts.

This last implication, largely consistent with both micro- and macro-founded evidence for Italy,

suggests that in order to empower the official economy it is necessary to pursue a mixed strategy,

aiming to reduce the fiscal burden, but also to raise firm efficiency. Indeed, in our simulation it is

crucial to improve the TFP, since a process of technological growth is very successful in promoting

official production.

24

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28

Appendix

Proposition 2 In the long run, the dynamic system pertaining to steady state System 11 admits a unique

steady state.

Proof System 11 can be written as follows:

First Step:

To show that the first equation expresses as a monotone and decreasing function of the stock of

capital K .

The expression derived from system 11 in the main text:

;

is a strictly decreasing and monotone function of K:

It implies that the first term of is always negative, such that we need to demonstrate that the

second term is negative too:

29

d

d

CKCK

b

aaaar

KKb

KaKsrKKaB

1

10

1)1(110

)(1

)1(1)1()1(

0

11210 aaaadK

Kd KKKaKKa

KKKaKKa aaaa 1)1(12)1( 1111

.0;0 )1()1()1(

r

asr

aB

d

d

CKCKK

1

)( 0;0 1

1

11

1

a

aBas

aa Cd

02

1

2

11

11

1

d

d

d

dddd

CKCdK

CK

CKCdKCKCdKdK

Kd1a

dK

Kd 0

01111 1)1(12)1( KKKaKKa aaaa

Using again the definition of as well as we obtain:

As μ

is a majorant of this last expression, we consider the case to obtain:

This condition can be considered a sufficient condition to obtain the required monotony of the relation

Second Step

The second equation expresses a monotone and increasing function of the stock of capital K.

Indeed, for each .

Given that the codomain of the first equation is while the second equation has codomain

, it follows that there exists a single value of K such that the two equations simultaneously

apply.

Proposition 3 The steady state of the dynamic system pertaining to steady state System 11 is always a

saddle path.

30

)(K dK

Kd

011 2

1

1

1)1(11

12)1(1

1

d

d

ddCK

CdKaaCK

aaCK

KaKa

011 11

2)1(2)1(1

1

ad

d

dCKCdKaaa

CKaKKa

011 111

1 ad

d

dCKCdKa

CKaa

0111

d

d

CKCdKaa

.011 ada

1

aaaa /1/1 2

.00

0

01 20 bdKd Kbb

1b

;0

;1

Proof : The dynamic system related to the steady state System 11 can be written as follows:

The Jacobian of this System of Equations evaluated at the steady state is:

and it has a trace and a determinant given by:

where

Local stability, and in particular saddle path stability, requires that the trace should be positive, while

the determinant should be negative, when evaluated at the steady state. Under our parametrization it

implies that the condition , which is the necessary condition to obtain a concave

objective function, is also a sufficient condition to achieve saddle path stability. Given the

demonstration of the first step of Proposition 2, it follows that

.

This result implies that the Determinant of Jacobian matrix of linearized System 11 is negative, and it

underlines that the equilibrium is a saddle path.

31

KIKKasrKaBr aaaa

0

1)1(100 )1(1)1()1(

0

22

//

IKr

;//; 220 KIrDETrTR

dKKasKaBdK aaaa/)1()1)(1()1(/ 1)1(122

0/ 22 K

0/ 22 K