metadata: authors: 0: author: Braun, Juan
1: author: Loayza, Norman V.
docna: 0: docna: Taxation, public services, and the informal
            sector in a model of endogenous growth
docty: Policy Research Working Paper
subtopic: Economic Theory & Research,Tax Law,Industrial Economics,Labor Markets,Disability,Capital Markets and Capital Flows,Capital Flows,Services & Transfers to Poor,Economic Assistance,Economic Growth,Access of Poor to Social Services
teratopic: Poverty Reduction
abstracts: cdata!: Large informal sectors are an important
            characteristic of developing countries.  The authors build a
            dynamic model in which the informal sector exists when
            overregulation (high tax rates and high cost for entering
            the formal sector) is coupled with an inefficient and
            corrupt system of compliance control.  They consider a
            production technology in which public services are essential
            and subject to congestion.  The public services are financed
            by taxes collected from the formal sector.  Informal
            producers evade taxes and, because of their illegal status,
            can use only some public services, cannot use capital or
            insurance markets, and are subject to stochastic penalties.
            The authors find that the relative size of the informal
            sector is negatively related to the severity of the
            penalties and positively related to tax rates and the extent
            of informal use of public services.  They also find that
            economies with larger informal sectors have lower capital
            return and growth rates because the contribution of public
            services to productivity decreases with informality.  They
            argue that self-interested bureaucracies create an economic
            environment that makes informality attractive or simply
            unavoidable because they profit from the presence of the
            informal sector.
repnme: repnme: Taxation, public services, and the informal
            sector in a model of endogenous growth
display_title: Taxation, public services, and the
            informal sector in a model of endogenous growth
listing_relative_url: /research/1994/08/698098/taxation-public-services-informal-sector-model-endogenous-growth
topicv3: Economic Growth m1326241 471,Informal Sector m1326258 1168,Capital Markets m1326967 332,Social Assistance m1327201 1466,Tax Crime m1327485 2075
publishtoextweb_dt: 2010-07-01T00:00:00Z
historic_topic: Poverty Reduction
origu: Development Economics and Chief Economist
no_of_pages: 44
model_extractions: | POLICY RESEARCH WORKING PAPER 1334

# Summary findings

Large informal sectors are an important characteristic of devdloping countries. Braun and Loayza build a dynamic model in which dhe informal sector exists when overregulation (high tax rates and a high cost for entering the formal sector) is coupled with an inefficient and corrupt system of complianee control.

They consider a production technology in which public services are essential and subject to congestion. The public services are financed by taxes collected from the formal sector. Informal producers evade taxes and, because of their illegal status, can use only some public services, cannot use captal or insurance markets, and are subject to stochastic penalties.

Braun and Loayza find that the relative size of the informal sector is negatively related to the severity of the penalties and positively related to tax rares and the extent of informal use of public services. They also find that economtcs with larger informal sectors have lower capita return and growth rates because the contribution of public services to productivity decreases with informality. They argue that self-interested bureaucracies cream an economic environment that makes informality attractive or simply unavoidable because they profit from the presence of the informal sc6tor.

- - This paper a product of the Macroeconomics and Growth Division, Policy Research Department is part of a larger effort in thedepartmentto study the effects of regulation oninequality and econcmic growth. Copiesof the paper are available free from the World Bank, 1818 H Street NW, Washington, DC 20433. Please contact Rebecca _Martir,_ roon N11-043, extension 39026 (39 pages). August 1994.

_TWe Polcy Research Woig Paper Seies disemieth jlndings of wrk i pross to encowge the exch_e of ida about development sse An objective of the serie s toge the m Oint cut quwicky. cuen if the presentations are less than_ **_fzlypolisybed T7he_** _papers_ **_carny_** _the names of the auths and_ **_sbold_** _be used and_ **_citrd_** _accordingly._ **_The frndings._** _interpretationsm and concluions are the authors' own and shoul not be awtibued to the World Bank, its Executive Board of Diros,_ or _any of its memcbr counfnes._ Produced by the Policy Research Dissemination Center
# TAXATION, PUBLIC SERVICES, AND THE INFORMAL SECTOR IN A MODEL OF ENDOGENOUS GROWTH*

Juan Braun Pontificia Universidad Catolica de Chile and Norman V. Loayza The World Bank JEL 011, 041, H26, H41 Keywords: Growth, Informal Economy, Tax-Evasion, Congestion Effects, Public Goods

-We thank Alberto Alesina, Robert Barro, John Driscoll, Edward Glaeser, Debraj Ray, Jaume _Ventua,_ and participants in the Economic Growth Workshop at Harvard University for helpful suggestions. "Address: The World Bank, 1818 H Street, N.W., Washington, D.C. 20433. Phone: (202) _458-_ 4767. Fax: (202) 522-1151.
# TAXATION, PUBLIC SERVICES, AND THE INFORMAL SECTOR IN A MODEL OF ENDOGENOUS GROWTH

# 1. INTRODUCTION

The informal sector is tie. set of economic units which do not comply with one or more government-imposed taxes and regulations but whose product is considered as legal.' The presence of large informal sectors in all economic activities is one of the most important characterisdcs of developing countries: Informal sectors employ between 35 and 65 percent of the labor force and produce 20 to 40 percent of GDP.<sup>2</sup> The informal sector arises when an excessive regulatory system is coupled with an inefficient and corrupt system of compliance control. An excessive regulatory system makes the formal economy costly and unatactive by imposing high entry costs to legality, through license fees and registration requirements, and high costs to remaining legal, through taxes, red tape, and labor, environmental, and various other regulations.?

However, escaping taxes and regulations is not costless: An informal status entails many disadvantages. When an informal activity is detected, stiff penalties, in the form of pecuniary fines or capital confiscation, are applied. Furthermore, because of their illegal status, they do not enjoy full and enforceable property rights over their capital and product This has a number of deleterious consequences: First, informal producers are poorly protected by the police and the judicial courts from crimes committed against their property. Second, since they lack the capacity to enter into legally bindiag contaal obligations, their access to capital markets, for 'For an overview of the definition and characteristics of informal economies, see Chapter 1. 2Chickering and Salahdine (1991), p. 3.

3De Sowo (1989).

-2-
financial, insurance, and corporative purposes, is seriously limited. And third, they find obstacles to use some other public services, such as social welfare, skill training programs, and government-sponsored credit facilities.

The bureaucracy, as the institution controlling and monitoring the regulatory system, plays a crucial role in the formation of informal economies. If the bureaucracy profits in some way from the presence of the informal sector, it will create an environment that makes informality attractive or simply unavoidable.

In this paper we model the presence of informal sectors in the economy and their relationship to economic growth. To accomplish this goal, we use the framework of the endogenous growth literature.' Specifically, we use the work in which govermnent's participation in production, through the provision of public goods and services, is considered explicitly, as in Barro (1990), and Barro and Sala-i-Martin (1992).

In the sense ihat the informal sector is modeled as not paying taxes, this paper can be considered as a general equilibrium model of tax evasion.<sup>5</sup> However, we depart from the tax evasion literature by considering informality as an alternative to legality, entailing different production relations to government institutions and services, other firms, and capital markets.

We also depart from the prevailing modelling approach to informal economies, approach which focuses on labor market segmentation and rural-urban migration.<sup>6</sup> 4 See Romer (1986), Lucas (1988), Barro (1990), and Rebelo (1991).

5One of the earliest and most influential tieoretical papers on tax evasion is Allingham and Sandmo (1972). Cowell (1990) and Tanzi and Shome (1993) survey the recent theoretical and empirical literature on the subject. Alm, McClelland, and Schulze (1992) present experimental evidence on the individual reasons for tax compliance.

6See Chaudhury (1989), Rauch (1991), Gupta (1993), and Chapter 3.

-3-
In a general sense, we follow the methodology outlined by Becker (1968) to the study of illegal behavior: Economic agents in our model are interested in optimizing the expected value of intertemporal utility and choose, accordingly, whether or not to belong to the informal sector. In Section II we set up the model. We consider a production technology in which publicly-provided goods and services are essential to private production and are financed by tax revenues from the formal sector. Examples of these publicly-provided goods are transportation facilities, public utilities, education and health programs, judicial courts, public credit agencies, and domestic security (police, prisons). These public services are rival (subject to congestion) and to some extent excludable: Informal producers can only use some of them. In Section III we study the steady state of the economy, a state when both formal and informal sectors grow at the same constant rate. We find that the relative size (in terms of capital or output) of the informal sector is negatively related to the severity of the penalties and positively related to tax rates, the extent of informal use of public services, and the exogenous productivity of the economy. Furtiermore, we find that the return on capital and, thus, the economic growth rate is negatively affected by the relative size of the informal sector; this is so because of the inherent disadvantages of informal activities and because the informal sector does not contribute to financing productive public services. Finally, we find that the presence of entry costs into the formal economy produces a steady state with a larger relative size of the informal sector and a lower rate of economic growth, when compared to the case with no access costs to fornality. In Section IV we analyze government's behavior. We first assume that government is optimizing a given social welfare function, and we find that the social optimum involves the disappearance of the informal sector. We then analyze the case when government is partially controlled by a sel-interested bureaucracy, which profits from the presence of the informal sector

-4-
through the appropriation of penalty revenues. We argue that short-sighted and sociallyunaccountable bureaucracies are the most harmful to economic growth and social welfare.

In Section V we introduce uncertainty in production to study how the inability to use insurance and capital markets, which allow risk diversification, makes informality less attractive. Section VI concludes.

# **1L.** PRODUCTION TECHNOLOGY AND UTILITY **OPTIMIZATION**

The economy is populated by a continuum of agents in the interval [0,11. Each of them is endowed with a (possibly different) starting level of a broad measure of capital, which is meant to include physical as well as human capital. They can operate a basic technology to produce a single good in the form of consumables or capital. Raw labor is not an input of production. Agents maximize$i expected value of discounted utility (U): _U Eofu(c(t))e -Pdt_ **()** There are two different sectors in the economy to vWhich agents choose to belong: the formal and the informal sectors. We refer to the people belonging to each sector as the "formals" and "informals," respectively. Formals pay taxes in the form of a proportional income tax, the proceeds of which are used to finance the provision of public services. The net-of-tax flow of output to formal producers is given by<sup>7</sup> 7The superscripts F and I correspond to the formal and informal sectors, respectively. Agents are indexed by the subscript i- Aggregate quantities omit this subscript.

_-5-_
_yl_ = _aFki_ (2) where _aF_ is the net-of-tax expected return on capital, i.e. flow of production per unit of capital. For informal producers, the flow of output is given by where a' denotes the return on capital in the informal sector. lnformals do not pay taxes.

However, they must pay a penalty when caught. Penalties consist of a fracdon of the capital belonging to informal agents. We assume that the proceeds from penalties are appropriated by government officials (the bureaucracy) for their own good (we expand on this issue in section V); therefore, penalty revenues are not used to finance public services.

We follow Barro and Sala-i-Martin (1992) in assuming that the net-of-tax retrn on capital depends on the available amount of public services relative to aggregate production: _ccs_ = ) y )/ where A is an exogenous productivity parameter, g is the flow of public services, r is the tax rate, _f_ is the fraction of public services used by informal producers, and y' = _(1-7)4_ + ey is aggregate production which congests public services<sup>8</sup> . Informals have access to the same basic technology, but they use only the fraction e, **O<e<** 1, of available public services. That is, informal producers can use only some public services without being caught with probability 1; sNote that since the informal sector only uses the fraction e of public services, we assume that y' only includes the fraction _E_ of total informal output.

-6-
then, trying to avoid being caught, they choose not to use some public services. Examples of public services not enjoyed by informal producers are the police, courts of law, and governmentsponsored credit and training programs.

Letfl be the ratio of informal to formal output. That is,

**_Ir_**

(1-i)'y Assuming that government uses the proceeds of taxes only to finance public services, we have g = So that, _F_ -A(1--r)( T ) (4) The effect of a bigger informal sector, higher f, is clear from (4). Infonnal producers congest public services but do not contribute to financing them; therefore, an increase in the relative size of the informal sector lowers productivity for every one in the economy. It is also clear from (4) that, for a given tax rate, formal producers would like the informal sector to shrink to extinction.

# Optimization

We concentrate on the study of the steady state of the economy, which is defined as the state where the ratio of informal to formal production is constant and the aggregate economy grows at a constant rate.

-7-
Define the current value function Vftk,',t) as the optimal value of expected discounted utility, measured as of time t. The value function depends on the individual capital stock at time z, that is, _k(t)._ In general, the value function also depends on the future evolution of the economy (which, of course, is not under the control of the individual); this dependence is allowed for by the independent argument t in the value funcdon. However, in the steady state, the form of the value function does not change with time (other than through changes in the individual's capital stock) because the problem faced by the individual is the same at any point in time. Since we study the economy in the steady state, our value functions will not be time dependent. Then, we simply write the value function as _Vf(k)._ The Formal Sector The formal agent's problem is to maximize U subject to Assume that instantaneous utility is logaridumic. For fcrmal agents, _V(kjl_ satisfies the following Bellman equation _pVF(ki)_ = **_MAX_** _I_ log(c) + _Vf(k1)(ak-c,) 1_ (6) where _V4F_ is the partial derivative of VI with respect to capital. The F.O.C. for maxinization is

-= **_Yk_** (ts3 **_Ci_**

That is, the consumer equates the marginal utility of current consumption to the marginal utility of capital. Therefore, V' satisfies the following differential equation:

**_p1V(k)_** = -log(Vk(k)) i _dc' 4(kC)k_ - 1

-a-
with boundary condition _ulm VF(k)e-P_ = O **f-r** The soludon for _V_ is given by where, _BF_ **=** 1 **_(aF-_ p** From the F.O.C., it is clear that consumption is given by _c, pk,,_ a fixed fraction of wealth. Therefore, the individual's capital stock evolves according to Let the distribution of capital in the economy at time t be given by the density function _f,(k)._ That _is, fAc(kddk_ is the "amount" of people with _k,_ = ko at time _t._ Also, let **I,** be the fraction of people that belongs to the formal secmor at time _t;_ then where the integral is taken over the set _F_ of formal agents. Total capitl! in the formal sector (kF) at time t is given by _kF_ **=** _f ,(k)& = p,E(kJiebF)_ When no capital flows to or from the formal sector, aggregation over formal individual _-9-_
budget constraints dictates die evolution of aggregate capital in the formal sector4.

_dk,_ F Therefore, when no capital flows to or from the formal sector, its growth rate of capital (-yF) is given by r a (9)

# **The Informal** Sector

Informals do not pay taxes, but they face a positive probability of being caught and, thus, having to pay a penalty, at any point in time. The penalty consists of the fraction b of capital or its equivalent in goods. Formally, the occurrence of this event is assumed to follow a Poisson process. The Poisson process is continuous in time but allows discreet or discontinuous changes in the state space. Let q,(t) be an independent Poisson process with the following probability structure: Prob {event does not occur in the time interval dt) = I - _Xd_ Prob {event occurs once in the interval _dr}_ = _Xdt_ Prob {event occurs more than once in the interval dt} = 0 We also assume that q, and _qj_ are independent for different individuals i and j.

The budget constraint for informal agent i is 9In fact, as is explained below, in the steady state with no entry costs, capital flows from the informal to the formal sector. Therefore, the growth rate of capital in the formal sector will be different from that in equation (9).

-10-
_dk, = Wkfdt - c* - 4bk_<sup>_dq_</sup> _1_ **(16)** Equadon (10) is the short-hand expression for the stochastic integral of _k4(t)._ Note that, as opposed to the usual continuous diffusion process, q1 is continuous in time but not in the state space. Thus, if the Poisson event occurs, there is a discontinuous jump in k; by the amount _-bk,._ This jump is different in nature to a flow change, which is the case with the first two components of the change in k.

Note that if informals could buy a penalty insurance, the stochastic nature of the penalties would be irrelevant. This possibility is precluded by the assumption that infonnals cannot use insurance markets; in this way, the effect of stochastic penalties on expected utility is preserved.

Informals maximize U subject to (10). Let _VNk_ be the optimal value of total expected utility _U,_ measured as of time , and starting in state _k,._ The Bellman equation for _V_ is _p V(k)_ = _MAX_ {log(c) + _Vk) (dIk-c)_ + _[V'(k,tl -b)) - V'Q4)])_ **(11)** **_CI_** Equation (11) states that the maximized flow retr _log(c)_ plus the expected change in _V_ has to be equal to _p V._ The first part of the expected change in total utility corresponds to the continuous variation in capital given by production and consumption. The last part is the discontinuous change in utility caused by penalties. The F.O.C. for maximization is given by Substituting the F.O.C. into the Bellman equatiun, we get the following differential equation for **9:** _pV'(kc_ = _-log(Vf(kc)) + 4[V'(kAI-b))-V'(k)f_ - 1

-11-
with boundary condition lim _V(k(t))e-P'_ = _O_ 7he soludon for r" is given by _Vl(k)_ =log(pk) + **_B'_** p (12) where,

**_B'_** - 1 [cc'- p +klog( -b)] p

NoMe that th tern _log(1-b)_ corresponds to the loss in utility caused by the expectation of capital expropriation. From the F.O.C., consuinption is given by c, = pok. Given optimal consumption, the informal individual capital stock evolves according to _(' p) dt- bkidq1_ (13) Let the measure of infornal people at time _t_ be _(1-I&._ Then aggregate informal capital is _kl= r(1-L)E(k 1_<sup>_Iie4_</sup> When no capital flows to or from the informal secor, the evolution of informal aggregate capital is dictated by the dhange in average capita in the sector. That is, to get the equation of motion for aggregate informal capital **_(w5,_** we take expected values (over individuals) in (13). Since the q processes are uncorreied E(k4/ _ide) =E(ki/ iel) A._ Then, _dk'_ = _(a'-p-Ab)k'dt_ Hence, when no capital flows to or from the infornal sector, the informal capital growth rate ()

-12-
is given by _y1 a'-p-Ab (14)_

# Ill. STEADY STATE

Agents in the economy choose at any point in time whether to belong to the formal or the informal sector. We do not allow the simultaneous participation- in both sectorst In the steady state the ratio of. informal to formal production or capital is constant (constantfi) and the economy grows at a constant rate. We analyze first the case when there is free entry into either sector and afterwards the case when there are some entry costs into the formal sector.

No Entry Costs to the Formal Sector in steady state informal agents want to switch to the formal sector whenever _VY'(k5 Vc (kD 90) p_ (15) _3 (O)_ = _e,JF_ = _A'r_ [C-(1-c)J : ~~~~~P _=-Alog(1-b) >O_ . ~. _P._ ~ is related to the decrease in utility due ~ ~ ~ ~ ~ ~ ~ **to** expete capital expropriation. The function _r_ or, where, gOJ can be thoug,ht of as the difference in utilities before fines.

- -13-
By the same token, in the steady state formals want to move to the informal sector when _g02 P._ In order for the informal sector to be present in the economy, at least g(,=O) has to be positive and greater than _P,_ that is, P _10[e -_ -. r)i> - (16) _A_ Note that the left-hand side of (16) is increasing in the tax rate. This means that, given the other parameters, the tax rat has to be high enough if there is to be an informal sector. The intaition for this is clear: The only advantage of being in the informal sector is not paying taxes.

Figure 1 shows g(6) as a function offl for the case where (16) obtains. Since P and _A_ are both positive, the inequality in (16) implies [e - (1-r)J >0, which is the condition for

* **'§** _< O._ The negative slope of the function g(1) means that an increase in congestion (through an increase in O1) affects the informal sector rate of return more severely than it affects the formal sector one.

Figure 1 helps us identify- the stay-state level of P and how it is affected by changes in the parameters; Figure I is not used to describe transitional dynanics. In the steady state, any individual is indifferent between the two sectors. This occurs when ihe ratio of formal to -informal production is. , where _g(fi) =P."),_ The growdt rates of bodL secors adjust so as to keep ,B equal to ,B; as we explain below, this requires a net flow of capital from the informal to the formal sector. Not that values -of ,B lower than ,B do not represent steady states because at those points g*0)> P, which means that all individuals prefer to be in the informal sector, dtus creating a change in $3. By the same- token, for values of ,B higher than P", _g6B)<P,_ which "'The superscripF t* denotes steady state.

-14-
means that all individuals prefer to be in the formal sector.

Let _-r_ be the cut-off tax rate at and below which there is no informal sector in the economy, given the other parameters. That is, r0 is implicitly given by equation (16) with equality: Then, the steady state level offl,Br, is given by ~~~~~(18) The effect of changes in different parameters on the value offK can be explained using Figure 1. An increase in the probability of being caught (X) or in the size of the penalty (b) incases P, thus producing a decline in the relative size of the informal sector. Higher tax rates hurt formals- relative to- infornals; and hence when r goes up, g60) moves upwards and to the right, thus increasingf#. In fact, considering,B -as a function of tax rates,f> is 0 for **_7<T,,_** and it increases monotonically with _r_ for _r>_ 70 (see Figure 2)..

When informal producers can use a higher fraction -of available public services (higher e), the relative size of the informal sector in the steady state obviously increases. A somewhat less obvious result is that improvements in exogenous'productivity,'measured by the parameter A, result in a relatively bigger infornal sector. The reason for this result is that for high tax rates and. given _(e -(1-T)]_ >0, the infornml sector capures a relatively larger faction of the productivity improvemenLt

-15-
# Growth

Recall the definition of i, Then for **_d/dt =_** 0, the growti rates of the formal and informal sectors have to be the same. From equations. (9) and (14), we know that if no capitl flows from one sector to the other, This means that if no capital switches sectors, the growti rate of informal capital is greater than that of formal capital, and, thus, ,B increases. This situation can not correspond to a steady stateTherefore, in steady state there will be a constant movement of capital from the informal to the formal sector. The amount of capital that switches sectors, _le,_ is obtained from the condition of equal growth rates and is given by <!-- Start of picture text --> V l= og(l -b) +b]<br>AZ C<br><!-- End of picture text --> Note that the first order approximation for log(l-b) is given exactly by _-b,_ thus if _b_ is small k' will be very close to 0.

The growth rate of the economy is given by <!-- Start of picture text --> =1 - - P>0<br><!-- End of picture text --> Substtuting forf' in the expression for cit <!-- Start of picture text -->
-16-<br><!-- End of picture text -->
<!-- Start of picture text --> .. ~~ r<br>(l-ijP<br>_F= e--t) ° (20)<br><!-- End of picture text --> Assume that b is small enough so that the growth rate is very close to cf-p. Given the negative effect of ,B on _af,_ the growth rate is decreasing in,f whenpl >0. Hence, as can be seen in equation (20), when _f_ > 0, the growth rate decreases with _r_ and e and increases with X and b.

When the steady-state size of the informal sector is 0 _(Tr•r9),_ the model collapses to the one analyzed by Barro and Sala-i-Martin (1992), in which a", as function of _r,_ is first increasing, reaches a maximum at _r=/ =aO/(1+aq),_ and then dedines. In our model, te behavior of _a"_ with respect to _r_ depends on whether _r._ is bigger or smaller than _r?_ Figures 3A and 3B graph _aF_ for _T.<-r_ and _CŽ>T,_ respectively. In both cases, for _> 7 0,_ ciFalways decines with r.

Note that,the rate of-return (a"),'and, thus, the growth rat, is always decliniing with the tax rae when tere is an informal seor in the economy >0), even in the case when higher taxes could have positive- effects on productivity, in the absence of an informal sector (see Figure 3A). The case when _T0 <X_ is particularly interestirg because it shows that the opimal tax policy in the absence of an informal sector (7) renders subopdmal return and growth rates when an informal sector is allowed for. The following explains why _aF-_ and, thus, the growth rate always decreases with higher tax-rates: When the-tax rate rises, the relative-size of the informal sector increases Cjf goes up). Suppose that despite such initial increase in **a** . F was higher man before. Considering the definitions for the rates of return in equation (4) and the assumption that [- - (1-r)l >0, it must be .the -case that _at_ increases proportionally more than _a";_ clearly, this is not a steady-se equilibrium (gP)='-aF is no longer equal to _F)._ Utilities are equalized across <!-- Start of picture text --> :7 - .<br><!-- End of picture text -->
sectors only when /i increases so much that **_i/_** is lower than it was before taxes went up.

# Entry Costs to **Formality**

We model the access costs to formality as a one-time fee paid to government; this fee is assumed to be proportional to the capital to become formal. As explained in the introduction, this access cost reflects regulations imposed by govermnent and its bureaucracy. These regulations serve no direct purpose, and, hence, they are a waste of resources from the social perspective. Let this one-time cost be given by the fraction 6 of capital, where 0<5 <1.

informals will switch to the formal sector when fornal utility less entry costs exceeds informal utility; that is, when or, where, <!-- Start of picture text --> W (k S VF((I'_a)k<br>g(r) P (W)<br>P' = P + plog(1-8)<br>< p<br><!-- End of picture text -->

# Note that P' can be positive or negative.

Since formAls face no entry costs to the informal sector, they will switch to the informal

# sector when

_g(u)_ P Hence, there is a zone of inaction, where nobody wants to switch sectors.

-18-
There are two cases to consider. The first occurs when the entry cost rate (6) is low enough so that P>P'> _Xb._ In this case, we assume that g(=O)>P'." This case is presented in Figure 4A.3 The steady state level of a is given by tie intersection of g'3) and _P'._ At , no formal agents want to move to the informal sector. On the other hand, informal agents are indifferent between the two sectors. Note that if no capital flows from one sector to the other, the informal sector will grow at a faster rate (g(fl) > Xb). Therefore, in order to keep ,B constant, there will be a constant flow of capital from the informal to the formal sector, as is the case when there are no access costs. The ratio of infonnal to formal production in the steady stat (B-) is given by where, <!-- Start of picture text --> O 0r<br>13*= A E-1-)a 1 (/l<br>E(P1<br>A<br><!-- End of picture text --> The second case occurs when the entry cost rate (a) is high enough so that P> _)b 2P'._ in this case, we assume that _gg3=O)>Xb._<sup>_1_</sup> _'_ This second case is presented in Figure 4B. aljs given by the intersection of g03) and _Xb._ In this steady state, neither formal nor infonnal agents "This assumption is analogous to the one in equation (16) for the case of no entry costs; it makes possible the presence of an infonnal sector in steady sate.

121 drawing Figures 4A and 4B, we assume that P' is positive. The analysis is the same if j _P'_ is negative.

"See foomote 11.

-19-
want to switch sectors, and both of them grow at the same rate (g(fl) =Xb). We have not modeled the transition to the steady state; nevertheless, the following is a rough characterization of the trnsition in a neighborhood around the steady state, neighborhood in which there is no flow of capital from one sector to the ocher: In Pigure 4B, betweenfl1 andfl2 no agent switches sectors; however, between 1, and _B,_ g6B)> _Xb,_ so that i> 'yF implying that ,B approaches p; and, between Po and _2,_ **_gO Xb,_** so that -y"<z-y, implying that a3 approaches a . In this second case, the ratio of informal toiformal production in the steady state (K) is given by <!-- Start of picture text --> 0<br>-* S| a '[e'-G 1 1<br><!-- End of picture text -->

<!-- Start of picture text --> (21')<br><!-- End of picture text --> <!-- Start of picture text --> fig aea_l.-s] =b (22')<br><!-- End of picture text --> Note that in this case the growth rate of the economy is given by _aF-p._ The relative size of the informal sector in this case is greater than that in the case of sufficiently low entry cost rates, which in turn is greater than that when there are no entry costs. Consequenly, th steady-state growth rate is highest when there are no entry costs to fornslity and lowest when the entry cost rate is sufficiently large.

-20-
# **IV.** THE BEHAVIOR OF GOVERNMENT

# Welfare

Let us define social welfare _(W_ as the sum of individual utilities. Then, Given that the one time cost to become formal represents a pure waste of resources, the optimal policy will have 5=0. If 6=0, formal and informal capital are interchangeable. This implies Sat the first term in the r.h.s. of equation (23), which is a function of the current distribution of capital, is independent of changes in policy parameters. Therefore, maximizing welfare with respect to the policy parameters is equivalent to maximizing the last two terms in equation (23).14 In equilibrium, if the informal sector exisrs (,'> 0), individual utility obtained in the formal sector is equal to that in the informal sector; therefore, _r=BP._ If the informal sector does not exist (f'=0), obviously every individual's utility depends on _e._ In either case, maximizing welfare amounts to maximizing BF From the expression for oplmal individual utility in the formal sector (equation (7)), we see that _B'_ is a positive function of oF. Therefore, maximizing welfare is equivalent to maximiizing _ci._ As -was shiown in the section on aggregate growth, the growth rate is for all practical purposes equal to _acl-p,_ and, thus, it is optimized by maxiniizing a'. Therefore, maximizing welfare is approximately equivalent to maximizing growth. From now on, when analyzing "Note that since the optinal choice of parameters does not depend on the current distribution or level of capital, the optimal solution is time consistent.

-21-
opimal welfare and growth, we concentrate on the maximization of at.

There are a number of parameters in the model. We are going to assume that four of them are policy parameters. They are the tax rate (r), the penalty rate (b), the fraction of public services used by informals (e), and the registration-cost rate (6). They seem to be the parameters that most realistically would be under government control.'<sup>5</sup> Note, however, that assuming that these four are the only policy parameters does not mean that we are restricted to suboptimal outcomes; in fact, as we show shortly, using these four parameters appropriately allows us to attain the optimal outcome.

From the perspective of social welfare, it is clear that 6 must be set equal to zero. What abOUt _r, b,_ and e?

Consider the relationship between aF and _r_ for given b and e. This is represented in Figures 3A and 3B. We see that of reaches a maximum at r9 when **_To<T,_** and at r when **_7TT._** In both cases fi=O. That is, in order for welfare, growth, and of to be maximized, it is necessary that the infornal sector vanishes.

The maximum at _r_ is superior to the maximum at re. As we know, a maximum at _T._ occurs when _r0_ iS relatively low; from (17), we learn that r, is low when the economy is exogenously very productive (high _A),_ public services do not contribute much to production (low a), participation of public services by informals is significant (high e), and the penalties are not very severe (low b). Therefore, by increasing the penalty rate and decreasing the fraction of public services used by informals, **_T0_** can be raised until it is at least as big as 7. In this way, ap 15We keep the assumption that the probability of detection (X) is exogenously given. In reality, this probability may be controlled by both govenment and economic agents, the former by detennining the amount of resources dedicated to policing the informal sector, and the latter by using appropriate "hiding" strategies. We keep X exogenous to simplify the analysis.

-22-

**t...**
would reach a maximum at 7.

Hence, when the policy variables can be chariged with no cost, the optimal policy is _7=7,=7-._ The fact that the optimal outcome is achieved with a proportional tax rate is explained by the congestion externality. As Barro and Sala-i-Martin (1992) show, 7 can be thought of as the user fee which effectively internalizes the congestion effect.

We have assumed that there is no cost associated with maintaining the penalty rate at a certain level and preventing infornals from using some public services. More realistically, if a more severe policy towards infornials involves a higher implementation cost, the optimal policy will consist of having the actual tax rate **_7_** equal to 7., and having b and E such that **_T._** is less than but close to _r;_ to be precise, optimal b and E occur when the marginal'cost of adjusting b and f (cost of policing the informal sector) is equal to its margiala benefit (which comes from having the tax rate, _7=7 0 ,_ closer tO 7). This analysis has the implication that optmal policies may seem to undertax the economy, for the optimal tax rate in tihis case falls short of **T7.** Raising fte tax rate to undertake what appears to be profitable public projects hurts tA economy, for it invites the formation of an informal sector.

Finally, although the vanishing of the infonnal sector is necessary to optimize social welfare, it is not a sufficient condition. Notice that if the penalty rate (b) is high enough or the fraction of public services used by informals (e) is low enough, no agent will choose to operate in the informal sector. Neverdheless, the tax rate may not be at its opfimal value.

Let us summarize and provide some economic interpretaion. For given parameter . alues, if the tax rate is below a certain hreshold level, there is no infomial sector in the economy. This is because the costs of being informal (penalties and less usage of public services) are bigger than its benefits (avoiding axes). In fact, as the tax rate increases from low

-23-
levels, productivity and welfare rise for everyone because the distortionary effect of taxes is more than compensated for by the beneficial effect of public services (which, of course, are tax financed). Government would want to raise the tax rate up to the point where productivity of public services is maximized. However, this optimal rate must be below the threshold rate; oterwise, the presence of the informal sector would add to the distortionary effect of taxes and this rate would no longer be optimal. To ensure that the threshold rate is at least as high as the optimal tax rate, government can increase penalties and prevent informals from using public srices, thus making- informality less profitable.

Bureaucracy d Ioformalit From the anaiysis in the previous section we learn that, for given parameters, an appropriate reduction of the tax rate and a sufficient severity towards the informal sector eliminate the incetives for economic agents to become informal. If everyone is better off without an informal sector, why may govermnent not pursue a policy to eliminate it?

We have treated government as an impersonal entity. In reality government is managed by a bureaucracy. This bureaucracy has the power to collect taxes and penalties and to administer the use of public services.

The bureaicracy collects penalties from informal agents. We have assumed that these penalties are not used to produce public services. If in fact the bureaucracy appropriates at least some of the penalty revenues, it has the incentive to promote the formation and growth of the informal sector. If the informal sector were to disappear, bureaucrats would lose their special rents.

The behavior of the bureuascy depends on the degree of cohesion and coordination

-24-
armong its members, the extent of its power to dictate policy, and its planning horizon.

Shleifer and Vishny (1993) compare the case of a bureaucracy which behaves as a single monopolist with that composed of a number of independent monopolists. They show that the latter type of bureaucracy leads to more corruption and economic distortions than the first one. They also point out that a well coordinated bureaucracy is more profitable to its members.

The behavior of the bureaucracy is also determined by its power to control different policy instruments such as tax and penalty rates, entry costs to formality, and usage of public services. When the bureaucracy is more accountable to the public, through an effective use of the political mechanisms of democracy, the powers to legislate in its own behalf diminish. The bureaucracy may have limited power over some policy instruments and vast powers over others. For instance, a bureaucracy with small legislative powers may have little control over the determination of tax rates but a large control over penalty rates and registration costs.to formality. The characteristics and strength of bureaucracy's power change considerably from country to counny. Related to the extent and qualifications of its power is the time horizon the bureaucracy considers in taking policy decisions. The analysis presented so far in the paper helps us understand this decision-rking process.

Policy decisions affect the relative size of the informal sector at any point in time (16) and its growth rate (,). As it was shown in previous sections, a relative expansion of the informal sector produces higher congestion of public services and, consequently, lower growth. Therefore, there tends to be a trade-off between a larger size of the informal sector (and, thus, a larger base from which to collect penalties) now and in the future. If the bureaucracy's planning horizon is rather short (may be because it follows the cycle of popular elections), it will sacrifice growth for a larger informal sector now. Depending on its power to control policy instrumnts,

-25-
die short-sighted bureaucracy will dictate high tax rates and rather low penalty rates, will make more public services available to informals, and will restrict the access to formality. A bureaucracy that enjoys a large planning horizon will take into account growth considerations more seriously, understanding the negative effect of the congestion of public services on growth. This bureaucracy will in fact be interested in a healthy formal sector, for it provides the resources to produce public services, which in turn determine the productivity of the informal sector. Relative to the short-sighted bureaucracy, this will impose lower tax rates, higher penalty rats, less' access to public services by informals, and fewer restrictions to formality. The farsighted bureaucracy behaves similarly to those which are accountable to the public, in so far as the inportance paid to growth is concerned.

The presence and traits of the informal sector in different countries is very much related to the characteristics of their bureaucracy.

# V. PRODUCTION UNCERTAIWNY AND CAPITAL MARKETS

In this secfion we -extend the simple model by introducing production uncertinty and capital markets. As it was pointed out in the introduction, one of the most important Ce characteristics of informality is the inability to use capital markets. That is, informal firms have restricted access to credit, and their ability to participate of joint ventures and insurance mairt is limited. in order to model this feature, we need to introduce some kind of uncertinty; we have chosen to introduce uncerminty in the production function.

We keep the same features as in the simple model presentd in previous sections, not considering entry costs.

The net-of-tax flow of production for individual firms in the formal sector is given by

-26-
_IF ) df(4)+_ where,

# _aF= A(1_

Each agent chooses the fraction w; of her capital, _k,,_ that she wishes to use for production. The net-of-tax expected return or flow of production per uiit of capital is given by /dt. The variable ; follows a standard Brownian Motion or Wiener process". The processes; _sa_ zj are independent for i different fromj. The parameter o2 is the variance of reurn Then, the variance of net-of-tax return is given by _O_<sup>_2_</sup> _dt,_ where **_or'==r(J-7),_** and _r_ is the tax rate. We assume a to be constant.

The flow of production for individual finns in the informal sector is

> **_I,_** Yl= £s **_CaJJd_** + **_oo4c. 'd'_** (25)

where, _-3i_ **_= A(e8)_** _- o_ The expected producdon flows o( and ccl are the same as in previous sections.

We assume ta formals can use the capital market for lending, borrowing, and diversifying risks. Informal producers cannot use the capital markets, for they have no legal claim to their capitl stock.

"1That is, _z(t)_ has stationary, independent increments, continuous sample paths, and is nommaily distributed with mean zero and variance **t.**

-27-
# **The Fonmal Sector**

The formal sector is formed by a large (infinite) number of agents. There is also a large nunber of intermediaries in the capital market These intermediaries borrow assets from formal agents and invest them in any of the individual technologies. Suppose a given intermediary with total assets equal to a invests in N different technologies, using _a/N_ units of capital in each of them. The total return is given by Since the zi processes are independent, when N goes to infinity the stochasic part of the return converges to 0. Hence, using this strategy the intermediary obtains R = _acids._ It is clear that this strategy is the best one available to the intermediary: any other produces the same expected return but a higher variance. The large number of intermediaries precludes the possibility of any of them takdng into account the congestion externality. We assume that capital markets are competitive and that there are no administrative costs to intermediaries. Then, given that the production technology is constant returns to scale, intermediaries will borrow and lend at the same interest rate Wv'. In sumnmary, agents in the formal sector will always choose to operate through the capital market, for that allows then to diversify away their production risk.

The ability to use capital markets allows formal agents to ignore the production-related uncertainty in their optimal decision making. Formal agents now face the same problem as in the case with no uncertainty in production. Therefore, the solution for optimal consumption and growth rate in the formal sector is the same as in section 1.

-28-
# The Informal Sector

Informal agents cannot use the capital markets so that each producer operates her own technology. Consequently, they cannot diversify away the risk inherent in production. The underlying assumption is that informals will not choose to form coalitions since they cannot enforce contracts. As we said above, informal agents cannot enforce contracts because they have no legal claim to their capital stock and do not enjoy the protection of courts of law.

The budget constraint for informal agent i is _dk,_ = _sakt# + akAflz_ - _cdt_ - _bk 1 dqi (26)_ Equation (26) is the short-hand expression for the stochastic integral of _k(t)._ Note that, as opposed to z,, _qi_ is continuous in time but not in the state space.

Note that cl can be interpreted as the effective borrowing rate for infornal producers. Production in the informal sector is carried out by family firms. In this sense the size of each informal flnn is very small (it is actually negligible in our model). On the other hand, in the formal sector, firms work jointly to diversify away their production uncertainty. In this sense, formal firms are much larger than informal family _firs._ Informals maximize U subject to (26). Let _V'(kd_ be the maximized current value of total expected utility U, starting in state k,. The Bellman equation for _V_ is The first part of the expected change in total utility corresponds to the continuous variation in capital given by production and consumption. The second part is the standard infinite variation correction for Ito processes. The last part is the discontinuous change in utility

-29-
caused by expected penaldes.

The F.O.C.s for maximizadon are given by We obviously require that wi be greater than 0 and smaller than 1. We choose not to impose this constraint directly; instead, we constrain the parameters of the model (as explained below) so **that** the condition obtains. The two equations in (28) are independent, and the second one is linear in the opimal fraction of capital used (w); therefore, we can solve for w; as follows: <!-- Start of picture text --> Vk(,L'kf)klAa<br><!-- End of picture text --> The optimal fraction of capital used in production (w) is increasing in the expected return and decreasing in the variance. The term in parentiesis in the denominator is the Arrow-Pratt measure of relative risk aversion.

Substituting (28) into (27), we get a differential equation for _V_ with boundary condition

**lim** **_VI(k4)ceP' =_ 0**

The solution for _V_ is given by where,

-30-
<!-- Start of picture text --> BX = E 1 + -iog(l-b) - 1<br><!-- End of picture text --> The consumption funcdon and optimal rate of utilizadon are given by We ensure that the utilization rate belongs to r0,1i by assuming **_ac_ c** **_a'._** Given optimal consumption and utilization rates, capital evolves according to Now, aggregate informal capital is To get the evolution of aggregate informal capital (A), we take expected values (over agents) in (31). Since the z, processes are independent, _E(4lid)_ =0. Hence, the growth rate j of the informal sector is given by Steady State In steady state infonnal agents want to switch to the formal sector whenever

# _V'(k,) s VF(i)_

or,

-31-
_g(0_ < P (33) where, Formals, in tum, want to move to the informal economy in the steady state when the inequality in (33) is reversed. Hence the rest of the analysis is the same as in the case of no uncertainty. The steady state (K) obtains when equation (33) is given with equality. As before, the key element that ensures the existence and stability of the steady state is te negative slope of g0J (Figure 1 also applies to this case). The new element here is that higher congestion also reduces the rate of capital utilization in the informal sector: When _a_<sup>_1_</sup> decreases because of a higher ,, uncertainty becomes relatively more important, thus lowering utility in the informal sector.

Using Figure 1, we note that when the production uncertainty increases (9 rises), the curve g(,) shifts to the left, thus decreasing P'. More uncertainty hurts the informal sector thus decreasing its relative size in steady state.

From equation (33) with equality, we can get an expression for /3, when ' > 0, Note dtat 70 is implicitly given by equation (34) when ,P =0; and as before, if 7<-r then j'=O.

The growth rate is given by the same expression as in the case of no uncertainty (equation 19), although the switching term is slightly different. The qualitative implication for growth and

-32-
welfare are similar to those of the simpler model.

# VI. CONCLUDING REMARKS

This paper studies the emergence of informal sectors and their impact on growth and welfare. We argue that the rise of informal sectors is a natural consequence of the restrictions imposed by governments on optimizing agents. An informal satus entails many disadvantages; namnely, inability to use the capital and insurance markets, lack of access to important public services, and propensity to suffer penalties and expropriations. Nevertheless, despite those disadvantages, some economic agents choose to become informal because the restrictions government imposes on them, by way of taxes and regulations, are overwhelming.

Economies with larger informal sectors are more inefficient because of the disadvantages inherent to infornality and because the loss of tax revenues hurts the provision of public goods and services. In this paper, we show that such inefficiency is reflected in low rates of return to all investmenit, stagnant growth, and suboptimal social welfare.

What explains government's socially inefficient behavior? It has been argued that such behavior can be explained by the inertia of bad laws, designed to meet the social needs of offier times and places. However, this explanation begs the question: what explains such inertia? We believe that bad laws, far from being removed, are put forward because they benefit groups in power. In this paper, we have identified such groups with government bureaucracy, which controls public services and has the power to expropriate capital from informnal agents. It thus follows that bureaucrats, having a vested interest in a large and growing informal sector, create the incentives for informality.

In reality, the bureaucracy is not the only interest group in society. Many groups would

-33-
like governmen **t** o legislate regulations on their behalf. As those special regulations are implemented, informal sectors, trying to avoid them, arise. With widespread informality, society at large suffers.

-34-