O
P. is related to the decrease in utility due to expete capital expropriation. The function
gOJ can be thoug,ht of as the difference in utilities before fines.
- -13-
. . ~ ~ ~ ~ ~ ~ ~ ~ ~ r
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) ? -
- @ 1 s zCe"-(l-s)] 1 .. ~~~~~(18)
EP~~~
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 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,
y (l = -T) cF-kF =Ea
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,
y- F= g(Pf)-Ab = -ALlog(1-b)+b] > 0
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 state-
Therefore, 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
V l= og(l -b) +b]
AZ C
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
=1 - - P>0
Substtuting forf' in the expression for cit
-16-
..~~ (l-ijP r
_F= e--t) (20)
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 (Trr9), 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 C>T, respectively. In both cases, for > 70, 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 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
:7 - .
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
W (k S VF((I'_a)k
or,
g(r) P (W)
where,
P' = P + plog(1-8)
< p
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
O 0r
13*= A E-1-)a 1 (/l
E(P1
where,
A
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.1' 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 j drawing Figures 4A and 4B, we assume that P' is positive. The analysis is the same if 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" 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.'5 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 0,
(1+C), = Ap[-(l-r) + 1-T)2 + 2;P$}] (34)
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 government to 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-
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Barro, R. (1990), "Goverment Spending in a Simple Model of Endogenous Grordth," Joural of
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Barro, R. and X. Sala-i-Martin (1992), "Public Finance in Models of Economic Growth," The
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Rauch, J. (1991), "Modelling the Informal Sector Formally," The Journal of Development
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Tanzi, V. and P. Shome (1993), "A Primer on Tax Evasion," International Monetary Fund,
Working Paper No. 93/21, March.
-36-
PIGURE 1
\r P
\~~~~~~~
I
bet* betx
FIGURE 2
'*1~~~~tn 11 ta
I~~~Iu
':~~~~~~~~~~~~~~~~~~~~~~~~~
FIGURE 3A
dphF
tauO t,- 1 tau
II
iIGUTRE 3B
I I
I I
taut tanO 1 ton
( , ~ ~ ~~~~~~~I\
FIGURE 4A
p
PR
L-- LImibda'b
beb' ba
FIGURE 4B
p
I la_)s*b
I I I g~~~~~~~~~ammd')
bet be".* beM2 beta
1
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