metadata: authors: 0: author: Loayza,Norman V.
docna: 0: docna: Labor regulations and the informal economy
docty: Policy Research Working Paper
subtopic: Economic Theory & Research,Rural Settlements,Industrial Economics,Labor Markets,Hydrology,Economic Growth,Agricultural Growth and Rural Development,Armed Conflict
teratopic: Finance and Financial Sector Development
abstracts: cdata!: The informal economy, which evades labor
            regulations, provides employment for much of the labor force
            in developing countries.  The author explores how labor
            regulations and imperfections in informal capital markets
            affect income inequality and the speed of industrialization.
            Empirical evidence shows that labor costs are higher in the
            formal sector, and that the cost of capital is higher in the
            informal sector (in part because many informal activities
            are illegal, so contracts are unenforceable).  The author
            develops a theoretical model based on such factor-cost
            asymmetry.  He applies it to an urban economy with and
            without ample supplies of labor from the rural sector.  The
            dynamic analysis considers rural-urban migration and optimal
            capital accumulation.  He finds the following.  First, labor
            regulations that mandate workers' compensation above
            its market-dictated level induce the formation of an
            informal sector and thus the dispersion of wages across
            homogeneous workers.  And labor regulations slow capital
            accumulation and retard the process of rural-urban
            migration.  Second, when capital allocation to informal
            producers becomes more efficient, the informal sector
            expands relative to the formal sector, the gap between
            formal and informal wages narrows, and rural-urban migration
            speeds up.  Finally, policies with an urban bias hasten
            rural-urban migration, inducing an expansion of the informal
            labor force relative to the total labor force.   Post-World
            War II experience in informal economies in Latin America
            motivates and in some respects supports the theoretical
            findings, says the author.
repnme: repnme: Labor regulations and the informal economy
display_title: Labor regulations and the informal economy
listing_relative_url: /research/1994/08/698097/labor-regulations-informal-economy
topicv3: Economic Growth m1326241 471,Informal Sector m1326258 1168,Water m1326522 137,Political Violence and War m1327310 2462,Rural Development m1504505 2667
publishtoextweb_dt: 2010-07-01T00:00:00Z
historic_topic: Finance and Financial Sector Development
origu: Development Economics and Chief Economist
no_of_pages: 50
author_keys: 0: author_key: 97109
model_extractions: I POLICY RESEARCH WORKING PAPER 1335

# Summary findings

The informal economy, which evades labor regulations, provides employment for much of the labor force in developing countries. Loayza explores how labor regulations and imperfections in informal capital markets affect income inequality and the speed of industrialization.

Empirical evidence shows that labor costs are higher in the formal sector, and that the cost of capital is higher in the informal sector (in part because many informal activities are illegal, so contracts are unenforceable). Loayza develops a theoretical model based on such factor-cost asymmetry. He applies it to an urban economy with and without ample supplies of labor from the rural sector. The dynamic analysis considers ruralurban migration and optimal capital accumulation. His findings: Labor rcgulations that mandate wvorkers' compensation above its market-dictated level induce the formation of an informal sector and thus the dispersion of wages across homogeneous workers. And labor regulations slow capital accumulation and retard the process of rural-urban migration.

* When capital allocation to informal producers becomes more efficient, the informal sector expands relative to the formal sector, the gap between formal and informal wages narrows, and rural-urban migration speeds up.

* Policies with an urban bias hasten rural-urban migration, inducing an expansion of the informal labor force relative to the total labor force.

Post-World War II experience in informal economies in Latin America motivates and in some respects supports the theoretical findings, says Loayza.

- - This paper a product of the Macroeconomics and Growth Division, Policy Research Department is part of a larger effort in thedepartmnentto studythe effects of regulation on inequality and economic growth. Copies of the paperare available free from the World Bank, 1818 H StreetNW, Washington, DC 20433. Please contact Rebecca Martin, room Ni 1-043, extension 39026 (46 pages). August 1994.

> _The Policy Research Working Paper Series disminates the findings of work in progess to encoumge the ezchange of ;da about development issus. An objrive ofthe series is to get he fwdings out icky. even if the presentations arn less than fully polished. Thc papers cay the names of the athors and sbould be usedand cited accordingly. The fmidings; interpretations, and conclusions are the ant ho 'own and should not be attributed to the World Bank its Exetive Board of L)wcstors_ **_o_** _r any of its member countries._

Produced by the Policy Rcsearch Dissemination Center
# LABOR REGULATIONS AND THE INFORMAL<sup>ECONOMY</sup>

Nornan V. Loayza The World Bank Address: The World Bank, N-11-039 1818 H Sreet, N.W. Washington, D.C. 20433 Phone: (202) 4584767 Fax: (202) 522-1151 JEL 011, 041, 054 Keywords: Growth, Regulations, Informal Economy, Rural-Urban Migration.

Many ta to Ale Alesina, Robert Barro, John Driscolil, Edward Glaeser, E. Somanathn, and participants in the Economic Gromwth- Workshop at Harvard UniverSity for helpful suggestions. I am speCially indebted to Debraj Ray and Jaune Ventra for many insightful discsions. Finaial support fom the Alfred P. Sloan Foundation is gratefilly acknowledged. 2 I.~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
# 1. INTRODUCFION

The formal sector is defined as the group of economic units that comply with regulations and taxes. By contrast, the informal sector evades onerous regulations but faces the disadvantages of working outside the legal system.

The informal economy, escaping labor regulations, provides employment to a considerable fraction of the labor force in developing countries. Tuirnham (1993) provides some estimates of informal labor employment for groups of countries at different stages of development. These are presented in Table 1. Informal employment declines in importance as the general level of development rises. However, it remains large even in high-income developing countries, in which it employs 31% of the labor force.

The present paper develops a theoredcal- model building over the asymmetry in factor costs evident in countries with informal economies: Whereas labor costs are higher in the formal sector, -for the informal sector capital is more expensive. Regulatons designed, in theory, to improve workers' welfare appear in various forms, namely, minimum wages, -finge benefits, social security, constraints on free hiring and dismissal, and-protection.to unions. Formal finns, because of their compliance with labor regulations, face higher labor costs. Portes, Castells, and Benton (1989) argue that "the best-known economic effect of the informalization process is to reduce the costs of labor substantially" (p. 30). Tokman (1992) writes that for small firms in Latin America, labor regulations augment labor costs by an average of around 20 percent, which is about equally divided between benefits and social securiiy contributions. Seturmnan (1981), after reviewing a series of studies in developing nations, concludes that the majority of -informalsector workers receive wages below the legal mnimum. The observed wage dualism is not

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explained by workers' skill differential across the two sectors; Fields (1990) writes that both tabular presentations and'multivariate analysis demonstrate,wage differendals for observationally equivalent labor' (p. 51).On the other hand, capital is more expensive to'informal producers. Broadly speaking, this is due to capital market imperfections which are exacerbated by some features of informal finns, such as small size, low physical capital intensity, and semi-illegality. As explained below, the present paper abstracts from issues regarding firm's size of operation and derives low informal sector capital intensity as a result of the model We argue that informal firms' seniillegal status, brought about by their evasion of labor regulations, worsens capital market imperfections facing them. Given.that informal activities are partially illegal, entrepreneurs can not exercise full property rights over them; therefore, contracts related to informal activities can not be properly enforced trough the judicial system. The inability to sign fully enforceable contac creates uncertainty and increases the transaction and monitoring costs in all business dealings conducted by informal finns. This applies especially to capital and financial markets. In his study of the Peruvian informal sector in 1985, De Soto (1989) reports that the average nominal borrowing rate for infonnal firms was 22% monthly, whereas for formal firms of comparable size, it was 4.9%. Huq and Sultan (1991) report that in Bangladesh informal firms paid rates between 48 to 100 %.annually for producidon loans, whereas the borrowing rate from commercial banks, for formal firms of similar characteristics, was around 12%.' The asymmnetry in factor costs across formal and informal sectors provides the structure of this paper. We _first_ analyze the static allocation of production factors across the two sectors that is consistent with a decentralized, full-employment equilibrium (Sections lII.A and M.B). We then develop a dynamic model in which the urban labor force grows through a rural-urban

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-

migration process, a la Harris and Todaro (1970), and capital accumulates according to an optimal program of savings and investment (Section III.).

Section II briefly analyzes the Latin American context in which informal economics arose in the post-Second World War period. Section IV offers some suggestions for future research.

# H. THE LATIN AMERICAN CONTEXT

In the post-Second World War years, Latin America experienced a remarkable demographic transformation. From 1950 to 1990, the proportion of the total population living in urban areas grew from about 40 to 70 percent. This tremendous expansion was mainly due to ttwo factors. The first consisted of improved medical and sanitation conditions in the cities, which led to high birth and low deati rates. The second, most important, factor was migration from rural areas. Table 2 presents some demographic indicators in Latin America. In Argentina, Chile, and Uruguay, which were already highly urbanized countries by 1950, urban population grew at a-pace similar to that of developed countries and reached more than 85% of total population by 1990. In other countries the process of urbanization occurred notably quickly: Brazil, Colombia, Mexico, and Peru almost doubled their respective shares of urban population in 40 years. Only in El Salvador and Guatemala, urbanization was slow during this period (Portes and Schauffler (1993)).

Rural-urban migration occurred because living standards, employment opportunities, and general economic conditions improved steadily in the cities relative to the countryside. The last column of Table 2 reports the average of the ratio of capital investment to GDP for the period 1950 to 1985. For Latin America as a whole, it was 17.4%. By far, most of this investnent

-~~~~~~~4
was allocated in the cities, thus creating jobs and better income opportunities in this areas. Interestingly, the lowest investment rates in the region are found in El Salvador and Guatemala, where urbanizadon was also sluggish.

Rural emigration was induced not only by capital formation in the cities but also by government policies that clearly favored urban over rural areas. Early in the post-Second World War period, the development strategy advocated by economists and followed by policy makers consisted of rapid urban industrialization. Urban-bias policies were gradually implemented to pull or push rural inhabitants to the cities to supply labor to the growing industrial sector. The UN Economic Commission for Latin America (ECLA) promoted thq model of import substitution industrialization, which advocated, together with high tariff protection and heavy state investment, domestic terms of trade that favored industry over agriculture (Portes and Schauffler, p. 34). Latin American governments embarked on numerous public projects; in the cities, including the construction and furnishing of schools and health faciiiies and the provision of electricity, water, and other utilities. F rthermore, roads and other means of tansportation were improved or constructed to facilite rural emigration to the cities (Williamson (1988)).

The disruption of international trade by World War I, the Great Depression, and World War II created dissatisfacdon with _Laissez-faire_ economic policy in Latin America. Populism and its associated movements responded to this discontent with strong state intervention in the economy. Several populists movements and leaders were formed in the Inter-War period, among them, Haya de la Torre and the American Popular Revolutionary Allianice (APRA) in Peru in the 1920's, and the Chilean Socialist Party in the 1930's; and in the 1940's, Juan Domingo Per6n and the Peronist Party in Argentina, Jorge Eliecer Gaitin in Colombia, and R6mulo Betancourt and Democratic Action in Venezuela. These leaders, their foilowers, andlor their ideas atained
power in their respective countries at several points in the "heyday" of populism from the 1930's to the 1960's and less strongly in the 1970's and 1980's (Drake 1991).1 Table 3 presents some populists episodes in Latin America during this period.

Populist policies sought to control the economy by means of direc. intervention or regulations. Prominent among the latter were labor regulations. Cardoso and Hehwege call minimum wage policies "the redistributive centerpiece of populism" (p. 68). Rather extensive labor legislati6n codes were enacted to purportedly further workers' welfare. These regulations, by effectively raising labor compensation above its market-dictated level, diminish the incentives for the industrial sector to provide work to the growing numbers of city inhabitants. Cardoso and Helwege conclude that "As the cornerstone of populist redistribution, minimum-wage increases promoted the welfare of relatively small groups at the expense of larger groups" (p. 62). As result of the state-induced excess labor supply in the cities, an informal sector, which evaded labor regulations, rose to give work to the masses of people for whom unemployment was not a viable option: "... informality represents the irruption of 'real' market forces in an economy straijacketed by mercantilist regulation."<sup>2</sup> The ILO's Regional Employment Program for Latin America and the Caribbean (whose Spanish acronym is PREALC) provides estimates of the urban informal labor force for virtually every country in Latin America. Given that most informal activities, _per se,_ are not recorded in official statistics, measuring informal production and labor force is very difficult Table 4 presents PREALC's estimates for 14 Lafin American countries for the years 1960, 1970, 1980, 'One exception to the waning of populism from the 1970's is the Alan Garcia administration in Peru from 1985 to 1990, which almost -brought the country to an economic and political collapse.

2Portes and Schauffler, p. 40, paraphrasing Hemando de Soto's view of informality in his book _The Other Path._

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and 1989. PREALC's estimation methodology presents serious shortcomings and inconsistencies, the most important of which is the exclusion of wage workers from early estimates.<sup>3</sup> For what is worth, Table 4 reveals a significant constancy of the proportion of urban informal workersover the last 3 decades, despite the tremendous changes, concerning industrialization and demographic transformation, experienced in Latin America.

The post-Secoiid World War Latin American experience with informnal economies motivates this study. Its pupose is to integrate and understand the relations between the most important features of the informal experience, namely, strong labor regulations, capital market imperfections, capital formation, and rural-urban migration. We want to understand the effects of labor regulations and informal capital market imperfections on income inequality, proxied in the model by the dispersion of urban wages, and the speed of industrialization, proxied by both capital accumulation and urbanization.

# III. THE MODEL

# A. THE ISOLATED URBAN ECONOMY

The urban economy is competitive and decentralized, witi firms hiring production factrs from their owners. All firms produce-one good (Y), which can be equivalently used for consumption or investnent. Firns share a basic production technology, which has the 3PREALC's estimaon strategy consists of identifying informal employment with entire occupational categories available from national censuses and household survwys. PREALC his consistently classified the self-enployed -excluding professionals and technicians- and remunerated family workers as informal workers. Only in early estimates, domestic servants were also included. In recent estimates (1989), owners and salaried workers of "small entlerprises" (whose size definiton change! from country to country) have been classified as informal workers. The exclusion of wage workern; in early classifications introduced a strong downward bias in the esfimates.

-.

**-7-**
neoclassical characteristics (namely, constant returns to scale, decreasing returns to each factor, and the Inada conditions) and the property that production factors are complementary to each other. For simplicity we assume that the production function is Cobb-Douglas and that capital (K) and labor (L) are the only factors of production. Output production is then given by _Y =_ **_AK-UL,_** Ocacl (1) Labor-market regulations are represented by the imposition of a minimum legal wage rate. Firms that obey the minimum wage legislation belong to the formal sector. Firms that ignore it belong to the informal sector. Fims cannot belong to both sectors at the same ime. -The illegal saus of informal firms makes contractual agreements more difficult and costy, especially in capital and financial markets. Because of additional monitoring and transaction costs, informal firms face a higher cost of capital than their formal counterparts. We modelt dse (per-unit) additional capital costs as proportional to the market-determined net rental rate of capitl. Capital owners receive the same nete rentl rare from either sector and, thus, are indifferent betwe the two.

# Formal-and Informal Sectors in an Isolated Urban Economy

At a point in time, the aggregate levels of labor and capital in urban areas are given. This is so because in the case of an isolated urban economy both labor and capinl grow gradually. The static solution consists of the market allocation of given urban aggregate labor and capital-across the formal and informal sectors.

4Clearly, net of monitoring and tansaction costs.

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(2) Profits for formal firm i are given by where W is the minimum legal wage rate, and R is the market-determined net capital rental rate<sup>5</sup> .

Profits for informal firm j are given by where WI is the market-deternined informal wage, and the parameter j, **p>** 1, is the factor of proportionality due to transaction and monitoring costs. This parameter measures the degree of inefficiency in capital allocation to informal firms.

Since the production technology is constant returns to scale, the size of firms in the economy is indeterminate. Finns in each sector choose the ratio of physical to human capital that maximizes their profits. There is one such ratio for all firms in the formal sector and another one for all firms in the informal sector. Because of this, in what follows we use subscripts to differentiate firms across sectors but not within each sector.

We now characterize the equilibrium situations for different levels of the minimum legal wage (W), _ceteris paribus._ There are three cases to be considered. First, the minimum legal wage is not binding so that only the formal sector exists. Second, the minimum legal wage is binding but not "too large" (as explained below) so that the formal and informal sectors coexist in 5We normalize the factor of proportionality due to monitoring and transaction costs to 1 in the formal sector. Therefore, the capital rental rate paid by formal producers is equal **to** the net rental rate received by capital owners.

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the economy. And third, the minimum legal wage is so large that the economy is completely informal.

**First case: The minimum legal wage is not binding.** In this case, the market wage with full employment in the formal sector is higher than the legal minimum. That is, since no worker will accept a wage lower than the market wage, **the whole economy is formal.** Profit maximization by firms, the zero-profit condition under perfect competition, and full-employment equilitrium determine the market wage rate (Wp) and the net capitl rental rate (R):

where, MPL) and MPKF denote the marginal products of labor and capital, respectively, in the formal sector; and K/L is the urban aggregate capital-labor ratio.

**Second case: The minimum legal wage is binding but not "too large."** In this case the minimum legal wage is higher than the unregulated market wage<sup>6</sup> . That is,

However, **the** minimum wage is not so high as **to** force **the** whole economy **to** be infornal. In this case, under full-employment equilibrium, the **formal and** the **informal sectors**

> **6The** unregulated market wage is the wage obtained in the absence of the minimum wage regulation.

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# **coexist** in the economy.

Profit maximization by firms, the zero-profit condition, and full-employment market clearing dictate the following equilibrium conditions. In the formal sector, <!-- Start of picture text --> MPLF Aa() =w<br>MPKF = A(1 -a)R , R<br><!-- End of picture text --> And in the informal sector, _MPL=_ **_A{m)_** w **_(8) MPKj,_** _A(1-a)()_ **_=(_** The minimum legal wage rate plays a pivotal role in the deternination of the net capital rental rate and the informal wage rate because it fixes the capital-labor ratio in die formaF-sector. From (6), <!-- Start of picture text --> KF = *~(10)<br>LF IAzJ<br><!-- End of picture text --> Equation (10) shows that KF/HF depends positively on the minimum wage (W) and negatively on

*-11-
# the productivity parameter (A).'

We can express **the** net capital rental rate as a function of the minimum wage rate by substituting (10) into (7):

**R= A(1-a)lmwaf)** _I_a wl'1_

Clearly, the net capiml rental rate is negatively related to the minimum wage.

Given **that** the cost of capital in **the** informal sector is equal to a fuxed proportion of that in the formal sector, the ratio K1/Ll is a fraction of the ratio **KF/LF.** Dividing (9) by (7), Then,

**_K/L_** 5_ () **_K,ILF K, KF_** _(13)_ **_LI L,_**

> 7Given that the minimum wage is binding, the inequality in equation **_(5)_** applies. Using the expression for KF/LF in equation (10) together with the inequality in (5), we find

**_K_** _KF_ **_L_** _LF_

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The informal sector is less capital intensive than the formal sector' because the former faces a higher cost of capital.' Clearly, the relative informal capital intensity varies inversely with the parameter t.

Since K,/L1 is determined by KF/LF, we can express tie informal wage rate as a funcdon of the minimum wage rate. Substituting (12) and (10) into (8), Clearly, the informal wage is lower an the legal minimum. This, of course, is consistent with the minimum wage being binding. The smailer wage in the informal sector is due to the sector's lower capital intensity. The informal wage increases with the legal minimum legal at a rate lower than one.

Full employment of production factors allows us to determnine the actual quantities of formal and informal Labor and capital. Using the definition of -y as the ratio of capital intensities in the two sectors (equation (12)), we can write <!-- Start of picture text --> K.<br><!-- End of picture text --> 'Note that lower capital intensity in the informal sector is consistent with KIL C KFILF under conditions of full employment In fact, since full employment means that K = KF + K, and L _=_ LF + L1, it follows from KIL c KF/L that 'Had we considered a more general specification for the additional capital costs fced by informal firms, a larger minimum wage would have reinforced the higher capital intensity in the formal sector.

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Given that K = KF + K1 and L = LF + Li, and substituting the expression for KF/LF from equation (10), the above expression can be manipulated to obtain Equation (15) provides expressions for LF and LI in terms of W, y, and the urban aggregate levels of labor and capital. An analogous procedure would allow us to find expressions for KF and K1: Equation (15) (or (16)) allows us to see how the coexistence of both sectors in the economy requires that, for given L and K, the legal minimum wage be in between two limiting values. The lower limit W' is the value at which the minimum wage is just binding. Then, Note, from equation (15), that when W is equal to W', LF is equal to L (and KF is equal to K). That is, at the lower limit W', the economy is still completely formal.

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The upper limit W' is the value at and above which no firm can afford to pay the legal wage while paying the competitive rental rate of capital. In fact, when W is equal to W", LF is equal to zero, and LI is equal to L (also **KF** = **0,.** K, = K). That is, at the upper limit Wm, the economy starts to be compktely informal. From equation (15), we can determine Wt: Note that W" varies inversely with -y.

Equations (15) and (16) were developed under the conditions that create an equilibrium where both formal and informal firms are present in the urban economy. It is, therefore, not surprising chat they make no sense when W is lower than W' or higher dtan Wt.

Let us examine how labor and capital in each sector respond to changes in the aggregate levels, for a given minimum legal we.

Suppose that the miimum legal wage is fixed at some level. Also, suppose th aggregate capital is constant. Figure 1 graphs L and L, as functions of L (for given K, W, -y) and K (for given L, W-, y). Let us focus on changes in urban aggregate labor (L). For small enough values of L, the minimum legal wage is not binding, and, therefore, L is equal to L; that is, all labor and capital are formal. As L increases beyond the threshold point L', L1F decreases, and therefore L1 rises faster dtan L. This continues until L is so large (relative to K, of course) that there is no longer an equilibrium in which L$ can be positive (from point L" on), and the whole economy is informal.

Consider only the region where-both sectors coexist so that equation (15) applies. Given that the wage and rental rates are fixedby the minimum legal wage, when L or K change, the economy acommodates by adjusting the relative sizes of the two sectrs. From (16), we can

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calculate the partial derivatives of LF and L, with respect to L: Labor employed in the informal sector increases more than proportionately to the increase in urban aggregate labor, and, thus, formal labor decreases. This can be explained as follows: An increase in urban aggregate labor makes the minimum wage more restrictive, in the sense that it becomes further above the unregulated wage. This induces an expansion of the relative size of the informal sector. Given that aggregate capital is constant and the capitSl-labor ratio in the informal sector must remain unchanged, such expansion is attained through a shift of capital fron the formal to the informal sector. Therefore, since the formal capital-labor ratio must also stay unchanged, formal labor decreases along with formal capital.

The effects of capital stock changes on the relative size- of both sectors can be analyzed analogously.

Third case:- The minimum legal- wage is so high that **ail** firms are informal. If the legal minimum wage is too high (W > W"), the equilibrium tiat allows formal and informal finns to coexist breaks down, and the only market-clearing solution is for all fums to be informal.

Profit maximizaton by firms, the zero-profit condition, and full employment equilibrium determine the market wage rate (W) and the net capital rental rate (R):<!-- Start of picture text -->
-16-<br><!-- End of picture text -->
The informal wage is now the same as that when the economy is completely formal. This is so because now the informal wage is also dictated by the relative scarcities of urban aggregate capital and labor. However, the net rental rate of capital is now smaller because the additional transaction and monitoring costs decrease tie value of capital.

# Comparative Statics

We now present a graphical exposition of the wage and net capital rental rates, as well as relative'<sup>0</sup> sector employment, in the three cases analyzed above. In the graphs, the subscript"UNR is used to denote the unregulated wage and capital rental rates, that is, te competitive rates that will occur in the absence of a minimum legal wage.

Figure 2 shows the wage and net capital rental rates, as well as relative labor employment, as functions of the miniimum legal wage, holding 7y and KIL constaft.t Figure 3 allows the informal capital allocation efficiency parameter y to vary, holding "'Throughout this paper, "relative" employment refers to employment relative to total employment in the urban economy. For instance, relative informal labor is L/L.

1 1Figure 2 shows the informal wage not jumping when the economy becomes completely. informal. That WI is continuous at W" can be proven by substituting W' (equation (18)) into the *formula for _WI_ when the two sectors coexist (equation (14)). By doing that, we obtain the same value for W1 as when the whole economy is informal (equation (20))..

By the same token, Figure 2 shows the net capital rental rate not jumping either when the economy moves from complete formality or when it becomes completely informal. Similararguments as for _WI_ can be made to prove that R is continuous at both.W' and W". Figure 3 implies a similar analysis

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_KIL_ constant and W at a given binding level. Note that when the additional capital costs to informal producers are sufficiently low (that is, -y >y"), the whole economy is informal.

Figure 4 allows the aggregate capital-labor ratio to vary, holding y and W constant.

# Conldusions and Policy implications (applied mainly to the niixed economy case)

1. The formal sector is more capital intensive than the aggregate economy, which in turn is more capital intensive than the informal sector.

2. When the minimum wage is increased because, for instance, government pursues populist policies to benefit the core of formal unions,

- a. Although the informal wage increases, the gap between formal and informal wages widens.

- b. The net capital rental rate decreases.

- c. The informal sector expands and the formal sector shrinks.

3. When the additional capital costs to informal producers diminish because, for instance, capital subsidies are- provided to informal firms or the informal sector develops a control and enforcement system that cuts down their transaction and monitoring costs,

- a. The informal- wage rises, and the gap between formal and infornal wages narrows.

- b. The informal capital rental rate decreases, approaching the net capial rental rate obtained

when no minimum legal wage is imposed.

- c. The informal sector expands and the formal sector shrinks.

4. As aggregate capital decreases relative to labor because, for instance, there is capital flight or labor immigration,

- a. The relative size of the informal sector rises. If only one aggregate factor changes, we can predict the absolute size of either sector. For instance, when labor imniigration occurs and the

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capital stock remains constant, the absolute size of the informal sector rises whereas the absolute size of die formal sector shrinks.

b. The wage and rental rates remain unchanged, not reflecting the relative scarcities of production factors.

# B. THE URBAN ECONOMY IN THE PRESENCE OF A RURAL SECTOR

**Rural-Urban** Migration Equirbrium

Assume that in rural areas the production technology does not require capital and is linear in labor (Lewis (1954)). That is,

**_Y=_** _BLR_

. (21) In the absence of government intervention, the rural wage (WR) is equal to the productivity parameter B.

There are no migration costs and there is complete turnover of workers in the formal and frlormal sectors. '<sup>2</sup> Therefore, all workers face the same migration decision, which considers only current wage opportunities in urban and rural areas. The migration equilibrium condition we use resembles that introduced by Harris and Todaro (1970). Assume that workers are risk 12We relax the assumption of complete job -tnover in the formal sector in Appendix A. We show that allowing for partial job turnover does -not change the qualitative results presented in the txt. Also, we show that the more accessible the formal sector to all workers, the higher the urban labor force and the relative size of the informal sector.

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neutral.'<sup>3</sup> Then, the migration equilibrium condition is given by

**_WE.- Alf_** _WR_

(22) where, M represents the per-period wage adjustment due to different cost of living in the cities; and WE is the urban expected wage. The assumption of complete job turnover in the cities implies that WE is equal to a weighted average of fonnal and informal wages with the weights given, respectively, by the relative size of the each sector.

Given that we allow the possibility of inmmediate labor relocation across the two areas, the equilibrium condition in (22) must hold at all times.'<sup>4</sup> Urban Formal and **Informal** Sectors with Ample Supplies of Labor from Rural Areas When in urban areas a binding, but not "too large," minimum legal wage is imposed, both formal and informal sectors arise in the economy.'<sup>5</sup> The analysis presented in the previous section for the mixed economy case applies, under the conditions outlined below, in the presence of a rural sector. In partcular, equations (6) to (16), which determine the informal wage and capital rental rates and the relative size of each sector, -still hold true.

"3Te Assumption of risk neutrality is -not necessary for the analysis but is algebraically convenient for the purpose of comparative statics. We are not interested in describing the effects of risk aversion on migration decisions.

> **_14In_** Harris and Todaro (1970), migration is a disequilibrium phenomenon. It occurs when the expected urban wage is higher than the rural wage. Implied in their analysis are migration costs that preclude the possibility of immediate relocation of labor from rural to urban areas (infinite migration rate). Therefore, in their model, the migration equilibrium condition is achieved only in the long run:

I"The range of minimum legal wages that produce the coexistence of both sectors is given below.
As explained shortly, in the presence of a rural sector with ample supplies of labor, the level of the labor force in the cities is no longer autonomously given; it is in fact a function of tle capital stock, ihe minimum wage, the additional capital costs to informal producers, and the adjusted rural wage. Therefore, equation (15), which determines the size of formal and informal sectors, must be rewritten to account.for the dependence of the urban labor force on those other variables.

Using equations (14) and (15.)t we find that the average wage in urban areas is a linear function of the urban aggregate capital-labor ratio: Substituting the expression for the urban average wage into the midgraton equilibiium condition (equation (22)), we find Equation (24) detrmines the size of the urban labor force that is consistent with migration equilibrium. The size of urban aggregate labor is increasing in the capital stock and

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the efficiency of informal capital allocation (-y), and decreasing in the adjusted rural wage (W1t+M). Furthermore, the size of the urban labor force when the whole economy is formal.is the same as when the economy is completely informal (L(W <W') = L(W W")). This is so because in both cases the urban wage equals the adjusted rural wage (as explained below). It can also be shawn that the size of urban aggregate labor in those two cases is always greater than when the economy is partially informal.'<sup>6</sup> Substituting equation (24) into (15) we find the relative size of fornal and informal labor employment in the presence of a rural sector: <!-- Start of picture text --> F= (1)(WRF M X<br>(25)<br>L l- J - - W:<br><!-- End of picture text --> As expected, the relative size of the informal sector increases with the minimum legal wage (W) and the efficiency of informal capital allocation (y), and. decreases with the adjusted rural wage (WR+M). The effects of changes in W, 'y, and WR+M. on the absolute size of formal and informal sectors go in the same direction as the effects on their respective relative sizes. This is not obvious, as it was in the case of an isolated urban economy, because of the additional effects of those parameters on the urban labor force.

In order for the urban economy to present both formal and informal sectors, the minimum legal wage must be between the values W' and Wn. The lower limit W' is the value at which the

> 161n fact, the size of the urban labor force, _ceteris paribus,_ first decreases, reaches a minimnm, and then increases with W.

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minimum wage is just binding (Lp/L I in equation (25)): (26) W _W+ M_ Note that W' is the unregulated urban wage in the presence of surplus labor from rural areas.

The upper limit W' is the value at which the economy just becomes completely informal (LF/L = 0 in equation (25)): Note that when W = W", the informal wage is equal to the adjusted rural wage (WI - WR+M), which, again, is the unregulated urban wage in the presence of surplus labor.

The graphical presentation used in the case of an isolated urban economy can also be applied here. The only change is that the unregulated rates, as well as the lower and upper limits W' and W", are now given in terms of the adjusted rural wage (WR+M).

Condusions and Policy **Implications** (applied mainly to the mixed-economy case)

1. Conclusions 1, 2, and 3 of the isolated-urban-economy case also apply here.

2. As aggregate capital decreases because, for instance, there is international capital flight or capital destruction, a. The absolute size of the urban labor force, as well as both formal and informal labor employment, decreases.

b. The respective relative sizes of formal and informal labor remain the same.

3. The size of the urban labor force in the cities at any point in time is no longer autonomous

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but varies directdy with the capital stock and the efficiency of Informal capital allocation, and inversely with the adjusted rural wage. Also, the size of the urban labor force in the absence of minimum wage regulations is greater than when they are imposed.

4. As the adjusted.rural wage (WR+M) decreases because, for instance, government follows an urban-bias policy through worsening the rural-urban terms of trade or improving public infrastructure and services in the cities, a. The urban labor force rises.

b. The relative and absolute size of the informal sector expands.

# C. DYNAMIC BEIHAVIOR OF THE ECONOMY: CAPITAL ACCUMULATION AND

# RURAL-URfBAN MIGRATION

The aggregate labor force and capitl stock in urban areas change through time, thus affecting the size of the fonnal and informal sectors. The -labor force in the cities expands by means of a rural-urban process of migration, and the capital stock grows according to a program of savings and investnent

# Capital **Acculatiou**

We assume that there are two different groups of individuals: Workers and capitalists.

Workers supply labor inelastically and do not save or borrow.<sup>17</sup> Capitalists do not work but '<sup>7</sup> hi reality this assumption means that workers' desired level of current consumption is higher than their wage. However, because of financial market imperfections, they are unable to obtain loans against their future higher income. Therefore, workers are constrained to consume only all their current wage. As we indicate iater, given that we are abstrating from technological progress, workers' wage converge to a finite value. If such value is below their desired income and they are

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rent out their capital to firms, and they save according to an optimal intertemporal program.

These assumptions amount to a version of Kaldor's model of distribution (Kaldor (1956), Alesina and Rodrik (1991)).

Normalize the size of the group of capital owners to 1. Capitalists solve the following

# dynamic program:

_Max fe_ **_fln(CQ )dt_** (28) **0**

# subject to

<!-- Start of picture text --> K(t) = R(t) K(O - C(t) t9<br><!-- End of picture text --> where C represents instantaneous consumption by capitalists and p is the subjective rate of time preference. The capital depreciation rate is assumed to be zero. The assumption that the instantaneous utility function is logarithmic proves to be very convenient, as we show shortly. Maxinization of discounted intertemporal utility in (28) subject to the instantaneous budget constraint in (30) implies the following necessary and sufficient conditions: <!-- Start of picture text --> C(t) = R(t) - p (30)<br>-IAR.)dv .(31)<br>lim K(t)e ' =3O<br><!-- End of picture text --> unable to use financialr markets, workers will never save or b -xrow.

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Equation (30), the Euler equadon, gives consumption growth as a function of the net capital rental rate. Equation (31), the transversality condition, ensures that not Htoo much" is saved.

The budget constraint, the Euler equation, and the transversality condition allow us to solve for the level of consumption as a function of the capital stock: _C(t) = p K(i)_ (32) The propensity to consume out of capital is equal to p, a constanL" Using the Euler equation, we obtain <!-- Start of picture text --> Kt) = C(t) = R.t)-p (33)<br>K(t) CQt)<br><!-- End of picture text --> From previous sections we know that as long as the urban economy is mixed (formal/informal), the capital rental rate is detennined by the minimum legal wage (W), as in equation (11). Given that we keep W fixed throughou **t** his analysis, the capital rental rate is also 18Had we used a general constant relative risk aversion (CRRA) utility function, the level of consumption would also have been a linear function of the capital stock. However, the propensity to consume out of capital would not, in general, have been a constant but a function of the entire future path of capital rental rates. This would have complicated the analysis since the path of rental rates depends on whether and when the future economy is partially or completely formal, which in tum depends-on the rate of capital accumulation. We conjecture that if the coefficient of relative risk aversion **_(0)_** is lower than 1, there exists a unique.equilibrium path for the capital stock. However, if 0> 1, the trajectory of the capital stock will present multiple equilibria because of the feedback effect of the rate of migration on the rate of capital accumulation. This feedback effect works as foflows: When a higher rate of migration occurs, rural areas are depopulated faster. After the rural sector is completely depopulated, the economy gradually becomes more formal. In a completely formal economy with capital accumulation, the rental rate gradually decreases. When 0>1, a lowering of the path of future rental rates leads to higher savings and capital accumulaion. This in tum produces a higher rate of migration, and the feedback chain s again.

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fLxed for as long as the economy is partially informal. Let's call this fixed level of the capital

# rental rate Ro.

## a

We assume that capiitlists are sufficiently "patient' so that R - p > 0. Therefdre, the economy's capital stock will grow at a constant rate for as long as the economy is partally infonnal.

Rural-Urban lMiration as the Result of Capital Accumulation and a Gradually Implemented

# Urban-Bias Policy

The migration equilibrium condition in (24) establishes a relationship betwee capitl acumulation and ural-urban migration. Taldng logs and then time derivatives in (24), we find

**_L._** _dlng(WOt+M,W,y)_ j _L dt K_ (34) **_K_**

The labor force in the cities will grow faster than aggregate capital for as long as the function g(.) increases over time: +(t) > 02' The implementafion of urban-bias policies can be represented -in our model by an exogenously-induced inrease in the finction g(.), through a decrease of the rural wage (Wi) and the cost-of-iving adjustment paramt (M).

"9In the text, we assunme that the urban labor force grows only through immigration. If urban population grows autonomously (that is, through births and deaths) at the rate n,, the<sup>rate of</sup> ilmmigration m will be given by

* ± **_K_**

There will be rural-urban migration as long as n. is not too large.

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Therefore, as long as the urban-bias policies are strengthened, the labor force in the cities grows faster than the capiial stock.

Urban policies are eventally curved and made stable. When the rural wage and the costof-living adjustment remain stable, the model predicts that the urban labor force grows at the same rate as the capital stock.

Dynamic Behavior or the Economy We- can now integrate the results from the previous two sections with those from capital accumulation to characterize ihe dynamic behavior of the economy. We can describe three phases in trms of the relative size of the informal economy.

First Phase: Expansion of the Relative (and Absolute) Size of the Informal Sector.

During this phase, urban-bias policies are gradually implemented: 0(t) > 0. Since capital grows at a constant rate, the urban labor growdt is given, from equation (34), by _L(t)_ -) _= (1|() + Ro_ -P(3a 3a

Clearly, the urban labor force grows faster an the capital stock. This decrease of the urban aggregate capital-labor ratio-produces, from equation (15) (or (25)), an expansion of the informal labor force relative to the urban aggregate.20 Urban-bias policies are curved before the rral sector is completely depopulated. When both the rural wage and the cost-of-living adjustment are no longer decreased but kept stable, the economy enters its second phase.

2DWe assume, however, that the economy remains mixed. This is true if the adjusted rural wage is not reduced too much (see equation (27)).

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## **Second Phase: Stability of the Relative Size of the Informal Sector.** When the

adjusted rural wage is stable, the urban labor force grows at the same rate as the capital stock: _A* = P-_ (34b) As long as there are workers left in the rural sector, the urban capital-labor ratio remains constant in **the** face of capital accumulation. From equation (15) (or (25)), this implies that the relative size of the informal sector remains unchanged.

If autonomous populadon growth in rural areas is not very large, and given that the flow of migrants to the cities is rising2' in this second phase, eventually, rural areas will be completely depopulated'. V/hen tis happens the economy enters its -third phase. Note that the greater the pool of rural workers, the larger the phase in which the relative size of the informal sector is stable.

**Third Phase: Contration of the Relative (and Absolute) Size of the Informual Sector and the Emergence of a Purely Formal Economy.** At the start of this phase the rural sectr has disappeared; and therefore migration and, thus, urban labor-force expansion have come to a halt. Then, the analysis of the isolated urban economy (Section **III.A)** applies to this phase.

During the early periods, the formal and informal sectors coexist. The capital stock accumulates at the constant rate R. - p; therefore, the aggregate capital-labor ratio steadily increases. From equation (15), this implies that the relative (and absolute) size of the informal "<sup>1</sup> Clearly, **the** flow of migrants is given by

# _L(t)_ = (Ra-p)L(t)

This is due, among other things, to the assumed rural liner technology. More realistically, if the rural wage increases fast enough as workers migrate to **the** cities, the rural sector will never be completely depopulated.

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sector shrinks until it disappears completely when the ninimum legal wage is just binding.23 When the economy is completely formal, capital accumulation produces a decrease of the capital rental rate, reflecting the relative scarcity of labor. Capital growth slows down as the rental rate approaches the subjective rate of time preference (p). Given that we have abstracted from exogenous technological progress and autonomous population growth, the steady state is characterized by zero economic growth.

Figure 5 graphs various quantities and rates during the three phases of the economy's dynamic behavior.

Conclusions and **Poliey** Implications.

1. Urban-bias policies accelerate the process of rural-urban migration at the cost of increasing the relative (and absolute) size of the informal sectDr and, therefore, lengthening the time the purely-urban economy takes to become completely formal. (See Appendix B for a detailed description of the length of transition to complete formality.)

2. In the absence of urban-bias policies and for given minimum legal wage and efficiency of informal capital allocation, the relative size of the informal sector remains constant in the face of 'We can show that at the time the flow of migrants stops, the minimum wage is binding in the sense that it is greater than the unregulated wage for the isolated urban economy. This unregulated wage is given by <!-- Start of picture text --> A - ( As( WR+M a(W$'<br><!-- End of picture text --> Given that the minimum wage was binding in the presence of a rural sector, we know that W > WR + M. Using this inequality, as well as the expressions for a0 and a, from (23), we find that <!-- Start of picture text -->
*Wu < A  {?)  -a1 =-W<br><!-- End of picture text -->

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capital accumulation. This is so because the urban labor force grows (through immigration) at the same rate as capital does to maintain the expected equality of wages across urban and rural areas.

3. When the minimum legal wage is increased, the capital growth rate falls, inducing a decrease in the growth rate of the urban labor force. A rise in the minimum legal wage delays the time to complete the rural-urban migration process and slows down the transition to a purely formal economy.

4. When the efficiency of informal capital allocation improves (-y increases), the process of rural-urban migration is completed faster but at the cost of delaying the next stage, in which the formal economy expands. This is so because an improvement of informal capital allocatioA induces informality. Nevertheless, as concluded in previous sections, a rise in -y brings the informal wage closer to the formal one.

# IV. EXTENSIONS FOR **FUTURE** RESEARCH

We believe that the theoretical analysis in this paper should be extended along the -following, two directons. The first one is to examine the welfare implications of informal economies and, therefore, the welfare effects of our various policy parameters. This could be done using the approach oudined by Sen (1974), which considers not only the average level'of income but also a measure of inequality. The second extension is to allow for endogenous determination of the minimum legal wage through the formation of coalidons. If the minimum legal wage is updated to satisfy some collective purpose, there exists the possibility of partial' economic informality in the long run.

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