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Informal sector in general equilibrium: welfare effects of trade policy reforms
International Review of Economics and Finance 10 (2001) 289 – 300
Informal sector in general equilibrium: welfare effects of trade policy reforms Saibal Kara,*, Sugata Marjitb,c a
Department of Economics, 5th Floor, Zulauf Hall, Northern Illinois University, De Kalb, IL 60115, USA b CESP, Jawaharlal Nehru University, New Delhi, India c Centre for Studies in Social Sciences, Calcutta, India Received 12 July 2000; received in revised form 28 November 2000; accepted 14 December 2000
Abstract The paper demonstrates the welfare effects of trade policy reforms in a general equilibrium framework, in the presence of an informal sector in the economy. The methodology we developed in the paper allows us to use a full-employment model with wage differential. Tariff cuts in this model have ambiguous effects because of the preexisting wage differential and due to the cross-effects in the three-good structure, which is used in some recent works in trade theory. Complementarity in production may lead to negative welfare effects despite improvements in terms of trade. D 2001 Elsevier Science Inc. All rights reserved. JEL classification: F11; F13 Keywords: Informal sector; Trade reform; General equilibrium; Welfare; Complementarity
1. Introduction Theoretical and empirical policy research in international economics addresses crucial questions about structural adjustments, both in the real and in the financial sectors of the developing economies. Among these, the theoretical papers in trade deal with the use of trade policies, tariffs or tariff equivalents to improve national welfare, appropriately defined. Here * Corresponding author. Tel.: +1-815-753-1363. E-mail address: [email protected] (S. Kar). 1059-0560/01/$ – see front matter D 2001 Elsevier Science Inc. All rights reserved. PII: S 1 0 5 9 - 0 5 6 0 ( 0 1 ) 0 0 0 8 8 - 0
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we address, how the consideration of informal sector, an area scarcely dealt with in a pure general equilibrium framework, works with more generalized applications of some of the basic theories related to trade policy. A survey of the literature reveals that, so far, considerations of the urban informal sector have been embedded in the rural–urban migration models of the traditional Harris–Todaro (henceforth, H–T) type. Gupta (1993), for example, considers a three-sector static model of a small open economy, with wage and employment determined endogenously in the informal sector. The hypothesis that rural migrants expect to get a job in the urban formal sector with some probability ‘l’, holds in these models, although, some of the subsidy policies in this structure run counter to those generated by the original model. The problem with these models is that, informal sector offers a wage that has to be lower than the rural wage, because the weighted average of formal and informal wages equals the rural wage. We argue that the poor laborers, moving freely between rural and urban centers, cannot afford to remain unemployed while expecting higher earnings only in the future. They form instead what is known as the urban informal sector, where they earn less than the urban formal wage rate. However, with free mobility of labor between the urban informal and the rural sectors, there is high probability that informal wage is closely related to the rural wage. Accordingly, in our model, we consider them equal. We capture these characteristics in a full-employment general equilibrium model. Subsequently, we wish to check the welfare implications of the trade policy reforms. With this view, we define a welfare parameter and see how it changes when trade policy reforms are introduced at various levels of the economy. In the existing literature, welfare implications of the trade reforms, with the informal sector as an important part of the economy, have not come up for much discussions so far. Leaving out the informal sector fails to capture the actual impact of such policy reforms, because, on an average, about 70% of the labor force in the LDCs belong to the informal sectors. Data from Southeast Asian, East European, African, and Latin American countries show varying rates of urban informal sector employment with a range going up from 15% to 20% in Turkey and Slovakia to 80% in Zambia, or even more, to about 83% in Myanmar. Moreover, considering the state of agricultural and rural activities in these countries, it is quite apparent that the total share of the informal sector in the economy as a whole would be very high (International Labour Organisation (ILO), 1999). This is also corroborated by some of the other studies, like that by Turnham (1993), which provide evidence that in low-income countries like Nigeria, Bangladesh, Ivory Coast, India, and elsewhere, the share of the urban informal sector is at least as high as 51%. Alternatively, seen from the point of view of the ‘minimum wage’ earners, only 11% of Tunisia’s labor force is subject to minimum wage; in Mexico and Morocco, a substantive number earns less than the minimum wage; in Taiwan, minimum wage is less than half of the average wage and so on (Agenor, 1996). Once again, the importance of the present theoretical construct is that, in the earlier literature, the informal sector, urban or rural, has not been modeled in a quasi full-employment general equilibrium framework such as this.1 Stark (1982), for example, has also noted
1
See Agenor and Montiel (1996).
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that there is a need for some more specifications while modeling informal sector in the presence of zero intersectoral transfer cost, perfect information, etc. In the H–T framework, he considers an extension, where the migrant faces a two-period time horizon and undertakes two competing strategies given the probabilities of getting a job in the formal sector in two different periods. In a similar H–T framework, Fields (1975) introduces another variation. According to this paper, open unemployment might exist in the presence of wage flexibility in the informal sector, when the migrant posits a trade-off between informal sector employment and the search for formal sector jobs. The familiar three-sector models of the kind are often used to address policy questions as under the H–T framework and policy effects differ when various assumptions are made regarding the mobility of labor and capital across sectors (Gupta, 1997).2 But, as mentioned earlier, the H–T type models must imply an informal wage rate lower than the rural wage rate — a phenomenon hard to justify with significant labor mobility between the two segments. Now, in order to reemphasize the need for the inclusion of the informal sector in a trade theoretic model, one might want to justify its significance. The term ‘informal sector’ was initially coined by ILO (1972) to mean, ‘‘illicit or illegal activities by individuals operating outside the formal sphere for the purpose of evading taxation or regulatory burden.’’ It may alternatively be defined as, ‘‘very small enterprises that use low-technology models and do not refer to legal status’’ (Webster & Fidler, 1996). Although generally, the informal sector activity pertains to nontraded items in the economy, from street vendors to domestic helps, in many countries they produce exportables and import substitutes with subcontracts from the formal sectors. In such cases, the formal sector adds the capital content (like, the brand name) only. In many other cases, small industries that produce garments, leather goods, small tools and machines, export directly without the formal regulations and procedures (University Grant Commission (UGC), India, 1996). Apart from that, in all the developing countries, agriculture is largely outside the formal net and agricultural outputs and consumer nondurables like fish and meat are largely exported. The domestic productions of these are as well protected at varying rates. Adequate consideration of these activities is therefore important with regard to policy changes, given the high share of employment involved in these sectors. The production structure that we use here bears resemblance to the ones developed in some recent papers in trade theory, dealing with complementarity in production. This is actually an application of the Gruen–Corden (1970) structure, laid out extensively in Jones and Marjit (1992) and Marjit and Beladi (1996, 1999). Our treatment of the informal sector exhibits a quasi-full-employment model amenable to interesting general equilibrium results. For macroeconomic applications of related structures, one may look at Agenor and Aizenman (1999), Agenor and Montiel (1996), etc. In a way, we exploit the notion of informality and complementarity in production to reflect on the welfare implications of liberal trade policies. The plan of the paper is the following. In Section 2, we present the basic model. In Section 3, we check the welfare implications of three policy changes and we conclude in Section 4.
2
See Grinols (1991).
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Section 5 presents the discussion and objectives of the paper. Appendix A provides the mathematical details and the proof of the propositions that we present in Section 3.
2. The model There are three sectors in a perfectly competitive small open economy. The Formal (F), the Informal (I), and the Rural (R). Capital (K), one of the factors of production, flows between F and I only, whereas production of R requires use of a specific factor Land (T). Labor is the other factor of production in all the three sectors, except that the formal wage rate is administered at w ¯ . Laborers try to find a job in the formal sector where the wage rate is w < w ¯. Those who cannot find a job are forced to work in the urban informal sector or in the rural sector earning. Hence, labor is fully employed in our structure although wage rates vary across sectors. The formal sector produces an import competing commodity; the informal sector also produces an import substitute, whereas the rural sector produces an exportable. We assume neoclassical technology and XF is capital intensive relative to XI, where ‘Xj’ along with other symbols is defined below. To build the system of equations, we use the following notations: Pj* Xj aij w¯ w r t K¯ L¯ T¯
World price of the jth commodity Output of the jth sector Fixed input coefficients Formal wage rate Wage rate in other sectors Return to capital Return to land Fixed stock of capital Fixed supply of labor Fixed supply of land
The system follows standard neoclassical assumptions, like constant returns to scale, diminishing returns to factor inputs, etc. The general equilibrium structure is therefore given as follows: wa ¯ LF þ raKF ¼ PF ð1 þ tF Þ
ð1Þ
waLI þ raKI ¼ PI ð1 þ tI Þ
ð2Þ
waLR þ taT R ¼ PR
ð3Þ
aLF XF þ aLI XI ¼ L¯ aLR XR
ð4Þ
¯ aKF XF þ aKI XI ¼ K
ð5Þ
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aT R XR ¼ T¯
293
ð6Þ
From the competitive price conditions as in Eqs. (1)–(3) and the full-employment conditions as in Eqs. (4)–(6), we solve for six unknowns, w, r, t, XF, XI, and XR. Eqs. (1) and (2) form the Heckscher–Ohlin subsystem or a ‘nugget’ (Jones & Marjit, 1992). As far as the structure of protection in such an economy is concerned, we will consider three different types of protectionary regimes. ‘tF’, ‘tI’, are tariff rates. Note that although w ¯ > w, labor does not leave the informal/agricultural sector, because given the capital constraint, only a certain number of workers can be employed in F. There is a job rationing of some sort in effect. Accordingly, people first queue up in the formal sector to get the high-paying job and the unsuccessful ones get absorbed in the other sectors.
3. The comparative statics In this section, we make two different specifications regarding the change in the structure of protection that the industries enjoy. First of all, let us consider that the formal sector and the informal sector are both protected at nonuniform rates. Then following trade liberalization, the formal sector faces a tariff cut, with all other things remaining unchanged. We make the following proposition based on such a change. Proposition 1: A tariff cut in the formal sector leads to a change in the national welfare, such that,
dV dLF þ tF PF SFF þ tI PI SIF e0: e0 iff ðw ¯ wÞ dtF dtF
Proof: See Appendix A, for detailed mathematical proof. We provide a brief intuitive explanation here. As tariff rate is lowered, return to capital falls and the formal sector contracts. Capital moves out of the formal sector and is employed in the informal sector. w goes up. Agricultural sector contracts, since (w ¯ w) contraction in LF reduces real income. But import demand for F goes up, raising tariff revenue as demand for F increases and production goes down. SFF < 0 captures this effect. As tF goes down, demand for XI goes down and its production goes up, reducing import demand for the informal sector, hence, tariff revenue goes down to that extent. SIF > 0 captures this effect. If the change in employment due to change in tariff, (dLF)/(dtF) > 0, is not very large or if the gap between the formal and informal wage is not too big either, then there is a welfare gain on account of the substitution term only. Next, we consider that the tariff on the informal sector output is lowered, with all other things remaining unchanged. We make the second proposition accordingly.
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Proposition 2: A tariff cut on the informal sector leads to a change in welfare, if the following condition holds: dV dLF þ tI PI SII þ tF PF SFI e0 e0; iff ðw ¯ wÞ dtI dtI Proof: See Appendix A, for detailed mathematical results. Once again, the intuitive explanation is presented as the following. A tariff cut on the informal sector will lead to a rise in the output and employment levels in the formal sector as also in the rural sector due to Rybczynski effect as capital flows out of the informal sector. This generates (dLF)/(dtI) < 0. The output falls in the informal sector itself and the demand goes up causing a rise in the import demand for the product. Accordingly, we have SII < 0 and there is a net welfare gain from the trade policy reform when we consider the cross-substitution effect to be negligible. This welfare gain is stronger, the bigger the initial gap between the formal and informal wage is. However, if the cross-effect, SFI > 0, is significant, then there is a welfare loss, although the final direction of [dV/dtI]e0, will depend upon the relative strength of the terms. Finally, we consider the change in price of the rural commodity. Let the price increase by exogenous causes, i.e., PˆR* > 0. The effect on the welfare of the small open economy is formulated as follows. Proposition 3: A price rise in the agricultural sector leads to a change in welfare if the following condition holds: dV dLF dMF dMI e0 iff ðw ¯ wÞ MR þ tF PF þ tI PI e0 dPR dPR dPR dPR Proof: See Appendix A and the intuitive explanation below. The intuitive explanation for the result above is as follows. As the price of the rural commodity goes up, output and employment rises in that sector. Labor moves out of the informal sector where both output and employment decreases. An interesting result is obtained in this model, whereby the wage rate does not change even if the price of the rural commodity increases. Return to capital also does not change and there is only a more than proportionate increase in the return to land following a price rise in the rural sector. Now using the equation of balanced trade, the change in the level of welfare (V) in the country due to a change in the price of commodity R, is captured as follows: dV dLF ¼ ðw ¯ wÞ MR þ tF PF SFR þ tI PI SIR dPR dPR
ð7Þ
where SFR = (dMF)/(dPR*) and SIR = (dMI)/(dPR*) are the substitutions in import demand due to change in price of the agricultural commodity. An increase in PR is just like a terms of trade improvement. Since MR < 0, welfare goes up. Labor is drawn away from I into R, and on the other hand, as XF goes up, so does LF due to
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Rybczynski effect. Hence, welfare goes up due to this effect as well. This is due to the complementarity relationship between XF and XR, a feature of Gruen and Corden (1970) and Jones and Marjit (1992) structures. Now, as demand for I goes up due to substitution effect and XI contracts, SIR > 0. This raises tariff revenue from I, leading to higher welfare. But XF increases and even if demand for F rises, MF can go down, i.e., SFR < 0, and that may be a source of welfare loss. It is straightforward to argue that, if tI = 0 and tF is very high, the adverse effect on welfare for SFR being negative can be substantial. Simplifying Eq. (7) (Eq. (8)), dLF ðw MR þ tI PI SIR ¯ wÞ dP dV R < 0 iff ; tF > dPR PF SFR
ð8Þ
If SFR < 0, SIR = 0, w ¯ is close to w and MR is not very high, high tariffs in F will make the terms of trade effect to be negative. Usually better terms of trade is welfare-improving. But here, complementarity induces an import-competing sector grow as well when the terms of trade has improved. In a typical full-employment model, w ¯ = w. There, with tI = 0, the result is more likely to occur as the condition boils down to (Eq. (9)): tF >
MR PF SFR
ð9Þ
Wage differential captures the positive welfare effect of improvement in employment in the formal sector.
4. Conclusion We summarize the basic findings of the paper. In the presence of informal sector in the economy, a tariff cut on the formal sector output might not be welfare-improving. For this to be unambiguously welfare-improving, it requires both negligible cross-substitution effect in other sectors and negligible employment effect in the formal sector. Secondly, a reduction in tariff in the informal sector increases welfare, as long as input demand in the formal sector expands. This may be jeopardized by a rise in XF. If cross-effects are ignored, i.e., if tF is very low, welfare unambiguously rises following a tariff cut in the informal sector. Finally, the rise in price of the agricultural commodity will also be strictly welfare-improving as long as the fall in import demand for the formal good due to PˆR* > 0 is negligible. There would nevertheless be a striking possibility that the welfare level in the economy is reduced when there is a fall in import demand for the formal commodity owing to an increase in the price of the agricultural good. The purpose of this analysis has been to provide a simple general equilibrium framework for developing countries characterized by informal sector, and thereby perform the usual trade policy experiments in this set up. Tariff cuts have ambiguous results even if it is a fullemployment competitive model, because of the wage differential and the presence of the cross-effects in consumption and production. Typically, when either tF or tI = 0, the welfare
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effect of a tariff cut is usually positive. But with preexisting high tariffs in other sectors and complementarity in production, welfare results can go either way.
5. Discussion and objectives Let us now contrast the results of our structure with the one where the informal sector is absent from the model. If there is no informal sector, what we have is a standard specific-factor model a` la Jones (1971) with only one difference. Here people try to find a job in the formal sector and only those who are unemployed get absorbed in agriculture. A tariff cut in F will give usual results. XF will fall, LF will fall, and MF will rise. This is very similar to what we have in our model except the cross-effect on I. However, with I in place, rising XI absorbs labor and helps to raise w as r falls. But without I, w must fall as laborers crowd in the rural sector. If tI > 0, declining MI is a source of welfare loss in our model, which is not captured in the structure without the informal sector. If informal sector produces an importsubstituting product and it is protected, expansion in informal output increases distortion. A rise in PR in the two-sector model leads to a rise in welfare due to terms of trade effect, as well as by the volume of trade effect as MF goes up. But as LF falls, it hurts welfare. What our model suggests is that, with the informal sector in place, a complementarity result emerges, which may in fact reduce MF, since XI contracts. Such a result occurs only because XI contracts and helps the other protected sector to expand. Finally, how does the real income of laborers get affected through policy reforms? A decline in tF increases w and increases real income of the existing workers in the informal and agricultural sector. But as LF drops, workers are pushed out of the formal sector. These workers suffer real income loss. Typically, a tariff cut redistributes income in face of the ‘outsiders’ who do not receive the patronage of the trade unions. A decline in tI reduces the real income of the informal workers and increases that of the unionized workers, since w ¯ is fixed and other prices are held constant. As PR increases, real income of the workers already employed in the formal and informal sectors, goes down. But there is labor outflow from the informal to the formal sector 3 measured by dLF. Their real income increases if and only if [((w ¯ w)/w) > PˆR]. 3
In the absence of distinction between wage rates in the informal and rural sectors, there remains no reason to distinguish between these two sectors. In fact, there is no obstacle in the model in combining the informal and rural sectors. In that case, all characteristics of the model reduce to the standard 2 2 2 model of trade. This argument can be tested as follows. Let’s add initial tariff (tR) to the rural sector as it is initially in the formal and informal sectors. Then evaluate the effect of trade liberalization in the rural sector (dtR 6¼ 0) on welfare (dV), thus adding another proposition. The result turns out to be a special case of Proposition 2 in the paper, which evaluates the welfare effect of trade liberalization in the informal sector. This is due to the fact that the rural sector is just the informal sector without capital. In fact, this added proposition would be a generalization of Proposition 3 in the paper. Alternatively, if we drop the rural sector from the model, the comparative results in Propositions 1, 2, and 3 regarding the formal and informal sectors remain unchanged. Although it is true that the informal sector and the rural sector are very similar, there is one important difference. A rise in PR* ‘does not’ help informal workers. But a rise in P*I ‘must increase’ w. This is an important point of difference.
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Acknowledgments We are indebted to the referee for helpful comments. The usual disclaimer applies.
Appendix A. Proof of Proposition 1 ‘^’ denotes percentage changes in the variables. From Eq. (1), rˆ ¼
dtF < 0 as dtF < 0 qKF
From Eq. (2) substituting rˆ, wˆ ¼
dtF qKI >0 qKF qLI
And finally from Eq. (3), tˆ ¼
dtF qKI qLR <0 qKF qLI qT R
Differentiating and manipulating Eqs. (4) and (5) (see Jones, 1965), lLR 2 ˆXF ¼ 1 w þ lKI qLI sI þ lLI lKI qLI sI rðl ˆ KI þ lLI ÞðlKF qLF sF þ lKI qLI sI Þ ˆ lKI sR D qTR 1 lLR Xˆ I ¼ l q s þ l l s þ l s q s þ l q s Þ : rðl w l ˆ LF KI LI I ˆ KF LF F KF LI I KF R KI LI I D qTR ˆ F < 0, X ˆ I>0. Where, D=(lLFlKI lKFlLI) < 0, and accordingly X From Eq. (6), XR ¼
T¯ aTR
Therefore, aLR XR ¼
aLR T¯ aTR
Thus, (Eq. (1.1)), aˆ LR þ Xˆ R ¼ aˆ LR aˆ T R ¼ sR ðwˆ tÞ ˆ
ð1:1Þ
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ˆ t) Or, (w ˆ = (wˆ)/(qTR), such that, (Eq. (1.2)), w ¯Lˆ R ¼ aˆ LR þ Xˆ R ¼ sR ˆ < 0 qT R
ð1:2Þ
Also, (Eq. (1.3)), Xˆ R ¼
qLR sR wˆ < 0 qTR
ð1:3Þ
We use the above results to arrive at the change in welfare parameter.From the condition of balanced trade, PF ð1 þ tF ÞdDF þ PI ð1 þ tI ÞdDI þ PR dDR tF PF dDF tI PI dDI ¼ PF ð1 þ tF ÞdXF þ PI ð1 þ tI ÞdXI þ PR dXR tF PF dXF tI PI dXI or, (Eq. (1.4)), dV ¼ PF ð1 þ tF ÞdXF þ PI ð1 þ tI ÞdXI þ PR dXR þ tF PF dMF þ tI PI dMI
ð1:4Þ
where, dV = P*F (1 + t)dDF + P*I dDI + PR*dDR. Now, P*F (1 + tF)dXF + P*I (1 + tI)dXI + PR*dXR =(w¯ wÞdLF . As, dLF = (dLI + dLR), dK¯ = 0, dT¯ = 0. Thus, dV ¼ ðw ¯ wÞdLF þ tF PF dMF þ tI PI dMI Let us now define the import demand function as follows, PF ð1 þ tF Þ PI ð1 þ tI Þ PR MF ¼ MF ; ; ;V w w w ¯ ¯ ¯
ð1:5Þ
ð1:6Þ
Differentiating Eq. (1.6), dMF ¼ SFF dtF þ mF dV and dMI ¼ SIF dtF þ mI dV where, SFF=(dMF)/(dtF) and SIF=(dMI)/(dtF); mF=(dMF)/(dV) and mI=(dMI)/(dV). Substituting the above in Eq. (1.5), dV ¼ ðw ¯ wÞdLF þ tF PF SFF dtF þ tF PF mF dV þ tI PI SIF dtF þ tI PI mI dV Or, (Eq. (1.7)), dV ¼
ðw ¯ wÞdLF þ tF PF SFF dtF þ tI PI SIF dtF ð1 tF PF mF tI PI mI Þ
mI =(mI)/((1 + tI)P*), it follows that 0 < (1 tFPF* mF Now, as mF =(mF)/((1 + tF)P*), F I tIP*I mI)<1.
ð1:7Þ
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Therefore, dV dLF e0 iff ðw wÞ þ tF PF SFF þ tI PI SIF e0: dtF dtF Proved. Proof of Proposition 2 From Eq. (1), rˆ = 0 and from Eq. (2), wˆ=(dtI)/(qLI) < 0 as dtI < 0. Again, from Eq. (3), tˆ = (dtI/qLI)(qLR/qTR)>0. The employment and output levels in the agricultural sector are: Lˆ R ¼ sR
wˆ > 0; qT R
XˆR ¼
qLR sR wˆ > 0 qTR
From Eqs. (4) and (5), we solve for XF and XI as in Proposition 1, and for, D < 0, XˆF>0, ˆXI < 0. Accordingly, LˆF>0, LˆI < 0. Now, using the condition of balanced trade and following above (Eq. (2.1)), dV ¼ ðw ¯ wÞdLF þ tF PF dMF þ tI PF dMI
ð2:1Þ
The import demand function for I is written as: PF ð1 þ tF Þ PI ð1 þ tI Þ PR ; ; V MI ¼ MI w w w ¯ ¯ ¯ Differentiating, dMI = SIIdtI + mIdV and dMF = SFIdtI + mFdV where, SII = dMI =dtI and SFI = dMF/dtI; mI = dMI/dV and mF = dMF/dV (Eq. (2.2)), dV ¼
ðw ¯ wÞdLF þ tI PI SII dtI þ tF PF SFI dtI ð1 tF PF mF tI PI mI Þ
As before, with 0 < (l tFPF* mF tIP*I mI) < l (Eq. (2.3)), dV dLF þ tI PI SII þ tF PF SFI e0: e0; iff ðw ¯ wÞ dtI dtI Proved. Proof of Proposition 3 From Eqs. (1) and (2), rˆ = 0, wˆ = 0. From Eq. (3), tˆ = PˆR* /qTR>0 as Pˆ*R >0. ˆ R>0: Also, XR = T¯/aTR, and LˆR = aˆLR + XˆR = aˆLR ˆaT R ¼ ðsR =qTR ÞP
ð2:2Þ
ð2:3Þ
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Changes in the output levels in all the sectors are given as follows: X¯ R ¼
qLR sR Pˆ R > 0; qTR
Xˆ F ¼
1 sR ˆ lLR P > 0; D qT R R
ˆI ¼ X
1 lKF sR ˆ lLR P <0 D lKI qTR R
as Pˆ R > 0 and D < 0: Accordingly, LˆF>0, LˆI < 0, and LˆR>0. Now, using the condition of balanced trade and differentiating (Eq. (3.1)), dV ¼ ðw ¯ wÞdLF dPR MR þ tF PF dMF þ tI PI dMI Therefore (Eq. (3.2)), dV dLF dMF dMI e0 iff ðw ¯ wÞ MR þ tF PF þ tI PI e0 dPR dPR dPR dPR
ð3:1Þ
ð3:2Þ
Proved.
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Informal sector in general equilibrium: welfare effects of trade policy reforms Saibal Kara,*, Sugata Marjitb,c a
Department of Economics, 5th Floor, Zulauf Hall, Northern Illinois University, De Kalb, IL 60115, USA b CESP, Jawaharlal Nehru University, New Delhi, India c Centre for Studies in Social Sciences, Calcutta, India Received 12 July 2000; received in revised form 28 November 2000; accepted 14 December 2000
Abstract The paper demonstrates the welfare effects of trade policy reforms in a general equilibrium framework, in the presence of an informal sector in the economy. The methodology we developed in the paper allows us to use a full-employment model with wage differential. Tariff cuts in this model have ambiguous effects because of the preexisting wage differential and due to the cross-effects in the three-good structure, which is used in some recent works in trade theory. Complementarity in production may lead to negative welfare effects despite improvements in terms of trade. D 2001 Elsevier Science Inc. All rights reserved. JEL classification: F11; F13 Keywords: Informal sector; Trade reform; General equilibrium; Welfare; Complementarity
1. Introduction Theoretical and empirical policy research in international economics addresses crucial questions about structural adjustments, both in the real and in the financial sectors of the developing economies. Among these, the theoretical papers in trade deal with the use of trade policies, tariffs or tariff equivalents to improve national welfare, appropriately defined. Here * Corresponding author. Tel.: +1-815-753-1363. E-mail address: [email protected] (S. Kar). 1059-0560/01/$ – see front matter D 2001 Elsevier Science Inc. All rights reserved. PII: S 1 0 5 9 - 0 5 6 0 ( 0 1 ) 0 0 0 8 8 - 0
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we address, how the consideration of informal sector, an area scarcely dealt with in a pure general equilibrium framework, works with more generalized applications of some of the basic theories related to trade policy. A survey of the literature reveals that, so far, considerations of the urban informal sector have been embedded in the rural–urban migration models of the traditional Harris–Todaro (henceforth, H–T) type. Gupta (1993), for example, considers a three-sector static model of a small open economy, with wage and employment determined endogenously in the informal sector. The hypothesis that rural migrants expect to get a job in the urban formal sector with some probability ‘l’, holds in these models, although, some of the subsidy policies in this structure run counter to those generated by the original model. The problem with these models is that, informal sector offers a wage that has to be lower than the rural wage, because the weighted average of formal and informal wages equals the rural wage. We argue that the poor laborers, moving freely between rural and urban centers, cannot afford to remain unemployed while expecting higher earnings only in the future. They form instead what is known as the urban informal sector, where they earn less than the urban formal wage rate. However, with free mobility of labor between the urban informal and the rural sectors, there is high probability that informal wage is closely related to the rural wage. Accordingly, in our model, we consider them equal. We capture these characteristics in a full-employment general equilibrium model. Subsequently, we wish to check the welfare implications of the trade policy reforms. With this view, we define a welfare parameter and see how it changes when trade policy reforms are introduced at various levels of the economy. In the existing literature, welfare implications of the trade reforms, with the informal sector as an important part of the economy, have not come up for much discussions so far. Leaving out the informal sector fails to capture the actual impact of such policy reforms, because, on an average, about 70% of the labor force in the LDCs belong to the informal sectors. Data from Southeast Asian, East European, African, and Latin American countries show varying rates of urban informal sector employment with a range going up from 15% to 20% in Turkey and Slovakia to 80% in Zambia, or even more, to about 83% in Myanmar. Moreover, considering the state of agricultural and rural activities in these countries, it is quite apparent that the total share of the informal sector in the economy as a whole would be very high (International Labour Organisation (ILO), 1999). This is also corroborated by some of the other studies, like that by Turnham (1993), which provide evidence that in low-income countries like Nigeria, Bangladesh, Ivory Coast, India, and elsewhere, the share of the urban informal sector is at least as high as 51%. Alternatively, seen from the point of view of the ‘minimum wage’ earners, only 11% of Tunisia’s labor force is subject to minimum wage; in Mexico and Morocco, a substantive number earns less than the minimum wage; in Taiwan, minimum wage is less than half of the average wage and so on (Agenor, 1996). Once again, the importance of the present theoretical construct is that, in the earlier literature, the informal sector, urban or rural, has not been modeled in a quasi full-employment general equilibrium framework such as this.1 Stark (1982), for example, has also noted
1
See Agenor and Montiel (1996).
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that there is a need for some more specifications while modeling informal sector in the presence of zero intersectoral transfer cost, perfect information, etc. In the H–T framework, he considers an extension, where the migrant faces a two-period time horizon and undertakes two competing strategies given the probabilities of getting a job in the formal sector in two different periods. In a similar H–T framework, Fields (1975) introduces another variation. According to this paper, open unemployment might exist in the presence of wage flexibility in the informal sector, when the migrant posits a trade-off between informal sector employment and the search for formal sector jobs. The familiar three-sector models of the kind are often used to address policy questions as under the H–T framework and policy effects differ when various assumptions are made regarding the mobility of labor and capital across sectors (Gupta, 1997).2 But, as mentioned earlier, the H–T type models must imply an informal wage rate lower than the rural wage rate — a phenomenon hard to justify with significant labor mobility between the two segments. Now, in order to reemphasize the need for the inclusion of the informal sector in a trade theoretic model, one might want to justify its significance. The term ‘informal sector’ was initially coined by ILO (1972) to mean, ‘‘illicit or illegal activities by individuals operating outside the formal sphere for the purpose of evading taxation or regulatory burden.’’ It may alternatively be defined as, ‘‘very small enterprises that use low-technology models and do not refer to legal status’’ (Webster & Fidler, 1996). Although generally, the informal sector activity pertains to nontraded items in the economy, from street vendors to domestic helps, in many countries they produce exportables and import substitutes with subcontracts from the formal sectors. In such cases, the formal sector adds the capital content (like, the brand name) only. In many other cases, small industries that produce garments, leather goods, small tools and machines, export directly without the formal regulations and procedures (University Grant Commission (UGC), India, 1996). Apart from that, in all the developing countries, agriculture is largely outside the formal net and agricultural outputs and consumer nondurables like fish and meat are largely exported. The domestic productions of these are as well protected at varying rates. Adequate consideration of these activities is therefore important with regard to policy changes, given the high share of employment involved in these sectors. The production structure that we use here bears resemblance to the ones developed in some recent papers in trade theory, dealing with complementarity in production. This is actually an application of the Gruen–Corden (1970) structure, laid out extensively in Jones and Marjit (1992) and Marjit and Beladi (1996, 1999). Our treatment of the informal sector exhibits a quasi-full-employment model amenable to interesting general equilibrium results. For macroeconomic applications of related structures, one may look at Agenor and Aizenman (1999), Agenor and Montiel (1996), etc. In a way, we exploit the notion of informality and complementarity in production to reflect on the welfare implications of liberal trade policies. The plan of the paper is the following. In Section 2, we present the basic model. In Section 3, we check the welfare implications of three policy changes and we conclude in Section 4.
2
See Grinols (1991).
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Section 5 presents the discussion and objectives of the paper. Appendix A provides the mathematical details and the proof of the propositions that we present in Section 3.
2. The model There are three sectors in a perfectly competitive small open economy. The Formal (F), the Informal (I), and the Rural (R). Capital (K), one of the factors of production, flows between F and I only, whereas production of R requires use of a specific factor Land (T). Labor is the other factor of production in all the three sectors, except that the formal wage rate is administered at w ¯ . Laborers try to find a job in the formal sector where the wage rate is w < w ¯. Those who cannot find a job are forced to work in the urban informal sector or in the rural sector earning. Hence, labor is fully employed in our structure although wage rates vary across sectors. The formal sector produces an import competing commodity; the informal sector also produces an import substitute, whereas the rural sector produces an exportable. We assume neoclassical technology and XF is capital intensive relative to XI, where ‘Xj’ along with other symbols is defined below. To build the system of equations, we use the following notations: Pj* Xj aij w¯ w r t K¯ L¯ T¯
World price of the jth commodity Output of the jth sector Fixed input coefficients Formal wage rate Wage rate in other sectors Return to capital Return to land Fixed stock of capital Fixed supply of labor Fixed supply of land
The system follows standard neoclassical assumptions, like constant returns to scale, diminishing returns to factor inputs, etc. The general equilibrium structure is therefore given as follows: wa ¯ LF þ raKF ¼ PF ð1 þ tF Þ
ð1Þ
waLI þ raKI ¼ PI ð1 þ tI Þ
ð2Þ
waLR þ taT R ¼ PR
ð3Þ
aLF XF þ aLI XI ¼ L¯ aLR XR
ð4Þ
¯ aKF XF þ aKI XI ¼ K
ð5Þ
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aT R XR ¼ T¯
293
ð6Þ
From the competitive price conditions as in Eqs. (1)–(3) and the full-employment conditions as in Eqs. (4)–(6), we solve for six unknowns, w, r, t, XF, XI, and XR. Eqs. (1) and (2) form the Heckscher–Ohlin subsystem or a ‘nugget’ (Jones & Marjit, 1992). As far as the structure of protection in such an economy is concerned, we will consider three different types of protectionary regimes. ‘tF’, ‘tI’, are tariff rates. Note that although w ¯ > w, labor does not leave the informal/agricultural sector, because given the capital constraint, only a certain number of workers can be employed in F. There is a job rationing of some sort in effect. Accordingly, people first queue up in the formal sector to get the high-paying job and the unsuccessful ones get absorbed in the other sectors.
3. The comparative statics In this section, we make two different specifications regarding the change in the structure of protection that the industries enjoy. First of all, let us consider that the formal sector and the informal sector are both protected at nonuniform rates. Then following trade liberalization, the formal sector faces a tariff cut, with all other things remaining unchanged. We make the following proposition based on such a change. Proposition 1: A tariff cut in the formal sector leads to a change in the national welfare, such that,
dV dLF þ tF PF SFF þ tI PI SIF e0: e0 iff ðw ¯ wÞ dtF dtF
Proof: See Appendix A, for detailed mathematical proof. We provide a brief intuitive explanation here. As tariff rate is lowered, return to capital falls and the formal sector contracts. Capital moves out of the formal sector and is employed in the informal sector. w goes up. Agricultural sector contracts, since (w ¯ w) contraction in LF reduces real income. But import demand for F goes up, raising tariff revenue as demand for F increases and production goes down. SFF < 0 captures this effect. As tF goes down, demand for XI goes down and its production goes up, reducing import demand for the informal sector, hence, tariff revenue goes down to that extent. SIF > 0 captures this effect. If the change in employment due to change in tariff, (dLF)/(dtF) > 0, is not very large or if the gap between the formal and informal wage is not too big either, then there is a welfare gain on account of the substitution term only. Next, we consider that the tariff on the informal sector output is lowered, with all other things remaining unchanged. We make the second proposition accordingly.
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Proposition 2: A tariff cut on the informal sector leads to a change in welfare, if the following condition holds: dV dLF þ tI PI SII þ tF PF SFI e0 e0; iff ðw ¯ wÞ dtI dtI Proof: See Appendix A, for detailed mathematical results. Once again, the intuitive explanation is presented as the following. A tariff cut on the informal sector will lead to a rise in the output and employment levels in the formal sector as also in the rural sector due to Rybczynski effect as capital flows out of the informal sector. This generates (dLF)/(dtI) < 0. The output falls in the informal sector itself and the demand goes up causing a rise in the import demand for the product. Accordingly, we have SII < 0 and there is a net welfare gain from the trade policy reform when we consider the cross-substitution effect to be negligible. This welfare gain is stronger, the bigger the initial gap between the formal and informal wage is. However, if the cross-effect, SFI > 0, is significant, then there is a welfare loss, although the final direction of [dV/dtI]e0, will depend upon the relative strength of the terms. Finally, we consider the change in price of the rural commodity. Let the price increase by exogenous causes, i.e., PˆR* > 0. The effect on the welfare of the small open economy is formulated as follows. Proposition 3: A price rise in the agricultural sector leads to a change in welfare if the following condition holds: dV dLF dMF dMI e0 iff ðw ¯ wÞ MR þ tF PF þ tI PI e0 dPR dPR dPR dPR Proof: See Appendix A and the intuitive explanation below. The intuitive explanation for the result above is as follows. As the price of the rural commodity goes up, output and employment rises in that sector. Labor moves out of the informal sector where both output and employment decreases. An interesting result is obtained in this model, whereby the wage rate does not change even if the price of the rural commodity increases. Return to capital also does not change and there is only a more than proportionate increase in the return to land following a price rise in the rural sector. Now using the equation of balanced trade, the change in the level of welfare (V) in the country due to a change in the price of commodity R, is captured as follows: dV dLF ¼ ðw ¯ wÞ MR þ tF PF SFR þ tI PI SIR dPR dPR
ð7Þ
where SFR = (dMF)/(dPR*) and SIR = (dMI)/(dPR*) are the substitutions in import demand due to change in price of the agricultural commodity. An increase in PR is just like a terms of trade improvement. Since MR < 0, welfare goes up. Labor is drawn away from I into R, and on the other hand, as XF goes up, so does LF due to
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Rybczynski effect. Hence, welfare goes up due to this effect as well. This is due to the complementarity relationship between XF and XR, a feature of Gruen and Corden (1970) and Jones and Marjit (1992) structures. Now, as demand for I goes up due to substitution effect and XI contracts, SIR > 0. This raises tariff revenue from I, leading to higher welfare. But XF increases and even if demand for F rises, MF can go down, i.e., SFR < 0, and that may be a source of welfare loss. It is straightforward to argue that, if tI = 0 and tF is very high, the adverse effect on welfare for SFR being negative can be substantial. Simplifying Eq. (7) (Eq. (8)), dLF ðw MR þ tI PI SIR ¯ wÞ dP dV R < 0 iff ; tF > dPR PF SFR
ð8Þ
If SFR < 0, SIR = 0, w ¯ is close to w and MR is not very high, high tariffs in F will make the terms of trade effect to be negative. Usually better terms of trade is welfare-improving. But here, complementarity induces an import-competing sector grow as well when the terms of trade has improved. In a typical full-employment model, w ¯ = w. There, with tI = 0, the result is more likely to occur as the condition boils down to (Eq. (9)): tF >
MR PF SFR
ð9Þ
Wage differential captures the positive welfare effect of improvement in employment in the formal sector.
4. Conclusion We summarize the basic findings of the paper. In the presence of informal sector in the economy, a tariff cut on the formal sector output might not be welfare-improving. For this to be unambiguously welfare-improving, it requires both negligible cross-substitution effect in other sectors and negligible employment effect in the formal sector. Secondly, a reduction in tariff in the informal sector increases welfare, as long as input demand in the formal sector expands. This may be jeopardized by a rise in XF. If cross-effects are ignored, i.e., if tF is very low, welfare unambiguously rises following a tariff cut in the informal sector. Finally, the rise in price of the agricultural commodity will also be strictly welfare-improving as long as the fall in import demand for the formal good due to PˆR* > 0 is negligible. There would nevertheless be a striking possibility that the welfare level in the economy is reduced when there is a fall in import demand for the formal commodity owing to an increase in the price of the agricultural good. The purpose of this analysis has been to provide a simple general equilibrium framework for developing countries characterized by informal sector, and thereby perform the usual trade policy experiments in this set up. Tariff cuts have ambiguous results even if it is a fullemployment competitive model, because of the wage differential and the presence of the cross-effects in consumption and production. Typically, when either tF or tI = 0, the welfare
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effect of a tariff cut is usually positive. But with preexisting high tariffs in other sectors and complementarity in production, welfare results can go either way.
5. Discussion and objectives Let us now contrast the results of our structure with the one where the informal sector is absent from the model. If there is no informal sector, what we have is a standard specific-factor model a` la Jones (1971) with only one difference. Here people try to find a job in the formal sector and only those who are unemployed get absorbed in agriculture. A tariff cut in F will give usual results. XF will fall, LF will fall, and MF will rise. This is very similar to what we have in our model except the cross-effect on I. However, with I in place, rising XI absorbs labor and helps to raise w as r falls. But without I, w must fall as laborers crowd in the rural sector. If tI > 0, declining MI is a source of welfare loss in our model, which is not captured in the structure without the informal sector. If informal sector produces an importsubstituting product and it is protected, expansion in informal output increases distortion. A rise in PR in the two-sector model leads to a rise in welfare due to terms of trade effect, as well as by the volume of trade effect as MF goes up. But as LF falls, it hurts welfare. What our model suggests is that, with the informal sector in place, a complementarity result emerges, which may in fact reduce MF, since XI contracts. Such a result occurs only because XI contracts and helps the other protected sector to expand. Finally, how does the real income of laborers get affected through policy reforms? A decline in tF increases w and increases real income of the existing workers in the informal and agricultural sector. But as LF drops, workers are pushed out of the formal sector. These workers suffer real income loss. Typically, a tariff cut redistributes income in face of the ‘outsiders’ who do not receive the patronage of the trade unions. A decline in tI reduces the real income of the informal workers and increases that of the unionized workers, since w ¯ is fixed and other prices are held constant. As PR increases, real income of the workers already employed in the formal and informal sectors, goes down. But there is labor outflow from the informal to the formal sector 3 measured by dLF. Their real income increases if and only if [((w ¯ w)/w) > PˆR]. 3
In the absence of distinction between wage rates in the informal and rural sectors, there remains no reason to distinguish between these two sectors. In fact, there is no obstacle in the model in combining the informal and rural sectors. In that case, all characteristics of the model reduce to the standard 2 2 2 model of trade. This argument can be tested as follows. Let’s add initial tariff (tR) to the rural sector as it is initially in the formal and informal sectors. Then evaluate the effect of trade liberalization in the rural sector (dtR 6¼ 0) on welfare (dV), thus adding another proposition. The result turns out to be a special case of Proposition 2 in the paper, which evaluates the welfare effect of trade liberalization in the informal sector. This is due to the fact that the rural sector is just the informal sector without capital. In fact, this added proposition would be a generalization of Proposition 3 in the paper. Alternatively, if we drop the rural sector from the model, the comparative results in Propositions 1, 2, and 3 regarding the formal and informal sectors remain unchanged. Although it is true that the informal sector and the rural sector are very similar, there is one important difference. A rise in PR* ‘does not’ help informal workers. But a rise in P*I ‘must increase’ w. This is an important point of difference.
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Acknowledgments We are indebted to the referee for helpful comments. The usual disclaimer applies.
Appendix A. Proof of Proposition 1 ‘^’ denotes percentage changes in the variables. From Eq. (1), rˆ ¼
dtF < 0 as dtF < 0 qKF
From Eq. (2) substituting rˆ, wˆ ¼
dtF qKI >0 qKF qLI
And finally from Eq. (3), tˆ ¼
dtF qKI qLR <0 qKF qLI qT R
Differentiating and manipulating Eqs. (4) and (5) (see Jones, 1965), lLR 2 ˆXF ¼ 1 w þ lKI qLI sI þ lLI lKI qLI sI rðl ˆ KI þ lLI ÞðlKF qLF sF þ lKI qLI sI Þ ˆ lKI sR D qTR 1 lLR Xˆ I ¼ l q s þ l l s þ l s q s þ l q s Þ : rðl w l ˆ LF KI LI I ˆ KF LF F KF LI I KF R KI LI I D qTR ˆ F < 0, X ˆ I>0. Where, D=(lLFlKI lKFlLI) < 0, and accordingly X From Eq. (6), XR ¼
T¯ aTR
Therefore, aLR XR ¼
aLR T¯ aTR
Thus, (Eq. (1.1)), aˆ LR þ Xˆ R ¼ aˆ LR aˆ T R ¼ sR ðwˆ tÞ ˆ
ð1:1Þ
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ˆ t) Or, (w ˆ = (wˆ)/(qTR), such that, (Eq. (1.2)), w ¯Lˆ R ¼ aˆ LR þ Xˆ R ¼ sR ˆ < 0 qT R
ð1:2Þ
Also, (Eq. (1.3)), Xˆ R ¼
qLR sR wˆ < 0 qTR
ð1:3Þ
We use the above results to arrive at the change in welfare parameter.From the condition of balanced trade, PF ð1 þ tF ÞdDF þ PI ð1 þ tI ÞdDI þ PR dDR tF PF dDF tI PI dDI ¼ PF ð1 þ tF ÞdXF þ PI ð1 þ tI ÞdXI þ PR dXR tF PF dXF tI PI dXI or, (Eq. (1.4)), dV ¼ PF ð1 þ tF ÞdXF þ PI ð1 þ tI ÞdXI þ PR dXR þ tF PF dMF þ tI PI dMI
ð1:4Þ
where, dV = P*F (1 + t)dDF + P*I dDI + PR*dDR. Now, P*F (1 + tF)dXF + P*I (1 + tI)dXI + PR*dXR =(w¯ wÞdLF . As, dLF = (dLI + dLR), dK¯ = 0, dT¯ = 0. Thus, dV ¼ ðw ¯ wÞdLF þ tF PF dMF þ tI PI dMI Let us now define the import demand function as follows, PF ð1 þ tF Þ PI ð1 þ tI Þ PR MF ¼ MF ; ; ;V w w w ¯ ¯ ¯
ð1:5Þ
ð1:6Þ
Differentiating Eq. (1.6), dMF ¼ SFF dtF þ mF dV and dMI ¼ SIF dtF þ mI dV where, SFF=(dMF)/(dtF) and SIF=(dMI)/(dtF); mF=(dMF)/(dV) and mI=(dMI)/(dV). Substituting the above in Eq. (1.5), dV ¼ ðw ¯ wÞdLF þ tF PF SFF dtF þ tF PF mF dV þ tI PI SIF dtF þ tI PI mI dV Or, (Eq. (1.7)), dV ¼
ðw ¯ wÞdLF þ tF PF SFF dtF þ tI PI SIF dtF ð1 tF PF mF tI PI mI Þ
mI =(mI)/((1 + tI)P*), it follows that 0 < (1 tFPF* mF Now, as mF =(mF)/((1 + tF)P*), F I tIP*I mI)<1.
ð1:7Þ
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Therefore, dV dLF e0 iff ðw wÞ þ tF PF SFF þ tI PI SIF e0: dtF dtF Proved. Proof of Proposition 2 From Eq. (1), rˆ = 0 and from Eq. (2), wˆ=(dtI)/(qLI) < 0 as dtI < 0. Again, from Eq. (3), tˆ = (dtI/qLI)(qLR/qTR)>0. The employment and output levels in the agricultural sector are: Lˆ R ¼ sR
wˆ > 0; qT R
XˆR ¼
qLR sR wˆ > 0 qTR
From Eqs. (4) and (5), we solve for XF and XI as in Proposition 1, and for, D < 0, XˆF>0, ˆXI < 0. Accordingly, LˆF>0, LˆI < 0. Now, using the condition of balanced trade and following above (Eq. (2.1)), dV ¼ ðw ¯ wÞdLF þ tF PF dMF þ tI PF dMI
ð2:1Þ
The import demand function for I is written as: PF ð1 þ tF Þ PI ð1 þ tI Þ PR ; ; V MI ¼ MI w w w ¯ ¯ ¯ Differentiating, dMI = SIIdtI + mIdV and dMF = SFIdtI + mFdV where, SII = dMI =dtI and SFI = dMF/dtI; mI = dMI/dV and mF = dMF/dV (Eq. (2.2)), dV ¼
ðw ¯ wÞdLF þ tI PI SII dtI þ tF PF SFI dtI ð1 tF PF mF tI PI mI Þ
As before, with 0 < (l tFPF* mF tIP*I mI) < l (Eq. (2.3)), dV dLF þ tI PI SII þ tF PF SFI e0: e0; iff ðw ¯ wÞ dtI dtI Proved. Proof of Proposition 3 From Eqs. (1) and (2), rˆ = 0, wˆ = 0. From Eq. (3), tˆ = PˆR* /qTR>0 as Pˆ*R >0. ˆ R>0: Also, XR = T¯/aTR, and LˆR = aˆLR + XˆR = aˆLR ˆaT R ¼ ðsR =qTR ÞP
ð2:2Þ
ð2:3Þ
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Changes in the output levels in all the sectors are given as follows: X¯ R ¼
qLR sR Pˆ R > 0; qTR
Xˆ F ¼
1 sR ˆ lLR P > 0; D qT R R
ˆI ¼ X
1 lKF sR ˆ lLR P <0 D lKI qTR R
as Pˆ R > 0 and D < 0: Accordingly, LˆF>0, LˆI < 0, and LˆR>0. Now, using the condition of balanced trade and differentiating (Eq. (3.1)), dV ¼ ðw ¯ wÞdLF dPR MR þ tF PF dMF þ tI PI dMI Therefore (Eq. (3.2)), dV dLF dMF dMI e0 iff ðw ¯ wÞ MR þ tF PF þ tI PI e0 dPR dPR dPR dPR
ð3:1Þ
ð3:2Þ
Proved.
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