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International Review of Economics and Finance 33 (2014) 172–185
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International Review of Economics and Finance
j ourna l homepage: www.e lsev ie r .com/ locate / i re f
Trade and wage inequality: A specific factor model withintermediate goods☆
Alokesh Barua⁎, Manoj Pant 1
Centre for International Trade and Development, School of International Studies, Jawaharlal Nehru University, New Delhi - 110067, India
a r t i c l e i n f o
☆ We would like to acknowledge the suggestions othank Professor Ravi Batra for comments on an earlie⁎ Corresponding author. Tel.: +91 11 26704393 (O
E-mail addresses: [email protected], alokesh.b1 Tel.: +91 11 26704393 (O).
http://dx.doi.org/10.1016/j.iref.2014.04.0041059-0560/© 2014 Elsevier Inc. All rights reserved.
a b s t r a c t
Article history:Received 16 July 2013Received in revised form 28 April 2014Accepted 28 April 2014Available online 9 May 2014
In this paper we try to address the current debate on the link between trade liberalization andwage inequality in developing countries within a general equilibrium framework. For this we setup two distinct models of trade. First, assuming a specific factor model with full employment weshow that for a small developing economywage inequality is related to labour productivity ratherthan freer trade per se. The model also suggests that while trade may increase wage inequality,this does not imply that poverty increases aswages of unskilledworkers increase. However, in thesecond model with surplus labour specific to the non-traded agricultural good which is also anintermediate good, we show that the twowage ratesmove in opposite direction; but either of thetwo wage rates could increase depending on whether the export good is skilled or unskilledlabour intensive. Interestingly, in the event of rising wage inequality, the model predicts thatabsolute poverty may rise.
© 2014 Elsevier Inc. All rights reserved.
JEL classification:F11F13
Keywords:Trade and wage inequality
1. Introduction
That trade liberalization may affect real wages is a standard result of the celebrated Heckscher Ohlin Samuelson (HOS) modelof trade theory. Application of its corollary, the Stolper Samuelson (SS) theorem, clearly implies that after trade real wage rateswould go up in labour surplus economies and go down in capital surplus ones. Since developed countries can be considered to becapital surplus, this implies that trade between developed and developing countries would reduce wage rates in developedcountries and hence decrease wage inequality between countries. If we extend the model to a three factor world with capital,skilled and unskilled labour and assume that skilled labour and capital are complimentary, a simple extension of the SS theoremwould imply that increasing wage inequality between skilled and unskilled labour within a country, say, a developed nation, is aconsequence of increased trade liberalization in developed countries after the GATT came into force in 1948. In this paper we shalltalk about wage inequality within rather than between countries.
This decline in real wages of the unskilled labour in developed countries could also imply that trade leads to increased povertyin those countries. This was a subject of some concern in the USA in the 1990s. Early modelling of skilled and unskilled labour andstructural unemployment can be seen in Batra and Slottje (1993) who set up an extended HOS model to show how poverty in aneconomy like the USA could increase with trade liberalization. The HOS model, of course, only applies to trade between countrieswhich differ somewhat in their endowments as, for example, in the case of trade between developed (North) and developing
f two anonymous referees which greatly improved the final version of this article. We would also like tor draft of this paper.)[email protected], [email protected] (A. Barua), [email protected] (M. Pant).
173A. Barua, M. Pant / International Review of Economics and Finance 33 (2014) 172–185
countries (South). Hence, the model also implies that as wage inequality increases in one country, it must decline in the other.However, empirical studies, by and large, do not support this hypothesis and show that increased trade is in fact accompanied byincreasing wage inequality between unskilled and skilled labour in both developing and developed countries (Cline, 1997; for anextensive survey see Harrison, McLaren, & McMillan, 2010).
Clearly, since both increasing and decreasing real wages of skilled and unskilled labour consistent with a decline or increase inthe relative wages of skilled and unskilled labour, it seems necessary to model changes in the absolute real wages of unskilledlabour vis a vis skilled labour. Batra and Slottje (op.cit.) and Beladi and Batra (2004) model this issue of changes in relative andabsolutewages. In Batra and Slotje (op. cit), a tricky argument has been put forward that a fall (rise) in the average wage implies adecline (rise) in unskilled wage rate, since unskilled workers are assumed to earn a negative premium over the average wage, W ,which is determined competitively in the market. Now, a competitive firm pays a worker the average wage plus a positivepremium for the skill above some level and a negative premium for skill below that level. Thus, a fall in, W, necessarily implies adecline in the earnings of the low skilled workers. Thus, the model predicts that in a small economy with constant prices, a rise inthe labour force leads to a fall in, W , and hence increases in poverty or wage inequality.
In general, theoretical literature on this subject is scanty. Earlier work has tried to reconcile the empirical results with the HOStheory in one of two ways. One, by arguing that the issue is unrelated to trade; and wage inequality is, it is argued, increasingbecause of technology bias against unskilled labour (see, Wood, 1997). Two, that some of the assumptions of the HOS theorem areviolated. Thus, Deardorff (2001); Xiang (2007) have argued that in presence ofmultiple cones of diversification between countries,increased wage inequality may arise as a theoretical possibility. In one paper, Beladi & Batra (2004) addressed this issue byincorporating nontraded goods and specific factors in a general equilibrium model of trade. If unskilled labour is specific to thenontraded goods sector, wage inequality could increase if the output of the non-traded goods falls with increased trade; andwages of unskilled labour fall even faster than of skilled workers.
More recent models have looked at the issue of trade and wage inequality in the context of models where production isoutsourced. Here, while Batra and Beladi (2010) introduced outsourcing in a general equilibrium HOS model, others havedeparted from the perfectly competitive general equilibrium models by arguing that products are heterogeneous and consist of anumber of processes some being skilled labour intensive and others using more of unskilled labour. Over time, as transport costsdecline the production is fragmented with unskilled labour intensive processes outsourced to developing countries. In the latter,however, these processes are relatively skilled labour intensive. Hence, wage inequality will tend to increase in both sets ofcountries after trade. This is obviously a departure from the HOS assumptions of product homogeneity and non-factor intensityreversal. There are various variants of this basic approach. For an extensive survey see Harrison et.al (op.cit).
With the establishment of the WTO in 1995, the issue of trade liberalisation and wage inequality has once again receivedattention particularly in the context of empirical studies for developing countries like India, China and South Korea (see, forexample, Dutt, Mitra, and Ranjan (2009) and Hasan, Mitra, Ranjan, and Ahsan (2012); Mehta, and H, R,, (2012) and Mitra andShin (2012). In the same way, theoretical models have moved beyond the general equilibrium trade models to look at modelswith heterogeneous firms and imperfect labour markets. Thus in Davidson and Matusz (2012), firms face labour search costs inhiring and an inoptimal worker profile may be acceptable in the face of high search costs. The effect of trade on hiring/firingworkers depends on how it impacts the search incentives via changing the size of the market, competition, etc. Job creation isendogenous while job destruction is exogenous in Ranjan (2012). In this two sector trade model, price changes through trade leadto productivity shocks so that jobs are destroyed in the import sector and created in the export sector. The net effect of trade onunemployment (and hence wages) is ambiguous. In another variant, Bakhtiari (2012) models heterogeneous firms with skilledand unskilled labour and production outsourcing via trade. Using parametric values, the paper works out conditions under whichrelative wages of skilled and unskilled labour may increase with trade.
The brief survey shows that increasing wage inequality within and across countries seems to need some departure from thestandard general equilibrium HOS model. In this paper we have made an attempt to explain the phenomenon of increasingrelative wage inequality within the HOS general equilibrium framework using two separate models. In the first, we introduce aspecific factor. Here, productivity is crucial to the link between trade and wage inequality as in Bakhtiari (op.cit) but outsourcingis not necessary.
In the second model, we include a non-traded intermediate good used as an input in the production of final goods. Here, wealso attempt to model the characteristics of agriculture and employment in developing countries in particular where the issue ofthe link between trade and wage inequality has assumed serious political overtones. One specific innovation from earlier generalequilibrium models is that the non-traded good while being a consumption good also serves as an input into the productionprocess of other sectors. It is then shown that increased trade can lead to increased or decreased wage inequality even for a smalldeveloping country. We have also shown that the increasing relative wage inequality can co-exist with an increase in the absolutewages of both skilled and unskilled labour. The conditions under which this happens are also fairly simple unlike in earlier modelson this issue. By looking at absolute wages of unskilled labour we are also able to relate our arguments to the discussion on thelink between trade and poverty. Thus, we are able to show that even if trade leads to an increase in wage inequality that does notnecessarily imply that it also leads to an increase in poverty. In general, one does not need to take recourse to models of imperfectcompetition and/or outsourcing to reconcile trade theory with the empirical evidence on changes in relative and absolute wagesof skilled and unskilled wages.
In the next two sections we develop the two models with characteristics of a typical developing country. The model ofSection 2 is a simple one with one specific factor while Section 3 presents the model with non-traded intermediate good. Finallyin Section 4 we conclude with some policy suggestions.
174 A. Barua, M. Pant / International Review of Economics and Finance 33 (2014) 172–185
1.1. A stylised developing economy
The most defining feature of developing countries is surely the dominance of the agricultural sector. In India, for example,while the agricultural sector accounts for only about 15 of GDP, it accounts for about 50 of employment. Further, almost 95% offarmers own small plots that barely provide enough output for their own subsistence. It is only after satisfying their own needsthat these farmers provide the marketable surplus which feeds into the organised sector.
Second, it is also well known that in India only 10 of the labour force works in the organisedmanufacturing sector and 90 workin small scale industries and the informal sector. Much of this employment is actually self employment activity of the agriculturallabour in small hotels, local trades and construction with limited skill requirements. These are mainly family efforts to increaseincome through off season employment. In the construction sector, for example, most contractors rely on off season agriculturalworkers for the bulk of their labour force. At the same time this small scale sector accounts for about 40 of exports particularly insmall engineering, textiles and leather goods.
The organised sector is growing but is running against the constraint of insufficient skilled labour. Government retrainingprograms are now being run to impart skill training to unskilled labour so that they can graduate to the ranks of skilled labour.Much of this training takes place in non-university institutions called the Indian Technical Institutes (ITIs). A considerable numberof students here come from the ranks of the agricultural youth who no longer want to work in the agricultural sector particularlyafter they have acquired some necessary skill and training.
As mentioned above, the agricultural sector in India accounts for about 50 of employment and 15 of GDP. The latter share inparticular has been declining over time indicating that per capita incomes in this sector have been falling relative to other sectorsof the economy. With high levels of population below the poverty line democratic compulsions have compelled the governmentto legislate welfare measures like the Right to Food Act (RTF, 2013) and the National Rural Employment Guarantee Act (NREGA,2005). However, to implement such programs the government must itself make compulsory preemptive purchases of foodsgrains to stock the public distribution system. This reduces the availability of agricultural production in two ways one, by reducingthe marketed surplus, and, two, by reducing incentives to the agricultural labour force to work in the sector. We argue that astheir basic needs are covered, many in the farming sector are able to take time off for re-skilling to join the ranks of the skilledlabour in the organised sector. There is considerable evidence that farming is no longer a very profitable occupation especially forsmall and marginal farmers. In fact, in India, about 30 of farmers find farming unprofitable while 40 would prefer to work in somenon-farming occupation if given the choice (see, NSSO, 2005).
2. Model 1
Assume there are two sectors X1 (manufacturing.) and X2 (services) using capital (K) and labour (L). Capital, K, is specific to X1
and unskilled labour, LU, to X2. Relative price of X2 is P. In developing countries, the service sector does not fit the classic definitionof services and generally includes a lot of self employed in the trade and hotel industries Thus, for example, in India domesticwholesale and retail trade, real estate and construction services accounted for about 47 of the output of the services sector in 2007(see, Banga and Kumar (2009)). Much of the labour in these industries is what we would classify as unskilled labour.
The production functions in the two sectors are given by
X1¼X1 K1; L1ð Þ ð1Þ
X2 ¼ X2 LU; L2� �
ð2Þ
It is assumed both functions are linearly homogenous. Assuming full employment of all inputs we have,
L1 þ L2 ¼ L ð3Þ
LU ¼ LU ð4Þ
K1 ¼ K1 ð5Þ
The specifications in Eqs. (4) and (5) reflect the assumptions that unskilled labour and capital are sector specific.Given the factor market equilibrium conditions under competition, skilled wage, WS, is equated in both sectors so that we
have,
WS ¼ X1L ¼ P: X2
L ð6;7Þ
XL1 and XL
2 are the marginal physical productivities of skilled labour in sector 1 and 2 respectively.
WhereSimilarly, for unskilled labour we haveWU ¼ P: X2U ð8Þ
175A. Barua, M. Pant / International Review of Economics and Finance 33 (2014) 172–185
The subscript, U, in above represents unskilled labour. Thus, XU2 stands for marginal physical productivity of unskilled labour in
sector 2.Therefore, the model has the following 8 endogenous variables, viz., X1, X2, K1, L1, L2, LU, WS and WU which are to be determined
from the above 8 equations and the given three parameters, K1; L; and LU . The model is thus internally consistent.
2.1. Comparative statics2 results
From Eq. (6) and Eq. (7) using Eqs. (1), (2), (4) and (5) gives us
From
From
2 See
WS ¼ P: X2L LU ; L2� � ¼ X1
L K1; L1� � ð9Þ
Eqs. (3) and (9) are two equations in two unknowns, L1 and L2. Totally differentiating the equationswith respect toL1; L2 and L wecan show that
And
dL1dL
N0
dL2d L
N0
)ð10Þ
This does not depend on capital intensities since there is no substitution between L and LU or K. Also, given specific factors, Eq.(9) implies from Eqs. (1) and (2) that both X1 and X2 must increase. This is the well known result that with specific factors theRybczynski result breaks down (see, Bhagwati, Panagriya, and Srinivasan (1998)).
Again, differentiating Eq. (3) and Eq. (9) totally with respect to L1; L2 and LU gives us that
And
dL1dLU
b0
dL2dLU
N0
)ð11Þ
t the increase in supply of the specific factor increases the output of the sector where it is employed.
so thaThe results for the Stolper–Samuelson (SS) effect are more interesting. Thus, total differentiation of Eq. (9) givesdWS
dP¼ P X2
LLdL2dP
þ X2L ¼ X1
LLdL1dP
ð12Þ
Eq. (3) and Eq. (12) we get
And
dL2dP
¼ X2L
X1LL þ P: X2
LL
� �N0dL1dP
b0
)ð13Þ
Eq. (6) and Eq. (8) we get
And
dWS
dP¼ X1
LLdL1dP
N0
dwu
dP¼ X2
U þ P: X2UL :
dL2dP
N0
)ð14Þ
the signs in Eq. (14) are derived by using Eq. (13).
whereOnce again the standard SS result does not hold in the presence of specific factors since wages of both skilled and unskilledlabour increase. The intuition is obvious. An increase in the price of X2 implies an increase in the value of the marginal product ofboth skilled and unskilled labour (by Eqs. (6,7) – (8)) thus increasing wages all round. However, this implies a shift in skilledlabour from X1 to X2 so that the production of X2 rises and that of X1 falls. Hence, an increase in the price of the product increasesthe return to both factors employed in its production.
Suppose this country exports commodity 2. Hence, increased trade (an increase in P) would increase the wages paid to bothskilled and unskilled labour as shown in Eq. (14). This result contradicts the SS results a la Leamer (1995) as discussed above. In
Appendix A for the derivations of the results of this section.
176 A. Barua, M. Pant / International Review of Economics and Finance 33 (2014) 172–185
other words, an increase in both skilled and unskilledwages with trade liberalization, as observed for both developed and developingcountries, is perfectly consistent with a modified HOS model. Thus, we have the following proposition about the absolute wagehypothesis:
Proposition 1. Trade liberalization for a small country where unskilled labour is specific to the export sector will lead to an increase inthe absolute wage rates of both skilled and unskilled labour.
2.2. Wage inequality
What about the issue of wage inequality? Here we get some interesting results.Define, W, as the relative wage of unskilled to skilled labour, then
Where
3 Thisat a rapunskille
W ¼ WU
WS
Then it can be shown (see Appendix A) using Eq. (12) and Eq. (14) that
dWdP
¼ dWU
dP− dWS
dP¼ X2
U−X2L 1þ τ½ � ð15Þ
τ ¼PX2
UL–P X2LL
n oX1LL þ P X2
LL
� � b0 and initially W ¼ 1
Now, the absolute value of τ being greater or less than unity determines the sign of dWdP :More specifically;
And
dWdP
N0 for τj jN1
dWdP
b0 for τj jb1 only if X2L≫X2
U
)ð16Þ
q. (16) it is clear that for wage inequality to increase, dWdP b0, marginal productivity of skilled labour must be higher than for
From Eunskilled labour. In general, we would expect this to hold in most developing countries. If this difference is sufficiently high thenwage inequality could increase.
Proposition 2. In small open economies with a large body of unskilled labour force specific to the export sector, trade liberalization canlead to a decline in the relative wages or increasing wage inequality only if the skilled labour is more productive than unskilled labour
This brings out the general point that the issue is not one of trade liberalization per se but the differing productivities of skilledand unskilled labour. It is the latter that leads to increasing wage inequality rather than trade liberalization per se. For countrieslike India exports tend to be dominated by the unorganized sector with a preponderance of unskilled labour.3 The hypotheses ofPropositions 1 and 2 seem to be confirmed by some recent empirical evidence. Thus, Hashim and Banga (2011) in a study for Indiashow that in the period 1998–2005, increased trade has been accompanied by increasing wage inequality despite increase in thewages of unskilled labour. Our results show that this is probably due to the huge gap in productivity between skilled and unskilledlabour in the export sector.
Thus, we are able to construe a relative wage hypothesis within an absolute wage hypothesis where one is not necessarily inconflict with the other.
The coexistence of rising wage inequality in the presence of increasing absolute wages of both skilled and unskilled labourallows us to derive our third important proposition:
Proposition 3. Trade liberalization may lead to rising wage inequality. However, this does not imply that the absolute level of povertywould also increase and it may in fact decline.
Hence, it may still be true that there is increasing discontentment with trade due to falling relative wages. This is a bit like aDussenberry effect: even though absolute real wages of all labour is going up, the increasing wage inequality is leading to somediscontent. This probably explains the current dissatisfaction with trade liberalization in many developing countries.
sector comprises products like textiles, handicrafts, etc. In recent years exports of the Information Technology (IT) related services have been increasingid pace and constituted 50% of service exports. However, even here the dominant category are Business Process Outsourcing (BPO) services whered labour dominates (see, Banga and Kumar (op.cit)).
177A. Barua, M. Pant / International Review of Economics and Finance 33 (2014) 172–185
3. Model 2
As in Model 1, we assume that the country is a small one which takes world prices of tradable as given. There are two sectorsproducing final goods X1 and X2. Once again we call them Manufacturing and Services. However, now there is a third sector, forexample agriculture, producing an intermediate good, M, which is used in the production of both X1 and X2 but is also available asbasic food for consumption, A, by the unskilled labour. M is also a non-traded good4. Think of A as the amount of agriculturalproduction M which is surplus production after meeting intermediate requirements of X1 and X2. This is then procured by thegovernment to distribute to the unskilled labour under various social welfare schemes. There are two factors of production LS andLU However, while LS is used in the production of all three sectors; LU (unskilled labour) is specific to the sector, M. The totalsupply of unskilled labour, LU is given of which LU is employed gainfully in M. This implies that LU¼ 1−uð Þ LU Here u is the rate of
unemployment of unskilled labour. u is determined by labourers and depends on the level of subsistence food they get. The higheris A, the lesser the incentive for workers to work for production of M.5 They can remain unemployed in order to get an educationand become part of LS. u is a kind of frictional unemployment. It represents a parameter which can change if the governmentthrough various schemes increases wage payments to labour. In that case, some labourers (given by u) will prefer to remainunemployed to increase their skills through training and other schemes.
The model then is,
Hence
and
4 Fortraded.restricti
5 Farmscheme2005(o
X1 ¼ X1 LS1;M1
� �ð17Þ
X2 ¼ X2 LS2;M2
� �ð18Þ
M ¼ M LSm; LU� �
ð19Þ
Cm1 X1 þ Cm2 X2 þ A ¼ M ð20Þ
CLU M ¼ LU ð21Þ
the Cij's, the ith factor required per unit of the jth sector, or, in other words are the input output coefficients. Here CL1, CL2
Whereand CLM are the unit requirements of skilled labour to produce one unit of X1, X2 and M, respectively. Similarly, Cm1, Cm2 are theunit requirements of the intermediate good, M, per unit outputs of X1 and X2 and CLU is the unit requirement of unskilled labourper unit production of M.The full employment conditions are,
CL1 X1 þ CL2 X2 þ CLM M ¼ LS ð22Þ
LU ¼ 1−uð Þ LU ;0bub1 ð23Þ
ut any loss of generality we can put LU ¼ 1. Our focus in this paper is on u.
WithoThe marketable surplus increases as agricultural production increases. This allows the government to distribute more to theunemployed via various social welfare schemes.We model this as,
A ¼ α M;αb1 ð24Þ
ssumption is that the marketable surplus increases with the level of production.)
(The aPerfect mobility of skilled labour implies that the skilled wage, WS, is equalized across sectors so thatWS ¼ P1 MPLS1 ¼ P2 MPLS
2 ¼ Pm MPLSm ð25Þ–ð27Þ
some countries like India there is evidence to show that, due to domestic consumption requirements, most basic agricultural commodities are largely non-Exports of most agricultural goods are subject to clearance by the authorities and in large production items like wheat, milk etc. periodically exportons are clamped for domestic political reasons.ers are assumed to have a time preference in the sense of a leisure–income trade off. If A increases and is distributed by the government in some welfarethen farmers are assumed to put off work today for leisure time which is used to acquire skills to graduate to the class of skilled labour. See also, NSSO,p.cit.)
178 A. Barua, M. Pant / International Review of Economics and Finance 33 (2014) 172–185
The determination of the wage of the specific factor, WU, is given by
WU ¼ Pm MPum ð28Þ
As is usual, we need a numeraire good. So
P1 ¼ 1 ð29Þ
Eqs. (17)–(29) comprise the 13 equations of our model and the 13 endogenous variables are the X1, X2, L1,S L2S, LmS , Lu, M,
M1, M2, WS, WU, A and PM. Hence, some solution exists. The parameters are α, LS, the structural parameter, u, and price P2 of thesecond commodity.
Using Eqs. (20), (21) and substituting from other equations in the model we can reduce the model to a system of 3 equationsin X1, X2 and M.
CL1 X1 þ CL2 X2 þ CLM M ¼ LS ð30Þ
CLU M ¼ 1−uð Þ ð31Þ
Cm1 X1 þ Cm2 X2 þ α−1ð ÞM ¼ 0 ð32Þ
Here Eqs. (30)–(32) can be solved for the three variables of the model, X1, X2 and M. By appropriate substitution in the modelthe other variables can be solved for.
3.1. Comparative statics results6
Total differentiation of Eqs. (30)–(32) w. r. t LS gives us
dX1
dLSN ¼ b0 iff
L2M2
b ¼ NL1M1
dX2
dLSN ¼ b0 iff
L2M2
N ¼ bL1M1
dM
dLS¼ 0
)ð33Þ
From Eq. (33) it is clear that an increase in the supply of skilled labour (with unchanged commodity prices) leads to anincrease in the output of commodity (X2) which uses skilled labour intensively relative to the intermediate good and reduces theoutput of the other commodity, X2. Hence, the Rybczynski theorem holds. However, the output of the intermediate good remainsunchanged as shown in the third equation in Eq. (33).
Ourmodel provides scope for analysing the effects of increased rate of unemployment on the output supply.While theremay be avariety of reasons for unemployment, in ourmodelwe argue that it may be the effects of government intervention via social schemesto distribute larger quantities of food to the unemployed. We have argued that this would increase u. Total differentiation of Eqs.(30)–(32) gives
dX1
dub ¼ N0 iff
L2M2
N ¼ bL1M1
dX2
duN ¼ b0 iff
L2M2
N ¼ bL1M1
dMdu
b0
)ð34Þ
The intuition is obvious. An increase in u would lead to a decline in output of M. This also implies some release of skilledlabour, LS, from production of M. The lower availability of M for both X1 and X2 would require some reallocation of resources inthese sectors to accommodate the lower availability ofM and the skilled labour released fromM. Full employment would requirea decline in the output of the sector which is relatively less intensive in the use of M relative to LS as this also allows fullemployment of the skilled labour released from M. This is shown in Eq. (34) above.
3.1.1. Effect of government interventionAn important aspect of our model is the role of government procurement in the agricultural sector. Often the government in
developing countries has to increase its preemptive purchases of food grains due to demand for greater distribution of food grainsto the poor and also as a buffer against the rainy days. In India this has been legislated via the Right to Food (RTF) Act. In ourmodel the government intervention works through an increase in the parameter α.
179A. Barua, M. Pant / International Review of Economics and Finance 33 (2014) 172–185
Total differentiation of Eqs. (30)–(32) with respect to α yield
dX1
dαb ¼ N0;
dX2
dαN ¼ b0 iff
L2M2
N ¼ bL1M1
ð34aÞ
Thus, suppose government increases preemptive purchases in the agricultural sector. This would reduce the amount of Mavailable for the other two sectors since A increases. For full employment of skilled labour, LS, the output of the sector which usesM less intensively must decline and the output of the other sector increased to absorb the reduction in M and increase in LSreleased from the contracting sector.
This has some interesting implications. Suppose the export sector, X2 uses M intensively. This could happen if, for example, X2
represents the food processing sector. In that case, preemptive purchase by the government would reduce exports.
Proposition 5. For countries which export agricultural commodities, preemptive purchases by the government to service social sectorschemes would reduce exports by reducing the output of the agricultural sector.
The content of Proposition 5 may seem obvious. However, in our model what we are arguing is that the increased distributionof, for example, food through compulsory procurement (as in many developing countries) in the agricultural sector when coupledwith educational training skills of workers reduces the supply of unskilled labour to agriculture thus reducing output. Since thisoutput is an input into the export sector this may lead to a decline in agricultural exports. Hence one could see both decline inexports and increasing structural unemployment coexisting. However, this increase in unemployment is not the consequence ofreduced exports. The causation in fact runs in the reverse direction. It is, for example, often argued that reduced exports have ledto increased unemployment. What we are arguing is that this may not always be true. The link here between exports andunemployment is not so clear.
3.1.2. Wage inequality againIn this paper the focus is on what happens to wage inequality as this economy increases trade. We assume again that
commodity 2 is the exported commodity so that the consequence of trade is a parametric increase in P2. This parametric variationis applied to the model developed above.
The price equations of the model can be written as
CL1 WS þ CM1 PM ¼ 1 ð35Þ
CL2 WS þ CM2 PM ¼ P2 ð36Þ
CLM WS þ CLU WU ¼ PM ð37Þ
In Eq. (35), P1 = 1, since commodity 1 is the numeraire good. Substituting for PM from Eq. (37) into Eqs. (35) and (36) we canwrite,,
θ1 θ2θ3 θ4
� WSWU
� ¼ 0
1
� P2 ð38Þ
Here θ1 and θ3 are the direct and indirect requirements of skilled labour for producing one unit of outputs X1 and X2,respectively. Similarly, the indirect requirements of unskilled labour are given by θ2 and θ4. In the Appendix B we show that thedeterminant of the matrix, θ,
θ≷ ¼ 0 iffL1M1
≷ ¼ L2M2
, its sign depends on the relative skill – intensity of the two commodities, X1 and X2. Solving Eq. (38) using Cramer's rule, we
that isgetdWS
dP2¼ −θ2
.θb ¼ N0 iff
L1M1
N ¼ bL2M2
dWU
dP2¼ θ1
.θN ¼ b0 iff
L1M1
N ¼ bL2M2
)ð39Þ
From Eq. (39) we see that if the export sector, sector 2, is relatively skilled – labour intensive compared to sector 1 in terms ofthe intermediate good, that is, L2
M2N L1
M1so that θ b 0, then wages of skilled workers increases and that of unskilled labour decreases
when this country's trade increases. In general, the relative wage,W ¼ WUWS
as defined in Eq. (15) above, unambiguously falls or risesdepending on the relative intensity of use of skilled labour to intermediate good in the production of the two commodities.
180 A. Barua, M. Pant / International Review of Economics and Finance 33 (2014) 172–185
Proposition 6. In small countries with a large unskilled labour force specific to the agricultural sector, increased trade leads to anincrease (decrease) in wage inequality if the export sector is more (less) intensive in the use of the skilled labour relative to theintermediate agricultural good. The increase (decrease) of inequality is accompanied by an increase (decrease) in wages paid to skilledlabour and a decrease (increase) in wages paid to unskilled labour.
This, of course, is the well known Stolper–Samuelson result but with a twist. An increase in the price of X2 leads to an increase inthe production of X2 and a decline in the production of X1 under full employment conditions. However, a unit reduction of X1 releasesless amount of skilled labour than what is required in X2. This leads to a rise in the demands for skilled labour. On the other hand,the decline in the output of the sector X1 releases more intermediate good than could be absorbed in the expanding sector, X2, at theprevailing factor prices, that is, L1/M1 b L2/M2. The price of the intermediate goods falls, which leads to substitution of theintermediate good for skilled labour. Thiswould result in a decline in thewage of the unskilled labour. Thuswage inequality increases.If, on the other hand, the sector X1 is relatively skilled labour intensive then the exactly opposite situation will prevail, that is, theskilled wage will fall and the unskilled wage will increase resulting in a decline in wage inequality.
However, in contrast to the paper by Batra and Beladi (op.cit), our results on wage inequality are not conditional and onlyrequire that products must have differing factor intensities.
Our model also provides lessons for developing countries like India. It is not that trade increases wage inequality and povertybut the fact that the export sector does not extensively employ products of the intermediate good (agricultural) sector wheremost of the poor and unskilled labour is employed. Our model thus makes a case for developing a manufacturing sector based onexports of processed agricultural goods. In the current scenario where the growth of exports in India is based largely on a servicesector which has few linkages to agriculture, trade is likely to lead to an increase in wage inequality and absolute poverty.
In Banga and Kumar (op.cit.) it has been shown that in India the fastest growing exports are of the service sector where 50% ismade up of IT services, specifically, software services. However, at $40 billion in 2008–09, these constitute less than 1% of the GDPof about $4.5 trillion. Hence it is unlikely that even exports of the BPO sector (where unskilled labour dominates) would make anydent on wage inequality. The problem seems to be stagnant exports of the small manufacturing sector where most of theunskilled agricultural labour could be absorbed.
4. Conclusion
Empirical studies by and large reject the most important hypothesis of the Heckscher–Ohlin–Samuelson (HOS) model thattrade will improve both inter and intra country wage inequality. Theoretical studies using general equilibrium models have triedto explain this by arguing that the issue of inequality is not linked to trade. Other studies argue that the basic assumptions of theHOS model are violated so that its predictions are not observed. A third set of such studies have modified the HOS model toinclude specific factors and intermediate goods but are unable to get unconditional results on wage inequality. That wageinequality could increase with trade thus seems to be best explained by using imperfect competition models of trade and productheterogeneity. Finally, there is the theoretical issue of reconciling the absolute wage hypothesis with the relative wage hypothesiswithin the standard HOS framework. The last step is necessary to reconcile observed empirical trends with theoretical models.
In this paper we have attempted to set up two models and specifically model wage inequality. The simple model with specificfactors indicates that the basis for inequality is differing productivities of skilled and unskilled labour. The model also suggests thatwhile trade may increase wage inequality this does not imply that poverty increases as wage of unskilled workers also increase.
We also set up a modified HOS model which specifically incorporates the structural features of developing countries. Themodel includes specific factors and a non-traded good which is itself an input into the production process. The model givesunambiguous results on the impact of trade on wage inequality which depends on the link between the non-traded good and theexport sector. The weaker this link the more likely that trade will result in increased wage inequality. This suggests that what isrelevant is the structure of trade and not trade per se.
In many developing countries today there is considerable concern over the growing wage inequality as global trade expands.We suggest that the solution here to be found in domestic policies like productivity improvements and linkages of non-trade andtrade goods sectors. Protective trade policies are not a solution.
Appendix A
Model 1
From Eqs. (6,7) in the text and using Eqs. (3)–(5), we get
X1L�K; L1
� � ¼ pX2L L2; �Lu� � ðA:1Þ
Totally differentiating Eq. (A.1) above and given that K and L are fixed, we get,
δX1L1=δL1
� �dL1 ¼ p δX2
L=δL2� �
d L2 þ X2L L2; �Lu� �
dp
Or
Or,
Or
Or,
181A. Barua, M. Pant / International Review of Economics and Finance 33 (2014) 172–185
δX1L=δL1
� �dL1– pδX2
L=δL2� �
dL2 ¼ X2L L2; �Lu� �
dp ðA:2Þ
From Eqs. (3)–(5) in the text
dL1 þ dL2 ¼ 0
dL1 ¼ −dL2 ðA:3Þ
Now, using Eq. (A.3) in Eq. (A.2), we get
− δX1L=δL1 þ pδX2
L=δL2h i
dL2 ¼ X2L L2; �Lu� �
dp
dL2=dp ¼ −X2L L2; �Lu� �
= δX1L=δL1 þ pδX2
L=δL2h i
dL2=dp ¼ −X2L L2; �Lu� �
= X1LL þ pX2
LL
h iN0 ðA:4Þ
(Since, by the concavity property of the production function both X1LL and p X2
LL are negative). Therefore,So, from Eq. (A.3)
dL1=dpb0
Again, totally differentiating the Eqs. (6,7) in the text we get,
dWS ¼ X1LLdL1 ¼ pX2
LLdL2 þ X2LdP
Therefore,
dWS=dp ¼ X1
LLdL1=dp ¼ pX2LLdL2=dpþ X2
L ðA:5Þ
So, from Eq. (A.4), and the fact that X1LL b 0,
X1LLdL1=dpN0 implies dWS
=dpN0
The equality relation of Eq. (A.5) requires that the expression
pX2LLdL2=dpþ X2
LN0
e positive.
must bSimilarly, totally differentiating Eq. (8) in the text we getdWU=dp ¼ X2
U þ pX2UL:dL2=dpN0 ðA:6Þ
(Since, X2U N 0 being the marginal productivity of unskilled labour and d L2/d p N 0 by Eq. (A.4) and X2
UL N 0 since more ofskilled labour on a given specific unskilled labour raises the productivity of unskilled labour)
Now, we define, W = WU/WS,
dW=dp ¼ dWU=dp−dWS
=dp¼ X2
U þ p:X2UL:dL2=dP– p:X2
LL:dL2=dPþ X2L
n o ðA:7Þ
Substituting from Eq. (A.4) for d L2/d p, we write the above expression as,
¼ X2U–X
2L þ p:X2
UL–p:X2LL
n o−X2
L= X1LL þ p:X2
LL
� �n o¼ X2
U–X2L 1þ λð Þ
ðA:8Þ
Where λ = {p.X2UL − p.X2
LL}/{X1LL + p.X2
LL} b0 (since marginal products are diminishing).These results are shown in Eq. (15) in the text.
182 A. Barua, M. Pant / International Review of Economics and Finance 33 (2014) 172–185
Rybczynski effect
Effects of increase in Skilled Labour (LS)At constant commodity prices, we can write from Eq. (A.2)
or
δX1L=δL1
� �dL1 ¼ p δX2
L=δL2� �
dL2 ðA:9Þ
From full employment Eq. (3) in the main text
dL1 þ dL2 ¼ dL
Dividing both sides of Eq. (A.9) by d L we get
δX1L=δL1 dL1=dLð Þ ¼ pδX2
L=δL2 dL2=dLð Þ ðA:10Þ
Since, marginal productivities are positive it follows from Eq. (A.10) that
dL1=dLN0 and dL2=dLN0
Appendix B
Model 2
Eqs. (30)–(32) in the text can be written as
CL1 CL2 CLM0 0 CLU
Cm1 Cm2 α−1ð Þ
0@
1A X1
X2M
0@
1A ¼
LS1−u0
0@
1A ðB:1Þ
C V ¼ Z ðB:2Þ
Where C is the coefficient matrix, V is a column matrix representing the variables in the system and Z is column matrixrepresenting the parameter of our system. Here CL1, CL2 and CLM are the unit requirements of skilled labour to produce one unit ofX1, X2 andM, respectively. Similarly, Cm1, Cm2 are the unit requirements of the intermediate good per unit outputs of X1 and X2 andCLu is the unit requirement of unskilled labour per unit production of M.
C ¼CL1 CL2 CLM0 0 CLU
Cm1 Cm2 α−1ð Þ
0@
1A
;
V¼X1X2M
0@
1A and Z ¼
LS1−u0
0@
1A
On simplification, we get,
C½ � ¼ −CL1 CLU Cm2 þ CL2 CLU Cm1 ¼ CLU Cm1 Cm2CL2
Cm2− CL1
Cm1
�
¼ CLU Cm1 Cm2L2M2
− L1M1
�
That is,
C ≷ ¼ 0 as L2=M2≷ ¼ L1=M1
In other words, if X2 is relatively skilled – labour intensive compared to X1 in terms of the intermediate goods then Cdeterminant will be positive or alternatively, if X1 is relatively skilled – labour intensive compared to X2 in terms of theintermediate goods then C determinant will be negative.
183A. Barua, M. Pant / International Review of Economics and Finance 33 (2014) 172–185
Comparative static analyses: effects of the changes in factor endowment, the rate of unemployment and Government Procurement Policy(i) Differentiating B.1 with u & α unchanged gives us the effects of change in LS as given in Eq. (33) in the text.
And
C½ �dX1dX2dM
24
35 ¼
100
24
35 dL
–
S
The Cij's in [C] are unchanged, given unchanged commodity prices. Solving the above using Cramer's rule we get
dX1
dLS¼ − 1
CCLU Cm2e 0 as
L2M2
≷ ¼ L1M1
dX2
dLS¼ 1
CCLU Cm1≷ ¼ 0 as
L2M2
≷ ¼ L1M1
dMdLS
¼ 1C
:0 ¼ 0
(ii) Differentiating of B.1 with LS & α unchanged gives us the effects of changes in u as shown in Eq. (34) in the text.
C½ �dX1dX2dM
24
35 ¼
0−10
24
35 du
Solving the above using Cremer's rule gives us
dX1du
¼ 1C
− 1−αð Þ CL2−CLM Cm2f g
Therefore,
dX1du
e 0 asL2M2
≷ ¼ L1M1
Similarly,
dX2du
¼ 1C
1−αð Þ CL1 þ CLM Cm1f g
Therefore,
dX2du
≷ ¼ 0 asL2M2
≷ ¼ L1M1
Finally,
dMdu
¼ 1C
CL1 Cm2−CL2 Cm1f g
Substituting from |C| we get
dMdu
¼ CL1 Cm2−CL2 Cm1f gCLU Cm1 Cm2
L2M2
− L1M1
�
The expression in the numerator above can be simplified as
dMdu
¼Cm1 Cm2
CL1
Cm1− Cl2
Cm2
�
CLU Cm1 Cm2L2M2
− L1M1
�
Or,
Or,
And
Here
184 A. Barua, M. Pant / International Review of Economics and Finance 33 (2014) 172–185
dMdu
¼−Cm1 Cm2
L2M2
− L1M1
�
CLU Cm1 Cm2L2M2
− L1M1
�
dMdu
¼ − 1CLU
b0
(iii) Differentiating B.1 assuming that LS & u unchanged gives the effects of changes in α on the final goods as shown inEq. (34a) in the text.
C½ �dX1dX2dM
24
35 ¼
00
−m
24
35 dα
Solving by Cremer's rule we get
dX1dα
¼ 1C
m CL2 CLUf g
Therefore,
dX1dα
≷ ¼ 0 asL2M2
≷ ¼ L1M1
dX2dα
¼ 1C
m CL1 CLUf g
dX2dα
≷ ¼ 0 asL2M2
≷ ¼ L1M1
Finally,
dMdα
¼ 0
Comparative statistic analyses: the effects of price changesThis is the Stolper Samuelson result assuming all factor supplies are constant FromEqs. (35)–(37) in the text, substituting for Pm in
Eqs. (35) & (36) we get
CL1 þ Cm1CLMð ÞWS þ Cm1CLUð ÞWU ¼ 1
CL2 þ Cm2CLMð ÞWS þ Cm2CLUð Þ WU ¼ P2
We can rewrite these equations in Matrix form as given below (Eq. (38)) in the text,
θ1 θ2θ3 θ4
� WSWU
� ¼ 1
P2
� ð38Þ
Here θ1 and θ3 are the direct and indirect requirements of skilled labour for producing one unit of outputs X1 and X2, respectively.Similarly, the indirect requirements of unskilled labour are given by θ2 and θ4.
We can write Eq. (38) in vector notation as,
θ:W ¼ P ðB:3Þ
θ ¼ θ1θ4‐ θ2 θ3¼ Cm1 Cm2 CLU
L1M1
− L2M2
�
Theref
Differe
And
185A. Barua, M. Pant / International Review of Economics and Finance 33 (2014) 172–185
ore,
θ≷ ¼ 0 asL1M1
≷ ¼ L2M2
ntiating Eq. (38) totally we get
θ1 θ2θ3 θ4
� dWSdWU
� ¼ 0
1
� dP2 ðB:4Þ
Where the θ's stand for the shares of factors in the unit cost of production and moreover the sign of the θ determinant dependson the same condition as in V.
In deriving Eq. (B.4) we have used the condition that cost minimization ensures that
wS dθ1 þWU dθ2 ¼ 0
wS dθ3 þWU dθ4 ¼ 0
Solving Eq. (B.4) by using Cramer's rule gives us Eq. (39) in the text.
And
dWS
dP2¼ − θ2
θe 0 as
L1M1
≷ ¼ L2M2
dWU
dP2¼ θ1
θ≷ ¼ 0 as
L1M1
≷ ¼ L2M2
)ð39Þ
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