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International trade and quality of labour
Author’s Accepted Manuscript International Trade and Quality of Labour Sarbajit Chaudhuri, Sugata Marjit
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S1059-0560(16)30362-8 http://dx.doi.org/10.1016/j.iref.2017.03.018 REVECO1403
To appear in: International Review of Economics and Finance Received date: 15 December 2016 Revised date: 12 March 2017 Accepted date: 13 March 2017 Cite this article as: Sarbajit Chaudhuri and Sugata Marjit, International Trade and Quality of Labour, International Review of Economics and Finance, http://dx.doi.org/10.1016/j.iref.2017.03.018 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
1
International Trade and Quality of Labour
Sugata Marjit
Sarbajit Chaudhuri
Department of Economics, University of
Centre for Studies in Social Sciences, Calcutta, India.
Calcutta, India. E-mails: [email protected]
E-mail: [email protected]
[email protected]
This version: March 12, 2017
Abstract: This paper argues that better prospect for exports induces firms to distinguish high quality workers from low quality workers by providing an incentive wage. Thus, trade leads to identification of labour quality, widening the wage gap between the high quality (skilled) and the low quality (unskilled) workers. The results are derived in a model containing both moral hazard and adverse selection problems. We provide a different argument from the ones as available in the existing literature including the standard Shapiro-Stiglitz (1984) shirking model. Finally, the results of the paper have some important policy implications.
Keywords: Quality of labour; incomplete information; incentive contract; international trade; wage gap; Ricardian trade model.
JEL Classification: D86; F16; J31; L15.
This paper has been revised in the light comments of two anonymous referees of this journal to whom the authors are thankful. The usual disclaimer, however, applies.
Corresponding author.
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1. Introduction
A well-known textbook result in the theory of international trade is that a country will take part in international trade and export a commodity only if the relative price of the exports good at the international market is greater than its autarkic price. Given this, the following could be a plausible situation in a low income country. In the situation of autarky the firms producing a commodity may not be concerned about the quality of the output because the price of a high-quality output is low owing to demand scarcity in the home market. Consequently, a representative profit-maximizing firm in the competitive industry might have no incentive to distinguish between workers having different levels of quality from a pool of heterogeneous workforce and offer higher (lower) wages to workers possessing higher (lower) quality because the detection mechanism involves some costs. However, the workers possessing a certain level of quality are capable of producing a high-quality output of the commodity that cannot be produced by other workers having lesser competence. The same firm, nonetheless, when international trade opens up resulting in a higher price for the high-quality outputs in the international market might be interested to produce and export some amount of the high-quality product. Consequently, the prospect of a booming exports market for better quality controlled items that can be produced only by workers possessing a certain level of skill might induce the firm to isolate better quality workers from the rest of the clan.
1
In this paper, we would try to model the behavior of the firm under the above situation. Our work is mainly related to two different literatures: (i) the literature on trade liberalization and wage inequality; and, (ii) the literature on asymmetric information and wage differentials.
1
Throughout this paper the two terminologies, “labour quality” and “labour productivity” have been interchangeably used.
3 The recent literature on trade and wage inequality elegantly summarized in Feenstra (2004) and described in Marjit and Acharyya (2006) for general readers, points towards the trade-technology debate in explaining the rising wage gap across skills within an economy. Acemoglu (1998) argues that skilled-biased technological progress, a resultant of the trade liberalization, explains the rising wage inequality in the industrialized countries. Oladi et al. (2011) have shown how FDI flow in the high-skill exports sector in the presence of non-traded final good can increase the wage inequality although it raises the real wages of both skilled and unskilled labour. Nevertheless, at the same time there is no denial of the fact that rising wage gap is a phenomenon in many of the developing 2
countries as well. Because the relative wages have moved against unskilled labour in the developing economies in which unskilled labour is the abundant factor is contrary to the predictions of the standard Heckscher-Ohlin trade model with Stolper-Samuelson theorem at its core calls for theoretical explanations. Feenstra (2004), Zhu and Trefler (2005) etc. come up with explanations in terms of increased foreign direct investment (FDI) in high-skill sectors. Conversely, Pi and Chen (2016), Pi and Zhou (2014), Anwar and Sun (2015), Barua and Pant (2014), Marjit and Acharyya (2003), Chaudhuri and Yabuuchi (2007, 2008), have explained the increasing wage inequality in the Southern countries in terms of some of the essential characteristics of the developing economies 3
e.g. factor market imperfections, presence of non-traded goods, dualistic structures etc.
However, what is missing in this literature is a microeconomic mechanism that links trade liberalization to wage inequality with or without asymmetric informational problems.
2
The empirical studies of Robbins (1994, 1995, 1996) have pointed out that while the inequality has narrowed in the East Asian countries, the Latin American countries like Mexico, Chile, Costa Rica and Columbia have experienced increasing skilled-unskilled wage gap following the liberalized trade and investment policies. Besides, Harrison and Hanson (1999) and Beyer et al. (1999) have observed that trade reforms in 1980s were associated with sharp deterioration in the skilled-unskilled wage inequality in Mexico and Chile, respectively. Curie and Harrison (1997) and Revenga (1997) have also come to the same broad conclusion. On the other hand, indirect studies on poverty by Khan (1998) and Tendulkar et al. (1996) also possibly indicate that
the wage inequality has increased after trade openness in the South Asian countries including India. 3
Also see Beladi et al. (2008), Marjit et al. (2004) and Chaudhuri (2008) in this context.
4
On the other hand, the literature that discusses asymmetric informational problems and wage differentials includes works of Shapiro and Stiglitz (1984) (S-S (1984), hereafter), MacLeod and Malcomson (1988), Akerlof and Yellen (1990), Basu et al. (2010), Jones and Marjit (1995) etc.
The S-S (1984) work discusses the role of an incentive contract to overcome the moral hazard problem of a firm under competitive conditions.4 It explains how unemployment/ job rationing can motivate the workers to be more disciplined and less job-shirking. Let us discuss the incentive mechanism they have suggested as follows.
If the i th firm offers a wage Wi , which is higher than the market-clearing level W0 , it raises the worker‟s expected loss arising out of job-shirking. Because if caught while shirking she would be fired and has to accept a job in other firms at a lower wage, W0 . Competition among firms would ensure that all firms would eventually be offering the higher wage,
W Wi
clearing wage,
for all i . Since the actual wage, Wi is greater than the market-
W0 the demand for labour falls short of the aggregate supply at W which i
in turn leads to involuntary unemployment of labour. The existence of unemployment motivates (acts as an incentive to) the workers not to shirk in their duties. However, the attitudes of the workers towards risk play an important role in this context.
On the other hand, MacLeod and Malcomson (1988) using a game-theoretic model have shown that if the rent from an employment contract is sufficiently large, firms may use either the efficiency wage instrument (high wage combined with threat of firing like the 4
The initial appraisal of the S-S (1984) model was due to its “competitive” nature. It appeared that both of the product and labour markets are perfect. However, a scrutiny of the paper reveals that firms are not wage-takers in the labour market. Although the i th firm sets the ball on the motion and determines the incentive wage, which is higher than the market-clearing wage, to get rid of the „moral hazard‟ problem other firms follow suit and ultimately offer the same wage. At this high wage the aggregate demand for labour falls short of its supply that leads to involuntary unemployment. In the present paper as well the firms are wage-makers although they are pricetakers in the product market.
5 one we find in the S-S (1984) model) or performance pay (e.g.an end-of-period bonus) to motivate workers to perform well. In their model economic agents are risk-neutral. Hence, this rent is the difference between the return to the current mutual agreement and that in the spot market for labour. If either the worker shirks or the firm does not pay the bonus, a separation occurs, which harms the offending party through a loss of the future rent from the contract.
Besides, Akerlof and Yellen (1990) have suggested another mechanism to mitigate the moral hazard problem which is known as the “fair wage-effort hypothesis”. There exists a psychological perception of the workers on what constitutes a „fair wage‟: The higher the wage rate relative to the standard of reference which the workers consider fair, the higher would be the work effort supplied by the workers in equilibrium. The profit-maximizing firm minimizes its unit cost of labour and chooses the „fair wage‟ that it would offer. Consequently, this causes involuntary unemployment thereby leading to wage dispersion between the different groups of worker (e.g. employed and unemployed). Then again, Basu et al. (2010) have shown that in the presence of both moral hazard and adverse selection problems, non-compliance with minimum wage legislation can indeed be an equilibrium phenomenon in a model of minimum wage policy with imperfect competition. In another paper by Jones and Marjit (1995) better quality workers have to accept a lower wage over an initial period when firms are learning about their quality. Hence, the onus is with the workers to convince the firms that they are of better quality and take the one period loss to signal their quality.
In all of these works, we come across different incentive wage mechanisms under different situations to overcome the asymmetric informational problems. Nonetheless, none of the above papers links international trade to wage dispersion among the workers. However, the following two papers look precisely at the effect of trade on quality upgrading and its consequences for workers in a world without uncertainty.
6 Verhoogen (2008) proposes a mechanism that links trade to wage inequality in developing countries, and investigates its empirical implications on Mexican manufacturing plants. In this model with heterogeneous plants and quality differentiation, more productive plants produce higher-quality goods for exports relative to less productive plants that produce only for the domestic market. The higher productive plants pay higher wages to maintain a higher-quality workforce. An exogenous shock in the form of exchange rate devaluation leads more-productive plants to increase exports, upgrade quality of goods produced, and to raise wages relative to less-productive plants within the same industry, thereby increasing within-industry wage dispersion. Nevertheless, in this paper we do not find any specific mechanism by which trade enhances productivity of labour.
Yeaple (2005) in terms of a general equilibrium trade model offers a competing explanation for the size and non-production wage differentials between exporting and non-exporting firms with heterogeneous workforce. Firms have complete information regarding the quality of labour. They take decision regarding entry, adoption of production technology, whether to export; and, the decision regarding the type of workers to employ. In equilibrium, the interaction between the characteristics of competing technologies, international trade costs, and the availability of workers of heterogeneous skill gives rise to firm heterogeneity. As mentioned above, Yeaple (2005) does not deal with adverse selection and moral hazard problems.
In the circumstances, the present paper is devoted to relate the above two distinct literatures with a view to examine how in a world of asymmetric information international trade could provide an incentive to firms to differentiate the heterogeneous workforce with respect to their labour quality and increase workers‟ effort, and thereby their quality that eventually leads to skilled-unskilled wage inequality.
7 In our proposed model there is uncertainty in period 1 because the firm cannot distinguish 5
between workers with respect to their quality. However, by offering a high incentive wage to all workers in period 1 and observing the quality of outputs they produce the firm is able to distinguish between high-quality and low-quality workers from period 2. The workers who do not put in sufficient effort to attain the threshold labour quality ( Z ) requiring for producing the high-quality output, would automatically be detected by the inferior quality of output they produce and be offered a low wage ( W0 ) in the subsequent periods. The wage of low-quality workers falls after the initial period because they are reassigned to producing low-quality goods.
6
The incentive contract that we have suggested can effectively tackle both the moral 7
hazard and adverse selection problems facing by the firm in period 1. Furthermore, we have provided a theory of determination of endogenous wage differentials between workers of different quality. Finally, our analysis explains how opening up of the economy (trade liberalization) may lead to widening of skilled-unskilled wage inequality.
2. The model
2.1 Description of the model and its assumptions
Consider an infinite-period decision-making problem of a firm where good X is produced by means of labour only. Commodity X can be of two qualities: a good (exportable)
5
Worker‟s quality is assumed private information. In period 1, firms cannot make payment contingent on the quality of output, which creates moral hazard/adverse selection problem for the employer. 6
It is important to note that there would be no such job switching for low-skill workers in the full information model, and hence no wage decline, because the workers could be separated between low and high-quality from the beginning of their employment. 7
How our incentive mechanism takes care of the moral hazard problem has been elaborately discussed at the end of section 2.4.
8 quality ( X * ) and an inferior quality ( X I ). Competitive conditions prevail in the product market. The good quality output ( X * ) can be sold (exported) at a high price, P * . On the other hand, the inferior quality of output ( X I ) can at best be sold in the domestic market at a price, P with P P * . Hence, there could be two production divisions of the firm: (i) one division that produces X * ; and, (ii) another one that produces X I . However, the firm has to take the decision whether to produce the good quality output at all. We would subsequently see that this decision would crucially hinge on the price difference, ( P * P) .
In the labour market, there is a market-clearing wage, W0 although the firm has the liberty to offer a higher wage to some of its workers, if it finds it profitable.8 The firm faces a certain number of heterogeneous workers who differ with respect to quality of labour services they can provide ( Z ) with Z [0,1] . However, by putting in an extra effort it is possible for every worker to attain a certain a threshold level of quality, Z , which is required to produce the high-quality output, X * . A relatively high-quality worker (with a high Z ) has to offer a lower effort (if not, any extra effort at all) to attain the threshold quality, Z while a relatively low-quality worker (with a low Z ) has to put in more effort to attain that quality ( Z ). On the other hand, the higher the effort (lower the value of Z ) the greater would be the associated cost, C , (disutility of putting in an extra effort) on the part of the worker in order to attain Z level of quality and vice versa so that C '(Z ) 0 .
The number of workers employed by the firm is normalized to unity. Z denotes the labour quality of the marginal worker hired by the firm for its high-quality division. Because Z [0,1] , the lower (higher) the optimum value of Z the lower (higher) would be labour
quality of the marginal worker which in turn implies higher (lower) employment in the
8
The optimality of the incentive wage contract has been examined in section 2.4.
9 9
segment that produces high-quality output. In other words, (1 Z ) and Z denote the levels of employment in the high-quality and low-quality production divisions, respectively. We have already mentioned that the low-quality output is sold in the domestic market at the low price, P .
The firm has incomplete information about the quality of its workers and cannot distinguish between high and low-quality workers at the initial situation. In the absence of any exports prospects the firm has to sell its entire product in the domestic market where the commodity price is low. In such a situation the firm may not find it profitable to screen its workers in terms of quality.
Nevertheless, if there arises an exports possibility that assures a higher price for the good quality product, the firm may find it profitable to offer a wage W , greater than the low existing market wage, W0 to all of its workers in period 1 for two reasons: (i) to distinguish between high and low-quality workers by observing the quality of output they produce; and, (ii) to make a higher profit producing at least some amount of good quality output ( X * ) and selling the same at a higher price, P * . The rest is sold (in the domestic market) at the low price, P . In other words, if the firm offers W level of wage to all of its workers in the first period, not only the possibility of getting a higher (international) price for at least a part of its output, and thereby earning a higher level of profit opens up but also it helps the firm to distinguish between high and low-quality workers and economize on wage cost in the subsequent periods. This is because it would then offer W and W0 wages to the high and low-quality workers, respectively. Hence, the firm in this model is not necessarily a wage-taker. In fact, the whole idea behind this exercise is wage-making. The firm is a wage-maker in the case of good quality workers although is a wage-taker for the rest because it would offer them (the latter group) the prevailing low market wage and assign them to produce the low-quality output for the domestic market.
9
If the interpretation of the symbol, Z seems confusing, one can alternatively use two different symbols for denoting the labour quality and the level of employment in the high-quality division.
10 2.2 Decision-making problem of the worker
Given the assumptions of the model the i th worker, irrespective of her quality ( Z i ), receives the incentive (high) wage, W in period 1. In this period, she has the following two options. The first option is to put in the extra effort for being able to produce the good quality output, and be labeled as high-quality worker in period 2. Once her quality is revealed and is considered as a high-quality worker in period 2, she will receive the high wage in period 2 and continue to receive the same in the subsequent periods as well. However, in this case she has to incur a cost (disutility of putting in an extra effort) given by C ( Z ) with C '(Z ) 0 where Z is her quality. Her sum of discounted net incomes, denoted U G , is
given by
U G [W C (Z )] [W C (Z )] 2 [W C (Z )] 3[.] ...... [
W C (Z ) ] 1
` (1)
where is the rate of time preference with 1 . On the contrary, if she decides not to put in an extra effort she would be labeled as lowquality worker in period 2. She would in any case receive the high wage, W in period 1 but will continue to receive the existing low market wage, W0 in each of the subsequent periods. In this case, her sum of discounted incomes, denoted U B , will be given by the following.
U B W W0 [ 2 3 ...... [W
1
W0 ]
(2)
Comparing both equations (1) and (2) we get the condition that she will put in that extra effort in order to attain the threshold level of labour quality iff U G U B
11 i.e. iff (W W0 ) C (Z )
(3)
2.3 Decision-making problem of the firm
We assume that each worker produces one unit of output, irrespective of whether she is a good worker or not. Nonetheless, the quality of output differs. After normalizing the number of workers employed by the firm to unity the sum of discounted profits of the firm when it sells at least a part of its output in the international market is as follows. * [ P *(1 Z ) PZ W ] [ P *(1 Z ) PZ W (1 Z ) W0 Z ] 2 [ P *(1 Z ) PZ W (1 Z ) W0 Z ] 3[..] ......
[ P *(1 Z ) PZ W ]
[ P *(1 Z ) PZ W (1 Z ) W0 Z ] (1 )
1 * ( )[ P *(1 Z ) PZ W Z (W W0 )] 1
(4)
The problem of the firm is to maximize (4) with respect to Z and W , and subject to the constraint as given by (3). This maximization exercise leads to the following proposition.
Proposition 1: In equilibrium the discounted value of the difference between the actual wage paid and the existing wage, (W W0 ) must equal the cost of putting in an extra effort, C ( Z ) required for attaining the threshold level of labour quality, Z .
Proof:
In the above constrained maximization exercise of the firm, the Lagrange function is written as follows.
12
1 Max ( )[ P *(1 Z ) PZ W Z (W W0 )] [ (W W0 ) C ( Z )] 1 Z ,W
(5)
where is the Lagrange multiplier and 0 .
Assuming interior solutions for the two choice variables Z and W the first-order and Kuhn-Tucker conditions are obtained as follows.
(
1 )( )[( P * P) (W W0 )] C '( Z ) 0 Z 1
(6)
(
1 1 Z )( )[1 Z ] 0 [ ]0 W 1 (1 )
(7)
) [ (W W0 ) C ( Z )] 0; and, ( ) 0 (
(8)
From (7) and (8) it follows that the constraint given by (3) would be binding in equilibrium. Hence, we have the following equation.
(W W0 ) C (Z )
(9)
This proves proposition 1. Substituting the value of from (7) in equation (6), using (9), and simplifying we can obtain the following equation.
1 Z C (Z ) ( )C '( Z ) ( P * P) p *
(10)
In (10), p * denotes the price difference between the high-quality and the low-quality outputs of the commodity in the presence of international trade where p* ( P * P) .
The optimum value of Z is found from (10). We find that the optimum Z is a function of p *( P * P) only. In other words, it is independent of the parameter, W0 . Once Z is
obtained the equilibrium value of W is obtained from (9) which, however, depends on both p * and W0 .
13 Equation (9) can alternatively be rewritten as follows.
W W0
C (Z )
(9.1)
Differentiating equation (9.1) we find that
(
2W C ( Z ) W C ( Z ) 0 according to C(Z ) 0 . ) 0 ; and, ( 2 ) Z Z
(9.2)
Now from (9.1) it is evident that the optimum W is greater than W0 for any Z [0, Z ) and, 10 that W is a decreasing function of Z because C(Z ) 0 . The determination of the
optimum W for a given Z (already determined from (10)) can be diagrammatically shown in terms of figure 1. (Space for Figure 1)
In figure 1, the initial (prevailing market) wage is shown by the horizontal line W0 while the curve AB represents equation (9.1). If the optimum Z is Z * , the equilibrium wage that the firm would offer under the incentive contract is W * which, however, rises if Z falls.
2.4 Optimality of the incentive contract
Now, our objective is to show that for a sufficiently high value of p * the firm might find it optimal to offer W to all of its workers in period 1. We are going to prove that the optimality of the incentive contract crucially hinges on the magnitude of the price
10
It may be noted that once the quality of the i th worker reaches the threshold level ( Z ) she does not need to put in any extra effort to be labeled as high-quality worker and receive the incentive wage, W , in the subsequent periods too. Hence, as Z moves from 0 to Z , the cost of (need for) putting in any extra effort tends towards zero. Hence, in the limiting case, when Z Z , we have C ( Z ) 0 . Therefore, the AB curve in figure 1 asymptotically moves towards the horizontal line, W0 .
14 difference of the commodity between the international and the domestic markets.11 The result that we obtain is presented in the form of the following proposition. Proposition 2: There exists a critical size of p * (say p * ) such that if p* p * , * 0 . In other words, if the price difference of the commodity between the international and domestic markets is sufficiently high, the offering a higher wage to all the workers in period 1 is the optimal policy of the firm.
Proof:
Assuming the sum of discounted profits of the firm when it sells its entire output in the domestic market, 0 , to be positive we can write 0 ( P W0 )[1 2 ....] =
( P W0 ) >0 (1 )
From (11) it follows that we are actually assuming,
(11) P W0
.
Subtracting (11) from (4) we obtain
1 ( * 0 ) ( )[ P *(1 Z ) PZ W Z (W W0 )] ( P W0 )[1 2 ....] 1 1 ( )[( P * P)(1 Z ) (W W0 )(1 Z )] 1
(12)
Using (9) and simplifying, equation (12) may be rewritten as follows.
1 C (Z ) ( * 0 ) ( )[( P * P)(1 Z ) (1 Z )( )] 1
(12.1)
Now,
11
In a different context, Mukherjee (2008) has shown that the size of the product market is pivotal in explaining the co-existence of foreign direct investment and exports even in a world without uncertainty.
15
d ( * 0 ) 1 dZ 1 Z ( )[(1 Z ) ( ){C ( Z ) p * ( )C '(.)}] dp * 1 dp *
Using equation (10) we write
d ( * 0 ) 1 Z ( )0 dp * 1
(13)
d 2 ( * 0 ) (dZ / dp*) [ ]0 2 dp * 1 Also
(14)
From (12.1) we note that ( * 0 ) 0 when p* ( P * P) 0 . Besides, from (13) and (14) it follows that ( * 0 ) is a monotonically increasing function of p * and is convex downwards.
Hence, we would find a critical level of of p * (say p * ) such that
* 0
if p* p * . In
other words, if the price difference of the commodity between the international and domestic markets is sufficiently high, the offering a higher wage to all of the workers in period 1 is the optimal policy of the firm.
This proves our proposition 2.
The curve showing the relationship between
( * 0 )
and p * would be like the one
which is shown in figure 2.
(Space for Figure 2)
Thus, the opening up of international trade that results in a higher price received by the firm for its high-quality output may provide an incentive to offer a higher wage by the firm to all of its workers in overcoming both the adverse selection and moral hazard problems relating to the quality of its employees.
16 A pertinent question at this juncture is whether there is a shirking problem in the subsequent periods even in the present setting. Following the initial period, labour quality of each of the workers is revealed and the firm knows whether a particular worker puts in her optimum effort. It may, however, be argued that a good worker, who exerts the sufficient effort to attain the threshold level of labour quality, Z in the (n 1) th period, has still the option of not exerting the optimum effort in the n th period, producing a lowquality product, and of collecting the incentive wage for that ( n th) period. This is because by assumption, the wage rate cannot be adjusted to reflect the quality of the good produced by her in the same period. Even if she still claims to be a good quality (highskilled) worker and demands the high incentive wage in the (n 1) th period, there is no reason for the firm to entertain such an unethical claim. This is because in the (n 1) th period by observing the quality of output she has produced in the n th period the firm can easily prove that she did not put in an extra effort in that period. Hence, it would offer her only the low wage, W0 in the (n 1) th period.
However, the equilibrium condition given by (9) in the wage contract will deter this shirking. If any of the workers deviates from her optimum effort supply decision she would only suffer because her sum of discounted net incomes would fall. On the other hand, the firm also would not have any reason to deviate from its decision on the incentive wage and pay the workers (or at least some of them) a lower wage in any future period. Because if it does then those workers whose marginal costs of putting in extra effort are greater than the new lower wage, would immediately stop putting in the extra effort to produce the high-quality output. Both of the parties‟ actions are verifiable. The action on the part of the firm would only adversely affect its profitability. Hence, any deviation from the equilibrium W and Z would not be beneficial to either of the two parties.
17 3. Comparative statics
In this section of the paper we would like to examine the consequences of an increase in the international price of the high-quality product, P * or an increase in the existing market wage, W0 on the number of good quality workers employed by the firm(s) and the incentive wage. The results that we obtain relating to changes in P * are stated in terms of the following two propositions. Proposition 3: The higher the difference between the international and domestic prices of the commodity, the lower would be the quality of the marginal worker employed by the firm. In other words, the firm hires a larger number of good quality workers with an increase in the international price of the high-quality output.
12
Proposition 4: Opening up of international trade accentuates the relative wage inequality between skilled and unskilled labour.
Proof of proposition 3:
Differentiation of equation (10) yields
(
dZ ) 0 dp * [2 C '(.) (1 Z )C "(.)] if C "(.) 0.
(15)
and, ( 0) d Z 3 C ( Z ) dZ ) [ ]( ) 0 according to C(Z ) 0 2 2 dp * {2 C '(.) (1 Z )C "(.)} dp * (+) (-) 2
(
2
(15.1)
Hence, the number of good quality workers employed by the firm increases with an increase in the international price of the high-quality output. The initial labour quality of 12
A good quality worker, having at least the threshold level of labour quality, Z is capable of producing the high-quality output that can be exported at the international price, P * . If her initial labour quality is less (not less) than Z she requires (does not require) putting in an extra effort to attain Z .
18 the marginal worker employed in the high-quality division decreases with an increase in the number of workers employed. Hence, the marginal worker in that division has to put in more extra effort with an increase in p * so that she could attain the threshold level of labour quality, Z for producing the good quality output and be labeled as a good quality worker.
This proves proposition 3.
Proof of proposition 4:
Differentiation of (9) leads to the following. (
dW C '( Z ) dZ ) [ ( )] 0 dp * dp * (-) (-)
(16)
From equation (16) it then follows that
(
d (W W0 ) )0 dp *
(16.1)
Hence, an increase in the international price of the high-quality product, given the domestic price of the low-quality product raises the skilled-unskilled wage inequality.
13
Thus, proposition 4 is proved.
This is a crucial result of this theoretical exercise.
The results presented in propositions 3 and 4 can be diagrammatically explained in terms of figure 3. (Space for Figure 3)
13
Note that the workers who decide to attain the threshold level of labour quality, Z by putting in extra effort are termed as skilled workers and receive the high incentive wage, W . The remaining workers who decide not to put in an extra effort cannot produce the high-quality output. Because of this they are labeled as unskilled and receive the low wage, W0 . Hence, the absolute skilledunskilled wage gap is (W W0 ) .
19 In panel b of figure 3, CD curve represents equation (15) where Z is found to be a negative function of p * . In panel a of figure 3, we show W and (W W0 ) as functions of p * . A change in p * leads to a change in Z which in turn changes both the incentive
wage ( W ) and the wage gap ( W W0 ) across skills. Because an increase in p * lowers the quality of the marginal worker employed by the firm in the high-quality division, a higher incentive wage, W has to be offered to lure her to perform well (note that her marginal cost of putting in an extra effort is also higher). This is how an increase in p * raises W that in turn raises (W W0 ) .
At this position, it is not difficult to examine the consequences of a change in the existing (autarkic) market wage, W0 on the incentive wage and the levels of employment in the two production divisions. The results that we obtain are presented in the form of the following proposition. Proposition 5: Any change in the prevailing market wage in the economy cannot change the labour quality of the marginal worker employed by the firm in its high-quality division. Hence, the levels of employment in the two production divisions remain unaffected. However, it causes a less than proportionate change in the incentive wage.
Proof:
Differentiating equations (9) and (10) and simplifying we find that (
W dZ W W0 EW ,W0 ( ) ( 0 ) 1 ) 0; W0 W W dW0 and, .
Here,
EW ,W0
is the elasticity of W with respect to
W0
. In other words, it measures the
W responsiveness of the incentive wage, W due to a change in the current market wage, 0 .
20 Hence, a change in the existing market wage, W0 , cannot change the level of employment in the high-quality division, ( 1 Z ) and that in the low-quality division, Z . Nonetheless, it causes a less than proportionate change in the incentive wage, W .
This proves proposition 5.
As long as p * is given, Z is determined from equation (10). Therefore, any changes in
W0 will not affect Z . This happens if and only there is a one-to-one correspondence between W and W0 . This has further interesting implication for the degree of wage inequality. Proportional change in W with respect to a proportional change in W0 will always be less than unity because absolute change in W will exactly be equal to absolute change in W0 , but W W0 , hence the result. If two countries, one having higher initial wage than the other and facing a given p * are subjected to the process of quality revelation of workers, the relative wage gap will be smaller for the richer economy.
4. Comparison with the S-S (1984) work
In this section of the paper, we would like to make a detailed comparison between our results and those of the famous Shapiro-Stiglitz (S-S) (1984) model because it is a close counterpart of our work.
The S-S (1984) paper concentrates solely on the moral hazard problem that a firm under competitive product market faces. It has devised an incentive wage mechanism to overcome that problem. On the contrary, in the present model there are both adverse selection and moral hazard problems. The firm faces a heterogeneous labour force with different labour quality. Therefore, it cannot distinguish between high-quality workers who with or without putting in an extra effort are capable of producing a high-quality output and other workers who despite having low-quality decide not to exert the right
21 amount of effort to be able to produce the high-quality output. We have devised an incentive mechanism where the firm by offering the same incentive wage to all of its workers in period 1 and observing the quality of outputs that they have produce in period 2 is able to differentiate between the two types of worker. Thus, from period 2 and onwards the uncertainty regarding workers‟ quality ceases to exist. This mechanism solves the moral hazard problem as well because the good quality workers, who continue to receive the high incentive wage in the subsequent periods, including period 2, would have no reason to put in less effort in any of the subsequent periods. This is because the firm would be able to identify shirking of jobs by those workers from the quality of output they have produced in the next period. This should be clear if we look at the binding constraint of the workers which is given by equation (9). This issue has already been adequately discussed at the end of section 2.4. An important question at this juncture is whether the „low-quality workers‟ who are being offered the existing low wage, W0 by the firm after the first period and the „low wage‟ they receive can be renamed to „unemployed‟ and „unemployment benefit‟, respectively. Let us now attempt to provide an answer to this question.
In this hypothetical scenario, there is no domestic market for the low-quality output. Hence, the firm does not produce anything in the no trade situation which in turn implies that there is no employment for workers at autarky. However, each of them receives the unemployment benefit, W0 from the government. Alternatively, we can think of a situation where there is a domestic market for quality output. Nonetheless, the demand is so low such that it is not profitable for the firm to produce anything at the given reservation wage, W0 . Hence, in either of the two situations the employment level is zero. Now, suppose that the possibility of international trade opens up so that the firm gets the opportunity to export high-quality output at a reasonably high price at the international market, P * .
The firm faces a heterogeneous labour force with varying labour quality. To begin with there are both adverse selection and moral hazard problems. In period 1, the firm offers
22 the high incentive wage, W to those workers who with or without putting in an extra effort can attain the threshold labour quality, Z and produce the high-quality output for exports. The quality of a worker is identified in period 2 from the quality of output she has produced in period 1. Subsequently, only the good quality workers will be employed and be offered the incentive wage, W . The remaining workers decide not to put in an extra effort to produce the high-quality output, remain unemployed and continue to receive the unemployment benefit, W0 . Why the shirking problem on the part of the employed workers in the subsequent periods cannot arise has already been explained at the end of section 2.4. Hence, from period 2, uncertainty ceases to exist. All of the qualitative results of our analysis except proposition 5 will continue to hold even in this modified scenario.
14
Hence, it makes only a very little difference if „low-quality worker‟ and „low wage‟ are reworded to „unemployed worker‟ and „unemployment benefit‟, respectively. In other words, once the revelation of quality of labour is made, in period 2 and thereafter the situation becomes almost the same what we find in the S-S (1984) work. However, it is trade liberalization, which makes the present case more or less akin to the S-S (1984) situation. Hence, the present exercise may be viewed as an application of the key intuition of the S-S (1984) model in the context of trade liberalization.
Nonetheless, it is important to note that the level of employment in the present case rises and the initial quality of the marginal worker employed by the firm continuously falls with an increase in the international price of the high-quality output, P * . This becomes clears if one looks at figure 3. In panel b, figure 3, the CD curve shows the relationship between the equilibrium value of Z and p * (or P * in the present hypothetical situation). With an increase in P * the equilibrium value of Z decreases; and, hence the level of employment, (1 Z ) increases. For a sufficiently high value of P * , the equilibrium value
14
The results have been proved in Appendix 1. It shows why proposition 5 has to be partially modified in this present hypothetical case.
23 of Z could even be zero. At that point full-employment could be attained. Therefore, the possibility of attaining full-employment in this setting cannot be ruled out.
5. A General Equilibrium Analogue
In this section, we build up a simple Ricardian model, based on the micro foundation of the incentive mechanism which has already been developed in the earlier sections for overcoming the asymmetric informational problems, to depict the possible path of wage distribution resulting from trade liberalization using a competitive general equilibrium setting. Besides, this portion is also aimed at establishing that the main result of our partial equilibrium analysis is easily applicable at least to the simple Ricardian general equilibrium trade model. Finally, we would like to compare our main results with those of Bond (2008) which also provides a labour contract theoretic approach in the Ricardian context.
Thus far, we have shown that if the price of the good increases beyond a critical level, firms will offer a wage W W0 in a way to induce a mass of ( 1 Z ) workers to produce the high-quality good for exports.
Let us now start from a competitive Ricardian economy producing both the high-quality and the low-quality goods. Thus due to free entry and free exit assumption both and * vanish.
From (4) [ P *(1 Z ) PZ W ZC (Z )] 0
(17)
where Z continues to be determined from equation (10).
Therefore, P * p * Z ( p*) Z ( p*)C (Z ( p*)) W
(18)
24 and from 0 we know P W0
(19)
We also have a sector where quality is not so important and the homogeneous good is represented by x with WaLx Px 1
(20)
P and P * are, therefore, measured in units of 1 .
If to start with the closed economy did not have any demand for high-quality good, say Y , the choice is really between producing x and y . Equations (19) and (20) coupled with the standard full-employment condition (21) and demand condition (22) will yield the standard Ricardian equilibrium outcome and the autarkic relative price, P . aLx x y L
(21)
Dx ( P) Dy
(22)
As the economy opens up for trade, it faces the possibility of selling a high-quality product at P* P . First note that W W0 with
W W0
C ( Z ( p*))
(23)
LZ number of workers cannot produce high-quality good and therefore can choose to work in x or in y or both at a wage W0 1/ aLx . If W0 1/ aLx , then production of x will cease altogether. If we have W0 1/ aLx , the reverse is true. Therefore, equilibrium wage in the other sector will be given by W where W Max( P,
1 ) aLx
(24)
The following sequence of outcomes is in order. (a) Initially in autarkic equilibrium everyone gets W0 produced.
1 and both x and y are aLx
25 (b) If trade opens up without the possibility of exporting the high-quality product facing a rest of the world relative price P , only x or y will be produced and W Max( P,
1 ) . We do not discuss this case and assume P P . aLx
(c) With the possibility of earning P* P , the firms make the wage offer W W0 to everyone for a while (one period in our model). This implies that x and y both cease to be produced as skill needs time to be revealed.
Once skill is revealed there are essentially two sets of workers, one earning W and the other W . Either Y and x are produced or Y and y are produced. The path of wage distribution in general equilibrium is shown in figure 5.
(Space for Figure 5)
Starting from a point like A where everyone earns W0 , the system jumps to B where all workers earn W during the revelation period. Then it moves to C where relative wage settles down along OC at
W (W0 W ) . Eventually, trade widens the wage gap. W0
In Bond (2008) international trade affects the productivity of labour through changes in the quality of intermediate inputs. Besides, in his model there is no uncertainty and hence no asymmetric informational problems. Furthermore, contracting frictions are not verifiable in court. On the contrary, we have provided a mechanism, through which trade in the presence of asymmetric informational problems may lead to revelation of labour quality, isolates the skilled from the unskilled, and eventually leads to a wage gap. The path of wage movement resulting from trade liberalization has been shown using a simple Ricardian trade model that is based on the microeconomic wage-based incentive mechanism that we have developed in the first part of our work.
26 6. Concluding remarks:
This paper argues that the prospect of a larger exports market for a high-quality good induces firms to distinguish between high-quality workers and low-quality workers offering them a higher wage. Since shirking is not a big problem in the paper, the standard Stiglitz-Shapiro (1984) avenue of providing a higher than equilibrium wage does not arise.
15
However, the firms engaged in exports have an extra incentive to
identify high-quality workers. Screening costs involve paying everyone a higher wage for one period and then identify the better ones from a pool of heterogeneous workforce. Workers respond optimally to such a strategy and eventually a separation occurs generating a wage gap. We then graft this model onto a Ricardian framework and derive implications for evolution of wage distribution.
There are three critical contributions of the paper.
16 , 17
First, this shows how rising
exports prospect generates more productive use of labor by identifying the high-quality
15
That the moral hazard problem is automatically taken care of by the incentive wage mechanism that we have suggested has been discussed at the end of section 2.4. 16
Our paper might be linked to certain real life situations. A classic example in the context of our paper could be the increasing demand for call centre services of high-quality, situated mostly in some developing countries, resulting from trade liberalization. The skilled workers who work in those places are heterogeneous in nature because of the differences in their communication skills, abilities to responding to customer queries and satisfying them. Consequently, the higher the demand for such services, the higher would the demand for high-quality workers and hence the better would be their pay packages. 17
The implications of the results of this paper are expected to influence economic policies regarding educational attainment and international trade. In this respect, changing demographics are also likely to have a strong impact on the links between international trade and labor quality. For instance, there may be important links between ageing and trade. While ageing of the working age population (until prime-age) generally increases average labor quality due to larger return to previous investment in human capital, it may result in lower incentives for current investment in human capital. Ageing is thus likely to result in downward pressure on the contribution of labor quality to aggregate productivity growth. We are thankful to one of the two anonymous referees for drawing our attention to such interesting implications of our results that in the earlier version of the paper we did not include.
27 workers. Thus, it is a framework that explicitly links trade with labour productivity.
18
Second, the paper shows how trade generates the skilled-unskilled wage inequality by providing a mechanism which is completely different from the standard ones suggested in the literature.
19
Finally, an outcome is highlighted which suggests that the equilibrium
degree of wage inequality in richer nations will be less pronounced than that in poorer countries.
Further extension of this paper will involve explicit consideration of investments by the firms to improve labor quality, global market fluctuations, and unemployment of the skilled and the unskilled labour and the relationship between trade, productivity, and economic growth.
References: Acemoglu, D. (1998): ‘Why do new technologies complement skills? Directed technical change and wage inequality‟, Quarterly Journal of Economics 113(4), 1055-1089. Akerlof. G. A. and Yellen, J. L. (1990): „The fair wage-effort hypothesis and unemployment‟, Quarterly Journal of Economics 105(2), 255-283. Anwar, S. and Sun, S. (2015): „Taxation of labour income and the skilled–unskilled wage inequality‟, Economic Modelling 47, 18 – 22. Barua, A. and Pant, M. (2014): „Trade and wage inequality: A specific factor model with intermediate goods‟, International Review of Economics and Finance 33, 172 – 185.
18
In our work firms are homogenous, and we have not analyzed the link between international trade and product quality that has been done using models of firm heterogeneity in Melitz (2003), Egger and Kreickemeier (2009), Helpman et al. (2010), Bas and Ledezma (2015) etc. Note that the basic objective of our analysis is to emphasize the link between international trade and labour quality. 19
High-quality and low-quality workers may be termed as skilled and unskilled workers,
respectively. Although it is possible for every worker to attain the threshold quality, Z by putting in an extra effort and become a high-quality worker, in equilibrium some of them decide not to put in that extra effort and remain as low-quality workers. These workers are termed as unskilled workers. On the contrary, the high-quality workers are labeled as skilled workers.
28 Bas, M. and Ledezma, I. (2015): „Trade liberalization and heterogeneous technology investments‟, Review of International Economics 23(4), 738–781. Basu, A.K., Chau, N.H. and Kanbur, R. (2010): „Turning a blind eye: costly enforcement, credible commitment and minimum wage laws‟, The Economic Journal 120 (543), 244269. Beladi, H., Chaudhuri, S. and Yabuuchi, S. (2008): „Can international factor mobility reduce wage inequality in a dual economy?‟, Review of International Economics 16(5), 893-903. Beyer, H., Rojas, P. and Vergara, R. (1999): „Trade liberalization and wage inequality‟, Journal of Development Economics 59(1), 103-123. Bond, E.W. (2008): „Input quality, relational contracts and international outsourcing‟, Pacific Economic Review 13(4), 391-404. Chaudhuri, S. (2008): „Wage inequality in a dual economy and international mobility of factors: do factor intensities always matter?‟ Economic Modelling 25(6), 1155-1164. Chaudhuri, S. and Yabuuchi, S. (2008): „Foreign capital and skilled–unskilled wage inequality in a developing economy with non-traded goods‟, in Sugata Marjit, Eden S.H. Yu (eds.) Contemporary and Emerging Issues in Trade Theory and Policy (Frontiers of Economics and Globalization, Volume 4), Emerald Group Publishing Limited, Chapter 12, 225-250. Chaudhuri, S. and Yabuuchi, S. (2007): „Economic liberalization and wage inequality in the presence of labour market imperfection‟, International Review of Economics and Finance 16(4), 592-603. Currie, J. and Harrison, A. (1997): „Trade reform and labor market adjustment in Morocco‟, Journal of Labour Economics 15(3), 44-71. Egger, H. and Kreickemeier, U. (2009): „Firm heterogeneity and the labour market effects of trade liberalization‟, International Economic Review 50(1), 187–216. Feenstra, R.C. (2004): Advanced International Trade: Theory and Evidence, Princeton University Press. Harrison, A. and Hanson, G. (1999): „Who gains from trade reform? Some remaining Puzzles‟, Journal of Development Economics 59(1), 125-154.
29 Helpman, E., Itskhoki, O., and Redding, S. (2010): „Inequality and unemployment in a global economy‟, Econometrica 78(4), 1239–1283. Jones, R.W. and Marjit, S. (1995): „Labour market aspects of enclave-led growth‟, The Canadian Journal of Economics 28, S76-S93. Khan, A.R. (1998): „The impact of globalization in South Asia‟, in A.S. Bhalla (ed.), Globalization, Growth and Marginalization, Macmillan. MacLeod, B. W. and Malcomson, J. M. (1988): „Implicit contracts, incentive compatibility, and involuntary unemployment‟. Econometrica 57(2), 447-480. Marjit, S. and Acharyya, R. (2006): „Trade liberalization, skill-linked intermediate production and the two-sided wage gap‟, Journal of Policy Reform, 9(3), 203-217. Marjit, S., Beladi, H. and Chakrabarti, A. (2004): „Trade and wage inequality in developing countries‟, Economic Inquiry 42(2), 295-303. Marjit, S. and Acharyya, R. (2003): International Trade, Wage Inequality and the Developing Countries: A General Equilibrium Approach. Heidelberg: Physica/Springer Verlag. Melitz, M.J. (2003): „The impact of trade on intra-industry reallocations and aggregate industry productivity‟ Econometrica 71(6), 1695–1725. Mukherjee, A. (2008): „Unionised labour market and strategic production decision of a multinational‟, The Economic Journal 118 (532), 1621-1639. Oladi, R., Gilbert, J. and Beladi, H. (2011): „Foreign direct investment, non-traded goods and real wages‟, Pacific Economic Review 16(1), 36-41. Pi, J. and Chen, X. (2016): „The impacts of capital market distortion on wage inequality, urban unemployment, and welfare in developing countries‟, International Review of Economics and Finance 42, 103 – 115. Pi, J. and Zhou, Y. (2014): „Foreign capital, public infrastructure, and wage inequality in developing countries‟, International Review of Economics and Finance 29, 195 – 207. Revenga, A. (1997): „Employment and wage effects of trade liberalization: the case of Mexican manufacturing‟, Journal of Labour Economics 15(3), S20-S43. Robbins, D. (1994): „Philippine wage and employment structure 1978 – 1983‟, HIID. Robbins, D. (1995): „Trade, trade liberalization and inequality in Latin America and East Asia: Synthesis of seven country studies‟, HIID.
30 Robbins, D. (1996): „HOS hits facts: facts win: evidence on trade and wages in Developing world‟, HIID. Tendulkar, S., Sundaram, D.K. and Jain, L.R. (1996): „Macroeconomic policies and poverty in India 1966-67 to 1993-94‟, manuscript, ILO, New Delhi. Shapiro, C. and Stiglitz, J.E. (1984): „Equilibrium unemployment as a worker discipline device‟, American Economic Review 74, 433-444. Verhoogen, E. A. (2008): „Trade quality upgrading, and wage inequality in the Mexican manufacturing sector‟, Quarterly Journal of Economics 123(2), 489-530. Yeaple, S. R. (2005): „A simple model of firm heterogeneity, international trade, and wages‟, Journal of International Economics 65(1), 1- 20. Zhu, S.C. and Trefler D. (2005): „Trade and inequality in developing countries: a general equilibrium analysis. Journal of International Economics 65, 21-48.
31 Appendix 1: The case with unemployment benefit
Suppose that the domestic market for low-quality output does not exist. Hence, to begin with all of the workers are unemployed. However, each of them receives an unemployment benefit, W0 from the government. In the absence of the domestic market,
P 0 . Besides, W0 is considered the reservation income of each worker. In this case, the constraint (3) of the workers remains intact. The sum of discounted profits of the firm, denoted ** is given by
1 1 ** ( )[( P * W )(1 Z ) (1 ) ZW ] ( )[ P *(1 Z ) W (1 Z )] 1 1
(A.1)
The firm maximizes ** with respect to Z and W ; and, subject to the reservation income constraint of the workers as given by (3).
The Lagrange function is as follows.
1 * ( )[ P *(1 Z ) W (1 Z )] *[ (W W0 ) C ( Z )] 1
(A.2)
where * is the Lagrange multiplier with * 0 .
The first-order conditions of maximization are as follows.
1 ( )( W P*) * C ( Z ) 1
(A.3)
1 ( )( Z 1) * * 0 1 (-)
(A.4)
The Kuhn-Tucker conditions are the following.
32 * ) [ (W W0 ) C ( Z )] 0; and, * * *( )0 * (
(A.5)
From (A.4) and (A.5) it follows that the constraint given by (3) would be binding in equilibrium. Hence, we have the following equation.
(W W0 ) C (Z )
(9)
This shows that proposition 1 remains unaffected even in the modified situation. Substituting * from (A.4) in (A.3) and simplifying we obtain the following equation.
1 Z C (Z ) ( )C ( Z ) ( P * W0 )
(A.6)
Totally differentiating equations (9) and (A.6) and solving we obtain the following results.
(
dZ 3 dZ 2 ) ( ) 0;( ) ( ) 0; dW0 dP *
(
dW ) ( )[ C ( Z ) (1 Z )C ( Z )] 0; dW0 (+)
(-)
(+)
( 0)
and,
(A.7)
(-) dW C ( Z ) ( ) [ ] 0; dP * (+) [{ C ( Z ) (1 Z )C ( Z )} 2C ( Z )] 0 where,
(-)
(+)
( 0)
(-)
(A.8)
33 dZ dW )0 ( )0 From (A.7) we find that dP * ; and, dP * . These imply that an increase in the (
international price of the high-quality output lowers the quality of the marginal worker and raises the incentive wage. The latter suggests that the wage inequality, (W W0 ) increases with an increase in P * .
Hence, propositions 3 and 4 remain intact.
Differentiating equation (A.1) with respect to P * we get
(
d ** 1 dZ dW dZ )( )[(1 Z ) P *( ) (1 Z )( ) W ( )] dP * 1 dP * dP * dP *
(A.9)
dZ dW ) ( ) Substituting the values of dP * and dP * from (A.7) in equation (A.9) and simplifying (
one obtains the following.
(
d ** 1 Z )( )0 dP * 1
(A.9.1)
d ** ) Differentiating dP * with respect to P * we find the following. (
(
d 2 ** 1 dZ ) [( )( )] 0 2 dP * 1 dP * (-)
(A.10)
Because the optimum ** is a monotonically increasing function of P * , proposition 2 also remains unaltered.
However, proposition 5 needs to be partially modified. Let us see how.
From (A.7) we find that (
(
dZ )0 dW0 ; and, dW ) 0. dW0
(A.11)
34 Hence, an increase in the unemployment benefit (reservation income of each worker) raises not only the incentive wage but also the labour quality of the marginal worker employed by the firm. The latter implies that it lowers employment. The intuition is straightforward. Because of an increase in the opportunity income of each worker the profit-maximizing firm must raise the incentive wage. This follows directly from the binding constraint, given by equation (3). Otherwise, the firm cannot lure the marginal worker to put in the extra effort to reach the threshold labour quality, Z so that she can produce the high-quality output. In this situation the firm employs fewer workers than previously because the marginal cost of employing an additional worker has increased.
dW ) dW 0 From (A.7) and (A.8) we substitute the expression for in . After simplification we (
0(
find that
dW W W0 ) 1 EW ,W0 ( ) 1 E W W dW0 W W 0 0 . Because , . Here, W ,W0 is the elasticity
of W with respect to W0 .
These results partially modify proposition 5 as follows. Proposition 5.1: An increase (a decrease) in the unemployment benefit lowers (raises) the level of employment of the firm under the incentive contract. However, it causes a less than proportionate change in the incentive wage.
35
Figures
W ,W0 A
W **
W* B
W0
Z
O
Z **
Z*
Figure 1: Determination of W for a given Z
36
( * 0 ) ( * 0 )
O
p*
Figure 2: The
p*
( * 0 )
curve as function of p * .
37
W ,(W W0 )
W
W0 Figure 3, panel a: W and
(W W0 ) as positive
O
p1 *
functions of p * .
p2 *
p*
Z
C Z1
Z2
O
p1 *
D
p2 *
Figure 3, panel b: Z as a negative function of p *
p*
38
Skilled
W
C
3
B
2
1 W0 aLx
A 1
45
0
Unskilled W0
1 aLx
W
Figure 4: Path of wage distribution in general equilibrium
www.elsevier.com
PII: DOI: Reference:
S1059-0560(16)30362-8 http://dx.doi.org/10.1016/j.iref.2017.03.018 REVECO1403
To appear in: International Review of Economics and Finance Received date: 15 December 2016 Revised date: 12 March 2017 Accepted date: 13 March 2017 Cite this article as: Sarbajit Chaudhuri and Sugata Marjit, International Trade and Quality of Labour, International Review of Economics and Finance, http://dx.doi.org/10.1016/j.iref.2017.03.018 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
1
International Trade and Quality of Labour
Sugata Marjit
Sarbajit Chaudhuri
Department of Economics, University of
Centre for Studies in Social Sciences, Calcutta, India.
Calcutta, India. E-mails: [email protected]
E-mail: [email protected]
[email protected]
This version: March 12, 2017
Abstract: This paper argues that better prospect for exports induces firms to distinguish high quality workers from low quality workers by providing an incentive wage. Thus, trade leads to identification of labour quality, widening the wage gap between the high quality (skilled) and the low quality (unskilled) workers. The results are derived in a model containing both moral hazard and adverse selection problems. We provide a different argument from the ones as available in the existing literature including the standard Shapiro-Stiglitz (1984) shirking model. Finally, the results of the paper have some important policy implications.
Keywords: Quality of labour; incomplete information; incentive contract; international trade; wage gap; Ricardian trade model.
JEL Classification: D86; F16; J31; L15.
This paper has been revised in the light comments of two anonymous referees of this journal to whom the authors are thankful. The usual disclaimer, however, applies.
Corresponding author.
2
1. Introduction
A well-known textbook result in the theory of international trade is that a country will take part in international trade and export a commodity only if the relative price of the exports good at the international market is greater than its autarkic price. Given this, the following could be a plausible situation in a low income country. In the situation of autarky the firms producing a commodity may not be concerned about the quality of the output because the price of a high-quality output is low owing to demand scarcity in the home market. Consequently, a representative profit-maximizing firm in the competitive industry might have no incentive to distinguish between workers having different levels of quality from a pool of heterogeneous workforce and offer higher (lower) wages to workers possessing higher (lower) quality because the detection mechanism involves some costs. However, the workers possessing a certain level of quality are capable of producing a high-quality output of the commodity that cannot be produced by other workers having lesser competence. The same firm, nonetheless, when international trade opens up resulting in a higher price for the high-quality outputs in the international market might be interested to produce and export some amount of the high-quality product. Consequently, the prospect of a booming exports market for better quality controlled items that can be produced only by workers possessing a certain level of skill might induce the firm to isolate better quality workers from the rest of the clan.
1
In this paper, we would try to model the behavior of the firm under the above situation. Our work is mainly related to two different literatures: (i) the literature on trade liberalization and wage inequality; and, (ii) the literature on asymmetric information and wage differentials.
1
Throughout this paper the two terminologies, “labour quality” and “labour productivity” have been interchangeably used.
3 The recent literature on trade and wage inequality elegantly summarized in Feenstra (2004) and described in Marjit and Acharyya (2006) for general readers, points towards the trade-technology debate in explaining the rising wage gap across skills within an economy. Acemoglu (1998) argues that skilled-biased technological progress, a resultant of the trade liberalization, explains the rising wage inequality in the industrialized countries. Oladi et al. (2011) have shown how FDI flow in the high-skill exports sector in the presence of non-traded final good can increase the wage inequality although it raises the real wages of both skilled and unskilled labour. Nevertheless, at the same time there is no denial of the fact that rising wage gap is a phenomenon in many of the developing 2
countries as well. Because the relative wages have moved against unskilled labour in the developing economies in which unskilled labour is the abundant factor is contrary to the predictions of the standard Heckscher-Ohlin trade model with Stolper-Samuelson theorem at its core calls for theoretical explanations. Feenstra (2004), Zhu and Trefler (2005) etc. come up with explanations in terms of increased foreign direct investment (FDI) in high-skill sectors. Conversely, Pi and Chen (2016), Pi and Zhou (2014), Anwar and Sun (2015), Barua and Pant (2014), Marjit and Acharyya (2003), Chaudhuri and Yabuuchi (2007, 2008), have explained the increasing wage inequality in the Southern countries in terms of some of the essential characteristics of the developing economies 3
e.g. factor market imperfections, presence of non-traded goods, dualistic structures etc.
However, what is missing in this literature is a microeconomic mechanism that links trade liberalization to wage inequality with or without asymmetric informational problems.
2
The empirical studies of Robbins (1994, 1995, 1996) have pointed out that while the inequality has narrowed in the East Asian countries, the Latin American countries like Mexico, Chile, Costa Rica and Columbia have experienced increasing skilled-unskilled wage gap following the liberalized trade and investment policies. Besides, Harrison and Hanson (1999) and Beyer et al. (1999) have observed that trade reforms in 1980s were associated with sharp deterioration in the skilled-unskilled wage inequality in Mexico and Chile, respectively. Curie and Harrison (1997) and Revenga (1997) have also come to the same broad conclusion. On the other hand, indirect studies on poverty by Khan (1998) and Tendulkar et al. (1996) also possibly indicate that
the wage inequality has increased after trade openness in the South Asian countries including India. 3
Also see Beladi et al. (2008), Marjit et al. (2004) and Chaudhuri (2008) in this context.
4
On the other hand, the literature that discusses asymmetric informational problems and wage differentials includes works of Shapiro and Stiglitz (1984) (S-S (1984), hereafter), MacLeod and Malcomson (1988), Akerlof and Yellen (1990), Basu et al. (2010), Jones and Marjit (1995) etc.
The S-S (1984) work discusses the role of an incentive contract to overcome the moral hazard problem of a firm under competitive conditions.4 It explains how unemployment/ job rationing can motivate the workers to be more disciplined and less job-shirking. Let us discuss the incentive mechanism they have suggested as follows.
If the i th firm offers a wage Wi , which is higher than the market-clearing level W0 , it raises the worker‟s expected loss arising out of job-shirking. Because if caught while shirking she would be fired and has to accept a job in other firms at a lower wage, W0 . Competition among firms would ensure that all firms would eventually be offering the higher wage,
W Wi
clearing wage,
for all i . Since the actual wage, Wi is greater than the market-
W0 the demand for labour falls short of the aggregate supply at W which i
in turn leads to involuntary unemployment of labour. The existence of unemployment motivates (acts as an incentive to) the workers not to shirk in their duties. However, the attitudes of the workers towards risk play an important role in this context.
On the other hand, MacLeod and Malcomson (1988) using a game-theoretic model have shown that if the rent from an employment contract is sufficiently large, firms may use either the efficiency wage instrument (high wage combined with threat of firing like the 4
The initial appraisal of the S-S (1984) model was due to its “competitive” nature. It appeared that both of the product and labour markets are perfect. However, a scrutiny of the paper reveals that firms are not wage-takers in the labour market. Although the i th firm sets the ball on the motion and determines the incentive wage, which is higher than the market-clearing wage, to get rid of the „moral hazard‟ problem other firms follow suit and ultimately offer the same wage. At this high wage the aggregate demand for labour falls short of its supply that leads to involuntary unemployment. In the present paper as well the firms are wage-makers although they are pricetakers in the product market.
5 one we find in the S-S (1984) model) or performance pay (e.g.an end-of-period bonus) to motivate workers to perform well. In their model economic agents are risk-neutral. Hence, this rent is the difference between the return to the current mutual agreement and that in the spot market for labour. If either the worker shirks or the firm does not pay the bonus, a separation occurs, which harms the offending party through a loss of the future rent from the contract.
Besides, Akerlof and Yellen (1990) have suggested another mechanism to mitigate the moral hazard problem which is known as the “fair wage-effort hypothesis”. There exists a psychological perception of the workers on what constitutes a „fair wage‟: The higher the wage rate relative to the standard of reference which the workers consider fair, the higher would be the work effort supplied by the workers in equilibrium. The profit-maximizing firm minimizes its unit cost of labour and chooses the „fair wage‟ that it would offer. Consequently, this causes involuntary unemployment thereby leading to wage dispersion between the different groups of worker (e.g. employed and unemployed). Then again, Basu et al. (2010) have shown that in the presence of both moral hazard and adverse selection problems, non-compliance with minimum wage legislation can indeed be an equilibrium phenomenon in a model of minimum wage policy with imperfect competition. In another paper by Jones and Marjit (1995) better quality workers have to accept a lower wage over an initial period when firms are learning about their quality. Hence, the onus is with the workers to convince the firms that they are of better quality and take the one period loss to signal their quality.
In all of these works, we come across different incentive wage mechanisms under different situations to overcome the asymmetric informational problems. Nonetheless, none of the above papers links international trade to wage dispersion among the workers. However, the following two papers look precisely at the effect of trade on quality upgrading and its consequences for workers in a world without uncertainty.
6 Verhoogen (2008) proposes a mechanism that links trade to wage inequality in developing countries, and investigates its empirical implications on Mexican manufacturing plants. In this model with heterogeneous plants and quality differentiation, more productive plants produce higher-quality goods for exports relative to less productive plants that produce only for the domestic market. The higher productive plants pay higher wages to maintain a higher-quality workforce. An exogenous shock in the form of exchange rate devaluation leads more-productive plants to increase exports, upgrade quality of goods produced, and to raise wages relative to less-productive plants within the same industry, thereby increasing within-industry wage dispersion. Nevertheless, in this paper we do not find any specific mechanism by which trade enhances productivity of labour.
Yeaple (2005) in terms of a general equilibrium trade model offers a competing explanation for the size and non-production wage differentials between exporting and non-exporting firms with heterogeneous workforce. Firms have complete information regarding the quality of labour. They take decision regarding entry, adoption of production technology, whether to export; and, the decision regarding the type of workers to employ. In equilibrium, the interaction between the characteristics of competing technologies, international trade costs, and the availability of workers of heterogeneous skill gives rise to firm heterogeneity. As mentioned above, Yeaple (2005) does not deal with adverse selection and moral hazard problems.
In the circumstances, the present paper is devoted to relate the above two distinct literatures with a view to examine how in a world of asymmetric information international trade could provide an incentive to firms to differentiate the heterogeneous workforce with respect to their labour quality and increase workers‟ effort, and thereby their quality that eventually leads to skilled-unskilled wage inequality.
7 In our proposed model there is uncertainty in period 1 because the firm cannot distinguish 5
between workers with respect to their quality. However, by offering a high incentive wage to all workers in period 1 and observing the quality of outputs they produce the firm is able to distinguish between high-quality and low-quality workers from period 2. The workers who do not put in sufficient effort to attain the threshold labour quality ( Z ) requiring for producing the high-quality output, would automatically be detected by the inferior quality of output they produce and be offered a low wage ( W0 ) in the subsequent periods. The wage of low-quality workers falls after the initial period because they are reassigned to producing low-quality goods.
6
The incentive contract that we have suggested can effectively tackle both the moral 7
hazard and adverse selection problems facing by the firm in period 1. Furthermore, we have provided a theory of determination of endogenous wage differentials between workers of different quality. Finally, our analysis explains how opening up of the economy (trade liberalization) may lead to widening of skilled-unskilled wage inequality.
2. The model
2.1 Description of the model and its assumptions
Consider an infinite-period decision-making problem of a firm where good X is produced by means of labour only. Commodity X can be of two qualities: a good (exportable)
5
Worker‟s quality is assumed private information. In period 1, firms cannot make payment contingent on the quality of output, which creates moral hazard/adverse selection problem for the employer. 6
It is important to note that there would be no such job switching for low-skill workers in the full information model, and hence no wage decline, because the workers could be separated between low and high-quality from the beginning of their employment. 7
How our incentive mechanism takes care of the moral hazard problem has been elaborately discussed at the end of section 2.4.
8 quality ( X * ) and an inferior quality ( X I ). Competitive conditions prevail in the product market. The good quality output ( X * ) can be sold (exported) at a high price, P * . On the other hand, the inferior quality of output ( X I ) can at best be sold in the domestic market at a price, P with P P * . Hence, there could be two production divisions of the firm: (i) one division that produces X * ; and, (ii) another one that produces X I . However, the firm has to take the decision whether to produce the good quality output at all. We would subsequently see that this decision would crucially hinge on the price difference, ( P * P) .
In the labour market, there is a market-clearing wage, W0 although the firm has the liberty to offer a higher wage to some of its workers, if it finds it profitable.8 The firm faces a certain number of heterogeneous workers who differ with respect to quality of labour services they can provide ( Z ) with Z [0,1] . However, by putting in an extra effort it is possible for every worker to attain a certain a threshold level of quality, Z , which is required to produce the high-quality output, X * . A relatively high-quality worker (with a high Z ) has to offer a lower effort (if not, any extra effort at all) to attain the threshold quality, Z while a relatively low-quality worker (with a low Z ) has to put in more effort to attain that quality ( Z ). On the other hand, the higher the effort (lower the value of Z ) the greater would be the associated cost, C , (disutility of putting in an extra effort) on the part of the worker in order to attain Z level of quality and vice versa so that C '(Z ) 0 .
The number of workers employed by the firm is normalized to unity. Z denotes the labour quality of the marginal worker hired by the firm for its high-quality division. Because Z [0,1] , the lower (higher) the optimum value of Z the lower (higher) would be labour
quality of the marginal worker which in turn implies higher (lower) employment in the
8
The optimality of the incentive wage contract has been examined in section 2.4.
9 9
segment that produces high-quality output. In other words, (1 Z ) and Z denote the levels of employment in the high-quality and low-quality production divisions, respectively. We have already mentioned that the low-quality output is sold in the domestic market at the low price, P .
The firm has incomplete information about the quality of its workers and cannot distinguish between high and low-quality workers at the initial situation. In the absence of any exports prospects the firm has to sell its entire product in the domestic market where the commodity price is low. In such a situation the firm may not find it profitable to screen its workers in terms of quality.
Nevertheless, if there arises an exports possibility that assures a higher price for the good quality product, the firm may find it profitable to offer a wage W , greater than the low existing market wage, W0 to all of its workers in period 1 for two reasons: (i) to distinguish between high and low-quality workers by observing the quality of output they produce; and, (ii) to make a higher profit producing at least some amount of good quality output ( X * ) and selling the same at a higher price, P * . The rest is sold (in the domestic market) at the low price, P . In other words, if the firm offers W level of wage to all of its workers in the first period, not only the possibility of getting a higher (international) price for at least a part of its output, and thereby earning a higher level of profit opens up but also it helps the firm to distinguish between high and low-quality workers and economize on wage cost in the subsequent periods. This is because it would then offer W and W0 wages to the high and low-quality workers, respectively. Hence, the firm in this model is not necessarily a wage-taker. In fact, the whole idea behind this exercise is wage-making. The firm is a wage-maker in the case of good quality workers although is a wage-taker for the rest because it would offer them (the latter group) the prevailing low market wage and assign them to produce the low-quality output for the domestic market.
9
If the interpretation of the symbol, Z seems confusing, one can alternatively use two different symbols for denoting the labour quality and the level of employment in the high-quality division.
10 2.2 Decision-making problem of the worker
Given the assumptions of the model the i th worker, irrespective of her quality ( Z i ), receives the incentive (high) wage, W in period 1. In this period, she has the following two options. The first option is to put in the extra effort for being able to produce the good quality output, and be labeled as high-quality worker in period 2. Once her quality is revealed and is considered as a high-quality worker in period 2, she will receive the high wage in period 2 and continue to receive the same in the subsequent periods as well. However, in this case she has to incur a cost (disutility of putting in an extra effort) given by C ( Z ) with C '(Z ) 0 where Z is her quality. Her sum of discounted net incomes, denoted U G , is
given by
U G [W C (Z )] [W C (Z )] 2 [W C (Z )] 3[.] ...... [
W C (Z ) ] 1
` (1)
where is the rate of time preference with 1 . On the contrary, if she decides not to put in an extra effort she would be labeled as lowquality worker in period 2. She would in any case receive the high wage, W in period 1 but will continue to receive the existing low market wage, W0 in each of the subsequent periods. In this case, her sum of discounted incomes, denoted U B , will be given by the following.
U B W W0 [ 2 3 ...... [W
1
W0 ]
(2)
Comparing both equations (1) and (2) we get the condition that she will put in that extra effort in order to attain the threshold level of labour quality iff U G U B
11 i.e. iff (W W0 ) C (Z )
(3)
2.3 Decision-making problem of the firm
We assume that each worker produces one unit of output, irrespective of whether she is a good worker or not. Nonetheless, the quality of output differs. After normalizing the number of workers employed by the firm to unity the sum of discounted profits of the firm when it sells at least a part of its output in the international market is as follows. * [ P *(1 Z ) PZ W ] [ P *(1 Z ) PZ W (1 Z ) W0 Z ] 2 [ P *(1 Z ) PZ W (1 Z ) W0 Z ] 3[..] ......
[ P *(1 Z ) PZ W ]
[ P *(1 Z ) PZ W (1 Z ) W0 Z ] (1 )
1 * ( )[ P *(1 Z ) PZ W Z (W W0 )] 1
(4)
The problem of the firm is to maximize (4) with respect to Z and W , and subject to the constraint as given by (3). This maximization exercise leads to the following proposition.
Proposition 1: In equilibrium the discounted value of the difference between the actual wage paid and the existing wage, (W W0 ) must equal the cost of putting in an extra effort, C ( Z ) required for attaining the threshold level of labour quality, Z .
Proof:
In the above constrained maximization exercise of the firm, the Lagrange function is written as follows.
12
1 Max ( )[ P *(1 Z ) PZ W Z (W W0 )] [ (W W0 ) C ( Z )] 1 Z ,W
(5)
where is the Lagrange multiplier and 0 .
Assuming interior solutions for the two choice variables Z and W the first-order and Kuhn-Tucker conditions are obtained as follows.
(
1 )( )[( P * P) (W W0 )] C '( Z ) 0 Z 1
(6)
(
1 1 Z )( )[1 Z ] 0 [ ]0 W 1 (1 )
(7)
) [ (W W0 ) C ( Z )] 0; and, ( ) 0 (
(8)
From (7) and (8) it follows that the constraint given by (3) would be binding in equilibrium. Hence, we have the following equation.
(W W0 ) C (Z )
(9)
This proves proposition 1. Substituting the value of from (7) in equation (6), using (9), and simplifying we can obtain the following equation.
1 Z C (Z ) ( )C '( Z ) ( P * P) p *
(10)
In (10), p * denotes the price difference between the high-quality and the low-quality outputs of the commodity in the presence of international trade where p* ( P * P) .
The optimum value of Z is found from (10). We find that the optimum Z is a function of p *( P * P) only. In other words, it is independent of the parameter, W0 . Once Z is
obtained the equilibrium value of W is obtained from (9) which, however, depends on both p * and W0 .
13 Equation (9) can alternatively be rewritten as follows.
W W0
C (Z )
(9.1)
Differentiating equation (9.1) we find that
(
2W C ( Z ) W C ( Z ) 0 according to C(Z ) 0 . ) 0 ; and, ( 2 ) Z Z
(9.2)
Now from (9.1) it is evident that the optimum W is greater than W0 for any Z [0, Z ) and, 10 that W is a decreasing function of Z because C(Z ) 0 . The determination of the
optimum W for a given Z (already determined from (10)) can be diagrammatically shown in terms of figure 1. (Space for Figure 1)
In figure 1, the initial (prevailing market) wage is shown by the horizontal line W0 while the curve AB represents equation (9.1). If the optimum Z is Z * , the equilibrium wage that the firm would offer under the incentive contract is W * which, however, rises if Z falls.
2.4 Optimality of the incentive contract
Now, our objective is to show that for a sufficiently high value of p * the firm might find it optimal to offer W to all of its workers in period 1. We are going to prove that the optimality of the incentive contract crucially hinges on the magnitude of the price
10
It may be noted that once the quality of the i th worker reaches the threshold level ( Z ) she does not need to put in any extra effort to be labeled as high-quality worker and receive the incentive wage, W , in the subsequent periods too. Hence, as Z moves from 0 to Z , the cost of (need for) putting in any extra effort tends towards zero. Hence, in the limiting case, when Z Z , we have C ( Z ) 0 . Therefore, the AB curve in figure 1 asymptotically moves towards the horizontal line, W0 .
14 difference of the commodity between the international and the domestic markets.11 The result that we obtain is presented in the form of the following proposition. Proposition 2: There exists a critical size of p * (say p * ) such that if p* p * , * 0 . In other words, if the price difference of the commodity between the international and domestic markets is sufficiently high, the offering a higher wage to all the workers in period 1 is the optimal policy of the firm.
Proof:
Assuming the sum of discounted profits of the firm when it sells its entire output in the domestic market, 0 , to be positive we can write 0 ( P W0 )[1 2 ....] =
( P W0 ) >0 (1 )
From (11) it follows that we are actually assuming,
(11) P W0
.
Subtracting (11) from (4) we obtain
1 ( * 0 ) ( )[ P *(1 Z ) PZ W Z (W W0 )] ( P W0 )[1 2 ....] 1 1 ( )[( P * P)(1 Z ) (W W0 )(1 Z )] 1
(12)
Using (9) and simplifying, equation (12) may be rewritten as follows.
1 C (Z ) ( * 0 ) ( )[( P * P)(1 Z ) (1 Z )( )] 1
(12.1)
Now,
11
In a different context, Mukherjee (2008) has shown that the size of the product market is pivotal in explaining the co-existence of foreign direct investment and exports even in a world without uncertainty.
15
d ( * 0 ) 1 dZ 1 Z ( )[(1 Z ) ( ){C ( Z ) p * ( )C '(.)}] dp * 1 dp *
Using equation (10) we write
d ( * 0 ) 1 Z ( )0 dp * 1
(13)
d 2 ( * 0 ) (dZ / dp*) [ ]0 2 dp * 1 Also
(14)
From (12.1) we note that ( * 0 ) 0 when p* ( P * P) 0 . Besides, from (13) and (14) it follows that ( * 0 ) is a monotonically increasing function of p * and is convex downwards.
Hence, we would find a critical level of of p * (say p * ) such that
* 0
if p* p * . In
other words, if the price difference of the commodity between the international and domestic markets is sufficiently high, the offering a higher wage to all of the workers in period 1 is the optimal policy of the firm.
This proves our proposition 2.
The curve showing the relationship between
( * 0 )
and p * would be like the one
which is shown in figure 2.
(Space for Figure 2)
Thus, the opening up of international trade that results in a higher price received by the firm for its high-quality output may provide an incentive to offer a higher wage by the firm to all of its workers in overcoming both the adverse selection and moral hazard problems relating to the quality of its employees.
16 A pertinent question at this juncture is whether there is a shirking problem in the subsequent periods even in the present setting. Following the initial period, labour quality of each of the workers is revealed and the firm knows whether a particular worker puts in her optimum effort. It may, however, be argued that a good worker, who exerts the sufficient effort to attain the threshold level of labour quality, Z in the (n 1) th period, has still the option of not exerting the optimum effort in the n th period, producing a lowquality product, and of collecting the incentive wage for that ( n th) period. This is because by assumption, the wage rate cannot be adjusted to reflect the quality of the good produced by her in the same period. Even if she still claims to be a good quality (highskilled) worker and demands the high incentive wage in the (n 1) th period, there is no reason for the firm to entertain such an unethical claim. This is because in the (n 1) th period by observing the quality of output she has produced in the n th period the firm can easily prove that she did not put in an extra effort in that period. Hence, it would offer her only the low wage, W0 in the (n 1) th period.
However, the equilibrium condition given by (9) in the wage contract will deter this shirking. If any of the workers deviates from her optimum effort supply decision she would only suffer because her sum of discounted net incomes would fall. On the other hand, the firm also would not have any reason to deviate from its decision on the incentive wage and pay the workers (or at least some of them) a lower wage in any future period. Because if it does then those workers whose marginal costs of putting in extra effort are greater than the new lower wage, would immediately stop putting in the extra effort to produce the high-quality output. Both of the parties‟ actions are verifiable. The action on the part of the firm would only adversely affect its profitability. Hence, any deviation from the equilibrium W and Z would not be beneficial to either of the two parties.
17 3. Comparative statics
In this section of the paper we would like to examine the consequences of an increase in the international price of the high-quality product, P * or an increase in the existing market wage, W0 on the number of good quality workers employed by the firm(s) and the incentive wage. The results that we obtain relating to changes in P * are stated in terms of the following two propositions. Proposition 3: The higher the difference between the international and domestic prices of the commodity, the lower would be the quality of the marginal worker employed by the firm. In other words, the firm hires a larger number of good quality workers with an increase in the international price of the high-quality output.
12
Proposition 4: Opening up of international trade accentuates the relative wage inequality between skilled and unskilled labour.
Proof of proposition 3:
Differentiation of equation (10) yields
(
dZ ) 0 dp * [2 C '(.) (1 Z )C "(.)] if C "(.) 0.
(15)
and, ( 0) d Z 3 C ( Z ) dZ ) [ ]( ) 0 according to C(Z ) 0 2 2 dp * {2 C '(.) (1 Z )C "(.)} dp * (+) (-) 2
(
2
(15.1)
Hence, the number of good quality workers employed by the firm increases with an increase in the international price of the high-quality output. The initial labour quality of 12
A good quality worker, having at least the threshold level of labour quality, Z is capable of producing the high-quality output that can be exported at the international price, P * . If her initial labour quality is less (not less) than Z she requires (does not require) putting in an extra effort to attain Z .
18 the marginal worker employed in the high-quality division decreases with an increase in the number of workers employed. Hence, the marginal worker in that division has to put in more extra effort with an increase in p * so that she could attain the threshold level of labour quality, Z for producing the good quality output and be labeled as a good quality worker.
This proves proposition 3.
Proof of proposition 4:
Differentiation of (9) leads to the following. (
dW C '( Z ) dZ ) [ ( )] 0 dp * dp * (-) (-)
(16)
From equation (16) it then follows that
(
d (W W0 ) )0 dp *
(16.1)
Hence, an increase in the international price of the high-quality product, given the domestic price of the low-quality product raises the skilled-unskilled wage inequality.
13
Thus, proposition 4 is proved.
This is a crucial result of this theoretical exercise.
The results presented in propositions 3 and 4 can be diagrammatically explained in terms of figure 3. (Space for Figure 3)
13
Note that the workers who decide to attain the threshold level of labour quality, Z by putting in extra effort are termed as skilled workers and receive the high incentive wage, W . The remaining workers who decide not to put in an extra effort cannot produce the high-quality output. Because of this they are labeled as unskilled and receive the low wage, W0 . Hence, the absolute skilledunskilled wage gap is (W W0 ) .
19 In panel b of figure 3, CD curve represents equation (15) where Z is found to be a negative function of p * . In panel a of figure 3, we show W and (W W0 ) as functions of p * . A change in p * leads to a change in Z which in turn changes both the incentive
wage ( W ) and the wage gap ( W W0 ) across skills. Because an increase in p * lowers the quality of the marginal worker employed by the firm in the high-quality division, a higher incentive wage, W has to be offered to lure her to perform well (note that her marginal cost of putting in an extra effort is also higher). This is how an increase in p * raises W that in turn raises (W W0 ) .
At this position, it is not difficult to examine the consequences of a change in the existing (autarkic) market wage, W0 on the incentive wage and the levels of employment in the two production divisions. The results that we obtain are presented in the form of the following proposition. Proposition 5: Any change in the prevailing market wage in the economy cannot change the labour quality of the marginal worker employed by the firm in its high-quality division. Hence, the levels of employment in the two production divisions remain unaffected. However, it causes a less than proportionate change in the incentive wage.
Proof:
Differentiating equations (9) and (10) and simplifying we find that (
W dZ W W0 EW ,W0 ( ) ( 0 ) 1 ) 0; W0 W W dW0 and, .
Here,
EW ,W0
is the elasticity of W with respect to
W0
. In other words, it measures the
W responsiveness of the incentive wage, W due to a change in the current market wage, 0 .
20 Hence, a change in the existing market wage, W0 , cannot change the level of employment in the high-quality division, ( 1 Z ) and that in the low-quality division, Z . Nonetheless, it causes a less than proportionate change in the incentive wage, W .
This proves proposition 5.
As long as p * is given, Z is determined from equation (10). Therefore, any changes in
W0 will not affect Z . This happens if and only there is a one-to-one correspondence between W and W0 . This has further interesting implication for the degree of wage inequality. Proportional change in W with respect to a proportional change in W0 will always be less than unity because absolute change in W will exactly be equal to absolute change in W0 , but W W0 , hence the result. If two countries, one having higher initial wage than the other and facing a given p * are subjected to the process of quality revelation of workers, the relative wage gap will be smaller for the richer economy.
4. Comparison with the S-S (1984) work
In this section of the paper, we would like to make a detailed comparison between our results and those of the famous Shapiro-Stiglitz (S-S) (1984) model because it is a close counterpart of our work.
The S-S (1984) paper concentrates solely on the moral hazard problem that a firm under competitive product market faces. It has devised an incentive wage mechanism to overcome that problem. On the contrary, in the present model there are both adverse selection and moral hazard problems. The firm faces a heterogeneous labour force with different labour quality. Therefore, it cannot distinguish between high-quality workers who with or without putting in an extra effort are capable of producing a high-quality output and other workers who despite having low-quality decide not to exert the right
21 amount of effort to be able to produce the high-quality output. We have devised an incentive mechanism where the firm by offering the same incentive wage to all of its workers in period 1 and observing the quality of outputs that they have produce in period 2 is able to differentiate between the two types of worker. Thus, from period 2 and onwards the uncertainty regarding workers‟ quality ceases to exist. This mechanism solves the moral hazard problem as well because the good quality workers, who continue to receive the high incentive wage in the subsequent periods, including period 2, would have no reason to put in less effort in any of the subsequent periods. This is because the firm would be able to identify shirking of jobs by those workers from the quality of output they have produced in the next period. This should be clear if we look at the binding constraint of the workers which is given by equation (9). This issue has already been adequately discussed at the end of section 2.4. An important question at this juncture is whether the „low-quality workers‟ who are being offered the existing low wage, W0 by the firm after the first period and the „low wage‟ they receive can be renamed to „unemployed‟ and „unemployment benefit‟, respectively. Let us now attempt to provide an answer to this question.
In this hypothetical scenario, there is no domestic market for the low-quality output. Hence, the firm does not produce anything in the no trade situation which in turn implies that there is no employment for workers at autarky. However, each of them receives the unemployment benefit, W0 from the government. Alternatively, we can think of a situation where there is a domestic market for quality output. Nonetheless, the demand is so low such that it is not profitable for the firm to produce anything at the given reservation wage, W0 . Hence, in either of the two situations the employment level is zero. Now, suppose that the possibility of international trade opens up so that the firm gets the opportunity to export high-quality output at a reasonably high price at the international market, P * .
The firm faces a heterogeneous labour force with varying labour quality. To begin with there are both adverse selection and moral hazard problems. In period 1, the firm offers
22 the high incentive wage, W to those workers who with or without putting in an extra effort can attain the threshold labour quality, Z and produce the high-quality output for exports. The quality of a worker is identified in period 2 from the quality of output she has produced in period 1. Subsequently, only the good quality workers will be employed and be offered the incentive wage, W . The remaining workers decide not to put in an extra effort to produce the high-quality output, remain unemployed and continue to receive the unemployment benefit, W0 . Why the shirking problem on the part of the employed workers in the subsequent periods cannot arise has already been explained at the end of section 2.4. Hence, from period 2, uncertainty ceases to exist. All of the qualitative results of our analysis except proposition 5 will continue to hold even in this modified scenario.
14
Hence, it makes only a very little difference if „low-quality worker‟ and „low wage‟ are reworded to „unemployed worker‟ and „unemployment benefit‟, respectively. In other words, once the revelation of quality of labour is made, in period 2 and thereafter the situation becomes almost the same what we find in the S-S (1984) work. However, it is trade liberalization, which makes the present case more or less akin to the S-S (1984) situation. Hence, the present exercise may be viewed as an application of the key intuition of the S-S (1984) model in the context of trade liberalization.
Nonetheless, it is important to note that the level of employment in the present case rises and the initial quality of the marginal worker employed by the firm continuously falls with an increase in the international price of the high-quality output, P * . This becomes clears if one looks at figure 3. In panel b, figure 3, the CD curve shows the relationship between the equilibrium value of Z and p * (or P * in the present hypothetical situation). With an increase in P * the equilibrium value of Z decreases; and, hence the level of employment, (1 Z ) increases. For a sufficiently high value of P * , the equilibrium value
14
The results have been proved in Appendix 1. It shows why proposition 5 has to be partially modified in this present hypothetical case.
23 of Z could even be zero. At that point full-employment could be attained. Therefore, the possibility of attaining full-employment in this setting cannot be ruled out.
5. A General Equilibrium Analogue
In this section, we build up a simple Ricardian model, based on the micro foundation of the incentive mechanism which has already been developed in the earlier sections for overcoming the asymmetric informational problems, to depict the possible path of wage distribution resulting from trade liberalization using a competitive general equilibrium setting. Besides, this portion is also aimed at establishing that the main result of our partial equilibrium analysis is easily applicable at least to the simple Ricardian general equilibrium trade model. Finally, we would like to compare our main results with those of Bond (2008) which also provides a labour contract theoretic approach in the Ricardian context.
Thus far, we have shown that if the price of the good increases beyond a critical level, firms will offer a wage W W0 in a way to induce a mass of ( 1 Z ) workers to produce the high-quality good for exports.
Let us now start from a competitive Ricardian economy producing both the high-quality and the low-quality goods. Thus due to free entry and free exit assumption both and * vanish.
From (4) [ P *(1 Z ) PZ W ZC (Z )] 0
(17)
where Z continues to be determined from equation (10).
Therefore, P * p * Z ( p*) Z ( p*)C (Z ( p*)) W
(18)
24 and from 0 we know P W0
(19)
We also have a sector where quality is not so important and the homogeneous good is represented by x with WaLx Px 1
(20)
P and P * are, therefore, measured in units of 1 .
If to start with the closed economy did not have any demand for high-quality good, say Y , the choice is really between producing x and y . Equations (19) and (20) coupled with the standard full-employment condition (21) and demand condition (22) will yield the standard Ricardian equilibrium outcome and the autarkic relative price, P . aLx x y L
(21)
Dx ( P) Dy
(22)
As the economy opens up for trade, it faces the possibility of selling a high-quality product at P* P . First note that W W0 with
W W0
C ( Z ( p*))
(23)
LZ number of workers cannot produce high-quality good and therefore can choose to work in x or in y or both at a wage W0 1/ aLx . If W0 1/ aLx , then production of x will cease altogether. If we have W0 1/ aLx , the reverse is true. Therefore, equilibrium wage in the other sector will be given by W where W Max( P,
1 ) aLx
(24)
The following sequence of outcomes is in order. (a) Initially in autarkic equilibrium everyone gets W0 produced.
1 and both x and y are aLx
25 (b) If trade opens up without the possibility of exporting the high-quality product facing a rest of the world relative price P , only x or y will be produced and W Max( P,
1 ) . We do not discuss this case and assume P P . aLx
(c) With the possibility of earning P* P , the firms make the wage offer W W0 to everyone for a while (one period in our model). This implies that x and y both cease to be produced as skill needs time to be revealed.
Once skill is revealed there are essentially two sets of workers, one earning W and the other W . Either Y and x are produced or Y and y are produced. The path of wage distribution in general equilibrium is shown in figure 5.
(Space for Figure 5)
Starting from a point like A where everyone earns W0 , the system jumps to B where all workers earn W during the revelation period. Then it moves to C where relative wage settles down along OC at
W (W0 W ) . Eventually, trade widens the wage gap. W0
In Bond (2008) international trade affects the productivity of labour through changes in the quality of intermediate inputs. Besides, in his model there is no uncertainty and hence no asymmetric informational problems. Furthermore, contracting frictions are not verifiable in court. On the contrary, we have provided a mechanism, through which trade in the presence of asymmetric informational problems may lead to revelation of labour quality, isolates the skilled from the unskilled, and eventually leads to a wage gap. The path of wage movement resulting from trade liberalization has been shown using a simple Ricardian trade model that is based on the microeconomic wage-based incentive mechanism that we have developed in the first part of our work.
26 6. Concluding remarks:
This paper argues that the prospect of a larger exports market for a high-quality good induces firms to distinguish between high-quality workers and low-quality workers offering them a higher wage. Since shirking is not a big problem in the paper, the standard Stiglitz-Shapiro (1984) avenue of providing a higher than equilibrium wage does not arise.
15
However, the firms engaged in exports have an extra incentive to
identify high-quality workers. Screening costs involve paying everyone a higher wage for one period and then identify the better ones from a pool of heterogeneous workforce. Workers respond optimally to such a strategy and eventually a separation occurs generating a wage gap. We then graft this model onto a Ricardian framework and derive implications for evolution of wage distribution.
There are three critical contributions of the paper.
16 , 17
First, this shows how rising
exports prospect generates more productive use of labor by identifying the high-quality
15
That the moral hazard problem is automatically taken care of by the incentive wage mechanism that we have suggested has been discussed at the end of section 2.4. 16
Our paper might be linked to certain real life situations. A classic example in the context of our paper could be the increasing demand for call centre services of high-quality, situated mostly in some developing countries, resulting from trade liberalization. The skilled workers who work in those places are heterogeneous in nature because of the differences in their communication skills, abilities to responding to customer queries and satisfying them. Consequently, the higher the demand for such services, the higher would the demand for high-quality workers and hence the better would be their pay packages. 17
The implications of the results of this paper are expected to influence economic policies regarding educational attainment and international trade. In this respect, changing demographics are also likely to have a strong impact on the links between international trade and labor quality. For instance, there may be important links between ageing and trade. While ageing of the working age population (until prime-age) generally increases average labor quality due to larger return to previous investment in human capital, it may result in lower incentives for current investment in human capital. Ageing is thus likely to result in downward pressure on the contribution of labor quality to aggregate productivity growth. We are thankful to one of the two anonymous referees for drawing our attention to such interesting implications of our results that in the earlier version of the paper we did not include.
27 workers. Thus, it is a framework that explicitly links trade with labour productivity.
18
Second, the paper shows how trade generates the skilled-unskilled wage inequality by providing a mechanism which is completely different from the standard ones suggested in the literature.
19
Finally, an outcome is highlighted which suggests that the equilibrium
degree of wage inequality in richer nations will be less pronounced than that in poorer countries.
Further extension of this paper will involve explicit consideration of investments by the firms to improve labor quality, global market fluctuations, and unemployment of the skilled and the unskilled labour and the relationship between trade, productivity, and economic growth.
References: Acemoglu, D. (1998): ‘Why do new technologies complement skills? Directed technical change and wage inequality‟, Quarterly Journal of Economics 113(4), 1055-1089. Akerlof. G. A. and Yellen, J. L. (1990): „The fair wage-effort hypothesis and unemployment‟, Quarterly Journal of Economics 105(2), 255-283. Anwar, S. and Sun, S. (2015): „Taxation of labour income and the skilled–unskilled wage inequality‟, Economic Modelling 47, 18 – 22. Barua, A. and Pant, M. (2014): „Trade and wage inequality: A specific factor model with intermediate goods‟, International Review of Economics and Finance 33, 172 – 185.
18
In our work firms are homogenous, and we have not analyzed the link between international trade and product quality that has been done using models of firm heterogeneity in Melitz (2003), Egger and Kreickemeier (2009), Helpman et al. (2010), Bas and Ledezma (2015) etc. Note that the basic objective of our analysis is to emphasize the link between international trade and labour quality. 19
High-quality and low-quality workers may be termed as skilled and unskilled workers,
respectively. Although it is possible for every worker to attain the threshold quality, Z by putting in an extra effort and become a high-quality worker, in equilibrium some of them decide not to put in that extra effort and remain as low-quality workers. These workers are termed as unskilled workers. On the contrary, the high-quality workers are labeled as skilled workers.
28 Bas, M. and Ledezma, I. (2015): „Trade liberalization and heterogeneous technology investments‟, Review of International Economics 23(4), 738–781. Basu, A.K., Chau, N.H. and Kanbur, R. (2010): „Turning a blind eye: costly enforcement, credible commitment and minimum wage laws‟, The Economic Journal 120 (543), 244269. Beladi, H., Chaudhuri, S. and Yabuuchi, S. (2008): „Can international factor mobility reduce wage inequality in a dual economy?‟, Review of International Economics 16(5), 893-903. Beyer, H., Rojas, P. and Vergara, R. (1999): „Trade liberalization and wage inequality‟, Journal of Development Economics 59(1), 103-123. Bond, E.W. (2008): „Input quality, relational contracts and international outsourcing‟, Pacific Economic Review 13(4), 391-404. Chaudhuri, S. (2008): „Wage inequality in a dual economy and international mobility of factors: do factor intensities always matter?‟ Economic Modelling 25(6), 1155-1164. Chaudhuri, S. and Yabuuchi, S. (2008): „Foreign capital and skilled–unskilled wage inequality in a developing economy with non-traded goods‟, in Sugata Marjit, Eden S.H. Yu (eds.) Contemporary and Emerging Issues in Trade Theory and Policy (Frontiers of Economics and Globalization, Volume 4), Emerald Group Publishing Limited, Chapter 12, 225-250. Chaudhuri, S. and Yabuuchi, S. (2007): „Economic liberalization and wage inequality in the presence of labour market imperfection‟, International Review of Economics and Finance 16(4), 592-603. Currie, J. and Harrison, A. (1997): „Trade reform and labor market adjustment in Morocco‟, Journal of Labour Economics 15(3), 44-71. Egger, H. and Kreickemeier, U. (2009): „Firm heterogeneity and the labour market effects of trade liberalization‟, International Economic Review 50(1), 187–216. Feenstra, R.C. (2004): Advanced International Trade: Theory and Evidence, Princeton University Press. Harrison, A. and Hanson, G. (1999): „Who gains from trade reform? Some remaining Puzzles‟, Journal of Development Economics 59(1), 125-154.
29 Helpman, E., Itskhoki, O., and Redding, S. (2010): „Inequality and unemployment in a global economy‟, Econometrica 78(4), 1239–1283. Jones, R.W. and Marjit, S. (1995): „Labour market aspects of enclave-led growth‟, The Canadian Journal of Economics 28, S76-S93. Khan, A.R. (1998): „The impact of globalization in South Asia‟, in A.S. Bhalla (ed.), Globalization, Growth and Marginalization, Macmillan. MacLeod, B. W. and Malcomson, J. M. (1988): „Implicit contracts, incentive compatibility, and involuntary unemployment‟. Econometrica 57(2), 447-480. Marjit, S. and Acharyya, R. (2006): „Trade liberalization, skill-linked intermediate production and the two-sided wage gap‟, Journal of Policy Reform, 9(3), 203-217. Marjit, S., Beladi, H. and Chakrabarti, A. (2004): „Trade and wage inequality in developing countries‟, Economic Inquiry 42(2), 295-303. Marjit, S. and Acharyya, R. (2003): International Trade, Wage Inequality and the Developing Countries: A General Equilibrium Approach. Heidelberg: Physica/Springer Verlag. Melitz, M.J. (2003): „The impact of trade on intra-industry reallocations and aggregate industry productivity‟ Econometrica 71(6), 1695–1725. Mukherjee, A. (2008): „Unionised labour market and strategic production decision of a multinational‟, The Economic Journal 118 (532), 1621-1639. Oladi, R., Gilbert, J. and Beladi, H. (2011): „Foreign direct investment, non-traded goods and real wages‟, Pacific Economic Review 16(1), 36-41. Pi, J. and Chen, X. (2016): „The impacts of capital market distortion on wage inequality, urban unemployment, and welfare in developing countries‟, International Review of Economics and Finance 42, 103 – 115. Pi, J. and Zhou, Y. (2014): „Foreign capital, public infrastructure, and wage inequality in developing countries‟, International Review of Economics and Finance 29, 195 – 207. Revenga, A. (1997): „Employment and wage effects of trade liberalization: the case of Mexican manufacturing‟, Journal of Labour Economics 15(3), S20-S43. Robbins, D. (1994): „Philippine wage and employment structure 1978 – 1983‟, HIID. Robbins, D. (1995): „Trade, trade liberalization and inequality in Latin America and East Asia: Synthesis of seven country studies‟, HIID.
30 Robbins, D. (1996): „HOS hits facts: facts win: evidence on trade and wages in Developing world‟, HIID. Tendulkar, S., Sundaram, D.K. and Jain, L.R. (1996): „Macroeconomic policies and poverty in India 1966-67 to 1993-94‟, manuscript, ILO, New Delhi. Shapiro, C. and Stiglitz, J.E. (1984): „Equilibrium unemployment as a worker discipline device‟, American Economic Review 74, 433-444. Verhoogen, E. A. (2008): „Trade quality upgrading, and wage inequality in the Mexican manufacturing sector‟, Quarterly Journal of Economics 123(2), 489-530. Yeaple, S. R. (2005): „A simple model of firm heterogeneity, international trade, and wages‟, Journal of International Economics 65(1), 1- 20. Zhu, S.C. and Trefler D. (2005): „Trade and inequality in developing countries: a general equilibrium analysis. Journal of International Economics 65, 21-48.
31 Appendix 1: The case with unemployment benefit
Suppose that the domestic market for low-quality output does not exist. Hence, to begin with all of the workers are unemployed. However, each of them receives an unemployment benefit, W0 from the government. In the absence of the domestic market,
P 0 . Besides, W0 is considered the reservation income of each worker. In this case, the constraint (3) of the workers remains intact. The sum of discounted profits of the firm, denoted ** is given by
1 1 ** ( )[( P * W )(1 Z ) (1 ) ZW ] ( )[ P *(1 Z ) W (1 Z )] 1 1
(A.1)
The firm maximizes ** with respect to Z and W ; and, subject to the reservation income constraint of the workers as given by (3).
The Lagrange function is as follows.
1 * ( )[ P *(1 Z ) W (1 Z )] *[ (W W0 ) C ( Z )] 1
(A.2)
where * is the Lagrange multiplier with * 0 .
The first-order conditions of maximization are as follows.
1 ( )( W P*) * C ( Z ) 1
(A.3)
1 ( )( Z 1) * * 0 1 (-)
(A.4)
The Kuhn-Tucker conditions are the following.
32 * ) [ (W W0 ) C ( Z )] 0; and, * * *( )0 * (
(A.5)
From (A.4) and (A.5) it follows that the constraint given by (3) would be binding in equilibrium. Hence, we have the following equation.
(W W0 ) C (Z )
(9)
This shows that proposition 1 remains unaffected even in the modified situation. Substituting * from (A.4) in (A.3) and simplifying we obtain the following equation.
1 Z C (Z ) ( )C ( Z ) ( P * W0 )
(A.6)
Totally differentiating equations (9) and (A.6) and solving we obtain the following results.
(
dZ 3 dZ 2 ) ( ) 0;( ) ( ) 0; dW0 dP *
(
dW ) ( )[ C ( Z ) (1 Z )C ( Z )] 0; dW0 (+)
(-)
(+)
( 0)
and,
(A.7)
(-) dW C ( Z ) ( ) [ ] 0; dP * (+) [{ C ( Z ) (1 Z )C ( Z )} 2C ( Z )] 0 where,
(-)
(+)
( 0)
(-)
(A.8)
33 dZ dW )0 ( )0 From (A.7) we find that dP * ; and, dP * . These imply that an increase in the (
international price of the high-quality output lowers the quality of the marginal worker and raises the incentive wage. The latter suggests that the wage inequality, (W W0 ) increases with an increase in P * .
Hence, propositions 3 and 4 remain intact.
Differentiating equation (A.1) with respect to P * we get
(
d ** 1 dZ dW dZ )( )[(1 Z ) P *( ) (1 Z )( ) W ( )] dP * 1 dP * dP * dP *
(A.9)
dZ dW ) ( ) Substituting the values of dP * and dP * from (A.7) in equation (A.9) and simplifying (
one obtains the following.
(
d ** 1 Z )( )0 dP * 1
(A.9.1)
d ** ) Differentiating dP * with respect to P * we find the following. (
(
d 2 ** 1 dZ ) [( )( )] 0 2 dP * 1 dP * (-)
(A.10)
Because the optimum ** is a monotonically increasing function of P * , proposition 2 also remains unaltered.
However, proposition 5 needs to be partially modified. Let us see how.
From (A.7) we find that (
(
dZ )0 dW0 ; and, dW ) 0. dW0
(A.11)
34 Hence, an increase in the unemployment benefit (reservation income of each worker) raises not only the incentive wage but also the labour quality of the marginal worker employed by the firm. The latter implies that it lowers employment. The intuition is straightforward. Because of an increase in the opportunity income of each worker the profit-maximizing firm must raise the incentive wage. This follows directly from the binding constraint, given by equation (3). Otherwise, the firm cannot lure the marginal worker to put in the extra effort to reach the threshold labour quality, Z so that she can produce the high-quality output. In this situation the firm employs fewer workers than previously because the marginal cost of employing an additional worker has increased.
dW ) dW 0 From (A.7) and (A.8) we substitute the expression for in . After simplification we (
0(
find that
dW W W0 ) 1 EW ,W0 ( ) 1 E W W dW0 W W 0 0 . Because , . Here, W ,W0 is the elasticity
of W with respect to W0 .
These results partially modify proposition 5 as follows. Proposition 5.1: An increase (a decrease) in the unemployment benefit lowers (raises) the level of employment of the firm under the incentive contract. However, it causes a less than proportionate change in the incentive wage.
35
Figures
W ,W0 A
W **
W* B
W0
Z
O
Z **
Z*
Figure 1: Determination of W for a given Z
36
( * 0 ) ( * 0 )
O
p*
Figure 2: The
p*
( * 0 )
curve as function of p * .
37
W ,(W W0 )
W
W0 Figure 3, panel a: W and
(W W0 ) as positive
O
p1 *
functions of p * .
p2 *
p*
Z
C Z1
Z2
O
p1 *
D
p2 *
Figure 3, panel b: Z as a negative function of p *
p*
38
Skilled
W
C
3
B
2
1 W0 aLx
A 1
45
0
Unskilled W0
1 aLx
W
Figure 4: Path of wage distribution in general equilibrium