Impact of Trade Liberalisation on Wage Inequality and Skill Formation: A Theoretical Analysis

Abstract

We consider a small open economy with three sector and four factors. Agricultural sector produces output with unskilled labour and land. Manufacturing sector and skill formation sector produce output with skilled labour and capital. Skill formation sector transforms the unskilled labour into skilled labour. We also consider an extended version of this model where agricultural sector also uses capital. So capital is mobile between all three sectors. Both change in the price of manufacturing sector and capital stock alter skill formation in a similar direction. But change in the price of manufacturing sector leads to change in skilled–unskilled wage inequality in the same direction whereas due to change in capital stock it changes in opposite direction. In our extended study, where capital is mobile between all three sectors, the results of the basic model are unaltered.

JEL Codes: F13, J31

Keywords

Wage inequality skilled labour unskilled labour skill formation general equilibrium trade liberalisation

Introduction

Difference in skill among workers (skilled–unskilled labour), the existence of wage inequality, skill formation, unemployment due to difference in skill, these are the important issues in the literature of trade and labour economics. Due to mismatch of skills among the workers there exists difference in wages as well. Thus, there exists wage inequality in the economy. This income inequality increased in US between 1960s and 1970s¹ and in European countries between 1978 and 1988 (see, e.g., Katz et al., 1992; Lawrence, 1994). We find similar picture in many developing countries (DCs) because wage inequality problem has worsened in many Latin American and South Asian countries in the mid-1980s (see, e.g., Banga, 2005; Beyer et al., 1999; Borjas & Ramey, 1993; Dev, 2000; Wood, 1997). The only exception here is East Asian countries between 1960s and 1970s where skilled–unskilled wage actually improved (see, e.g., Acharyya & Marjit, 2000; Wood, 1997). Different studies point out different reasons for this increase in income inequality. Trade liberalisation and technological progress are the main two controversial reasons of this phenomenon.² Many empirical studies point out other causes of this growing inequality such as international outsourcing (refer to Feenstra & Hanson, 1997), increase in the price of skill intensive good (refer to Beyer et al., 1999; Hanson & Harrison, 1999; Harrison & Hanson, 1999), entry of overpopulated low-income countries such as Bangladesh, China, India, Indonesia and Pakistan in the global market (Wood, 1997).

There exists a lot of theoretical works dealing with the issue of this growing wage inequality. They adopt the framework of static competitive general equilibrium models³ of small open economies in which there exist two different types of labour—skilled and unskilled. The ratio of wage rate of the skilled worker to that of the unskilled worker is taken as a measure of wage inequality in these models. We can divide the existing theoretical literature into two groups. One group of models assumes exogenous supply of skilled labour and this group includes works of Gupta and Dutta (2012, 2010a, 2010b), Chaudhuri (2008, 2004), Yabuuchi and Chaudhuri (2007), Chaudhuri and Yabuuchi (2008, 2007), Beladi et al. (2008), Marjit and Acharyya (2006, 2003), Marjit and Kar (2005), Marjit et al. (2004), Dutta and Ghosh (2021) and Mahata et al. (2020). Hence, these models cannot analyse the role played by endogenous skill formation on the skilled–unskilled wage inequality. Another small group of models considers endogenous formation of skilled labour with static competitive general equilibrium models; and this group includes works of Beladi et al. (2011), Gupta and Dutta (2010a), Yabuuchi and Chaudhuri (2009), Kar and Beladi (2004) and Marjit and Acharyya (2003). But most of them assume unskilled labour and capital use as the factor of production in the skill formation sector except Gupta and Dutta (2010a), where skill formation sector uses skilled labour and capital as inputs. However, Gupta and Dutta (2010a) consider a four-sector general equilibrium model where effect of change in different parameters on skilled–unskilled wage inequality depends on intensity ranking between different sectors; whereas in our model it is independent of intensity ranking.

In our study, we analyse the effect of change in different globalisation-related parameters on DCs’ skilled–unskilled wage inequality and skill formation, in presence of various types of capital mobility (domestic and foreign capital) among different sectors. We consider a small open economy with three sectors and four factors. Agricultural sector produces output with unskilled labour and land. Manufacturing sector and skill formation sector produce output with skilled labour and capital. Like Gupta and Dutta (2010a), we consider skill formation sector transforms the unskilled labour into skilled labour; and, in this static model, this transformation takes place instantaneously.⁴ Here, skill formation sector is considered as an education sector, where production of new skilled labour means the transformation of a part of unskilled labour into new skilled labour. These new skilled workers are added to the existing stock of skilled workers at the next point of time. So, in this static model, the production of new skilled workers does not affect the stock of existing skilled workers. This educational service is internationally non-traded. We consider that total number of labours present in the economy is exogenously given. We also consider an extended version of this model where agricultural sector also uses capital. So capital is mobile between all three sectors in the extended model.

We now turn to explain the motivation behind addressing this research gap. In reality, skilled workers are employed in various manufacturing units producing technologically sophisticated traded products; and also, a substantial part of skilled labour is employed in non-traded educational sector. It is well known that the education sector that transforms the unskilled labour into skilled labour cannot run without skilled labour. Teachers in educational institute are always skilled workers. This motivates us to introduce endogenous skill formation with the help of skilled labour in this model.

We derive interesting results related to globalisation, such as change in tariff rate and capital inflow, from our model. Both trade liberalisation and investment liberalisation improve the skilled unskilled wage gap but trade liberalisation lowers the skill formation and investment liberalisation raises it. In our extended study where capital is mobile between all three sectors, rise in the price of manufacturing sector raises both the skilled–unskilled wage inequality and skill formation if the manufacturing sector is capital intensive compare to agricultural sector.

This article is organised as follows. The second section describes the basic model with mobility of capital among manufacturing sector and skill formation sector only. The third section analyses extended version with mobile capital among all three sectors; and concluding remarks are made in the last section.

The Basic Model

Most of the less developed countries (LDCs) or DCs have a traditional agricultural sector which uses unskilled labour and land as inputs. Another feature of the LDCs or DCs is a manufacturing sector which uses skilled labour and capital as inputs. This model has these certain features. This model follows all the assumptions of small open economy. There are three sectors and four primary factors in this model. Sector 1 is the rural agricultural sector, which uses unskilled labour and land as inputs. Sector 2 is the urban manufacturing sector which uses skilled labour and capital as inputs. Sector S is the skill formation sector, which uses skilled labour and capital as inputs. Sectors 1 and 2 produce traded good, while sector S produces non-traded goods. Here, the production of the skilled labour means the transformation of the unskilled workers into skilled worker, and in this static model, the transformation takes place instantaneously. All the factor endowments are exogenously given. Skilled labour and capital are mobile between sectors 2 and S.⁵ But unskilled labour and land are specific to sector 1. Factor prices in these three sectors are fully flexible and this factor price flexibility ensures full employment of all the factors in the economy. All the markets are competitive in nature.

Following notations are used in the model

a_L1 Unskilled labour output ratio in sector 1.

a_N1 Land output ratio in sector 1.

a_S2 Skilled labour–output ratio in sector 2.

a_SS Skilled labour–output ratio in sector S.

a_K2 Capital–output ratio in sector 2.

a_KS Capital–output ratio in sector S.

P_i Effective producer price of the good, produced in the ith sector, I = 1,2,S.

W_U Wage of the unskilled workers.

W_S Wage of the skilled workers.

R Return on land.

r Return on capital.

X_i Final output of the ith sector, I = 1,2,S.

S Total supply of the skilled labour obtained as output in sector S.

L Exogenously given total labour force in the economy.

K Exogenously given total capital.

N Exogenously given total land.

Model is described by simple general equilibrium framework by the following equations:

W_{U} a_{L 1} + R a_{N 1} = P_{1}

(1)

W_{S} a_{S 2} + r a_{K 2} = P 2

(2)

W_{S} a_{S S} + r a_{K S} = P S

(3)

W_{S} - W_{U} = P S

(4)

a_{N1} X_{1} = N

(5)

a_{S2} X_{2} + a_{SS} S = S

(6)

a_{L 1} X_{1} = L - S

(7)

a_{K 2} X_{2} + a_{K S} S = K

(8)

There are eight unknown variables in the economy, that is, W_U, W_S, R, r, N, X₁, X₂, S. And there are eight independent equations. P₂ and K are the parameters in this model. The production structure does not hold decomposition property. Thus, the factor prices cannot be solved independent of the factor endowment. Equations (1), (2) and (3) exhibit profit maximising equilibrium condition in sectors 1, 2 and S, respectively. Equation (4) shows that the competitive education sector or the skill formation sector charges a price of educational service equal to the individual’s marginal benefit of acquiring education which, in turn, is equal to the skilled–unskilled wage gap. Equations (5)–(8) represent the full employment condition in the factor market. Here in this model, we consider that skilled–unskilled wage gap already exists in the model like most of the LDCs. Our treatment to skilled labour in this model is similar to the treatment to intermediate goods made in the existing literature on trade and general equilibrium. The output of the education sector is the transformation of unskilled labour into skilled labour; and this is identical to the supply of skilled labour, S, in this static model.

In fact, Equations (3) and (4) provide the micro-foundation of skill formation in this static set up. Using these two equations, we obtain

W_{S} = a_{ss} W_{S} + a_{KS} r + W_{U} .

Here, W_U is the opportunity cost of being educated and (a_ss W_S + a_KSr) is the average cost of acquiring education. Hence, an unskilled worker sacrifices an amount of (a_SS W_S + a_KSr + W_U) while acquiring education. W_S is the amount he gets after being educated. The representative worker chooses to be skilled (unskilled) if the skilled wage rate outweighs (falls short of) his combined cost of acquiring education; and these two are the same in the equilibrium. If the supply of skilled labour is very low, then the marginal productivity of skilled labour in the skilled labour using sector is very high. So, the skilled wage rate will also be very high in the competitive skilled labour market. On the other hand, the supply of unskilled labour will be very high leading to a low unskilled wage rate. So, there will stay an incentive to gain skill in this case. This mechanism prevents the equilibrium supply of skilled labour from being zero.

Working of the general equilibrium model is described as follows. We determine R and X₁ from Equations (1) and (5) as functions of W_U. Then we solve for S from Equation (7) as a function of W_U. Using Equations (2), (3) and (4), we determine W_S and r as functions of P_S and W_U. Using Equations (6) and (7), we solve for X₂ as function of P_S and W_U. Then from Equation (8), we determine W_U as a function of P_S. Finally, using Equations (2), (3) and (4) and putting the values of all the variables as functions of P_S, we solve for P_S.

Totally differentiating Equations (1), (2), (3) and (4), we get

{\hat{W}}_{U} θ_{L 1} + \hat{R} θ_{N 1} = \hat{P_{1}} = 0

(9)

θ_{S 2} {\hat{W}}_{S} + θ_{K 2} \hat{r} = {\hat{P}}_{2}

(10)

θ_{SS} {\hat{W}}_{S} + θ_{KS} \hat{r} = {\hat{P}}_{S}

(11)

P_{S} {\hat{P}}_{S} = W_{S} {\hat{W}}_{S} - W_{U} {\hat{W}}_{U}

(12)

Comparative Statics

Case 1: Change in the price of the manufacturing product (P₂)

{\hat{W}}_{U} = \frac{(λ_{K 2} F - G)}{(E + λ_{K 2} F - G)} {\hat{P}}_{2}^{6}

(13)

{\hat{W}}_{S} = [\frac{θ_{KS} (W_{S} - W_{U}) + θ_{K 2} W_{U} \frac{(λ_{K 2} F - G)}{(E + λ_{K 2} F - G)}}{θ_{KS} (W_{S} - W_{U}) + θ_{K 2} W_{U}}] {\hat{P}}_{2}

(14)

From Equations (13) and (14), we get

{\hat{W}}_{S} - {\hat{W}}_{U} = [\frac{θ_{KS} (W_{S} - W_{U}) (\frac{E}{E + λ_{K 2} F - G})}{θ_{KS} (W_{S} - W_{U}) + θ_{K 2} W_{U}}] {\hat{P}}_{2}

(15)

and

\hat{S} = - E (\frac{λ_{K 2} F - G}{E + λ_{K 2} F - G}) {\hat{P}}_{2}

(16)

where $E = [\frac{λ_{L 1}}{θ_{N 1}} (S_{LL}^{1} - S_{NL}^{1}) \frac{(L - S)}{S}] < 0;$

F = \frac{W_{U} (λ_{S 2} S_{SS}^{2} + λ_{SS} S_{SS}^{S})}{λ_{S 2} [θ_{KS} (W_{S} - W_{U}) + θ_{K 2} W_{U}]} < 0

G = [\frac{(λ_{K 2} S_{KS}^{2} + λ_{KS} S_{KS}^{S}) W_{U}}{θ_{KS} (W_{S} - W_{U}) + θ_{K 2} W_{U}}] > 0

From Equations (13) and (14), we find that unskilled wage and skilled wage increases with the price of the manufacturing sector. From Equation (15), we get that wage inequality increases when the price of the manufacturing sector increases. Finally, from Equation (16), we get positive relationship between the skill formation and price of manufacturing product. So, we have the following.

Proposition 1. An increase (decrease) in the price of the manufacturing product raises (lowers) both the skilled and unskilled wage rate. And it also raises (lowers) the skilled–unskilled wage gap and the skill formation in the economy.

We now explain Proposition 1 intuitively. Tariff cut as a part of trade liberalisation lowers the price of the manufacturing product. This leads to fall in the demand for the skilled labour because the producers in the manufacturing sector produce less manufacturing product. This leads to fall in the demand for skilled labour and skill formation. So, the demand for unskilled labour also falls in the skill formation sector which comes from agricultural sector. This unskilled labour is now available for agricultural sector. The expansion of agricultural sector requires land and unskilled labour. Land is fixed in supply. So, its return rises but return to unskilled labour falls, as there is excess supply of unskilled labour. The contraction of skill formation releases capital and skilled labour. So, return to both these factors fall. These two factors are also required in manufacturing sector, so impact on manufacturing sector is ambiguous. So, return to both unskilled labour and skilled labour falls. But fall in skilled wage rate is more than unskilled wage rate. So, ultimately the skilled–unskilled wage gap falls.

Case 2: Change in capital (K) in the economy

{\hat{W}}_{U} = (\frac{1}{G - E - F λ_{K 2}}) \hat{K}

(17)

{\hat{W}}_{S} = [\frac{θ_{K 2} W_{U}}{(θ_{KS} (W_{S} - W_{U}) + θ_{K 2} W_{U}) (G - E - F λ_{K 2})}] \hat{K}

(18)

From Equations (17) and (18), we get

{\hat{W}}_{S} - {\hat{W}}_{U} = - [\frac{θ_{KS} (W_{S} - W_{U})}{(θ_{KS} (W_{S} - W_{U}) + θ_{K 2} W_{U}) (G - E - F λ_{K 2})}] \hat{K}

(19)

and

\hat{S} = - (\frac{E}{G - E - F λ_{K 2}}) \hat{K}

(20)

From Equations (17) and (18), we find that unskilled wage and skilled wage increases with capital inflow. From Equation (19), we have inverse relationship between wage inequality and inflow of capital. Finally, from Equation (16) we get positive relationship between skill formation and inflow of capital. So, we propose the following.

Proposition 2. If there is capital inflow (outflow) in the economy, then the unskilled wage rate and skilled wage rate and the skill formation in the economy increase (decrease) but the skilled–unskilled wage gap decreases (increase).

Intuitive explanation of Proposition 2 is as follows. Inflow of foreign capital as a part of investment liberalisation raises the skill formation sector. This rise in skill formation requires unskilled labour too. So, unskilled wage rate rises and production of agricultural good falls. The extra skilled labour produce is available in next period. The production of manufacturing good requires skilled labour too, so impact on manufacturing sector due to rise in capital inflow is ambiguous. As there is excess demand for skilled labour both in manufacturing and skill formation sectors, so skilled wage rate rises. Here, the impact of manufacturing sector is ambiguous. Skill formation rises which require unskilled labour, so rise in unskilled labour wage rate is more than rise in skilled labour wage rate and skilled–unskilled wage inequality falls.

Here, we conclude both trade liberalisation and investment liberalisation lower the skilled–unskilled wage gap but trade liberalisation lowers the skill formation and investment liberalisation raises it.

Extension of the Model—Mobile Capital Case

We further extend the model by allowing capital to mobile between all the sectors to check the robustness of the results obtained in the basic model. In this extended model, there are only three inputs. Land is not considered as an input in this extended model. Agricultural sector now requires unskilled labour and capital as factors of production. All the assumptions remain the same. There are now seven equations to solve for seven unknowns—W_S, W_U, P_S, r, S, X₁, X₂. Equation (5) is omitted as land is not a factor of production now. All the other equations remain the same except Equations (1) and (8).

Equations (1) and (8) are modified as follows.

W_{U} a_{L 1} + r a_{N 1} = P 1

(1.1)

a_{K 1} X_{1} + a_{K 2} X_{2} + a_{K S} S = K

(8.1)

Comparative Statics

Case 1: Change in the price of the manufacturing product (P₂)

{\hat{W}}_{S} - {\hat{W}}_{U} = [\frac{θ_{KS} (W_{S} - W_{U})}{(θ_{K 2} - θ_{K 1}) W_{U} + θ_{L 1} θ_{KS} (W_{S} - W_{U})}] {\hat{P}}_{2}

(21)

and

\hat{S} = H [\frac{θ_{K 1} (θ_{KS} W_{S} + θ_{SS} W_{U})}{(θ_{K 2} - θ_{K 1}) W_{U} + θ_{L 1} θ_{KS} (W_{S} - W_{U})}] {\hat{P}}_{2}

(22)

where $H = \frac{λ_{K 1} λ_{S 2} (S_{KL}^{1} - S_{LL}^{1}) (θ_{KS} W_{S} + θ_{SS} W_{U}) + λ_{S 2} (λ_{K 2} S_{KS}^{2} + λ_{KS} S_{KS}^{S}) - λ_{K 2} (λ_{S 2} S_{SS}^{2} + λ_{SS} S_{SS}^{S})}{λ_{S 2} θ_{K 1} (θ_{KS} W_{S} + θ_{SS} W_{U}) (λ_{K 2} + λ_{KS})}$

On the right-hand side (R.H.S) of Equation (21), i_K1, i_K2, i_K3, i_L1, (W_S – W_U) are positive. (i_K2 – i_K1) is also positive. In developing and less developed economies, agricultural sector is labour intensive. While, manufacturing sector is capital intensive. Thus, from the above assumption, we get this factor endowment condition as, $\frac{a_{L 1}}{a_{K 1}} > \frac{a_{S 2}}{a_{K 2}}$ . From this we get, (i_K2 – i_K1) > 0. Thus, both the numerator and denominator on the left-hand side (L.H.S) of Equation (21) is positive. So, P₂ has a positive relationship with skilled–unskilled wage inequality.

On the R.H.S of Equation (22), mathematical expression H is positive. i_K1, i_K2, i_KS, i_L1,(W_S – W_U), (i_K2 – i_K1) are also positive. Thus, P₂ has a positive relationship with S.

Proposition 3. Rise (fall) in the price of the manufacturing product raises (lower) both skilled–unskilled wage inequality and skill formation in the economy.

Rise in the price of the manufacturing product raises the demand for skilled labour because the producers in the manufacturing sector want to produce more to earn higher profit. So, the skilled wage rate increases. Now, to fulfil the requirement of high demand of skilled labour, the skill formation sector expands. So, the skill formation in the economy increases. Thus, the supply of unskilled labour falls given a fixed labour force. So, the unskilled wage rate increases. The extra capital required for the expansion of skill formation sector comes from the manufacturing and agricultural sector to the skill formation sector, and the extra skilled labour comes from the manufacturing sector to the skill formation sector. So, the demand for the skilled labour comes from both the manufacturing and skill formation sectors. And, it should also be noted that the producers in the manufacturing sector would not let go much of the skilled labour and capital, as it is beneficial for them to produce more in this situation. So, the skilled wage rate increases more than the unskilled wage rate. Thus, the skilled–unskilled wage inequality increases.

Case 2: Change in capital (K) in the economy

Capital inflow or outflow does not affect factor prices in the economy. As the economy has decomposable property in this extended model, change in capital (K) would not affect unskilled wage rate (W_U), skilled wage rate (W_S) and skilled–unskilled wage inequality (W_S − W_U). Now, as the factor prices remain constant, factor endowments would not change either.

\hat{S} = [\frac{L - S}{(1 - λ_{K 1}) L - S}] \hat{K}

(23)

In Equation (23), (L – S) and (1 – m_K1) are positive. In less developed and developing economies, agricultural sector is labour intensive. Thus, we could consider that m_K1 is very small. So, (1 – m_K1) L – S > 0 when m_K1 is very small. By this above assumption, skill formation in the economy has a positive relationship with capital.

Proposition 4. Skill formation in the economy rises (falls) with capital inflow (outflow), when the allocative share of capital in the agricultural sector is very small.

The intuition behind the result summarised in Proposition 4 is given below. An increase in capital stock in the economy raises the production in the skill formation sector as skill formation sector is a capital-intensive sector. Factor prices are solved without using factor market equilibrium equations. So, change in capital has no impact on factor prices.

Conclusion

We consider a small open competitive economy with three sectors and four factors. Agricultural sector produces output with unskilled labour and land. Manufacturing sector and skill formation sector produce output with skilled labour and capital. Skill formation sector transforms the unskilled labour into a skilled labour. We consider that the total number of labours present in the economy is exogenously given. So, unskilled labour and land are specific to the agricultural sector. Skilled labour and capital are mobile between the manufacturing sector and skill formation sector. We also consider an extended version of the model, where capital is mobile between all three sectors. So, agricultural sector also uses capital in place of labour as input in the extended model.

We derive interesting results both from our basic model and extended model. Both trade liberalisation and investment liberalisation improve the skilled–unskilled wage inequality but trade liberalisation lowers the skill formation and investment liberalisation raises it. In our extended study where capital is mobile between all three sectors, we get similar results as the basic model except that here change in exogenous capital has no effect on the skilled–unskilled wage inequality due to decomposition effect. So, in our model results are independent of factor intensity ranking between manufacturing sector and skill formation sector which is not the case in Gupta and Dutta (2010a, 2010b). But in our model, change in skilled–unskilled wage depends on capital mobility among different sectors.

However, our model is an abstract and does not consider many important aspects of reality. We rule out the possibility of unemployment as factor prices are flexible. Imperfection of markets is not considered. Also, we consider a static model where skilled labour and capital do not accumulate over time. We plan to do further research in future removing these problems.

Footnotes

Declaration of Conflicting Interests

The authors declared no potential conflicts of interest with respect to the research, authorship and/or publication of this article.

Funding

The authors received no financial support for the research, authorship and/or publication of this article.

Appendices

Notes

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Impact of Trade Liberalisation on Wage Inequality and Skill Formation: A Theoretical Analysis

Abstract

Keywords

Introduction

The Basic Model

Comparative Statics

Case 1: Change in the price of the manufacturing product (P2)

Case 2: Change in capital (K) in the economy

Extension of the Model—Mobile Capital Case

Comparative Statics

Case 1: Change in the price of the manufacturing product (P2)

Case 2: Change in capital (K) in the economy

Conclusion

Footnotes

Declaration of Conflicting Interests

Funding

Appendices

Notes

References

Case 1: Change in the price of the manufacturing product (P₂)

Case 1: Change in the price of the manufacturing product (P₂)