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The Coexistence of High Unemployment and Good Economic Performance in Large Open Developing Countriesroie_1053 767..780

Ming-cheng Wang, Chen-ray Fang, and Li-hsuan Huang*

Abstract The Harris–Todaro labor reallocation mechanism is embedded into a North–South trade model and a theoretical model is provided to explain the coexistence of high unemployment and good economic perform- ance as large developing countries become more open to trade. The relative improvement in the total factor productivity of the Southern manufacturing sector is conjectured to give rise to this phenomenon. Although it induces an increase in the demand for labor in the Southern urban areas, this increase in demand is outweighed by an increase in supply brought by the reallocation of labor from rural to urban areas. The final result is higher unemployment. The model is supported by some empirical evidence.

1. Introduction

Over the 1991–2010 period, some large developing countries, for example, Brazil, Russia, India, and China, have posted extraordinarily higher rates of growth than ever before. As far as openness to trade is concerned, it is well understood that the adoption of technology from more advanced countries could enhance a country’s factor accu- mulation and total factor productivity (TFP) (Bhattacharya and Raychaudhuri, 2004; Weil, 2005). Moreover, it is predicted by the neoclassical trade theory that openness to trade should increase demand for labor in relatively labor-abundant countries, which in turn, should lead to a fall in the unemployment rate. However, observations do not support this prediction. Surprisingly high economic growth performance and high unemployment rates have coexisted over the 1991–2010 period in the afore-mentioned countries. International Financial Statistics,1 compiled by the International Monetary Fund, illustrate that Brazil suffers from an annual unemployment rate as high as 8.88% with a growth rate of 3.68% (2000–2008). In Russia, the average unemployment rate is 6.72% with an average rate of growth from 2000 to 2008 of 5.8%. In the same period, the unemployment rate and rate of economic growth for India and China have been 9.69% and 7.14%, and 3.96% and 9.99%, respectively.2 These unemployment figures are by any definition high, especially when compared to the past. We have been thus motivated to provide a theoretical explanation for the seemingly inconsistent economic outcomes between the strong economies and high rates of unemployment in these large developing countries as they have become more open to trade, particularly since the 1990s.

All of the above large developing countries have experienced rising trade depen- dence and productivity over the 1991–2010 period (International Monetary Fund

* Wang: National Central University, 300 Chungda Road, Chungli 320, Taiwan. Tel: +886-3-4226903; Fax: 886-3-4222876; E-mail: [email protected]. Fang: National Taipei University, 151 University Road, San Shia, New Taipei City 237, Taiwan. Tel: +886-2-26748189~67132, Fax: +886-2-26739880, E-mail:roger@ mail.ntpu.edu.tw. Huang: National Central University, 300 Chungda Road, Chungli 320, Taiwan. The authors would like to thank the anonymous referees for their helpful suggestions and comments.

Review of International Economics, 20(4), 767–780, 2012 DOI:10.1111/j.1467-9396.2012.01053.x

(IMF), 2009).3 To highlight their significance to the world, they were all rated in the list of the top ten countries by the year of 2000, both in terms of economic size and population. The other six largest economies all fell into the category of Organisation for Economic Co-operation and Development (OECD) countries (Weil, 2005). More- over, the trade volume between the large developed and developing countries also showed a surprisingly fast tendency to increase. Let us take the trade relationship between the USA and China as an example. Since 2007 China has become the third largest exporter to the USA. Another well-known fact is that main exporting destina- tions for products from the above large developing countries are primarily developed countries.4 Although the profound consequence of the closer relationship between large countries with significant differences in economic development has been empha- sized in international trade theory, the unemployment issue is ignored in most of the conventional trade models, such as Dornbusch et al. (1977, 1980) (DFS hereafter), meaning that models of the standard DFS-type are inadequate to account for the above unemployment issues in these large developing economies.

Therefore, in this study we embed the Harris–Todaro (1970) labor reallocation mechanism into a DFS trade model with two countries, known as the North and the South. Both countries are specified to be large, so that changes in their economic conditions will exert an influence on the world economy. We then offer a plausible explanation for the above puzzling issue by exploring how the large developing coun- tries’ rates of unemployment are influenced by a relative improvement in their TFP.

In our model, we include two kinds of products, a type of agricultural product and a continuum of manufactured goods. The setting of this continuum of manufactured products benefits us by leading to an investigation of the consistently observed dra- matic changes in product composition during the process of opening. The model for examining countries that experience comparatively higher unemployment rates along with fast economic growth incorporates the Harris–Todaro labor reallocation mechan- ism, which stipulates that labor migrates from rural to urban areas and that real urban wage rigidity exists. Note that in the celebrated work of Harris and Todaro (1970), a two-sector model is used to explain the high urban unemployment in African countries, where inflexibility of price adjustments as well as the migration of labor from rural to urban areas causes the realized employment to be lower than the equilibrium level. The model is essentially a two-sector closed-economy model that is unable to explain the effects of international trade. To the best of our knowledge, although the Harris– Todaro framework is utilized in some trade models, these all focus on issues related to small open economies (Bhatia, 2002; Fung et al., 1999; Khan, 1980; Kreickemeier, 2005). Our model can be thought of as an extension of the Harris–Todaro model to large open economies.5

Justifications for incorporating the Harris–Todaro labor reallocation mechanism into our North–South trade model are two-fold. First, during the initial stages of develop- ment, better economic conditions driven by economic growth accelerate the pace at which the rural population is drawn into urban areas in search of higher-wages.6

Second, wage rigidity is driven by efficiency wages and/or institutional arrangement is commonly observed in such developing countries during the process of economic development. Real wage rigidity in urban areas is identified as one of the major driving forces for the persistence of high unemployment in developing countries (Riveros and Bouton, 1994, p. 697).7 Wage rigidity thus seems to be a non-negligible aspect when we look into the issue of unemployment in these fast-growing large economies.

Our model explains the coexistence of the high unemployment and the good eco- nomic performance of large developing countries to be a consequence of the relative

768 Ming-cheng Wang, Chen-ray Fang, and Li-hsuan Huang

improvement in the Southern TFP. The intuitions are as follows. The relative improve- ment in the TFP in the Southern manufacturing sector causes an improvement in the comparative advantage of the Southern marginal industries, a feature obtained by the DFS model. This creates an increase in the demand for labor in the Southern urban areas; which in turn leads to a migration of labor from rural to urban areas. However, the increase in the demand for labor is outweighed by the increase in the supply brought by reallocation from rural to urban areas, resulting in higher unemployment and wage inequality.

2. The Model

Basic Assumptions

Consider a trade model with two kinds of products: agricultural goods and manufac- tured goods. There is only one type of agricultural product (X). Yet, there is a continuum of manufactured goods, indexed by z ∈[0, 1]. There are two large countries, the North and the South. The agricultural good is produced only in the rural areas of the South. Labor and land are used as the factors of production for agricultural goods. The South also uses labor and capital as inputs for the production of manufactured goods in urban areas. The North produces only manufactured goods. The agricultural good, as opposed to a continuum of manufactured goods, is treated as the numeraire in the model. Assume that the Northern TFP for manufactured goods is superior to that of the South. Full employment in the Northern labor market and the Southern rural areas is also assumed. However, urban unemployment in the South does exist, as a result of a binding minimum wage (Harris and Todaro, 1970), and/or efficiency wage considerations (Shapiro and Stiglitz, 1984). All markets are assumed to be perfectly competitive. Capital can move freely internationally. To simplify the analysis, we assume that the South is a price taker of the Northern capital rental price and we further assume that the Northern capital rental price is exogenous.8 Labor, however, can only move domestically. No transportation costs are considered and there are no policies that restrict the movement of goods between countries.

Borderline Good

The index of manufactured goods z is ranked in accordance with the capital–labor ratio. By construction, a commodity that has a higher index means that it has a larger capital–labor ratio. The production function of commodity z is specified as

Q z AK z N z z zz z( ) = ( ) ( ) < ( ) < ∀( ) − ( )β β β1 0 1, , , (1)

where Q(z), K(z), and N(z) are the output, capital input, and labor input, respectively, of industry z; b(z) is the capital share. In the model, b′(z) > 0 is assumed such that the intensity of capital increases with the product index z. A is the TFP that applies to all manufacturing industries within a country and is determined by the infrastructure, research and development capacity, adoption of foreign technology, education, legal system, etc.

Let w be the real wage rate and r be the real rental price of capital (both are measured in Southern agricultural output). The profit function of a representative firm in industry z, p (z), is

π z p z Q z rK z wN z( ) = ( ) ( ) − ( ) − ( ),

UNEMPLOYMENT AND GOOD ECONOMIC PERFORMANCE 769

where p(z) is the price of commodity z in terms of X. The optimality conditions of the representative firm result in

rK z wN z

z z

( ) ( )

= ( )

− ( ) β β1

Zero economic profit under perfect competition implies that

p z Q z rK z wN z( ) ( ) = ( ) + ( ). (2)

Plugging equation (1) and the above optimality condition into equation (2), one can obtain

p z A

z r w z z zz z z z( ) = ( ) ( ) ≡ ( ) − ( )[ ]( ) − ( ) − ( ) ( )− 1

11 1φ φ β ββ β β β, .where (3)

The variables pertaining to the North and the South are denoted by the superscript n and s, respectively. We assume that the two countries have the same capital share and labor share for the same industry. Free mobility of capital goods across national borders implies that both countries are subject to the same rental price for capital. With equation (3), and given the same rental price for capital, the relative cost (i.e. the relative price) of producing commodity z is

p z p z

A A

w w

M s

z( ) ( )

= ⎡ ⎣⎢

⎤ ⎦⎥

− ( )1 β

, (4)

where wM s is the minimum wage rate in the Southern urban area (measured in X).

Denote K i and N i as the endowment of capital and labor for country i (i = n, s). Assume also that the North has relatively abundant capital, i.e. K N K Nn n s s> . The Northern wage rate is higher than the Southern wage rate, i.e. w wn M

s > 1, as the Northern TFP is assumed to be superior to that of the South, i.e. An > As, and the South has relatively abundant labor resources. Note that the function of pn(z)/ps(z) is, by assumption, continuous in z. Thus, equation (4) and the assumption that b′(z) > 0 together imply ∂[pn(z)/ps(z)]/∂z < 0. The relative Northern price thus decreases with the index. The relative Northern labor cost of goods with a smaller z is higher, since w wn M

s> . With this setup, if the index of borderline (cut-off) goods under free trade ẑ, is defined as p z p zn sˆ ˆ( ) = ( ), then the South produces more labor-intensive goods in the range z z∈[ )0, ˆ , while the North produces more capital-intensive goods in the range z z∈[ ]ˆ, 1 .9

By using equation (4) and the definition for borderline good ẑ, we obtain the following:

w w

A A

M s

z n

⎡ ⎣⎢

⎤ ⎦⎥

= − ( )1 β ˆ

. (5)

Equation (5) specifies the competitive margin, i.e. ẑ, as a function of relative wage and relative TFP.

Southern Rural Sector

The production function of the Southern agricultural product is as follows:

X A T Ns A s s

A s= ( ) ( ) < <−α α α1 0 1, ,

770 Ming-cheng Wang, Chen-ray Fang, and Li-hsuan Huang

where Xs, AA s , T s, and N A

s represent the Southern agricultural output, the agricultural TFP, the land endowment, and the labor input in the Southern agricultural sector, respectively. Let tA

s and wA s denote the rental price of land and the wage rate (both

measured in X) in the Southern agricultural sector. Then the payments for land and labor in the South are as follows: t T XA

s s s= α and w N XAs As s= −( )1 α , respectively.

Labor Migration

Let NB s denote the South’s urban labor force. Then

N N Ns A s

B s= + . (6)

Let u denote the South’s urban unemployment rate and let NM s be the employment in

the Southern manufacturing sector. Then

N N z dz u NM s

M s

B s= ( ) = −( )∫0

1 1 , (7)

where (1 - u) is the probability of a worker being employed in the urban area. The expected urban wage is w uM

S 1 −( ). Migration equilibrium is reached when

w u wA s

M s= −( )1 . (8)

Equation (8) can be rewritten as

w w u

M s

A s

= − 1

1 .

Thus, 1/(1 - u) also measures the wage inequality between the Southern urban and rural areas.

Note that full employment in the Southern rural areas is assumed in our model, the number of unemployed workers in the urban area, denoted as Us, is thus equivalent to the total number of unemployed in the South. Denote us as the South’s unemployment rate, the relationship between the two unemployment rates in the South, namely us and u, can be expressed as u N U uNs s s B

s≡ ≡ .

Real Balance of Payments

On the demand side, it is assumed that both countries have the same preference for simplicity. In line with the DFS, the utility function of the representative household is

V c b z c z dzX= −( ) + ( ) ( ) < <∫1 0 10 1

η ηlog log , ,

where cX indicates the consumption of agricultural goods and c(z) represents the consumption of commodity z. Utility maximization implies that the expenditure for manufactured goods is

p z c z b z I z( ) ( ) = ( ) ∀, ,

where I indicates the national income, b(z) is the expenditure share of z, with ∫ ( ) =0

1 b z dz η being the expenditure share for all manufactured goods, and 1 - h the

expenditure share for agricultural goods. Denote Kn the employment of capital in the North and therefore K Kn n− is the

North’s outward foreign direct investment. The Northern GNP and the Southern GNP (both measured in X) are

UNEMPLOYMENT AND GOOD ECONOMIC PERFORMANCE 771

I w N rK r K K w N rKn n n n n n n n n≡ +( ) + −( ) = + ,10 (9) and

I w N w N rK t Ts M s

M s

A s

A s s

A s s= + + + ,

respectively. The Southern income is further expressed as a linear function of the labor and capital

income for both countries as below. Substituting equations (6), (7), and (8) into the above Is equation results in

I u w N rK t Ts M s s s

A s s= −( ) + +1 ,

where the first term of the right-hand side represents the total labor income in the South. Substituting the land payment equation, represented by t T XA

s s s= α in the section of the Southern rural sector, and Xs = (1 - h)(Is + In) into the above Is equation, together with equation (9), we obtain

I u w N rK w N rKs M s s s n n n=

− −( ) −( ) +[ ]+ −( )

− −( ) +[ ]1

1 1 1

1 1 1α η α η α η

. (10)

The equilibrium condition of the real balance-of-payments can be written as

b z I dz I b z I dz K K K Kn z n S

S S S S( ) + −( ) − ( ) − −( )⎡⎣ ⎤⎦ + −( ) =∫ ∫0 1

1 0 ˆ

ˆ .η

The square brackets in this equation denote the South’s current account balance in real terms,11 where ∫ ( )0

ẑ nb z I dz represents the value of exports of Southern manufactured goods, (1 - h)In represents the value of exports of Southern agricultural goods, ∫ ( )ẑ

sb z I dz 1

is the value of Southern imports of manufactured goods, and K Ks s−( ) represents the value of Southern imports of capital goods.12 Notice that balance of payments in equilibrium implies balanced trade in terms of commodities in our model. Therefore, the net export of Southern commodities is zero:

b z I dz I b z I dzn z n s

z ( ) + −( ) − ( ) =∫ ∫0

1 1 0

ˆ .η

Let θ ˆ ˆ

z b z dz z

( ) ≡ ∫ ( )0 denote the expenditure share for Southern manufactured goods for both countries. The net export equation can now be rewritten as

θ η η θˆ ˆ .z I z In s( ) + −[ ] = − ( )[ ]1

The left-hand side represents Southern commodity exports and right-hand side represents Southern commodity imports.

Substituting equations (9) and (10) into the above equation and rearranging terms yield

θ α η η θˆ ˆ .z w N rK z u w N rKn n n Ms s s( ) + −( ) −( )[ ] +( ) = − ( )[ ] −( ) +[ ]1 1 1 (11)

Southern Labor Market

Using equations (8) and labor payment equation, represented by w N XA s

A s s= −( )1 α in

the previous subsection, we obtain

N w

X u w

I IA s

A s

M s

n s= −( ) = −( )

−( ) −( ) +( )1 1 1 1

1 1α α η . (12)

772 Ming-cheng Wang, Chen-ray Fang, and Li-hsuan Huang

Moreover, by the definitions of b(z) and 1 - b(z), we have

w N z b z dz I I a z I IM s

M s z n s n s= − ( )[ ] ( )⎡⎣

⎤ ⎦ +( ) = ( ) +( )∫ 10 β

ˆ ˆ , (13)

where a z z b z dz z

ˆ ˆ

( ) ≡ ∫ − ( )[ ] ( )0 1 β . The Southern labor market equilibrium is derived by combining equations (6), (12),

(13), (7), (9), and (10) together

N u w

a z I I

u w

M s

s n

M s

= −( )

−( ) −( ) + ( )[ ] +( )

= −( )

−( ) −( ) +

1 1

α η

aa z

u w N rK w N rKM s s s n n n

( )[ ]

× − −( )

−( ) + + +[ ]1 1 1

1 α η

(14)

where

1 1 1

1 − −( )

−( ) + + +[ ] = + ≡ α η

u w N rK w N rK I I IM s s s n n n s n w. (15)

In equation (14) the right-hand side is the derived Southern labor demand and the left-hand side is the Southern labor force.

3. The Effects of an Improvement in the Southern TFP

We now combine the efficient specialization condition, represented by equation (5), with the condition of balanced trade, represented by equation (11), and equilibrium in the Southern labor market, represented by equation (14). The equilibrium triple w z un, ,ˆ( ) is simultaneously determined by the above three conditions. That is, the

equilibrium relative wage ( w wn M s ), the associated geographic specialization pattern,

and Southern urban unemployment rate are determined simultaneously. The unique equilibrium of the system is thus determined jointly based on the tastes, TFP, and endowments of the two countries. The equilibrium production, Southern urban and rural employment ( NM

s and N A s ), Southern unemployment, and Southern wage

inequalities can all be recovered from the model, once the equilibrium triple w z un, ,ˆ( ) is determined. Because the main goal of this paper is to explain the

real world phenomenon that high unemployment coexists with rapid economic growth in some large developing countries, we now consider the effects of an improvement in the TFP of the Southern manufacturing sector. The reasons for this comparative static exercise are as follows. With the same amount of inputs, an increase in the Southern TFP (relative to the Northern) enables the South to produce more for manufacturing goods that it has already had comparative advantages. More- over, the South gains new comparative advantages as well. A better economic performance of the South is thus assured as a result of an improvement in the South- ern TFP. We now examine the effects of such a change on the South’s unemployment rate.

Proposition 1. In equilibrium, (i) the index of borderline good ẑ increases with South- ern TFP, and (ii) the Northern wage wn decreases with Southern TFP.

UNEMPLOYMENT AND GOOD ECONOMIC PERFORMANCE 773

Proofs of propositions are provided in Results 2 and 3 in the Appendix. Intuitively, given the initial relative wage, an improvement in the TFP of the Southern manufac- turing sector implies that there is a loss in the range of commodities produced in the North, i.e. a larger borderline index ẑ, and a corresponding trade deficit in the North. This induces a decline in Northern wage wn, which serves to restore the balanced trade and to offset, in part, the decline in the North’s comparative advantage. These results resemble those obtained with the DFS model. However, certain opposing forces, which affect the Southern labor market, but are not addressed in the DFS model, serve to explain the impact on the unemployment rate herein, and are stated in Proposition 2 below.

Note that one important implication of Proposition 1 is that an increase in the South’s comparative advantage leads to changes in export composition. That is, certain products being imported to the South are now produced by Southern firms.

Proposition 2. In equilibrium, the South’s urban unemployment rate, the South’s unem- ployment rate, and wage inequalities between the Southern urban and rural areas increase with Southern TFP.

It is shown in Result 4 in the appendix that the South’s urban unemployment rate, u, increases with an improvement in the TFP of the Southern manufacturing sector. Result 5 in the appendix shows that South’s urban labor force, NB

S , increases as well. With the relationship between the two unemployment rates in the South, as stated in the section on labor migration that u N U uNs s s B

s≡ ≡ , Result 6 in the appendix then shows that the South’s unemployment rate increases as a result of increases in both the South’s urban unemployment rate and urban labor force, originally in response to an improvement in the Southern TFP. Note also that 1/(1 - u) measures the wage inequal- ity between the Southern urban and rural areas (see equation (8)). In sum, the South’s urban unemployment rate, the South’s unemployment rate, and wage inequalities between the Southern urban and rural areas all increase with Southern TFP. Hence, proposition 2 indicates that the increase in the rate of unemployment is a consequence of the relative improvement in the Southern TFP.

At first glance, this result may seem striking. Why would an increased demand for Southern urban labor, owing to an increase in the marginal productivity of urban labor and an increase in marginal industries (represented by a larger borderline good index), lead to an increase in the rate of unemployment? Without resorting to directly interpret the complicated mathematical results of the underlying simultaneous system, a further and more intuitive examination into the South’s labor markets is given below, to show that the above demand-driven mechanism is outweighed by forces brought by the labor reallocation mechanism in the North–South trade setup.

An increase in demand for labor in the Southern urban areas, in essence, induces labor reallocation from rural areas towards the cities, as the expected wage in the urban areas rises. The immediate effects of this labor reallocation process are an increase in urban labor supply in the South. The next issue will then be the relative strength of this supply-driven force and the above demand-driven force in the model.

In examining the relative strength of the above two opposing forces in determining the overall effect, we look into the effect of an improvement in the TFP of the Southern manufacturing sector on the world income, as defined in equation (15). The world income, measured by the agricultural product, shrinks as a result of an improvement in the TFP of the Southern manufacturing sector. The shrink in the world income is intuitive, because the relative price of the agricultural product to manufacturing goods

774 Ming-cheng Wang, Chen-ray Fang, and Li-hsuan Huang

rises, or equivalently, the relative prices of manufacturing goods to the agricultural product falls, after an improvement in the TFP of the Southern manufacturing sector. This has important implications for the effects of an improvement in the TFP of the Southern manufacturing sector on the South’s rate of unemployment.

From Proposition 1, we find that the Northern wage wn decreases with an improve- ment in the TFP of the Southern manufacturing sector. Thus, holding the South’s urban unemployment rate u at its original equilibrium level before the economy restores a new equilibrium, the world income (in terms of the Southern agricultural product), as defined in equation (15), decreases in response to an improvement in the TFP of the Southern manufacturing sector. The reduced world income then pushes down demand for all goods, whether agricultural or manufacturing, which results in a decrease in demand for labor in both urban and rural areas. As a result, the wage rate in the Southern agricultural sector wA

s falls. This process of adjustment continues until the new equilibrium is restored. With a constant wM

S , a higher level of u is warranted as the equilibrium relationship between wA

s and u, as indicated in equation (8), needs to be satisfied in the new equilibrium.13

4. Discussion and Conclusions

This section provides some stylized facts that lend support to both the issues taken on and the theoretical predictions of this study.

First, dramatic changes in export composition in the four large developing countries mentioned in the introduction section were consistently observed during the 1990s. China has shown the most significant changes with its rate of high-tech exports rising from 7.7% in the early 1990s to 30% in the period from 2006 to 2008. Brazil has also shown dramatic changes. Russia and India have not shown an increasing tendency for the production of high-tech exports. However, their TFP has also risen significantly, which must have, in turn, contributed to changes in the composition of their exports (World Bank, 2008). In one empirical study, Li (1997) found that economic reform caused marked improvements in the TFP of 272 Chinese state enterprises between 1980 and 1989, and that over 87% of the TFP growth was attributable to improved incentives, intensified product market competition, and improved factor allocation. Chand and Sen (2002) also found empirically that trade liberalization in the Indian manufacturing sector had an affirmative effect on TFP growth.

Moreover, empirical observations on changes in economic performance in Brazil, Russia, India, and China over the 1991–2010 period are reinforced by several notable facts. First of all, urbanization in the four countries has accelerated over this period. China’s urban population rose from 30.0% in the period of 1991–1995 to over 40% in the period of 2006–2008. Brazil, Russia, and India also exhibited a similar pattern, with some showing an even higher ratio. Thus, economic conditions leading to higher living standards in urban areas have attracted a large proportion of rural labor to migrate to the cities. Labor reallocation thus seems to be one of the most commonly observed changes in the above large developing countries.

Finally, data supports that the widening of wage inequalities between rural and urban areas and the deterioration of income distribution in these large developing countries have been significant. For example, the Gini coefficients worsened especially after 2000 in China. According to the World Bank’s estimate for China in 1997, 75% of the income inequality arose from differences between urban and rural areas. Further evidence is supplied by Lin et al. (2004) who found the 1982 urban/rural relative income rate to be 1.82. However, this value had risen sharply to 2.42 by 2000.

UNEMPLOYMENT AND GOOD ECONOMIC PERFORMANCE 775

The above stylized facts support our conclusions and model. To be specific, since the 1990s, one can generally observe in the above four large developing countries, the coexistence of high economic growth and unemployment, along with radical urbaniza- tion, dramatic changes in export composition and speedy deterioration in wage inequality. This study proposes a theoretical framework to explain these phenomena.

In our model, a high rate of unemployment emerges as a consequence of a relative improvement in the Southern TFP. Specifically, the relative improvement in the TFP in the Southern manufacturing sector causes changes in the comparative advantages of the Southern marginal industries, which in turn leads to a migration of labor from rural to urban areas. To sum up, the coexistence of high rates of economic growth and unemployment in the four large developing countries of Brazil, Russia, India, and China over the 1991–2010 period, and the increasing trade interaction between some large developing and developed countries reinforce the accuracy of our theoretical model. Along with relative improvement in the Southern TFP, our prediction is that as long as there are wage rigidities, a phenomenon commonly observed in large develop- ing countries during the process of economic opening, Southern unemployment and wage inequality would persist or even become worse.

Appendix

Total Differentiation of the Model

The total differentiation of equations (5), (11), and (14) yields

1 1

− ( )[ ] − ′ ( ) −[ ]

− +( ) ( ) − ( )[ ]

β β

α αη η θ

ˆ ˆ

z w

z w w

N I

b z z

n n

M s

ln ln

11 1 1

−( ) −( ) + ( )[ ] −( )

−( ) +

α η θ ẑ u w N

u w N rK

N u w N r

M s s

M s s s

M s s KK I

z b z a z

rK I

u u w N r

s n

M s s+

− ( )[ ] ( ) −( ) −( ) + ( )

− −( ) +

1 1 1 1

1 1

β α η

ˆ ˆ ˆ

KK I

d u

u s n

+( )

⎡

⎣

⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢

⎤

⎦

⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥

−

⎡

⎣

⎢ ⎢ ⎢ ⎢ ⎢

⎤

⎦

⎥ ⎥ ⎥ ⎥ ⎥

11 1 1

1 1A

dA A

dA z dw w

w I

dN r I

dK u N

un n

s s M

M s

n n

− + − ( )[ ] − − + −( )

−( β ˆ

)) +

+ −( )

−( ) + +

−( ) +

w N rK dw

u w u w N rK

dN r

u w N rK d

M s s s M

M s

M s s s

1 1 1

w u w N rK I

dN r

u w N rK I dK

rK I w

M s s s n

n s n

M s

− −( ) + +

+ +

1 1 11

1 1

−( ) + +( )

+ +

−( ) + +( ) −

u w N rK I dw

rK I N u w N rK I

dN r

M s s s n M

s n

s M s s s n

−−( ) + +

⎧

⎨ ⎪ ⎪

⎩ ⎪ ⎪

⎫

⎬ ⎪ ⎪

⎭ ⎪ ⎪

⎡

⎣

⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢

⎤

⎦

⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥

u w N rK I dK

M s s s n

s ⎥⎥ ⎥

(A1)

where ′( )β ẑ is an abbreviation of d z

dz z z

β ( ) = ˆ

Comparative Statistics

Result 1: D > 0.

Let the determinant of the coefficient matrix on the left-hand side of (A1) be D, then

776 Ming-cheng Wang, Chen-ray Fang, and Li-hsuan Huang

Δ = − ( )[ ]

− +( ) ( ) − ( )[ ] −( ) −( ) + ( )[ ]

−(

1 1

1 1 1

α αη η θ α η θ

ˆ ˆ ˆ

z w

b z z z

)) −( ) +

− ( )[ ] ( ) −( ) −( ) + ( )

1 1 1

w N u w N rK

z b z a z

rK I

M s s

M s s s

s nβ α η

ˆ ˆ ˆ 11

1 1

1 2 −

−( ) + +[ ]

+ ′ ( ) ⎛ ⎝⎜

⎞ ⎠⎟

−( ) u

u w N rK I

z w w

N I

u w

M s s s n

M s

β ˆ log

NN u w N rK

N u w N rK I

rK I

u u w N r

M s s s

M s s s n

s n

M s s

1 1 1

−( ) +

−( ) + + +

− −( ) + KK I

z w

z w w

s n

M s

+[ ]

= − ( )[ ] + ′ ( ) ⎛ ⎝⎜

⎞ ⎠⎟

1 1

1 2β βˆ ˆ log ,Δ Δ (A2)

where

Δ1 1 1 1 1 1

= −( ) ( ) − +

− ( )[ ] −( ) −( ) + ( )[ ] +

−( ) u b z

z z rK I

u w

s n

ˆ ˆ ˆ

α αη η θ α η θ MMs s s n

M s s

N rK I

z a z

u w N u w

+ +[ ] ⎧ ⎨ ⎩

− − ( )

−( ) −( ) + ( ) −( )

−( ) 1

1 1 1

1 β

α η ˆ

ˆ ss s s

N rK

u b z z z

+ ⎫ ⎬ ⎭

> −( ) ( ) − +

− ( )[ ] −( ) −( ) + ( )[ ] 1

1 1 1 1

ˆ ˆ ˆ

α αη η θ α η θ −−( ) + +( )

⎧ ⎨ ⎩

− − ( )

−( ) −( ) + ( ) −( )

−

u w N rK I

z a z

u w N

M s s s n

M s s1

1 1 1

1 β

α η ˆ

ˆ uu w N rK

u b z b z dz

M s s s

( ) + ⎫ ⎬ ⎭

= −( ) ( ) −( ) −( ) + ( )

− −( ) −∫

1 1

1 1 1

ˆ ˆ

α η α ηη β

β β

( ) − ( )

+ − ( ) − ( )

( )

−( ) −( ) +∫1

1 1

0ˆ ˆ

z z z

b z dz

u w N u w N rKz

M s s

M s s ss

z z

⎧

⎨ ⎪⎪

⎩ ⎪ ⎪

⎫

⎬ ⎪⎪

⎭ ⎪ ⎪

( )[ ] > > − ( ) ≥ − ( )

from equation since

11 0 1 1 1β β ˆ ,, , ˆ .∀ ∈[ ]z z0 (A3)

Δ2 1

1 1

1 =

−( ) + + −( )

+ −

−( ) −( ) +

N u w N rK I

u rK I

I u w N

u w N r

M s s s n

s n

M s s

M s s KK s

⎛ ⎝⎜

⎞ ⎠⎟ > 0.

As a result, D > 0.

Result 2: ∂

∂ ˆ

log z

As = >

Δ Δ

2 0.

Result 3: ∂

∂ w

slog = − <

Δ Δ

1 0.

Result 4: ∂ ∂ u u

A N b z

I z z

1 1 1 1 1

1 1

−( )( ) =

( ) −( ) −( ) + ( ){ − − ( )−( )log Δ ˆ ˆ ˆα η θ βα 11 0−( ) + ( )} >η a ẑ .

[see (A3)]

∂ ∂ u u

As 1

0 −( )( )

> log

naturally implies that ∂

∂ u

Aslog > 0.

Result 5: ∂ ∂

log log

N A

A s

s < 0,

∂ ∂

log log

N A

B s

s > 0.

From equation (12),

UNEMPLOYMENT AND GOOD ECONOMIC PERFORMANCE 777

∂ ∂

log log log

N A

rK I u u w N rK I

u A

A s

s n

M s s s n s

= +

−( ) −( ) + +[ ] ⎡ ⎣ ⎢

⎤ ⎦ ⎥1 1 ⎛⎛ ⎝⎜

⎞ ⎠⎟ +

−( ) + + ⎡ ⎣⎢

⎤ ⎦⎥ ⎛ ⎝⎜

⎞ ⎠⎟

= −( ) +

N u w N rK I

w A

u rK

M s s s n

∂ ∂ log

u w N rK I N b z

M s s s n

( ) −( ) + +

⎡ ⎣ ⎢

⎤ ⎦ ⎥

( )⎡ ⎣⎢

⎤ ⎦⎥ −( ) −( ) +1

1 1 1 1Δ

α η θ ˆ̂ ˆ

ˆz z

a z

N u w N rK I

M s s s n

( ) −

− ( ) −( ) −( ) + ( )

⎡ ⎣⎢

⎤ ⎦⎥

− −( ) + +

⎡ ⎣⎢

1 1 1

β α η

⎤⎤ ⎦⎥

−( ) ( )

− + − ( )[ ] −( ) −( ) + ( )[ ]

⎡ ⎣⎢

⎤ ⎦⎥

1 1

1 1 1

Δ u b z

z z rK s

ˆ ˆ α αη

η θ α η θ ++

−( ) + + ⎡ ⎣⎢

⎤ ⎦⎥

⎧ ⎨ ⎩

− − ( )

−( ) −( ) + ( ) ⎡ ⎣⎢

⎤

I u w N rK I

z a z

M s s s n1

1 1 1

β α η

ˆ ˆ ⎦⎦⎥

−( ) −( ) +

⎡ ⎣⎢

⎤ ⎦⎥ ⎫ ⎬ ⎭

1 1

u w N u w N rK

M s s

M s s s

from Result and Result 33 1

1 1 1

1 1

[ ]

= −( ) ( )

−( ) + + ⎡ ⎣⎢

⎤ ⎦⎥ −( ) −( ) + (

u b z N u w N rK I z

M s s s n

ˆ ˆΔ α η θ )){

+⎛ ⎝⎜

⎞ ⎠⎟ −

− + − ( )

⎡ ⎣⎢

⎤ ⎦⎥

+ −( ) + +

rK I I z

rK I u w N rK

s n

M s s s

1 1

α αη η θ ˆ II

z a z

u w N u

M s s

⎡ ⎣⎢

⎤ ⎦⎥

⎡ ⎣⎢

⎤ ⎦⎥

+ − ( )

−( ) −( ) + ( ) ⎡ ⎣⎢

⎤ ⎦⎥

−( ) −

1 1 1

1 1

β α η

ˆ ˆ (( ) +

− +⎡

⎣⎢ ⎤ ⎦⎥ ⎫ ⎬ ⎭ <

w N rK rK I

IM s s s

s n

n 0.

By using equation (11), i.e. 1 1

1 1− +

− ( ) ⎡ ⎣⎢

⎤ ⎦⎥ −( ) + + ⎡ ⎣⎢

⎤ ⎦⎥ =

α αη η θ ẑ u w N rK I IMs s s n n

, and the

fact that 1

1 1

−( ) −( ) +

< < +u w N

u w N rK rK I

I M s s

M s s s

s n

n , the inequality holds. We thus obtain

∂ ∂

log log

N A

A s

s < 0 . Furthermore, given constant N s,

∂ ∂

log log

N A

A s

s < 0 and N N Ns As Bs≡ +

together imply that ∂ ∂

log log

N A

B s

s > 0.

Result 6: ∂ ∂

log log

u A

s > 0.

By definitions of South’s unemployment rate us and urban unemployment rate u, we

have u N U uNs s s B s≡ ≡ . Then,

∂ ∂

log log

u A

N A

s s

B s

s = + > 0. The inequality comes

from Result 4 and Result 5.

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Notes

1. Global Market Information Database (see IMF, 2009). 2. Though China has enjoyed the most significant growth, with a relatively low rate of unem- ployment, doubts have been cast in the literature that there has been a serious understatement by official unemployment data in China. Zhai and Wang (2002), for example, argue that the urban unemployment rate could possibly be as high as 9.3%. 3. As measured by the trade amount over gross domestic product (GDP) and the industrial production index, respectively. 4. In addition, the USA, Japan, and Germany have long been the main exporting destinations for large developing countries such as Brazil, Russia, India, and China. For example, in the year 2008, the USA and Japan were China’s two primary export destinations with exporting shares as high as 17.6% and 8.1%, respectively, accounting for more than one fourth of her total exports. Empirical observations thus support the development of a closer trade relationship between large countries at different stages of economic development over the past two decades. 5. Note that when examining the above issues, we treat these large developing countries as already interacting economically, to some extent, with the rest of the world. Thus, we do not compare the autarky economy with the free trade economy. 6. China’s urban population rose from 19.6% in 1980 to nearly 40% in 2003. Brazil, Russia, and India also exhibited a similar pattern (World Bank, 2008). 7. Arbache (2001), and Knight and Li (2005) show the importance of efficiency wage payments in the Brazilian manufacturing labor market in the 1980s and 1990s and for urban China, respectively. The minimum wage rate as a percentage of the average wage for Brazil in the year 2007 was as high as 42.41% (International Labor Office (ILO), 2008, Table 2, p. 36), higher than the global average of 39% (2004–2007).

UNEMPLOYMENT AND GOOD ECONOMIC PERFORMANCE 779

8. These assumptions mean that the South is small in the Northern capital market though it is large in international trade and the determination of the Northern capital rental price is out of scope of this paper. 9. Note that equation (4) shows that the relative price of a particular commodity z in both countries is determined by the relative TFP and relative labor costs. The determination of the relative price of a particular good in our model is thus the same as that in the Ricardian production structure, although our production function exhibits two production factors. This is essentially because both countries share the same international capital rental price. Complete specialization is thus assured, i.e. after trade opens up, neither country produces goods without a comparative advantage. 10. A country’s GDP and the investment income add up to her gross national product (GNP). The Northern GDP is w N rKn n n+ . Given that the North has a capital outflow, the Northern investment income is r K Kn n−( ), where K Kn n− is the North’s outward FDI. 11. The Southern current account should include investment income paid by the South in terms of real commodities. This is in fact part of Southern exports. These two terms cancel each other out, so are absent in the equilibrium condition of the real balance-of-payments. 12. The term K Ks s−( ) also represents the South’s financial account balance. According to the IMF, a capital account lists the acquisition and disposal of non-productive and non-financial assets (intangible assets such as patents and goodwill). Compared to current and financial accounts, the capital account balance is negligible. Moreover, items included in capital accounts are not included in the model. Therefore, a capital account does not appear in the balance of payments. 13. The change of unemployment rate in response to an improvement in the Southern TFP in terms of labor supply–demand diagram is depicted as follows. In the Southern urban sector, an improvement in the TFP leads to a rightward shift in the labor demand curve and a higher employment results at the intersection of the fixed urban wage and the new labor demand curve. Meanwhile, the decrease in world income (in terms of the Southern agricultural product) causes the labor demand curve to shift leftward. Furthermore, better working opportunity along with higher expected wage in the urban areas creates an incentive for rural workers to migrate to the urban sector, pushing a rightward shift of the urban labor supply. As we discuss in the main text and prove in the appendix, the relatively larger rightward shift in the labor supply curve results in a higher unemployment rate.

780 Ming-cheng Wang, Chen-ray Fang, and Li-hsuan Huang

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