A multi-sectoral balance-of-payments-constrained growth model with sectoral heterogeneity

Structural Change and Economic Dynamics 39 (2016) 31–45

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A multi-sectoral balance-of-payments-constrained growth model with sectoral heterogeneity夽 Hiroshi Nishi Faculty of Economics, Hannan University, 5-4-33, Amami Higashi, Matsubara-shi, Osaka 580-8502, Japan

a r t i c l e

i n f o

Article history: Received 5 March 2014 Received in revised form 7 April 2016 Accepted 17 June 2016 Available online 27 June 2016 JEL classification: B50 F12 O41 Keywords: Multi-sectoral Thirlwall’s law International competition Structural heterogeneity

a b s t r a c t This study builds a multi-sectoral balance-of-payments-constrained growth model that incorporates structural heterogeneity between sectors and countries, such as differences in labor productivity, price competition, shares of exports and imports, and the quality of commodities. The model in the current paper generates more comprehensive results than those presented by Thirlwall (1979), Blecker (1998), and Araujo and Lima (2007), even though it contains their properties and reproduces their implications. Furthermore, compared with these existing works, the current model sheds more light on the relationship between the trade structure, international competition, productivity dynamics, and economic growth. It also shows the differences between industrial and macroeconomic phenomena, by presenting an example that illustrates how changes in nominal wages, the Kaldor–Verdoorn effect, and the degree of market competition in both countries affect economic growth in the home country. © 2016 Elsevier B.V. All rights reserved.

1. Introduction This study builds a multi-sectoral balance-of-paymentsconstrained (BOPC) growth model. I comprehensively reveal how the economic growth of the home country is impacted by changes in the (i) wage growth rate, (ii) growth rate of the foreign country, (iii) dynamics of labor productivity, and (iv) increase in international competition. These issues are examined in the presence of heterogeneity in labor productivity, cost-price competition, export and import shares, and the quality of commodities between sectors and countries. The BOPC growth model is a post-Keynesian, demand-led approach that postulates that the balance-of-payments position of a country imposes a limit on effective demand, to which supply can usually adapt. As is well known and I show below, in the canonical expression of BOPC growth, the economic growth rate of a country is determined by the so-called Thirlwall’s law that originates in Thirlwall (1979).1 Thirlwall’s law implies that a country’s

夽 I am grateful to the anonymous referees for their helpful comments. This work was supported by JSPS Grant-in-Aid for Scientific Research (A) 25245023. E-mail address: [email protected] 1 Thirlwall (2012) explains that Thirlwall’s original model is built on the proposition of a limit to the external deficit–GDP ratio, beyond which financial markets become nervous. In other words, its basic idea is that economic growth with an http://dx.doi.org/10.1016/j.strueco.2016.06.002 0954-349X/© 2016 Elsevier B.V. All rights reserved.

GDP growth rate is dependent on the GDP growth rates of other countries and that the ratio of the income elasticities of demand for exports and imports reflects non-price competitiveness. On the basis of this result, an economic policy implication is derived that to be non-price competitive, it is important to increase the attractiveness of the home country’s exports compared with imported goods. Thirlwall’s law reveals the mechanism of economic growth in the open economy context by focusing on a country’s quantitative (exports, imports, and economic growth) and qualitative (non-price competitiveness) aspects. Soukiazis and Cerqueira (2012) survey the development of various BOPC models, among which I extend the multi-sectoral model. I review the existing literature in Section 2 in detail. By taking BOPC growth as a long-run phenomenon, these models assume purchasing power parity (PPP). Variations in the terms of trade (the real exchange rate) are normally considered to be irrelevant for BOPC growth. This assumption implies that the models do not sufficiently

ever-growing deficit is unsustainable. This is why the standard BOPC model starts with the condition of a balance-of-payments equilibrium. It should also be noted that the BOPC model was established with critical implications for the export-led growth model à la Kaldor (1970), whose idea was formalized by Dixon and Thirlwall (1975). This is because the export-led growth model ignores the role of import demand and neglects the BOPC condition in determining the rate of economic growth. See also Blecker (2013) for a comprehensive survey of this topic and Razmi (2013) for a unification of the characteristics of both theories.

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H. Nishi / Structural Change and Economic Dynamics 39 (2016) 31–45

consider some important effects of relative price variations for economic growth. These variations come from changes in nominal wages, sectoral differences in labor productivity, market structure, and the price competitiveness of firms. Consequently, the relationship between these intriguing determinants of relative prices (terms of trade) and BOPC growth remains relatively unexplored in the existing literature. It is important to consider the causes and consequences of changes in relative prices, especially in a multi-sectoral model. First, the empirical evidence shows that the impact of the establishment of PPP and relative prices on economic growth is mixed. Second, even if relative price effects are not likely to work in the long run (i.e., PPP holds in the long run), the effects still work in the shortto medium-run periods. In this process, the long-run growth path is not necessarily independent of a chain of shorter periods, which is the reason that relative price effects should not be neglected. Third, in the disaggregated model, the nominal exchange rate cannot simultaneously offset the change in relative prices in many sectors. Taking these factors into consideration, it is more appropriate to build a BOPC model that can also capture the influence of relative price changes on economic growth. This study further extends the multi-sectoral BOPC growth model by including international competition and productivity dynamics. By incorporating cumulative causation and relative price effects, the current paper builds a model that is applied not only to long-run periods, but also to medium-run periods. I set up a model that places heterogeneous industrial structures, such as the different growth rates of labor productivity, exports and imports, preferences for commodities, and market competition, at the core of the analysis in the following manner. First, this study constructs a multi-sectoral model in which there is international trade between two countries that have multiple sectors in line with Pasinetti (1981, 1993), and Araujo and Lima (2007). Second, the market competition aspect of BOPC growth is introduced based on the Kaleckian model. Extending Blecker (1998)’s idea to multi-sectoral models, I assume international cost-price competition between each sector of both countries. Third, the structural aspects of BOPC growth such as sectoral export and import shares, market structure, and price competitiveness as well as the dynamics of productivity differences among sectors are investigated by using the concept of the Kaldor–Verdoorn effect.2 Thus, this paper reveals how structural heterogeneities, identified as changes in the sectoral composition of exports and imports, sectoral labor productivity dynamics, and intensifying international price competition, affect the economic growth rate of the home country. Although some of these attempts have been made in the existing literature, the current paper presents an economic growth model that can be used to comprehensively understand these results. Furthermore, it reveals some important results, hitherto undiscovered, by addressing the four questions mentioned above. I especially find that (i) the current model sheds more light on the relationship between the trade structure, international competition, productivity dynamics, and economic growth than the model in Araujo and Lima (2007). Specifically, (ii) the effect of a wage increase on the economic growth rate depends on the sum of cost-price competition elasticity, weighted by the share of exports and imports. Because of this, a rise in the home wage does not

2 Introducing these effects into the multi-sectoral model with international competition is reasonable because productivity dynamics are one of the determinants of cost and price competitiveness. Furthermore, it is this circulatory effect on the economic growth rate that Kaldorian export-led growth has emphasized under cumulative causation (Dixon and Thirlwall, 1975; Setterfield and Cornwall, 2002). However, as indicated in the preceding footnote, the canonical export-led model ignores the role of imports and thus the BOPC condition. With regard to the role of changes in relative prices in BOPC models, see also Section 2.

necessarily decrease economic growth. This result contrasts with that of Blecker (1998). (iii) It also shows an example of the difference between industrial and macroeconomic phenomena. At the industrial level, a rise in the wage rate in the home country necessarily deteriorates each sector’s trade balance, whereas its impact on the trade balance at the macroeconomic level is not necessarily the same. Such an implication may be close to what Keynesian economics has emphasized thus far as the fallacy of composition: it is not established that something is true of the macroeconomy just because it is true of some industry that composes the macroeconomy. The remainder of the paper is organized as follows. Section 2 reviews the contribution of the existing literature on BOPC models. Section 3 builds an extended version of the multi-sectoral BOPC growth model with heterogeneous industrial structures. Section 4 first derives the economic growth rate under the multisectoral BOPC growth model with international competition and then explains the generality of the model. Furthermore, by way of a comparative static analysis, this section presents several theoretical and political implications that are specific to the multi-sectoral version of the BOPC growth model with structural heterogeneity. Section 5 presents my conclusion. 2. Related literature Many contributions have been made since the seminal work of Thirlwall (1979). Soukiazis and Cerqueira (2012) comprehensively summarize the recent contributions with regard to the history, theory, and empirical evidence of BOPC growth models. The BOPC growth model has been subject to many extensions to account for several issues. According to Thirlwall (2012), the main research directions cover many topics such as incorporating capital flows, interest payments on debt, and terms of trade movement or disaggregating the model by commodities (multi-sectoral model) and trading partners to conduct an empirical investigation. The original Thirlwall’s law assumed that revenues from exports pay for imports. However, given that some economies attract financial capital, this assumption is too restrictive. Thus, Thirlwall’s law has been revised to take into account the flows of financial capital. Thirlwall and Hussain (1982) is a seminal paper that includes capital inflows. By doing so, the authors find the short-run growth effects of real capital flows. The model is empirically analyzed from the 1950s to the 1970s, showing that capital inflows prompt economic growth in some countries. In this model, changes in export prices also affect the economic growth of developing countries by way of the real value of net financial inflows. Contrary to this model that allows a perpetually rising ratio of net borrowing, Moreno-Brid (1998) addresses the long-run sustainability condition of indebtedness in the BOPC growth model, while Moreno-Brid (2003) adds interest payments on debt. In this framework, the sustainability condition of indebtedness is defined as the constant ratio of deficit to GDP, and the interest payment out of capital flows is included. These frameworks reveal that the existence of capital flows affects BOPC growth rates and that interest payments impose a constraint on these rates. The impact of terms of trade or the role of relative prices in BOPC growth seems to be controversial. In many BOPC models, there are no relative price effects, and Thirlwall’s law is derived as a longrun growth rate. However, according to some empirical studies, the results of the dynamics of relative prices or the real exchange rate and its impact on economic growth are mixed. For instance, Alonso and Garcimartin (1998) empirically show that relative prices play no role in economic growth because price elasticities are so low and relative prices do not adjust the BOPC disequilibrium. On the contrary, by applying the cumulative causation model to OECD countries, Leon-Ledesma (2002) empirically finds that prices do

H. Nishi / Structural Change and Economic Dynamics 39 (2016) 31–45

change in response to productivity growth and that changes in relative prices have a significant impact on export growth from 1965 to 1994. Further, Bahmani-Oskoee (1995) reveals that PPP fails to hold for less developing countries. In fact, the empirical evidence for whether PPP is established and whether relative prices affect economic growth is mixed. Taking these results, it is more appropriate to build a BOPC model that can also capture the role of relative price changes in economic growth. The current study employs a sectorally disaggregated model with some theoretical extensions. Existing multi-sectoral models of BOPC growth are inspired by the structural economic dynamics of Pasinetti (1981, 1993) that emphasize the structure of demand and production in an economy. Araujo and Teixeira (2003), Araujo and Lima (2007), Araujo et al. (2013), Araujo (2013), Gouvea and Lima (2010), Cimoli and Porcile (2010, 2014), Missio and Jayme (2012), and Bagnai et al. (2012) are of interest for the current study. Araujo and Teixeira (2003) construct a Pasinettian structural change model that incorporates consumption, capital goods, and international trade. On the basis of this, they then confirm the validity of Pasinetti’s insight into the structural change of production and expenditure in the international context. Araujo and Lima (2007) is also a Pasinettian structural dynamic model that recognizes the role of demand-led structural change in economic growth. As seen below, one of the most important contributions of their study is that it clearly explains the growth mechanism that is based on structural change. Araujo et al. (2013) and Araujo (2013) introduce the role of technological progress by using the Kaldor–Verdoorn cumulative causation effect also emphasized by the current paper. The former reveals that the existence of this effect enhances BOPC growth, whereas the latter explains that cumulative causation leads to a widening gap in income per capita between rich and poor nations. However, as indicated below, in these studies, the impact of changes in the determinants of relative prices under international price competition is not clear because they suppose that PPP holds over time in each sector. I complement this remaining issue in this paper.3 Cimoli and Porcile (2010, 2014) develop a multi-sectoral BOPC growth model based on the Ricardian approach with a continuum of goods à la Dornbusch et al. (1977). These studies emphasize the role of technological and structural change, which leads to an increase in cost competitiveness, on economic growth. Dutt (2002) and Sasaki (2009) apply the BOPC growth model to the North-South trade model. As in the current study, these models also admit the role of changes in relative prices. The model in Dutt (2002) simultaneously determines the rate of growth of the North and the South as well as the evolution of the North-South terms of trade. While the terms of trade vary, they become constant in the long-run equilibrium, which determines growth in rich and poor countries. The model shows that if the income elasticity of imports for the South is higher than that for the North, the world economy will eventually come to an equilibrium in which the gap between the North and the South will grow indefinitely. Sasaki (2009) extends a Ricardian trade model with a continuum of goods in order to consider a situation where the South faces the balance-of-payments constraint.

3 The relationship between the model in this paper and those should be explained more. Araujo (2013) considers cumulative causation in a multi-sectoral BOPC growth model by introducing a sectoral Verdoorn’s law by which growth endogenously induces technological progress. This law makes the model cumulative and circular. The purpose of Araujo et al. (2013) is to demonstrate the effect of the real exchange rate on economic growth under a multi-sectoral BOPC growth model. Their model is original in that it endogenizes the income elasticity of demand for exports and imports to the level of the real exchange rate and technological progress. Without considering price competitiveness in the model (i.e., even if one supposes PPP), they show that changes in the exchange rate (devaluation) can spur economic growth. It is common that these models suppose PPP. Moreover, the cumulative causation process in the BOPC model is not driven by relative price changes.

33

By using the model, he demonstrates the catching-up conditions of the South and also argues about the importance of price competitiveness and Verdoorn’s law for the catching-up process. For example, if the South is in a catching-up process, a policy intended to improve its international price competitiveness exerts a positive effect on its growth. It should thus be noted that these studies also admit the influence of relative prices on long-run growth. Empirical studies also report that the multi-sectoral Thirlwall’s law is a good predictor of the actual growth rate of income. By using data for Latin American and Asian countries, Gouvea and Lima (2010) empirically show that the multi-sectoral Thirlwall’s law fits better than the original Thirlwall’s law. Bagnai et al. (2012) present a multi-country BOPC model that emphasizes bilateral terms of trade and market shares, but it has a similar implication for the multi-sectoral BOPC growth model. On applying the model to SubSaharan African economies, they find that the multi-country model performs better than the original Thirlwall’s law. These studies have shown important results that are specific to multi-sectoral analysis. Above all, Araujo and Lima (2007), Araujo et al. (2013), and Araujo (2013) are the closest in spirit to the current study. They show the mechanism of BOPC growth in a multi-sectoral context and conclude that the growth rate of per capita income in the home country is also influenced by changes in the shares of imports and exports in each sector. Their model emphasizes the structure of production and non-price competitiveness in each sector as determinants of economic growth. The models presented so far usually assume PPP and focus on the role of non-price competition and the trade share in each sector. Most studies have assumed that changes in the real exchange rate do not affect economic growth, either because the price elasticities of exports and imports are low or because the rate does not have a systematic tendency to appreciate or depreciate in the long run. However, it is still important to consider variations in relative prices, especially in terms of industrial sectors. This is because relative prices still affect the price competitiveness of each sector and are determined by sectorally different factors such as productivity and market structure. Missio and Jayme (2012) investigate the role of the real exchange rate in innovation and the endogeneity of the income elasticities of imports and exports in the multi-sectoral BOPC growth model. They show that an exchange rate policy that maintains a competitive exchange rate contributes to faster economic growth by inducing technological progress. On the basis of their empirical study, Bagnai et al. (2012) insist that the assumption of a constant real exchange rate, routinely made in most studies, is inappropriate. Taking the foregoing review of BOPC growth models into consideration, the innovations of the model presented herein are as follows. First, I construct a multi-sectoral model in which there is international trade between two countries that have multiple sectors. Second, I introduce market competition and changes in relative prices into this multi-sectoral BOPC growth model based on the Kaleckian insight. Third, I reveal the importance of the structural aspects of BOPC growth. These novelties are also presented in a more comprehensive framework that can contain the properties and reproduce the implications of Thirlwall (1979), Blecker (1998), and Araujo and Lima (2007) on the basis of the multi-sectoral BOPC growth model.

3. Setup of the model 3.1. The BOPC condition, and export and import demand functions The following is a list of the main notations for the home country used in this paper. The subscript i indicates a variable for the

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H. Nishi / Structural Change and Economic Dynamics 39 (2016) 31–45

ith sector. YD : total output (total income), Yi : output (income), Ei : employment, qi : labor productivity, pi : price of the commodity, xi : export demand, w: nominal wage rate, e: nominal exchange rate between two countries, mi : import demand, ci : unit labor cost, zi : gross markup ratio. The same variables in the foreign country are expressed by adding the subscript F to the variable (e.g., the nominal wage rate in the foreign country is wF ). The international trade of commodities between two countries, namely the home country and foreign country, is considered. My focus is on the determinants of economic growth in the home country. Both countries have n sectors; each sector produces the same commodity in both countries, but with different levels of productivity. Each sector is represented by the index i = 1, 2, . . ., n and the ith sector produces commodity i. Each sector in both countries has heterogeneous characteristics related to export and import shares, productivity growth, pricing, and the structure of market competition. I assume that commodity i produced in each country is an imperfect substitute and that the ith sector of the home country is in competition with the same sector in the foreign country across the cost-price level of production. There is an important difference between Araujo and Lima (2007) and the current model with regard to trade goods and specialization. Whereas the former supposes international trade under complete specialization, I do not make this assumption. In Araujo and Lima (2007), only when the price of commodity i in the home country is lower than that in the partner country does the home country have a comparative advantage in producing commodity i and can, therefore, export it. Similarly, only when the price of commodity i in the home country is higher than that in the partner country does the home country import the commodity. This study intends to generalize this scope. I suppose intra-industry trade in which an economy both exports and imports commodity i, for which the ith sector is in competition with the trade partner country. When the circumstances of international competition are considered, such a supposition is reasonable. In this study, the BOPC condition is measured in nominal terms at a macroeconomic level. Although the trade balance may not be in the equilibrium in each sector, trade has to be balanced at the aggregate level. In a multi-sector context, the total value of exports (imports) comprises the total value of exports (imports) from each sector of the economy. Therefore, the trade balance at the aggregate level is given by n 

pi xi =

n 

i=1

pFi emi ,

(1)

i=1

where the left-hand side (LHS) represents the total value of exports in the home country and the right-hand side (RHS) represents the total value of imports in the home country in one period. In order for this trade balance to be maintained over time, the time rate of change in total exports and imports must be equal. Therefore, n  i=1 n

 i=1

p xi

n i

px i=1 i i

(ˆpi + xˆ i ) =

i (ˆpi + xˆ i ) =

n 

n  i=1

p emi

n Fi

p emi i=1 Fi

ˆ i) (ˆpFi + eˆ + m (2)

ˆ i ). i (ˆpFi + eˆ + m

i=1

Eq. (2) is the BOPC condition in the growth term, where the hat px symbol represents the growth rate of each variable. i ≡ ni i ∈

patterns of the country.4 If the ith sector of the home country produces a commodity that is only for domestic use, its share of exports is zero (i.e., i = 0). Similarly, if the home country does not import commodity i from the foreign country, its share n of imports is zero (i.e., i = 0). It should also be noted that  = 1 and i=1 i

n

i = 1 by definition. Following Thirlwall (1979), I assume that the export and import demand functions for each commodity are given by the Cobb–Douglas functional form. First, the export demand (the foreign demand) function for commodity i is given by i=1

xi = xi

 ep −εFi Fi

pi

YFFi ,

(3)

where xi is a constant term, εFi < 0 is the relative price elasticity, and Fi ≥ 0 is the income elasticity of demand for exports of commodity i. This formalization means that if the real exchange rate, measured by the price of commodity i, appreciates (i.e., a fall in epFi /pi ), exports of commodity i decrease. Eq. (3) also means that booms in the foreign country (i.e., a rise in YF ) induce higher exports of commodity i. By taking the logarithms of Eq. (3) and differentiating with respect to time, the growth rate of the exports of commodity i is obtained as follows: xˆ i = −εFi (ˆe + pˆ Fi − pˆ i ) + Fi Yˆ F .

(4)

This is the dynamic form of exports of commodity i. Second, the import demand function for commodity i is given by mi = mi

 ep εDi Fi

pi

YDDi ,

(5)

where mi is a constant term, εDi < 0 is the relative price elasticity, and Di ≥ 0 is the income elasticity of demand for imports of commodity i. When the real exchange rate, measured by the price of commodity i, depreciates (i.e., a rise in epFi /pi ), imports of commodity i decrease. Eq. (5) also means that an increase in the home country’s income (i.e., a rise in YD ) induces higher imports of commodity i. The dynamic form of the import demand function is derived by following the same procedure as above. That yields ˆ i = εDi (ˆe + pˆ Fi − pˆ i ) + Di Yˆ D . m

(6)

Jointly with εFi < 0 and εDi < 0, I assume that the Marshall–Lerner condition with respect to trade in the ith industry holds. That is, |εFi | + |εDi | > 1. 3.2. Price, production cost, and international competition My model of pricing, production cost, and international competition is developed by disaggregating the model in Blecker (1998). Blecker (1998) examines the relationship between BOPC growth and changes in wage cost (or living standards) by employing a partial exchange-rate-pass-through model. According to this model, when home production becomes more costly relative to foreign production as measured by the relative unit labor cost, the markup rate is reduced so as to keep the commodity more competitive and preserve market share. The relative unit labor cost is also affected by the nominal exchange rate that may fluctuate depending on the conditions in international financial markets. By introducing

px i=1 i i

[0, 1] denotes the market share of the ith industry in a country’s p em ∈ [0, 1] denotes the total exports (in volume) and i ≡ nFi i p emi i=1 Fi

market share of the ith industry in the country’s total imports (in volume). I assume that these terms are exogenous and constant; they are historically given or determined by the specialization

4 Strictly speaking, both i and i are endogenous variables and change over time, because the exports and imports of the ith sector are defined in Eqs. (3) and (5), respectively. However, the model becomes analytically intractable if I treat them as endogenous variables. Therefore, these values are assumed to be constant and determined by the historical context of the economy.

H. Nishi / Structural Change and Economic Dynamics 39 (2016) 31–45

this idea into the current multi-sectoral model, the relationship between international competition, production cost, and commodity pricing in each sector is formalized. Following Kaleckian standard markup pricing, the price level of commodity i is determined by pi = zi wq−1 , i

(7)

where it is assumed that the level and growth rate of nominal wages across industries are unique to the country. That is, I assume wi = w ˆ and wˆ i = w. The gross markup ratio of the ith industry zi is endogenized to consider the relationship between international competition, production cost, and commodity price. In accordance with the formalization in Blecker (1998), the gross markup ratio is given by the following constant-elasticity function:



zi = z i

wq−1 i

−i

,

ewF q−1 Fi

(8)

where z i is a positive constant, wq−1 ≡ ci indicates the ith indusi

try’s unit labor cost in the home country, and wF q−1 ≡ cFi indicates Fi the ith industry’s unit labor cost in the foreign country.  i ∈ [0, 1) is the elasticity of the gross markup that reflects the degree of international cost-price competition. Eq. (8) implies that a rise in the unit labor cost of the ith industry in the home country relative to that in the other country leads to a price reduction by the firms in this sector. This reduction is brought about by cutting the gross markup ratio in order to keep firms’ products more competitive. For example, a large  i means that firms in this sector i consider cost-price competition to be severe. When there is a relative rise in the unit labor cost of the ith industry in the home country, firms in this sector significantly decrease their gross markup ratio and commodity price to preserve their price competitiveness in international trade. On the contrary, a small  i means that firms in this sector consider cost-price competition to be less severe. If  i is zero, markup pricing is independent of international competition across production costs and thus the firms in this sector behave almost like monopolists in international trade. The dynamics of the price and gross markup ratio of commodity i are given by ˆ − qˆ i = zˆi + cˆi , pˆ i = zˆi + w

(9)

zˆi = −i (ˆci − eˆ − cˆFi ).

(10)

By using these two equations, I get the rate of change in the price of commodity i as follows: pˆ i = (1 − i )ˆci + i eˆ + i cˆFi .

(11)

Eq. (11) means that the rate of change in the price of commodity i is determined by both the unit labor cost in the home country as well as the foreign country and the nominal exchange rate, weighted by the degree of competition. As cost-price competition becomes severe, firms in the ith sector have to consider the change in the unit labor cost in the foreign country and exchange rate fluctuations. The existing literature on the BOPC model has assumed that productivity dynamics are given exogenously (Thirlwall, 1979; Blecker, 1998; Araujo and Lima, 2007). However, such formalizations have serious problems, especially in examining sectoral differences in productivity that significantly affect export and import performance. As an extension of the existing literature, the dynamics of the unit labor cost are endogenized by adopting a Kaldorian perspective. The unit labor cost in the ith sector is given by ci ≡ w/qi . This can be rewritten as follows: ci ≡ w

E  i

Yi

=w

Y

D

Yi

·

Ei YD



.

(12)

35

I assume that income in the ith industry is proportional to total income in the country (Yi = ai YD ). Under this assumption, the ˆ − qˆ i , where qˆ i ≡ dynamics of the unit labor cost are then cˆi = w Yˆ D − Eˆ i is the growth rate of labor productivity. I suppose that this is endogenously determined by the Kaldor–Verdoorn mechanism. That is, qˆ i ≡ Yˆ D − Eˆ i = i Yˆ D ,

(13)

where  i ∈ [0, 1] represents the Kaldor–Verdoorn coefficient. The coefficient is specific to each industrial sector and measures the amplitude of the dynamic increasing returns, which are affected by other externalities, and the size of the market.5 By using Eq. (13), the rate of change in the unit labor cost in the ith sector of the home country is obtained as follows: ˆ − i Yˆ D . cˆi = w

(14)

Following Blecker (1998), an analogous set of pricing equations is assumed to hold for the foreign country. The price level of commodity i produced by the foreign country is given by pFi = zFi wF q−1 . Fi

(15)

The gross markup ratio of the ith sector in the foreign country is assumed to be determined in a manner similar to that of the home country. It is given by



zFi = z Fi

wq−1 i

Fi

ewF q−1 Fi

,

(16)

where z Fi is a positive constant and  Fi ∈ [0, 1) is the elasticity of the gross markup of the ith sector in the foreign country. This represents the degree of international cost-price competition. The implication is the same as in Eq. (8). That is, I regard a large value of  Fi as a case of intensive competition in this sector of the foreign country, while a small value implies monopolistic competition. In addition, I assume a joint restriction on the degree of competition that  i ∈ [0, 1),  Fi ∈ [0, 1) and  i +  Fi ∈ [0, 1). This condition is necessary to rule out the case that a rise in the relative unit labor cost in the home country would cause extreme profit-squeeze behavior. The unit labor cost in the ith sector of the foreign country is given by cFi ≡ wF /qFi , which can be rewritten as follows: cFi ≡ wF

E  Fi

YFi

=w

Y

F

YFi

·

EFi YF



,

(17)

where it is assumed that the income share of the ith industry in total income is constant in the foreign country (YFi = aFi YF ). I assume that labor productivity is also affected by the Kaldor–Verdoorn effect in the ith foreign sector. In a similar manner to the above manipulation, the dynamics of labor productivity are given by qˆ Fi = Fi Yˆ F , where  Fi ∈ [0, 1] represents the Kaldor–Verdoorn effect that is

5 Araujo (2013) and Araujo et al. (2013) consider that the production of a particular sector affects the particular productivity of that sector. On the contrary, it is assumed in the current paper that overall production in real terms affects the productivity of particular sectors. The reasons for this are as follows. First, I emphasize that the current cumulative causation is realized by the insight in Young (1928). As he emphasizes, increasing returns are a macroeconomic phenomenon. Hence, the mechanism of increasing returns cannot be discerned adequately by observing the effects in the size of a particular industry, and industrial operations should be seen as an interrelated whole (Young, 1928, p. 539). Based on his essential insight, increasing returns in Eq. (13) are defined by using a macroeconomic growth term. In addition, such a formalization does not exclude the implication that the production of a particular sector affects the productivity of that sector. In the current model, once the BOPC growth rate is determined, the growth rate of a particular sector is also determined by the BOPC growth rate. Because Yi = ai YD is assumed, where ai is constant share, this results in Yˆ i = Yˆ D . Therefore, when the equilibrium BOPC growth rate is realized, the model also implies that increasing returns work, as the production of a particular sector affects the particular productivity of that sector. That is, qˆ i = i Yˆ D = i Yˆ i is established in the equilibrium BOPC growth process.

36

H. Nishi / Structural Change and Economic Dynamics 39 (2016) 31–45

specific to each industrial sector in the foreign country. By using Eq. (17), the dynamics of the unit labor cost in the ith sector of the home country are obtained as follows: ˆ F − Fi Yˆ F . cˆFi = w

(18)

By the same token, dynamic pricing in the ith industry in the foreign country is obtained as follows: pˆ Fi = (1 − Fi )ˆcFi − Fi eˆ + Fi cˆi .

(19)

Eq. (19) means that the rate of change in the price of commodity i in the foreign country is determined by the unit labor cost in the home country as well as the foreign country as well as the nominal exchange rate, weighted by the degree of competition. The implication of this equation is similar to Eq. (11): as cost-price competition becomes severe, firms in the ith sector in the foreign country have to consider the change in the unit labor cost in the home country and exchange rate fluctuations. Finally, I derive the terms of trade and growth rates of exports and imports. Let the terms of trade (real exchange rate) in each sector be ri = epFi /pi . The rate of change in this term is determined by the following equation: rˆi = eˆ + pˆ Fi − pˆ i .

(20)

By substituting Eqs. (11) and (19) into (20), I obtain the determinants of the dynamics of terms of trade in each sector as follows: rˆi = i (ˆe + cˆFi − cˆi ),

(21)

where i ≡ (1 −  i −  Fi ) ∈ (0, 1] summarizes the degree of international competition. If the ith industry in both countries is not in competition ( i =  Fi = 0), the value of i is equal to unity. A change in the relative unit labor cost directly affects the evolution of the terms of trade in the ith industry. On the contrary, if the ith industry in only one of these countries is subjected to severe competitive pressure (i.e.,  i  1 or  Fi  1), or both are subjected to equally strong competitive pressure (fifty-fifty), the value of i is close to zero. In this case, a change in the relative unit labor cost does not affect the evolution of the terms of trade for the ith industry.6 Here, let me remark that in contrast to Araujo and Lima (2007), Araujo (2013), and Araujo et al. (2013), the current model tries to introduce the cumulative causation process into the multi-sectoral BOPC growth model through relative price changes. This is the mechanism emphasized by the Kaldorian export-led growth model, which is a manner different from these models. As Blecker (2013) states, the Kaldorian export-led growth model and BOPC model disagree on the theoretical assumption regarding the role of relative prices. While the former emphasizes the role of the change in relative price competitiveness driven by technological progress as the driving force for export growth in the medium run, the latter assumes that such changes dissipate in the long run due to PPP. In many cases, the BOPC growth model and cumulative causation are exclusive in the sense that the latter requires that PPP does not hold, while the former is built on this assumption. However, there is a rationale for considering both approaches simultaneously in the same framework, as I referred to in the

6 In the case of fifty-fifty competition, the terms of trade become independent of a change in the relative unit labor cost because commodity prices in both countries change almost proportionally. For instance, let me consider  i  0.5 and  Fi  0.5 by using Eqs. (11) and (19). A decrease in the unit labor cost in the foreign country reduces pˆ Fi by nearly 0.5 points, whereas firms in the home country reduce their commodity price pˆ i by nearly 0.5 points owing to cost-price competition. Consequently, the relative price pi /pFi remains almost constant. However, such a change in the unit labor cost has a different impact on the gross markup ratio of the two countries. It raises the ratio of the foreign country and reduces that of the home country. In other words, in this international competition model, intensive competition affects the profitability of each industry.

preceding sections. First, the empirical evidence for whether PPP is established and whether relative prices affect economic growth is mixed (see also 2), meaning that it is more appropriate to build a BOPC model that can also capture the role of relative price changes in economic growth. Second, even if Thirlwall’s law under PPP holds in the long run, the economic growth at which a country’s balance-of-payments constraint is satisfied could be affected by cumulative causation over the intervening medium-run periods. In other words, even if relative price effects are not likely to work in the long run, these effects still operate in the short- to medium-run periods. The long-run growth path is thus not necessarily independent of such a chain of shorter periods. Hence, relative price effects should not be neglected. Third, even if I admit PPP may hold in aggregated terms, there is no guarantee that it will hold on a sectoral basis. In the case of the aggregate model, PPP holds because changes in the nominal exchange rate offset the one-to-one change in relative prices at the aggregate level. However, such a mechanism does not work in the disaggregated model, since it is not plausible that the nominal exchange rate simultaneously offsets the change in relative prices in many sectors. While the nominal exchange rate is an aggregate variable, the relative price change is a sectoral phenomenon, as I set in Eq. (20). Hence, no mechanism can always assure the realization of PPP in all sectors at the same time. Once PPP does not hold and the Marshall–Lerner condition does hold, the cumulative causation effect can work in the multi-sectoral BOPC growth model. From the discussion above, the nominal value of exports in the ith sector is given by pi xi . Let me remark that the growth rate of xi , given by Eq. (4), depends on the terms of trade in the ith industry and the expansion of foreign income. By using Eqs. (4), (11), and (21), the growth rate of nominal exports in this sector is pˆ i + xˆ i = pˆ i − εFi (ˆe + pˆ Fi − pˆ i ) + Fi Yˆ F = cˆi (1 − i + εFi i ) + (ˆe + cˆFi )(i − εFi i ) + Fi Yˆ F .











1−Ai



(22)

Ai

The changes in the unit labor costs in each economy’s sector follow Eqs. (14) and (18). By substituting these equations into Eq. (22), I get the growth rate of nominal exports in the ith sector as follows: ˆ − i Yˆ D ) + Ai (ˆe + w ˆ F − Fi Yˆ F ) + Fi Yˆ F pˆ i + xˆ i = (1 − Ai )(w ˆ − (w ˆ −w ˆ F − eˆ )Ai ] − (1 − Ai )i Yˆ D + (Fi − Ai Fi )Yˆ F . = [w (23) The nominal value of imports adjusted by the exchange rate in the ith sector is defined by pFi emi . In a manner similar to the above formalization, I can derive the growth rate of this value as follows: ˆ i = pˆ Fi + eˆ + εDi (ˆe + pˆ Fi − pˆ i ) + Di Yˆ D pˆ Fi + eˆ + m = cˆi (Fi − εDi i ) + (ˆe + cˆFi )(1 − Fi + εDi i ) + Di Yˆ D .









Bi





1−Bi

(24)

Furthermore, by using Eqs. (14) and (18), I get ˆ i = Bi (w ˆ − i Yˆ D ) + (1 − Bi )(ˆe + w ˆ F − Fi Yˆ F ) + Di Yˆ D pˆ Fi + eˆ + m ˆ F + eˆ + (w ˆ −w ˆ F − eˆ )Bi ] = [w − (1 − Bi )Fi Yˆ F + (Di − Bi i )Yˆ D .

(25)

The economic implications of the parameters Ai and Bi should be mentioned. Ai ≡  i − εFi i =− εFi (1 −  Fi ) + (1 + εFi ) i > 0 is the degree

H. Nishi / Structural Change and Economic Dynamics 39 (2016) 31–45

of competition, weighted by the price elasticity of demand for exports. Similarly, Bi ≡  Fi − εDi i =− εDi (1 −  i ) + (1 + εDi ) Fi > 0 is also the degree of competition, but weighted by the price elasticity of demand for imports. In other words, Ai and Bi represent the complex effect of the structure of cost-price competition on imports and exports in the ith sector. If the ith industries in both countries do not compete with each other, then  i = 0 and  Fi = 0 hold. Consequently, i = 1, Ai =− εFi , and Bi =− εDi . In addition, because I assumed that |εFi | + |εDi | > 1, it is true that 1 − Ai − Bi = i (1 + εFi + εDi ) < 0 holds. This is the Marshall–Lerner condition for each sector that takes international competition into consideration. 4. Multi-sector BOPC growth with sectoral heterogeneity 4.1. Derivation of the growth rate and its generality This section demonstrates that my model has generality in that includes the important aspects of Thirlwall (1979), Blecker (1998), and Araujo and Lima (2007) on the BOPC growth rate. A multisectoral BOPC growth condition is given by Eq. (2), which means that the time rate of change of both total exports and total imports should be equal. By substituting Eqs. (23) and (25) into Eq. (2), this condition is rewritten as n 

ˆ −w ˆ F − eˆ )Ai − (1 − Ai )i Yˆ D + (Fi − Ai Fi )Yˆ F ˆ − (w i w

n 

=

ˆ −w ˆ F − eˆ )Bi − (1 − Bi )Fi Yˆ F ˆ F + eˆ + (w i w

+(Di − Bi i )Yˆ D .



Yˆ F

n 

i Fi +

i=1

ˆ +w

n 

n 



Fi [i (1 − Bi ) − i Ai ]

i=1 n 

ˆ F + eˆ ) [i (1 − Ai ) − i Bi ] + (w

i=1

=

 n 1 

+

[i Ai − (1 − Bi )i ]



[i (1 − Ai ) − i Bi ]

i=1



ˆ F − Fi Yˆ F + eˆ )[i Ai − (1 − Bi )i ] (w

,

where I define i ≡ i Di +  i [i (1 − Ai ) − i Bi ] and n  i=1

i Di +

n 

i [i (1 − Ai ) − i Bi ].

D Yˆ D − F Yˆ F +  Yˆ D − F Yˆ F , (1 −  − F )(1 + εD + εF )

(30)

where  Yˆ D − F Yˆ F is the endogenously determined productivity growth difference between two countries that is given exogenously in Blecker (1998). Eq. (30) is essentially the same as the formalization driven in Blecker (1998).䊐 Blecker (1998) explains that a country cannot generally achieve full-employment growth with balanced trade simultaneously, while maintaining relatively high wage growth. Let me illustrate this explanation in a simple case, where the productivity difference is zero, by putting  =  F = 0. In this case, the BOPC condition is given by ˆ −w ˆ F − eˆ = w

D Yˆ D − F Yˆ F . (1 −  − F )(1 + εD + εF )

(31)

(27)

i=1

≡

(29)

Because I assumed |εD | + |εF | > 1, the sign of the denominator of Eq. (31) is negative. Thus, there is a tradeoff between the wage rate and economic growth, and thus so-called wage-led growth is not possible in the BOPC context.9 If the wage rate in the home country is relatively high compared with that in the foreign country at a

i=1

i=1

n 



n

ˆ i Fi Yˆ F + w

ˆ −w ˆ F − eˆ )(1 − A − B) + Yˆ F [F − F (1 − A − B)] (w . D + (1 − A − B)

(26)

The LHS represents the growth rate in total exports and the RHS represents that in total imports. Hence, the difference between these two terms approximates the growth rate of net exports, which is zero when trade is balanced over time. After some algebraic manipulation to solve Yˆ D , I get the economic growth rate of the multi-sectoral BOPC growth model under international competition:



Proof. In the case where there is only one sector, i = n = 1, I denote i = i = 1,  i = ,  Fi =  F , Di = D , Fi = F ,  i = ,  Fi =  F , εDi = εD , and εFi = εF . Then, Eq. (27) becomes

ˆ −w ˆ F − eˆ = w

1 Yˆ D =

Proposition 1. If I aggregate the multi-sectoral model into one sector, the current model results in Blecker (1998)’s model with endogenous productivity growth.

As in Blecker (1998), Eq. (29) can be expressed in terms of the relative wage dynamics:



i=1

and Lima (2007) call their formalization of the BOPC growth rate “the multi-sectoral Thirlwall’s law,” which is constructed in a pure labor economy on the basis of Pasinetti (1981, 1993)’s structural economic dynamics model. According to their multi-sectoral Thirlwall’s law, the growth rate of per capita income in the home country is a result of changes in the composition of demand or the structure of production that come from changes in the share of each sector. Inspired by not only Araujo and Lima (2007) but also Blecker (1998), the current multi-sectoral model further incorporates the role of international competition and the Kaldor–Verdoorn effect. Hence, the current model may more comprehensive than these existing representative BOPC models because it can show the implications of Thirlwall (1979), Blecker (1998), and Araujo and Lima (2007) as special cases.8 Let me deduce some propositions from the current model, while paying attention to the relationship with these models.

Yˆ D =

i=1

37

(28)

i=1

I assume the value of is positive and the growth rate of output Yˆ D is always positive. This is indeed assured by a sufficiently high growth rate of output in the foreign country Yˆ F .7 Araujo

7 In this case, the growth rate of sectoral output is also positive, since the growth rate of a particular sector is determined by the BOPC growth rate.

8 Nell (2003) and Bagnai et al. (2012) also call their model “the generalized version of Thirlwall’s Law.” According to Nell (2003), Thirlwall’s BOPC growth model is a specific case involving a bilateral trade relationship between one country and the rest of the world. In their paper, the specific case is generalized into multilateral trade relations between an individual country and blocks of countries. Thus, their model is general in the sense that Thirlwall’s law is extended to a multi-country setting. This shows that BOPC growth is determined by not only income and the relative price elasticity of bilateral imports and exports, but also bilateral imports and export market shares. Although my model supposes trade between two countries, it incorporates trade between multiple sectors (commodities), the effect of international competition, and the role of the Kaldor–Verdoorn effect in each sector. 9 Wage-led growth normally refers to an increase in the wage share that raises the economic growth rate by stimulating consumption and investment demand (Rowthorn, 1981; Bhaduri and Marglin, 1990). In these Kaleckian growth models, the wage works as the source of demand as well as a cost of production. The BOPC literature, however, focuses more on the role of wages as a production cost.

38

H. Nishi / Structural Change and Economic Dynamics 39 (2016) 31–45

given growth rate Yˆ D , it causes a trade deficit in the home country. To reduce this trade deficit, the home country has to either cut nominal wage growth to increase price competitiveness or reduce the economic growth rate to decrease imports. According to Blecker (1998), the former corresponds to the neoclassical strategy and the latter corresponds to a non-competitive case in the post-Keynesian sense. The current model also presents Blecker’s implications for international competitiveness.

Proof. If PPP holds, rˆ = −(ˆc − cˆF − eˆ ) = 0. By using Eqs. (14) and (18), the changes in the terms of trade remain constant as long as the following condition holds:

rate of the foreign country is the only determinant of the home country’s growth rate. By contrast, the novelty of Araujo and Lima (2007) is that the home country can still raise its growth rate if it can manage to change the sectoral composition of exports and imports. That is, the overall growth rate is also determined by the structural change that changes the composition of exports and imports such that the weighted income elasticity of exports grows faster than that of imports. Thus far, the current paper has built a multi-sectoral BOPC growth model that incorporates some structural heterogeneity and is more general than those in the literature. Even within this extended framework, some further extension may be possible. I illustrate an example of productivity growth that follows wage dynamics in the appendix.

ˆ −w ˆ F − eˆ ) − ( Yˆ D − F Yˆ F ) = 0. cˆ − cˆF − eˆ = (w

4.2. Comparative statics: importance of sectoral structure

Proposition 2. The aggregate model leads to the original Thirlwall’s law if I assume that PPP holds.

(32)

ˆ =w ˆ F + eˆ and Therefore, for PPP to hold, it is necessary that w  =  F = 0. By substituting these conditions into Eq. (30), I get Yˆ D =

F Yˆ F . D

(33)

This is nothing but the original Thirlwall’s law.䊐 Eq. (33) means that long-run growth depends on the economic growth rate of the foreign country multiplied by the ratio of the income elasticity of exports to imports. If the home country aims to grow, it must be able to improve income elasticity that represents non-price competitiveness; for example, it must focus on providing quality commodities that satisfy consumers’ preferences rather than on cost-price competition. Thirlwall (1979) also applies this equation to developed countries over the period 1951–1973 (–1976) and finds a correspondence between the actual growth rate and the growth rate predicted by Thirlwall’s law. Proposition 3. The current multi-sectoral model generates a result that is close to Araujo and Lima (2007) if I assume no inflation in the sectors of both countries and PPP. Proof. When PPP holds at a zero inflation rate in both countries, pˆ i = pˆ Fi = eˆ = 0 is satisfied. Then, the rate of change in exports and ˆ i = Di Yˆ D , imports in the ith sector is pˆ i + xˆ i = Fi Yˆ F and pˆ Fi + eˆ + m respectively. By using these conditions and Eq. (2), I get the following result:

n i Fi Yˆ D = ni=1 Yˆ F . i=1

(34)

i Di

Like Araujo and Lima (2007), by summing over Eq. (4) under zero inflation and using some algebraic manipulation, I get

n xˆ i ˆ YF = ni=1 .

(35)

 i=1 Fi

By substituting Eq. (35) into Eq. (34), I obtain

n

n 

One of the features of the current model is that it enables a comprehensive understanding of the important aspects of existing models. Furthermore, the current model has another novelty that is clearly explained by disaggregating it by using the effects of changes in relative prices. One of its most important implications is that even if an economic phenomenon holds true at the industry level, it may not do so at the macroeconomic level. The structure of the economy, reflected by the share of imports and exports of each sector, also plays an important role in understanding this implication. Below, I explain this by way of comparative statics on the effects of changes in wages, the Kaldor–Verdoorn effect, and the condition of market competition in both countries. Let me begin with the comparative statics on the changes in nominal wage rates in both countries. In Blecker’s model, an increase in relative nominal wages necessarily leads to stagnation in the growth rate of the home country when the Marshall–Lerner condition is assured. By contrast, the results of the current model are not necessarily so. In this regard, I get the following proposition. Proposition 4. A change in the home and foreign wage rates has a contrasting effect on economic growth. When a rise in the home wage increases economic growth, a rise in the foreign wage decreases economic growth. When a rise in the home wage decreases economic growth, a rise in the foreign wage increases economic growth. ˆ and w ˆ F in Eq. (27), I Proof. By differentiating Yˆ D with regard to w get





  ∂Yˆ D 1 1− i Ai − i Bi , = ˆ ∂w n



n

i=1

i=1

(37)



  1 ∂Yˆ D =− 1− i Ai − i Bi , ˆF ∂w where

n

1−

n

n

i=1

i=1

n n i Ai −  B ≶ 0. i=1 i=1 i i n

(38)

Therefore,

when

This result is close to what Araujo and Lima (2007) call the multisectoral Thirlwall’s law.䊐

A +  B , a rise in the home wage increases 1> i=1 i i i=1 i i economic growth, whereas a rise in the foreign wage n decreases n economic growth. By contrast, when 1 < A + B,a i=1 i i i=1 i i rise in the home wage decreases economic growth, whereas a rise in the foreign wage increases economic growth.䊐

Whereas Araujo and Lima (2007) derive the multi-sectoral Thirlwall’s law that shows the growth rate of per capita income in labor coefficient terms in a pure labor economy, I derive Eq. (36) in terms of nominal and national income. In both cases, the structure of the economy, reflected by the ratio of the sum of the income elasticities of exports and imports, weighted by the share of each industry, is important for economic growth. Thirlwall (1979) explains that given the income elasticities of imports and exports, the growth

Because changes in relative prices are mostly ignored in both the original and the multi-sectoral Thirlwall’s laws, this proposition is not obtained. By contrast, Blecker (1998)’s model focuses on the role of international competitiveness. However, n n as his model supposes an aggregated case, 1 − A −  B results in i=1 i i i=1 i i (1 −  −  F )(1 + εD + εF ), which is necessarily negative according to the Marshall–Lerner condition. Hence, a change in nominal wages in the home country always has a negative relationship with the

Yˆ D =

n i=1

 i=1 i Fi

i Di

n

 i=1 Fi i=1

xˆ i .

(36)

H. Nishi / Structural Change and Economic Dynamics 39 (2016) 31–45

economic growth rate in his model. In contrast to the existing literature, a rise in the home wage rate does not necessarily decrease economic growth in the current model. This is because the macroeconomic performance of exports and imports depends on the sum of the price competition elasticities, weighted by the market share of each sector. Related to Proposition 4, the differences between the industrial and macroeconomic dynamics in the trade balance should be also emphasized. To illustrate this, first, let me consider the impact of changes in the nominal wage rate on the trade balance of the ith sector. Let tbi be the difference between the growth rates of nominal exports and imports. This is given by ˆ − (w ˆ −w ˆ F − eˆ )Ai ] − (1 − Ai )i Yˆ D + (Fi − Ai Fi )Yˆ F } tbi = {[w ˆ F + eˆ + (w ˆ −w ˆ F − eˆ )Bi ] − (1 − Bi )Fi Yˆ F + (Di − Bi i )Yˆ D }. − {[w (39) ˆ gives the impacts of a rise in Differentiating tbi with respect to w home wages on the balance of payments in the ith sector as follows:

∂tbi = 1 − Ai − Bi = i (1 + εFi + εDi ) < 0. ˆ ∂w

(40)

With a rise in the home wage rate, the growth rate of nominal exports increases by (1 − Ai ) and that of nominal imports by Bi . Consequently, the difference between the export and import growth rates is (1 − Ai − Bi ) = i (1 + εFi + εDi ). This is necessarily negative under the Marshall–Lerner condition. Thus, a wage increase in the home country necessarily deteriorates the trade balance of an industrial sector. In this case, ceteris paribus, a fall in the GDP growth rate in the home country is required to restrain import growth in order to recover the balance of payments in this sector. Thus, there is always a tradeoff between a high wage rate and a high economic growth rate under the BOPC condition at the sectoral level. On the contrary, this is not necessarily the case at the macroeconomic level. Let TB be the difference between the growth rates of nominal exports and imports at the aggregate level. This is given by TB =

n 

ˆ − (w ˆ −w ˆ F − eˆ )Ai ] − (1 − Ai )i Yˆ D + (Fi − Ai Fi )Yˆ F i [w

i=1

−

n 



ˆ F + eˆ + (w ˆ −w ˆ F − eˆ )Bi ] i [w

i=1

−(1 − Bi )Fi Yˆ F + (Di − Bi i )Yˆ D .

(41)

ˆ gives the impacts of a rise in Differentiating TB with respect to w home wages on the aggregate balance of payments in the home country as follows:

  ∂TB i Ai − i Bi . =1− ˆ ∂w n

n

i=1

i=1

(42)

Eq. (42) states that at the macroeconomic nlevel, the overall growth  (1 − Ai ) and that of rate of nominal exports increases by i=1 i

n

 B as a consequence of a rise in the nominal imports by i=1 i i wage rate. Thus, the difference between the export and n import A − growth rates at the macroeconomic level is given by 1 − i=1 i i

n

 B . This is not necessarily negative, even if I assume the i=1 i i Marshall–Lerner condition. The market share of each sector matters for determining the macroeconomic performance of exports and imports. More intuitively, even if a rise in the wage rate decreases the net exports of a sector because the Marshall–Lerner condition works strongly there, when its export and import shares (i.e., i and i ) are small,

39

the macroeconomic impact of the rise in the wage rate is not so large as to decrease the overall growth rate of net exports. The overall performance of exports and imports is determined as the sum of these weighted average impacts. If this composite effect leads to higher growth in exports than in imports, the economic growth rate of the home country (Yˆ D ) must rise so that the BOPC condition can be satisfied, as stated by Proposition 4. Hence, industrial performance and macroeconomic performance to change the wage rate are not parallel. The discussion so far is summarized in the following corollary of Proposition 4. Corollary 1. A change in the home wage rate may have a contrasting effect on the trade balance at the sectoral and macroeconomic levels. A wage increase in the home country necessarily deteriorates the trade balance of the industrial sector, whereas a wage increase in the home country does not necessarily lead to the deterioration of the trade balance of the aggregate economy. Next, because I introduced the Kaldor–Verdoorn effect into the multi-sectoral BOPC growth model as an important extension, I examine its impact on macroeconomic growth. In this case too, changes in this effect have differing impacts on exports and imports at the industrial and macroeconomic levels. Proposition 5. A rise in the effect of dynamic increasing returns to scale (i.e., a rise in the Verdoorn coefficient  i ) in the home country decreases its economic growth rate if a cut in the domestic unit labor cost decreases the degree of contribution of exports more than that of imports in that sector. Proof. By totally differentiating Yˆ D and  i with respect to Eq. (26) and rearranging the result, I get dYˆ D Yˆ D (−i (1 − Ai ) + i Bi ). = di

(43)

If −i (1 − Ai ) + i Bi is negative, a rise in the Verdoorn coefficient has a negative impact on economic growth. By contrast, if −i (1 − Ai ) + i Bi is positive, a rise in this coefficient has a positive impact on economic growth.䊐 It is important to understand why such a mechanism works. By referring to Eqs. (22) and (24), when the unit labor cost in the ith sector of the home country is cut, −(1 − Ai ) measures the change in the growth rate of nominal exports in the ith sector, whereas −Bi measures that of nominal imports. In an aggregate model, −i (1 − Ai ) − (−i Bi ) =− (1 − A − B) is always positive. Thus, a decrease in the unit labor cost has less impact on the growth rate of nominal exports than that of nominal imports in the ith sector. As a result, the BOPC condition is eased, which contributes to raising the economic growth rate. Therefore, in the aggregated model, a rise in the Verdoorn coefficient necessarily has a positive impact on the growth rate of the home country. However, these effects are weighted by each sector’s share of exports and imports in the current multi-sectoral model. Even if a cut in the unit labor cost decreases imports more than exports in the ith sector of the home country, when the share of imports in the ith sector (i ) is small and its export share (i ) is large, its impact on exports and imports at the macroeconomic level may be reversed: as a result of a cut in the unit labor cost, the BOPC condition is more severe, which contributes to lowering the economic growth rate.10

10 A cut in the unit labor cost decreases the growth rate of nominal imports. On the contrary, the sign of −(1 − Ai ) depends on the value of Ai . If 0 < Ai < 1, a cut in the unit labor cost leads to a fall in the growth rate of nominal exports; if Ai > 1, the cut leads to a rise in the growth rate of nominal exports. The example here may occur when 1 − Ai is a non-negative value and a cut in the unit labor cost leads to a fall in the growth rate of nominal exports.

40

H. Nishi / Structural Change and Economic Dynamics 39 (2016) 31–45

In the disaggregated model, a rise in the Verdoorn coefficient may have a negative impact on economic growth in the home country. By the same token, the impact of a rise in the effect of dynamic increasing returns to scale in the foreign country on economic growth can be investigated. I get the following corollary of Proposition 5. Corollary 2. A rise in the effect of dynamic increasing returns to scale (i.e., a rise in the Verdoorn coefficient  Fi ) in the ith sector of the foreign country increases the economic growth rate of the home country if a cut in the foreign unit labor cost decreases the degree of the contribution of imports more than that of exports in that sector. Proof. By totally differentiating Yˆ D and  Fi with respect to Eq. (26) and rearranging the result, I get dYˆ D Yˆ F = (−i Ai + i (1 − Bi )). dFi Theta

(44)

If −i Ai + i (1 − Bi ) is negative, a rise in the Verdoorn coefficient in the foreign country has a negative impact on the home country’s economic growth. By contrast, if −i Ai + i (1 − Bi ) is positive, a rise in this coefficient has a positive impact on the home country’s economic growth.䊐 −Ai measures the change in the growth rate of the nominal exports of the ith sector, whereas −(1 − Bi ) measures that of nominal imports when there is a cut in the unit labor cost in the ith sector of the foreign country. In the aggregate model, a rise in the effect of dynamic increasing returns to scale in the foreign country necessarily decreases the economic growth rate of the home country, because export growth decreases more than import growth according to the Marshall–Lerner condition. By contrast, this is not necessarily so in this multi-sectoral version, because this condition is weighted by the sectoral composition. Even if there is a cut in the unit labor cost in the ith sector of the foreign country because of a rise in the Verdoorn coefficient, when the share of imports of the ith sector (i ) is large and its exports share (i ) is small, nominal import growth decreases more than export growth at the macroeconomic level.11 This leads to a trade surplus at the macroeconomic level. To recover the BOPC condition, the economic growth rate of the home country must therefore rise. Thus, this exercise also shows the importance of distinguishing the industrial and macroeconomic impacts of a rise in the Verdoorn coefficient. According to the generalized Thirlwall’s law, foreign income is one of the principle sources of effective demand that contributes to a rise in economic growth. However, in the current extended model, the effect of a rise in foreign income is more complicated. Proposition 6. The effect of foreign economic growth is both positive and negative, depending on the volume and cost effects on nominal export and import growth. Proof.

By differentiating Yˆ D with respect to Yˆ F in Eq. (27), I get





n n  1  ∂Yˆ D = i Fi + Fi [−i Ai + i (1 − Bi )] . ∂Yˆ F i=1

(45)

i=1

As shown in Eq. (44), the sign of −i Ai + i (1 − Bi ) can be negative or positive. If it is positive for all i, an expansion of the foreign

11 A cut in the unit labor cost in the foreign country decreases the growth rate of nominal exports. On the contrary, the sign of −(1 − Bi ) depends on the value of Bi . If 0 < Bi < 1, a cut in the unit labor cost in the foreign country leads to a fall in the growth rate of nominal imports, and if Bi > 1, the cut leads to a rise in the growth rate of nominal imports. For instance, when 1 − Bi is a non-negative value, a cut in the unit labor cost in the foreign country leads to a fall in the growth rate of nominal imports.

economy necessarily contributes to economic growth in the home country. However, if the sum of  Fi [−i Ai + i (1 − Bi )] is negative and it offsets the first term on the RHS of Eq. (45), an expansion of the foreign economy leads to a low rate of economic growth in the home country.䊐 The first term on the RHS of Eq. (45) represents that a rise in Yˆ F leads to an increase in foreign demand. Therefore, I call this the “volume effect.” As the multi-sectoral Thirlwall’s law has indicated (Araujo and Lima, 2007), this effect works strongly when the sectoral income elasticity of demand for imports is lower and that of demand for exports is higher. In addition to the volume effect, a rise in Yˆ F has a positive impact on productivity growth and reduces the unit labor cost in the foreign country. This causes relative prices to change. This impact on both nominal export and import growth at the macroeconomic level is represented by the second term in Eq. (45); therefore, I call this the “cost effect.” As shown in Corollary 2, the cost effect on the growth rate of the home country is negative when it leads to a higher decrease in nominal import growth than export growth at the macroeconomic level. If this impact is sufficiently strong to offset the volume effect, the home country’s economic growth stagnates.12 Inspired by Blecker (1998), another novel feature of the current paper is introducing competition between two countries in the multi-sectoral BOPC growth model. The aggregated BOPC model shows that increased pressure on price competition decreases the growth rate of nominal imports more than that of nominal exports and thus a trade surplus is generated. Under the BOPC condition, this surplus is adjusted by a rise in the growth rate of the home country, ceteris paribus, at a given relative rate of home wages. However, as Eq. (31) also implies, there is a tradeoff between economic growth and the relative increase in the home wage rate. This tradeoff is more rigid if the competitive pressure for cost-pricing behavior (i.e., a rise in ) is more severe. In this case, even if the relative rate of home wages is cut, its impact on the economic growth rate becomes limited. My investigation provides a new implication about the effect of changes in the structure of market competition on growth and income distribution. To compare this with the essence of Blecker (1998), let me examine this impact in a simple case where productivity growth is zero ( i = 0 and  Fi = 0). Then, I get the following proposition. Proposition 7. The impact of an increase in international competition in the ith sector of the home country on economic growth depends on its share of exports and imports. Proof. Suppose the Verdoorn coefficient is zero as a simple case. Let TB be the difference between the growth rate of nominal exports and imports, given by TB =

n 

ˆ − (w ˆ −w ˆ F − eˆ )Ai + Fi Yˆ F } i {w

i=1

−

n 

ˆ F + eˆ + (w ˆ −w ˆ F − eˆ )Bi + Di Yˆ D }. i {w

(46)

i=1

By differentiating TB with respect to  i , I get

∂TB ˆ −w ˆ F − eˆ )[i (1 + εFi ) + i εDi ]. = −(w ∂i

(47)

12 In a special case in which the Kaldor–Verdoorn effect is perfect in each sector of the foreign country ( Fi = 1), substituting this into Eq. (45) shows that the effect of a rise in the foreign economic growth rate is expressed by the sum of the impacts of the multi-sector Thirlwall’s law and the increase in the foreign wage.

H. Nishi / Structural Change and Economic Dynamics 39 (2016) 31–45

41

ˆ −w ˆ F − eˆ is positive, the sign of ∂TB/∂ i depends When the sign of w on that of i (1 + εFi ) + i εDi . Although the Marshall–Lerner condition stipulates |εFi | + |εDi | > 1, Eq. (47) also includes the share of exports and imports. Therefore, the sign of i (1 + εFi ) + i εDi may be either positive or negative. For example, consider that the export share of the ith sector is relatively large and its import share is small. In this case, the sign of i (1 + εFi ) + i εDi can be positive and increasing price competition in this sector would have negative impacts on the balance of payments of the home country. Consequently, the growth rate of the home country must fall to recover the BOPC condition.䊐

Table 1 The structure of model.

Proposition 7 presents an implication that is in sharp contrast to Blecker (1998). In Blecker (1998), both i and i are unity and the Marshall–Lerner condition results in nominal imports falling more than nominal exports because of severe competition (i.e., TB > 0). This disequilibrium in the trade balance is rebalanced by a rise in the economic growth rate of the home country. By contrast, Proposition 7 reveals that if the absolute value of εFi is small and if price competition becomes more severe in a sector with a relatively large export share, the economy will stagnate, because such competition has negative impacts on the macroeconomy as well as on the sectoral trade balance. In the current model, even if the Marshall–Lerner condition is satisfied at the sectoral level, the share of exports and imports may reverse the impact of a change in the degree of competition on the growth rates of exports and imports. By the same token, the impact of an increase in international competition in the ith sector of the foreign country on the home country’s economic growth can be summarized by the following corollary.

adding assumptions. In other words, the current model is more generalized and can consider their analytical scope as special cases. Introducing sectoral heterogeneity in production costs and the degree of price competition into a multi-sectoral model is a novel contribution of this study. By doing so, this study attempts to contribute to identifying the exact mechanism that determines BOPC growth, beyond that shown by Thirlwall (1979), Blecker (1998), and Araujo and Lima (2007). Table 2 summarizes the main results obtained by the comparative statics that have not been conducted in sufficient detail in the above literature. When the export share of the ith industry is large and its import share is small, a rise in the Verdoorn coefficient in both countries has a negative effect on the growth rate of the home country. This is because it leads to the deterioration of the trade balance of the home country at the macroeconomic level, necessarily lowering the home country’s growth rate to satisfy the BOPC condition. However, their impacts are reversed when the export share of the ith industry is small but its import share is large. In addition, a rise in  i —an increase in price competition pressure in the ith sector in the home country—has a negative impact on the balance of payments and thus the growth rate of the home country decreases. This occurs because the export share of the ith industry is large and its import share is small. In the same structure of production, a rise in  Fi has a positive impact on the balance of payments of the home country, and the home country’s growth rate thus increases. The impact of a rise in the foreign economic growth rate does not fit into this table because it depends on both the volume and the cost effects, as shown in the first and second terms, respectively, on the RHS of Eq. (45). In the standard multi-sectoral BOPC growth model, its effect is positive because only the volume effect works. However, if I introduce the Kaldor–Verdoorn effect, the story becomes complicated. A boom in the foreign economy also has a positive impact on productivity growth and reduces the unit labor cost in the foreign country. When nominal import growth decreases

Corollary 3. The impact of an increase in international competition in the ith sector of the foreign country on the home country’s economic growth also depends on the share of exports and imports. Proof. Suppose the Verdoorn coefficient is zero as a simple case. By differentiating TB in Eq. (46) with respect to  Fi , I get

∂TB ˆ −w ˆ F − eˆ )[i εFi + i (1 + εDi )]. = −(w ∂Fi

(48)

ˆ −w ˆ F − eˆ is positive, the sign of ∂TB/∂ Fi depends When the sign of w on that of i εFi + i (1 + εDi ). Eq. (48) also includes the share of exports and imports. Therefore, the sign of i εFi + i (1 + εDi ) may be either positive or negative.䊐 Given a positive value of the relative home wage rate, more intensive international competition in the ith sector of the foreign country necessarily has a positive impact on economic growth in the home country in Blecker (1998), according to the Marshall–Lerner condition. However, if I disaggregate the model and focus on the sectoral composition of imports and exports, another possibility is discovered. Suppose the absolute value of εDi is small. If the import share of the ith sector is large, whereas the export share is small, the sign of i εFi + i (1 + εDi ) can be positive. Then, increasing price competition in this sector in the foreign country has a negative impact on the balance of payments of the home country. Consequently, the growth rate of the home country must fall to recover the BOPC condition. 4.3. Summary of the results Table 1 summarizes the relationship between representative existing BOPC models and the current model. The structure of the current model comprehensively includes the main characteristics of Thirlwall (1979), Blecker (1998), and Araujo and Lima (2007) and it can easily be reduced to them by

If one adds assumptions that

The current model Eq. (27) is close to Original Thirlwall’s law

All sectors are aggregated into one sector and PPP holds All sectors are aggregated into one sector and labor productivity is exogenous PPP holds at each sector under no inflation in both countries

Blecker model

Araujo and Lima model

Table 2 The impacts on the growth rates of home country. If the sum of price-competition elasticities weighted by market share is A rise in:

Less than unity

More than unity

ˆ w ˆF w

Positive Negative

Negative Positive

When the value of A rise in:

i is large and i is small

i is small and i is large

i  Fi i  Fi

Negative Negative Negative Positive

Positive Positive Positive Negative

Note: The range of Ai and Bi matters for the impact of  i and  Fi on the economic growth as I mentioned in the corresponding part. Similarly, the range of |εi | and |εFi | also matters for the impact of  i and  Fi on the economic growth.

42

H. Nishi / Structural Change and Economic Dynamics 39 (2016) 31–45

more than export growth at the macroeconomic level because of this cost effect, and this impact is sufficiently strong to offset the volume effect, economic growth stagnates. Finally, one of the most important results obtained in this paper is that a wage increase in the home country has a different impact on the trade balance at the industrial and macroeconomic levels. In the preceding literature, a rise in the home wage rate increases the production cost and leads to the deterioration of the terms of trade. As a result, the economy stagnates. Thus, it is in the interests of both the industries and the national economy to improve the trade balance. However, the current model has a different implication, especially when the sum of the price competition elasticities for exports and imports weighted by their market share is less than unity. In this case, although a rise in the home wage still deteriorates the trade balance in a sector, as shown in Eq. (40), it has a favorable effect on the macroeconomic growth of the home country. This is because the national economy is composed of heterogeneous sectors that have different shares of exports and imports. Under such an economic structure, although a wage increase could have a potential positive effect on macroeconomic growth, this may not be realized in the economy. This is because each industry has reason to oppose the increase in the home wage rate that may shrink its export share and lead to the deterioration of the sectoral trade balance. The current model thus implies the structural difficulty of increasing wages in an economy composed of heterogeneous sectors.

than Araujo and Lima (2007)’s model. This is shown by the comparative statics on the effects of changes in nominal wages, the Kaldor–Verdoorn coefficient, and the degree of market competition in both countries. For example, suppose that the unit labor cost in the home country is higher than that in other countries. Higher competitive pressure on the ith sector of the home country decreases the economic growth rate when its export share is large and import share is small. Third, my theoretical investigation also shows differences between industrial and macroeconomic phenomena. As explained in Proposition 4 and Corollary 1, for example, an increase in the wage rate has different impacts on exports and imports at the industrial and macroeconomic levels. At the industrial level, a rise in the wage rate of the home country necessarily leads to the deterioration of one sector’s trade balance owing to the Marshall–Lerner condition. By contrast, its impact on exports and imports at the macroeconomic level does not necessarily generate the same result. This is because the impact of the home wage increase on macroeconomic exports and imports also depends on the industrial structure reflected in the share of exports and imports. When the economy is composed of an industrial structure that has a small share of exports and imports, an increase in the home wage rate does not always lead to a decrease in the rate of economic growth. Furthermore, the industrial structure of the economy also matters for how changes in the growth of the foreign economy, the Kaldor–Verdoorn coefficient, and the market structure in each sector affect macroeconomic growth in the home country.

5. Conclusion The importance of the multi-sectoral BOPC growth model lies in the finding that despite the absence of international growth, an economy can still grow at a higher rate by bringing about structural change. This study built a multi-sectoral BOPC growth model that incorporates structural heterogeneity such as differences in labor productivity, price competition, export and import shares, and the quality of commodities between sectors and countries. On the basis of the model, this study investigated the effects of different shocks on the economic growth rate of the home country. It was shown that the multi-sectoral Thirlwall’s law developed in the current paper generates more comprehensive results than those presented by Thirlwall (1979), Blecker (1998), and Araujo and Lima (2007). The current model contains their properties and reproduces their implications. First, similar to the original Thirlwall (1979)’s law, one country’s growth rate is directly related to other countries’ growth rates and the income elasticity of demand for exports, whereas it is inversely related to the income elasticity of demand for imports. Second, similar to the original Blecker (1998) model, there is a tradeoff between a high growth rate and the wage rate. This tradeoff becomes more severe when cost-price competition intensifies; this is reflected in the rise in the degree of the exchange rate pass-through. Third, similar to the original Araujo and Lima (2007) model, changes in the composition of demand or structure of production that are manifested as changes in the export and import shares of each sector are also important for economic growth. In addition to these results, this extension of the model generates novel implications for industrial structure, cost-price competition, and the determinants of economic growth rates in the BOPC context. First, while there is a tradeoff between the wage rate and growth rate in Blecker (1998)’s model, the current model explains not only their tradeoff case but also another case: a rise in the home wage rate does not necessarily lead to a lower economic growth rate. Rather, it depends on the sum of the price competition elasticities, weighted by export and import shares. Second, the model sheds more light on the relationship between industrial structure, international competition, and economic growth

Appendix13 Introduction of wage dynamics The current model has other applications. For example, the empirical evidence for Kaldor’s stylized facts suggests that wage dynamics follow productivity dynamics in the long run. When wage dynamics follow productivity growth in each sector of each econˆ F = Fi Yˆ F are established, which leads to cˆi = 0 ˆ = i Yˆ D and w omy, w and cˆFi = 0. In this case, the growth rates of price in each sector in the home and foreign countries are given by pˆ i = i eˆ and pˆ Fi = −Fi eˆ , respectively. The growth rates of nominal exports and imports in sector i are therefore pˆ i + xˆ i = eˆ Ai + Fi Yˆ F ,

(49)

ˆ i = eˆ (1 − Bi ) + Di Yˆ D . pˆ Fi + eˆ + m

(50)

After some algebraic manipulation to solve Yˆ D , I get the economic growth rate of the multi-sectoral BOPC growth model under wage dynamics under the Kaldorian stylized fact,

n

Yˆ D =

n eˆ [i Ai − (1 − Bi )i ] . ni=1

ˆ +

 Y i=1 i Fi F

i=1

i Di

(51)

This result has implications similar to that of Eq. (27) with regard to the impact of change in Yˆ F and eˆ on Yˆ D . The growth rate of income in the home country is still a result of changes in the composition of demand or the structure of production. Moreover, when I aggregate the multi-sectoral model into one sector, my model results in Blecker (1998)’s model with a constant unit labor cost. In fact, when there is only one sector i = n = 1, the same procedure with Eq. (29) gives Yˆ D =

13

1 [F Yˆ F − eˆ (1 −  − F )(1 + εD + εF )], D

(52)

In summarizing this appendix, the discussion with referees was really useful.

H. Nishi / Structural Change and Economic Dynamics 39 (2016) 31–45

which can be further expressed in terms of relative wage dynamics: −ˆe =

D Yˆ D − F Yˆ F . (1 −  − F )(1 + εD + εF )

(53)

Eq. (53) retains the essence of the formalization driven in Blecker (1998) with respect to eˆ and Yˆ D . In this case, a devaluation of the nominal exchange rate induces economic growth in the home country. Change in the Verdoorn coefficient and partial specialization While introducing the cumulative causation process, this paper considers the effect of changes in the Verdoorn coefficient reinforcing the productivity gains under the assumption of partial specialization in Section 4.2. The assumption of partial (incomplete) specialization in this setting is justified by the following reasons. First, this paper emphasizes that following Setterfield (1998)’s Keynesian–Kaldorian spirits, cumulative causation does not ensure a deterministic outcome in the long run. In other words, the long run is not something to be approached or tended towards because any movement—even movement towards a particular position of the equilibrium—will change the conditions of the equilibrium. Moreover, history matters in the sense that current activities are conditioned by a given and immutable past, and the future is subject to fundamental uncertainty (Setterfield, 1998, pp. 533–4). This is why I do not suppose that cumulative causation brings about some deterministic outcome such as full specialization; rather, a shock should be considered to be a part of this process. Second, I investigate changes in the Verdoorn coefficient under partial specialization because of the cost-price competition environment. In such a case, it is natural to suppose that changes in the Verdoorn coefficients for sectors in economies under partial specialization play an important role in surviving cost-price competition. As mentioned below, many sectors both export and import in the real world. The current model supposes that the same sectors in two countries compete with each other across lower costs and prices in intra-industry trading. Thus, it is also cost-price competition that justifies changes in the Verdoorn coefficient, as examined under the partial specialization pattern within the current framework. Third, in reality, many goods are mutually exported and imported between countries. By using the Grubel–Lloyd index, WTO (2008) shows that many products are traded in the intra-industry context, especially technologically advanced goods between the German and US sectors. By surveying the related literature, the report also indicates that intra-industry trade remains important, although bilateral intra-industry intensities vary according to the trading partners concerned. Thus, intraindustry trade can be widely observed in the real world. However, such an intra-industry trade structure does not square with perfect specialization, which predicts that an industry is either an exporter or an importer, not both. By contrast, it does square with the model of partial specialization in which an industry can be both an exporter and an importer. This being said, the trade structure might plausibly be affected by a change in the Verdoorn coefficient as follows: an increase in the Verdoorn coefficient in a sector fosters specialization, while enhancing the productivity growth of the sector. On the contrary, the export share of that sector is also expanded by specialization, while productivity growth changes exports, which leads to further specialization. For example, there are studies that simulate the coevolution of the growth rate, specialization, and industrialization as reflected in the income elasticity of exports in a Kaldorian export-led model and a BOPC model (Fiorillo, 2001; Botta, 2009). However, they do not incorporate market competition and thus assume away the role of cost-price competition. In addition, it is not

43

conclusive that only full specialization exists in terms of the theory. The theoretical model also shows that the specialization pattern is not limited to complete specialization; it can also be incomplete or even a cyclical pattern (Los and Verspagen, 2006). Although the emergence of a new industry (or good) may radically influence the specialization pattern in the longer run in the cumulative causation process, I also consider such a specialization process caused by a change in the Verdoorn coefficient in the next appendix. However, the current paper builds a model that also considers the short- and medium-run impacts, as mentioned at the outset of the paper. Let me remark that the extension of the model in the next appendix should be regarded as suggesting that a change in the Verdoorn coefficient has only a gradual and temporary impact on the specialization pattern since the comparative statics analysis is only a snapshot. In addition, although I illustrated a rise in the Verdoorn coefficient, a fall is plausible (e.g., in declining industries or stagnating sectors). Thus, the Verdoorn coefficient may both rise and decline according to the period, sector, and country, and its impact on specialization may therefore differ accordingly. In these senses, the impact of a change in the Verdoorn coefficient on the partial specialization pattern should be taken as transitory. Verdoorn coefficient and evolution of specialization In this paper, sectoral specialization is assumed to be partial and both export and import activities involve cost-price competition. It is also assumed that both export and import shares are exogenous and constant, that is, the structure of trade or degree of specialization is given. However, the structure of trade or degree of specialization could plausibly change gradually with a change in the Verdoorn coefficient. In other words, an increase in the Verdoorn coefficient in a sector might foster specialization. This specialization then increases exports in that sector, leading to further specialization and so on. The current framework could be extended to examine the effect of such a specialization process. For example, the relationship between changes in the Verdoorn coefficient and patterns of specialization may be expressed by defining i and i as the function of  i . Let me define i ( i ,  j ) and i ( i ,  j ), where j = / i. The values of i and i are affected by the change in  in other sectors j, since the sum of exports and imports is constant (unity). When a rise in the Verdoorn coefficient in a sector fosters specialization, an increase in  i leads to a rise in i and a fall in i . That is, di ( · )/di = ii ( · ) > 0 and di ( · )/di = ii ( · ) < 0, which means that the export share of commodity i increases in the economy by way of specialization, while the import share of commodity i decreases. As the sum of exports and imports is constant (unity), a rise in the export share in a sector (e.g., i) means a fall in this share in another sector (e.g., j). Similarly, when the import share in a sector falls (e.g., i), this share in another sector rises (e.g., j). That is, dj ( · )/di = ji ( · ) < 0 and dj ( · )/di = ji ( · ) > 0. Under this framework, because a rise in the export (import) share in a sector reduces the export (import) share in another sector by  the same degree, it is established that ii ( · ) = −ji ( · ) =  > 0 and −ii ( · ) = ji ( · ) =  > 0. By taking these conditions into consideration and totally differentiating Yˆ D and  i with respect to eq. (26), I get Yˆ D 1  dYˆ D = [−i ( · )(1 − Ai ) + i ( · )Bi ] + [ {(ˆpi + xˆ i ) di ˆ i ) − (ˆpFj + m ˆ j )}], − (ˆpj + xˆ j )} −  {(ˆpFi + m

(54)

ˆ for i and j follow Eqs. (4) and where the dynamics of pˆ + xˆ and pˆ F + m (6), respectively. These growth rates are supposed to be positive.

44

H. Nishi / Structural Change and Economic Dynamics 39 (2016) 31–45

The temporal impact of a rise in the Verdoorn coefficient and specialization on economic growth is ambiguous. An increase in the coefficient in sector i leads to an increase in productivity, which amplifies its growth of exports and imports. This is what the first term in Eq. (54) indicates, and its effects are explained in the same manner as in Eq. (43). In addition, an increase in the coefficient also causes specialization in sector i. In the process of specialization, this increases the share of exports in sector i, while reducing that in sector j. On the contrary, it decreases the share of imports in sector i, while increasing that in sector j; the terms in the second parenthesis in Eq. (54) indicate these contributions. By way of these dual routes, the trade balance at the macroeconomic level is determined, which is somewhat complicated. When the export growth of sector i is larger than that of sector j and the import growth of sector j is larger than that of sector i, the trade balance is more likely to be positive, and economic growth thus occurs. Such a case is more likely under the process of specialization for sector i. On the contrary, when the export growth of sector j is larger than that of sector i and the import growth of sector i is larger than that of sector j, the trade balance is more likely to be negative, and thus growth is restrained. Hence, the dynamics of change in the Verdoorn coefficient and specialization create possibilities for both the improvement and the deterioration of the trade balance and economic growth. However, in an extreme case, when the economy is fully specialized in sector i, I get the relatively simple result that the economic growth rate of the home country only depends on the degree of competition in the corresponding sector. Let me next consider the case in which such a process continues until the economy is fully specialized. When sector i is fully specialized, a rise in the Verdoorn coefficient no longer induces a change in the share of exports and imports. Therefore, ii ( · ) = ij ( · ) = 0 and ii ( · ) = ij ( · ) = 0 hold. This is because once fully specialized, all further changes in the Verdoorn coefficient on the structure of trade are neutralized. In addition, under full specialization, exports are realized by only sector i, and that sector does not import. Therefore, i (·) =1 and i (·) =0 also hold. In this case, Eq. (54), which captures the impact of the Verdoorn coefficient on economic growth, is rewritten as follows: dYˆ D 1 = − (1 − Ai )Yˆ D , di

(55)

which can be either positive or negative. As explained in the body of the paper, 1 − Ai includes the degree of competition, weighted by the price elasticity of demand for exports, which may be both positive and negative with Ai > 0. These two scenarios can be explained as follows. The first is a positive case. An increase in the coefficient in sector i leads to an increase in productivity, which decreases relative prices and thus improves price competitiveness in the home country, stimulating export growth. If this impact on the fall in the export price (1 −  i ) is smaller than the rise in export growth (εFi i ), nominal export growth increases (i.e., 1 − Ai < 0). Higher economic growth is then realized to maintain the balance-of-payments constraint. The second case is a negative one. An increase in the coefficient in sector i leads to a rise in productivity, which decreases relative prices and thus improves price competitiveness in the home country, stimulating export growth. If this impact on the fall in the export price is larger than the rise in export growth, nominal export growth decreases (i.e., 1 − Ai > 0). Lower economic growth is then realized to maintain the balance-of-payments constraint. In both cases, once the economy is fully specialized in sector i, the rise in the Verdoorn coefficient can only reinforce competitiveness in this sector, staying fully specialized. The improvement in

competitiveness then stimulates export growth. Nevertheless, the difference in economic growth results from its relative impact on the export price and export growth.

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