A multi-sectoral approach to the Harrod foreign trade multiplier

Trigg, Andrew B.; Araujo, Ricardo Azevedo Article A multi-sectoral approach to the Harrod foreign trade multiplier European Journal of Economics and Economic Policies: Intervention (EJEEP) Provided in Cooperation with: Edward Elgar Publishing Suggested Citation: Trigg, Andrew B.; Araujo, Ricardo Azevedo (2018) : A multi-sectoral approach to the Harrod foreign trade multiplier, European Journal of Economics and Economic Policies: Intervention (EJEEP), ISSN 2052-7772, Edward Elgar Publishing, Cheltenham, Vol. 15, Iss. 1, pp. 91-104, https://doi.org/10.4337/ejeep.2017.0024 This Version is available at: https://hdl.handle.net/10419/277407 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. 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Trigg* Department of Economics, The Open University, Milton Keynes, UK Ricardo Azevedo Araujo** Department of Economics, University of Brasilia, Brazil With this inquiry, we seek to develop a multi-sectoral version of the static Harrod foreign trade multiplier, by showing that it can be derived from an extended version of the Pasinettian model of structural change and international trade. This new version highlights the connections between the balance of payments and levels of employment and production. It is also shown that from this disaggregated version of the Harrod foreign trade multiplier we can derive an aggregate version of the multiplier. By following this approach we go a step further in establishing the connections between the structural economic dynamic and the balance-of-payments-constrained-growth approaches. Keywords: structural economic dynamics, foreign trade multiplier, balance-of-paymentsconstrained growth JEL codes: O19, F12 1 INTRODUCTION ‘The causes which determine the economic progress of nations belong to the study of international trade …’Alfred Marshall, Principles of Economics, Book Four (1890) This paper deals with the relationship between income determination and balance-ofpayments equilibrium in a structural economic dynamic –SED hereafter –setting. In particular, the paper delivers a multi-sectoral version of the static Harrod foreign trade multiplier (Harrod 1933) by showing that it can be derived from an extended version of the Pasinettian model (Pasinetti 1993) that takes into account foreign trade (Araujo/ Teixeira 2004). Besides, in order to prove the consistency of our approach, we also show that by departing from the multi-sectoral Harrod foreign trade multiplier we can obtain the aggregate version, with an emphasis on the role played by economic structures in determining output performance. The disaggregated version of the multiplier is then shown to keep the original flavour of the aggregate version since it predicts that the output * Email: [email protected]. ** Email: [email protected]. Ricardo Araujo wishes to express thanks for financial support from the Brazilian Council of Science (CNPq). A preliminary version of this paper was presented to the 19th FMM Conference of the Research Network Macroeconomics in Berlin, 2015. We would like to thank, without implication for any remaining errors, two anonymous referees for helpful comments. Received 27 January 2015, accepted 13 October 2016 European Journal of Economics and Economic Policies: Intervention, Vol. 15 No. 1, 2018, pp. 91–104 First published online: March 2017; doi: 10.4337/ejeep.2017.0024 © 2018 The Author Journal compilation © 2018 Edward Elgar Publishing Ltd The Lypiatts, 15 Lansdown Road, Cheltenham, Glos GL50 2JA, UK and The William Pratt House, 9 Dewey Court, Northampton MA 01060-3815, USA of each sector is strongly affected by its export ability, which highlights that the validity of Harrod’s original insight is not restricted to the aggregate level. The SED framework is adopted as the starting point for our analysis. Initially, this model was conceived for studying the interactions between growth and structural change in a closed economy 1 (see Pasinetti 1981; 1993). However, more recently it was formally extended to take into account international flows of goods (see Araujo/Teixeira 2004), and a balance-of-payments-constrained growth rate was derived in this set-up under the rubric of the multi-sectoral version of Thirlwall’s law (see Araujo/Lima 2007). Such extensions have proven that the insights provided by Pasinettian analysis remain valid for the case of an open economy: the interaction between tastes and technical change is responsible for variations in the structure of the economy, which in turn affect the overall growth performance. This view is also implicit in the balance-of-payments-constrained-growth –BPCG hereafter –approach, to the extent that variations in the composition of exports and imports lead to changes in the structure of the economy and determine the output growth consistent with balance-of-payments equilibrium (see Thirlwall 2013). By assuming that the real exchange rate is constant and that trade must be balanced in the long run, the BPCG approach asserts that there is a very close correspondence between the growth rate of output and the ratio of the growth of exports to the income elasticity of demand for imports. Indeed, this result is the prediction of a dynamic version of the Harrod (1933) trade multiplier known as Thirlwall’s law (see Thirlwall 1979). It can also be argued that the particular dynamics due to the interaction of technical change and patterns of demand are taken into account in the BPCG approach, since observed differences in the income elasticities of demand for exports and imports reflect the non-price characteristics of goods and, therefore, the structure of production (Thirlwall 1997: 383). But in fact, by using the aggregate Keynesian model as its starting point, the literature on both the static and dynamic Harrod foreign trade multiplier is advanced in terms of an aggregate economy, in which it is not possible to fully consider particular patterns of demand and productivity for different goods. Harrod (1933) considered an open economy with neither saving and investment nor government spending and taxation. In this set-up, income, Y, is generated by the production of consumption goods, C, and exports, X, namely: Y¼CþX. It is assumed that all income is spent on consumption goods and imports ðMÞ,suchthatY¼CþM. The real terms of trade are constant and balanced trade is assumed: X¼M. If we assume a linear import function such as M¼mY , where mis the marginal propensity to import, after some algebraic manipulation this yields: Y¼1 mX:(1) Expression (1) is known as the static Harrod foreign trade multiplier, 2 under which the main constraint on income determination is the level of export demand in relation to the 1. The Pasinettian model presents both a static and dynamic multi-sectoral analysis, a characteristic that contrasts with other multi-sectoral models such as input–output analysis, which is predominantly static in approach. 2. The dynamic Harrod foreign trade multiplier is connected to the Hicks supermultiplier. While the former considers just the impact of the growth rate of exports on the growth rate of output, the latter also takes into account the feedbacks that a higher growth rate of exports has on other components of autonomous expenditure. According to McCombie (1985: 63), ‘an increase in exports will allow other autonomous expenditures to be increased until income has risen by enough to induce an increase in imports equivalent to the initial increase in exports’. 92 European Journal of Economics and Economic Policies: Intervention, Vol. 15 No. 1 © 2018 The Author Journal compilation © 2018 Edward Elgar Publishing Ltd propensity to import. McCombie/Thirlwall (1994: 237) claim that ‘Harrod put forward the idea that the pace and rhythm of industrial growth in open economies were to be explained by the principle of the foreign trade multiplier which at the same time provided a mechanism for keeping the balance-of-payments in equilibrium’. Any change in Xbrings the balance of trade back into equilibrium through changes in income and not in relative prices. According to that view, the Harrod foreign trade multiplier is an alternative to the Keynesian determination of income through the investment multiplier. The subsequent development of Harrod’s analysis has been to study the growth implications of his model; but, as pointed out by Thirlwall (2013: 83), Harrod himself never managed to accomplish such a task. This has been carried out by a number of authors who built on the insights of Kaldor (1966) as a starting point (see for example Thirlwall 1979; McCombie 1985; Setterfield 2010). Probably the main outcome of this strand has been developed in terms of a dynamic version of the Harrod foreign trade multiplier that became known in the literature as Thirlwall’s law (McCombie/Thirlwall 2004). According to this view, the Harrod multiplier was turned into a theory of BPCG, in which the growth process is demand-led rather than supply-constrained. Assuming constant real exchange rates and that trade must balance in the long run, there is a very close correspondence between the growth rate of output and the ratio of the growth of exports to the income elasticity of demand for imports, namely π: ΔY Y¼1 π ΔX X:(2) According to this expression, which derives from (1), the growth rate of output, ΔY Y,is related to the growth rate of exports, ΔX X, by the inverse of the propensity to import, represented by m. Thus in a balanced trade framework with the real terms of trade constant, countries are constrained to grow at this rate, which in its continuous time version became widely known as Thirlwall’s law. 3 According to this view the balance-of-payments position of a country is the main constraint on the overall growth rate, since it imposes a limit on demand to which supply can (usually) adapt. As it turns out, observed differences in growth performance between countries are associated with particular elasticities of demand for exports and imports. In this context, structural change features as one of the sources of change in the elasticity of income for exports and imports, with such elasticities being seen as the weighted average of sectoral elasticities. In such a view, structural change due to variations in the shareofexports/importsmaygiverisetochanges in aggregate elasticities. Arguably, a country whose structure is concentrated on sectors that produce raw materials, for instance, will have a lower income elasticity of demand for exports than a country specializing in the production of sophisticated goods. From this perspective we may conclude that the policy implications of the SED and the BPCG approaches are similar: underdeveloped countries should pursue structural changes in order to produce and export goods with a higher income elasticity of demand (see Thirlwall 2013). Previous attempts to establish connections between these two strands have proven fruitful. Results such as the multi-sectoral version of Thirlwall’s law (Araujo/Lima 2007) and the disaggregated version of the cumulative model (Araujo 2013 and Araujo/Trigg 2015) have shown that demand, captured mainly by income elasticities, can play a central role in determining growth rates even in the long run. These developments have shown 3. Note, however, that according to McCombie (1985: 71) the conciliation between Thirlwall’s law and the dynamic foreign trade multiplier is not so straightforward since the former is based on a multiplicative import function while the latter is based on a linear import function. A multi-sectoral approach to the Harrod foreign trade multiplier 93 © 2018 The Author Journal compilation © 2018 Edward Elgar Publishing Ltd that disaggregated assessments of well-established results in that literature can give rise to new insights (see Pasinetti 2005). Kaldor himself abandoned the aggregate view in search of a sectoral and regional approach that would emphasize divergence of growth rates, dynamic returns of scale, cumulative causation and path dependence in economic development (see for example Hein 2014). Taking a disaggregated approach led him to conclude that the manufacturing sector plays a key role in establishing the pace of economic growth due to its positive effects on overall labour productivity growth. Such effects are related to the existence of significant forward and backward linkages in the production chain of the manufacturing sector, whereby a productivity gain in one industry may be spread to others due to such linkages. Following such developments, the so-called ‘Kaldor growth laws’(Kaldor 1966 and Thirlwall 1987) convey a strong sectoral flavour in so far as the manufacturing sector is seen as the ‘engine of growth’. In such a view the process of economic development is conceived not only as economic growth but also as a type of structural change in which the transfer of labour from low to high productivity sectors plays an important role in determining overall productivity. However, despite the importance given by Kaldor to a disaggregated analysis, the formal model employed to support his verbal reasoning (see Dixon/Thirlwall 1975 and Thirlwall 1997) is built in terms of an aggregate economy. And the main component of this model is a dynamic version of the Harrod foreign trade multiplier, as derived in Araujo/Trigg (2015). This provides a basis for the analysis here, following the Kaldorian view that output and output growth are determined by external constraints, considering the driving force of growth as demand rather than supply, thereby disregarding other constraints such as saving and capital capacity. 4 In order to carry out the present analysis we have adopted a procedure analogous to the one advanced by Trigg/Lee (2005) and extended by Araujo/Trigg (2015) to consider international trade. The former work explores the relationship between the Keynesian multiplier and Pasinetti’s model of pure production in a closed economy, by showing that it is indeed possible to derive a simple multiplier relationship from multi-sectoral foundations in a closed version of the Pasinetti model; hence a scalar multiplier can legitimately be applied to a multi-sector economy. By departing from this result, Araujo/Trigg (ibid.) have derived an initial formulation of the multi-sectoral disaggregated Harrod foreign trade multiplier. Here we go a step further by showing through aggregation the consistency of such a formulation with the original Harrod foreign trade multiplier. A direct mathematical translation is provided between these multi-sectoral and aggregate Harrod systems. Such a formulation requires the introduction of the price system: a task not performed by Araujo/Trigg (ibid.). Following this approach, we show, for instance, that the equilibrium Pasinettian solution for the system of physical quantities may be obtained as a particular case of the solution given by the multi-sectoral Harrod foreign trade multiplier, derived here when the condition of trade balance is satisfied. With this analysis, we intend 4. Thirlwall (2012: 22) acknowledges that ‘growth may be constrained either by domestic saving or by foreign exchange, and that the role of foreign borrowing in the development process is to relieve whichever is the dominant constraint. Chenery’s view, like that of Prebisch, was that for most developing countries, at least in the intermediate stage of economic development, the dominant constraint is likely to be a shortage of foreign exchange associated with balance of payments deficits, so that growth would be balance-of-payments constrained’. But even by recognizing that there may be other constraints to the growth process, the message of the BPCG model remains; namely, it is not possible for a country to grow consistently at a rate much different from that which allows equilibrium in the balance of payments. 94 European Journal of Economics and Economic Policies: Intervention, Vol. 15 No. 1 © 2018 The Author Journal compilation © 2018 Edward Elgar Publishing Ltd to emphasize the view that in the presence of a favourable economic structure a country’s aggregate output level may be improved by relaxing the balance-of-payments constraint. The paper is structured as follows. In Section 2, we present an extended version of the multi-sectoral Pasinettian model of international trade, followed in Section 3 by a consideration of the multi-sectoral Harrod multiplier. Section 4 shows how the original scalar Harrod multiplier can be derived from these multi-sectoral foundations, exploring how this relates to the Harrod matrix multiplier. In Section 5 some conclusions are provided. 2 SYSTEMS OF PHYSICAL AND MONETARY QUANTITIES IN AN EXTENDED VERSION OF THE PASINETTIAN MODEL TO INTERNATIONAL TRADE The SED and the BPCG approaches embody a shared view that demand plays an important role in the growth process, but with different degrees of emphasis. While the SED framework focuses on structural changes accruing from the existence of particular growth rates of demand and technical change for each sector, the BPCG literature considers that elasticities of demand for exports and imports are responsible for explaining particular growth experiences (see Thirlwall 2012). A common feature of both approaches is that the notion of equilibrium plays a central role. While in the BPCG approach equilibrium in the balance-of-payments is a required condition of sustainability in the long run, the SED approach shows that the most probable macroeconomic consequence of the growth process is disequilibria, which translate into structural unemployment. But it is undeniable that even in the SED approach equilibrium in the balance of payments should be observed in the long run. The direct consequence of this characteristic is that the evolving patterns of technical change and preferences cannot be exogenous but will be subject to an external constraint, as highlighted in the BPCG approach. An important feature of the SED approach is that it can establish normative conditions for full employment of the labour force and conditions for equilibrium in the balance of payments, although it is straightforward to prove that the former will not generally be satisfied. To formally consider these insights, a starting point is the extended version of the pure labour Pasinettian model of foreign trade as advanced by Araujo/Teixeira (2004). Demand and productivity vary over time at a particular rate in each sector of two countries; the advanced country is denoted by Aand the underdeveloped country by U. Assume also that both countries produce n–1 consumption goods, but with different patterns of production and consumption. In order to establish the basic notation, it is useful to choose one of the countries, let us say U, to express physical and monetary flows. The system of physical quantities may be expressed as: I−ðcþξceÞ −a1 X Xn ¼0 0 2 6 43 7 5; 3 7 5 2 6 4 3 7 5 2 6 4(3) where Iis an (n–1) × (n–1) identity matrix, 0is an (n−1) null vector, X¼ X1 ⋮ Xn−1 2 6 43 7 5is the (n–1) column vector of physical quantities, c¼ a1n ⋮ an−1;n 2 6 43 7 5is the (n–1) column A multi-sectoral approach to the Harrod foreign trade multiplier 95 © 2018 The Author Journal compilation © 2018 Edward Elgar Publishing Ltd vector of consumption coefficients, ce¼ ae 1n ⋮ ae n−1;n 2 6 6 43 7 7 5 refers to the (n–1) column vector of foreign demand coefficients, and a¼½an1⋯an;n−1is the (n–1) row vector of labour coefficients. Xndenotes the quantity of labour in all internal production activities. The household sector in country Ais denoted by ^nand the population sizes in both countries are related by the coefficient of proportionality ξ. According to Pasinetti (1993), system (3) is a homogenous and linear system; hence a necessary condition to ensure non-trivial solutions of the system for physical quantities is det I−ðcþξceÞ −a1 "# ¼0:(4) Condition (4) may be equivalently written (see Araujo/Teixeira 2004) as: aðcþξceÞ¼1:(40) If condition (4′) is fulfilled then there exists a solution for the system of physical quantities in terms of an exogenous variable, namely Xn. In this case, the solution of the system for physical quantities may be expressed as: X Xn "# ¼ðcþξceÞXn Xn "# :(5) From the first n–1 lines of (5), we conclude that in equilibrium the physical quantity of each tradable commodity to be produced in country U, that is, Xi,i¼1; ::: ; n−1, will be determined by the sum of the internal and foreign demand, namely ainXnand ξae inXn respectively. The last line of (5) shows that the labour force is fully employed. It is important to emphasize that solution (5) holds only if condition (4′) is fulfilled. If (4′) does not hold, then the non-trivial solution of physical quantities cannot be given by expression (5). The economy depicted by system (3) may also be represented by a system of monetary quantities, where total wages are spent on domestic consumption goods (represented by domestic coefficients, c) and imports of foreign goods (represented by import coefficients, cm). The monetary system may be written as: pw½ I−ðcþcmÞ −a1 "# ¼½00;(6) where p¼p1⋯pn−1 ½is the (n–1) row vector of money prices, cm¼ am 1n ⋮ am n−1;n 2 6 6 43 7 7 5 is the (n–1) column vector of consumption import coefficients, and wis the uniform wage. Like system (3), system (6) is also a homogenous and linear system; hence a necessary condition to ensure non-trivial solutions for prices should be observed, that is: det I−ðcþcmÞ −a1 "# ¼0:(7) 96 European Journal of Economics and Economic Policies: Intervention, Vol. 15 No. 1 © 2018 The Author Journal compilation © 2018 Edward Elgar Publishing Ltd Condition (7) may be equivalently written (see Araujo/Teixeira 2004) as: aðcþcmÞ¼1:(70) If condition (7′) is fulfilled then there exists a solution for the system of monetary quantities in terms of an exogenous variable, namely w. In this case, the solution of the system for monetary quantities may be expressed as: pw½¼aww½:(8) From the first n–1 lines of (8), we conclude that in equilibrium the price of each tradable commodity is given by the amount of labour employed in its production, that is, pi¼ainw,i¼1; ::: ; n−1. If expressions (5) and (8) hold simultaneously, it is possible to show after some algebraic manipulation that they express a new condition, which can be viewed as embodying a notion of equilibrium in the balance of trade. If aðcþξceÞ¼1 and aðcþcmÞ¼1, then by equalizing the left-hand side of both expressions we obtain: aðξce−cmÞ¼0:(9) The fulfilment of conditions (4′)and(7′) implies equilibrium in the trade balance but the reverse is not true. Note for instance that if aðcþξceÞ¼0:9 and aðcþcmÞ¼0:9, the trade balance condition will also be fulfilled by equalizing the right-hand side of both expressions, but this situation corresponds to unemployment and underexpenditure of national income. That is, the trade balance equilibrium implies neither full employment of the labour force nor full expenditure of national income. This possibility has been somewhat emphasized by the BPCG approach. The idea is that the full expenditure of national income in a context of balance-of-payments equilibrium means that even if such income is spent abroad as imports, such expenditure will be compensated in terms of exports, leading to equilibrium in the labour market. According to our alternative rationale, however, based on (9), a trade deficit may lead to a level of employment different from full employment equilibrium. According to this view, the main constraint on the performance of a country is related to the balance of payments, which must be balanced in the long run. In this set-up a poor export performance may lead to low levels of employment and national output, thus showing that the external constraint may be more relevant than shortages in saving and investment, for developing countries in particular. In this context, the Harrod foreign trade multiplier plays a decisive role since it changes the focus of determination of national income from investment to exports. From the first line of expression (8), we know that p¼aw.Hence by assuming a wage unit, namely w¼1, money prices are equal to labour coefficients, and the equilibrium in the trade balance may be rewritten as: pðξce−cmÞ¼0:(90) In the next section, a disaggregated version of the Harrod foreign trade multiplier is derived from the system of physical quantities. The system of monetary quantities will be employed in order to arrive at the aggregate version of the static Harrod foreign trade multiplier. 3 DERIVATION OF THE MULTI-SECTORAL STATIC HARROD FOREIGN TRADE MULTIPLIER The idea of developing a multi-sectoral version of the Keynesian multiplier dates back to derivations by Goodwin (1949) and Miyazawa (1960) of a disaggregated version of the income A multi-sectoral approach to the Harrod foreign trade multiplier 97 © 2018 The Author Journal compilation © 2018 Edward Elgar Publishing Ltd multiplier in Leontief’s framework, from a relatively simple Keynesian structure. Both authors emphasized that although there are important differences between the Keynes and Leontief approaches, a bridge between them –namely a disaggregated version of the multiplier –could provide a potentially important development for the literature. In order to derive a multi-sectoral version of the Harrod foreign trade multiplier, let us adopt a procedure similar to the one advanced by Trigg/Lee (2005) and extended by Araujo/Trigg (2015). Dealing with the original Pasinettian model, Trigg/Lee (2005) had to assume that investment in the current period becomes new capital inputs in the next period and that the rate of depreciation is 100 per cent (that is, all capital is circulating capital) in order to derive the Keynesian multiplier. By considering an economy extended to foreign trade, however, we do not need this hypothesis. Let us rewrite the system of physical quantities in (3) as: I−c −a1 "# X Xn "# ¼E 0 "# :(30) Note that the difference between expression (3) and (3′) is that in the latter we isolate the vector of sectoral exports E¼ξXnceon the right-hand side. We may rewrite system (3′)as: X−cXn¼E −aX þXn¼0: ((10) From the last line of system (10), it follows that: Xn¼aX:(11) Note that the employment level, Xn, is now not exogenous as in (5) since we are solving the system by considering the possibility of unemployment. That was not admissible for the solution of (5) since, there, the existence of full employment is a necessary condition for the existence of non-trivial solutions. Pre-multiplying throughout the first line of (10) by aand using (11) yields aX ¼acaX þaE. By isolating aX, we obtain the employment multiplier relationship: aX ¼1 1−ac aE;(12) where 1=1−ac is a scalar employment multiplier (Trigg/Lee 2005). This is an employment multiplier relationship between the employment level aX and the total labour embodied in exports aE, where the scalar employment multiplier is 1=1−ac. Here we can dispense with the assumption of circulating capital in a pure labour economy by Trigg/ Lee (ibid.) because we have an exogenous variable, namely aE, that can be isolated in theincome=aggregatedemandequationthatgivesrisetothemultiplier.Since E¼ξXnce, expression (12) may be rewritten as: aX ¼ξace 1−ac Xn:(120) From expression (7′), 1 −ac ¼acm. It is worth remembering that implicit in this expression is the notion of full expenditure of national income. By substituting this result into expression (12′), it can be re-expressed as aX ¼ξace acmXn:(1200) 98 European Journal of Economics and Economic Policies: Intervention, Vol. 15 No. 1 © 2018 The Author Journal compilation © 2018 Edward Elgar Publishing Ltd