ECON

Comparative Advantages and Demand in the New Competitive Ricardian Models

Carlos A. Cinquetti1

Abstract We survey the new Ricardian models of bilateral trade, which are seen as trac- table structure for multi-country trade models addressing either cost or demand linkages to trade. Cost-based Ricardian models advance new forms of compara- tive advantages that are irrespective of autarky price and, in some cases, even of opportunity cost. A less noticed feature is their reliance in demand function that does not disturb cost-based prices. Demand-based Ricardian models hinge especially on non-homothetic preferences for asymmetric goods and the supply- side ordering of goods mirrors the demand-side ordering. We also critically discuss extensions of these latter competitive models to trade in quality. We fur- ther seek to identify all these models vis-à-vis the Ricardo–Haberler–Deardorff tradition.

JEL: F10, 019, D5

Keywords Ricardian models, multi-country economies, comparative advantages, demand, trade cost, non-homothetic preferences

Introduction

The newest multi-good, multi-country trade models promoted a revival of the competitive Ricardian trade models. The latter introduced some radical novelties such as comparative advantages hinging neither on opportunity cost, nor on

Foreign Trade Review 53(1) 29–48

2018 Indian Institute of Foreign Trade

SAGE Publications sagepub.in/home.nav

DOI: 10.1177/0015732516681884 http://ftr.sagepub.com

Corresponding author: Carlos A. Cinquetti, Economics Department, São Paulo State University, Rod. Araraquara-Jaú, Km 01 Araraquara, SP 14800-901 Brazil. E-mail: [email protected]

1 Economics Department, São Paulo State University, Rod. Araraquara-Jaú, SP, Brazil.

Article

30 Foreign Trade Review 53(1)

autarky prices and, at the other extreme, comparative advantages are not even central. As a result, a puzzling question that follows is how can these models be defined as Ricardian.

The first thing to bear in mind, when thinking about this question, is the con- cern with treatable general equilibrium in trade models, which traditionally involved focusing on the supply side of that equilibrium (see Caron, Fally, & Markusen, 2014). Stronger reasons for simplification arise in multi-good, multi- country models, which led to the Ricardian technology. However, the classical pairwise Ricardian comparative advantages of Dornbusch, Fischer and Samuelson (1977, DFS hereinafter) does not fit to such a world economy. The paradigmatic solution by Eaton and Kortum (2002, EK hereinafter) is a cost–insurance–freight (CIF) price comparative advantage that orders exporters’ share within each importing market with the help of a cumulative (Fréchet) probability distribution, in which a worldwide parameter of technology variation shapes the cost linkage to trade. To reintroduce industries, which are only subsumed in EK, Costinot, Donaldson and Komunjer (2011) advance a bilateral trade model at industry level, which yields a new index of revealed comparative advantages. Instead, Shikher (2012) expands EK by introducing industries through intermediate goods. The resulting new cost function, which accounts for the input–output linkages, enables screening the impact of trade upon each industry in each country.

Previously some clues have been given as to how these models succeed in achieving a treatable equilibrium in a multi-country trading economy with inter- national technology differences. Another important side for accomplishing it is a device introduced by DFS: a form of demand that is neutral as to the ordering of cost-based prices. As shown below, demand has a peculiar role upon prices even in the two-country Ricardian model.

Another strand of Ricardian model focuses on demand linkages to trade. An early reference is the widely ignored three-sector model developed by Jones (1979, Chapter 17)1—a reverse DFS model—whose two relative prices enable several variations with regard to how (international) demand conditions trade gains. In multi-good economies, the demand elasticities for goods are reduced to the income and the own-price elasticity of demand (Wilson, 1980), which paves the way to North–South trade models with non-homothetic preferences. An early development by Flam and Helpman (1987) seeks to advance over models of hori- zontal differentiation (Helpman & Krugman, 1985) by addressing vertical differ- entiation, whereas later developments by Matsuyama (2001) seek to frame this trade in product quality into multi-good economies. Extensions of these model- ling of trade in quality to multi-country economies (Fieler, 2011b; Jaimovich & Merella, 2015) have not attracted equal attention for reasons we discuss below. Contrariwise, taking good asymmetry irrespective to quality, Fieler (2011a) obtains a EK’s model with a North–South flavour. That is, she simply considers group of goods with specific income elasticity of demand which, together with a certain supply-side characteristic, conditions not only the North–South trade but also the North–North and the South–South trade as well.

The challenge to attain a tractable equilibrium of prices and trade prices and trade directions is another one in these Ricardian models focusing on demand

Cinquetti 31

linkages to trade as well. For instance, in Jones’s (1979) three-sector model of demand linkages to trade, it suffices the simple Ricardian technology, whereas the multi-good, multi-country models further resort to a supply-side ordering of goods that mirrors their demand ordering.

In this survey of the new Ricardian models, we first show that they are the structure of multi-country trade models addressing either cost or demand linkages to trade. In other words, they can no longer be seen as the models of comparative advantages. Second, we try to mathematically pin point each model’s main con- tribution. Our third goal is to simultaneously define these new models with respect to the Ricardo–Harberler–Deardorff (RHD) tradition of comparative advantages. We focus on theory and do our best to do so in a Ricardian (didactical) sense.

The remainder of this article proceeds as follows. The next section emphasizes the role of demand in the textbook Ricardian 2-good model and introduces the RHD theorem. Section ‘Ricardian Models with Neutral Demand’ addresses the new cost-based Ricardian models, while Section ‘Ricardian Models with Non- neutral Demand’ addresses the new demand-based Ricardian models. The last section presents our concluding remarks.

The Ricardo–Harberler–Deardorff Tradition

Although Ricardo’s (1817) analysis of international trade features three eco- nomic agents (capitalists, workers and landlords) and a corresponding political economy,2 he considers only labour (workers) when formulating comparative advantages. His central development with regard to Smith (1776) lies in taking price as a relative value as an anticipation of late general equilibrium analyses (Pareto, 1909).

This means that in a 2-good, 2-country world economy, the home country can have absolute advantages in both sectors, ai < ai

* and ai׳ < ai׳ *, but price (compara-

tive) advantages in just one:

p p

a a

a a

p p

i

i

i

i

i

i

i

i

  ′ ′ ′

 *

*

*

* ,

(1)

where a represents the labour-input coefficient and superscript * represents the foreign country. This basis of trade in Equation (1)—comparative advantages—is thus grounded on the difference of autarky prices, pA ≠ p*A. And, as perceived by Ricardo (1817), international prices deviate from the autarky prices and so from labour costs.3

Gottfried von Harberler (1930, as cited in Caves, 1967) casts Equation (1) into opportunity cost, thus building a bridge to general equilibrium analyses. However, it is frequently overlooked that demand has no impact on relative prices in such a competitive 1-factor economy without joint production—that is—the non-substi- tution theorem (Kurz & Salvadori, 1995). As shown in Figure (1), preferences can change the allocative position of the autarky equilibrium, xA, but not the equilib- rium price, which is given by the production possibility frontier.

32 Foreign Trade Review 53(1)

Nevertheless, preferences can affect price in an international economy. As shown in Figure 1, given convex preferences, aggregate excess of demand sets interna- tional prices p ≥ pA that solve the trade-balance equilibrium, px = p(xc – xp), with a corner equilibrium of full specialization at xp, and the consumer’s allocation at xc. Thus, the international economy overcomes the non-substitution theorem and demand gains a role upon prices. Thus, the textbook Ricardian model is established.

An ultimate step towards generalization of comparative advantages is Deardorff (1980), who starts the analysis from the efficiency of the international equilibrium

pAx > px, (2)

insofar as px is less costly. Rearranging Equation (2), one obtains

(pA – p) x (p) > 0, (3)

meaning that imported goods (i.e., positive excess of demand) are those whose autarky prices are above their trade prices, and exported goods are those whose autarky prices are lower than their trade price. Equation (3) is called the general law of comparative advantages in that market prices are compatible with any technology, and the inner (vector) product of Equation (3) predicts a trade pattern in goods in general, on average, not in each specific good. For a N-good economy with trade barriers and intermediate goods, the trade linkages from comparative costs become weaker (Deardorff, 1979).

As shown below, the general law and the RHD tradition (Bernhofen, 2005) help us in understanding the novelties of the new Ricardian models.

x c

xA

x p

x 1

Figure 1. Autarky and Trade Equilibrium

Source: Authors’ own.

Cinquetti 33

Ricardian Models with Neutral Demand

Autarky price is an unappealing empirical aspect of comparative advantages.4 In the Ricardian Equation (1), pA can be transformed into actual prices as a a

p w w

a a

i

i

i

i

*

*

*

*> = > ′

′

. With N-ordered industries

a a

a a

w w a a

a a

i

i

i

i

n

n

1

1

1

1

* * *

* *

... / ... .> > > = > > >+ +

ω

(4)

International specialization is thus determined by productivity and labour prices, with goods prices given by pi ≤ w

cai c, with equality if good i is produced by coun-

try c = j. Noticing that comparative cost advantages in Equation (4) only apply to a competitive 1-factor economy.

The strong linkage of comparative advantages implied by the inequalities in Equation (4) is overcome in multi-country models, as well as in those following the RHD theorem.

The Dornbusch–Fischer–Samuelson Model

Exogenous technology is a useful assumption in some analyses, although rejected by the evidence (Davis, Weinstein, Bradford, & Shimpo, 1997).5 However, in a general demand form, any change in costs in Equation (4) can lead to multiple prices.

The DFS model solves this N-good conundrum with a classical-like demand, defined by expenditure shares, bi(pi) = pici(pi)/Y, and based on a Cobb–Douglas utility function. Thus, each bi is constant. Goods become net complements, which warrant a definite and invariable relationship between the demand for goods and the demand for labour. Goods are also set into a continuum unit interval, x~ = [0,1], which not only enables first-order effects but also nearly nullifies the bi, which helps to attenuate the disputable economy in which all goods are net complements.

The point is that this neutral demand with respect to cost-based price ordering in Equation (4), warrants a simple and definite derived demand for labour. More to the point, a given equilibrium wage, , determines the set of home- and for-

eign-produced goods, k b x dx k x

=∫ ( ) ( )

 



0 and 1

1 − =∫k b x dx

k x ( )

( )  



, which, under

trade balance, is the same as the share of these economies in the world’s expendi- ture (wL + w*L*), where L and L* are the labour forces of home and foreign, respectively. The relative derived demand for labour is then given by

ω=

− =



 



 

k x k x L L

B x L L

( ) ( ) . /

; .* *







1 1

(5)

34 Foreign Trade Review 53(1)

In a continuum of goods, Equation (4) can be written as ω= =A x a x a x

( ) ( ) ( )

*







. The international (home-relative) supply function of x~ is then

x A= , −1( )ω

(6)

which gives the labour-minimizing cost of supplying z worldwide. Notice that the supply schedule A–1(ω) is downward sloping, whereas the demand schedule B x LL( );

∗ is upward sloping. Most unusual, however, is the 1-factor general equilibrium, in which  deter-

mines the specialization set at home and abroad and therefore which technology is active. The international economy, which overcomes the non-substitution theo- rem in the 2-goods economy, is fundamental here: it grants the market selection of the technologies.

The DFS gives a very straightforward view—especially in a graphical analy- sis—of comparative advantages as a relationship between the factor market and the good market, in which  sets k(x) for given absolute advantages. For instance, a homogeneous technology change at home shifts A–1() upward, but  increases along the upward sloping B x LL( );

∗ schedule grants that ∆ < ∆A–1(). Acemoglu and Ventura (2002) develop over this result, emphasizing that economic growth with interdependence produces diminishing returns to scale even with constant return-to-scale technologies, since international demand for goods pushes down the exporting country’s ‘factoral terms of trade,’  = ∑(pi / pi

*).(ai * / ai). There were

indeed several developments of the DFS in the trade and growth literature.

Geography and Trade

With iceberg trade cost, t > 1, comes non-traded goods, giving more flavour to a trade model hinging on net complements. With I ≥ 3 countries, not only the law of one price underlying Equation (4) falls apart, but also the bilateral trade volume becomes a central issue. Most importantly, within this new geographical setting, the pairwise sequence, ′ =A x A xt( )

( ) over the N goods collapses. Wilson (1980) solves this latter problem by reducing the trade relationship to

the fraction of goods, k, that each country d demands from any country o, as given by

pd(k) = min{pod(k); o = 1,...O}. (7)

This pricing equation definitely implies a CIF price model of comparative advantages.

EK develop it into a country-level model of bilateral-trade. The CIF prices on d is then

p k

c z k

tod o

o od( ) ( )

= ,

(8)

Cinquetti 35

where co is the input cost in country o, tod is a vector of physical and cultural bar- riers, and zo(k) is the randomly drawn technology efficiency of o in the world economy, which determines k, the extensive margin of o into d.

The country unit cost co is given by the function

co = wo bo

1–b, (9)

where o is the price of intermediate goods, which is given by the price index in country o. Intermediate goods enrich the Ricardian description of the worldwide technology differences.

Comparative advantages, in this CIF price model, are defined by d’s domestic prices distribution, in which each pod(k) characterizes the extensive margin of each o into d, {od}(k). Given the huge set of bilateral-trade, {od}(k) is a random realiza- tion of a cumulative probability distribution on zo(k): Fo(z) = Pr[Zo ≤ z]. Built on a Fréchet distribution of extreme, this Fo(z) takes the following form:

F zo T z T c to o o o od( ) exp exp ( )= = ,− −

− − 

 

θ θ θρ

(10)

where Ti represents o’s technology (absolute) advantage, and  represents a worldwide index of global technology variation. This meaning reminds the set N in the DFS, which increases trade volume. In the second zo is substituted from Equation (8), so (cotod), sets the price efficiency of o on Fo(z). In fact, (cotod)

– is a global-like comparative advantages, in which the (production and trade) costs linkage to trade is conditioned by the global parameter .

The lower the Fo(z), the higher o’s contribution to d’s cumulative price distri- bution, God (p) = 1 – Fo(z). Therefore, the share of each o in d’s expenditure is given by

π θ

θ od

od

d

od o od

o

O

o o od

od

d

G p G p

T c t

T c d

X X

= = = , −

=

−∑ ( ) ( )

( )

( ) 1

(11)

where Xd represents the country’s total expenditures and Xod is the fraction spent on goods from i. To and  are pro-trade forces, whereas tod is the anti-trade force. Simulations yield the  for which bilateral trades in Equation (11) best fit the actual world data.

Import shares in Equation (11) have unit-price elasticity, given consumer demand from a constant elasticity of substitution (CES) utility and firm demand from Equation (9). Thus, cost differences alone dictate price differences, although goods are not net complements as in the DFS model.

EK is a supply-side structural gravity model, in which trade volume stems from technology differences, input cost and trade barriers. From another perspec- tive, it is a model of bilateral trade between countries with a Ricardian specializa- tion term. Inasmuch as this model is not concerned with trade patterns, its comparative advantages, (cotod)

–, are not grounded on opportunity cost, as are the previously defined Ricardian models.6

36 Foreign Trade Review 53(1)

Costinot et al. (2011) reintroduce industries by taking goods k as differentiated and demand for varieties v coming from CES preferences. This love of varieties preferences, intra-industry trade follows, with CIF prices conditioning expenditures according to pkd(v) = min1≤o≤O{c

k od(v) = t

k od.wo / z

k o(v)}. For simplicity, changes to c

k od = t

k od

wo / z k o. The predicted trade flows are equally determined by a Fréchet distribution:

Fo k(z) = exp[–(z / zo

k)–], (12)

where zko > 0 is fundamental productivity, defining the world’s efficiency frontier in industry k. The z/zko in Equation (12) is meant to express zo׳

k / zo k, as explained

below, whereas  indicates technology heterogeneity at industry k, which is assumed to be the same for all industries.

From (12), together with consumer demand, a new revealed comparative advantages (NRCA) index is derived for d’s imports from any pair of exporters,

o and o׳: NRCA koo d x x

x x od k

od k

od k

od k′ = , ′ ′

′ ′

( )    

where x~od(k) represents exports from o to d.

Comparing it to Balassa’s (1965) RCA koo X X X X k o o

k o o′ /

/ = ′ ′( ) , based on the Equation (4),

first, the fundamental difference is that RCAoo׳ (k) is a pairwise comparison of exporters o and o׳ in the world economy, whereas NRCAdoo׳(k) orders comparative advantage in each destination (importing) market, which implies that we do not have advantage of o over o׳ in general for a set of goods. Second, NRCARdoo׳, k׳ is a country’s ordering for each industry k, in which k׳ is just a numeraire, unlike the N-good sequence of comparative advantages of the RCAoo׳(k).

From the previously specified relationships, the NRCARdoo׳(k) is given by

ln x x x x

ln z z z z

od k

o d k

od k

o d k

o k o k

o k

o k

 

 

 

 

′ ′

′ ′

′ ′

′ ′



 



 =



 θ 



 −



 



 ,′

′

′ ′

ln t t t t od k o d k

od k o d k

(13)

where z~ is the observed productivity, kzo

kzo kzo

kzo

/ ′ ′/ ′′

is the comparative (opportunity)

cost, and dod k dod

k

dod k do d

k /

′ / ′ ′

is the comparative trade cost. International trade drives a

wedge between observed and fundamental productivity, z~ and z, respectively, thus conveying a notion of trade linkages other than Deardorff (1979). The fundamen- tal point here, which is common to all these Ricardian gravity models, is a com- parative advantage model that has no autarky counterpart.7

Conversely, Shikher (2012) introduces industries into the EK’s model through intermediate goods. That is, rather than Equation (9), unit cost of industry k in o is given by co(k) = wo

bok 1–b, with input prices given by a Cobb–Douglas function,

o(k) = ∏ K k=1po

km(m), in which km, the share of industry m in the output of k, is taken from input–output tables. This latter evidence limits the sample size: to eight industries and nineteen countries in Shikher (2012).

Consumers in each importing d follow ‘the winner (the exporter with the best price) takes all,’ as in EK, and the CIF price is given by

Cinquetti 37

p k T k t k c kd

o

O

o od o( ) ( )( ( ) ( ))= , =





   





   

∑γ θ 1

(14)

where parameter  follows from the CES preferences as in EK, and To k is an esti-

mated measure of industry k’s productivity in country o. Although  conditions the impact of (tod(k)co(k)) on trade, the latter does not define comparative advan- tages as shown below.

Inter-industry trade occurs because each industry m supplies several intermedi- ate goods l to industry k. In this sense, the intensive margin defines trade flows both here and in Costinot et al. (2011). That is, productivity zo(lk) and the corre- sponding prices, pod (lk) = co (k)tod(k) / zo (lk), determine the share of each Xod (k) in each Xd (k). More to the point

π

γ θ

od od

d o

od o

d

k X k X k

T k t k c k p k

( ) ( ) ( )

( ) ( ( ) ( )

( ) = =



 



  , −

(15)

which indicates the industry’s bilateral trade between o and d. As suggested in Equation (14), country o has comparative advantages if To (k) / To׳ (k׳) > To (k)/ To׳ (k׳), similar to Costinot et al. (2011).

The endogenous  and its effect on industry cost, co (k), is the way through which trade barriers in one industry spread throughout all industries, via their backward and forward linkages. Simulations from the computable general equi- librium render an accurate picture of impacts from trade cost on industrial employ- ment and total welfare.

Romalis (2004) focuses instead on country’s trade pattern with respect to the world, which enables a comparative advantages chain in a multi-country economy. Trade barriers matter here, only for engendering unequal factor prices and thus technology differences, whereas the Dixit and Stiglitz’s (1977) monopolistic competition warrants not only intra-industry trade but also a constant ratio of price to marginal cost,8 which coupled with homothetic technology renders an international ranking of the industries according to their factor intensity. Based on that, factor prices (two factor proportions with respect to a third one) determine each country position in the global comparative chain of goods in a North–South economy that is unfolded into so many countries belonging to them. Comparative advantages are also expressed by the number of firms per sector. That is why Romalis (2004) calls it a quasi-Heckscher–Ohlin (HO) prediction: for its reliance on the monopolistic competition and for not predicting trade in each factor’s service.

Morrow (2010, p. 46) expands this model with TFP differences and takes each country’s opportunity costs with respect to the mean world economy. The result is Ricardo–HO (RHO) comparative advantages. Given that both firm’s scale and the market power are constant under monopolistic competition—so similar to perfect competition—the RHO can be seen as a global-market extension of the RHD tradition. The Ricardian technology based on a multi-factor total factor productiv- ity (TFP) is similar to Costinot et al. (2011), but the RHO is not Ricardian, inas- much as one of the two technology differences is endogenous.

38 Foreign Trade Review 53(1)

Ricardian Models with Non-neutral Demand

In the previously mentioned models, trade based on cost differences (or changes) alone is warranted by some forms of neutral demand. Otherwise, demand can determine both price change and trade gains, especially in a 3-good economy with two relative prices. With I ≥ 3 countries, international demand differences can determine the bilateral trade and the international prices as well. This section addresses these demand linkages to trade.

Trade Gains from Technical Progress: The Three-good Model

Jones’s (1979) reversal DFS model9 is certainly the first formalization of the com- plex manner in which demand can condition trade gains. His three-good model resembles that of Lewis (1954), but departs from both Lewis’s (1954) model and Ricardo’s (1817) model in that it has a demand function.

To briefly review it, let good 2 be a non-tradable price numeraire and a1 < 0 be the technical progress in the home export sector. The foreign gain is then

dy* = –D1 *dp1, (16)

which is conditioned to demand share, D1 *, a feature that is absent in both the DFS

and EK models. With x once again indexing goods, the home gain is then

dy = (x1 – D1)dp1 + {p1dx1 + dx2}. (17)

Given full employment, the expression in brackets can be transformed into a1dx1 + a2dx2 = –x1da1, which can be transformed to –x1dp1, so Equation (17) is reduced to

dy = –D1dp1. (18)

Therefore, contradicting Lewis (1954), technical progress in the export sector cannot result in immiserizing growth. However, if the home gain is higher, its export share is lower, confirming the bleak prospects for commodity-exporting economies.

The outcome shifts altogether when x2 becomes a traded good in which the home country has comparative advantages. Given that wages are no longer con- stant in a2, p1 is no longer proportional to â1, whereas p3, which is no longer tied to numeraire p2, can either rise or fall according to international market clearings. More precisely, given D3 = D3 (p1, p3, y), D E p E p dy

m p D3 3

1 1 3

3 3

3

3 3 = + + , showing

that D̂3 is conditioned not only by cross- and own-price elasticity but also by m3, the marginal propensity to consume (import) these goods. A decrease in p1 causes a substitution away from x3 if x1 and x3 are gross substitutes, pushing p3 down- ward. The result reminds us of the well-known case of the North’s synthetic goods harming the South’s exports of natural goods.

To evaluate the paradox that technical progress in the imported good makes the foreign country worse off, consider its income change:

Cinquetti 39

dy* = –p1D1 * p1 + p3D3p3. (19)

Thus, dy* < 0 depends on both dp1 < dp3 and on the weights D1 * and D3, where

D3 = (x3 * – D3

*). As demonstrated by Jones (1979), the income gain from the initial decline in p1 prevents p3 from decreasing as much as p1, when all goods are net substitutes and when the substitution effects are high. The latter condition is easily met by the fact that –E3

3 = E1 3 + E2

3, such that the own-price elasticity is greater than the cross-price elasticity, E1

3. However, when goods 2 and 3 are net complements, then the cross-price elasticity, E1

3, will exceed the own-price elasticity effect, E3 3,

leading to dp3 < dp1 < 0. Finally, regarding the income effect, foreign imports both goods 1 and 2, so its import share, D1

*, is smaller than its export share, D3, and we thus fall back into the previously mentioned paradox.

In sum, the full-fledged demand relationship in Jones’s (1979) demand-based Ricardian model shows that immiserizing growth is conditioned not by the price elasticity of demand for the exported goods alone, as in Bhagwati (1958),but for all (imported and exported) goods. Aside from small-country models in which international prices are fixed (e.g., Brecher & Díaz-Alejandro, 1977), this alterna- tive approach to immiserizing growth is the most suitable to North–South models examined next.

The Multi-country, Multi-good Model

If we extend this model to a multi-good economy, the equilibrium prices would become inextricably complex. However, as Wilson (1980) notices, in such an economy the income impact of any good’s price becomes negligible, so only the own-price and income elasticity of demand matter. This setting is perfect for mod- els of trade with non-homothetic demand based on good’s characteristics other than their quantity.

Fieler (2011a) is, certainly, the most referential multi-country Ricardian model with non-homothetic demand thus far. She extends EK by grouping the k goods into different types , and preferences of the representative consumer are given by

τ

σ

τ τ

τ τ

σ σ τ

τ τ τα σ

σ=

/( ) − / 

 



∑ ∫ −



 



 



  



  

1

1

0

1 1

1

S

x k dk( )( )  



 

  

/

, >

=∑

σ

α

τ

τ τ

στ

1

11and ( ) .

(20)

The x (k  ) is the quantity of each k

 and a

 is their corresponding weights. The

most peculiar of this non-traditional CES function in Equation (20) is that s  rep-

resents a constant income elasticity. That is more clearly illustrated by the relative demand for two types of goods (Fieler, 2011a):

x x

P P

τ

τ

σ σ τ τ α

τ τ αλ

α

α τ τ

τ

τ ′

− −

′ ′ −=



 



 ,′

′

1

1

(21)

40 Foreign Trade Review 53(1)

where  is the Lagrangian multiplier associated with the inverse of the consumer’s budget constraint, whereas P represents the price indexes of each type of goods identified by the subscript. Therefore, if s

 > s

׳ then x / x׳ increases with income. Assuming differences in the EK’s parameter, such as 

 < 

׳, meaning that goods  are more intensively traded than ׳, then wealthier countries would both trade more among themselves and less with respect to their GDP. This EK model with a heterogeneous demand structure fits the data better than the EK (see Fieler, 2011a). At the end we have a North–South gravity model with a demand- and supply-side structure. Notably, this comprehensive formalization of a multi-coun- try trading economy is enabled not only by the EK’s simple comparative advan- tages but also by a supply-side ordering that mirrors the demand-side ordering, that is, s

 > s

׳ ⇔  < ׳. Caron et al. (2014) develop Fieler (2011a) with Costinot et al.’s (2011) com-

parative advantages so as to reach an industry’s model of bilateral trade that are determined by opportunity costs, trade costs and non-homothetic preferences. They (Caron et al., 2014) actually develop both a Ricardian and an HO model, in which skill-intensive goods are assumed to be more income elastic. Besides Fieler’s (2011a) prediction that wealthier countries trade more among themselves and less with respect to their GDP, this industry’s model of bilateral trade uncov- ers several others missing trade (Trefler, 1995) of the traditional Heckscher– Ohlin–Vanek (HOV) model. Besides the simple comparative advantage (Costinot et al., 2011) what here warrants a tractable industry model of bilateral trade with HO’s technology and non-homothetic preferences is the ordering of good’s trade parameters 

 according to their demand parameters s

 .

Another strand of Ricardian model with non-homothetic preferences addresses trade and product quality. An early development is the two-country, two-good (one of each is differentiated) model by Flam and Helpman (1987). Matsuyama (2001) advances the DFS to a continuum of goods model with quality and non-homothetic preferences. In both of these North–South trade models, the income elasticity of demand conditions the international price of quality attached to goods.

Jaimovich and Merella (2012) provide an interesting development of Matsuyama’s (2001) two-country approach by introducing a structural shift in the preference for goods associated with a quality level qk. That is, consumer demands all k products, but only one q of each, so that preferences over the quality-adjusted consumption index, Ck, take the following form:

U lnC k dk

C x k x k x k x k x k x k

k

k

qk

= ,

= < ≥

<

∫ ( ) ( ) ( ) ( ) ( ) ( ) ( )

with if if if

1 1 1xx k x kqk( ) ( )if ≥

  

 1

(22)

In this utility-adjusted quantity, the xk < 1 are basic goods, whereas the xk ≥ 1 are non-basic goods whose utility increases with q(k).

Jaimovich and Merella (2012) further assume that the quality upgrading costs are lower for high-quality goods, as described by the following cost functions:

c a k q c a k qkq

k kq

k= / = /∗ ∗( ) ( ) .( ) ( )η ηκ κand

(23)

Cinquetti 41

The k ∈ [0, 1] inversely orders qk ∈ [0, 1], so that the cost elasticity of quality upgrading,  (k) > 1, falls with q. As seen, the global technology frontier, , adjusts countries H and F’s (designed by *) technologies. An increase in either  or the population size leads to a larger increase in the world demand for high-quality goods, given the non-homothetic preferences in Equation (22), and thus to higher gains to the country that initially happened to have comparative advantages in non-basic goods. Therefore, goods’ intrinsic characteristics dictate which country gains the most: the country that by chance first specialized in the most dynamic and highly priced goods.10 This approach coincides with a tradition in develop- ment theory (e.g., Prebisch, 1950), in which the basis of trade and its gains are not grounded on a country’s characteristics.

Fieler (2011b) develops a multi-country Ricardian model of trade in quality. As illustrated by the following consumer problem in d, for given endowment e and income wd, it relies on a different form of preferences:

max ( ) ( )

( ( ) ) ( ) . {k K}

{k K} d d

q k x k dk

to p q k k x k dk ew ∈

∈

∫ ∫

,

, ≤subject

(24)

Consumers buy either 0 or 1 of each good k with quality q(k) when x(k) = 1. The resulting demand function is non-homothetic: wealthier consumers buy the most expensive and high q(k) goods because the optimum p(q, k) is constrained by 1/n, where  (the Lagrangian multiplier) represents for the marginal utility of income. For the sake of brevity, we skip the t cost in the CIF prices in Equation (24), and so the most evolving comparative advantages of exporters in destination market d.

Firms in countries with higher (lower) e—and thus higher (lower) w—maxi- mize profits by producing high (low)-quality products. This stems from the assumption that the comparative labour-input coefficient, a q k

a q k o

o

( ) ( ) ,

,′ , is decreasing in q,

following Flam and Helpman (1987). The outcome is then a trade pattern that is similar to the previously quoted 2-country models: developed (developing) coun- tries both export and import the most (least) costly varieties. In this sense, trade patterns stem from each country’s development level (endowment of human capi- tal), unlike Jaimovich and Merella (2012). However, this extension of Flam and Helpman (1987) to a multi-country economy, which leads to an HO story, requires a functional relationship from e to a q k

a q k o

o

( ) ( ) ,

,′ across the n countries, which is not

clearly presented in Fieler (2011b). To illustrate how q can be related to e, we can think of a 1-factor (human capi-

tal) Ricardian model by Acemoglu and Ventura’s (2002) and ignore for the time being multilateral trade. Utility follows 24, u = qx, and quality is costly in human capital q = f (e), f ׳(e) > 0, f ׳׳ (e) ≥ 0. Substituting them into the cost function c(x), one reaches

c q

c f e

ν ν

 



 =



 



 ,

( ) (25)

showing that c(x) falls with quality improvement (Boccard, 2010) because u increases with q. From Equation (25) we can then reach a Ricardo–Viner model

42 Foreign Trade Review 53(1)

in which comparative advantage in q stems from e, as suggested in the seminal work by Schott (2004).

Jaimovich and Merella (2015) attempts to solve it with a multi-country model for x(k) and q(k). Preferences for products k is given by a CES utility function (i.e., Dixit & Stiglitz, 1977), which grants that each importer demands all prod- ucts from each source country, whereas the subutility for quality follows closely in Equation (22). Consequently, wealthier importers spend a higher share on high- quality products. Ricardian technologies shape the supply of both x(k) and q(k), as expressed by the cost function

c q

q o k

o k

, = . ,

( ) η

κ (26)

The important change with respect to Equation (23) is the country specific cost elasticity of quality upgrading, o,k, which is randomly distributed across the o countries. And the cost of quality upgrading is smaller in those k sectors in which o has comparative advantage, that is, 2qok / ok < 0: Hence, as in Jaimovich and Merella (2012), specialization follows from goods characteristics alone.

A second random draw of [ 

, ] determines which countries belong to the Southern and Northern regions, respectively, and so which one supplies high-q goods. Hence, development levels do not stem from exogenously given country characteristics, but rather from chance events from a random distribution of tech- nology level. That solves the loophole in Fieler (2011b), but with a disputable empirical content.

In an ampler assessment of these Ricardian models, the first thing to notice is that q’s comparative advantages is formalized in the traditional Ricardian way: a pairwise comparison of countries—o(k) / o׳(k) or o(k) comparatively to the world’s mean—in a sequence of quality. This yields very simple, pedagogical presentation to the subject and is grounded on the fact that the quality margin— usually the unit value of exported products—is independent of both the intensive and extensive margins of trade. However, referring these q(k) advantages to a random technology distribution of [

 , ] across k countries, rather than their

development level is a solution with weak empirical appeal for handling coun- try’s development level.

Another problem is the competitive approach to quality competition, which is but one way of avoiding the perfect competition (Boccard, 2010). Not surpris- ingly, the preferences of these competitive Ricardian models are borrowed from industrial organization (IO) models of quality competition (Boccard, 2010)11 which the international 1-factor international economy reverts to a competitive price: in each domestic factor market, labour cost captures all marginal revenue. Accordingly, the pricing of quality is exclusively connected to cost selection among international exporters (Fieler, 2011b; Jaimovich & Merella, 2015), which means assuming away, especially in the empirical analysis, the variation of the price premium among exporters within each importing country or that each exporter charges different prices for each destination. These latter facts, as argued by Baldwin and Harrigan (2011), mean free on board (FOB) pricing in the quality

Cinquetti 43

competition, that is, exporters that make prices. In sum, as shown in Cinquetti and Faria (2016), the distinct price premium (markup) exporters charge in each importing market varies with both consumers’ willingness to pay and the intensity of market competition.

The perfect competition assumption also enforces approaching q as subsumed in x. For instance, in Jaimovich and Merella (2015) the q’s performance is simply a by-product of x′s cost competition, of comparative advantages. Although this cost approach reminds the (multi-product) firm’s core (e.g., Eckel, Iacovone, Javorcik, & Neary, 2015), in these analyses, following the literature on quality competition (see Belleflamme & Peitz, 2015, ch. 12), the information nature around q requires that its upgrading be connected with marketing investment in order to convey the firm’s specific q. Besides different, quality and cost competi- tion also vary in industries with differentiated and non-differentiated products (Eckel et al., 2015). In Cinquetti and Faria (2016), which focuses on differentiated goods, the connection between sectoral comparative advantages and goods’ price- premium goes through exporter’s learning about the most desired q(k) character- istics by international consumer (Artopoulos, Friel, & Hallak, 2013), and this learning reinforces firm’s market power.

As a conclusion, it is possible to say that a theoretical agnosticism might be a more effective simplification—other than the Ricardian simplification–for ana- lyzing some problems in multi-country economies, as exemplified by Hidalgo, Klinger, Barabási and Hausmann ’s (2007) framework for economic complexity. For instance, from the minimum conditional probability of RCA between pair of products, this computer-based network derives a reach picture of industries’ pro- duction chain. The size of this network varies with country’s development level, and it can further account for horizontal and vertical product differentiation, as shown in Ferrarini and Scaramozzino (2015).

Conclusion

Ricardian advantages structure many new multi-country models focusing on cost linkages to trade. They bear little resemblance to traditional Ricardian advantages, and the first one is a global-like notion of comparative advantages that mixes worldwide trade linkage with producer’s cost in a cumulative (Fréchet) probability distribution that orders exporters within each importing market. In EK’s original formulation, the worldwide parameter of technological heterogeneity links export- er’s marginal costs (encompassing geographic variables) to import shares, which represents the extensive margin of bilateral trade. Developments towards indus- tries’ bilateral trade reintroduce opportunity cost and trade flow is referred to the intensive margin. A pure model of intra-industry bilateral trade renders a new and insightful index of RCA, whereas another focus on inter-industry trade via inter- mediate goods (input–output table), which offers an ampler view of the welfare impacts of international trade. Less noticed, though no less important, this class of model relies on forms of demand that are neutral as to the cost-based prices.

44 Foreign Trade Review 53(1)

While the DFS model is a reference for the given models, Jones’s (1979) 3-sector model is a reference for the new Ricardian models that focus on the demand linkages to trade. His full consideration of cross- and own-price elas- ticities of demand provides a whole new perspective on immiserizing growth. In multi-good models the cross-price elasticity can be ignored, which facilitates the analysis around non-homothetic preferences and goods’ asymmetry. Further developing it to multi-country economies, renders more accurate models of bilat- eral trade. A heroic assumption holding this comprehensive bilateral trade model with a supply and a demand structure is that goods’ income elasticity of demand, orders their cost linkages to trade.

Associating goods asymmetry to product quality renders interesting pedagogi- cal models of North–South trade with non-homothetic preferences. However, as a theoretical framework they face two major difficulties: (a) fitting a competitive approach to an imperfectly competitive subject (i.e., quality competition) and (b) the ordering of a country’s quality advantage can hardly be divorced from a HO story, especially in a multi-country economy.

Summarizing, the Ricardian technology structures a wide range of bilateral trade models in multi-country economies, which were more concerned with geog- raphy and technology differences as bases of trade. This multi-country trade set- ting enforces comparative advantages with no reliance on autarky prices or even on opportunity costs, which means a fundamental departure from the RHD tradi- tion. On the other hand, the Ricardian models with non-homothetic preferences, in which trade is based on development level, can be seen as revenge against the RHD tradition.

Acknowledgements Early comments and suggestions by R. Jones, C. Fieler, D. Bernohofen, J. Moenius, D. Levcovitz, J. H. Faro and R. N. Faria are gratefully acknowledged. This work was initially advanced during my sabbatical at the University of Colorado, which was supported by Sao Paulo State University and CAPES under Grant [BEX 0867/09–8]. Early financial support from Fapesp [2009/07636–2] is also gratefully acknowledged.

Notes 1. That was not ignored in the seminal survey by Matsuyama (2008) who, however,

improperly classifies Jones (1979) as a development of DFS. 2. As expressed in the so-called Ricardo–Viner model (see Findlay, 1984). 3. This proposition is ignored by neo-Ricardians, including the otherwise noteworthy

analysis by Pasinetti (1981, Chapter11). 4. Bernhofen & Brown (2005) overcome this problem by examining a country whose

total trade volume was only 2 per cent of its GDP—Japan’s Meiji revolution—but this exceptional case only reinforces the problem with this approach. However, Deardorff (1984) emphasizes that unobserved autarky prices can be substituted by factor endowments.

5. This empirical rejection undermines the opposite claim by neo-Ricardians (Kurz & Salvadori, 1995), based on technology re-switching. An empirical tests of the Ricardian model for several Organisation for Economic Co-operation and Development (OECD) countries finds a too low R2 (Golub & Hsieh, 2000), whereas a comparative analysis of

Cinquetti 45

the USA with respect to Brazil, finds that comparative cost only achieves the negative sign with dummy variables for resource-based sectors, together with a latent variable for factor proportions (Cinquetti, 2008).

6. In which comparative advantages might even reduce bilateral trade (Oladi & Beladi, 2010).

7. Finicelli, Pagano, & Sbracia’s (2013) analysis of Ricardian selection is a concrete example of how trade affects productivity—that is, average productivity—in a way that is irrespective of autarky’s comparative advantages.

8. In each country i cost is given by C(, x~) = [f + qMi]si x~

wi

1–x~, where qM is the marginal cost, s and w are the prices of skilled and unskilled labour, respectively, and x~ ranks industries according to their skilled-labour intensity.

9. Jones was the referee of the DFS and advised Wilson (1980) and his co-authored text- book (Caves, Frankel & Jones, 1999) is also unique in highlighting that the Ricardian model overcomes the role of demand upon prices in a competitive **one-factor economy.

10. Thus Jaimovich & Merella (2012) attribute the growth trajectories of colonial Jamaica and Argentina to their original specializations in sugar cane and cattle, respectively, with no reference to the implied share of slave labour in both activities and its impact on both labour incentives and reallocation.

11. These are oligopoly models. Contrariwise, most models of trade in quality assume monopolistic competition (e.g., Hallak & Schott, 2011; Kluger & Verhoogen, 2011; Hummels & Klenow, 2005; Bernard, Redding, & Schott, 2011), which involves qual- ity-adjusted preferences for horizontally differentiated goods.

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