Diversification through Trade

Transcription

1 Diversification through Trade Francesco Caselli Miklos Koren Milan Lisicky Silvana Tenreyro First draft: May This draft: January 2014 Abstract A widely held view is that openness to international trade leads to higher GDP volatility, as trade increases specialization and hence exposure to sector-specific shocks. We revisit the common wisdom and argue that when country-wide shocks are important, openness to international trade can lower GDP volatility by reducing exposure to domestic shocks and allowing countries to diversify the sources of demand and supply across countries. Using a quantitative model of trade, we assess the importance of the two mechanisms (sectoral specialization and cross-country diversification) and provide a new answer to the question of whether and how international trade affects economic volatility. We would like to thank Pete Klenow, Fabrizio Perri and Jaume Ventura for helpful conversations, and seminar participants at Princeton, Yale, UCL, LBS, LSE, CREI, and ESSIM. Calin Vlad Demian and Federico Rossi provided superb research assistance. Caselli acknowledges financial support from the Luverlhume Fellowship. Koren acknowledges financial support from the European Research Council (ERC) starting grant Tenreyro acknowledges financial support from the ERC starting grant London School of Economics, CEP, CfM, CEPR. Central European University, MTA KRTK, CEPR. European Comission. Corresponding author: Tenreyro <s.tenreyro@lse.ac.uk>. 1

2 I Introduction An important question at the crossroads of macro-development and international economics is whether and how openness to trade affects macroeconomic volatility. A widely held view in academic and policy discussions, which can be traced back at least to Newbery and Stiglitz (1984), is that openness to international trade leads to higher GDP volatility. The origins of this view are rooted in a large class of theories of international trade predicting that openness to trade increases specialization. Because specialization (or lack of diversification) in production tends to increase a country s exposure to shocks specific to the sectors (or range of products) in which the country specializes, it is generally inferred that trade increases volatility. This paper revisits the common wisdom on two conceptual grounds. First, the paper points out that the existing wisdom is strongly predicated on the assumption that sectorspecific shocks (hitting a particular sector) are the dominant source of GDP volatility. The evidence, however does not support this assumption. Indeed, country-specific shocks (shocks common to all sectors in a given country) are at least as important as sector-specific shocks in shaping countries volatility patterns (e.g. Koren and Tenreyro, 2007). The first contribution of this paper is to show analytically that when country-specific shocks are an important source of volatility, openness to international trade can lower GDP volatility. In particular, openness reduces a country s exposure to domestic shocks, and allows it to diversify its sources of demand and supply, leading to potentially lower overall volatility. This is true as long as the volatility of shocks affecting trading partners are not too big, or the covariance of shocks across countries is not too large. In other words, we show that the sign and size of 2

3 the effect of openness on volatility depends on the variances and covariances of shocks across countries. The paper furthermore questions the mechanical assumption that higher sectoral specialization per se leads to higher volatility. Indeed, whether GDP volatility increases or decreases with specialization depends on the intrinsic volatility of the sectors in which the economy specializes in, as well as on the covariance among sectoral shocks and between sectoral and country-wide shocks. We make these points in the context of a quantitative, multi-sector, stochastic model of trade and GDP determination. The model builds on a variation of Eaton and Kortum (2002), Alvarez and Lucas (2006), and Caliendo and Parro (2012), augmented to allow for countryspecific, and sector-specific shocks. In each sector, production combines equipped labour with a variety of tradeable inputs. Producers source tradable inputs from the lowest-cost supplier (where supply costs depend on the supplier s productivity as well as trade costs), after productivity shocks have been realized. This generates the potential for trade to insure against shocks, as producers can redirect input demand to countries experiencing positive supply shocks. However, labor must be allocated to sectors before productivity shocks are realized. This friction allows us to capture the traditional specialization channel, because it reduces a country s ability to respond to sectoral shocks by reallocating resources to other sectors. We use the model in conjunction with sector-level production and bilateral trade data for a large number of countries to quantitatively assess two questions: 1) how would a move to costless trade in agriculture and manufacturing affect volatility in different countries? And 2) how have changes in trading costs since the early 1970s affected volatility in the countries 3

4 in our sample? Both exercises use as inputs the stochastic properties of country-specific sectoral productivity shocks, which we back out from the model on the basis of sector-level data on gross output, value added, and bilateral trade flows data. To assess the effect of changes in trade barriers since the 1970s we also back out country-and-sector specific paths of trade costs. We find that removing trade barriers in agriculture and manufacturing would reduce volatility in most countries in our sample. The reduction in volatility varies significantly across countries, with Mexico experiencing the largest reduction and Belgium-Luxembourg seeing virtually no change. The general decline in volatility due to trade is the net result of the two different mechanisms discussed above, sectoral specialization, and country-wise diversification. The country-wise diversification mechanism contributes to lower volatility in 85 percent of the countries in our sample, indeed suggesting that there is scope for diversification through trade. Equally interestingly, and against conventional wisdom, higher sectoral specialization does not always lead to higher volatility. Indeed, for a majority of countries in our sample, the sectoral-specialization channel would contribute to lower volatility. This is because shocks to the sectors in which these economies would specialize under free trade are negatively (or less positively) correlated with other sectoral or country-wide shocks. As with the overall net effect of trade on volatility, the relative importance of the two mechanisms we highlight varies across countries. In all, however, the effect of the specialization mechanism tends to be smaller relatively to the diversification mechanism. Regarding the second question, changes in GDP volatility since the 1970s due to lower trading costs have generally been negative, meaning that globalization has contributed to 4

5 lower overall volatility - again contrary to the conventional view. 1 However, these effects are generally modest, with only some of the smaller countries in the sample (e.g. Ireland, the Netherlands, Belgium-Luxembourg) having experienced significant declines in volatility thanks to trade. 2 And there are exceptions at the other extreme as well, with a few countries, most notably Norway, experiencing a significant increase in volatility attributable to trade. The country-wise diversification mechanism contributed to lower volatility in more than 90 percent of the countries in the sample. In turn, the sectoral specialization channel led on average to higher volatility, though the effects from this channel are quantitatively very small. 3 To summarize, our study challenges the standard view that trade increases volatility. It highlights a new mechanism (country diversification) whereby trade can lower volatility. It also shows that the standard mechanism of sectoral specialization usually deemed to increase volatility can in certain circumstances lead to lower volatility. The analysis indicates that diversification of country-specific shocks has generally led to lower volatility during the period we analyze, and has been quantitatively more important than the specialization mechanism. Openness to trade however will not always lead to lower volatility: the sign and size of the effect varies across countries. This might partly explain why direct evidence on the effect crisis. 1 We stop the analysis in 2007 as our model abstracts from the financial factors underlying the current 2 Note that these are the countries for which further moves to free trade our previous question would not lead to significant additional reductions in volatility; most of the volatility reduction appears to have been already seized by these countries. 3 It is not necessarily puzzling that the sectoral concentration channel tends to lead to increased volatility in the historical application, while it promises reduced volatility in the hypothetical experiment of removing all (further) barriers to trade. The trade barriers that have been removed historically may have led to a pattern of specialization that could be very different from the pattern emerging from the removal of all further barriers. 5

6 of openness on volatility has been ambiguous at best. Some studies find that trade decreases volatility (e.g., Cavallo, 2008; Strotmann, Döpke, and Buch, 2006; Burgess and Donaldson, 2012; and Donaldson, 2014), while others find that trade increases it (e.g., Rodrik, 1998, Easterly, Islam, and Stiglitz, 2000, Kose, Prasad, and Terrones, 2003, and di Giovanni and Levchenko, 2009). The model-based analysis can circumvent the problem of causal identification faced by many empirical studies, allowing for counterfactual exercises that isolate the effect of trade costs on volatility. Moreover, it can cope with highly heterogenous trade effects across countries. Before proceeding, we should emphasize that we focus the analysis on GDP volatility because for most countries in the world, GDP and consumption fluctuations are almost perfectly correlated. Hence, accounting for GDP volatility goes a long way in accounting for consumption volatility (see Figures 1 and 2). 4 Accordingly, in the modeling section, we abstract from financial trade in assets. 5 The remainder of the paper is organized as follows. Section II reviews the literature. Section III presents the model and solves analytically for two special cases, autarky and costless free trade. Section IV introduces the data, calibration and quantitative results. Section V presents concluding remarks. The Appendix contains further derivations and a detailed description of the datasets used in the paper. 4 Figure 1 shows the volatilities of per capita consumption and GDP. Figure 2 shows the volatilities of aggregate consumption and GDP. 5 There is an obvious analogy between diversification through trade in goods and diversification through trade in financial assets. However, trade in assets stabilizes consumption, not GDP (indeed, trade in assets might increase GDP volatility, as capital would tend to flow to high productivity countries and amplify productivity shocks), whereas in contrast, trade in goods stabilizes GDP and as a by-product, also consumption. Given the patterns in Figure 1, there appears to be limited asset diversification across countries. 6

7 II Literature Review A number of empirical studies have used variation across countries to analyze the effects of trade openness on volatility. Some studies, most notably Rodrik (1998), Easterly, Islam, and Stiglitz (2000), Kose, Prasad, and Terrones (2003) find that trade openness increases volatility, while others, including Cavallo (2008) and Bejan (2006), find that trade openness decreases volatility. Causal inference in these studies, however, suffers from common endogeneity problems stemming from ommitted variables and reverse causality. Di Giovanni and Levchenko exploit variation across countries and across sectors, concluding that trade openness leads to higher volatility. Strotmann, Döpke, and Buch (2006) exploit variation across firms in German and infer that exposure to international trade increases firm-level and aggregate volatility. While the use of sector- or firm-level data allows researchers to control for a number of country-specific determinants of volatility, omitted-variable biases at lower levels of aggregation, reverse causality, and possibly heterogenous effects of trade openness across countries remain potential concerns. 6 To isolate the causal effect of trade openness on volatility, we build on a variation of the theoretical model formulated by Eaton and Kortum (2002), further extended by Alvarez and Lucas (2006) and Caliendo and Parro (2012). The model is amenable to quantitative calibration and has proven useful at replicating trade flows and production patterns across countries. Variations of this model have been used to address a number of questions in international economics. For example, Hsieh and Ossa (2011) study the spillover effects of 6 Trade is by no means the only determinant of volatility. For studies of other determinants of volatility, see Kose, Prasad, and Terrones (2003), Raddatz (2006), Koren and Tenreyro (2007, 2011, 2013), Berrie, Bonomo and Carvalho (2013), and the references therein. 7

8 China s growth on other countries; di Giovanni, Levchenko, and Zhang (2014) study the global welfare impact of China s trade integration and technological change; Levchenko and Zhang (2013) investigate the impact of trade with emerging countries on labour markets; Burstein and Vogel (2012) and Parro (2013) study the effect of international trade on the skill premium; Caliendo, Rossi-Hansberg, Parro, and Sarte (2013) study the impact of regional productivity changes on the U.S. economy, and so on. None of these applications, however, focuses on the impact of international trade on volatility. The closest paper to ours, both on question and method, is Burgess and Donaldson (2012), who use a similar modeling framework in conjunction with data on the expansion of railroads across colonial India to assess whether real income became more or less sensitive to rainfall shocks, as India s regions became more open to trade. The authors find that the fall in transportation due to the railroad expansion reduced the impact of productivity shocks on real income, thus lowering volatility. Our analysis highlights that, while a reduction in volatility has been experienced by many countries as they became more open to trade, the size and sign of the trade effect on volatility may be and indeed has been different across different countries. 7 III A Model of Trade with Stochastic Shocks The baseline model builds on a multi-sector variation of Eaton and Kortum (2002), Alvarez and Lucas (2006), and Caliendo and Parro (2012), augmented to allow for stochastic shocks, as well as frictions to the allocation of non-produced (and non-traded) inputs across sectors. 7 There is a growing literature on the effect of globalization on income risk and inequality. We do not focus on distributional effects within countries in this paper, though it is obviously a very important issue, and a natural next step in our research. For recent theoretical developments in that area, see Anderson (2011) and the references therein. 8

9 A Model Assumptions The world economy is composed of N countries. At a given point in time t, each country n is endowed with L nt units of a primary (non produced) input, which we interpret as equipped labour. There are J sectors (or broad classes of goods) in the economy, whose output is combined into a final good through a Cobb-Douglas aggregate. In formulas, aggregate gross output in the economy is given by: Q nt = J ( ) j=1 Q j α j nt (1) where Q j t is the gross output in sector j and J j=1 αj = 1. Competitive firms in each sector j produce a composite good according to the following constant-elasticity-of-substitution (CES) technology: [ Q j 1 nt = q 0 nt(ω j ) η 1 η ] η dω j η 1 (2) where q nt (ω j ) is the quantity of good ω j used by country n in sector j at time t, and η > 0 is the elasticity of substitution across goods within a given sector. The intermediate goods ω j can be produced locally or imported from other countries. Delivering a good from country n to country m in sector j, results in 0 < κ j mn 1 goods arriving at m; we assume that κ j mn κ j mk κj kn m, n, and j and κj nn = 1. All costs incurred are net losses. 8 Under the assumption of perfect competition, goods are sourced from the lowest-cost producer, after adjusting for transport costs. The technology for producing q nt (ω j ) is given accordingly by the country of origin (m) with the lowest cost (with m = n when the good is produced 8 In the calibration, the κs will reflect all trading costs, including tariffs; so implicitly we adopt the extreme assumption that tariff revenues are wasted or at least not received by consumers. 9

10 locally): x mt (ω j ) = A j mtz m (ω j )l nt (ω j ) βj M mt (ω j ) 1 βj (3) where x mt (ω j ) is the production of good ω j by country m at time t, M mt (ω j ) is the amount of the aggregate composite good used by country m to produce x mt (ω j ) units of good ω j and l mt (ω j ) is the corresponding amount of equipped labour. Total factor productivity (TFP) levels vary across countries, sectors, and goods. Specifically, each intermediate good ω j in sector j of country n has a time-invariant idiosyncratic productivity factor z n (ω j ) and a timevarying factor A j nt common to all the goods ω j in sector j. Building on the literature, we assume the productivities z n (ω j ) follow a sector-specific, time-invariant Frechet distribution Fn(z) j = exp( Tnz j θ ). A higher Tn j shifts the distribution of productivities to the right, that is leading to probabilistically higher productivities. A higher θ decreases the dispersion of the productivity distribution, and hence reduces the scope for comparative advantage. Shocks to A j nt over time are interpreted as standard sectoral total factor productivity (TFP) shocks. The single final good can be used both as input in the production of intermediaries ω j or for final consumption, C nt. Hence, market clearing in the good markets implies: Q nt = C nt + N J n=1 j=1 1 0 M nt(ω j )dω j, where the integral aggregates over the unit-size continuum of goods ω j entering in the production of each sector s j aggregate good. 10

11 Clearing in the input market within a sector implies: L j nt = 1 0 l nt(ω j )dω j, where l nt (ω j ) denotes the amount of equipped labour used in the production of good ω j by country n. The inputs allocated to each sector, L j nt, with J k=1 Lk nt = L nt, are determined ex ante (before the realization of the shocks). We assume there is perfect risk-sharing within a country, but not across countries. 9 At the beginning of each period, a representative consumer decides on the optimal allocation of the primary input L nt into different sectors in order to maximize the expected value of utility; then (stochastic) shocks to productivity A j nt are realized, equipped labour is reallocated within a sector (but not across sectors), and production and consumption take place. The lack of ex-post reallocation across sectors in a given period aims at capturing the idea that in the short run, it is costly to reallocate productive factors across sectors. Hence, ex post, L j t is fixed until t The representative consumer s budget constraint in each period is: P nt C nt = J j=1 wj ntl j nt, where P nt is the price of the aggregate good (1), w j ntl j nt is the nominal value-added generated 9 See footnote 1 for a motivation for this assumption. 10 In the quantification, a period will be one year. This amounts to assuming that it takes at least a year for resources to be reallocated across sectors. 11

12 in sector j. Lifetime utility is given by U n = δ t u(c nt ), t=0 where u > 0. and u 0 and δ is the discount factor. Because there is no intertemporal trade and no capital in the economy, each period consumers maximize the expected static utility flow E [u (C nt )] and the equilibrium is simply a sequence of static equilibria (in the quantitative section, we allow for trade imbalances). In making his labor allocation decisions the representative consumer takes into account the joint probability distribution function of sectoral productivities, A j ns. In the analysis, we assume log utility and therefore the consumer solves: L j nt = arg max E t 1 [ln ( J j=1 wj nl j n P n )], s.t. : J j=1 Lj nt = L nt, (4) where E t 1 indicates that the expectation is taken before the realization of period t shocks.this leads to the following first-order conditions: L j nt L nt = E t 1 ( wnl j j n j w j n L j n ), (5) for all j. In words, the share of resources allocated to a given sector equals its expected share in value added. To gain intuition on this expression note that 1/ j w j n L j n is the marginal utility of consumption; thus, more resources are allocated to higher value-added sectors, after appropriately weighting by marginal utility. Consider, for further intuition, a (small) sector whose productivity is negatively correlated with the rest of the economy (that is, it has high 12

13 value added when the rest of the economy has low value added); in states of the world in which overall income is low, the marginal utility of consumption j w j n L j n will be high and hence the optimal allocation entails allocating more resources to this sector. (Log-linearizing this expression makes the role of second moments on the allocation of resources clearer.) In the closed economy, the value-added share is pinned down by the Cobb Douglas coeffi cients α j β j, which is constant, since in a closed economy with Cobb-Douglas technology there is no variation on expenditures (and sales) shares and log-utility implies the shares determine the sectoral allocation of resources. B Model Solution We first discuss the solution under autarky, and then turn to the solution under free trade. Solution under Autarky We solve the model backwards in two stages. First, we solve the model taking L j t as fixed; then we solve for the ex-ante optimal L j t s before the shocks are realized. We omit the country subscripts n for convenience. The demand for each sector s composite good is given by Q j t = α j ( P j t P t ) 1 Q t, (6) and the demand for each intermediate good is [ q t (ω j pt (ω j ) ) = P j t ] η Q j t, 13

14 where [ ] 1 P j 1 t = p 0 t(ω j ) 1 η dω j 1 η (7) is the aggregate price index in sector j, and P t = J j=1 αj α n j ( ) P j α j t. (8) The demand for non-produced inputs l t (ω j ) and produced inputs M t (ω j ) are given, respectively, by l j t (ω j ) = β j pt(ωj )q t(ω j ) w j t and M t (ω j ) = (1 β j ) pt(ωj )q t(ω j ) P t. Aggregating over all goods ω j in a given sector, we obtain w j t L j t = β j P j t Q j t (9) and, correspondingly, P t M j t = (1 β j )P j t Q j t. Autarky prices of intermediate goods are given by: p t (ω j ) = B [ j A j t z(ω j ) ] 1 ( ) w j β j t P 1 β j t, (10) where B j = ( β j) β j (1 β j ) (1 βj). Using (10) and the properties of the Frechet distribution, [ P j t = ξb j A j t (T j) ] 1 1 ( ) θ w j β j t P 1 β j t (11) where ξ = [ Γ ( )] θ+1 η θ, and Γ is the gamma function. Using (6), (9), and (8) we obtain real GDP: Y t = J w j t L j t j=1 P t = J j=1 R j [ ] α A j j β t ( ) L j αj β j β t, (12) where β = J j=1 αj β j and R j J ( j=1 β j α j) αj β j β (B j ) αj β (T j ) αj β θ is a time-invariant prod- 14

15 uct. We can now move one step backward and solve for the allocation of the primary input across sectors, L j t, j = 1,..., J. From (4) and (5), L j t = αj β j β L t. 11 Substituting into (12), GDP is given by: Y t = J j=1 R j ) (α αj β j j βj β β ( ) α A j j β t L t (13) In words, GDP varies with fluctuations in sectoral productivity, A j t, and aggregate resources, L t. Solution with International Trade The key difference in the internationally open economy is that inputs can potentially be sourced from different countries. Delivering a unit of good ω j produced in country m to country n costs: ( ) p j nmt(ω j ) = Bj w j β j mt P 1 β j mt A j mtκ j nmtz m (ω j ) where B ( ) j w j β j mt P 1 β j mt is the cost of the input bundle in country of origin m, sector j, at time t. Because of perfect competition, the price paid in country n will be p nt (ω j ), the minimum price across all N potential trading partners: p j nt(ω j ) = min { p j nmt(ω j ); m = 1,..., N }. Producers of the aggregate good in (1) minimize production costs taking prices as given. We assume the distribution of effi ciencies for any good ω j in sector j and country n are independent across countries and sectors and follow a time-invariant Frechet distribution: F j n(z) = exp( T j nz θ ). Under this assumption, the distribution of prices in sector j of country n, conditional on { } A j mt is given by m=1,...n Gj nt(p) j {A t} = Pr(P j nt < p) = 1 exp [ Φ j ntp θ] 11 The FOC are αj β j β E[u (C t )C t ] = υl j t where υ is the multiplier for the resource constraint. 15

16 where Φ j nt = N m=1 T j m ( B j (w j mt) βj P 1 βj mt A j mt κj nmt ) θ. Given that there is a continuum of ω j in each sector, by the law of large numbers the probability that country m provides a good in sector j at the lowest price in country n equals the fraction of goods that country n buys from country m in sector j: d j nmt = T j m ( B j (w j mt) βj P 1 βj mt A j mt κj nmt Φ j nt ) θ (14) that is, d j nmt is the fraction of country n s total spending on sector-j goods from country m at time t. The equilibrium in the open economy can be defined as following. Equilibrium Definition. An equilibrium in the open economy is defined as a set of resource allocations { } { L j nt, import shares d j nit}, prices {Pnt }, { Pnt} j, and {w j n } such that, given technology { } { A j it, T j it}, aggregate endowments {Lnt } and trading costs { κint} j i) consumers maximize expected utility, ii) firms minimize costs and, iii) markets for goods and inputs clear, and iv) trade is balanced. In equilibrium, prices and quantities satisfy (15)-(21): P nt = ( ) α j J 1 ( ) j P j α j α j nt n (15) Φ j nt = ( B j) θ N i=1 T j i P j nt = ξ j Φ j 1/ θ nt (16) ( ) A j θ P 1 βj it it ( ) w j β j it κ j nit θ (17) d j nmt = (B j ) θ T j m ( A j mt ) θ ( P 1 βj Φ j nt ) θ mt w jβj mt κ j nmt ; N m=1 d j nmt = 1 (18) 16

17 w j ntl j nt = β j N m=1 dj mnt [ α j + ( 1 β j ) w j mtl j mt w mt L mt ] w mt L mt (19) w nt L nt = J j=1 wj ntl j nt (20) L j nt L nt = E t 1 ( wnl j j n j w j n L j n Equations (15)-(17) show the equilibrium prices as a function of technology and input costs resulting from firms cost minimization and consumers maximization problems. The first equation in (18) shows the value of goods from sector j bought by country n from country m as a share of total spending on goods j by country n. The second equation says that the sum of spending shares on goods j from all countries m by country n (including n itself) add to 1, that is, imports plus domestic expenditures on goods j by country n, add up to the overall spending value on goods j by country n. Equation (19) gives the value of total sales accruing to the primitive factor in sector j of country n; it already incorporates the trade balance condition, i.e., total payments for goods flowing out of country m to the rest of the world equal payments flowing in country m from the rest of the world. 12 Equation (18) expresses total value added in the economy as the sum of sectoral value added. (Real value added is given by Y nt = wntlnt P nt.) Finally, (21) expresses the resource shares as a function of expected shares, following the first order conditions in (5). The model can conceptually be solved backwards in two steps. First, for any given set 12 In formulas, J j=1 Xj mt = N J n=1 j=1 dj nmtxnt, j where X j nt is total expenditure by country n on sector-j goods. The right-hand side is the total demand by all N countries for goods produced in country m. The left-hand side is the total expenditures by country m, which, under trade balance also equals its total sales. Recall that PmQ j j m is the total purchases of goods from sector j by country m.note PmtQ j j mt, the total purchases of goods from sector j by country m. Hence: PmtQ j j mt = α j w mt L mt + 1 βj w β mtl j j mt. j ) (21) 17

18 of values for L j nt, the first five sets of equations can be solved for P nt, w j nt, P j nt, d j nmt as a function of the κ j mnts and the augmented productivity factors defined as Z j nt T j n [ ( ) L nt A j 1/β j] β j θ nt (22) Then in a first stage, we can solve for the shares Lj nt L nt. As seen, with log utility the solution for Lj n L n simplifies significantly as it is the expected value of sectoral value-added shares; in the implementation, we will use the data to pin down these expectations to further simplify the problem. C Two illustrative cases: Autarky and Costless Trade To illustrate the mechanism of diversification through trade, we analyse a one-sector version of the model (that is, the Eaton-Kortum model) under two extreme cases for which we have closed-form analytical solutions for GDP: autarky and costless trade. We accordingly drop the sector subscripts. C.1 Volatility under Autarky Under complete autarky, value added in the one-sector economy is given by (13), which can be rewritten as: Y nt (Z nt ) 1 βθ 18

19 ( ) βθ. where Z nt T n L nt A 1/β Taking log-differences around the mean (or trend value in the nt empirics), we obtain, Ŷ nt = 1 βθ Ẑnt. Thus, in the one-sector economy under autarky, shocks to value added are driven exclusively by domestic shocks to the productive capacity of the economy, Ẑ nt. The variance of GDP, V (Ŷnt) thus depends on the variance of the shocks V (Ẑnt): V (Ŷnt) = 1 (βθ) 2 V (Ẑnt). C.2 Volatility under Costless Trade Under costless trade in the one-sector economy (κ nmt = 1), GDP per capita simplifies to: 13 ( Y nt = (ξb) 1/β Z 1 N ) 1 1+βθ nt Z 1 βθ 1+βθ mt m=1 and hence GDP fluctuations are given by: Ŷ nt = [ 1 Ẑ n βθ βθ N m=1 γ m Ẑ m ] where γ m = 1 1+βθ Z m N Z 1 1+βθ i=1 i Rearranging, we obtain: is the relative size of country j evaluated at the mean of Z j s. [ Ŷ nt = 1 γ n + βθ βθ 1 + βθ Ẑn βθ N m n γ m Ẑ m ] (23) 13 View derivations in the Appendix. 19

20 Volatility under free trade is hence given by: V ar(ŷnt) = ( ) 2 1 βθ ( γn +βθ 1+βθ ) 2 V ar( Ẑ nt ) + [ 2 γ n +βθ 1+βθ 1 1+βθ ] 2 m i γ2 mv ar(ẑmt) 1 1+βθ m n γ mcov(ẑm,ẑn) (24) Compared to the variance in autarky, V (Ŷnt) = 1 (βθ) 2 V (Ẑnt)., it is clear that the volatility due to domestic productivity fluctuations, V ar(ẑnt), now receives a smaller loading, as ) 2 < 1 since γn < 1. The smaller the country (as gauged by its share γ n ), the smaller ( γn +βθ 1+βθ the impact of domestic volatility of shocks, Ẑ n, on its GDP, when compared to autarky. Openness to trade, however, exposes the country to other countries productivity shocks and these contribute positively to volatility. Whether or not the gain in diversification (given by lower exposure to domestic productivity) is bigger than the increased exposure to new shocks depends on the variance-covariance matrix of shocks across countries. If all countries have the same constant variance V ar(ẑnt) = σ, and the Ẑnt are uncorrelated, volatility in free trade becomes: V ar(ŷnt) = ( 1 βθ ) { 2 (γn ) 2 [ + βθ βθ βθ ] 2 γ 2 m m i } σ (25) which is unambiguously lower than the volatility in autarky given that 14 ( ) 2 [ γn + βθ βθ 1 + βθ 14 since (βθ) 2 + 2βθγ n + j=1 γ2 j < (1 + βθ)2 as ] 2 γ 2 m < 1 m i 2βθγ n + j=1 γ 2 j < 2βθ

21 (recall γ m < 1 and N m=1 γ2 m 1). Of course, if other countries have higher variances or the covariance terms are important, then the weights countries receive matter and the resulting change in volatility cannot be unambiguously signed. IV Mapping the model into observables The equilibrium of the model is characterized by equations (15)-(21). We solve the model numerically, for which we need to calibrate the values of the exogenous trading costs κ j nmt, the productivity process Z j nt and the parameters α j, β j, θ and η. Largely due to data limitations, we consider three sectors in the analysis: agriculture, manufacturing, and services, where the latter is treated as non-tradable (that is, κ j nmt = 0 for all n m and κ j nmt = 1 for n = m.) We set α j so as to match the average share of each sector on total final uses from the OECD Input-Output tables across all countries. The betas for each sector are calculated as the ratio of value added to total output. A detailed description in the data is available in the accompanying Appendix. We allow for a relatively broad parametric range for θ, from θ = 2 to θ = 8, consistent with the estimates in the literature (see Eaton and Kortum, 2003, Donaldson 2013, and Simonovska and Wagh, 2011). We use θ = 4 as the baseline case, and report the results for other values when discussing the sensitivity of our results. We calibrate the elasticity of substitution across varieties η = 2, consistent with Broda and Weinstein (2006). The results are not sensitive to this parametric choice. We explain next how we obtain the processes for κ j nmt and Z j it using data on sectoral bilateral trade flows, value added, output, and prices. A detailed description of the data can 21

22 be found in the Appendix. Before we specify details, here is the intuition on how these series are backed-out from the model. We recover trade costs κ j nmt using information on bilateral trade shares. Intuitively, if two countries trade little with one another, this will signal high trade costs between the countries. Second, we recover productivities relative to a benchmark country using the market share of each exporter. If a country has a high export share in a sector, that is a sign of revealed comparative advantage, i.e. high relative productivity relative to the benchmark country. To calibrate the absolute level of productivities, we use price data for the benchmark country. We explain in detail and with formulas in the next section. A Implementation Kappas In order to perform counterfactual experiments we need to back out the historical realizations of the exogenous processes. Following the idea in Head and Ries (2011), we assume that bilateral trading costs are symmetric, that is: κ j nmt = κ j mnt, and hence trade costs can be backed out from data. Indeed, inverting the structural model, we obtain: d j nmtd j mnt d j mmtd j nnt = ( κ j nmt) 2θ. (26) The left hand side objects can be measured using data on imports and gross output. Specifically, d j nmt is the value of exports from m to n in sector j at t relative to total spending by n on sector j at time t, where total spending is measured as gross output plus imports minus exports by that sector and country at time t.the share d j mmt is obtained as a residual from 22

23 the accounting restriction: N d j mmt = 1 n m d j mnt Hence, for a given value of θ, we can obtain the time series of trading costs by sectors and country pair { κ j nmt}. Productivity in tradable sectors To back out the productivities, we proceed as follows. First, using the formula for d j nm in equation (18), after some algebra, we obtain: d j nm = (Bj ) θ ( ) ψ j β j θ m Z j m (κ j nm) θ (ym) j θβj PmΦ θ j, (27) n where ψ j m Lj m Lm (27) we have: and ym j Lj mwm j P m. We can exploit this to recover Zm. j In particular, inverting Z j mt = ( ( ) θ B j) θ ( ) d j nmt y j θβ j ( ) m κ j θ P j nt (ψ ) j θβ j nmt mt P mt (28) Dividing the productivity Z j mt of exporting country m on that of exporting country 0, we can get rid of P j nt: Z j mt Z j 0t = dj nmt d j n0t ( ) y j θβ j ( m y j 0 κ j nmt κ j n0t ) θ ( ) ( θ P0t P mt ψ j 0t ψ j mt ) θβ j (29) For n = 0, equation (29) becomes: Z j mt Z j 0t = dj 0mt d j 00t ( y j mt y j 0t ) θβ j ( ) ( ) (κ ) θ θβ j θ P0t ψ j j 0t 0mt P mt ψ j mt (30) 23

24 and hence Ẑ j mt = Ẑj 0t + ( ˆd j 0mt ˆd j 00t) + θβ ( ) j ŷm j ŷ j 0 θ (ˆκ j0mt + ˆP 0t ˆP ) mt + θβ (ˆψj j 0t ˆψ ) j mt (31) Thus, for a given series of changes in country 0, Ẑ0t, j we can recover the changes for every other country m, Ẑj mt, using data on changes in trade shares ˆd j 0mt, sectoral value added, ŷm, j GDP deflators ˆP mt, value added shares, ˆψ j mt, and trade costs ˆκ j 0mt (retrieved above). To recover Ẑj 0t, note from (28) that Z j 0t = ( ( B j) θ ( ) d j 00t y j θβ j 0t P j 0t P 0t ) θ (ψ ) j θβ j 0t (32) and hence Ẑ j 0t = ˆd ( j 00t + θβ j ŷ j 0t θ ˆP j 0t ˆP ) 0t θβ j ˆψj 0t (33) If we take country 0 to be the US, we only need additional data on sectoral GDP deflators for the US to recover the changes in Ẑj 0t.(Note that we do not need sectoral deflators for other countries.) To initialize the level of Z j 0t at t = 1972, note that we can choose the units of account of sectoral output so that P j = 1 j.(we take 1972 as the first year for our quantitative exercise in order to maximize country coverage, as there were countries without data for ). That is, at time t = 1972, for the US, units of measures in each sector are such that the price of the composite sectoral good is 1;this normalization implies that 24

25 the aggregate price in 1972 in the US is also 1 and Z j = d j ( ) y j θβ j ( ) 1972 ψ j θβ j (34) Formulas (33) and (34) yield the full series { Z j 0t}. To initialize Z j mt Z j 0t in 1970, we use the PWT relative price of output in that year: Z j m1972 Z j = dj 0m1972 d j ( y j m1972 y j ) θβ j ( ) ( ) (κ ) θ θβ j θ P01972 ψ j j m1972 P m1972 ψ j m1972 (35) Formulas (31) and (35) yield the panel of { Z j mt} for all other countries. Productivity in nontradables Because we treat services as nontradables in our quantitative analysis, to back out its productivity across countries and over time, we need to make use of additional equations from the structural model. In formulas, for services j = s, d s nm = 0 if n m and d s nm = 1 if n = m. To recover {Zmt}, s we proceed as follows. From equation (16) and (17), and using the formulas for { Zmt} j for tradables backed out above, we can obtain the aggregate sectoral prices for tradables j s as: P j nt = ξ j [ Φ j nt ] 1/ θ (36) where Φ j nt can be obtained as Φ j nt = (ψj nt) β j θz j nt(ynt) j θβj d j nt P θ nt, from (27) using m = n. Using the aggregate relative price levels from the PWT, we can recover the price level for services from 25

26 equation (15) and we can thus obtain the productivity series for the services sector as: Z s mt = [ ( ) ξ s Pmt (y sm) ] θ βs Pm s Intuitively, backed up levels of productivity in services would be high when we observe high value added and low relative prices in the sector. Sectoral versus aggregate shocks Note that the changes in productivity retrieved above, 1 β j Ẑm j 1 θ β j Âj mt + ˆL mt, (37) can be decompose into two factors: a sectoral factor, 1 β j Âj mt, and an aggregate factor ˆL mt. The interpretation of L mt as equipped labour means that it embeds a productivity component too. Given the functional form, the split between pure productivity and resources in L mt is not relevant from the point of view of aggregate volatility. (Equivalent, a shock in L mt will be equivalent to an aggregate shock to A j mts that leaves the relative productivities A j mt/a j mt unchanged j, j. For identification, we impose the restriction that α j β j Âj mt = 0. (38) Thus, changes in the sectoral productivity will correspond to changes in the relative weight of A j mt, while changes in aggregate productivity (affecting all sectors equally), as well as changes in overall resources, will be subsumed in L mt. We hence call sectoral shocks, those affecting Âj mt and aggregate shocks those affecting the aggregate factor ˆL mt. The identi- 26

27 fication restriction implies that any primitive aggregate shock affecting all sectors will be collected in ˆL mt. Summary of Procedure We can summarize the procedure as follows. 1. Obtain the κs from (26). 2. Compute ψ j mt as the sectoral value added share at time t. 3. Retrieve { Z j mt} from formulas (33), (34), (31), and (35) Retrieve L mt from (37) using (38) and compute L j mt = ψ j mtl mt. 5. Solve the equilibrium values of { d j nit}, {Pnt }, { P j nt}, and {w j n } using (15) to (20). B Counterfactuals We discuss next how we compute the equilibrium in the counterfactuals and how we identify the two mechanisms in the model. Numerical counterfactual equilibria We also need to solve for counterfactual equilibria. For each new value of κ, and the estimated sequence of { Z j mt}, we need to solve for the sequence of { L j mt}.the rational-expectations equilibrium is a fixed point of a below mapping on the space of all possible { L j mt} sequences. We proceed as follows. 1. Pick a set of { L j mt}. Given that {Lmt } is exogenous (but changing over time), this amounts to picking J 1 sectoral shares for each country in each year. 15 Units of accounts are chosen so that nominal sectoral prices in the US in 1970 equal 1. 27

28 2. Solve for w j mt using equations (15) to (20). 3. Run the regression w j mtl j mt/w mt L mt = exp(γj m + δ j mt) k exp(γk m + δ k mt) + ej mt 4. Obtain the prediction from the regression, and use it as a proxy for E t 1 (w j mtl j mt/w mt L mt ). 5. Set ˆL j mt = L mt E t 1 (w j ntl j mt/w nt L mt ). Compare ˆL j mt with the initial guess { L j mt}. If the sum of squared deviations are below stop. If not, go back to step (1). Productivities in counterfactual scenarios We are interested in decomposing the trade effect on volatility on the contributions of the two mechanisms, specialization and diversification. To achieve that, we need to identify the sources of shocks to productivity. We resort to a factor model that decomposes productivity shocks into these two components as follows. We proceed as follows. For each year t, we regress the de-meaned growth in log-productivities Z j n,t = log Z j n,t log Z j n,t 1 on sector and country specific effects: Z j n,t = β n,t + β j t + ξ j n,t where the βs are time-varying country and sector dummies effects with the restriction n β n = 0, that is the country effect is expressed relative to the world. β n,t is the countryspecific factor, affecting all sectors within the country; β j t is the global sectoral factor, affecting sector j in all countries; ξ j n,t is the idiosyncratic components, specific to the country and sector. 28

29 In the counterfactual exercises, we mute the country or sector factors by setting the corresponding βs equal to 0. V Quantifying the Effect of Trade on Volatility In this Section we seek to answer the two motivating questions. First, how would a move to free trade in manufacturing and agriculture affect volatility? Second, how have actual changes in trade costs from the early 1970s to 2007 affected volatility patterns? A Free Trade in Agriculture and Manufacturing The answer to the first question is summarized in Table 1, which is based on our benchmark calibration with θ = 4. Column (1) in the Table shows the volatility generated by the model. Volatility is computed as the standard deviation of annual growth rates over 35 years. This value is very close to the actual volatility experienced by these economies from 1972 through 2006, since the trading costs and productivity processes fed into the model are backed out from the data. Column (2) shows the volatility that would prevail if there were no global sectoral shocks. (Note that the latter is not always smaller than the benchmark volatility, as global sectoral shocks can covary negatively with country-specific shocks in some countries.) Computing this counterfactual measure is useful to assess the mechanisms through which trade affects volatility as it will become clear next. Column (3) shows the volatility that would prevail under free trade in manufacturing and agriculture and Column (4) shows this latter measure in the absence of global sectoral shocks. The last three columns in the Table allow us to assess the effect of trade on volatility and the contribution of the two mechanisms. 29

30 Specifically, column (5) measures the percent change in volatility that would be obtained if all trade barriers in manufacturing and agriculture were removed, that is, the percent difference between the figures in columns (3) and (1). Columns (6) and (7) decompose the volatility change induced by free trade into two components: the volatility change due to higher specialization (column 6) and the volatility due to higher diversification across country (column 7). The change in diversification is computed as the difference between the volatility in the absence of sectoral shocks (column 2) and the volatility under free trade in the absence of sectoral shocks (column 4); the difference is expressed relative to the benchmark volatility. The volatility due to specialization is simply the difference between columns (5) and (7). As Table 1 shows, virtually all countries in our sample would experience an increase in volatility if all barriers to trade in manufacturing and agriculture were removed. The biggest decrease in volatility would be experience by Mexico, which would see a reduction in volatility of 14 percent. The table points to significant heterogeneity in the magnitude of the effect. However, in most cases, the decline in volatility is driven by the diversification through trade. Changes in volatility due to changes in specialization have generally very little effect in volatility. Table 2 shows the change in volatility due to free trade and its decomposition for two other values of θ, θ = 2 and θ = 4. The general message is qualitatively robust: volatility in general would decline with a move to free trade in agriculture and manufacturing, with the volatility decline being higher for lower values of θ. The magnitude of the effect depends on the exact value of θ. 30

31 B Historical Changes in Volatility due to Trade Trading barriers have following significantly since the earlier 1970s. This decline in barriers (increase in κ) is illustrated in Figures 3 and 4, which show, correspondingly, the histograms of bilateral κs in manufacturing and agriculture in the first and last year of our sample. As the figure shows, the distribution of κ has moved to the right, indicating a decline in trading costs in both sectors. Table 3 investigates how these changes in trading costs since the 1970s have affected volatility in our sample of countries. Column (1) shows the average volatility in the baseline model using the calibrated kappas and the process of shocks, as explained in Table 1. Column (2) shows the level of volatility in our baseline model, after removing common sectoral shocks. Column (3) shows the average volatility under the assumption that trading costs stayed at their 1970s levels. Column (4) is similar to (3), after removing common sectoral shocks. Column (5) shows the percent change in average volatility due to actual changes in trading costs since the 1970s, that is, the percent difference between columns (1) and (3). Column (6) shows the contribution of specialization to the change in volatility in (5). Column (7) shows the contribution of diversification to the change in volatility in (5). As the table illustrates, based on a calibrated value of θ = 4, most countries experienced a decline in volatility due to trade; the average effect is relatively small, though there is non-negligible variation across countries, with some, such as Ireland and the Netherlands, seeing a material reduction in volatility. Interestingly, this result masks two opposite effects: on the one hand, volatility has increased due to higher volatility in all countries; on the other hand, volatility has declined due to the diversification mechanism. On net, the effect is a decline in volatility, as the quantitative contribution of the specialization channel is relatively 31

32 small. The findings thus cast doubt on the premise that openness to trade invariably leads to higher volatility. Table 4 shows the results for alternative values of θ. The sensitivity of the results is not negligible. Indeed, this exercise underscores the importance of this parameter and adds to the message of Arkolakis, Costinot, and Rodriguez-Clare (2012): to assess the effects of trade on key aggregate variables, the elasticity of trade to trade costs plays a key role. For θ = 2, the declines in volatility due to trade is as high as 48 percent in the case of the Netherlands. Low values of θ also exacerbate the heterogeneity in the effect of trade on volatility, questioning empirical estimates in the literature that do not allow for heterogeneity in this effect. Interestingly, in virtually all cases, the specialization mechanism contributed to higher volatility, although this effect is not quantitatively large. Most remarkably, the decline in volatility due to trade stems from the diversification channel, which counteracts the effect due to higher sectoral specialization, leading to a net decline in volatility in most countries. For θ = 8, the effects of international trade on volatility are generally very small, though specialization generally leads to higher volatility and diversification leads to lower volatility. VI Conclusions How does openness to trade affect GDP volatility? This paper revisits the common wisdom that trade increases volatility by leading to higher sectoral specialization. It argues that when country-specific shocks are an important source of volatility, openness to international trade can lower GDP volatility as it reduces exposure to domestic shocks and allows countries to 32

33 diversify the sources of demand and supply across countries. Building on Eaton and Kortum (2002) s quantifiable model for trade, the paper assesses the effect of trade on volatility and the role played by the two mechanisms, sectoral specialization and country diversification. A key finding of the paper is that reducing trade barriers in agriculture and manufacturing reduces volatility in most countries. The reduction in volatility, however, varies significantly across countries. This general decline in volatility due to trade is the net result of the two different mechanisms, sectoral specialization, and country-wise diversification. The latter effect tends to be quantitatively stronger and thus explains the tendency for a net decline in volatility with trade. The model sheds light on why the magnitude of the trade effect may differ across countries, depending on size, sectoral composition, trading partners, and the variance-covariance of shocks, among others. 33

34 VII Figures and Tables Standard deviation of per capita consumption growth Figure 1: Output and Consumption Growth Volatilities GNQ GAB TKM LBN OMN GNB LBR ATG AGO GUY SDN AFG BIH BRN GEO MNE MNG KIR NERMHL NGA SWZ SLB PNG SLE STPPLW QAT TJK UZB ERI BHS TTO GMB KGZ SYCHRV ZWE ZMB VCT TON LBY KNA LCA BDI GRD JOR MWI MDA YEM AZE NAM ALB BFA MRT SOM SYR SVK ETH BTN KHM BHR TLS WSM BMU ARE SAU FJI FSMLSO EST VUT KAZUKR BWA IRNIC ZAR RWA TZA BLZ CUB ARG HTI PAN CYP CHL COG COM CZE DZA MOZ DMA KEN MDG MUS MLI VEN TCD CIV BRB BEN CMR BLR GHA LKA HNDOM LAO JAM LTU MDV MKD GINCAF ISL MYS PER URYTGO RUS PAK TUR UGA CPV LVA MLT POL ROM PRY BGDCH2 BRA MAR COL CHN HKG IDN SVN SLV BGR CRI MEX EGYSEN KOR MAC NPL ISR HUN PRT THA SGP VNM ECU TUN ZAF ARM BOL IND GTM FIN IRL TWN AUT DNK ESP GRCPRI LUX NLD NOR NZL GBR CAN ITA GERSWEBEL JPN PHL USA AUS CHE FRA Standard deviation of per capita GDP grow th DJI

35 Standard deviation of consumption growth Figure 2: Output and Consumption Growth Volatilities DJI OMN TKM GAB GNB ATG AGO GUY SDN BRN GEO MNE MNG BIH AFG KIR NER MHL NGA SWZ PNG STPPLW SLE SLB QAT ERI TJK UZB BHS GMB HRV ZWE TTO KGZ SYC ZMB VCTTON KNA MDA LBY LCA YEM BDI AZE BFA BTN ETH GRD SYRMWI TLS MRT JOR EST BHR KHM NAM WSM SVK SOM BMU ARE BWA ALBFJI LSO VUT KAZ UKRNIC ZAR IRN TZA BLZ PAN CUB VEN ARGDZA COG COM CHL CYP BRB CIV CZE DMA FSM TCD KEN HTI MOZ MDG MUS MLI RWA LAO BEN CMR BLR GHA LKA CAF DOM JAM SAU URYTGO LTU MDV MKD MYS PER UGA PAKTUR CPV LVA GINMLT ISL POL ROM RUS PRY BRA SLV BGD COL CH2 SVN IDN HKGBGR MAR CRI EGY CHNHND HUN ISR MEX KOR NPL THA VNM PRT SEN SGP TUN ECU ZAF BOL IND TWN IRL FIN ARM MAC GTM GRC DNK ESP NLD NOR NZL PRI AUT GBRITA JPN LUX CAN BEL PHL GER SWE USA CHE AUS FRA LBR LBN GNQ Standard deviation of GDP grow th

36 Figure 3. Histogram of bilateral κ in Manufacturing. Years 1972 and

37 Figure 4. Histogram of bilateral κ in Agriculture. Years 1972 and