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2012; University of Chicago Press; Volume: 8; Issue: 1 Linguagem: Inglês
10.1086/663659
ISSN2150-8372
Autores Tópico(s)Global Financial Crisis and Policies
ResumoPrevious articleNext article FreeCommentAssaf RazinAssaf RazinCornell University, Tel Aviv University, and NBER Search for more articles by this author PDFPDF PLUSFull Text Add to favoritesDownload CitationTrack CitationsPermissionsReprints Share onFacebookTwitterLinked InRedditEmailQR Code SectionsMoreThe main contribution of the Di Giovanni and Levchenko paper is the development and estimation of a mean-variance measure of riskiness for the export sectors. This measure is potentially useful for the analysis of the trade-off between sectoral specialization, according to comparative advantage, and sectoral output volatility. Research in the comparative advantage-risk trade-off goes back four decades ago. Brainard and Cooper (1968), Kemp and Liviatan (1973), and Turnovsky (1974), introduced technological uncertainty into the deterministic Ricardian and Heckscher-Ohlin models of international trade. They quickly found that some of the main propositions of comparative advantage break down in the presence of uncertainty. As it turned out, the absence of tradable means for international risk sharing is the reason. A risk-averse representative consumer diversifies the economy’s factor allocation across sectors instead of a portfolio of tradable securities. Trade in financial assets permits a separation of factor allocation across sectors, which is done by stock market maximizing firms (from risk-averse households) choosing the portfolio of risk-sharing assets. In my early research with Elhanan Helpman (Helpman and Razin 1978), this is indeed how we resolve the nonspecialization puzzle, and the apparent breakdown of major international trade theorems under uncertainty. But Di Giovanni and Levchenko (2011, in this volume) model the comparative advantage-risk trade-off by assuming the existence of international trade in goods, but no international trade in risk-sharing assets. They derive a U-shaped relationship between the export’s industry concentration and comparative advantage measures. The U-shaped relationship is the focus of their empirical analysis. I. The Comparative Advantage-Risk Trade-off: Diagrammatical ExpositionConsider a Ricardian economy trading in two goods, R and S, with stochastic productivity coefficients, θS and θR. Let cidenote consumption of good i, and zi denote the portfolio share of stock i; i = R,S. Prices are piand qi, respectively. The representative consumer budget constraint, after uncertainty resolves, is given by:(1)cS+pRcR=θSzS+θRpRzR,yielding the representative consumer indirect utility function:(2)v(θSzS+θRpRzR;pR).The ex ante (that is, before the uncertainty resolves) asset-indifference curve is defined by E{v(θSzS+θRpRzR;pR)}=constant,where E is the expectation operator.In equilibrium, the asset-indifference-curve MRS is equal to the relative price of stock R in terms of stocks:(3)qR=E{vR(θSzS+θRpRzR;pR)}E{vS(θSzS+θRpRzR;pR)}.The representative firm maximizes its stock market value by choosing the supply of stock Zi, i = R,S, as follows: (4)MaxZS+qRZRs.t.LS+LR=1where Li is labor employed in sector i, i = R,S.Asset indifference curve is tangent to the linear transformation curve in the financial autarky case (see figure 1). Fig. 1. Composition of industrial production under financial autarky and trade in assets.View Large ImageDownload PowerPointUnder financial autarky the equilibrium allocation is diversified between the sectors. Now, shifting the joint probability distribution function of (θS,θR), by preserving the spreads but changing the first moments of the distribution, in favor of sector S (thereby strengthening comparative advantage) would change the slope of the asset indifference curve in the direction of specialization in S. A U-shaped relationship between sector diversification and comparative advantages ensues, like the Di Giovanni–Levchenko mean-variance relationship.However, in the presence of international trade in assets q¯R is exogenous, determined in the world market. The pursuit of stock market value maximization by firms leads to complete specialization in sector S. All labor is allocated to sector S, as shown in the figure. Comparative advantage reigns supreme and the U-shaped relationship between sector diversification and comparative advantages is gone.II. Measure of Risk Content of ExportsThe paper provides measures of how countries differ in the riskiness of the export commodity composition. To do this, the authors estimate the entire variance-covariance matrix of sectors. Then, they use export shares for each available country and time period to construct a summary measure of riskiness of a country’s export commodity structure (as in the Heckscher-Ohlin-Vanek factor Content of Trade). Using annual data on industry-level value added per worker growth over 1970–1999 for C countries and I sectors, they let yict be the value added per worker growth in country c, sector i , between time t –1 and t. They then construct the expressions:y˜ict=yict−1T∑t=1Tyictyict=1C∑c=1Cy˜icty˜ict: The cross-country average for each year and sector. The variance for each sector:σi2=1T−1∑t=1T(yit−y¯i)2.The covariance for each combination of sectors along the time dimension:σij2=1T−1∑t=1T(yit−y¯i)(yjt−y¯i).The resulting estimate gives a 30 × 30 variance-covariance matrix of sectors, denoted ∑.Decomposition of the Risk Content of ExportsThe risk content of exports is defined by:RCXct=actX′ ∑actXwhere actXis the share of each sector in total exports for each country and year; and actX is the 30×1 vector ofaictX. Authors are now able to provide a decomposition of the Risk Content of Exports:actX′∑actX=σ¯2∑i=1ℐ (aictX)2︸Herfxct+2a¯X∑i=1ℐ aictXσi2︸MeanRiskct+2 ∑j≠iℐ ∑i=1ℐ aictXajctXσij︸Covariancect+∑i=1ℐ (aictX−a¯X)2(σi2−σ¯2)︸Curvaturect−2a¯Xσ¯2︸Constant.The first term, Herfx, captures simple diversification that ignores riskiness differences across sectors. The second term, Mean Risk, is the average variance of a country’s exports. It is intended to be a complement to the “pure diversification” measure Herfx. The third term captures the covariance effect, or the off-diagonal components of ∑, which are generally insignificant.The fourth term, Curvature, captures the interaction between Herfx and Mean Risk. In a perfectly diversified economy, or when all sectors have the same variance, Curvature is zero. Curvature becomes positive when the economy specializes in riskiest sectors. Thus, specializing in safe sectors results in the negative Curvature. The last term, Constant, is common to all countries.III. A CaveatTheory tells us that the sectoral allocation of factor of production must depend on a more comprehensive measure of risk, covering all sectors of the economy, akin to Koren and Tenreyro (2007). All-sector variance-covariance matrix may have an effect on the commodity concentration of exports.IV. Measure of Revealed Comparative AdvantageAuthors construct a proxy for the strength of comparative advantage based on the Balassa (1966) measure of “revealed comparative advantage.” Key assumption is that the larger is the share of world exports that the country captures in a sector, the stronger is its comparative advantage in that sector.Using the Balassa (1966) measure, constructed under deterministic setups, the authors construct a risk-weighted comparative advantage as:RiskCAct=∑i σi2(Xict/XiWt1/l ∑i(Xict/XiWt))Xict are country c’s exports in sector i.XiWt are country world’s exports in sector i.σi2 is the sector-level volatility.Xict/XiWt is the share of world exports in sector i captured by country c, which normalized by the average share of world exports captured by the country.V. A CaveatThe standard concept of comparative advantage has to do with relative productivities and relative endowments. But absent data on technologies and endowments, many researchers are using a revealed measure, based on export shares. One problem is that having exports and imports within sectors the choice for shares could be based on gross exports or net exports, with no guidance from theory. Another problem is that export shares reflect fundamental factors underlying comparative advantage, trade barriers, riskiness of the export sectors compared to the riskiness of nonexport sectors, and the intersector correllations.Under uncertainty this is an ex post (that is, after uncertainty resolves), and not an ex ante measure, as theory guides us. To repeat, export shares under uncertainty by themselves reflect, in addition to comparative-advantage measures, the consumption patterns of trading countries and trade frictions. (Anderson and Van Wincoop [2004] estimate trade-friction costs as 70% of export costs.) Export shares also reflect riskiness—the very concept authors try to isolate out of the measure. VI. A (Nonparametric) EstimationAuthors use the Lowess procedure on cross-sectional data for Herfx and RiskCA, as well as five-year panel data.They estimate the regression equation: Herfxct=γ′cXct+g(RiskCAct)+ϵctg(RiskCAct) captures the non-linear relationship between Herfxct and RiskCActwhere Xct is a matrix of controls variables.They estimate a bivariate lowess between Herfxctand RiskCAct, and between each of the controls Xct and RiskCAct. Retain the residuals, denoting them H^erfxct and X^ct. They regress H^erfxct on X^ct, using OLS to obtain an unbiased estimate of γc. They use the estimated γ^cto purge the influence of the additional controls fromHerfxct: H^^erfxct= Herfxct – γ^′cXct. Proceeding further, they apply Lowess to H^^erfxct and RiskCAct to estimate the nonlinear relationship, g∙, between specialization and risk-weighted comparative advantage. The estimated relationship looks U-shaped (see figure 2).Fig. 2. Export concentration and riskView Large ImageDownload PowerPointThe estimated U-shaped relationship does not fit the data well. There are multiple ommitted variables, such as the volume of trade in financial assets and trade barriers, which are potentially accountable for the poor fit. VII. Global Allocation of Investment in CapacityPotentially important omitted variables are measures of the global allocation of investment through foreign direct investment.The global allocation of investment in capacity under uncertainty is analyzed by Grossman and Razin (JPE 1984 and IER 1985). We analyze the determinants of such international movements in a model with uncertainty and international trade in goods and securities. In our model, the world allocation of capital is governed, to some extent, by the asset preferences of risk-averse consumer-investors. In a one-good variant in the spirit of the MacDougall model, we find that relative factor abundance, relative labor force size, and relative production riskiness have separate but interrelated influences on the direction of equilibrium capital movements. These same factors remain important in a two-good version with Heckscher-Ohlin production structure. In this case, the direction of physical capital flow is determinate (unlike in a world of certainty) and may hinge on the identity of the factor that is used intensively in the industry with random technology. In essence, comparative advantage and global allocation of investment in capacity are jointly determined. 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