International Trade Field Exam August 2008 Answer any 5 of the following 6 questions. You have 4 hours to omplete this exam. 1. The Heksher-Ohlin-Vanek theorem (that a ountry is a net exporter of the servies of its relatively abundant fator(s) and a net importer of the servies of its relatively sare fator(s)) follow immediately from the H-O-V equation: where F = V s V F is ountry s vetor of net trade in fator servies (e.g., f j is the V is j th element of ountry s vetor, representing the net trade in fator j), the vetor of ountry s fator endowments, V the vetor of world fator endowments, and s is a salar representing ountry s share of world onsumption. (a) In this ontext, define (algebraially) what it means for ountry to be abundant in fator j. (b) Assuming balaned trade, how would one alulate s? (Hint: Let be world inome, and let be ountry s inome.) C Y Y () Suppose that trade is not balaned, and define surplus. How is s alulated in this situation? B as ountry s trade (d) One ruial assumption in deriving the H-O-V equation is that all onsumers everywhere have idential, homotheti preferenes. hy is this assumption important? i.e., how is it used in deriving the H-O-V equation? (e) One ruial assumption in deriving the H-O-V equation is that there are at least as many goods as there are fators of prodution. hy is this assumption important? (f) One ruial assumption in deriving the H-O-V equation is that all ountries have idential tehnology. In his JPE paper ( International Fator Prie Differenes: Leontief as Right!), Trefler allowed tehnology to differ aross ountries. In partiular, he formulated the following variation of the H-O-V equation:
' ' ( ) F =Π V s Σ Π V ' where Π is a matrix (speifi to ountry ) suh that all off-diagonal elements are zero and the diagonal element of the j th row represents the produtivity of fator j in ountry relative to that of some base ountry. Trefler then used data on the fator ontent of trade and on fator endowments for a set of ountries to alulate elements of Π suh that the data exatly fit the modified H-O-V equation without error. This does not permit Trefler to use standard tehniques of statistial inferene to test the model, but he argues that his results are supportive of the H-O-V model. On what basis does he make his argument? (g) The following box diagram illustrates the integrated world equilibrium where E represents the U.S. endowment of two fators (K and L) and E represents the world endowment of the same two fators. The line passing through E is a budget line. Assume that all of the assumptions of the H-O-V theorem hold. hat is the slope of the budget line? v K E v K E v L v L (h) Reprodue the diagram above in your blue book. Assume that the U.S. is a net exporter of both apital and labor servies, but all other assumptions of the H-O-V model ontinue to hold. Draw in an appropriate point representing U.S. onsumption of fator servies and show geometrially how to measure the net exports of both apital and labor servies. 2. The Melitz model of international trade with heterogeneous firms extends Krugman s model of monopolisti ompetition by modeling firms that differ in their produtivities. The following questions onern this extension.
(a) Melitz onsiders the ase of a representative onsumer with a CES utility funtion, in whih ase individual firms fae onstant-elastiity demand funtions. For Krugman s model with this partiular assumption, what an we onlude about the gains from trade? hat form do they take? Are there always gains from trade, or an losses our? Explain, using either an algebrai or graphial analysis. (For a graphial analysis, you do not need to derive the partiular urves that you are drawing, but you should explain what they represent, and provide a verbal explanation of their shapes.) (b) Both Krugman and Melitz model the entry and exit of firms into the industry. ith an unlimited number of firms willing to enter the industry if they expet to earn non-negative profits, how is it possible for high- and low-produtivity firms to both produe output in the Melitz model? Explain, inluding a desription of the relevant equilibrium onditions. () Melitz models export osts and onludes, the paper shows how the export osts signifiantly alter the distribution of the gains from trade aross firms. Desribe how and why the gains and losses from trade are distributed aross different types of firms, inluding whih firms gain market share and whih lose market share. (d) Does trade ause additional types of firms to enter the industry, or does it redue the number of types produing in the industry? Explain arefully. 3. During the 1980s, the U.S. distribution of inome beame more unequal, with real inomes inreasing for those at the top of the distribution, and real inomes stagnating or falling for those at the bottom of the distribution. Two auses have been suggested: skill-biased-tehnial hange (SBTC) and rapid expansion of trade, partiularly with low-inome ountries suh as China and India. (a) Assume that there are two fators of prodution (skilled and unskilled good). Draw the demand for skilled workers relative to the demand for unskilled workers in this two-setor eonomy. Explain the shape of this relative demand urve. (b) hat is the mehanism by whih the addition of an eonomy like China (abundant in unskilled workers) affets unskilled wages relative to skilled wages in the U.S.? Combine a urve illustrating the supply of skilled relative to unskilled workers with the relative demand urve illustrated in part (a) to illustrate your answer. hat is the evidene regarding the effet of this mehanism?
() Additional evidene suggests that similar hanges in inome distribution ourred throughout the world in both high-inome and low-inome ountries. Does this additional evidene support or refute the notion that the hanges were aused by the integration of China and India into the world eonomy? (d) Assume that there are two fators of prodution (skilled and unskilled good). How would SBTC affet the wages of skilled relative to unskilled workers if the hange ourred only in the skill-intensive setor? Combine a urve illustrating the supply of skilled relative to unskilled workers with the relative demand urve illustrated in part (a) to illustrate your answer. (e) Assume that there are two fators of prodution (skilled and unskilled good). How would HICKS-NEUTRAL tehnologial hange affet the wages of skilled relative to unskilled workers if the hange ourred only in the skill-intensive setor? Combine a urve illustrating the supply of skilled relative to unskilled workers with the relative demand urve illustrated in part (a) to illustrate your answer. (f) Assume that there are two fators of prodution (skilled and unskilled good). How would a small amount of immigration of unskilled workers (entering the U.S.) affet the wage of skilled workers relative to unskilled? How would a large amount of the same sort of immigration affet the wage of skilled workers relative to unskilled workers? In this ontext, what is the natural way to define small versus large? Combine a urve illustrating the supply of skilled relative to unskilled workers with the relative demand urve illustrated in part (a) to illustrate your answer. (g) Assume that there are two fators of prodution (skilled and unskilled workers), but now assume that all output is aggregated to a single omposite ommodity. Show how this affets the relative demand and relative supply for skilled versus unskilled labor, and show how skillbiased tehnial hange affets the wage of skilled workers relative to the wage of unskilled workers. 4. The following questions onern the horizontal and vertial multinational enterprises (MNE s) (a) Explain the differene between horizontal and vertial MNE s
(b) hat onditions lead to the existene of vertial MNE s in Helpman s model? Explain arefully. For a omplete answer, use the appropriate diagram. () hat onditions lead to the existene of horizontal MNE s? Use the model(s) developed by Markusen. (d) hat does the empirial evidene tell us about whether horizontal or vertial MNE s are most important in the world eonomy? (e) Helpman s model of vertial MNE s an also be used to partially explain outsouring, but it does not explain why firms would outsoure rather than use foreign diret investment. Provide a brief explanation for the hoie of outsouring that has appeared in the more reent literature. 5. The GDP funtion for the eonomy an be defined as N (, ) max ( ) N i 1 i i i i 1 i G p V = Σ p x v subjet to v = V where p = ( p p ) and V ( V V ),, 1 N =,, 1 M are the prie and endowment vetors. To estimate the GDP funtion for the eonomy, a onvenient approximation of the GDP funtion is the translog funtion whih an be written as 1 ln G = α +Σ α ln p +Σ β lnv + Σ Σ γ ln p ln p 2 1 M M N M + Σk= 1Σ l= 1δkl lnvk lnvl +Σi= 1Σk= 1φik ln piln Vk. 2 N M N N 0 i= 1 i i k= 1 k k i= 1 j= 1 ij i j (a) To ensure that the translog GDP funtion is homogenous of degree one in pries and endowments, what requirements should be imposed on the parameters? (b) Derive the output share of setor i in GDP in terms of pries and endowments. Then ompute the Rybzynski elastiities. () Harrigan (AER, 1997) applies the translog GDP funtion to estimate the effets of tehnology and endowments on international speialization. He assumes Hiks-neutral differenes in the industry prodution funtions. Denote industry prodution funtions by xi = Ax i i( vi), where A i may differ aross ountries. (Note that ountry indexes are suppressed.) Show how the translog GDP funtion should be modified. Also derive the output shares of setor i in GDP in terms of pries, tehnology, and endowments.
(d) Harrigan (AER, 1997) regresses industry output shares on endowments and the industry-level total fator produtivity (a measure of tehnology differenes). He onsiders six fators: two types of apital (produer durables and nonresidential onstrution), three types of labor (higheduated with some postseondary shooling, medium-eduated with some high shool, and low-eduated without high shool), and arable land. He also distinguishes seven major manufaturing setors: Food, apparel, papers, hemials, glass, metals, and mahinery. hat are our expetations of the oeffiients on endowments and total fator produtivity for different industries? 6. Consider small two-fator eonomy that an produe two goods (apitalintensive X and labor-intensive Y). Let Y be the numeraire good, aut P represent the autarky prie of X, and P the world prie of X. Assume aut that P < P. Finally, let w be the market-learing wage given P. (a) Suppose that the government sets a minimum wage wmin > w. Explain why the eonomy might ahieve full employment in autarky if P aut is suffiiently low. (Hint: Apply the Stolper-Samuelson theorem.) (b) Draw the market frontier (i.e., the prodution possibilities frontier distorted by the existene of the minimum wage) for this eonomy if it were open to trade. Explain its shape. () Explain how introduing trade an result in lower soial welfare for this eonomy ompared with autarky. Illustrate using ommunity indifferene urves and the market frontier that you drew in answer to part (b). (d) Now suppose that there are two ountries. The minimum-wage ountry is alled Europe. The other ountry, alled Ameria, has no legally-binding minimum wage. Further suppose that the minimum wage binds in Europe even in the absene of trade, so that in autarky Europe experienes some unemployment. Further suppose that the equilibrium Amerian wage is less than the European wage (set by the European government) in autarky. If the two ountries trade with eah other, whih ountry will have the omparative advantage in the relatively labor-intensive good? Explain why. (e) Given the assumptions of part (d), what happens to European and Amerian wages (relative to autarky wages) one trade is permitted? Explain. (f) Given the assumptions of part (d), what happens to European and Amerian employment one trade is permitted? Explain.