9 AN ACCOUNT OF GLOBAL FACTOR TRADE Global Factor Service Trade The FPE theory is extraordinarily ambitious It proposes to describe the endowments technologies production absorption and trade of all the countries in the world The HOV theorem predicts that a country s net export of factor services will equal the di erence between its endowment and the average endowment for a country of that size Leontief 1953 found a paradox United States relatively capital abundant but a net importer of capital services Maskus 1985 dubbed the paradox commonplace not an artifact of countries time periods etc Bowen et al 1987 argued that the theory does no better than a coin toss at predicting the factor content of exports Tre er 1995 identi es the mystery of the missing trade the amount of factors traded indirectly though trade in goods is much smaller than the volume suggested by theory He nds rejects the standard theory in favor of a modi cation that allows for a home bias in consumption and di erences in technologies across countries Gabaiz 1997 shows that even these modi cations of the theory do not t the data well Empirical work has failed to nd simple amendments to the theory that make it match the data If you have faith in the theory then you consider the model so intuitive that you would wonder how it could AN ACCOUNT OF GLOBAL FACTOR TRADE 1 ever be wrong If you have faith in the data then you consider the evidence so overwhelming that you would wonder why any more needs to be done This paper shows that the HOV model is down but not out that it can jump back up and win the ght But how can the ght still be won This paper gathers richer information about technology di erences across countries Previous studies generally had technology data for just the United States and no information on how consumption di ered across countries Here there is su cient data on technology and absorption to estimate a structural model and impose the resulting restrictions on the model One by one these assumptions can be relaxed to determine precisely where the problems with tting the model to the data occur The end result nds that countries export their abundant factors in roughly the correct magnitude so the study nds strong support for a suitably amended version of the HOV theory Theory We begin with a quick review of the factor content predictions of the standard HOV model Standard HOV Model Suppose the standard assumptions are met 1 The markets for goods and services are perfectly competitive 2 The number of traded goods is at least as large as the number of nontraded factors 2 AN ACCOUNT OF GLOBAL FACTOR TRADE 3 The distribution of endowments is consistent with all countries producing all goods 4 All countries have identical constant returns to scale production functions 5 There are no barriers to trade and transportation costs are zero 6 All countries share the same homothetic preferences over the goods Under FPE all countries will use the same techniques of production captured by the matrix of total factor inputs B W Full employment requires a country s factor demand B W Y to equal the endowment vector V where Y is the production vector 1 BW Y V 9 1 Under identical and homothetic preferences a country s demand D must be proportional to total world output Y W D sY W 9 2 B W D sB W Y W sV W 9 3 From these equations Then the factor content of a country s exports T Y D must be B W T B W Y D V sV W 9 4 De nition 1 The term B W T is the measured factor content of trade MFCT while V sV W is its predicted value the predicted factor content of trade PFCT 1 In terms of our previous notation technology matrix B is like A factor endowment vector V is K production vector Y is S and export vector T is X M AN ACCOUNT OF GLOBAL FACTOR TRADE 3 Proposition 2 Production Speci cation P1 The factor content of a county s production is its endowment of factors B W Y V Proposition 3 Trade Speci cation T1 A country s net export of factor services will equal the di erence between its endowment and the average endowment scaled by the country s size B W T V sV W Technology Suppose a country s measured technology matrix is Measured with the common technology matrix B W multiplied by a maError trix of errors B BW 9 5 Then the true technology matrix B W is replaced by a weighted average technology matrix B Proposition 4 Production Speci cation P2 BY V Proposition 5 Trade Speci cation T2 BT V sV W Hicks Neutral Technical DifCountries seem to have systematic di erences in productivity Suppose the technologies of countries di er ferences only by a country speci c Hicks neutral shift term B B W 9 6 If express a country s endowments in e ciency terms V 9 7 Ve then the standard results should hold use e ciency units henceforth Proposition 6 Production Speci cation P3 BY Ve Proposition 7 Trade Speci cation T3 BT Ve sVe W 4 AN ACCOUNT OF GLOBAL FACTOR TRADE Continuum Model Capital intensity of sectors appear to di er across countries Following Dornbusch Fisher and Samuelson 1980 order a continuum of industries to be strictly increasing in their capital labor ratios Following Xu 1993 suppose that if 1 units of a good are shipped one unit arrives due to iceberg style transportation costs needed to pin down production and thus trade volume and suppose that is arbitrarily close to one so that the transportation costs are trivial in magnitude All goods having the same proportional transport costs implies that countries will achieve the HOV predicted factor ows through the smallest volume of trade to minimize the transport cost involved The capital abundant country will export an interval of the most capital intensive goods the labor abundant country will export an interval of the most labor intensive goods and an intermediate range of goods will not be traded There is an aggregation problem goods produced in di erent countries that are classi ed as being in the same industry might not really be the same at all In this setting the estimated technology matrix will tend to understate the capital content and overstate the labor content of exports from the capital abundant country such as the United States and similarly but in reverse for the labor abundant country So the estimates of the factor content of trade will be biased toward zero for both countries thus contributing to the mystery of the missing trade An important implication of this theory is that industry factor usage for tradables will vary systematically with the country s capital