Nonhomothetic Preferences and International Trade

Transcription

1 Abstratroie_ Review of International Eonomis, 18(2), , 2010 DOI: /j x Nonhomotheti Preferenes and International Trade Jeffrey J. Reimer and Thomas W. Hertel* This study examines whether nonhomotheti preferenes underlie the missing trade problem assoiated with fator ontent of trade models. We first find that per apita inome goes a long way in explaining differenes in goods onsumption aross ountries. We then find a striking orrelation between the fator ontent of onsumption and per apita inome, and show that aounting for this is a key part of resolving the ase of the missing trade. However, nonhomotheti preferenes over broad ategories of expenditure play only a small role in this phenomenon. Rather, we find that as inome grows, spending is direted towards the relatively apital-intensive version of a given good. Sine reent researh shows that apital intensity is orrelated with quality (Shott, 2004), our results suggest that within-produt quality differenes are likely important for explaining the fator ontent of trade, whereas nonhomotheti preferenes over broad ategories of expenditure are muh less so. 1. Introdution Countries differ greatly in terms of per apita inome, and this measure has a systemati relationship with a wide variety of eonomi phenomena. Per apita inome has a partiularly robust relationship with the omposition of national onsumption. Evidene suggests that per apita onsumption in riher ountries deviates systematially from that in poorer ountries (Hunter and Markusen, 1988; Cranfield et al., 2000). Hunter (1991) builds on suh findings to show that nonhomotheti preferenes are an important determinant of goods trade. Changes in global per apita inomes will therefore have an effet on future trade patterns. For these reasons, nonhomotheti preferenes have found their way into numerous models of international trade (e.g. Linder, 1961; Markusen, 1986). Nonhomotheti preferenes have also been singled out as a way to make progress in understanding the fator ontent of trade, a onept generally assoiated with the work of Vanek (1968). Building on Heksher (1919) and Ohlin (1933), Vanek shows that ountries trade embodies their abundant fators. This framework has evolved into a laboratory for understanding how ountries endowments, tehnology, and demands fit together in general equilibrium (Davis and Weinstein, 2003). Reent work emphasizes resolving the mystery of the missing trade, whih is Trefler s (1995) name for his finding that the measured fator ontent of trade is onsistently muh smaller than Vanek s predition. This mystery has beome something of a summary measure regarding the extent of our ignorane about the determinants of international trade. A number of solutions to the mystery have been proposed, and two reent surveys highlight onsumer preferenes as an area of partiular interest. Davis and Weinstein (2003) observe that the demand side of the model ries out for more researh, and * Reimer: Oregon State University, Corvallis, OR 97331, USA. Tel: ; jeff.reimer@ oregonstate.edu. Hertel: Purdue University, West Lafayette, IN 47907, USA. Tel: ; hertel@purdue.edu. We thank partiipants at various seminars and anonymous reviewers for helpful omments Blakwell Publishing Ltd

2 PREFERENCES AND TRADE 409 Leamer (2002) observes that the homothetiity assumption rather badly violates the fats. Chung (2005) disusses the theoretial onditions under whih nonhomotheti preferenes ould help resolve the ase of the missing trade. Nonhomotheti preferenes imply that there is systemati variation in the broad ategories of goods demanded at different inome levels. Sine different goods are produed with different ombinations of fators, nonhomotheti preferenes will, in turn, have a systemati effet on the derived demand for fators. In the ase of two fators, apital and labor, one might imagine that rih-ountry onsumption will be biased towards apital-intensive luxuries, while poor-ountry onsumption is skewed towards labor-intensive neessities. In turn, sine rih ountries may be abundant in apital while poor ountries are abundant in labor, the fator ontent of trade will be ompressed sine eah ountry has a disproportionate preferene for the ommodity in whih they hold a omparative advantage. If preferenes are inappropriately restrited to be homotheti, the predited fator ontent of trade will outstrip the measured fator ontent of trade, and trade in fator servies may appear missing. The purpose of this paper is to quantify key differenes between the onsumer demand of rih and poor ountries, and test whether nonhomotheti preferenes offer a solution to the mystery of the missing trade. We first estimate a global demand system that allows for general forms of nonhomothetiity, inluding nonlinearities in the Engel urves, as well as homotheti preferenes. We then impute the fator ontent of demand and trade using ountry-speifi tehnology matries for a broad spetrum of ountries. We ignore the possibility onsidered in studies suh as Dalgin et al. (2008) that inome inequality within individual ountries is a determinant of aggregate demand and trade. By ontrast, we fous on inome inequality aross ountries and doument systemati differenes in their derived demand for fators and tehniques of prodution. A long literature has established that homotheti preferenes are not a reasonable assumption for haraterizing ross-ountry onsumption patterns (Lluh et al., 1977; Theil and Clements, 1987; Hunter and Markusen, 1988; Hunter, 1991). We extend this literature by developing improved estimates of international onsumption patterns and onduting an analysis of the fator ontent of trade. Our study also extends two studies that briefly onsider nonhomotheti preferenes and the fator ontent of trade (Bowen et al., 1987; Davis et al., 1997). Both studies suggest that nonhomotheti preferenes do not improve model performane in a substantive way. However, these two studies were arried out some time ago and treat the issue peripherally. For example, neither study estimates preferenes diretly from onsumption data. In turn, Bowen et al. (1987) fous on the strit Heksher Ohlin Vanek (HOV) model and do not find good performane with any of the generalizations. Subsequent studies have made onsiderable progress by relaxing assumptions suh as fator prie equalization. One this is done the ontribution of nonhomotheti preferenes may ome through more learly. Our speifiation draws upon the insights of these reent studies, thereby reduing the possibility that our results stem from problems in the underlying speifiation. The seond study to treat the role of nonhomothetiity in determining the fator ontent of trade is Davis et al. (1997). These authors apply a version of the HOV framework to subnational regions of a single, relatively homogeneous ountry (Japan). By restriting the model to a setting where the fator prie equalization assumption seems reasonable, progress is made in reoniling the measured and predited fator ontents of trade. However, ompared to international differenes, there is relatively little inome dispersion aross the regions of Japan, so the study is not a general test of 2010 Blakwell Publishing Ltd

3 410 Jeffrey J. Reimer and Thomas W. Hertel nonhomotheti preferenes. Our approah onsiders a broad-enough spetrum of ountries so that the potential importane of nonhomotheti preferenes is allowed to ome into play. A third study, Chung (2005), investigates the issue of nonhomotheti preferenes by introduing the notion of the inome elastiity of fator onsumption. He identifies onditions under whih the onventional HOV theorem will overpredit the fator ontent of trade ompared to nonhomotheti preferenes. This result holds to the extent that inome-elasti fators are on average abundant in rih ountries, and inome-inelasti fators are on average abundant in poor ountries. He then estimates a simple relationship between per apita inome and the fator ontent of onsumption. Using this estimated elastiity in a revised, nonhomotheti HOV model, he finds a nearly perfet fit between measured and predited fator ontent of trade. On the fae of it, it would seem that Chung (2005) has resolved the mystery of the missing trade, entirely via the introdution of nonhomotheti preferenes. However, there is a large leap from the strutural model that he develops, based on Linear Expenditure System (LES) preferenes and idential tehniques aross ountries, and the redued-form relationship between per apita inome and the fator ontent of onsumption that he estimates. Indeed, there are a number of other ompelling explanations for the strong relationship found between rising per apita inome and inreased apital intensity of onsumption. His results annot be taken as definitive evidene that nonhomotheti preferenes resolve the mystery of the missing trade. In addition to the lak of theoretial rigor underpinning the eonometri model of nonhomothetiity estimated by Chung (2005), there is the matter of the partiular form of nonhomothetiity that he postulates. The LES is simply an origin-displaed, Cobb Douglas funtion whih is not expeted to perform well aross a wide range of inomes. In this paper, we introdue a more general speifiation for nonhomothetiity, and test the LES as a speial ase. It is rejeted in our sample, whih is muh riher than the OECD-only sample exploited by Chung (2005). To distinguish among phenomena that are otherwise observationally equivalent, we inorporate our strutural model of demands into Davis and Weinstein s (2001) fator ontent of trade framework. We find that allowane for nonhomotheti preferenes helps resolve some of the missing trade. However, the role of nonhomotheti preferenes is small relative to other phenomena that we observe. The reason is that goods are produed with a mix of fators, and also rely on intermediate inputs that are themselves a mix of fators. While goods onsumption may vary aross ountries aording to per apita inome, this translates into smaller differenes in the fator ontent of onsumption. As with Chung (2005), there is a strikingly lear orrelation between ountries fator ontent of onsumption and their per apita inome. In turn, we find that high onsumption of loally abundant fators does help explain muh of the missing trade. However, this is not the result of nonhomotheti preferenes aross broad ategories of expenditure. Rather, it is due to extensive home bias in onjuntion with our finding that a 1% rise in per apita GDP is assoiated with a 0.90% rise in the apital/labor ratio of prodution. In short, rih ountries produe and onsume a relatively apitalintensive version of eah good. One explanation for our findings is that rih onsumers demand a higher quality version of a given good, and prodution of this quality is apital-intensive. In other words, as inome grows, spending is direted to higher-quality versions of all types of goods, and within-produt quality differenes are orrelated with a ountry s endowment of produtive fators Blakwell Publishing Ltd

4 PREFERENCES AND TRADE Coneptual Framework To assess the ontribution of non-homotheti preferenes to trade, the role of per apita inome must be isolated from all other reasons that demands differ aross ountries. In turn, the estimated demands should not violate the basi tenets of eonomi rationality. 1 We also need the estimated nonhomotheti expenditure shares to sum to one. This latter property requires an adding-up onstraint, whih would not be preserved in an ad ho regression onerning individual ommodities one at a time. These onsiderations warrant the use of a formal demand system derived from a utility-maximization problem. A demand system that fits with the paper s objetives is An Impliitly Diretly Additive Demand System (AIDADS). Developed by Rimmer and Powell (1996), it is a generalization of the LES used in Hunter and Markusen (1988) and Hunter (1991). Unlike onstant-elastiity-of-substitution forms, for example, AIDADS does not fore Engel urves through the origin. Unlike the LES model, AIDADS does not restrit Engel urves to be linear. 2 AIDADS also avoids the LES s ounterintuitive evolution of inome elastiities of demand as per apita inomes rise. 3 AIDADS performs espeially well when the estimation involves a ross-setion of ountries with extensive variation in per apita inome. Under suh irumstanes the expenditure shares of alternatives suh as the Almost Ideal Demand System (AIDS) often stray outside the unit interval. AIDADS is based on Hanoh s (1975) definition of impliit diret additivity: N Σ i = Ui( di u 1, )= 1, where {d1,..., dn } is the bundle of (per apita) demands indexed by good i {1,...,N} and ountry {1,...,C}. U i are twie-differentiable monotoni funtions satisfying the appropriate onavity onditions, and u is the unobservable utility level of ountry. Rimmer and Powell (1996) propose the following utility funtion for AIDADS: U ( d, u )= i i i i [ + ( )] [ + ( )] δ ψ exp u di ω i ln 1 exp u Aexp u ( ), for all i,. (1) Unknown parameters to be estimated inlude d i, y i, w i, and A. The parameters d i and y i represent the lower and upper bounds of marginal expenditure shares, while w i reflets the lower bound on onsumption for ommodity i. The expenditure onstraint is given by Σ i pd i i = d, where p i is the prie of ommodity i in ountry, and d is total per apita expenditure by a representative individual in ountry. Cost minimization shows that per apita nonhomotheti demands are: d i δi ψi exp u = ω i + 1 exp u + ( ) + ( ) d p w p, i where p and w are vetors of loal goods pries and the lower (subsistene) bounds on final demands, respetively. The minimal per apita expenditure is p w, while disretionary inome is [d - p w]. AIDADS satisfies symmetry and homogeneity by onstrution. Adding-up is obtained by restriting S id i =S iy i = 1, d i 3 0, and y i 2 1 for all i. We an get LES demands by restriting d i = y i for all i. Examination of the restrited version of (2) shows that marginal expenditure on good i is now invariant to utility, and hene to inome level. This is a signifiant restrition sine nonhomothetiity arises solely from the presene of the subsistene quantities, w i. 4 To obtain homotheti (2) 2010 Blakwell Publishing Ltd

5 412 Jeffrey J. Reimer and Thomas W. Hertel demands from (2), the restrition w i = 0 is added to the LES restrition. This yields Cobb Douglas demands, in whih average and marginal expenditure shares are equal, and therefore the average expenditure share is invariant to inome level. 5 To estimate AIDADS, let w i be the share of ommodity i in s expenditure. Equation (2) an then be rewritten as a stohasti share equation: w i + ( ) p i ω i δi ψiexp u = + d 1 exp u + ( ) d p w i d + ν, with ν i being disturbanes that are assumed to be jointly normal and independent over ountries, with zero mean and a onstant ovariane matrix. Following Greene (1993), a onentrated log-likelihood funtion is formed from (3): 0.5 ln( W ), where element (i, i ) ofw is given by wii C = i i C, with C being the number of ountries. The AIDADS defining equation is used to ompute u for any given set of parameters, pries, and inome. The likelihood funtion is minimized aording to the onstraints indiated above, and following the proedure suggested by Cranfield et al. (2000). In addition, the LES and Cobb Douglas versions of (2) are estimated by imposing the restritions noted above. The validity of eah of these restritions is evaluated using likelihood ratio tests. To inorporate these demands into the fator ontent framework we start with goods trade: = Σ 1 ( νν ) T Y D, (4) where T is a net export vetor, Y is net output, and D is demand. 6 Let Y W be world net output, and s be s share of world inome. In the speial ase of idential homotheti preferenes and idential goods pries, s demand is just its inome share of world net output: D = s Y W, and the goods trade identity an be rewritten as T = Y - s Y W. With the right assumptions, we get the familiar HOV expression: V - s V W, where V and V W denote the endowment vetor for and the world, respetively. However, this performs very poorly when tested with data, and we want to test the possibility that nonhomotheti preferenes an help. Sine we an no longer replae D in equation (4) with s Y W, we must work with D. We ould in theory express this in terms of the underlying AIDADS parameters using equation (2). However, this beomes notationally very umbersome. The most ompat way to state our speifiation is to use w AIDADS, whih is the (N 1) vetor of fitted expenditure shares. In the ase of LES, the (N 1) vetor of fitted expenditure shares is denoted w LES. Likewise, the vetor of fitted expenditure shares embodied in Cobb Douglas demands is w CD. 7 In the standard HOV fator ontent of trade model, equation (4) is premultiplied by a tehniques matrix that is ommon aross ountries. However, reent studies show when fator intensities are fored to be the same for all ountries, there is so muh missing trade that it is impossible to make muh sense of the results, and the benefit of new refinements (Trefler, 1995; Davis and Weinstein, 2001). If we are to make any sense of the fator ontent of trade, we must allow for fator prie inequality and different tehniques. We draw on the supply-side work of Davis and Weinstein (2001). Let B denote ountry s atual total fator inputs matrix as observed in the data. The typial element of B is B fi, where f indexes fators and i indexes goods. In the regression, fator inputs vary aording to: the partiular fator and industry being onsidered, for whih the regression oeffiient is b fi; the overall effiieny level of a ountry s fators, for whih (3) 2010 Blakwell Publishing Ltd

6 PREFERENCES AND TRADE 413 the oeffiient is q ; and a ountry s apital/labor endowment, for whih the oeffiient is g f. The regression speifiation is: ln Bfi = θ + βfi + γ f ln ( K L )+ ε fi, (5) where ε fi is an error term with lassial properties. To ensure that the effet of differenes in endowment apital/labor ratios (K /L ) do not bias the parameter representing differenes in overall fator effiieny levels (q ), the former s oeffiients are restrited to sum to zero: S fg f = 0. A normalization must be hosen for the ountry dummy variable, q, so we hoose q USA = 0. ˆθ affets the effiieny of the fators themselves, and the endowments vetors are expressed in effiieny-augmented form by dividing through by λ = exp( θ ˆ ). The fitted total fator input matrix is denoted ˆB. When tehniques differ by ountry, it is not lear a priori whih ountry s tehniques matrix to use when imputing the fator ontent of demand. We need a way to approximate the bilateral souring of goods while distinguishing nonhomotheti preferenes from home bias, whih may be observationally similar to nonhomothetiity. In effet, we need to take D in equation (4) and break it into its onstitute parts: D and M, where D is a vetor of s observed demand for its own goods, and M is a vetor of s observed demand for goods from. Our approah draws from speifiation (T7) of Davis and Weinstein (2001). The basi idea is to get bilateral import expenditure (summed aross all goods) from a gravity equation, subtrat this from total expenditure (summed aross ountries), and let expenditure on domesti goods be the residual. The details are as follows. Let X be aggregate gross output of ountry, and dist be the great-irle distane between apital ities of and. In turn, M denotes the atual import demand by for goods from, summed over all N goods. We inlude a Rest of World (ROW) region in our analysis, and our gravity model is modified to take this into aount. The gravity speifiation is written: ( )= + ( )+ ( ) exp imp ln M α0 α1ln s X α2 ln dist α3row α4row ζ, (6), where the a s are parameters to be estimated, and ζ is an error term with lassial properties. ROW exp and ROW imp are dummy variables that orrespond to instanes in whih the exporting ountry is the ROW, and the importing ountry is the ROW, respetively. These are used sine it is diffiult to ome up with a distane measurement between the ROW and any partiular ountry. Estimation of (6) with (C C) - C observations gives us estimates of the value of bilateral trade, summed over all N goods. This is denoted ˆM. The seond stage involves deriving the amount of ountry s overall expenditure that is soured from home. We denote this ˆD, with indiating that this onsumption is nontraded. First, let D be a salar representing s atual expenditure, aggregated over all soure ountries and goods. ˆD is then alulated as the residual of onsumption not aounted for by the gravity estimates of import demand: ˆ D D Mˆ = Σ. The above approximates overall bilateral trade expenditures, but says nothing about the omposition of goods onsumed within individual ountries, whih is given by w. In the ase of AIDADS, for example, our estimates of D and M are given by ˆ D w ˆ AIDADS = AIDADSD and ˆ M w ˆ AIDADS = AIDADSM, respetively. We now present the fator ontent of trade preditions, whih differ only in their representation of demand. Two are nonhomotheti (AIDADS and LES) while the other two are homotheti (Cobb Douglas and the traditional HOV approah). The AIDADS nonhomotheti trade test is: 2010 Blakwell Publishing Ltd

7 414 Jeffrey J. Reimer and Thomas W. Hertel ˆ ˆ BY BD Bˆ M V BD ˆ ˆ Bˆ + Mˆ = +, for all. (7) AIDADS AIDADS The left- and right-hand sides are the Measured and Predited Fator Contents of Trade, respetively (MFCT and PFCT). The atual endowment is net output (Y ) premultiplied by the observed total fator input matrix: V B Y. The Cobb Douglas homotheti trade test is: ˆ ˆ BY BD Bˆ M V BD ˆ ˆ Bˆ Mˆ + = CD + CD, for all. (8) Note that equations (7) and (8) embody the same predited tehniques matrix and predited bilateral souring of demand. This isolates the ontribution that nonhomotheti preferenes may give to the performane of equation (7). Tests onerning the two other demand-side speifiations are not displayed here, but are set up in similar fashion. 3. Empirial Results The demand system is estimated as a 1997 ross-setion for 52 ountries and 10 goods, while the fator ontent analysis is arried out for 20 ountries, 10 goods, and two fators of prodution. The data soure for both analyses is the Global Trade Analysis Projet (GTAP) version 5 dataset (Dimaranan and MDougall, 2002). 8 These data ombine detailed, fully reoniled trade and transport data with input output-based prodution, demand, and endowment data. For the fator ontent analysis, GTAP data are supplemented with World Bank and ILO data to onstrut physial measurements of apital and labor. Availability of physial measures of fator inputs limits the analysis to 20 ountries. 9 The Appendix provides more details about the data. AIDADS demand system parameter estimates are reported in olumns (1) (3) of Table 1.The parameters ˆδ i and ˆψ i represent the bounds of marginal expenditure shares. The former estimate for housing, eduation, health, publi servies (0.152) indiates that at very low inome levels this ategory aounts for as little as 15.2 ents of eah additional dollar of expenditure. The latter estimate (0.401) indiates that at very high inome levels, this ategory aounts for as muh as 40.1 ents of eah additional dollar of expenditure. The largest subsistene estimates are and for housing, eduation, health, publi servies and grains, vegetables, fruits. While ˆω i is zero in some ases, atual and predited onsumption is positive for every ommodity and ountry sine observed inome always exeeds the subsistene requirement. LES and Cobb Douglas parameter estimates are reported in olumns (5) (7) of Table 1. The assoiated parametri restritions are tested using likelihood ratio tests that are adjusted for sample size using Italianer (1985). Log likelihoods are alulated as -(C - 1)0.5 ln( Ŵ ) and are 686.3, 659.9, and in the ase of AIDADS, LES, and Cobb Douglas, respetively. Cobb Douglas restritions are rejeted, as the likelihood ratio test statisti is 97.2, exeeding the 5% ritial value of LES restritions are also restrited as the likelihood ratio test statisti is 45.1, exeeding the 5% ritial value of AIDADS is most onsistent with the data. This is onfirmed in Figure 1, whih plots fitted expenditure shares against inome in the ase of servies. The AIDADS estimates learly trak the pattern of expenditure better. Charts for other ategories of expenditure (not displayed for lak of spae) also have upward or downward trends, sometimes with interesting nonmonotoniities. Observed ross-ountry prie differenes add little to our explanation of onsumption differenes aross ountries. Figure 2 displays AIDADS fitted food shares 2010 Blakwell Publishing Ltd

8 PREFERENCES AND TRADE 415 Table 1. Demand System Estimates AIDADS LES Cobb Douglas Lower marginal share ( ˆδ i ) Upper marginal share ( ˆψ i ) Subsistene (ˆω i ) Expenditure elastiities Marginal exp. share ( δˆ i = ψˆ i) Subsistene (ˆω i ) Marginal exp. share ( δˆ i = ψˆ i) Grains, vegetables, fruits Meat, dairy, fish Proessed food, beverages, tobao Textiles, apparel, footwear Housing utilities Wholesale/Retail trade Manufatures/Eletronis Transport, ommuniation Business servies Housing, eduation, health, publi servies Note: AIDADS expenditure elastiities are evaluated at the means of the data Blakwell Publishing Ltd

9 416 Jeffrey J. Reimer and Thomas W. Hertel Expenditure share on margins and servies Log of per apita expenditure, 1997 US dollars Atual AIDADS LES Cobb Douglas Figure 1. Expenditure Shares at Mean World Pries and Atual Shares 0.50 Expenditure share all food exept meat Log of per apita expenditure, 1997 US dollars AIDADS at mean pries AIDADS at own pries Atual Figure 2. Expenditure Shares at Mean World Pries versus Own Pries evaluated at a ountry s own prie levels, in addition to those fitted at mean world pries, as well as atual shares. The fitted shares at mean world pries appear to predit as well as the fitted shares at observed pries, sine per apita inome is the dominant determinant of onsumption differenes within this setting. Sine per apita inome learly affets goods demand, it should also affet the derived demand for fators. We expet the fator ontent of trade to be ompressed, leading to the appearane of missing trade when preferenes are restrited to be homotheti. Upon estimating equations (7), (8), and their variants, we find that some of the missing trade problem is resolved by allowing onsumption to vary aording to per apita inome differenes. However, nonhomotheti preferenes do not make a major differene. This result is best seen in Figures 3 and 4, whih plot the Measured against 2010 Blakwell Publishing Ltd

10 PREFERENCES AND TRADE Measured fator of trade US labor -1.5 Germany apital -2.5 Predited fator of trade Figure 3. Fator Content of Trade: Nonhomotheti Preferenes Measured fator of trade US labor -1.5 Germany apital -2.5 Predited fator of trade Figure 4. Fator Content of Trade: Homotheti Preferenes Predited Fator Content of Trade under AIDADS nonhomotheti preferenes (equation (7)) and homotheti preferenes (equation (8)), respetively. Sine the points in both speifiations lie fairly lose to the 45-degree line, (7) and (8) perform muh better than the standard HOV model, for whih the points would be arrayed along the horizontal axis. 10 Of ourse, this aspet is not surprising, sine we have deviated from HOV in ways that the reent literature reommends. The key point of interest, however, is that the nonhomotheti speifiation performs only slightly better than the homotheti speifiation. This is verified by well-known missing-trade test statistis, whih we report in Table 2. Consider a regression of the MFCT on PFCT (no interept inluded). If the predition worked perfetly, the oeffiient would be unity. In the nonhomotheti AIDADS ase the slope oeffiient is 0.480, with a standard error of In the homotheti (Cobb Douglas) ase the slope oeffiient is 0.442, with a standard error of So nonhomotheti preferenes have some effet on the derived demand for fators. In 2010 Blakwell Publishing Ltd

11 418 Jeffrey J. Reimer and Thomas W. Hertel Table 2. Prodution and Trade Slope Coeffiient Tests Nonhomotheti preferenes (AIDADS) Nonhomotheti preferenes (LES) Homotheti preferenes (Cobb Douglas) Homotheti preferenes (world net output share) Perfet home bias Dependent variable: Measured fator ontent of demand Predited fator ontent of demand Standard error Adjusted R-square Dependent variable: Measured fator ontent of trade Predited fator ontent of trade Standard error Adjusted R-square Sign test Missing trade Notes: Regression is on 20 observations. Theoretial value of Predited is unity. Sign test reports the fration of sign mathes between measured and predited fator ontent of trade. Missing trade measure is the variane ratio of measured relative to predited fator ontent of trade. This ratio must be unity if there is no missing trade Blakwell Publishing Ltd

12 PREFERENCES AND TRADE 419 turn, some missing trade is found by inorporating AIDADS demands into the fator ontent of trade model. However, nonhomotheti preferenes do not play a large role. For nonhomotheti preferenes to have had a onsiderable effet on the fator ontent of demand, there has to be variation in the ratio of apital-to-labor that is used aross broad ategories of expenditure. Yet goods are produed with a mix of fators at the value-added stage, and also rely on intermediate inputs that are themselves an amalgam of labor and apital. To see this, onsider a situation in whih there are two goods, A and B, and two ountries with different per apita inomes. Suppose the shares of expenditure in the low-inome ountry are 2/3 and 1/3, respetively. The shares of expenditure in the high-inome ountry are 1/3 and 2/3, respetively. Suppose further that preferenes are ommon to both ountries, and trade equalizes the pries of A and B. The differential pattern of expenditure is therefore due solely to nonhomotheti preferenes. Now suppose in extreme irumstanes that the apital/labor ratios are suh that the fator ontent of good A is 100% labor (no matter where produed), while the fator ontent of good B is 100% apital (no matter where produed). Thus the low-inome ountry s fator ontent of demand has a apital/labor ratio of 1/3, while the high-inome ountry s is 2/3. In this ase, there is a diret orrespondene between nonhomothetiity in goods trade and in the fator ontent of trade. By ontrast, goods and fators never have a perfet one-to-one orrespondene. Goods are produed with a mix of fators at the value-added stage, and also rely on intermediate inputs that are themselves an amalgam of fators. For this reason, the apital/labor ratio in the fator ontent of demand is almost ertainly going to lie between 1/3 and 2/3 in eah ountry. In the above example, if the apital/labor ontent of goods A and B is idential, the two ountries fator ontent of demand will also be this ratio despite their differing omposition of demand. The rih variation in the omposition of demand gets blurred when one moves to the fator ontent of demand and, by extension, to the fator ontent of trade. Despite the fat that nonhomotheti preferenes have a smaller impat than we antiipated, there is a strikingly lear orrelation between ountries derived demands for produtive fators and ountries per apita inome. Consider a regression of the log of the K/L ratio assoiated with the derived demand for fators on the log of per apita GDP. A 1% rise in per apita GDP is assoiated with a 0.80% rise in the K/L ratio of final demand. This relationship is plotted in Figure 5 and is quite striking. This happens beause of three effets. First, regression analysis of equation (5) turns up extensive, systemati variation aross ountries with respet to the fator intensity of a given good. Seond, the fator intensities vary systematially aross rih and poor ountries. A 1% inrease in the endowment K/L ratio orresponds to a 0.986% inrease in the K/L ratio of prodution. In turn, a simple regression reveals that a 1% rise in per apita GDP is assoiated with a 0.90% rise in the K/L ratio of prodution. Figure 5 also displays this result. The third piee of the puzzle is that home bias is extensive among the ountries sampled. For the average ountry, 83.4% of onsumption is soured at home. These three reasons explain why a ountry s fator ontent of onsumption ends up being quite similar to its fator ontent of prodution. The following exerise illustrates how home bias and systemati differenes in prodution tehniques aross ountries bridge muh of the gap between the measured and predited fator ontent of trade. Consider a fator ontent of trade model in whih eah ountry has perfet home bias. In this ase the fator ontent of s demand is imputed by applying its own tehniques matrix ( ˆB ) to its demand under idential, homotheti preferenes (s Y W ): 2010 Blakwell Publishing Ltd

13 420 Jeffrey J. Reimer and Thomas W. Hertel 3.0 Log of apital/labor ratio Log of total per apita expenditure, 1997 US dollars Measured fator ontent of prodution Measured fator ontent of demand Figure 5. Plot of Capital/Labor Ratios on Per Capita Inome ˆ ˆ BY BD Bˆ M V BY ˆ W + = s, for all. (9) When (9) is implemented empirially, the oeffiient assoiated with a regression of the MFCT upon the PFCT is 0.562, with a standard error of (Table 2).This is atually better than the AIDADS result. The point is that allowing for systemati tehniques differenes in onjuntion with home bias resolves muh of the missing trade irrespetive of what assumption is made about the omposition of demands aross the inome spetrum. Taken together, these fats generate our finding that rih ountries produe and onsume apital-intensive goods, while poor ountries produe and onsume laborintensive goods. This finding is further larified by the following onsideration. For nonhomotheti preferenes to have an effet on the derived demand for fators, there has to be variation in the ratio of apital-to-labor that is used aross broad ategories of expenditure. For home bias to have an effet on the derived demand for fators, by ontrast, there has to be variation in the average apital/labor ratio used aross ountries. A omparison an be made by taking the standard deviations of the appropriate elements of the ˆB matries. We find that the average variation in K/L ratios aross goods within a ountry is less than 10% of a given good s variation in K/L ratios aross ountries. In other words, the K/L ratio of a given good tends to be muh more similar to other goods of the same ountry than it is to the version of the good produed by other ountries. In this ontext, the fator ontent of demand will be determined more by souring patterns related to home bias, than by the broad ategories of goods that are onsumed (in whih nonhomotheti preferenes play a role). 4. Conlusions We find that nonhomotheti preferenes help to resolve some of the missing trade. However, the role of nonhomotheti preferenes is small relative to other phenomena. We find a striking orrelation between ountries derived demands for produtive fators and ountries per apita inome. While we might have expeted this to result from nonhomotheti preferenes, it operates through an unrelated mehanism. The 2010 Blakwell Publishing Ltd

14 PREFERENCES AND TRADE 421 story starts with the way in whih we haraterize ountries prodution tehnology. Unlike other studies that onsider nonhomothetiity, we follow the reent literature and allow for the possibility of unequal fator pries and speialization by ountry. This approah shows that there is extensive variation in the amount of apital versus labor used by ountries to produe a given good. In this ontext we an think of a given good as a ontinuum of varieties differing in fator ontent. Countries speialize in a setion of this ontinuum aording to omparative advantage. Therefore, when viewed in terms of its apital/labor ontent, there are at least as many versions of a good as there are ountries. The variation in fator intensities aross ountries turns out to have a lose relationship to national per apita inomes. On average, a 1% rise in per apita GDP is assoiated with a 0.90% rise in the apital/labor ratio of prodution. To our knowledge this is the first suh estimate in the literature. In turn, we find that ountries exhibit extensive home bias. In partiular, the average ountry soures 83.4% of overall final demand from itself. Sine most onsumption is soured from home, a ountry s fator ontent of demand ends up being quite similar to its fator ontent of prodution. And sine the latter varies systematially aross rih and poor ountries, the derived demand for fators has a very strong relationship with per apita inome. This is the basis of our result. These results are further larified through the following. For nonhomotheti preferenes to have an effet on the derived demand for fators, there has to be variation in the ratio of apital-to-labor that is used aross broad ategories of expenditure. For home bias to have an effet, by ontrast, there has to be variation in the ratio of apital-to-labor used aross soures. We find that the average variation in K/L ratios aross goods within a ountry is less than 10% of a given good s variation aross ountries. In other words, the K/L ratio of a given good tends to be muh more similar to other goods of the same ountry than it is to the same good in other ountries. For these reasons, the fator ontent of demand is determined more by where a ountry gets its goods, than by the broad ategories of goods that it onsumes (in whih ase nonhomotheti preferenes would play a role). Our ultimate ontribution is to show that per apita inome is more intimately linked to key aspets of the international eonomy than previously understood. In turn, we find that if it is trade in fator servies that we are about, then nonhomotheti preferenes matter little in the fae of systemati differenes in prodution tehniques aross ountries, and in light of extensive home bias. This is not to say that further researh into nonhomothetiity as an explanation for the missing trade is unlikely to be produtive. An explanation for our results is likely to lie in additional forms of nonhomothetiity at the produt level that we are unable to observe diretly. Reent researh shows that within-produt quality differenes are highly orrelated with both a ountry s aggregate K/L ratio, and the ountry s use of K/L in a partiular setor (Shott, 2004). Thus, as inome grows spending may be direted to higher quality versions of a good, even when this broader expenditure ategory is a neessity. This idea may partly explain the home bias we observe, and is a fruitful area for further researh. Appendix The demand system is estimated as a 1997 ross-setion for 52 ountries and 10 ategories of expenditure. The expenditure share for good i in ountry is alulated as the expenditure (final demand) for i divided by s summed expenditure. The level of 2010 Blakwell Publishing Ltd

15 422 Jeffrey J. Reimer and Thomas W. Hertel expenditure on good i is obtained as follows. We start with the gross output vetors from the GTAP database. From this we subtrat the amount used as an intermediate in the prodution of all the setors in the ountry to obtain the net output vetor. To get expenditures on final demand, we subtrat the net export vetors from the net output. This yields a haraterization of final demand for use in the estimation of an AIDADS demand system that is onsistent with HOV experiments onduted in the paper. Pries are alulated by dividing imports valued at domesti market pries by imports valued at.i.f. pries. Thus tariffs are the only soure of ross-ountry prie variation. The 10 ategories of expenditure are similar to that of Hunter and Markusen (1988), Hunter (1991), Cranfield et al. (2000), and Reimer and Hertel (2004). One differene is that we break out margin servies (wholesale, retail, trade ativities) as a distint ategory, whih is essential for reoniling final demand expenditures with prodution data. Estimation of the tehniques regression (5) requires that fators be measured in physial units. However, GTAP prodution data measure fator usage in value terms. Separate strategies are used to derive the physial units of apital usage (B Ki, ) and labour usage (B Li, ) by ountry and industry i. In the ase of apital the approah of Trefler and Zhu (2005) and Reimer (2006) is followed, whih involves an assumption that industry apital stoks are proportional to industry payments to apital. The GTAP data report payments to apital in eah setor i of ountry (VFA i ) along with physial apital stok (VKB ) for a ountry as a whole, with the latter measurement taken from the Development Eonomis Analytial Database of the World Bank. Physial apital usage is then alulated as: B VFAi = VFA VKB i Ki,. i In the ase of labor, a setor-speifi wage per ountry is used to onvert GTAP labor payments data into physial units of labor usage. Wage data are taken from the Oupational Wages around the World (OWW) database, onstruted by Freeman and Oostendorp (2000). These are derived from the International Labour Organization s (ILO) Otober Inquiry database by alibrating the data into a normalized wage rate for eah oupation. 12 The number of ountries with original data for the ross-setion is 52. While the GTAP version 5 database breaks out 66 regions, several of these are regional omposites and are exluded from the analysis. For the fator ontent of trade analysis, only 20 of these an be analyzed (with one region orresponding to the Rest of World). This tradeoff arises due to the need to reonile the GTAP and ILO data. For the year of the GTAP database, 1997, the OWW data report oupational wage data for 49 industries, 161 oupations, and 59 ountries. The number of ountries that the two data sets have in ommon is 19. The representation of the Rest of World (ROW) is onstruted through a GDP-weighted aggregation of the remaining 33 ountries. 13 Per apita GDP among the 20 regions ranges from $240 for Malawi to $29,824 for the US. Aggregation of setors for fator ontent analysis Feenstra and Hanson (2000) show that measurement of fator servie trade is affeted by the level of setoral aggregation. This is surely relevant to the present study. To the extent there is systemati bias, the expetation is that fator servie trade is undermeasured. Nevertheless, this bias should affet our speifiations in the same way, suh that the test onerning nonhomothetiity is unaffeted Blakwell Publishing Ltd

16 PREFERENCES AND TRADE 423 Average fator and intermediate input intensities A setoral lassifiation omprises thousands of goods differentiated in terms of: whether they are used as an intermediate versus a final good, possibility of being traded, and whether exported or used at home (if tradable). Fator intensities likely to vary aross these end uses. While muh of this bias may anel out, there will be a net effet that is diffiult to disern in the absene of suffiiently detailed data. Yet, as with the above issue, the nonhomothetiity tests are unlikely to be ompromised. Fator aggregation Feenstra and Hanson (2000) show that measurement of fator servie trade is affeted by the level of setoral aggregation. This is surely relevant to the present study. To the extent there is systemati bias, the expetation is that fator servie trade is undermeasured. Nevertheless, this bias should affet our speifiations in the same way, suh that the test onerning nonhomothetiity is unaffeted. Definition of demand This study defines final demand as it is ommonly omputed for input output aounts, whih means it enompasses private household onsumption, investment, and government expenditures. The mean shares of these omponents are 0.71, 0.13, and 0.16, respetively. Trefler and Zhu (2000) suggest treating investment as a depreiable intermediate input instead of as an output of the eonomi system. This is an important point, and it would be interesting to look for systemati patterns within the omponents of final demand, but these issues are neessarily left to subsequent work. International fator effiieny differenes The proper measurement of fators aross ountries is a partiularly diffiult issue. Prodution regression (5) inludes a parameter (q) that proxies for international fator effiieny differenes. Yet this is an imperfet measurement of effiieny, sine, for example, labor that is effiient might simply embody a great deal of apital improvements. Nevertheless, the empirial analysis of preferene nonhomothetiity is unlikely to be biased as a result of this issue. Referenes Bowen, Harry, Edward Leamer, and Leo Sveikauskas, Multiountry, Multifator Tests of the Fator Abundane Theory, Amerian Eonomi Review 77 (1987): Chung, Chul, Nonhomotheti Preferenes as a Cause of Missing Trade and Other Mysteries, Georgia Institute of Tehnology working paper (2005). Cranfield, John, Paul Prekel, James Eales, and Thomas Hertel, On the Estimation of An Impliitly Additive Demand System, Applied Eonomis 32 (2000): Dalgin, Muhammed, Vitor Trindade, and Mitra Devashish, Inequality, Non-Homotheti Preferenes, and Trade: A Gravity Approah, Southern Eonomi Journal 74 (2008): Davis, Donald and David Weinstein, An Aount of Global Fator Trade, Amerian Eonomi Review 91 (2001): , The Fator Content of Trade, in Kwan Choi and James Harrigan (eds), Handbook of International Trade, Oxford: Basil Blakwell (2003). Davis, Donald, David Weinstein, Sott Bradford, and Kazushige Shimpo, Using International and Japanese Regional Data to Determine when the Fator Abundane Theory of Trade Works, Amerian Eonomi Review 87 (1997): Dimaranan, Betina and Robert MDougall (eds), Global Trade, Assistane, and Protetion: The GTAP 5 Data Base, West Lafayette, IN: Purdue University Press (2002). Feenstra, Robert and Gordon Hanson, Aggregation Bias in the Fator Content of Trade: Evidene from U.S. Manufaturing, Amerian Eonomi Review 90 (2000): Blakwell Publishing Ltd

17 424 Jeffrey J. Reimer and Thomas W. Hertel Freeman, Rihard and Remo Oostendorp, Wages Around the World: Wages Aross Oupations and Countries, NBER working paper 8058 (2000). Greene, William, Eonometri Analysis, New York, Mamillan (1993). Hanoh, Giora, Prodution and Demand Models with Diret or Indiret Impliit Additivity, Eonometria 43 (1975): Heksher, Eli F., The Effet of Foreign Trade on the Distribution of Inome, in Eli F. Heksher and Bertil Ohlin, Heksher Ohlin Trade Theory, Cambridge, MA: MIT Press (1991) [1919]. Hunter, Linda, The Contribution of Non-Homotheti Preferenes to Trade, Journal of International Eonomis 30 (1991): Hunter, Linda and James Markusen, Per Capita Inome as a Basis for Trade, in Robert Feenstra (ed.), Empirial Methods for International Trade, Cambridge, MA: MIT Press (1988). Italianer, Alexander, A Small-Sample Corretion for the Likelihood Ratio Test, Eonomis Letters 19 (1985): Leamer, Edward, Linking the Theory with the Data: That s the Core Problem of International Eonomis, in James Hekman and Edward Leamer (eds), Handbook of Eonometris, Amsterdam: Elsevier (2002). Linder, Staffan, An Essay on Trade and Transformation, Uppsala: Almqvist & Wiksell (1961). Lluh, Constantino, Alan Powell, and Ross Williams, Patterns in Household Demand and Savings, Oxford: Oxford University Press (1977). Markusen, James, Explaining the Volume of Trade: An Eleti Approah, Amerian Eonomi Review 76 (1986): Ohlin, Bertil, Interregional and International Trade, Cambridge, MA: Harvard University Press (1933). Reimer, Jeffrey, Global Prodution Sharing and Trade in the Servies of Fators, Journal of International Eonomis 68 (2006): Reimer, Jeffrey and Thomas Hertel, Estimation of International Demand Behavior for Use with Input Output Based Data, Eonomi Systems Researh 16 (2004): Rimmer, Maureen and Alan Powell, An Impliitly Additive Demand System, Applied Eonomis 28 (1996): Shembri, Lawrene, Comment on Per-Capita Inome, in Robert C. Feenstra (ed.), Empirial Methods for International Trade, Cambridge, MA: MIT Press (1987). Shott, Peter, Aross-Produt versus Within-Produt Speialization in International Trade, Quarterly Journal of Eonomis 119 (2004): Theil, Henri and Kenneth Clements, Applied Demand Analysis: Results from System-Wide Approahes, Cambridge, MA: Ballinger (1987). Trefler, Daniel, The Case of the Missing Trade and Other Mysteries, Amerian Eonomi Review 85 (1995): Trefler, Daniel and Susan Zhu, Beyond the Algebra of Explanation: HOV for the Tehnology Age, Amerian Eonomi Review Papers and Proeedings 90 (2000): , The Struture of Fator Content Preditions, NBER working paper (2005). Vanek, Jaroslav, The Fator Proportions Theory: The N-Fator Case, Kyklos 21 (1968): Notes 1. Sine we employ per apita demands at the aggregate level, not all the properties assoiated with individual onsumer demands survive the aggregation. The adding-up onstraint does survive. 2. We abstrat from the issue of inome heterogeneity within a ountry, whih an also affet a ountry s aggregate demand and trade, to fous on extensive variation in per apita inome aross ountries. 3. For neessities, LES inome elastiities always inrease with inome, while for luxuries, LES inome elastiities always derease with inome (Rimmer and Powell, 1996) Blakwell Publishing Ltd