A Decomposition of US Net Exports Growth Rates

Transcription

1 A Decomposton of US Net Exports Growth Rates Agelos Dels GEP, Unversty of Nottngham August 2007 Prelmnary and ncomplete. Please do not quote Abstract Ths paper s based on the work of Dxt and Woodland (982) on the determnants of growth rate of net exports (T ). It ncorporates the e ect of changes n commodty prces, whle allows for the presence of jontness n output quanttes n order to decompose the determnants of a change n the volume of net exports for an open economy wth nonbalanced trade. A general equlbrum analyss s mplemented where the revenue (GDP ) functon and the expendture functon are estmated for the US economy for the perod 963 to 99. Then a decomposton of the growth rate of the net exports s mplemented. It nvolves a terms of trade component, an endowment component, a technologcal change both n producton and consumpton and an ncome component. Keywords: Net Exports, US Trade, non-balanced trade,3sls JEL class caton: F, F4 GEP, School of Economcs, Unversty of Nottngham, Unversty Park, Nottngham, NG7 2RD, UK (emal: agelos.dels@nottngham.ac.uk)

2 Introducton One of the most characterstc phenomena of the last three decades n the world economy has been the rapd growth of nternatonal trade. In partcular the value of world merchandse trade has ncreased from 578 bllons n 973 to 5.4 trllons n 999 measured n current U.S. dollars (World Trade Organsaton, Annual Report). Ths translates to an annual average growth rate of 6% for the world trade, whle world output grew at an average of 3.7% per year over the same perod. Ths clearly underlnes the ncreasng sgn cance of nternatonal trade n the world economy. One of the countres that has contrbuted sgn cantly n ths dramatc ncrease of nternatonal trade s the US. US exports and mports of merchandse products account for the 2% of world mports and exports and 9% of US GDP for the year 2004 (US Economc Accounts,Bureau of Economc Analyss). Hence, nternatonal trade s an mportant part of the US economy, t s nterrelated to many producton and consumpton decsons and has been a frequent topc of nvestgaton for many researchers. There exsts a vast theoretcal lterature, see for example Krugman and Baldwn (987) and Feenstra (998), that o ers four man explanatons for the enormous changes n the volume of nternatonal trade. The rst core explanaton s the gradual abolton of restrctve trade polces, manly tar s and quotas, that have been ntroduced by most of the countres through blateral trade agreements wthn the World Trade Organsaton (WTO). The second s the advancement of technology that has resulted n lower transportaton costs. Due to more e cent and less costly means of transportaton, t has become pro table to exchange products n nternatonal markets that before these changes were not. Thrdly, t s argued that the growth n real ncome, n the developed countres at least, s another reason of explanng the hgher value and volume of nternatonal trade. Whle the last one (Feenstra, 998) suggests that the rse of outsourcng has led to ncreased trade volumes between host and home countres. Most of the emprcal work n the exstng lterature, ntated wth the work of Tnbergen (962), has tred to assess emprcally the factors that explan the growth of nternatonal trade usng the gravty model, see Deardor (998) for a survey. In a recent paper usng an augmented gravty model, Baer and Bergstrand (200), found that ncome growth accounts World Investment Report, Unted Natons, 999.

3 for 66% of trade growth for sxteen OECD countres for the perod Whle tar reductons can explan 26% and transport reductons 8% of trade growth respectvely. On the other hand d erent approaches have been followed n an attempt to answer the same queston lke the work of Rose (99) and Besedes (2005). Rose (99) argues that there are three more potental reasons, the convergence of captal labour ratos of countres, the fall n the relatve prce of tradeables to non tradeables and the growth of nternatonal reserves, that could explan the growth of world trade n an analyss of sxteen OECD countres for the perod He nds that for small open economes rses n real output, rses n nternatonal reserves and declnes n tar s can explan the growth of ther trade, whle for large open economes none of the explanatory varables n hs analyss has any statstcal sgn cance. Besedes (2005) uses a Rcardan model wth a contnuum of goods for ve OECD countres for the perod n order to decompose the growth rate of mport shares nto two components. The rst refers to changes n restrctve trade polces and the second to changes n the supply sde of the economy. He nds that the former cannot explan solely the growth of nternatonal trade and that changes n the supply sde of the economy, manly technologcal change, should also be n acton. Another stream of the emprcal lterature, Laursen and Meltzer (950), Persson and Svensson (985) and Mendoza (995), focuses on nomnal factors, manly exchange rate changes as possble determnants of the value of trade. But there reman some emprcal questons that have attracted very lttle or none of the nterest of researches. The rst s to asses emprcally wth the use of a general equlbrum analyss what determnes the changes n the volume of trade for a country. Economc theory tells that the answer lays on changes both n the producton and consumpton sde of the economy. Hence, the factors that determne the producton and consumpton pattern of a country a ect smultaneously the volume of ts trade. That s changes n the world prces of commodtes, changes n the endowments of the economy, technologcal changes both n the producton and consumpton and nally ncome changes. A change n the world prce for a commodty has two opposng e ects on the volume of net exports of a country. A decrease n the world prce of a commodty wll ncrease the quanttes exported for the country producng the commodty, but at the same tme wll ncrease ts consumpton and consequently ts volume of mports. The nal result s 2

4 an emprcal queston and depends on the prce elastctes of supply and demand. On the other hand, changes on the endowments of the economy wll change only the output produced and consequently wll alter the volume of net exports at the same drecton. Technologcal change n the producton sde of the economy, usually a postve one, wll ncrease output and consequently wll ncrease exports. But technologcal change on the demand sde and n partcular changes on the preferences of consumers towards commodtes could ether ncrease or decrease ther consumpton dependng on the drecton of the change on the preferences. Whle changes n ncome lead to hgher consumpton for all normal goods and consequently less net exports. All the above show that theoretcal predctons are necessary, but not su cent for determnng what actually drves the changes n the volume of net exports n an economy. It s necessary to have estmates about the producton and consumpton structure of the economy n order to be able to o er de nte answers on the queston what determnes changes n ts volume of net exports. In ths paper, rst I de ne an equlbrum where the economy s allowed to trade wth the rest of the world wthn the neoclasscal trade setup of a small country. Ths mples no mpedments to trade, exogenous world prces for the commodtes, no mmgraton of factors of producton, all countres producng all goods, a lnearly homogeneous technology n producton and also homothetc preferences at the home country. A producton equlbrum s then de ned wth the use of a revenue functon and smlarly a consumpton equlbrum s represented usng an expendture functon. Ths allows us to determne the trade equlbrum for the economy and consequently to dsentangle the d erent parts that explan a country s volume of net exports. The rst contrbuton of the paper, s the fact that I nclude both sdes of the economy, producton and consumpton, n the analyss and that I can dentfy the sgns and also magntudes of the d erent e ects that theory predcts. The second contrbuton s that followng a general equlbrum analyss I am able to decompose the changes of the volume of net exports nto ve d erent components. The rst s a terms of trade e ect that depends on the prce elastctes of demand and supply. The second re ects the changes n the endowments of the economy. The thrd represents the e ects of technologcal change n the producton. The fourth refers to the e ects on net exports arsng from changes on preferences over tme. The last one s the component that captures the e ects of ncome changes on the volume of 3

5 net exports. Hgher ncome levels mply hgher consumpton levels for all normal goods and consequently less net exports. Fnally, I allow for a more general technology n the producton sde that permts the presence of jontness n output quanttes (see Woodland 977 and Kohl 99). In addton, ths broader de nton of producton s technology that s usually avoded n return of more tractable theoretcal predctons seems to be supported by the data. Ths paper draws ts smple theoretc model from the work of Dxt and Woodalnd (982), but nether focuses on the specal case of an autarky equlbrum nor s nvestgatng only the e ect of a change of factor endowments on the volume of trade. I follow the emprcal mplementaton of Harrgan (997) and Kohl (993). I rst estmate a system of output equatons (exportable, mportable and non-tradable) derved from a Symmetrc Normalsed Quadratc Revenue functon ntroduced by Kohl (99, 993) usng a Three Stages Least Square (3SLS) estmaton. Equvalently a system of consumpton equatons derved from an expendture functon of a Gorman-Polar type, (Dewert and Wales 988) s estmated usng agan 3SLS. Then t s possble to calculate the tted volume of net exports for the economy and to proceed to the decomposton dscussed above. Wth such a decomposton and also wth the estmates obtaned from the revenue and expendture functon the sgns and also the magntude of all the ve d erent components can be constructed. Hence, I can explan the reasons for whch the net exports of a partcular commodty has been observed to move towards a spec c drecton. In partcular, I nd that the postve growth, 9.52% on average from 966 to 99, of net exports for the exportable good s manly explaned by better terms of trade and progressve technologcal change n the producton, despte a very large ncome e ect. In contrast, the negatve growth, -7.% on average over the whole perod, of net exports for the mportable good s due to a modest mprovement n the terms of trade, small postve bene ts through the endowments and preferences components, accompaned by a negatve mpact of technologcal change n the producton sde and a szeable ncome e ect. Fnally, the net exports for the non-tradable good grew rapdly, an average of 06% for the perod Ths seems to be the result of a combnaton of very good terms of trade and bene ts arsng from the change n the economy s endowments regardless of lagre opposng e ects n producton from regressve technologcal change, n preferences and ncome changes. The paper s organsed n seven sectons. Secton 2 descrbes the theoretcal model for the 4

6 economy, a trade equlbrum. The thrd dscusses the econometrc spec caton for both the revenue and the expendture functon. Secton 4 bre y descrbes the data used, whle the fth dscusses the estmaton methods mplemented and the results obtaned. Secton 6 nvolves the decomposton of the growth rate n the volume of net exports for the US economy for the perod and nally Secton 7 concludes the paper. 2 The Model Let F (y; v; t) = 0 be a transformaton functon for an economy wth a lnearly homogeneous technology, whch produces y = (y ; :::y n ) goods wth the use of m nputs, v = (v ; :::v m ); n a perfect compettve envronment where t s a tme ndex that captures technologcal change. Then, at gven nternatonal prces p = (p ; :::p n ) and domestc nputs v, there exsts a compettve producton equlbrum. In such equlbrum we can thnk of the economy as one that maxmzes the value of total output subject to the technologcal and endowment constrants. In other words there s a revenue or GDP functon such that: R(p; v; t) = max fpy : F (y; v; t) = 0g () y The revenue functon s ncreasng, lnearly homogeneous and concave n v and nondecreasng, lnearly homogeneous and convex n p. In addton f R(p; v; t) s d erentable then from Hottelng s Lemma (Dewert 974) the equlbrum output s: y(p; v; t) = R p (p; v; t) (2) On the consumpton sde the economy s preferences de ned over the n goods are represented by an expendture functon, whch s contnuous and twce d erentable n prces: E(p; u; t) = mn c fpc : u(c; t) ug (3) where u s the level of utlty and c = (c ; :::c n ) s the consumpton bundle and t s a tme ndex that captures shfts on the expendture functon due to changes n preferences for 5

7 the consumers. The expendture functon s non-decreasng, lnear homogenous and concave n prces and ncreasng n u. homothetc: In addton, t s assumed that the expendture functon s E (p; u; t) = E (p; t) u (4) From Shepherd s Lemma (Dewert 974) the consumpton vector of the economy s: c(p; u; t) = E p (p; u; t) (5) where E p s the rst partal dervatve of the expendture functon wth respect to product prces. The trade equlbrum s de ned as T IMB = R(p; v; t) E(p; u; t) (6a) T = R p (p; v; t) E p (p; u; t) (6b) that s the d erence between total value of producton and total expendture for the economy gves the trade mbalance (T IM B) for the economy and the d erence between producton and consumpton gves the economy s vector of the volume of net exports, T. In equlbrum the Hcksan demand functon, c H (p; u; t) = E p (p; u; t), has always the same value as the Marshallan demand functon, c M (p; m; t) = H p (p; m; t), where m ndcates total nomnal expendture for the economy, assumng that there s an ndrect utlty functon H (p; m; t) = u. Hence, I can substtute the Marshallan for the Hcksan demand functon n Eq (6b) T = R p (p; v; t) c M (p; m; t) (7) D erentatng totally Eq (7) I get dt = R pp dp + R pv dv + R pt dt c M p dp c M m dm c M t dt = R pp c M p dp + Rpv dv + R pt dt c M t dt c M m dm (8) where dp, dv, dm and dt are respectvely the change n product prces, factor endowments, 6

8 ncome and technology between two years. R pp s the second partal dervatve of the revenue functon wth respect to prces and R pv s the second partal dervatve of the revenue functon wth respect to prces and endowments respectvely. Whle c M p, c M t and c M m are the rst partal dervatves of the Marshallan demand functon wth respect to prces, technologcal change and ncome respectvely. Eq (8) s a decomposton of the changes n the volume of net exports nto ve components: the rst, R pp c M p dp, s a component smlar to changes n terms of trade 2 (tot) and depends on the substtutablty and complementarty of the goods n producton and consumpton the second, R pv dv, conssts of the e ect of changes n endowments on output and the entres of matrx R pv can have all possble sgns under the more general technology that allows jontness n output quanttes the thrd, R pt dt, captures technologcal change n producton. The sgn of R pt, the e ect of technologcal change on the supply of a good s postve, f technologcal change s progressve the fourth, c M t dt, ncorporates the e ect of changes n preferences over tme. But the sgn of c M t cannot be determned a pror. Preferences towards a good can change n ether drecton over the passage of tme the last one, c M m dm, s an ncome e ect component. For all normal goods c M m s postve and the total e ects depends on the drecton to whch ncome s headng Better terms of trade wll ncrease the net exports for the exported good and decrease the net exports for the mported assumng that only the prce of the exported good has ncreased. If both prces change n a fashon that results to better terms of trade, t s not clear what happens to the net exports of ether good. The nal outcome depends on the substtutablty and complementary of the goods n producton and consumpton. The reason s that the matrx R pp c M p s postve semde nte, snce the revenue functon s convex n prces and the expendture functon concave respectvely. The dagonal elements are all postve, whle 2 The rato of prces between an exported and an mported good. 7

9 the sgns on the o dagonal elements depend on the substtutablty and complementarty of the commodtes n both producton and consumpton. Hence, t s an open queston and rests on the estmaton of the parameters of the revenue and the expendture functon. Increases on endowments lead to ncreases n net exports as long as the endowment ncrease enhances output. In the standard neoclasscal trade model wth two goods and two nputs the Rybczynsk theorem dent es the sgns of the elements of matrx R pv. It states that an ncrease n the endowment that s used relatvely more ntensvely n the producton of a good wll cause an ncrease n ts producton and hence ts net exports. But f we depart from the 2 2 dmenson to more goods and nputs and also allow for jontness n output quanttes then no a pror predcton can be made. The sgns of the elements n R pv can have ether sgn 3 and once agan everythng depends on the estmates obtaned from the revenue functon. A progressve technologcal change of Hcks-neutral type on the producton, mples a postve R pt and equproportonate changes for all goods, ths leads to ncreases n trade, snce t allows for a rse n commodty supples. Hence, technologcal mprovement n the producton always ncreases net exports. Whle technologcal change n the consumpton sde or changes n the preferences does not have a de nte expected sgn. It could be ether postve or negatve. It depends on the drecton to whc consumers change ther preferences towards a spec c good as tme passes. For example, f consumers have changed ther preferences and tend to prefer more (less) of a spec c good now than before, then consumpton wll ncrease (decrease) and net exports wll fall (rse). Fnally, the e ect of a change n ncome on consumpton, c M m, s postve for all normal goods. Hence the sgn of the fth component depends on whether ncome s ncreasng or not. More ncome wll mply more consumpton and hence less net exports for every normal good and vce versa. The above dscusson has made clear, the reason both sdes of the economy should be ncluded n the analyss. Furthermore, t has stressed the necessty to obtan estmates of the revenue functon and Marshallan demand functons that wll allow us to decompose the actual changes of a country s volume of net exports. 3 see p 526 Woodland A.D., (977), "Jont Outputs, Intermedate Inputs and Internatonal Trade Theory", Internatonal Economc Revew, vol.8, no. 3, pp

10 3 The Econometrc Spec caton 3. The Revenue Functon The revenue functon s assumed to have the symmetrc normalzed quadratc functonal form as dscussed n Kohl (99, 993): 0 R(p; v; t) 2 + j= = j= 0 + j= = jv j A (c j p v j ) + 2 jv j A = h=! h p p h =! d p t + =! 0 j=! p =! 0 = j= k= p! jv j A 2 h ttt 2 + h t t 0 b jk v j v k e j v j A t j= j= jv j A (9) where p; and v; are the product prces and nput endowment vectors respectvely and t s an ndex of exogenous technologcal change. There are N(N ) + M(M ) + (N M) + 2 unknown parameters h, b jk, c j, d, e j, h t and h tt, where ; h = ; :::N and j; k = ; ::M. There are also N + M predetermned parameters and j. In partcular, and j are set equal to the share value of each product and nput respectvely at the base year. In order for the revenue functon to be exble, namely all ts rst and second dervatves to be de ned, symmetry condtons are mposed h = h ; b jk = b kj that reduce the estmated parameters and consequently mprove the e cency of the estmates. In addton the assumpton of lnear homogenety n p and v requre some addtonal restrctons: = = j= j =, and a h = b jk = h= k= d = e j = 0 (0) = j= Ths functonal form s attractve because t s exble and retans ts exblty under the mposton of convexty and concavty n prces and endowments, respectvely. The necessary and su cent condton for global concavty n nputs s that the matrx B = [b jk ] s negatve 9

11 sem-de nte and for global convexty that the matrx A = [a h ] s postve sem-de nte. If these are not sats ed then they are mposed followng Dewert and Wales (987) wthout removng the exblty propertes of the revenue functon. More spec cally, as Dewert and Wales (987) have shown global concavty on nputs can be mposed f matrx B s replaced by the negatve product of a lower trangular matrx and ts transpose 0. That s B = 0, where = jk and jk = 0 for every j < k; j ndcates rows and k ndcates columns of the matrx. In the same manner, global convexty on product prces can be mposed f matrx A s replaced by the product of a lower trangular matrx and ts transpose 0. Then A = 0 wth = [! h ] and! h = 0 for < h 4. Based on (9) the reward of the jth factor becomes: w j = 2 j N X 2 j = h= =! h p p h! 0 N! X +e j p t + j = The output supply of good th s: j= k=! p + = j= k= 0 b jk v j v k N X = 0 0 y = b jk v j v k j= p! jv j A j=! p = jv j A 2 + k=! 0 b jk v j= c j p + j = jv j A N X = d p! t h t t + N! X 2 j p h tt t 2 () 0 j= = jv j A! h p h h=! p 0!! 2 0 jv j A h p p h p + c j v j + jv j A t j= = h= = j= j= e j v j A t jv j A h t t + jv j A h tt t 2 (2) j= j= Equatons () and (2) together wth restrctons (0) form the rst system of equatons to be estmated. j= = 4 For more detals about mposng global concavty or convexty see Wley, Schmndt and Bramble (973). 0

12 3.2 Expendture Functon Assume the expendture functon E (p; u; t) of the economy to be homothetc of the Gormanpolar form, Dewert and Wales (988): E (p; u; t) = X a p + " 0 X p X 2 #! X j p p j A g p j + X t p t u (3) X where = E; I; N ndcates output, u s the utlty level and t ndcates changes on preferences. The parameters g are predetermned 5 and a,, j and t are the unknown ones. For well behaved preferences, we need to assume lnear homogenety and concavty n prces and also that expendture functon s non-decreasng wth respect to utlty. If concavty s not sats ed then t s mposed followng the method of Dewert and Wales (987) that was dscussed before for the case of the revenue functon. At the pont of normalzaton, prces are set to one (p s a untary column vector). These restrctons are necessary to guarantee standard preference choces for the consumers: X a = X j j = 0; X g = (4) Usng Shephard s lemma, the Hcksan demand functon c h for the th good s gven by: c h = (p; u; t) = a + 4 p + X! X j p j g p j! g X X X j p p j g p + t t5 u (5) j Settng (3) equal to the total nomnal expendture, T NE = P utlty (u) I get the ndrect utlty functon p c, and then solvng for the u = g (p; t; T NE) = P p + 2 j T NE P a p! P P P j p p j g p + P t p t (6) 5 g s set equal to the share of value for each good on total consumpton.

13 Then substtutng the ndrect utlty functon (6) nto the Hcksan demand (5) I get the Marshallan demand functon (c m ) for the th good c m = P 2 T NE a p! P 4 X! X P p + P P 2 j p p j g p + P j p j g p j t p t j! g X X X j p p j g p + t t a (7) j In order to dentfy all parameters, I mpose further normalsatons that mply more restrctons. I set technologcal change equal to one at the base year and I mpose restrctons on the parameters such that the denomnator of the rato n (7) s equal to unty P p + P P 2 j p p j (P g p ) + P t p t =. Hence, I mpose the followng restrctons X = and X t = 0 (8) So the base year s consdered as the reference pont that any prevous or future changes on preferences are compared wth. The Marshallan demand equatons (7) together wth restrctons (4) and (8) form the second system of equatons to be estmated. The expendture functon n Eq (3) s a money metrc utlty functon, m (p; c) = e (p; u (c)) (Samuleson, 974). It provdes nformaton on how much money all consumers would need at gven prces (p) n order to consume the observed bundle of goods (c). For xed levels of product prces the money metrc utlty functons, m (p; c), s equvalent to a utlty functon. The expendture functon s ncreasng n utlty, hence for gven product prces the only way to attan hgher utlty s to ncrease your spendng. An mportant feature of the money metrc utlty functon s that depends on observed varables, prces and consumpton bundles. On the other hand the Gorman-polar form mples the assumpton of the representatve consumer model for aggregatng preferences over all the consumers of the economy. 2

14 4 Data There are three nputs n our model, captal, v K, sklled labour, v S ; and unsklled labour,v U. Data for the value (V AD j ) and prce of captal and aggregate labour (W j ), at a 2-dgt SIC87 analyss are obtaned from Dale Jorgenson s database for the perod , where j = K; L and ndcates the 2-dgt ndustry. I construct the value added for captal and aggregate labour for the whole economy, V AD j = X V AD j, by addng the value added for captal and labour for all the 2-dgt ndustres, respectvely. Then the aggregate prce of captal and labour s calculated as a weghted average of ther prces n each 2-dgt ndustry wth weghts the share of each nput n every 2-dgt ndustry, W j = X V AD j V AD j W j. I get the quantty of captal and aggregate labour for the whole economy by dvdng ther value added by ther prce, Q j = V AD j W j, respectvely. The dvson of aggregate labour nto sklled and unsklled labour s mplemented by usng data from the NBER collecton of Mare-Wnshp Data, I get data on educatonal levels, weekly wages, status and weeks worked for full tme workers n 2-dgt SIC ndustres. I dvde workers nto sklled and unsklled followng Katz and Murphy (992), a worker s treated as sklled f he or she spent at least twelve years n educaton. Our sample contans only full tme workers, aged 6-45, that have completed ther educatonal grade and are workng n the prvate sector. Frst, I calculate the total number of weeks worked per year and also the annual wages and salares for sklled and unsklled workers 7. Then I dvde the annual value of wages and salares by the correspondng total weeks worked n order to calculate the full tme weekly wage for each group respectvely. After that I calculate the share of weeks worked for sklled and unsklled workers relatve to the total hours worked of all workers. Smlarly, I nd the shares of wages for each occupatonal group n the sample. Fnally, these shares are multpled wth the total quantty and total wages of aggregate labour, respectvely, obtaned from Jorgenson s data set n order to get the quantty and wages for sklled and unsklled workers n US. In our model there are three aggregate products, exportable, y E, mportable, y I ; and non tradable, y N. Intally the products are dvded nto tradeable and non-tradeables. A 2-dgt Followng Katz, L. and Murphy, K. (992) we nclude only full tme workers that have worked more than 39 weeks n that year. Also, top code wage and salares were multpled by.45 3

15 ndustry s termed tradable f the rato of ts exports plus mports dvded by ts revenue s above 0%, otherwse t s termed as non-tradable 8. Then tradable ndustres are grouped to exportables and mportables dependng on whether ther net exports are postve or negatve, respectvely. For the calculaton of value added of the three aggregate products I agan use Jorgenson s data set. Whle data for output de ators are obtaned from the Bureau of Economc Analyss at a 2-dgt SIC level. Snce these are avalable from 977 onwards, the values of output de ators for years before 977 are obtaned by nterpolaton assumng a constant growth rate equal to the growth rate between 977 and 978. The aggregaton of the three goods s acheved n three stages 9. Frst, I calculate each ndustry s value added (V AD ) by summng the value added of captal and labour of each 2-dgt ndustry, V AD = X V AD j. Then j the value added of each aggregate good, V AD A ; A ndcates the three aggregate outputs, s constructed by addng the value added of each 2-dgt ndustry that belongs to an aggregate product. For example, n order to calculate the value added of the exportable good, I add the value added of the followng ndustres SIC 20, SIC 28, SIC 35, SIC 36, SIC 37 and SIC 38 0 that have been termed as exportable followng the above rule. The aggregate prce of each aggregate good, P A ; A ndcates the three aggregate outputs E; I; N, s a weghted average of the prces of all 2-dgt ndustres, P ; ndcates a 2-dgt ndustry, that belong to an aggregate good, wth weghts the share of each 2-dgt ndustry, V AD V AD A. The aggregate quantty of output s calculated by dvdng the value of each aggregate good by ts aggregate prce, Q A = V AD A P A. Smlarly, the volume of net exports s calculated by dvdng the value of net exports for each aggregate good by ts correspondng aggregate prce. Data for consumpton are generally not avalable and when avalable, they are usually not relable. For these reasons, the volume of consumpton for each of the goods s calculated as the d erence between the volume of output and net exports: c = y T (9) 8 Trade data at a 2-dgt SIC87 level were obtaned onlne from the Centre for Internatonal Data at the Unversty of Calforna Davs. 9 Table shows the SIC categores that are ncluded n each aggregate good. 0 Look at Table, for an explanaton of the SIC codes of 2 -dgt nustres. 4

16 where y and c s the vector of producton and consumpton respectvely. 5 Estmaton I estmate the equaton sets () and (2) together wth the parameter restrctons (0) n order to get the parameters of the revenue functon. Although only estmates of (2) are necessary for the decomposton. I am estmatng both () and (2), because t mproves the e cency of the estmated parameters. The reason lays on the fact that the number of estmated parameters does not alter when (2) s jontly estmated wth () and as a result the degrees of freedom ncrease. The errors related to equatons () and (2) are assumed to be dentcally and ndependently dstrbuted wth zero expected value and a postve de nte covarance matrx. These equatons are jontly estmated by the teratve Three Stages Least Square (3SLS) estmator 2 appled to data for the US manufacturng sector over the perod from 965 to 99. There are sx equatons, three relatng to outputs and three relatng to factor rewards. The goods are exportables, mportables and non-tradeable and the three factors of producton are captal, sklled and unsklled labor. Table 2 shows the estmated parameters of the revenue functon and the R 2 for the system of the sx equatons. Most of the parameters are sgn cant and the system R 2 s 0.98, ndcatng that the overall estmaton seems to appear robust. Lnear homogenety n prces (p) and nputs (v) s sats ed, but ntally convexty for prces was not sats ed and was mposed followng Dewert and Wales (987). Three hypotheses have been tested usng the Wald test that follows a ch-squared dstrbuton wth n degrees of freedom X 2 (n), where n s the number of restrctons mposed. The rst s the hypothess of no convexty, n order to check whether the mposed convexty s accepted by the data. At 5% sgn cance level and 2 degrees of freedom I reject the null of no convexty, snce the Wald Statstc, 24.7, s greater than the crtcal value of The second test s mplctly testng the assumpton of the more general technology on the producton sde of the economy that allows for the presence of jontess n output quanttes. The null hypothess of a producton technology wthout jontness n output quanttes s rejected at a 5% level and 2 degrees of freedom, because the The degrees of freedom, under the 3SLS estmaton, are de ned as the product of the number of years observed tmes the number of equatons estmated mnus the number of the estmated parameters. 2 I use one year lagged values of product prces and endowments as nstruments. 5

17 Wald Statstc, 30.2, s greater than the crtcal value of The last hypothess that s tested s that of a spec caton for the revenue functon that would not nvolve technologcal change as one of the explanatory varables. Once agan the null hypothess of no-technologcal change s rejected at the 5% level of sgn cance, snce the ch-square crtcal value wth two degrees of freedom s smaller, 5.99, than the Wald Statstc of 74., mplyng that spec caton that ncludes technologcal change s consstent wth the actual data. Table 4 and Table 5 show the mean prce elastctes of output ( h ) and the nput (! h ) and technology (! t ) elastctes of output, respectvely. All own prce elastctes are postve, whch s a necessary but not su cent condton for convexty n prces. They range from 0:222 for the mportable good to 0:022 for the exportable, whch mples that the supply for all goods s nelastc. A rse n the prce of the mportable good decreases the supply of both the exportable and the non-tradable good, suggestng that the mportable good s a substtute n the producton wth both the exportable and non-tradable good. Whle an ncrease n the prce of the exportable leads to an ncrease n the supply of the non-tradable, whch mples that the two goods are complements n the producton. All nput elastctes of output are postve, wth the excepton of the elastcty of the nontradable wth respect to unsklled labour ndcatng that a % ncrease n the endowments of unsklled labour for the economy reduces the supply of non-tradable good by almost 6%. From the elastctes of output wth respect to technologcal change t s evdent that on average only the exportable good has ganed from technologcal mprovement, whle the other two goods have been a ected adversely. More spec cally, a % ncrease n technologcal change ncreases on average the supply of the exportable by 2.8%, whle at the same tme reduces the supply of the mportable and non-tradable by.3% and 0.7%, respectvely. The system of equatons (7) s estmated together wth restrctons (4) and (8) n order to obtan the estmates of the parameters for the Marshallan demand functons usng the Three Stages Least Square (3SLS) estmator 3 for the same perod as above. Three equatons of exportable, mportable and non-tradable Marshallan demand functons are estmated. The assumpton of lnear homogenety n product prces s sats ed. But concavty for product prces (p) faled ntally and was mposed followng the method proposed by Dewert and Wales (987). The null hypothess of no concavty s rejected at a 5% level, snce the Wald 3 I use one year lagged values of product prces and ncome as nstruments. 6

18 Statstc, 42.4, s greater than the crtcal value of the ch-square wth two degrees of freedom, Ths mples that the mposed concavty of the Marshallan demand functon wth respect to the product prces s sats ed by the data. In addton the null hypothess of no shfts n preferences over tme s also rejected, supportng the ntal spec caton for the Marshallan demand functons that nvolved such changes n preferences. Table 3 shows the estmates of the parameters of the Marshallan demand functons and the R 2 for the system of equatons. Most of the estmates are sgn cant and the system R 2 s Table 6 presents the Marshallan demand elastctes wth respect to prces, technology 4 and ncome. All own prces elastctes are negatve and for the case of the exportable and non-tradable goods ther demand s elastc. That s changes on the prces of tradable and non-tradable goods cause ampl ed changes on ther demands, respectvely. Exportable and non-tradable goods are substtutes, whle each other par of goods s charactersed by complementarty. From the technology elastctes of Marshallan demand s evdent that on average consumers have shfted ther preferences away from mportables goods and towards ether exportable or non-tradable ones, but the magntude of these e ects s qute small. Fnally, the ncome elastctes of all three goods are postve, suggestng that all of them appear to be normal goods as expected. The hghest average ncome elastcty s observed for the mportable good, :26. Whle the ncome elastctes of exportable and non-tradable are qute smlar, 0:989 for the exportable and 0:863 for the non-tradable. 6 Decomposton of the Growth Rate n US Commodty Net Exports In ths secton I decompose the growth rate of the volume of net exports for the three aggregate goods of US manufacturng, exportable, mportable and non tradable, nto ther ve components usng Eq (A) from the Appendx. Tables 7, 8 and 9 present on the rst two columns the growth rate of the tted volume of net exports (F tted) and ts approxmaton (Aprxoxmated) usng Eq (A), whle the last ve columns present the ve components of the decomposton of Eq (8) n growth format: a) the terms of trade component (T OT ), 4 More precsely, changes n preferences over tme. 7

19 b) the endowments component (Endowments), c) the technology component n producton (P roducton T echnology), d) the change n preferences over tme (P references) and e) the ncome component (Income) for the exportable (E), mportable (I) and non-tradable (N) good respectvely ( = E; I; N). From Table 7, we see that the average growth rate of the tted volume of net exports and the average growth rate of the approxmaton by Eq (A) have the same sgn for each subperod and are also very close n terms of magntude. Ths suggests that the approxmaton used n Eq (A) s a good representaton of the estmated model. The volume of net export for the exportable good ncreased by an average of 48% for the perod If only product prces had changed then the net exports of the exportables would have ncreased by 258 %, as t s seen from the terms of trade (T OT ) component. The endowments component has ncreased the growth rate of net exports of the exportable by 42%, ceters parbus. The e ect of technologcal change n the producton rased the growth of net exports by 28% whle the e ect of changes n preferences s also postve, but smaller n magntude 22%. The only negatve e ect was observed for the ncome component that resulted to a decrease of net exports of exportables by 403%. Hence, the strong postve e ect of the rst four components was weakened by the very strong negatve ncome e ect. For the perod the volume of net exports decreased on average by 29%. Ths s the result of a relatve worsenng of the terms of trade component, despte the much smaller magntude of the ncome component compared wth the prevous perod, whle all the other four components remaned relatvely stable. The terms of trade component led to an ncrease of net exports by 2%, ceters parbus, for the years between 979 and 99, whle for the prevous perod ts contrbuton was almost twelve tmes greater. It worth notcng that the terms of trade and ncome component were the hghest among all products for the perod The average growth rate of the volume of net exports for the mportable good and ts component are presented n Table 8. The values of the rst two columns, ndcatng the tted growth rate and the approxmated growth rate of the net exports of the mportable from Eq (8) are very close. Ths s smlar to the case of the exportable good and suggests that the approxmaton mplemented n Eq (A) s very close to the estmated model. The net exports of the mportable good were decreasng n a stable rate over the two sub-perods. An approxmately 20% and 4% decrease n the net exports of the mportable good for the rst 8

20 and second sub-perod, respectvely. The terms of trade component experenced a relatve worsenng for the mportable good, snce t fell from a 48% ncrease for the years to a 34% ncrease for the second sub-perod. Smlarly, the Endowments and Preferences components were postve but decreased n magntude over the two sub-perods. From 26% to 0% for the rst and from 4% to 3% for the second. In the case of the mportable good the Producton Technology component was negatve n both sub-perods, suggestng that techncal change s regressve for ts producton. Hence, f only techncal change had occurred then the net exports of the mportable would have fallen by 9% on average for the whole perod. The ncome component was negatve as n the case of the exportable, but much smaller n magntude, an average of 70% for the perod Table 9 reports the average growth rate of the net exports for the non-tradable good. They are postve and much hgher n magntude relatve to the growth rate of the two other goods. A possble explanaton could be along the lnes of a "catchng-up" argument. Snce the level of the net exports of the non-tradable were much smaller than the other goods, then t could be expected that ther net exports grow faster. In partcular, they grew by 06% on average over the perod The terms of trade component was postve and hgh n magntude, 53%, but smaller than the one of the exportable. A smlar story for the ncome e ect that t was negatve, -93%, but smaller n magntude than n the case of the rst good. The e ect of techncal change n producton was negatve and very bg n magntude, -80%, suggestng that techncal change has worsened the productve capabltes of the non-tradable good. Also the preferences component was negatve, -20%, mplyng that the consumers changed postvely ther preferences towards the non-tradable good that resulted n hgher consumpton and lower net exports, ceters parbus. Fnally, the Endowments component was postve and very large n magntude. In a hypothetcal scenaro that only endowments had been altered n US manufacturng for the perod , then the net exports of the non-tradable good would have ncreased by 447%. 7 Conclusons In ths paper, I extend the work of Dxt and Woodland (982), on the factors that determne changes of net exports (T ). Frst, the model focuses on a trade equlbrum that allows trade 9

21 mbalances. Second, t ncorporates the e ect of changes n commodty prces, whle t does not rule out the jontness n output quanttes. A general equlbrum analyss s mplemented where the revenue (GDP ) functon and the expendture functon are estmated for the US economy for the perod 963 to 99. Then a decomposton of the changes of the net exports s mplemented. It nvolves a terms of trade component, an endowment component, a technologcal change both n producton and consumpton and an ncome component. I also allow for a more general technology n the producton sde that permts the presence of jontness n output quanttes (see Woodland 977 and Kohl 99). Ths broader de nton of producton s technology that s usually avoded n return of more tractable theoretcal predctons s supported by the data. I follow the emprcal mplementaton of Harrgan (997) and Kohl (992). I rst estmate a system of output equatons derved from a Symmetrc Normalsed Quadratc Revenue functon ntroduced by Kohl (99, 993) usng a Three Stages Least Square (3SLS) estmaton. In addton a system of Marshallan demand functons derved from an expendture functon of a Gorman-Polar type, (Dewert and Wales 988) s estmated usng agan 3SLS. Then, t s possble to calculate the tted volume of net exports for the economy and to proceed to ts emprcal decomposton nto a terms of trade component, an endowment component,a technology component n producton, a change n preferences component and an ncome component as shown n Eq (8). It s evdent that the manly postve growth rate of the net exports of the exportable good for the rst thrteen years s explaned by better terms of trade combned wth a strong postve producton technology e ect, despte the hghest ncome e ect observed for all the three goods and perods. The followng tme perod the volume of net exports for the exportable decreased by 28% manly due to a relatve worsenng n the terms of trade of the exportable good, despte a weaker negatve ncome e ect. On the other hand, the negatve growth rate of the net exports of the mportable good are attrbuted to a szeable negatve ncome e ect, a slower mprovement n the terms of trade for the mportable and a negatve producton technology e ect. The negatve sgn of the producton technology component that mples a regressve techncal change for the producton of the mportable s consstent wth the argument that the mport-competng sector n the US has lost n terms of compettveness the last years due to adverse technologcal change. 20

22 Ths results nto dverson of resources from the mport-competng sector to the rest of the economy and consequently to a decrease n the volume of ts net exports. The net export of the non-tradable grew wth a hgh rate of 06% over the whole perod. Ths s explaned by a very strong postve terms of trade component of 53% combned wth a postve and huge Endowments component of a 356% ncrease, despte the negatve and hgh n magntude growth rate of the rest three components. In partcular, the negatve sgn for the Preferences component mples that domestc consumers have contnuously altered ther preferences n favour of the non-tradable good. From Tables 7, 8 and 9 we see that the growth rate of the volume of net exports was postve for the exportable and negatve for the mportable good on average for the whole perod. But the mportable experenced a hgher growth n absolute terms, whch mples that the net mports of the mportable grew faster than the net exports of the exportable. For the same perod, the growth rate of the volume of trade for the no-tradable was very hgh. Ths suggests that the composton of net exports between the three goods has changed over tme, wth the non-tradable to have ganed a bgger share. Fnally, the probably paradoxcal result of the decreasng volume of trade for the exportable good for over the perod can possbly be explaned by the bg and ncreasng n absolute terms trade de ct of the US economy. 2

23 Appendx Let dag (T ), Y, P, C M, V, X and M ndcate the dagonal matrx of net exports, producton of goods, product prces, Marshallan demands, endowments, tme and ncome respectvely. Rearrangng equaton. (8) I get [dag (T )] dt = [dag (T )] bt + [dag (T )] + [dag (T )] [dag (T )] dt P P V V dv Y dt C M C dm C M C M [dag (T )] C M C dt h Y [dag (T )] " yp C M [dag (T )] bp " P P dp +Y [dag (T )] " yv bv + Y [dag (T )] " yt bt C M [dag (T )] " M cm bm C M [dag (T )] " M ct b t (A) where b T, bp, bv, bt and bm ndcate the growth rate of net exports, product prces, endowments, technologcal change and ncome respectvely. Whle " yp, " M cp, " yv, " yt, " M cm and " M ct are the elastcty of output wth respect to product prces, the elastcty of consumpton wth respect to product prces, the elastcty of output wth respect to nputs, the elastcty of output wth respect to techncal change, the Marshallan elastcty of consumpton wth respect to ncome and the Marshallan elastcty of consumpton wth respect to technologcal change. Equaton (A) s the equvalent of equaton (8) n a growth format. The ve components are: the terms of trade component (T ET ) s h Y [dag (T )] " yp C M [dag (T )] " M cp bp. the Endowments component s Y [dag (T )] " yv bv. the P roducton T echnology component s Y [dag (T )] " yt bt. the P references component s C M [dag (T )] " M cm bm and 22

24 the Income component s C M [dag (T )] " M ct b t. 23

25 References Baer S. L. and Bergstrand J. H., "The Growth of World Trade: Tar s, Transport Cost and Income Smlarty", Journal of Internatonal Economcs, vol 53, pp -27, 200. Besedes T., "Decomposng the Growth of Trade ", workng paper, Centre for Internatonal Data at UC Davs. Dewert W. E. and Wales T.J., Flexble Functonal Forms and Global Curvature Condtons, Econometrca, vol. 55, pp 43-68, 987. Dewert W. E. and Wales T.J., "Normalzed Quadratc Systems of Consumer Demand Functons", Journal of Busness & Economc Statstcs, Vol. 6, No. 3, pp , 988. Dxt A.and Woodland A."The Relatonshp between Factor Endowments and Commodty Trade", Journal of Internatonal Economcs, vol.3:3-4, pp. 20-4, 982. Feenstra R. C., "Integraton of Trade and Dsntegraton of Producton n the Global Economy", Journal of Economc Perspectves, vol 2, ssue 4, pp 3-50, 998. Harrgan J., " Technology, Factor Supples and Internatonal Specalzaton: Estmatng the Neoclasscal Model", The Amercan Economc Revew, v. 87 no. 4, pp , 997. Katz L. and Murphy K., Changes n relatve wages, : supply and demand factors", Quarterly Journal of Economcs, CVII, 36-78, 992. Kohl U., Technology, Dualty, and Foregn Trade: The GNP Functon Approach to Modellng Imports and Exports", London: Harvester Wheatsheaf and Ann Arbor, MI: Unversty of Mchgan Press, 99. Kohl U., A Symmetrc Normalsed Quadratc GNP functon and the US Demand for Imports and Supply of Exports", Internatonal Economc Revew, vol. 34, , 993. Krugman P. and Baldwn R., "The Persstence of the US Trade De ct", Brookngs Papers on Economc Actvty, vol, pp. -43, 987 Laursen, Svend, and Lloyd A. Metzler, Flexble Exchange Rates and the Theory of Employment, Revew of Economcs and Statstcs, vol. 32, pp ,

26 Mendoza E. G., "The Terms of Trade, The Real Exchange Rate, and Economc Fluctuatons",Internatonal Economc Revew, Vol. 36, No., Feb., 995. NBER s Mare-Wnshp Data, Persson, Torsten & Svensson, Lars E O, "Current Account Dynamcs and the Terms of Trade: Harberger-Laursen-Metzler Two Generatons Later," Journal of Poltcal Economy, vol. 93(), pp , 985. Rose A., "Why Has Trade Grown Faster Than Income?", Canadan Journal of Economcs, May 99, no 2, pp Samuelson P. A., "Complementarty: An essay on the 40th Annversary of the Hcks-Allen Revoluton n Demand Theory", The Journal of Economc Lterature, vol. 2, pp , 974. Tnbergen J., "Shapng the World Economy", Twenteth Century Fund, New York, 962. Woodland AD, "Jont Outputs, Intermedate Inputs and Internatonal Trade Theory", Internatonal Economc Revew, vol.8:3, pp ,

27 Table : SIC Codes for Aggregate Goods Aggregate Good SIC Code Category Exportable Food & Kndred Products (SIC 20) Chemcals & Alled Products (SIC 28) Industral & Commerce Machnery & Computer Equpment (SIC 35) Electronc & Other Electrc Equpment (SIC 36) Transportaton Equpment (SIC 37) Instruments, Photographc, Medcal & Optcal Goods (SIC 38) Importable Textle Mll Products (SIC 22) Apparel & Other Fnshed Products (SIC 23) Lumber & Wood Products (SIC 24) Paper & Alled Products (SIC 26) Petroleum Re nng & Related Industres (SIC 29) Leather & Leather Products (SIC 3) Prmary Metal Industres (SIC 33) Mscellaneous Manufacturng Industres (SIC 39) Non-tradable Tobacco Products (SIC 2) Furnture & Fxtures (SIC 25) Prntng, Publshng & Alled Industres (SIC 27) Rubber & Mscellaneous Plastc Products (SIC 30) Stone, Clay, Glass & Concrete Products (SIC 32) Fabrcated Metal Products, Except Machnery (SIC 34) Table 2: Parameter Estmates of revenue functon Parameter Estmate t-stat Parameter Estmate t-stat a EE c IK a EI c IS a EN c IU a II c NK a IN c NS a NN c NU e K b KK e S b KS e U b KU d E b SS d I b SU d N b UU c EK h t c ES h tt c EU System R Hypothess Testng Wald Statstc X0:5 2 No convexty Wald(2) = 24: Non-jontness Wald(2) = 30: No technologcal change Wald(2) = 74: