Resource Wealth, Innovation and Growth in the Global Economy

Transcription

1 Resource Wealth, Innovaton and Growth n the Global Economy Petro F. Peretto, Duke Unversty Smone Valente, ET Zürch anuary 2, 2 Abstract We analyze the relatve growth performance of open economes n a two-country model where d erent endowments of labor and a natural resource generate asymmetrc trade. A resource-rch economy trades resource-based ntermedates for nal manufacturng goods produced by a resource-poor economy. Productvty growth n both countres s drven by endogenous nnovatons. The e ects of a sudden ncrease n the resource endowment depend crucally on the elastcty of substtuton between resources and labor n ntermedates producton. Under substtuton (complementarty), the resource boom generates hgher (lower) resource ncome, lower (hgher) employment n the resource-ntensve sector, hgher (lower) knowledge creaton and faster (slower) growth n the resource-rch economy. The resource-poor economy adjusts to the shock by rasng (reducng) the relatve wage, and experences a postve (negatve) growth e ect that s exclusvely due to trade. Keywords: Endogenous Growth, Endogenous Technologcal Change, Natural Resources, Internatonal Trade. EL Class caton Numbers: E, F43, L6, O3, O4 Introducton The dstrbuton of prmary resources across countres s an mportant determnant of trade patterns. Vrtually every economy endowed wth natural resources that can be processed nto essental factors of producton exports such resource-based commodtes and mports manufacturng goods from resource-poor economes. Ths asymmetrc trade structure stems from dfferent endowments and creates nterestng nterdependences: whle resource-poor economes specalze n manufacturng by force of nature, they gan from tradng non-prmary goods demanded by resource-rch countres specalzed n prmary producton. Lederman and Maloney (27) document that the lnks between trade structure and economc performance are emprcally robust: trade varables, especally natural resource abundance and export concentraton, are mportant determnants of economc growth. We thank Corrado D Mara, Mchael Moore, Rck Van der Ploeg, ohn Seater and semnar partcpants at Duke Unversty (TDM), Unversty of Oxford (OxCarre) and Queen s Unversty of Belfast for comments and suggestons. Smone Valente gratefully acknowledges nancal support by the Swss Natonal Scence Foundaton (grant IZKZ-25589).

2 Although typcal n realty, asymmetrc trade structures do not play a promnent role n the theoretcal lterature on nternatonal trade and economc growth. The benchmark framework of two-country models (e.g., Grossman and elpman 99) concentrates on the role of endogenous nnovaton n generatng convergence across tradng economes that exhbt productvty d erences (Feenstra, 996; Barro and Sala--Martn 997; Acemoglu and Zlbott, 2) and neglects the role of natural resources n drvng trade specalzaton. Natural resource abundance s promnent only n the parallel lterature on Dutch Dsease phenomena (Corden, 984) and/or the Curse of Natural Resources (Sachs and Warner, 995) stuatons n whch greater resource wealth produces negatve e ects on productvty growth but these contrbutons focus on resource-rch countres characterzed as small open economes where asymmetrc trade wth resource-poor countres plays at best a mnor role. In ths paper, we develop a two-country model of R&D-based growth featurng both nter-ndustry and ntra-ndustry trade. The resource-rch economy, that we call ome, exports resource-based ntermedates and d erentated nal manufacturng goods and mports only d erentated nal goods from the resource-poor economy, that we call Foregn. Both economes develop nnovatons that generate endogenous productvty growth. In ths framework, we analyze the e ects of resource booms sudden ncreases n ome s natural resource endowment due to unexpected dscoveres on expendture levels, nnovaton rates, productvty growth, the allocaton of labor across sectors, and welfare n both economes. Our analyss d ers from the Dutch-Dsease lterature n both ams and means. At the theoretcal level, our framework () dstngushes between physcal resource endowments and ows of resource ncome, () assumes that the resource-based sector s vertcally related to both domestc and foregn manufacturng sectors, and () s a fully general equlbrum model where nternatonal prces are endogenously determned by the world market equlbrum. At the conceptual level, we do not attempt to explan Dutch-Dsease phenomena. In our model greater resource abundance may yeld slower or faster growth, but our am s to characterze the transmsson channels between shocks to resource endowments, ncome levels, economc growth and welfare n the presence of asymmetrc trade. Ths research queston s emprcally mportant because the correlaton between resource abundance lterally nterpreted as the sze of the physcal endowment of natural resources and economc performance s stll unclear. When Sachs and Warner (995) rst documented a negatve correlaton and developed the so-called resource curse hypothess, they dent ed resource abundance wth the rato of resource exports to gross domestc product. Ths s an mperfect proxy for physcal abundance and s more a measure of specalzaton. Recent emprcal work by Brunnschweler and Bulte (28) shows that measurng resource abundance wth stock-based ndces whch are much better proxes of the sze of endowments reveals that the data strongly reject the resource curse hypothess snce resource abundance s postvely correlated wth growth and ncome levels. Our characterzaton of the transmsson channels between resource booms and economc growth bulds on two consderatons. Frst, n realty natural endowments are not drectly The resource curse hypothess s also challenged by Lederman and Maloney (27) albet n a d erent way. Snce the Sachs and Warner s (995) measure of resource abundance ncorporates e ects due to specalzaton and trade dependence, Lederman and Maloney (27) dsentangle these e ects by keepng the orgnal measure of abundance whle controllng for export concentraton n panel-based estmates. Ther results reject the orgnal resource curse hypothess: growth rates are found to be postvely correlated to resource abundance and negatvely correlated to export concentraton. 2

3 consumed but exploted by resource-processng rms that sell ntermedate nputs to manufacturng sectors producng nal goods. Snce the nternatonal prce of resource-ntensve goods s endogenous, the elastcty of global demand the sum of domestc and foregn demands for the processed resource s an mportant determnant of the transmsson of endowments shocks. Snce the prmary sectors of resource-rch countres are vertcally related to both domestc and foregn nal sectors, the elastcty of the demand for ntermedates re- ects the characterstcs of the technology employed by nal producers. Second, nternatonal trade mples that real ncome growth n each country depends on the productvty growth rates n the other economes. In a two-country framework endowment shocks n ome may a ect domestc productvty growth and leave Foregn productvty growth unchanged, but real ncome growth n Foregn can nonetheless be a ected by the shock through trade snce ome s productvty matters for Foregn s capacty to mport. We address these ponts by studyng the e ects of resource booms n a model where resource-based ntermedates may be ether complements or substtutes wth other nputs n the nal sector and ntra-ndustry trade n nal goods nduces feedback growth e ects between the two countres. We formalze the vertcal structure of ntermedate and nal sectors followng the closedeconomy model of Peretto (28), whch we extend to nclude a second country and asymmetrc trade. Both economes develop horzontal and vertcal nnovatons: gven total market sze, the rate of horzontal nnovaton determnes the sze of rms, whch n turn drves the rate of vertcal nnovaton and thereby long-run growth. An mportant property of the model s that steady-state growth rates are ndependent of endowments snce the market structure absorbs scale e ects n the long run. One ratonale for employng ths framework s emprcal plausblty: n models dsplayng scale e ects, the growth rate depends on ntal endowments and a resource boom has permanent growth e ects. In our model, nstead, resource booms a ect total factor productvty (TFP) growth durng the transton and yeld permanent e ects on the allocaton of labor and on the number of rms operatng n the resource-rch economy. Another ratonale for our framework s tractablty: we solve the model n closed form and thus have a transparent characterzaton of growth and welfare. Our ndngs concern three man ssues: the nature of the transmsson mechansm, the drecton of ncome and growth e ects, and the transtonal dynamcs mpled by the reallocaton of labor across sectors nduced by a resource boom. We show that a sudden rse n ome s resource endowment nduces a change n the demand for manufacturng goods produced by Foregn, whch trggers a change n the relatve wage but leaves Foregn s TFP growth una ected. In ome, nstead, labor moves across the prmary and manufacturng, wth permanent e ects on the equlbrum number of manufacturng rms and transtonal e ects on TFP growth. The balanced trade condton then mples that the varaton n TFP growth experenced by ome shows up n Foregn s mport prce ndex. In other words, there s transmsson due to trade of the dynamc e ects of the resource boom to the resource-poor country. Wth respect to the drecton of ncome and growth e ects, our analyss emphaszes the role of global resource demand. We show that the sgn of the growth e ect depends on whether labor and the raw resource are complements or substtutes n the producton of resource-based ntermedates. If they are substtutes, a resource boom rases ome s resource ncome and ts overall expendture on manufacturng goods. In Foregn, the wage ncreases due to ome s hgher demand for manufacturng goods. In ome, labor moves nto manufacturng and there s a permanent postve e ect on the equlbrum number of rms. Durng the transton, the 3

4 process of entry rases ome s TFP growth. Ths postve growth e ect n ome s then transmtted to Foregn through trade snce households n each country consume both domestc and mported goods. If labor and the raw resource are complements, nstead, the same mechansm works n the opposte drecton: a postve shock to ome s resource endowment lowers resource ncome and thereby ome s demand for Foregn s manufacturng goods. Consequently, Foregn s wage falls whle ome s number of rms converges to a lower steady-state level and the assocated transtonal growth e ects are negatve for both countres. The ntuton behnd these results s that the elastcty of substtuton n the ntermedate sector determnes the reacton of ome s resource ncome to an ncrease n the resource endowment. Substtutablty mples elastc demand for the raw resource, whch means that a postve shock to the resource supply requres a mld reducton n the resource prce so that the net e ect on resource ncome s postve. Complementarty, nstead, mples nelastc demand, whch means that the resource boom causes a fall of the resource prce so drastc that t more than o sets the larger quantty sold wth the result that resource ncome falls. The transtonal dynamcs of sectoral labor employment n the ome economy are drven by the coexstence of vertcal and horzontal nnovatons. The amount of labor employed n the manufacturng sector, n partcular, s subject to two e ects pushng n the same drecton. When the resource boom yelds hgher (lower) resource ncome, the rst e ect s a sudden ncrease (reducton) n labor employed n nal producton due to the upward (downward) jump n expendture on manufacturng goods. Subsequently, the process of net entry (net ext) of manufacturng rms yelds further ncreases (decreases) of employment n the producton of nal goods n ome. ence, the crowdng-n (crowdng-out) e ects generated by resource booms are self-renforcng due to the two, nterdependent dmensons of nnovaton. The plan of the paper s as follows. Secton 2 descrbes the model assumptons. Secton 3 characterzes the world compettve equlbrum and derves the man results. Secton 4 dscusses the connectons wth prevous lterature, and secton 5 concludes. 2 The Model There are two countres and two factors of producton: ome, denoted, has labor and a natural resource; Foregn, denoted F, has only labor. ome uses the natural resource and labor to produce a homogeneous, resource-based ntermedate nput. Both countres combne the resource-based nput wth labor to produce d erentated manufacturng goods. Consequently, ome exports both resource-based and manufacturng goods whle Foregn exports only manufacturng goods. Labor s homogeneous and moves freely across sectors wthn each country; for smplcty, t does not move across countres. Each economy develops both horzontal and vertcal nnovatons. 2. ouseholds Each country s populated by a representatve household wth L members, where = ; F s the country ndex. Each household member supples nelastcally one unt of labor, and populaton s assumed constant for smplcty. Indvdual utlty s a weghted average of consumpton of home and foregn goods. Preferences. Each country produces N varetes of consumpton goods. X, 2 ; N 4

5 s the quantty of good produced n country. Snce ths quantty sats es both domestc and foregn consumpton, we can wrte X = X h + X f, where X h s the quantty consumed n and X f s the quantty exported to F. Symmetrcally, manufacturng producton n Foregn equals X F = X F f + X F h, where X F f s the quantty consumed n F and X F h s the quantty exported to. Instantaneous utlty n each country s: 2 log u = log 4 Z N 2 log u F = ( ) log 4 X h L Z N X f L F 3 d5! 2 + ( ) log 4 3 d5 2 + log 4 Z N F Z N F X F h L X F f L F! 3 d5 3 d5 ; () ; (2) where > s the elastcty of substtuton across goods and 2 [=2; ) s domestc bas,.e., the weght that each consumer assgns to utlty from consumng goods produced n her country of resdence. For = =2, the model reduces to a standard one of symmetrc preferences across countres. We rule out = because t yelds no trade. We assume ntegrated world markets and abstract from trade frctons (e.g., tar s, transport costs) so that the law of one prce holds and P, the prce of good produced n country, apples n both ome and Foregn. Utlty maxmzaton. The household maxmzes U = Z e t log u (t) dt; (3) where > s the tme-preference rate. The nstantaneous expendture constrants are: E = E F = Z N Z N Z N F P X h d + P X f d + Z N F P F X F h d; (4) P F X F f d; (5) where E s the expendture of resdents of country on consumpton goods. The wealth constrants are: _ A = r A + W L + p + M E ; (6) _ A F = r F A F + W F L F E F ; (7) where A s assets, r the rate of return to assets, and W the wage rate. Snce the resource endowment and the resource-processng sector are located n ome, constrant (6) also ncludes dvdend ncome from resource-processng rms, M, and resource ncome p, where represents the resource endowment and p the market prce of the resource. 2.2 Manufacturng sector The manufacturng sector conssts of rms producng d erentated consumpton goods. In lne wth the growth lterature, we have sngle-product rms so that N represents the mass 5

6 of manufacturng rms operatng n country. Productvty growth stems from both vertcal and horzontal nnovatons. Each manufacturng rm performs R&D to ncrease ts own total factor productvty. At the same tme, outsde entrepreneurs perform R&D to develop new products and then set up rms to serve the market. Ths process of horzontal nnovaton ncreases the mass of rms N over tme. Producton. Each rm n each country produces wth the technology X = Z h M L X ; 2 ; N ; (8) where X s the quantty produced, L X s labor employed n producton, > s a xed labor cost, M s the quantty of the resource-based nput, Z s the stock of rm-spec c knowledge and 2 (; ) s the elastcty of the rm s total factor productvty wth respect to knowledge. Technology (8) exhbts constant returns to scale to rval nputs whle the rm can rase ts total factor productvty by rasng ts knowledge stock Z. Vertcal Innovaton. Each rm s knowledge evolves accordng to where > s a technologcal opportunty parameter, K = _Z = K L Z ; (9) Z N N Z d: () s the stock of publc knowledge n country and L Z s labor employed n R&D actvty. 2 For smplcty we set nternatonal knowledge spllovers at zero. Qualtatvely, nothng of substance changes f they are postve (see, e.g., Peretto 23). orzontal nnovaton (entry). The mass of manufacturng rms n each country evolves accordng to how much labor s devoted to developng new products and to startng up operatons. For each entrant, denoted wthout loss of generalty, the labor requrement translates nto a sunk cost that s proportonal to the value of the producton good. Formally, lettng L N denote labor employed n start-up actvty by each entrant, the entry cost equals W L N = Y, where Y P X s the value of producton of the new good when t enters the market and > s a parameter representng technologcal opportunty. Ths assumpton captures the noton that entry requres more e ort the larger the antcpated volume of producton. 3 Entry creates value V (t) = Z t X (v) e R v t [r (s) ]ds dv; () 2 Peretto and Smulders (22) provde explct mcro-foundatons for the knowledge aggregator (). 3 Ths assumpton can be ratonalzed n several alternatve ways and does not a ect the generalty of our results (see Peretto and Connolly 27). In partcular, we would obtan dentcal dynamcs of the mass of rms by assumng, nstead, a consoldated R&D sector producng blueprnts wth lnear technology and makng zero pro ts. 6

7 where X s the nstantaneous pro t ow, r (v) s the nstantaneous nterest rate and > s the nstantaneous death rate of rms. 4 Free entry requres V = Y = W L N ; (2) whch says that the value of the new rm must equal the entry cost for each entrant. 2.3 Intermedate sector n ome The ntermedate nput s produced by resource-processng rms n country. Ths sector captures the key propertes of the economc use of the natural resource and thus drves many of our results. In partcular, resource-processng rms use a CES producton technology that brngs to the forefront the role of the degree of substtuton/complementarty between labor and the natural resource n the producton of the ntermedate nput. For smplcty, we assume that ths sector s compettve. Producton. Let M be the quantty of resource-based nput used n country. The total output of the ntermedate sector M s splt between the quanttes sold to domestc and to foregn nal producers, Z N Z N F M = M + M F = M d + M F d; where M s the amount of ntermedate used by the -th manufacturng rm n country. The ntermedate s produced by an nde nte number of dentcal compettve rms n ome under constant returns to scale. The technology of the ntermedate sector s thus represented by M = &L M + ( &) R ; (3) where & 2 (; ) s a weghtng parameter and s the elastcty of substtuton: labor and the natural resource are complements when < and substtutes when >. As!, technology (3) reduces to the Cobb-Douglas form L & M R &. Total pro ts of the ntermedate sector equal M = P M M W L M pr, where P M s the prce of the resource-based good and p the prce of the natural resource. Market-clearng Equlbrum. The lnk between resource use, R, and the resource endowment,, can take varous forms. To keep the analyss smple, we assgn full and well-de ned property rghts over the endowment to the household and assume full utlzaton at each pont n tme of a non-depletable resource stock. ence, n equlbrum R = and M = hold. The results do not change f R s a constant fracton of, whch would be the case f, e.g., the resource were renewable and the extracton rule to keep a constant ow of resource use. Snce our am s to study the e ects of resource booms, represented by sudden ncreases n, the assumpton of constant resource use s not partcularly restrctve: even n the case of exhaustble resources, a sudden jump n the resource stock would mply an upward shft n the tme pro le of extracted resource ows at each pont n tme. 5 4 The man role of the nstantaneous death rate s to avod the asymmetrc dynamcs and assocated hysteress e ects that arse when entry entals a sunk cost. Such unnecessary complcatons would dstract attenton from the man pont of the paper. 5 If we model the resource stock (t) as an exhaustble one, the harvestng rule would be R (t) = ~ e ~t, 7

8 2.4 Balanced trade The asymmetrc structure of trade mples that ome exhbts a structural de ct n manufacturng: beng the sole suppler of resource-based ntermedates, the value of ts manufacturng mports necessarly exceeds the value of ts manufacturng exports. We rule out trade n assets, so that trade n goods s balanced n each nstant. Formally, then, the balanced-trade condton requres Z N P M M F + Z N F P X f d = P F X F h d; (4) where the left-hand sde s the value of total exports from ome to Foregn,.e., the value of resource-based exports plus the value manufacturng exports, and the rght-hand sde s the value of manufacturng exports from Foregn to ome. 3 The World General Equlbrum In ths world economy there are N +N F + global goods markets: n each d erentated good market, the law of one prce apples and the local monopolst sets the global prce P gven the global demand curve; n the market for the resource-based good M, the global prce P M s set compettvely at the pont where the collectve supply of ome producers meets global demand. As the raw natural resource R s not tradeable, the ome s nternal market for the resource clears when local demand meets local supply. The two labor markets clear separately n each country, determnng the local wages. We rule out trade n assets so that there are two compettve nancal markets: n each country the supply of nvestment funds from savers meets the demand from ncumbent rms and entrepreneurs to determne the local nterest rate. The no-arbtrage condton establshes that returns be equalzed across alternatve uses wthn each country, thereby determnng the allocaton of savng across ncumbent rms and entrepreneurs. 3. Equlbrum Condtons The equlbrum of the world economy s characterzed by the followng condtons (all dervatons are n the Appendx). Each consumer allocates a fracton of expendture to domestc goods. Accordngly, the values of manufacturng producton n each country are Y = E + ( ) E F and Y F = E F + ( ) E : (5) The tme paths of expendtures are determned by the Keynes-Ramsey rules _E =E = r and _E F =E F = r F ; (6) and the demand schedule for each manufacturng good s X = a P ; (7) where ~ s the reference dscount rate, and an exogenous ncrease n would translate R (t) upwards at any t. In the present model, we have a smpler but qualtatvely dentcal e ect snce an upward jump n corresponds to a proportonal upward jump n R. 8

9 where a Y = R N P d. Ths term contans only aggregate varables and s therefore taken as gven by each producer. Each monopolst sets ts prce at a constant mark-up over margnal cost. Snce the markup s nvarant across varetes and rms choose dentcal ntertemporal R&D strateges, the equlbrum s symmetrc: n country each monopolst employs the same amount of labor, L Z, n rasng ts own productvty, as well as the same amounts of labor and resource-based nput, L X and M, to produce the same quantty sold at the same prce. Aggregatng the condtonal factor demands across rms yelds M = Y L X = N + ( ) By symmetry, the typcal rm s knowledge stock s Z _Z P M ; (8) Y W : (9) = Z and evolves accordng to Z = L Z N ; (2) where L Z = N L Z s aggregate employment n vertcal R&D. Symmetry also mples that the value of the rm s proportonal to the value of ts own producton, and that the equlbrum rate of horzontal nnovaton s V = Y =N ; (2) _N N = W L N Y : (22) The rates of vertcal and horzontal nnovaton n (2) and (22) are nterdependent through the no-arbtrage condton that the assocated returns, rz W = _ Y L W + N W Z N ; (23) rn Y = N Y N + N W Y + L Z N ; (24) must be equal. The nancal market n each country clears when the resultng summary return to nvestment equals the return to assets demanded by savers n (6),.e., when r = rz = r N. In country the ntermedate sector conssts of an nde nte number of compettve rms that produce up to the pont where the prce equals the margnal cost. In equlbrum we thus have P M = C M W ; p, where C M (:; :) s the unt cost functon assocated to (3). The condtonal demands for the natural resource and labor read pr = S R M W ; p P M M; (25) W L M = S R M W ; p P M M; (26) where S R M W ; p ( &) p (&) (W ) + ( &) p (27) 9

10 s the elastcty of the unt-cost functon wth respect to the resource prce. The resource market clears when R =. Notce that SM R W ; p s ncreasng n p f the natural resource and labor are complements ( < ), decreasng n p f they are substtutes ( > ), and ndependent of p n the specal Cobb-Douglas case ( = ). Combnng (8) wth (25) we obtan p = SM R W ; p Y + Y F : (28) Ths relaton determnes the prce of the natural resource as a functon of the value of world manufacturng producton and ome s endowment of the resource. Snce the resource-processng sector only exsts n country, the market-clearng condtons for labor read L = L X + L Z + L N + L M and L F = L F X + LF Z + LF N, respectvely. The set of equlbrum relatons s then completed by the balanced-trade condton. In the Appendx we show that balanced trade mples that the values of expendture and manufacturng producton n the two countres are lnearly nterdependent. In partcular: E F E = + E Y = and and Y F Y = + 2 ; (29) E F Y F = : (3) It follows from (5) and (29) that balanced trade nduces nterest rate equalzaton snce a constant expendture rato E F =E mples r = r F. Ths property suggests that our assumpton of separated nancal markets s ndeed a smpl caton that has no substantal e ect on the results Instantaneous Equlbrum and Comparatve Statcs We take as our numerare the ome wage. Ths normalzaton mples that the equlbrum values of manufacturng producton n both countres are constant at each pont n tme and s therefore equvalent to normalzng (nomnal) expendture. 7 Ths approach s standard n the trade lterature, e.g., Grossman and elpman (99), and mples that the real growth rate of each economy s represented by the growth rate of the physcal unts appearng n the utlty bundles ()-(2). For expostonal clarty, we study the determnaton of the equlbrum values of nomnal expendtures n ths secton and study the assocated growth rates n physcal quanttes n secton 3.5. Gven W, the nstantaneous equlbrum relatons reduce to a system of four statc equatons determnng smultaneously the resource prce p, the values of manufacturng 6 Results (29)-(3) hnge on the assumpton that the manufacturng technology s Cobb-Douglas. If we posted a manufacturng technology wth elastcty of factor substtuton d erent from, e.g., a CES, the term n these expressons would be country-spec c snce t would be a functon of the factor prces W and P M. We could stll characterze the world general equlbrum along the lnes that we follow n the paper, but we would obtan essentally the same results at the cost of a vastly more complcated analyss. 7 The normalzaton W yelds the statc system (3)-(34) determnng constant equlbrum values for manufacturng producton. From (29)-(3), balanced trade mples constant ratos between expendtures and producton n each country. As a consequence, the values of ome and Foregn expendtures, E and E F, are constant over tme, whch mples r = r F = from the Keynes-Ramsey rules (6).

11 producton Y and Y F, and the foregn wage W F : Y = L + p + (3) ; Y = L f (p) ; (32) Y F = Y ; (33) W F = L F Y F ; (34) where we have de ned the constant = + 2 and the functon f (p) ( + ) SM R (; p) : (35) We use subscrpts to denote the equlbrum values determned by (3)-(34). The system has the desrable property of beng block-recursve, wth equatons (3)-(32) determnng autonomously constant values Y and p, and the remanng two equatons then determnng constant values Y F and W F. We can thus proceed n steps. ome Producton and Resource Prce. Equaton (3) descrbes how manufacturng producton per capta depends on the endowment per capta, va the latter s e ect on resource ncome and thus on expendture. Ths s a lnear relaton whereby an ncrease (decrease) n resource ncome, p, ncreases (decreases) the value of producton va ncreased (reduced) expendtures. Equaton (32) descrbes how the resource prce, and hence resource ncome, depends on manufacturng producton per capta va ts e ect on the demand for the natural resource. Ths relaton s non-lnear and ts slope depends on the unt-cost elastcty SM R (; p) through the functon f (p) de ned n (35). Ths mples that the propertes of the equlbrum depend on whether the ntermedate sector nputs, R and L M, are complements, substtutes, or none of the two. The upper dagrams of Fgure llustrate the determnaton of the equlbrum values Y and p n the three cases. The lower dagrams descrbe the e ects of exogenous varatons n the resource endowment,, on equlbrum values. When the resource endowment rses, the resource prce falls n all cases but the e ect on Y depends on the elastcty of substtuton: manufacturng producton per capta falls when <, rses when >, and remans the same when =. The economc nterpretaton of these comparatve-statcs results s dscussed n Proposton below. Foregn Producton and Relatve Wage. Due to nternatonal trade the value of Foregn s manufacturng producton s drectly related to ome s: (33) says that a change n Y yelds a proportonal change n Y F ; (34) then says that the change n Y F yelds a proportonal change n W F n the same drecton. The key to these e ects s that the change n ome s supply of the resource-based nput requres a change n the same drecton n the value of Foregn s manufacturng producton snce Foregn must ncrease the value of ts manufacturng exports to pay for the hgher value of ts resource-based mports. The nduced change n the demand for labor causes the Foregn wage to move n the same drecton. We summarze these results as follows.

12 Proposton Followng an ncrease n, the resource prce p falls. Expendture n ome, and expendture and the wage n Foregn, move n the same drecton as resource ncome n ome: dy sgn dy F = sgn dw F = sgn d (p ) = sgn ; d d d d where d (p ) d 8 < : < f < = f = > f > ; (36) so that resource ncome rses (falls) f labor and the natural resource are substtutes (complements). If the resource-processng technology s Cobb-Douglas, the e ect of the change of on resource ncome s zero. The ntuton for these results s twofold. Frst, the elastcty of substtuton n the ntermedate sector determnes the change n ome s resource ncome n response to an ncrease n the resource endowment: an ncrease n always reduces the equlbrum prce p, but the net e ect on resource ncome, d (p ) =d, depends on the elastcty of substtuton between labor and the resource. If >, the demand for the natural resource s elastc so that a postve shock to the resource supply yelds a mld reducton of the equlbrum prce. Accordngly, resource ncome rses and drves up equlbrum expendture and producton. In contrast, < mples nelastc demand, whch yelds a drastc reducton of the equlbrum resource prce and a fall of resource ncome that drves down expendture and producton. Second, the nterdependence between the resource-rch and resource-poor economes due to balanced trade mples postve feedbacks: the value of producton and expendture n the two countres move n the same drecton n response to the resource boom. The expanson/contracton of actvty n ome nduces an expanson/contracton n Foregn. A very mportant aspect of ths nterdependence s the e ect on Foregn s wage. Snce Foregn obtans resource-based ntermedates by sellng manufacturng goods to ome, an ncrease n ome s resource ncome generates a pressure on Foregn s wage through the ncrease n the demand for ts tradeable nal goods. 3.3 Innovaton Rates In both countres, aggregate productvty ncreases over tme due to vertcal and horzontal nnovatons. Substtutng r = nto (23) we obtan that the typcal rm s knowledge stock evolves accordng to _Z (t) Z (t) = ( Y W N (t) ( + ) f N (t) < N Y + W f N (t) N : (37) Ths expresson asserts that rms undertake vertcal nnovatons accordng to the share =N of the wage-adjusted total market for manufacturng products, Y =W, that they capture: the larger the rato Y = W N, the more they nvest and the faster they grow. The wage adjustment re ects the fact that R&D s n unts of labor and that t s an endogenous sunk cost that rms can spread over ther own volume of producton Y =N. If the mass of rms exceeds N, the rato Y = W N falls below the crtcal threshold where they shut down R&D altogether. 2

13 Accordngly, the mass of rms evolves accordng to 8 h ( ) _N (t) >< N (t) = ( + ) W ( + ) Y N ( ) (t) (+) h >: ( + ) N (t) (+) W Y f N (t) < N f N (t) N : (38) We concentrate on the rst type of equlbra, where vertcal nnovaton s postve, and assume that N (t) < N always holds (see the Appendx for detals). A nce property of (38) s that t s a logstc equaton that can be drectly ntegrated to obtan the tme path of the number of rms. De nng the coe cent ( ) ( + ), the explct soluton s N (t) = N ss + e t N ss N ; (39) where N N () s gven at t =. In the long run, we have: lm t! N (t) = N ss lm t! _Z (t) Z (t) = z ss ( ) ( + ) ( ) ( ) ( ) ( + ) Y W ; (4) ( + ) : (4) Results (4)-(4) mply that productvty growth n the long run s exclusvely drven by vertcal nnovatons. Durng the transton, the ncrease n rms knowledge s accompaned by a process of net entry, or ext, n the manufacturng busness. In the long run, the mass of rms converges to a constant equlbrum value and knowledge accumulaton s the only source of productvty growth. Nevertheless, t would be msleadng to conclude that horzontal nnovaton yelds only a transtonal e ect on productvty growth. In fact, t plays a crucal role n determnng the e ect of endowments. The mportant property of the lmt zss s that t s ndependent of the endowments, L and L because changes n endowments trgger changes n the wage-adjusted value of manufacturng producton, Y =W, whch are fully absorbed by the mass of rms, Nss, as (4) shows. Ths result hghlghts the general absence of scale e ects n the class of models that allow for both vertcal and horzontal nnovaton. Moreover, explotng the closed-form solutons for the paths of the key state varables N and N F, we can characterze n detal how each economy adjusts to the resource boom. Innovaton rates n ome. Assume that ncreases suddenly at tme t and, for smplcty, that the economy s n steady state at t. Consder rst the case >. From Proposton, the resource boom causes an mmedate and permanent ncrease n Y. From (4), ths ncrease n market sze yelds an ncrease n the steady-state mass of rms Nss. From (38), the rate of net entry N _ =N jumps up and then declnes, takng the economy gradually and smoothly from N (t ) to the new steady state. From (37), the upward jump n expendture Y yelds an ntal jump up of the rate of vertcal nnovaton Z _ =Z. As the mass of rms grows durng the transton the e ect of the larger market sze s absorbed and n the long run the value of the producton of each rm, Y =N (t), returns to the same steady-state level as before the shock. Consequently, the rate of vertcal nnovaton also returns to the steady-state 3

14 level n (4) whch s ndependent of the endowments L and. The drecton of these e ects s reversed when <. In ths case, the resource boom nduces a drop n Y and thereby n Nss. Durng the transton there s net ext from the manufacturng busness, _N <, whch drves the rate of vertcal nnovaton back to the pre-shock level zss. Innovaton rates n Foregn. The Foregn economy adjusts to the resource boom n ome by smply changng ts volume of producton and ts wage wthout exhbtng any change n the dynamcs of nnovaton rates. The crucal equaton for ths result s (34), showng that the rato between equlbrum expendture and wage s constant and ndependent of ome s resource endowment. If > ( < ) the resource boom ncreases (decreases) Foregn expendture Y F va trade see (33) and Proposton but the Foregn wage W F ncreases (decreases) proportonally. From (38), a constant rato Y F =W F mples no e ects on the rate of horzontal nnovaton N _ F =N F, and thereby unchanged dynamcs n the rate of vertcal nnovaton Z _ F =Z F. We summarze these results as follows. Proposton 2 If > ( < ), an ncrease n generates a hgher (lower) steady-state level of the mass of rms n the ome economy, whch ncreases (decreases) both the rates of horzontal and vertcal nnovaton durng the transton. In the long run, both nnovaton rates n ome converge to the same steady-state levels as before the shock,.e., _N =N = and _ Z =Z = z ss. The Foregn economy fully absorbs the shock by ncreasng (decreasng) the wage, wth no e ects on transtonal or long-run nnovaton rates. In the next subsecton, we explot the closed-form solutons derved above to determne the exact behavor of sectoral employment levels durng the transton. 3.4 The Reallocaton of Labor n ome The e ects of the resource boom on nnovaton rates hnge on a reallocaton mechansm that changes the employment shares of the varous economc actvtes. Ths reallocaton follows drectly from the market-clearng condtons (see Appendx): L N (t) = Y + L Z (t) = Y L X (t) = N (t) + ( ) L M (t) = L ( ) ( + ) Y + N (t) ; (43) N (t) ; (42) Y ; (44) Y : (45) Assume that ncreases at tme t and consder rst the case >. Recall that the mass of rms at the tme of the shock, N (t ), s pre-determned and does not jump. From Proposton 2, the resource boom yelds an mmedate ncrease n Y and the e ects on ome s allocaton of labor are as follows. 4

15 >From (42), employment n start-up actvtes, L N (t), jumps up at tme t. gher expendture moves labor nto entry operatons that drve the gradual ncrease n the mass of rms N (t) towards Nss. Importantly, after the ntal upward jump, employment n entry gradually declnes but converges to a hgher steady-state wth respect to the pre-shock steady-state level (see Appendx). Smlar dynamcs characterze the transton of L Z (t). From (43), labor employed n vertcal nnovaton s postvely related to expendtures but negatvely related to the mass of rms: L Z (t) jumps up wth Y at t and then gradually declnes as N (t) grows. The ntal jump s not fully absorbed by entry, however, and the new steady-state level of L Z (t) s hgher than ts pre-shock level. Labor employed n manufacturng producton reacts d erently. From (44), L X (t) jumps up wth Y at t and, after the ntal jump, keeps rsng as the entry process attracts even more labor nto producton. ence, L X (t) converges to a level that exceeds the pre-shock steady state for two reasons: (a) each rm wshes to produce more because the market s larger and (b) the larger market supports more rms. Fnally, equaton (45) shows that total labor employed n the resource-processng sector s negatvely related to expendture and ndependent of the mass of rms: L M (t) adjusts nstantaneously to the sudden ncrease n Y due to the endowment shock wth no further dynamcs. We summarze all these results n Fgure 2, left graphs. The e ects of a resource boom n the opposte case < obvously yeld specular transton paths (Fgure 2, rght graphs). These results suggest two remarks. Frst, the two forces drvng ths transton the mmedate ncrease n market sze and the process of net entry t nduces o set each other n the long run so that employment per rm n producton, L X (t) =N (t), and vertcal nnovaton, L Z (t) =N (t), s ndependent of the endowments L and. Ths exact o set whch s the key to the elmnaton of the scale e ect s the reason why the growth acceleraton generated by the resource boom s only temporary. Second, the crowdng-n (crowdng-out) e ects generated by resource booms n the manufacturng sector are self-renforcng due to the two, nterdependent dmensons of nnovaton: after the ntal jump, the process of net entry (net ext) yelds further ncreases (decreases) of total labor employed n nal producton along the transton to the new long-run equlbrum. 3.5 Total Factor Productvty, Growth and Welfare The closed-form solutons derved above allow us to characterze analytcally the relatve growth performance of tradng economes and the welfare e ects of resource booms. Substtutng the equlbrum relatons obtaned n the utlty functons () and (2), nstantaneous utlty levels equal (see Appendx) log u (t) = log + log T (t) T F (t) ; (46) log u F (t) = log F + log T F (t) T (t) : (47) Expressons (46)-(47) decompose utlty levels n two terms. The rst s represented by the ntercept, whch s constant over tme and depends on the equlbrum values of expendtures, 5

16 wages and resource prce: F " Y # " F Y # F L CX (; C M (; p )) L F CX F (W F ; C M (; p )) ; (48) " Y # " F Y # F L CX (; C M (; p )) L F CX F (W F ; C M (; p )) ; (49) where and F are exogenous constants de ned n the Appendx. The second term s tmevaryng and s the weghted average of the total factor productvty ndces of both economes de ned as: T (t) Z (t) N (t) and T F (t) Z F (t) N F (t) : The weghts assocated to the aggregate TFP ndces n (46)-(47) are and, that s, the parameters representng preferences for domestc and mported nal goods. Ths result clar es that the growth rate of each economy depends on the total factor productvty growth of both economes due to trade. If productvty growth n one economy, say ome, s a ected by a country-spec c shock, real ncome growth and welfare dynamcs n Foregn respond even though Foregn TFP growth s not a ected by the shock. Equatons (46)-(47) allow us to splt the overall welfare e ect of a resource boom nto () level e ects at t and () transtonal growth e ects after t. The nstantaneous level e ects are captured by the ntercept terms and F : from Proposton, a sudden ncrease n generates mmedate jumps n equlbrum expendtures, the relatve wage and the resource prce (Y ; Y F ; W F ; p ). Snce the rm-spec c knowledge stocks (Z ) and the mass of rms (N ) n both countres are xed at tme t, the nstantaneous e ects of the resource boom on u (t ) are only due to the jumps of and F. The transtonal growth e ects arsng after t, nstead, are due to the dynamcs of the TFP ndces. As shown n Proposton, a sudden ncrease n mod es nnovaton rates only n ome. The resultng transtonal dynamcs n ome s total factor productvty T (t) a ect, n turn, the growth rates of utlty n both economes. The fact that the mass of rms n each country follows a logstc process allows us to characterze the behavor of TFP n closed form. Proposton 3 In each country the behavor of TFP levels over tme s gven by log T (t) = log T + gss t + + e t ; (5) where and Y 2 + ( ) W Nss = ( ) ( + ) ; N ss N s a country-spec c value that remans constant throughout the transton. 6

17 Proof. See the Appendx. The tme paths of T (t) and T F (t) capture the combned e ects of a resource boom on market sze and knowledge accumulaton n each economy. To see the e ects on welfare n ome, we substtute result (5) n (46) and calculate present-value utlty U from (3), obtanng where U = log T T F + (5) + log + g {z } ss + ( ) gss F + + ( ) F ; {z } Statc Term {z } Transtonal Growth Term Long-run Growth Term + + : Expresson (5) decomposes welfare n ome n three parts. The statc term captures the baselne value of nstantaneous utlty n (46), whch s a weghted average of the expendtureto-producton-cost ratos observed n the two countres. The second term s a weghted average of the long-run growth rates n the two countres. The thrd term s a weghted average of the changes n market sze determnng the transtonal growth rates n the two countres. Snce an exogenous ncrease n does not modfy long-run growth rates, resource booms a ect welfare through varatons n the statc term (statc e ects) and n the transtonal growth term (transtonal e ects). Spec cally:. From (48), the statc e =@ has two components. The rst component says that when rses, p n the denomnator falls whle Y rses (falls) f > ( < ). The second component s slghtly more complcated because there s an adverse wage e ect that tends to o set the e ect of the drop n the resource prce: W F moves n the same drecton as Y. Whether foregn goods become more or less expensve depends on the relatve strength of the two e ects. Consequently, the sgn of the statc e ect s generally ambguous.. Snce F s ndependent of, the transtonal e ect of a resource boom shows up only through, whch moves n the same drecton as Y and therefore rses (falls) f > ( < ). Gven the quas-symmetry of the model, the expresson for welfare n Foregn s qualtatvely dentcal. We thus don t show t to save space. The d erence s that the change n welfare due to the resources boom s fully mported. Expresson (5) allows us to dentfy a clear trade-o that does not arse n the closedeconomy verson of ths model (Peretto 28). To see t most clearly, consder the case of substtuton, whch yelds an elastc resource demand. In closed economy, > yelds a welfare ncrease due to an upward jump n utlty at tme, followed by a temporary growth acceleraton that eventually des out. In ths paper, we have a smlar ome e ect whch s however accompaned by a Foregn e ect nduced by nternatonal trade. Usng (48) and 7

18 rearrangng terms n (5), we have U = ( " log T T F + log # ) =L ) CX (; C + M (; p )) + {z } ome Term ( " F +( ) log # ) F =L F ) CX F (W F + ; C M (; p )) + F : {z } Foregn Term As rses, > mples that the ome term ncreases due to a postve statc e ect, d(y =CX )=d >, and to a postve transtonal e ect, d =d >. The Foregn term, however, may react n ether drecton snce the sgn of " d d log F (Y # F =L F ) CX F (W F (52) ; C M (; p )) s generally ambguous. Followng a resource boom wth >, f the ncrease n the Foregn wage s weak relatve to the reducton of the resource prce, unt producton costs n Foregn fall and (52) s postve. In ths case, the Foregn e ect renforces the ome e ect and the overall e ect on ome welfare s postve. If the wage ncrease domnates the fall n p, nstead, (52) s negatve and the Foregn E ect contrasts the ome e ects. The role of nternatonal trade s evdent also n the case of complementarty. When <, the resource boom trggers such a drastc fall of p that expendture Y falls as well, and generates a growth slowdown the so-called Curse of Natural Resources. If the economy s closed, the curse manfests tself as a temporary slowdown as the economy returns to the same steady-state growth rate as before the shock. In our open economy model, the curse manfests tself also n the Foregn economy. The reason s that the fall of ome expendture Y trggers a fall of Foregn expendture Y F whch n turn trggers a fall of ts wage. 4 Dscusson As noted n the Introducton, the theoretcal lterature on nternatonal trade and nnovatondrven economc growth usually abstracts from asymmetrc trade structures nduced by uneven endowments n spec c prmary factors. It focuses on convergence ssues and catchng-up processes whereby laggng economes may reduce structural growth d erentals wth technology leaders through knowledge spllovers (Grossman and elpman 99), ows of deas (Rvera-Batz and Romer 99), mtaton (Barro and Sala--Martn 997) or trade n ntermedate nputs (Feenstra 996). Our analyss adopts a smlar two-country framework but focuses on the relatve performance between resource-rch and resource-poor economes and the correlaton between resource abundance, ncome levels and growth. The analyss of resource-rch economes s typcally assocated wth the parallel lterature on Dutch-Dsease phenomena and/or the Curse of Natural Resources. The emprcal case for the resource curse hypothess bulds on the results of Sachs and Warner (995) who observed that many resource-rch countres dsplay slow growth. Several theoretcal studes explan the curse by followng the logc of Dutch Dsease models (Corden, 984): they characterze 8 +

19 resource-rch countres as small open economes tradng resource-based commodtes at xed nternatonal prces, and nterpret the resource curse as a productvty slowdown generated by sectoral booms sudden ncreases n resource ncomes due to exogenous shocks that rase the sze or the productvty of the resource-ntensve sector n the economy. The conventonal vew s that these booms harm economc growth because the reallocaton of labor and captal toward the resource ntensve sector results nto the crowdng-out of strategc, knowledgecreatng sectors (Van Wjnbergen, 984; Krugman, 987; Gylfason et al., 999; Torvk, 2). Our analyss d ers from the resource-curse lterature n several ways. At the conceptual level, we do not attempt to explan the resource curse: n our model greater resource abundance may yeld slower or faster growth, but the central am of the analyss s to characterze n detal the transmsson channels between shocks to resource endowments, ncome levels and economc growth n the presence of asymmetrc trade and endogenous nnovatons. At the formal level, three man aspects d erentate our analyss from Dutch-Dsease models. Frst, Dutch Dsease models do not dstngush between physcal resource endowments and resource wealth: resource booms are characterzed as sudden ncreases n the relatve pro tablty of the prmary sector generated by technologcal shocks, ncreases n the world prce of the resource, or exogenous mprovements n terms of trade. Unexpected dscoveres of new resource endowments are treated n the same way as an exchange rate gft (e.g., Torvk, 2) but ths s admttedly an approxmaton: studyng the correlaton between natural endowments and economc growth requres dstngushng between physcal resource endowments and ows of resource ncome. Second, n our model, prmary sectors of resourcerch countres are vertcally related to both domestc and foregn nal sectors, and the elastcty of demand for ntermedates s the crucal transmsson channel between endowment shocks and aggregate productvty. Ths aspect s generally neglected n Dutch-Dsease models snce they gnore vertcally related markets. Thrd, Dutch-Dsease models vew resource-rch countres as small open economes. If the world prce of the resource s exogenously xed, a sudden ncrease n the resource endowment mmedately translates nto a rse n the value of the resource and thereby nto an upward shft of the tme-pro le of resource rents. Ths mechansm, however, neglects the role of prce e ects that, as our analyss emphaszes, determne the extent to whch resource-rch economes are able to explot the natural endowment to obtan addtonal ncome. Interestngly, n hs semnal paper Corden (984) regards the lack of prce e ects as a smplfyng assumpton: extra exports of [the resource-ntensve good] owng to techncal progress n the [resource-ntensve] sector or any other reason may lower the world prce of [the resource-ntensve good]. Ths s an obvous e ect, and we can suppose that t has already been ncorporated n the calculaton of the sze of the boom. (Corden, 984: p.367). The subsequent lterature, however, does not extend the basc framework to nclude prce e ects va endogenous terms of trade. These d erences n assumptons are re ected n our results. In Dutch-Dsease models based on small open economes (Van Wjnbergen, 984; Krugman, 987; Gylfason et al., 999; Torvk, 2), greater resource abundance s assocated wth () hgher resource ncome, () hgher employment n the resource-ntensve sector, () less knowledge creaton and slower growth. In our model, nstead, resource ncome may ncrease or decrease after a resource boom and the resultng dynamcs d er. Spec cally, we show that under substtutablty the resource boom generates () hgher resource ncome, () lower employment n the resourcentensve sector, () hgher knowledge creaton and faster growth. Under complementarty, nstead, a resource boom generates () lower resource ncome, () hgher employment n the 9