Distortions in Two Sector Dynamic Models with Incomplete Specialization *

Transcription

1 Dstortons n Two Sector Dynamc Models wth Incomplete Specalzaton * Erc W. Bond a# and Robert A. Drskll a a Vanderblt Unversty Abstract We extend the Jones (1971 analyss of the effects of dstortons n statc 2x2 trade models to the case of a two sector dynamc general equlbrum model of a small open economy wth captal accumulaton. In contrast to the short run results, the drecton of mpact of factor market dstortons on steady state values do not depend on the value and physcal ntensty rankng of the sectors. However, the value and physcal ntensty rankngs play an mportant role n the dynamcs n the neghborhood of the steady state. Dfferences between value and physcal ntensty rankngs of the sectors, whch gave rse to paradoxes n the statc model, are shown to lead to local ndetermnacy or nstablty n the dynamc model. JEL Classfcaton: F10, F11 Keywords: dynamcs, trade, factor market dstortons 1. Introducton In an mportant paper, Jones (1971 showed how dstortons n factor markets could nterfere wth some of the famlar comparatve statcs results from the two factor, two good producton model that s assocated wth the Heckscher-Ohln theory of nternatonal trade. The paradoxcal results nclude the possblty that an ncrease n the relatve prce of a good results n a decrease n ts supply and the possblty that a tax mposed on the earnngs of a factor n one sector results n an ncrease n the output of that sector. One of the key fndngs of hs paper was to show that these paradoxcal outcomes arse f the * Ths paper was prepared for the 2006 APJAE Symposum n Internatonal Trade to honour Ronald W. Jones. We thank conference partcpants for helpful comments. # Correspondng author: Erc W. Bond, Department of Economcs, Vanderblt Unversty, VU Staton B#351819, 2301 Vanderblt Place, Nashvlle, TN E-mal: erc.bond@vanderblt.edu, Tel: ( , Fax: (

2 62 magntude of the dstortons s such that the rankng of the sectors by the share of captal n unt costs (referred to as the value measure of captal ntensty dffers from the rankng of sectors by captal labor ratos (the physcal measure. 1 The purpose of ths paper s to extend the statc analyss of factor market dstortons to a dynamc two sector model n contnuous tme. Ths queston s of nterest because two sector dynamc models wth constant returns to scale have arsen n a number of contexts. Examples nclude the lterature on endogenous growth and the long run effects of factor taxaton. 2 As n the statc case, the exstence of factor taxes can generate paradoxcal results f the dstortons are suffcently large. For example, Bond, Wang and Yp (1996 show that n an endogenous growth model wth accumulaton of both physcal and human captal the adjustment to the balanced growth path may exhbt ether local ndetermnacy or local nstablty f dstortons are suffcently large. Interestngly, the case of ndetermnacy (nstablty of the balanced growth path arses when the sector producng human captal s captal ntensve n the physcal (value measure but labor ntensve n the value (physcal measure. 3 Thus, the paradoxcal behavor of the dynamc model s also lnked to dfferences n physcal and value ntensty rankngs. In ths paper we focus on the case of a small open economy n whch one sector produces a traded consumpton good and the other sector produces a non-traded nvestment good, so that the economy wll exhbt a steady state. We show that n ths case the dynamc model can be characterzed by addng an ntertemporal arbtrage condton and a captal accumulaton equaton to the full employment and zero proft condtons of the statc model. Ths model allows us to contrast the short run and long run effects of dstortons and to characterze the local dynamcs n the neghborhood of the steady state for a small open economy n a partcularly smple way. Ths paper hghlghts the fact that although the potental for dfferences n rankngs between value and physcal ntenstes play an mportant role n the dynamc model, there are mportant dfferences between the statc and dynamc models. One dfference concerns the relatonshp between factor market dstortons and the returns to factors of producton. In the statc model, the drecton of the mpact of factor market dstortons on factor prces depends crtcally on whether the taxes are mposed on the captal ntensve or labor-ntensve sector (when measured n the value sense. In contrast, the mpact on the return to captal of taxes mposed on factors n the nvestment good sector s the same regardless of whether the nvestment good sector s captal ntensve or labor 1 A second possblty s that the transformaton schedule s convex to the orgn. However, ths possblty s not dentcally lnked to the reversal of value and physcal ntenstes. 2 For example, Lucas (1988 and Bond, Wang, and Yp (1996 examne a closed economy model wth physcal and human captal accumulaton, Bond, Trask and Wang (2003 analyse the open economy case, and Mles-Ferret and Roubn (1998 study the effects of factor taxaton n a closed economy. 3 Smlar results are obtaned by Benhabb, Meng, and Nshmura (2000 for the case where there are externaltes from factor usage. They assume that the externaltes are such that both the socal producton functon and the prvate producton functons exhbt constant returns to scale. Meng and Velasco (2004 also obtan these results n examnng a model n whch only captal accumulates, as n the model we consder n ths paper.

3 63 ntensve. The reason for ths s that n the steady state, the return to captal s ted to the prce of the nvestment good through an ntertemporal arbtrage condton. A smlar fndng concerns the mpact of factor taxes on the steady state captal stock, where all factor taxes except a tax on labor n the consumpton good sector wll reduce the steady state captal stock. Physcal and value ntensty rankngs do not play a role n the comparatve statcs for steady state captal because of the lnk to the output of the nvestment good. We also study the characterstcs of the dynamc system n the neghborhood of the steady state. We frst show that the dynamc system wll have a saddle path f the rankngs of the sectors on value and physcal ntensty are the same, although whether or not a factor prce equalzaton property holds along the transton path depends on whch sector s captal ntensve. In the cases where the physcal and value ntensty rankngs dffer, the system wll not have a saddle path. If the nvestment good sector s captal ntensve n the value sense and labor-ntensve n the physcal sense, the system wll exhbt local ndetermnacy n that there wll be a contnuum of paths convergng to the (unque steady state. If the nvestment good sector s labor-ntensve n the value sense and captal ntensve n the physcal sense, then the steady state wll be unstable. The stablty propertes of ths dynamc model contrast wth those obtaned by Neary (1978, who appended a dynamc adjustment process to the statc model n whch factors flowed n the drecton of the sector n whch the return was hgher. Hs adjustment process exhbted nstablty n all cases where the physcal and value ntensty rankngs dffered. We now turn to the descrpton of the two factor, two good dynamc model of a small open economy that we analyze. We lmt our attenton n ths paper to analyss of the nteror solutons n whch the economy s ncompletely specalzed. The potental for specalzaton n the case where value and physcal ntenstes dffer s explored n a companon paper (Bond and Drskll ( The Producton Model We consder a two good, two factor dynamc model, n whch one sector produces a consumpton good and the other an nvestment good that provdes addtons to the captal stock (K. The consumpton good s assumed to be trade on world markets, but the nvestment good s non-traded. The stock of labor (L s taken as exogenously gven. Each good s produced under condtons of constant returns to scale and perfect competton usng labor and captal, wth factors beng exchanged n compettve factor market. Factors are assumed to be mperfectly moble between sectors of the economy, n the sense that there are exogenously gven barrers to moblty that prevent the equalzaton of factor returns across sectors. We wll refer to these barrers to moblty as sector-specfc taxes, although an equvalent formulaton could be gven n whch these barrers represent sector-specfc externaltes from factor usage or the exstence of a fxed unon wage dfferental. Lettng w and r denote the after-tax return to labor and captal receved by households and t j the tax rate on ncome from factor j n sector, the pretax cost of the respectve factors n sector wll be w = wt L and r = rt K, where T j 1/(1 t j. In the statc Heckscher-Ohln model, the producton sde can be solved recursvely when producton s ncompletely specalzed as has elegantly been shown by Jones (1965

4 64 for the case wthout dstortons and Jones (1971 for the case wth dstortons. Assumng that both goods are produced, the compettve proft condtons n sector requre that p = c (wt L, rt K (1 Equaton (1 yelds solutons for the factor prces ( w(p,t, r(p,t, where T denotes the vector of factor market dstortons. Ths llustrates the factor prce equalzaton property of the statc trade model, whch s that factor prces wll be ndependent of factor supples as long as endowments are such that both goods are produced. 4 The full employment condtons for labor and captal requre that c w1 (wt L1, rt K1 X 1 + c w2 (wt L2, rt K2 X 2 = L c r1 (wt L1, rt K1 X 1 + c r2 (wt L2, rt K2 X 2 = K (2 Gven ( w(p,t, r(p,t these equatons yeld solutons for the output levels ( ~ X 1 (p,k,t, ~ X 2 (p,k,t. In the case of a statc small open economy where both goods are traded, relatve prces can be treated as exogenously gven by world markets and equatons (1 and (2 are suffcent to solve for factor prces and output levels. In the dynamc small open economy model that we consder the nvestment good s non-traded, so the prce must be consstent wth domestc market-clearng. In order for Good 2 to be held, ts prce must be such that the rate of return earned on the nvestment n the captal good s equvalent to that on alternatve assets. Assumng that there s an nternatonally traded bond that yelds a constant return equal to the dscount rate (ρ of households and that captal deprecates at rate δ, t can be shown that the household s optmzaton problem wll requre that the followng ntertemporal arbtrage condton hold at each pont n tme. 5. p = (ρ + δp r Ths condton requres that the rate of return on captal net of deprecaton, whch s the rental rate (r/p from a unt plus the captal gan from holdng the good (ṗ/p, equal ρ. The fnal equaton requred for the soluton of the dynamc model s the equaton for the accumulaton of the captal good (3 4 In the model wth factor market dstortons and two traded goods, factor prce equalzaton across countres would hold only between countres that also had the same level of factor market dstortons. 5 Let household preferences for the consumpton good be gven by U = 0 u(c t e ρt dt. If households have access to an nternatonal bond market where they can lend or borrow at rate ρ, the household budget constrant wll be C t = w t L + r t K t + ρb t Ḃ t p t (. K t + δk t, where B t s the stock of bonds at tme t. The exstence of a traded bond wth return equal to the dscount rate means that the margnal utlty of consumpton wll be equated at all ponts n tme, so that households wll have a constant level of consumpton. Investment decsons n captal wll be made to maxmze the present value of ncome, so that nternatonal trade serves as a means of consumpton smoothng n ths model.

5 . K = X 2 δk 65 (4 Equatons (1 to (4 characterze the producton sde of the dynamc open economy model. Gven the solutons w(p,t, ~ ~ r(p,t, X ~ 1 (p,k,t, X ~ 2 (p,k,t for factor prces and output levels from the statc model, equatons (3 and (4 yeld a system of dfferental equatons n p and K. Note however that ths dynamc system wll also have a block recursve structure. Substtutng the soluton ~ r(p,t nto (3 wll ensure that ṗ s ndependent of factor supples. We utlze ths property to study the mpact of factor market dstortons on steady state prces n Secton 3 below. In Secton 4, we utlze (4 and the soluton X ~ 2 (p,k,t from the statc model to study mpact of taxes on the steady state captal stock n Secton 4. Fnally, we study local dynamcs of the system (3 and (4 n Secton Factor Prces, Goods Prces, and Taxes The mpact of goods prces and factor taxes on factor prces wth ncomplete specalzaton can be obtaned by total dfferentaton of (1, whch yelds θ L1 ˆp + θ L1 θ L2 ( ˆT L1 ˆT L2 + θ K1 θ L2 ˆT K1 θ L1 ˆT K2 ˆr = (5 θ K1 ˆp + θ K1 ( ˆT K1 ˆT K2 + θ L1 ˆTL1 θ L2 ˆT L2 ŵ = where a ˆ over a varable denotes a percentage change and θ K1 r c r /c = 1 θ L1 s the share of captal costs n unt costs n sector. Sector 2 s captal ntensve n the value sense f > θ K1. These comparatve statcs effects are well known from Jones (1971. The frst term n each expresson captures the Stolper-Samuelson result: a factor wll experence a more than proportonal ncrease n ts return from an ncrease n the prce of the good n whch t s used ntensvely and a decrease n return from an ncrease n the prce of the other good. The remanng terms show that a factor loses from an ncrease n taxes on any factor n the sector n whch t s used ntensvely, and benefts from taxes on factors n the other sector. Thus t s the sectoral n whch taxes are mposed, and not the dentty of the factor beng taxed, that determnes the mpact on after tax returns n the short run at fxed output prces. The steady state return to captal can be obtaned from the ntertemporal arbtrage condton (3 to be SS r = δ + ρ p (6 The exstence of a steady state output prce p SS s ensured f the technologes are such that mn r(p/p ρ + δ max r(p/p. Snce r(p/p s a monotone functon of p for all factor p p

6 66 ntensty rankngs, there can be at most one value of p SS. Substtutng (6 nto the compettve proft condton for Good 2 yelds c 2 (w SS T L2, r SS T K2 = r SS /(ρ + δ. Snce the unt cost functon s homogeneous of degree 1 n factor prces, t follows that the steady state wage / rental rato wll be determned by the factor taxes n Sector 2 alone. Dfferentatng ths condton yelds ŵ SS ˆr SS = ˆT L2 ˆT K2 (7 θ L2 The steady state wage / rental rato wll be decreasng n taxes on factors located n Sector 2. Any tax on factors n Sector 2 wll rase the cost of producton, whch must reduce w SS /r SS n order to keep r SS /p SS constant. Combnng (7 wth the compettve proft condton from Sector 1 yelds the solutons for the mpact of taxes on the respectve factor returns ˆr SS = ˆp SS = θ L1 ( ˆT L2 ˆT L1 + θ L1 ˆTK2 / θ L2 ˆT K1 (8 ŵ SS = θ L1 ˆT L1 ˆT K1 ˆT L2 ˆT K2 / θ L2 The steady state relatve prce of nvestment goods, and hence the steady state return to captal, wll be ncreasng n the factor taxes on the nvestment good sector and decreasng n the taxes on the consumpton good sector. The steady state return to labor s decreasng n all of the tax rates, reflectng the shftng of taxes onto the nelastcally suppled factor n the long run. A proportonal ncrease n all taxes wll rase the cost of the nvestment good f the nvestment good sector s captal ntensve n the value sense. Snce steady state prces are ndependent of factor supples, ths model wll generate factor prce equalzaton n the steady state for all countres wth the same level of factor market dstortons. Equatons (7 and (8 llustrate two dfferences mportant between the mpact of factor taxes on factor returns between nstantaneous and steady state effects. The frst s that the drecton of the mpact of factor taxes on factor returns n the steady state does not depend on whch sector s the captal ntensve sector, because the return on captal s ted to the relatve prce of the nvestment good n the steady state. A second dfference s that a proportonal ncrease n all taxes wll reduce the steady state wage / rental rato, whereas n the statc model there was no effect on the wage rental rato. Increasng the tax on all factors reduces the attractveness of nvestments n captal, and wll thus rase the relatve cost of captal servces n the steady state. 4. Output Effects of Factor Taxaton n the Short and Long Run We now turn to an analyss of the mpact n factor market dstortons on the level of outputs and the steady state level of the captal stock. In order for the soluton ( w(p,t, r(p,t obtaned above to be consstent wth the full employment condtons (2, t must be the case that

7 67 m n k (p,t c r /c w < k K/L < max k (p,t (9 We establsh below that ths condton must hold when evaluated at the steady state values of p and K f subsdes to captal are not too large. Sector s sad to be captal ntensve n the physcal sense f k > k j, whereas t s captal ntensve n the value sense f r k /w > r j k j /w j. These two rankngs wll agree as long as (T K T Lj /(T Kj T L < k j /k, whch requres that the relatve tax bas aganst captal not be too large n the physcally captal ntensve sector. 6 The comparatve statcs for output changes wth fxed factor supples can be derved as n Jones (1971. Lettng λ j denote the share of factor j {L,K} employed n Sector {1,2} and γ L w c /c w (γ w w K r c /c r the own prce elastcty of demand for labor (captal r r n Sector, 7 we have λ L1 λ ˆX1 L2 ˆL + Σ λ L γ L (ŵ ˆr + ˆT L ˆT K = 1 = 2 λ K1 λ K2 ˆX2 ˆK Σ λ K γ K (ŵ ˆr + ˆT L ˆT K = 1 2 (10 The terms on the rght hand sde of (10 show that at constant factor prces, an ncrease n T L /T K wll ncrease the demand for captal and reduce the demand for labor. Ths can be thought of as the factor demand effect of factor taxaton, because ts mpact depends on whch factor s beng taxed. It follows from (5 that there wll also be an ndrect effect of factor taxaton, snce changes n factor taxes on the captal (labor ntensve sector wll rase (lower w/r. Ths latter effect can be descrbed as the output tax effect of factor taxaton, snce ts mpact depends on the sector n whch the tax s mposed. 6 Meng and Velasco (2004 analyse a case n whch the sectoral producton functon takes the form α β X = L K K β, where α 1 α > 0, β > 0, 1 α β 0, and K denotes the ndustry captal stock. The dstorton n ths case arses from the externalty from captal, whch frms gnore n makng decsons on the level of captal. In ths case the loc of factor prces that are consstent wth factor market equlbrum (.e. the equatng of prvate margnal products to the factor prce wll have the form w = p α (r /β (α 1/α. These condtons yeld equlbrum condtons analogous to those n (1, where the socal factor shares α and (1 α play the role of the value shares and determne the mpact of goods prce changes on factor prces. The captal labor ratos, on the other hand, are determned by the prvate factor shares α and β. 7 The elastcty of substtuton n Sector wll be σ γ L + γ K. The symmetry of the substtuton matrx mples that γ L = θ K σ.

8 68 Substtutng from (5 nto (10 and solvng yelds λ K2 ˆL λ L2 ˆK α 1 ˆp + j Σ {K,L} β j1 ( ˆT j1 ˆT j2 ˆX 1 = λ K2 λ L2 ( (λ K2 λ L2 λ L1 ˆK λ K1 ˆL α 2 ˆp + j Σ {L,K} β j2 ( ˆT j1 ˆT j2 ˆX 2 = + λ K2 λ L2 ( (λ K2 λ L2 (11 where α λ Km ( 2 Σ j=1 λ Lj γ Lj + λ Lm ( 2 Σ j=1 λ Kj γ Kj > 0 for,m {1,2}, m and β j λ Km (λ L1 γ L1 θ j2 + λ L2 γ L2 θ j1 + λ Lm (λ K1 γ K1 θ j2 + λ K2 γ K2 θ j1 > 0 for j {K,L};,m {1,2}, m. The frst term n each expresson s the Rybczynsk effect, whch shows that an ncrease n the stock of a factor of producton wll ncrease the output of the good that uses that factor ntensvely (n the physcal sense and decrease the output of the other good. It s the physcal factor ntenstes that are relevant for the Rybczynsk effect wth factor market dstortons. The second term n each expresson shows that an ncrease n the relatve prce of Good 2 wll rase the output of Good 1 and reduce the output of Good 2 f the value and physcal factor ntenstes agree. The remanng terms n (11 show that a tax on factors n one sector wll rase the output of that sector and reduce output n the other sector when the value and factor ntenstes agree. The output tax effect domnates the factor demand effect, because a tax on labor or captal n Sector wll reduce the output of Good regardless of whch factor s used ntensvely n Sector. As n the case of output prce changes, a counter-ntutve result s obtaned when the value and factor ntensty rankngs dffer. From (4, the steady state captal labor rato wll be the value k SS K SS /L that solves E(k = X 2 (p SS,k/L δk = 0. The functon E(k wll be lnear n k wth E( k 1 < 0, so a unque value of k SS consstent wth ncomplete specalzaton wll exst f t can be shown that E( k 2 > 0. Utlzng (6 and the compettve proft condtons we have E(k SS = (ρ + δt k2 k SS + w SS T L2 δk SS. A suffcent condton for E( k 2 > 0 s that T K2 > δ/(ρ + δ, so that a steady state wth ncomplete specalzaton wll exst as long as the subsdy to captal n the nvestment good sector s not too large. The effects of factor taxes on the steady state captal stock are obtaned by solvng the system (10 usng ˆX 2 = ˆK and substtutng for ŵ ˆr from (7. Ths yelds λ L1 λ K2 γ K2 + λ K1 λ L2 γ L2 ˆK SS = λ L1 (γ L1 + γ K1 ˆTL1 ˆT K1 ˆT L2 ˆT K2 ˆT K2 (12 θ L2 θ L2 λ K1 The frst set of terms n (12 reflect substtuton effects n Sector 1 from parameter changes. Factor taxes on Sector 2 rase the relatve cost of captal n Sector 1 as shown n (7, leadng to substtuton of labor for captal. Taxes on factors n Sector 1 wll not affect (w/r SS, but wll cause substtuton between factors n Sector 1. An ncrease n the tax on labor (captal n Sector 1 wll result n substtuton away from labor (captal leadng to an

9 69 ncrease (decrease n the steady state captal tax. The remanng terms n (12 capture substtuton effects n Sector 2. The change n the relatve factor cost n Sector 2 s gven by the change n T L2 w SS /(T K2 r SS. Ths relatve factor cost s ndependent of T L2 but decreasng n T K2 from (7, so only the tax on captal creates substtuton of captal for labor n Sector 2. Equaton (12 shows that the effect of changes n factor taxes on the captal stock (and hence the output of the nvestment good does not depend on whch sector s captal ntensve, or on whether the value and physcal ntenstes agree. Ths stands n sharp contrast to the statc results n (11. Value ntenstes played a role n the statc output effect of tax changes because they determned the drecton of change n the wage/rental rato. However, the drecton of the change n the steady state wage rental rato n response to a tax change does not depend on the value ntensty of the sectors as shown n (7. The relatve physcal ntenstes of the sectors do not matter because captal must be adjusted to match the output of Sector 2 n the steady state (.e. the determnant of the matrx on the left hand sde of (10 s smply λ K1 when ˆX 2 = ˆK. 5. Local Dynamcs We conclude the analyss of the equlbrum wth ncomplete specalzaton by analyzng the dynamcs of the system n the neghborhood of the steady state. Lnearzng the system of dfferental equatons (3 and (4 n the neghborhood of the steady state yelds. dp A 0 p p = SS d K. B Γ K K SS (13 (ρ + δ (1 X 2 α 2 δ(1 λ K2 A B Γ ( (λ K2 λ L2 λ K2 λ L2 The sgn of the coeffcent A s determned by the Stolper-Samuelson effect from (5, and wll be negatve f Industry 2 s captal ntensve n the value sense. Smlarly, the sgn of Γ s determned by the Rybczynsk effect and wll be postve f Good 2 s captal ntensve n the physcal sense. Due to the block recursve structure of the system, the dagonal elements of ths matrx wll be the egenvalues. The system wll exhbt saddle path stablty f the egenvalues have opposte sgns, and t s clear from the defntons of the terms that the egenvalues wll have opposte sgns f the value and physcal ntenstes agree. However, the dynamcs of the system wll dffer substantally dependng on whch sector s captal ntensve, so we consder each case n turn. 8 8 The coeffcent B wll be postve ff the physcal and value ntenstes agree. It s ths element whch reflects the perverse output-prce responses when physcal and value ntensty rankngs dffer, and plays a crtcal role n the stablty analyss conducted by Neary (1978. However, n the dynamc process studed here ths term has no mpact on the local stablty of the system.

10 70 We begn by consderng the two cases n whch the value and physcal ntenstes agree. If > θ K1, an ncrease n the prce of Good 2 rases the rental on captal more than proportonally by the Stolper-Samuelson theorem. Ths wll requre a reducton n the captal gan on nvestment goods to restore the net return on captal to ρ, whch results n a stable prce adjustment process for Good 2 (A < 0. If λ K2 > λ L2, the adjustment process of captal (at fxed p s unstable (Γ > 0 because an ncrease n the captal stock wll rase the output of the nvestment good more than proportonately. The dynamc adjustment process s llustrated n Fgure 1, whch shows the phase dagram for ths case. The k (p loc wll be downward-slopng n ths case, because w/r s a decreasng functon of p. The ṗ = 0 locus wll be horzontal at pss, wth ṗ < 0 for p > pss. The. k= 0 locus wll have a slope of Γ/B, whch wll be negatve n the neghborhood of the steady state. The prce of the nvestment good wll declne (ncrease along the saddle path as captal accumulates (decumulates toward the steady state level. The adjustment of the prce s such that t stablzes the adjustment process of captal. It can also be seen that factor prce equalzaton would not hold along the adjustment path to the steady state between two countres wth the same factor market dstortons but dfferent captal stocks, because the relatve prce of the nvestment good vares wth the level of the captal stock. The absence of factor prce equalzaton along the transton path s not surprsng, snce there are two non-traded factors of producton and only one traded good n ths model. Fgure 1: Saddle path wth θ k2 > θ k1 and λ k2 > λ L2 P P ss. k = 0 k 2 (p k 1 (p k Fgure 2 shows the adjustment process for the case n whch < θ K1 and λ K2 < λ L2. The slope of the k (p loc s reversed n ths case, as s the slope of the. k = 0 locus. The prce adjustment process s unstable n ths case, because an ncrease n p reduces the return to captal and requres an ncrease n the rate of captal gan to satsfy the ntertemporal arbtrage condton. Wth an unstable prce adjustment process, the saddle path must be characterzed by a constant value of p at the steady state level. The captal stock wll converge to the steady state level wth a constant prce n ths case because ncreases n the captal stock result n a decrease n the output of the nvestment good (.e. Γ < 0. In ths case factor prce equalzaton would also hold along the adjustment path to the steady state for countres wth dentcal factor market dstortons.

11 71 Fgure 2: Saddle path wth θ k2 > θ k1 and λ k2 > λ L2 P k 2 (p. k = 0 k 1 (p P ss k We now turn to the two cases n whch physcal and value ntensty rankngs dffer. In the case where Good 2 s captal ntensve n the value sense (A < 0 but labor ntensve n the physcal sense (Γ < 0, the system wll exhbt local ndetermnacy because the prce adjustment process s stable and the captal adjustment process (at fxed prces s also stable. Thus from an ntal value of k there wll be a contnuum of p values for whch the system wll converge to the (unque steady state. In the case where Good 2 s labor ntensve n the value sense (A > 0 but captal ntensve n the physcal sense (Γ > 0, the system wll exhbt dynamc nstablty Conclusons Our analyss has shown how factor market dstortons affect the steady state prce levels and stocks of captal n a small open economy wth a non-traded nvestment good. In the long run, the fact that the return on captal s ted to the prce of the nvestment good by the ntertemporal arbtrage condton means that the relatve share of captal costs n the respectve sectors wll not play a role n determnng the mpact of factor taxes on factor ncomes. A smlar concluson s obtaned for the steady state captal stock, where the fact that output s ted to the captal stock means that the drecton of tax changes on the steady state captal stock are ndependent of the value and physcal ntensty rankngs. However, the value and physcal ntenstes do play an mportant role n the dynamcs of the model n the case of ncomplete specalzaton. In partcular, the model may exhbt ether local ndetermnacy or nstablty n the case where value and physcal ntensty rankngs of sectors dsagree. In the case of an unstable steady state, the analyss of the mpact of taxes on steady state values becomes rrelevant as these values would not be 9 The results on nstablty and ndetermnacy for ths case are obtaned by Meng and Velasco (2004 for the case where technologes are Cobb-Douglas.

12 72 observed. In Bond and Drskll (2006, we extend ths analyss to consder the possblty of equlbra wth complete specalzaton. We show that the case where value and physcal ntenstes dsagree also leads to a multplcty of equlbra n the statc model, whch generates the potental for addtonal dynamc paths mxng complete and ncomplete specalzaton. References Benhabb, Jess, Qngla Meng and Kazuo Nshmura, 2000, Indetermnacy under Constant Returns to Scale n Multsector Economes, Econometrca, 68, Bond, Erc W., and Robert Drskll, 2006, Dstortons n Two Sector Dynamc General Equlbrum Models, manuscrpt. Bond, Erc W., Kathleen Trask and Png Wang, 2003, Factor Accumulaton and Trade: Dynamc Comparatve Advantage wth Endogenous Physcal and Human Captal, Internatonal Economc Revew, 44, Bond, Erc W., Png Wang and Chong Yp, 1996, A General Two-Sector Model of Endogenous Growth wth Human and Physcal Captal: Balanced Growth and Transtonal Dynamcs, Journal of Economc Theory, 68, Jones, Ronald W., 1971, Dstortons n Factor Markets and the General Equlbrum Model of Producton, Journal of Poltcal Economy, 79, Jones, Ronald W., 1965, The Structure of Smple General Equlbrum Models, Journal of Poltcal Economy, 73, Lucas, Robert E., 1988, On the Mechancs of Economc Development, Journal of Monetary Economcs, 22, Meng, Qngla and Andres Velasco, 2004, Market Imperfectons and Instablty n Open Economes, Journal of Internatonal Economcs, 64, Mles-Ferett, Gan Mara and Nourel Roubn, 1998, On the Taxaton of Human and Physcal Captal n Models of Endogenous Growth, Journal of Publc Economcs, 70, Neary, Peter J., 1978, Dynamc Stablty and the Theory of Factor Market Dstortons, Amercan Economc Revew, 68,