Real Exchange Rate and Economic Growth -- A Theoretical Re-examination of the Balassa Hypothesis

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1 Rel Exchnge Rte nd Econoic Growth -- Theoreticl Re-exintion of the Blss Hypothesis Yunf Zhu* din. McFrlne bstrct We forulte odel with three sectors nd two countries linked by interntionl trde in generl equilibriu frework to re-exine the theoreticl foundtions of the Blss Hypothesis. The three sectors consist of two trdble nd one nontrdble. rices nd exchnge rtes re deterined by the interction of dend nd supply cross the two countries. The odel llows for differentil technologicl chnge cross countries nd sectors. Our odel exines under wht conditions the Blss Hypothesis holds. We find tht the Blss Hypothesis y not hold in the cse of productivity chnges in the trdble sector but y hold in the reverse direction in when there re productivity chnges in the nontrdble sector. Keywords: generl equilibriu, interntionl trde, rel exchnge rte JE Clssifiction: D58, F, F3 *Deprtent of Econoics, University of Mnitob uzhuy@cc.unitob.c Deprtent of Econoics, University of Mnitob cfrl@cc.unitob.c We thnk. Ryn Copton, Hicket. Guny, John Serieux, Wyne Sipson, nd indsy Tedds for helpful coents. ll reining errors re our own.

2 Rel Exchnge Rte nd Econoic Growth. Introduction The well known Hrrod-Blss-Suelson Hypothesis, (Hrrod, 973; Blss, 964; Suelson, 964 or siply the Blss Hypothesis, sets out chnnel through which rel vribles, in prticulr productivity chnges, cn ffect the rel exchnge rte. The Blsshypothesis postultes tht s the process of econoic growth unfolds the effect of reltively higher productivity growth in the trdble sector rises the reltive price of the nontrdble to trdble sector within country. This in turn hs iplictions for the rel exchnge rte cross countries. Blss s rguent cn be surized s follows. In the originl forultion of the Blss hypothesis there re two sectors, trdble nd nontrdble sector (Blss, 964. Econoic growth is pririly driven by productivity iproveents in the trdble sector nd there is little or no difference in the productivities of non-trdble sectors between rich nd poor countries. In ddition, for the trdble sector, the lw of one price pplies to rich nd poor countries nd under copetitive lbour rket the se wge pplies to nontrdble nd trdble sectors within countries. Thus, the reltive price of the non-trdble sector will be higher in rich countries thn in poor countries. This iplies tht the price of ny given bsket of goods will be higher in rich country thn in poor country. The Blss Hypothesis postultes tht if econoic growth is driven by productivity iproveents in the trdble sector, then higher productivity growth will led to seculr rel exchnge pprecition. The Blss Hypothesis is intuitively ppeling nd theoreticl proofs hve been proposed (Gndolfo, 00, but the epiricl support hs been ixed (Froot nd Rogoff, 994; Bhni-Oskooee nd Niroond, 996. Notwithstnding this; uthors tend to ttribute the ixed epiricl results to the ssuptions de bout the underlying forces generting econoic growth itself nd its ipct on the rel exchnge rte. For exple, econoic growth y soeties be driven by productivity iproveent in the trdble sector nd t other ties by productivity iproveents in the non-trdble sector. In ddition, the rel exchnge rte y be influenced by cpitl flows (Hrberger, 003. The theoreticl foundtion of the hypothesis is rrely questioned itself s in Hrberger (003

3 Rel Exchnge Rte nd Econoic Growth I hve no hesitncy in recognizing tht wht I now cll the Blss effect follows directly, if indeed productivity tends to be significntly ore stgnnt in the nontrdble re nd ore dynic in the trdbles sectors. In y view, nerly everybody grees tht, ceteris pribus, productivity dvnce in trdbles leds to currency pprecition nd productivity dvnce in nontrdbles to currency deprecition In this pper, we deprt fro the existing literture by questioning the theoreticl prt of the Blss Hypothesis theoreticlly. We intin ll the ssuptions in the Blss Hypothesis except, within generl equilibriu frework; we divide the trdble sector into exporting nd iporting sectors nd explicitly tke the externl blnce into considertion. The odel lso includes nontrdble sector. Our findings re tht the Blss hypothesis generlly does not hold under the ssuptions of our odel. The rest of the pper is orgnized s follows. Section presents the generl equilibriu odel. Section 3 ssesses the Blss Hypothesis nd its iplictions for the rel exchnge rte. Section 4 concludes.. Model Consider odel which consists of two countries nd three sectors (unlike the originl forultion in Blss (964. Sectors nd re the trdble sectors nd sector 3 is the nontrdble sector. We ssue perfectly copetitive product nd lbour rkets with blnced trde (excess dend is equl to zero nd no trnsction costs. Country is endowed with units of lbour nd country with units. Money incoes re given by nd for country nd country respectively. Technologicl progress is treted s exogenous. In ddition, there re no brriers to inter-sector lbour obility. To get explicit solutions it is necessry to ke the following siplifying ssuption. In prticulr, we shll ssue tht country hs the coprtive dvntge in the production of good nd country hs the coprtive dvntge in the production of good. Thus country specilizes in good nd country specilizes in good. In the originl text, nontrdbles is in plce of trdbles in quote. We believe this ws typo error.

4 Rel Exchnge Rte nd Econoic Growth. roduction The production functions for the three sectors re of the for: Y ( ij ij ij where index i, represents countries, index j 3,, represents sectors, nd is productivity preter. Given speciliztion ccording to coprtive dvntge entioned erlier, 0, 0 nd thus Y 0 nd Y 0 so we cn write ij Country : Y, Y 3 33 nd + 3 Country : Y, Y 3 33 nd + 3. Wges, rices, nd Exchnge rtes et wi be the wge rte for workers in country i, i the oney incoe for country i, ij doestic prices nd r the noinl exchnge rte (the vlue of one unit of oney in country denointed in ters of country s oney. Fro the foregoing we cn write: w ( 33 w (3 33 j, (4 r j j The following reltions hold for countries nd respectively: For country, Since w nd thus w /, then fro ( we cn write, w (5 3

5 Rel Exchnge Rte nd Econoic Growth nd w 3 (6 3 3 Siilrly in country, fro eqution (3, w (7 nd w 3 (8 3 3 For the trdble sector purchsing power prity holds, therefore: r r (9 nd (0 r r.3 references For country i the preferences of representtive household re represented by Cobb-Dougls(C- D utility functions of the for: U i X X X ( i i i i i i i3 Where, X ij is the consuption of good j fro sector j in country i nd ij ' s ( i,, j,, 3 re constnts such tht, 0 <. The dend functions re: < ij The C-D utility function necessrily iposes fixed expenditure shre on ech good nd y liit the generlity of the results. 4

6 Rel Exchnge Rte nd Econoic Growth Country X ( X r( r X ( ( 3 ( 3 ( 3 3 Country X ( r X X ( ( ( r 3 3 ( 3 3 ( Equilibriu In equilibriu dend equls supply nd thus we cn write for country i, ( i,, for the non-trdble sector: Yi 3 X i3 i 3i3 ( i i i 3 Which iplies, i,, i, i3 ( i i i i Since 3 i, i ij j 5

7 Rel Exchnge Rte nd Econoic Growth Reclling tht 0 nd 0 then following reltions follow Country : Country : ( nd ( + 3 ( nd ( + 3 For the trdble sectors, equilibriu iplies: Y + X X or + ( + r X X ( r Y + r + + Finlly we cn obtin n expression for the noinl exchnge rte, r, by solving ny one of the two equtions bove, r ( Hving obtined the equilibriu exchnge rte, we cn substitute it into (9 nd (0, to get: r (9 (0 r Equtions (5-(8, (9, (0 nd ( constitute the solution to the generl equilibriu syste. 6

8 Rel Exchnge Rte nd Econoic Growth 3 The Blss Hypothesis nd the Rel Exchnge Rte 3. The Blss Suelson Hypothesis Hving lid out the odel bove we now investigte if the effect iplied by the Blss Hypothesis holds. Now if the hypothesis holds then, ceteris pribus, when lbour productivity iproves in country, the price of fixed bsket of goods will be reltively higher in country thn in country. In the odel the reltive price in the nontrdble sectors cross countries is given by: 3 r (3 3 3 Fro eqution (3, the reltive price in the nontrdble sector between the two countries does not depend on the productivities in the trdble sector, but depends insted on the lbour force, consuer preference nd lbour productivities in the nontrdble sector in the two countries. Thus the Blss Hypothesis y not hold in the cse of lbour productivity iproveent in the trdble sector but is vlid in reverse in the cse of lbour productivity iproveent in the nontrdble sector. Why is there difference? The Blss Hypothesis does not tke into considertion the effect of interntionl trde on the reltive price cross countries. Specificlly, the Hypothesis sserts tht when lbour productivity iproveent tkes plce in country, the price in the nontrdble sector reltive to the trdble sector will increse in tht country but rein unchnged in the other country. Thus, the reltive price of fixed bsket of goods will increse in the country with lbour productivity iproveent. Our odel tkes the effect of interntionl trde into ccount. et us consider the price of sector 3 reltive to sector in ech country s n exple. Fro (5 nd (6, the price in the nontrdble sector reltive to trdble sector in country is: 7

9 Rel Exchnge Rte nd Econoic Growth (4 Fro (8 nd (0, the price of the nontrdble sector reltive to trdble sector in country is (5 Now, when lbour productivity increses, not only does the price in sector 3 increse reltive to sector in country, but the reltive price of sector 3 to sector in country increses proportionlly. Hence, the productivity iproveent in the trdble sectors y hve no effect on the reltive price of fixed bsket goods between the two countries. However, when lbour productivity 3 increses, the price of sector 3 reltive to sector in country decreses, but the reltive price of sector 3 to sector in country reins unchnged. In this cse the productivity iproveent in the nontrdble sector will decrese the reltive price of fixed bsket goods in the country in which the iproveent occurs, ceteris pribus. 3. Rel Exchnge Rte et R r denote the rel exchnge rte given by * r R r (6 where nd * denotes the ggregte doestic nd foreign price levels respectively. We cn define the rel exchnge rte with respect to the consuer price index or the ters of trde. I. Consuer rice index et country be the doestic country nd country be the foreign country in wht follows. Given the utility function we cn write the doestic nd foreign price levels s the su of the 8

10 Rel Exchnge Rte nd Econoic Growth price level in ech sector weighted by the shre of incoe spent in tht sector. For the doestic price level we hve: nd the foreign price level is given by: * nd the rel exchnge rte is thus * r R r ( Fro (7, productivity chnge in the trdble sectors, such s chnge in or, hs n biguous effect on the rel exchnge rte. However, productivity chnge in the nontrdble sector, such s chnge in 3 or 3, hs n unbiguous effect on the rel exchnge rte. n increse in 3 will led to increse in R r : tht is, the rel exchnge rte will deprecite. On the other hnd n increse in 3 will led to the decrese in r R, or n pprecition of the rel exchnge rte. II. Ters of Trde rices of exports nd iports for country re respectively given by: * nd nd the rel exchnge rte using is thus: 9

11 Rel Exchnge Rte nd Econoic Growth * ( r R r ( (8 Obviously, fro eqution (8 the dvnce of productivity in the trdble sector for country will led to n iproveent in the ters of trde for country (deteriortion of the ters of trde for country. 4. Conclusion The Blss Hypothesis describes one chnnel through which productivity chnges ffect the rel exchnge rte. The theoreticl foundtion of the hypothesis hs rrely been clled into question even though it hs not enjoyed full epiricl support. We forulte odel with three sectors nd two countries linked by interntionl trde. Our odel does not support the theoreticl predictions of the Blss Hypothesis. We find tht the theoreticl shortcoing of the Blss Hypothesis lies in its filure to tke into ccount the effect of interntionl trde on the reltive price cross countries. ccording to the Blss Hypothesis the effect of productivity iproveents in one country is not trnsitted to other countries. In our odel such spill over effects re tken into ccount through interntionl trde linkges. So if there is productivity iproveent in the trdble sector in country this leds to reltive price chnges between trdble nd nontrdble sectors, not only in country but lso in country becuse of trde linkges. Fro the foregoing the Blss hypothesis y not hold if lbour productivity iproveent tkes plce in the trdble sector. In prticulr, under our ssuptions, productivity iproveents in the trdble sector y hve no effect on the reltive price of fixed bsket of goods cross countries. If vrition in the prediction of the hypothesis is ccepted, then it y be vlid in the cse of productivity iproveents in the nontrdble sector. In this cse, productivity iproveents in the nontrdble sector will decrese the reltive price of fixed bsket of goods in the country in which the iproveent occurred. If econoic growth is driven pririly by productivity iproveent in the trdble sector, then higher growth y not led to seculr rel exchnge rte pprecition. Furtherore, if econoic growth is driven pririly by productivity iproveent in the nontrdble sector, higher growth y be led to seculr rel exchnge rte deprecition. 0

12 Rel Exchnge Rte nd Econoic Growth References Blss B. (964. The purchsing power prity doctrine: Repprisl, Journl of oliticl Econoy, 7, Bhni-Oskooee, M nd Niroond F (996. Reexintion of Blss's roductivity Bis Hypothesis Econoic Developent nd Culturl Chnge, 45(, Froot, K. nd Rogoff, K. (994. erspectives on nd ong Run Rel Exchnge Rtes, Ntionl Bureu of Econoic Reserch Working per No Gndolfo, G. (00. Interntionl Finnce nd Open Econoy Mcro-econoics. Springer Verglg. ppendix Chpter 5. Hrberger,. (003. Econoic Growth nd The Rel Exchnge Rte: Revisiting the Blss- Suelson Effect. per prepred for Conference orgnized by The Higher School of Econoics, Moscow pril Hrrod, R. (973. Interntionl econoics. nd ed. Cbridge: Cbridge University ress. Suelson,. (964. Theoreticl Notes on Trde probles, Review of Econoics nd Sttistics, 56,