Journal of Economics and Businss Vol. II 2009, No 2 Tst of a V-Shapd lationship btwn th Expctd al Effctiv Exchang at and al Output: Th Cas of Franc u Hsing, SOUTHEASTEN LOUISIANA UNIVESIT Abstract Applying a simultanous quation modl incorporating th montary policy raction function and th intractiv dummy variabl tchniqu, this papr finds that ral GDP and th xpctd ral ffctiv xchang rat xhibit a V-shapd rlationship, suggsting that xpctd ral dprciation raiss ral output during arly yars whras xpctd ral apprciation incrass ral output in rcnt yars. Hnc, rcnt ral apprciation of th uro would work in favor of Franc. Othr findings ar that a highr govrnmnt dbt ratio, a highr ral stock pric, a highr ral EU intrst rat, and a lowr xpctd inflation rat would incras ral output for Franc. Kywords: MPF, UIP, Expctd ral dprciation or apprciation, Govrnmnt dbt, World intrst rat, Expctd inflation JEL Classification: F41, F31 Introduction cnt ral apprciation of th uro has ld to rnwd intrst in its impact on ral output in th EU mmbr countris including Franc. al apprciation of th uro would rduc xports, incras imports, and caus nt xports and aggrgat xpnditurs to dclin. On th othr hand, ral apprciation of th uro would rduc import prics, lowr inflation, may caus th cntral bank to 11
rduc th ral intrst rat, and stimulat consumption and invstmnt xpnditurs. Hnc, whthr ral apprciation or ral dprciation of th uro would rduc or incras ral output for Franc nds to b xamind. This papr attmpts to study th rols of th xpctd ral ffctiv xchang rat and othr major macroconomic variabls in dtrmining output fluctuations for Franc. First, th papr incorporats th montary policy raction function in th formulation of th modl as th cntral bank dtrmins its short-trm intrst rat basd on an inflation targting of lss than 2%. Scond, th papr tsts whthr th xpctd ral ffctiv xchang rat and ral output may xhibit diffrnt rlationships during diffrnt sub-sampl priods. Th dummy variabl tchniqu is mployd to tst if th intrcpt and/or th slop cofficint of th xpctd ral ffctiv xchang rat may hav changd. Third, comparativ static analysis is applid in ordr to dtrmin th possibl rspons of quilibrium ral GDP to a chang in on of th xognous variabls. Thr ar svral major studis xamining th impact of currncy dprciation or dvaluation on output. Krugman and Taylor (1978) stat that on of th conditions for currncy dvaluation to hav a contractionary impact is if xports ar initially lss than imports. Edwards (1986), Upadhyaya (1999), Bahmani- Oskoo, Chomsisngpht, and Kandil (2002) and Christopoulos (2004) find that currncy dvaluation or dprciation could hav a contractionary, an xpansionary, or no ffct dpnding upon th countris or tim priods in mpirical work. Chou and Chao (2001) and Bahmani-Oskoo and Kutan (2008) indicat that dprciation or dvaluation is inffctiv or has littl impact in th long run. Studis rporting dprciation or dvaluation is xpansionary includ Gylfason and Schmid (1983) xcpt for th U.K. and Brazail, Gylfason and isagr (1984) for dvlopd countris. On th othr hand, studis showing that dprciation or dvaluation is contractionary includ Gylfason and isagr (1984) for LDCs, ogrs and Wang (1995), Morno (1999), Kamin and ogrs (2000), Chou and Chao (2001) in th short run, and Bahmani-Oskoo and Mitza (2006) for 24 non-oecd countris. Ths prvious studis hav mad significant contributions to th undrstanding of th subjct. Ths findings suggst that th impact of ral dprciation could b xpansionary, contractionary or nutral and dpnds on th country, tim priod, th formulation of a modl, and th mthodology mployd in mpirical work. To th author s bst knowldg, fw of th prvious studis hav focusd 12
on th hypothsis that th impact of th ral xchang rat on ral output may b nonlinar and vary ovr tim. Th Modl Suppos that aggrgat xpnditurs ar a function of ral output, th domstic ral intrst rat, govrnmnt spnding, govrnmnt tax rvnus, th ral financial stock pric, and th ral ffctiv xchang rat, that th ral intrst rat is dtrmind by th inflation rat, ral output, th ral ffctiv xchang rat, and th world ral intrst rat, that th ral ffctiv xchang rat is affctd by th domstic ral intrst rat, th world ral intrst rat, and th xpctd ral ffctiv xchang rat, and that th inflation rat is dtrmind by th xpctd inflation rat, th output gap, and th ral ffctiv xchang rat. Applying and xtnding Taylor (1993, 1995), omr (2000, 2006) and Svnsson (2000), w can xprss th opn-conomy IS function, th montary policy raction function, uncovrd intrst parity, and th augmntd aggrgat supply function as: = W (,, G, T, A, ) (1) = (,,, ) (2) = Z(,, ) (3) * = + α ( α (4) 1 ) 2 whr, = ral GDP in Franc, = th domstic ral intrst rat, G = govrnmnt spnding, T = govrnmnt tax rvnus, A = th ral financial stock pric, = th ral ffctiv xchang rat (EE), (An incras mans ral apprciation of th currncy.) = th inflation rat, = th world ral intrst rat, * α 1,α 2 = th xpctd ral ffctiv xchang rat, = th xpctd inflation rat, = potntial output for Franc, and = paramtrs 13
Solving for four ndognous variabls,,, and simultanously, w can xprss quilibrium ral GDP as: * = (, G, T, A,, ; α, α, ). (5) 1 2 Th Jacobian for th ndognous variabls is givn by: J = (1 W ) Z W W Z (1 W [ α 2 Z (1 W ) + α1w + α1z W ] > 0. ) (6) ( / G ) / T or A W xpct that th sign of / is positiv. Th ffct of an incras in th xpctd ral ffctiv xchang rat on quilibrium ral GDP is uncrtain bcaus th ngativ impact of dcrasd nt xports may b lss or gratr than th positiv impacts of a lowr inflation rat and a lowr ral intrst rat du to montary asing: / = Z ( W + W α 2 W ) / J > or < 0. (7) Th ffct of a highr world ral intrst rat on quilibrium ral GDP is uncrtain as th first trm in th parnthsis in (8) is positiv whras th rmaining trms in th parnthsis in (8) ar ngativ: / = ( Z W + Z W + Z W + W α 2 Z W ) / J > or < 0. (8) A highr xpctd inflation rat would caus quilibrium ral GDP to dclin partly bcaus th cntral bank would rais th ral intrst rat to contain inflation and partly bcaus a highr ral intrst rat would caus ral apprciation and rduc nt xports: / = ( Z W + W ) / J < 0. (9) Empirical sults Th data wr collctd from th Intrnational Financial Statistics (IFS), which is publishd by th Intrnational Montary Fund. al GDP is masurd in billion uros. Th laggd ral ffctiv xchang rat is usd to rprsnt th xpctd ral ffctiv xchang rat. Du to lack of complt data for budgt dficits, th ratio of govrnmnt dbt to GDP is slctd to rprsnt fiscal 14
policy. Th shar pric indx is dividd by th harmonizd consumr pric indx to driv th ral stock pric indx. Th world ral intrst rat is rprsntd by th rfinancing intrst rat of th Europan Cntral Bank (ECB) minus th inflation rat in th EU. Th inflation rat is th prcnt chang in th harmonizd consumr pric indx in Franc. Th xpctd inflation rat is rprsntd by th laggd inflation rat. Excpt for th dummy variabl and th xpctd inflation rat with zro or ngativ valus, all othr variabls ar masurd in th log scal. Aftr calculating th prcnt chang and taking lags, th sampl rangs from 1999.Q3-2008.Q3. Th rlationship btwn th xpctd ral ffctiv xchang rat and ral GDP is prsntd in Graph 1. It sms that th rlationship is nonlinar and xhibits a V-shap. In othr words, thy hav a ngativ rlationship during 1999.Q3-2000.Q4 and a positiv rlationship during 2001.Q1-2008.Q3. Th thrshold ral GDP in 2001.Q1 was 367.07 billion uros. Thrfor, a dummy variabl DUM is gnratd with a valu of 0 during 1999.Q3-2000.Q4 and 1 othrwis. An intractiv dummy variabl DUM x LOG( ) is also gnratd to tst whthr th slop cofficint of th xpctd ral ffctiv xchang rat may hav changd. Basd on th ADF tst, variabls hav unit roots in th lvl form and ar stationary in th first-diffrnc form. According to th unrstrictd cointgration rank tst in Tabl 1, thr ar 5 cointgrating rlationships. Th vctor-rror corrction modl is not applid du to a rlativly small sampl siz in th study. Estimatd paramtrs, standard rrors, t-statistics, and othr rlatd rsults ar prsntd in Tabl 2. Bcaus a rducd form quation is stimatd, ndognity would not b an issu. Th Nwy-Wst mthod is applid in ordr to corrct for autocorrlation and htroskdasticity simultanously whn thir forms ar unknown. As shown, 96.4% of th bhavior of ral GDP can b xplaind by th svn right-hand sid variabls. All th cofficints ar significant at th 1%, 5% or 10% lvl. al GDP is positivly associatd with th intractiv dummy variabl DUM x LOG( ), th ratio of govrnmnt dbt to GDP, th ral stock pric, and th ral rfinancing rat st by th Europan Cntral Bank and ngativly influncd by th dummy variabl, th xpctd ral ffctiv xchang rat, and th xpctd inflation rat. Th cofficint of th xpctd ral ffctiv xchang rat is stimatd to b -0.515 during 1999.Q3-2000.Q4 and 0.660 (= -0.515 + 1.175) during 2001.Q1-2008.Q3. Svral diffrnt vrsions ar tstd. Whn th intrcpt and intractiv dummy variabls ar not includd in th stimatd rgrssion, th adjustd 2 is 15
stimatd to b 0.841, and th cofficint of th xpctd ral ffctiv xchang rat is ngativ but insignificant at th 10% lvl. This rsult may b mislading as possibl diffrnt intrcpts and/or slops ar not tstd. If th ratio of govrnmnt consumption spnding to GDP rplacs th govrnmnt dbt ratio, its cofficint is positiv but insignificant at th 10% lvl. Whn th Europan Cntral Bank s ral rfinancing rat is rplacd by th U.S. ral fdral funds rat, its cofficint is positiv and significant at th 10% lvl. Howvr, th us of th ral fdral funds rat causs th cofficints of th govrnmnt dbt ratio, th ral stock pric, and th xpctd inflation rat to b insignificant at th 10% lvl. If th xpctd inflation rat is rprsntd by laggd inflation rat of th non-harmonizd CPI, its cofficint is ngativ but insignificant at th 10% lvl. To sav spac, ths rsults ar not printd hr and will b mad availabl upon rqust. Thr ar svral commnts. Th V-shapd rlationship btwn th xpctd ral ffctiv xchang rat and ral GDP suggsts that th rcnt trnd of ral apprciation of th uro against th U.S. dollar would work in favor of Franc du to its positiv impact on ral output. Expansionary fiscal policy may b considrd to stimulat th conomic slowdown. As th stock markt is rvrsing its downward trnd, th walth ffct and th balanc-sht ffct (Kuttnr and Mossr, 2002) of a highr stock pric would incras houshold consumption and businss invstmnts. It would b dsirabl for th cntral bank to maintain transparncy and indpndnc in ordr to rduc inflationary xpctations. Summary and Conclusions This papr has xamind th impacts of xpctd ral dprciation or apprciation and othr changing macroconomic conditions on output fluctuations in Franc. Th modl is formulatd basd on a simultanous quation modl incorporating th opn-conomy IS function, th montary policy raction function, uncovrd intrst parity, and an augmntd aggrgat supply function. Equilibrium ral GDP is postulatd to b a function of th dummy variabl, th xpctd ral ffctiv xchang rat, th intractiv dummy variabl with th xpctd ral ffctiv xchang rat, th ratio of govrnmnt dbt to GDP, th ral stock pric, th EU ral rfinancing rat, and th xpctd inflation rat. A gnralizd last squars mthod is mployd in mpirical work to yild consistnt stimats for th covarianc and standard rrors. 16
Thr is vidnc of a V-shapd rlationship btwn th xpctd ral ffctiv xchang rat and ral output, suggsting that xpctd ral dprciation would incras ral output up to 2000.Q4 whras xpctd ral apprciation would rais ral output aftr 2000.Q4. Bsids, a highr ratio of govrnmnt dbt ratio, a highr ral stock pric, a highr EU rfinancing rat, or a lowr xpctd inflation rat would hlp rais ral output. Thr may b aras for futur study. A quadratic function may b applid to dtrmin th turning point of ral GDP whn th rlationship btwn th xpctd ral ffctiv xchang rat and ral GDP changs from bing ngativ to bing positiv. If th data ar availabl, th ratio of govrnmnt dficit to GDP may b slctd to rprsnt fiscal policy. Th modl dvlopd in this papr may b considrd for othr countris to dtrmin whthr it may apply. Th xpctd ral xchang rat and th xpctd inflation rat may b constructd by mor sophisticatd mthodologis. Graph 1. Scattr diagram btwn ral GDP and th xpctd EE 110 Expctd ral ffctiv xchang rat 105 100 95 90 340 350 360 370 380 390 400 410 420 al GDP 17
Tabl 1. Unrstrictd cointgration rank tst (maximum ignvalu) Hypothsizd Max-Eign 0.05 No. of CE(s) Eignvalu Statistic Critical Valu Prob.** Non * 0.992514 171.3164 52.36261 0.0000 At most 1 * 0.792287 55.00592 46.23142 0.0046 At most 2 * 0.729626 45.77819 40.07757 0.0103 At most 3 * 0.692936 41.32448 33.87687 0.0054 At most 4 * 0.590057 31.21078 27.58434 0.0163 At most 5 0.431471 19.76458 21.13162 0.0768 At most 6 * 0.375347 16.46957 14.26460 0.0220 At most 7 * 0.256112 10.35526 3.841466 0.0013 Nots: Max-ignvalu tst indicats 5 cointgrating qn(s) at th 0.05 lvl * dnots rjction of th hypothsis at th 0.05 lvl **MacKinnon-Haug-Michlis (1999) p-valus 18
Tabl 2. Estimatd rgrssion of LOG() for Franc Variabl Cofficint Std. Error t-statistic Prob. C 7.367149 0.499142 14.75964 0.0000 DUM -5.304512 0.520391-10.19333 0.0000 LOG( ) -0.514685 0.100702-5.110957 0.0000 DUM x LOG( )1.175333 0.113668 10.34002 0.0000 LOG(D) 0.193376 0.092739 2.085166 0.0460 LOG(A) 0.034020 0.014072 2.417499 0.0221 LOG( ) 0.011954 0.005149 2.321805 0.0275-0.005918 0.003202-1.848295 0.0748 Adjustd -squard 0.964187 Akaik info. critrion -6.312255 Schwarz critrion -5.963949 F-statistic 139.4589 Prob (F-statistic) 0.000000 Sampl priod 1999.Q3 2008.Q3 MAPE 2.469236 19
Nots: is ral GDP. DUM is a dummy variabl with a valu of 0 during 1999.Q3-2000.Q4 and a valu of 1 during 2001.Q1-2008.Q3. is th xpctd ral ffctiv xchang rat. D is th ratio of govrnmnt dbt to GDP. A is th ral stock pric. is th EU ral rfinancing rat. is th xpctd inflation rat. MAPE is th man absolut prcnt rror. Th Nwy-Wst mthod is mployd in mpirical work. 20
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