Real Exchange Rate and the Productivity Growth Rates. using Panel Data TSUYOSHI KUBOTA Ten-no-dai, Tsukuba, Ibaraki, Japan

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1 Real Exchange Rate and the Productvy Growth Rates usng Panel Data SUYOSHI KUBOA he Doctoral Program n Polcy and Plannng Scences, he Unversy of sukuba, -- en-no-da, sukuba, Ibarak, Japan Abstract In ths paper, we try to explan the fluctuaton of real exchange rates usng the Balassa- Samuelson (B-S) theory. Accordng to the B-S theory, f a country has a hgher productvy growth rate than does s tradng partner, then the country s real exchange rate wll apprecate. hs paper s tested usng panel data and the dfferences n the labor productvy growth rates of the tradable-goods and non-tradable sectors between two countres. he results may be summarzed as follows. () he varaton n the real exchange rate s affected by the betweencountry dfference n the labor productvy growth rate of the non-tradable sector rather than that of the tradable sector. () In most countres, the expected sgns hold.

2 I. IRODUCIO he Balassa-Samuelson (B-S) theory, whch descrbes fluctuatons n real exchange rates, has been tested n emprcal studes n the past. Accordng to the B-S theory, f a country has a hgher productvy growth rate than s tradng partner, then the country s real exchange rate wll apprecate. Studes that support the B-S theory nclude DeGregoro et al. (994), Chnn et al. (996), and Canzoner et al. (996). Froot et al. (99) dsputes the theory. DeGregoro et al. (994) found that for short run fluctuatons of real exchange rates, both the tradable-goods and non-tradable sectors are mportant. hey also found that the dfference n the productvy growth rate of the tradable sector was more mportant n explanng long run fluctuatons. In ths paper, we try to explan exchange rate fluctuatons by the between-country dfferences n productvy growth rates of the tradable and non-tradable sectors usng the B-S theory. We fnd that our analyss supports the Balassa-Samuelson effect but dffers from the result of DeGregoro et al. (994), snce we fnd that the dfference n the productvy growth rate of the non-tradable goods sector s the more mportant factor. he expected sgns hold for Random Coeffcents Model. hs paper s composed of four sectons. In the next secton we descrbe the model. We explan the B-S theory and the econometrc analyss used. hese econometrc analyss use panel data and three dfferent models: the Dummy Varable Model (DVM), the Error Components Model (ECM), and Swamy s Random Coeffcents Model (Swamy s RCM)(Swamy (970)). In secton III we report the estmated results after descrbng the data sets and the estmated models. Conclusons are presented n secton IV. II. MODELS Fgure and shows the rates of change of the real exchange rates of major ndustralzed countres. hese rates of change are obvously nconstant. As s clear n Fgure -, the varaton of the nomnal exchange rate causes short run varatons n the real exchange rate due to short run nomnal prce rgdes, but n the long run real exchange rate varatons have to be explaned by real factors. One theory explanng the devaton of the real exchange rate from s long-run purchasng power pary (PPP) was proposed by Balassa (964) and Samuelson (964). We consder a small country producng both tradable-goods and non-tradable goods, where both goods are produced under the constant returns to scale producton functon: Y = AF( K, L), Y = AG( K, L), () where () s the tradable (non-tradable) good; K and L are the -th sector s capal and labor nput, respectvely; and A s the -th sector s productvy parameter (=,). Labor s completely moble between sectors, but not between countres. hus whn a country each sector has the For example, the U.K. and Italy have smlar fluctuatons to Germany and France untl 99, but very dfferent fluctuatons from 99 onwards followng whdrawal from the European Monetary System. he explanaton here refers to Obstfeld et al. (996), Chap.4 and Froot et al. (995).

3 same wage w. Capal s completely moble between sectors and between countres. hus the domestc rate of return on capal s equal to the world nterest rate, r. he rate of change of the real exchange rate can be decomposed nto varous components: qˆ = - g æ q = - g ç è q ( pˆ - pˆ ) L L Aˆ q - q L L Aˆ ö + g ø ( ˆ ˆ A - A ). () hs paper uses panel data. Most papers use tme seres data, and very few use cross sectonal data or panel data. here are two man advantages n usng panel data nstead of tme seres or cross sectonal data. Frst, n the case of small sample szes, panel data enables larger degrees of freedom than do eher cross sectonal or tme seres methods. Second, panel data allows us to analyze effects that cannot be handled by cross sectonal or tme seres methods. For example, dynamc movements cannot be analyzed usng cross-sectonal data, and tme seres approaches lead to analyss only about each country and not the specfc effects whn each country. he use of panel data does have s lmatons, however. here s the possbly that estmates vary greatly dependng on the model used. he models used n ths paper nclude the DVM, the ECM, and Swamy s RCM. However, the assumptons satsfyng each case were not found to exst. herefore, the DVM estmates are used as a benchmark, and the estmated results n the ECM and Swamy s RCM are reported when the parameter les at rght angles to the explanatory varables. III. ESIMAIO of MODELS All data are annual observatons from 97 to 99. he U.S. dollar omnal Exchange Rate (rf(or rh)) and the Consumer Prce Index (CPI, 64) are taken from the IMF s Internatonal Fnancal Statstcs. All data are n natural log form. he CPI s computed from data for the followng eleven countres: Japan, Italy, Germany, France, the Uned Kngdom, Belgum, Denmark, Fnland, etherlands, orway and Sweden. he labor productvy growth rates of both the tradable and non-tradable goods sectors are based on the OECD s atonal Account 4. Industres that are ncluded n the tradable and nontradable sectors use the classfcaton of DeGregoro et al. (994) 5. he tradable sector ncludes Agrculture, huntng, forestry and fshng, Mnng and quarryng, Manufacturng, hough Swamy s RCM s replaced by a Seemngly Unrelated Regresson (SUR), f the orthogonaly assumpton s not satsfed, then we report the SUR result snce accepts orthogonaly n all cases. 4 he growth rate of labor productvy s determned by takng the natural log of GDP dvded by the number of employees n both the tradable goods and non-tradable goods sectors, and takng the lag of order one. 5 DeGregoro et al. (994) defned and classfed tradable goods. radable goods are the rato of the total exports among the 4 OECD countres to total output of these countres exceedng 0 percent.

4 ransport, storage and communcaton. he non-tradable goods sector ncludes Electrcy, gas and water, Constructon, Wholesale and retal trade, restaurants and hotels, Fnance, nsurance, real estate and busness servces and Communy, socal and personal servces ; and Producers of Government Servces and Other Producers as non-market servces. It matters whether data are consstent. () In the USA, the Uned Kngdom and orway, Other Producers are not ncluded. () In Italy, France and Belgum, Mnng and quarryng, Communy, socal and personal servces are not ncluded. () In France, Wholesale and retal trade, restaurants and hotels, ransport, storage and communcaton, Fnance, nsurance real estate and busness servces are not ncluded. We brefly show the results of our models here. he DVM s estmated usng equaton (); the ECM s estmated usng equaton (4); and Swamy s RCM s estmated usng equaton (5). D q Dq Dq = b = b = b + + b + b + b = m ( DA ) + b ( DA ) ( DA ) + b ( DA ) ( DA ) + b ( DA ) ( DA ) + m ( DA ) + u (5) = = = = m D + m m d + d - t= t= l D + u t t l d + u where q s the real exchange rate (q=e-(p-p )); D s the lag operator of dfference ; represents country ; t s tme; e s the natural log of the nomnal exchange rate to the US dollar; p(p ) s the natural log of the prce level n the -th country s currency (the USA); D (D t ) s the countryspecfc (tme-specfc) fxed effect dummy varable; d (d t ) s the random effect varable; D A ( D ) s the rate of labor productvy growth of the tradable sector n country (the A USA); D A ( D ) s the productvy growth of the non-tradable goods sector n country (the A USA); and u s the statonary dsturbance term. b and b are parameters. Accordng to B-S theory, f the productvy growth rate of the tradable sector s hgher n country than n the Uned States, the real exchange rate apprecates. herefore, the expected sgn of b s negatve. If s negatve, the B-S theory explans the fluctuaton of the real exchange rate and the falure of PPP. On the other hand, the expected sgn of b s posve. hen f the productvy growth rate of the non-tradable goods sector s hgher n country, the real exchange rate wll deprecate, and B-S theory s supported. here s a dfference n the fluctuaton of real exchange rates by country, as shown n Fgure -. m, and m show random devatons from b and b on average, and show the dfference, b, b, by country 6. able shows the estmated results of the B-S theory. hs table s dvded nto estmates from the DVM (OLS) as a benchmark at the top, from ECM n the mddle, and from t t () (4) 6 he explanatory power of the B-S theory dffers n each country, as ponted out by Obstfeld (995).

5 Swamy s RCM at the bottom. he estmated values nclude the jont country and tme effects, country effects only, and tme effects only (m and z ndcate the Hausman test statstc (Hausman (978)) and the Pudney test statstc (Pudney (978)), respectvely). he DVM (OLS) estmates ndcate standard errors modfed by MacKnnon and Whe s HC (MacKnnon et al. (985)) when heteroscedastcy exsts. From these latter results, one can say that the dfferences n the factor n real exchange rate fluctuatons, except n the case of Swamy s RCM. he expected sgns hold n all cases. he dfference n the tradable goods sectors s nsgnfcant, but the domestc currency apprecates to 58 percent relatve to the U.S. dollar f ths sector s labor productvy growth rate s one percent hgher n the domestc country relatve to that of the Uned States. On the other hand, the dfference n the non-tradable goods sector s sgnfcant n all cases, and the expected sgns hold, too. hs means that the domestc currency deprecates 0 to 55 percent relatve to the U.S. dollar f the non-tradable goods sector has a labor productvy growth rate that s one percent hgher n the domestc country than n the Uned States. hese results dffer from DeGregoro et al. (994) n that the between-country dfference n labor productvy growth rates of non-tradable goods sector has greater the explanatory power n terms of real exchange rate fluctuatons than does the tradable goods sector. hese results may be due to the fact that the real exchange rate adjusts the nomnal exchange rate by the CPI, and the CPI ncludes the nontradable goods sector, whch accounts for 50 to 60 percent of each country s output. However, the explanatory power of the B-S theory vares greatly by country, as ponted out by Obstfeld (995). able shows the estmates by country usng Swamy s RCM. he expected sgns hold n almost all cases, though the use of the RCM model prohbs more detaled comparsons between countres. Moreover, Japan s results suggest that a deprecaton of the real exchange rate through the perod shown by Fgure -. IV. COCLUSIO he results n ths paper may be summarzed as follows. () o explan fluctuatons n the real exchange rate, we examne between-country dfferences n labor productvy growth rates of the tradable goods and non-tradable goods sectors. We fnd that a change n the real exchange rate s more lkely to be nfluenced by productvy dfferences n the non-tradable goods sector than by productvy dfferences n the tradable goods sector. () In most countres the mpact of between-country dfferences n sectoral labor productvy growth rates has the expected sgn effect on the real exchange rate, consstent wh the B-S theory. Further research ncludes the followng extenson. hs paper has focused on the supply sde of the B-S theory; the analyss can be extended to consder demand sde varables, such as consumpton, government expendure and so on.

6 References Balassa, Bela (964) he Purchasng Power Pary Doctrne: A Reapprasal, Journal of Polcal Economy, 7, Canzoner, Matthew B.; Cumby, Robert E. and Dba, Behzad (996) Relatve Labor Productvy and the Real Exchange Rate n the Long Run: Evdence for a Panel of OECD Countres, BER Workng Paper, 5676 Chnn, Menze and Johnston, Lous (996) Real Exchange Rate Levels, Productvy and Demand Shocks: Evdence from a Panel of 4 Countres, BER Workng Paper, 5709 DeGregoro, Jose; Govannn, Alberto and Wolf, Holger C. (994) Internatonal Evdence on radables and ontradables Inflaton, European Economc Revew, 8, Froot, Kenneth A. and Rogoff, Kenneth (99) he EMS, the EMU, and the ranson to a Common Currency, n BER Macroeconomcs Annual (Ed.) Blanchard, Olver and Fscher, Stanley, pp Froot, Kenneth A. and Rogoff, Kenneth (995) Perspectves on PPP and Long-Run Real Exchange Rates, n Handbook of Internatonal Economcs vol. (Ed.) Grossman, Gene M. and Rogoff, Kenneth, pp Hausman, J. A. (978) Specfcaton ests n Econometrcs, Econometrca, 46, MacKnnon, J. G. and Whe, H. (985) Some Heteroskedastcy Consstent Covarance Matrx Estmators wh Improved Fne Sample Propertes, Journal of Econometrcs, 9, Obstfeld, Maurce (995) Internatonal Currency Experence: ew Lessons and Lessons Relearned, Brookngs Papers on Economc Actvy, 9-0. Obstfeld, Maurce and Rogoff, Kenneth (996) Foundatons of Internatonal Macroeconomcs, MI Press. Pudney, S. E. (978) he Estmaton and estng of Some Error Components Models, London School of Economcs, mmeo. Samuelson, Paul A. (964) heoretcal otes on rade Problems, Revew of Economcs and Statstcs, 5,

7 Swamy, P. A. V. B. (970) Effcent Inference n a Random Coeffcent Regresson Model, Econometrca, 8, pp.-.

9 able. Factor of the specfc effects of Balassa-Samuelson theory (Swamy RCM) Japan Italy Germany France UK Belgum Denmark Fnland etherlands orway Sweden

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