m2 demand relation and effective exchange rate in japan: a cointegration analysis

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Page 1: M2 demand relation and effective exchange rate in Japan: a cointegration analysis

This article was downloaded by: [Stony Brook University]On: 20 December 2014, At: 18:30Publisher: RoutledgeInforma Ltd Registered in England and Wales Registered Number: 1072954 Registered office: MortimerHouse, 37-41 Mortimer Street, London W1T 3JH, UK

Applied Economics LettersPublication details, including instructions for authors and subscription information:http://www.tandfonline.com/loi/rael20

M2 demand relation and effective exchange ratein Japan: a cointegration analysisH. YamadaPublished online: 07 Oct 2010.

To cite this article: H. Yamada (2000) M2 demand relation and effective exchange rate in Japan: a cointegrationanalysis, Applied Economics Letters, 7:4, 229-232, DOI: 10.1080/135048500351564

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Page 2: M2 demand relation and effective exchange rate in Japan: a cointegration analysis

M2 demand relation and e� ective exchangerate in Japan: a cointegratoin analysis

H. Y A MA DA

Department of Economics, Otaru University of Commerce, 3-5-21 Midori, Otaro,Hokkaido 047-8501 , JapanE-mail: [email protected]

Received 26 May 1998

The paper examines whether M2 demand in Japan does not form a cointegratedsystem unless the e� ective exchange rate is included. We focus on testing statisticalsigni® cance of the coe� cient for the e� ective exchange rate in the long-run equilibriumM2 demand relation. Empirical results indicate that it is signi® cant, which suggeststhat the e� ective exchange rate is necessary for Japanese M2 demand cointegration.

I . INTR ODUCTION

The money demand relation is one of the most funda-mental relationships among macroeconomic variables.However, based on careful empirical investigation, Miyao(1996) shows that there is no empirical evidence that sup-ports M2 demand cointegration in Japan under the trivari-ate framework comprising real money balance, real incomeand the nominal interest rate.

On the other hand, over the last few years there has beensome evidence that M2 money demand does form a coin-tegrated system if the e� ective exchange rate is included asan additional explanatory variable.1 McNown and Wallace(1992) conclude that the e� ective exchange rate is necessaryfor M2 demand cointegration in the United States withquarterly data from 1973:2 to 1988:4. FollowingMcNown and Wallace (1992), Bahmani-Oskooee andShabsigh (1996) give empirical evidence for this hypothesiswith regard to the Japanese economy with quarterly datafrom 1973:1 to 1990:4.

Bahmani-Oskooee and Shabsigh (1996) conclude that thee� ective exchange rate is necessary for M2 demand cointegra-tion based on the fact that there is no evidence for M2 coin-tegration without the e� ective exchange rate, but there isevidence for M2 cointegration when the e� ective exchangerate is added. However, this does not necessarily indicatethat the e� ective exchange rate is necessary for M2 demand

cointegration because there is a possibility that the e� ectiveexchange rate only enters into the short-run dynamics of theerror correction model of M2 demand. A signi® cance test ofthe coe� cient of the e� ective exchange rate in the long-runequilibrium M2 demand relation is necessary to test thehypothesis.

The purpose of this paper is to re-examine the Bahmani-Oskooee and Shabsigh (1996) empirical evidence that M2demand in Japan does not form a cointegrated system unlessthe e� ective exchange rate is included. In addition, when theempirical evidence for the hypothesis is found, we testwhether the causal relationship from the e� ective exchangerate to M2 money demand exists. This paper is organized asfollows. In Section II we explain the data and introduce theeconometric model. In Section III we report the empirical® ndings. A summary and discussion are given in Section IV.

IV. DA TA A ND ECONOMETR IC MODEL

We test the hypothesis using the following four variables:(a) the natural logarithm of real M2+ CD (mt), (b) thenatural logarithm of the real GDP (yt), (c) the nominalovernight Call rate (rt),2 and (d) the natural logarithm ofthe nominal e� ective exchange rate (et). Note that anincrease of the nominal e� ective exchange rate re¯ ects anappreciation of the yen. mt is calculated by subtracting the

Applied Economics L etters ISSN 1350± 4851 print/ISSN 1466 ± 4291 online # 2000 Taylor & Francis Ltdhttp://www.tandf.co.uk/journals/tf/13504851.htm l

Applied Economics L etters, 2000, 7, 229 ± 232

229

1 Bahmani-Oskooee and Shabsigh (1996, pp. 2, 3) give a brief survey of the relationship between money demand and exchange rate.2 Miyao (1996) used the level of Call rate, whereas Bahmani-Oskooee and Shabsigh (1996) used the Call rate after natural logarithm transformation.

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Page 3: M2 demand relation and effective exchange rate in Japan: a cointegration analysis

natural logarithm of the GDP de¯ ator from the naturallogarithm of M2+ CD. Monthly data such as the Callrate and M2+ CD are transformed by averaging over thethree months within the quarter. Real GDP, GDP de¯ ator,and nominal M2+ CD are seasonally adjusted. All data areobtained from the `Data Stream’ database.3

The observation periods used in this study are from1973:2 to 1990:4 (we refer to this sample as the s̀ubsample’ ,hereafter), which is the sample used by Bahmani-Oskooeeand Shabsigh (1996) and from 1973:2 to 1997:3 ( we referto this sample as the f̀ull sample’ , hereafter).4

We consider the following kth order vector autoregres-sive (VAR) model to test the hypothesis:

xt ˆ · ‡ ¯t ‡ F 1xt¡1 ‡ ¢ ¢ ¢ ‡ F kxt¡k ‡ ut ;

ut ¹ i:i:d:N…0 ; å u†; t ˆ 1 . . . ;T…1†

Miyao’ s (1996) speci® cation is xt ˆ …mt ;yt ;rt† 0 andxt ˆ …mt ;yt† 0 in Equation 1. Since the purpose of thispaper is to examine the role of the e� ective exchange ratein M2 demand, we specify xt ˆ …mt ;yt ; rt ;et† 0 as inBahmani-Oskooee and Shabsigh (1996). Of course, it ispossible to consider xt ˆ …mt ;yt ;et† 0 as in Miyao (1996).However, since xt ˆ …mt ;yt ;rt ;et† 0 includes xt ˆ …mt ;yt ;et† 0 ,we consider only xt ˆ …mt ;yt ;rt ;et† 0 . We assume that ¯ ˆ 0because the inclusion of the linear trend in Equation 1implicitly assumes that variables possibly contain a quad-ratic time trend. Although Bahmai-Oskooee and Shabsigh(1996) report the results both with and without a constantterm (·), we deal only with the case with a constant term.This is because the exclusion of a constant term implicitlyassumes that there is no linear trend in macroeconomicvariables such as money balance and real income, andthat there is no intercept term in the cointegrating relation,and this speci® cation appears to be incorrect.

II I . EMPIR ICA L R ESULTS

Selection of lag length. In order to examine the cointe-grating relation among the variables, we must select anappropriate lag length k in the VAR model (Equation 1).We selected k using such model selection criteria as theAkaike Information Criterion (AIC) and the Hannan±Quinn Criterion (HQC), setting the maximum lag at 8and the minimum at 1. Note that, since we set the maxi-mum lag at 8, the second quarter of 1975 corresponds tot ˆ 1 in Equation 1.

As a result, for both sample periods, AIC and HQCselected k ˆ 2. If this selected lag length is true, then thenull hypothesis F 3 ˆ 0 when the VAR (3) model is esti-

mated should not be rejected. We tested this hypothesisby the likelihood ratio test (LRT). The p-values of thetest for the subsample case and for the full sample casewere 75.2% and 67.3%, respectively. These results supportthe adopted value. For these reasons, we set the lag lengthas two.

Cointegration test. The standard VAR (k) model Equa-tion 1 can be transformed into a vector error correctionmodel (VECM) as

D xt ˆ · ‡ Y 1 D xt¡1 ‡ ¢ ¢ ¢ ‡ Y k¡1 D xt¡k‡ 1 ‡ ¡A 0xt¡1 ‡ ut

…2†where both ¡ and A are 4 £ r full-column rank matrices.Here, r is the cointegrating rank. Of course, there is no ¡ orA when r ˆ 0. In addition, let both ¡ and A be identitymatrices of the order of four when r ˆ 4.

In order to determine the cointegrating rank r, we util-ized LRTs such as the trace test (Trace) and the maximumeigenvalue test (L-max), proposed in Johansen (1991).Table 1 reports the results. `Trace (10%)’ and `L-max(10%)’ in the table are, respectively, the 10% critical valuesfor the trace test and for the maximum eigenvalue test, andare taken from Osterwald-Lenum (1992, Table 1). Fromthis table we see that both tests selected r ˆ 2 for the sub-sample period at the 10% level. On the other hand, for thefull sample period, the trace test selected r ˆ 3 at the 10%level and the maximum eigenvalue test selected r ˆ 1 at the10% level. As a consequence , we calculated the roots forthe characteristic equation of the system

jz2I4 ¡ z F 1 ¡ F 2j ˆ 0

since the cointegrating rank r corresponds to four minusthe number of roots close to unity.5 The second and thirdlargest roots for the subsample were 0.90 and 70.13, re-spectively. These results support r ˆ 2 for the subsampleperiod. For the full sample period, the second and thirdlargest roots were 0.83 and 0.27, respectively. These resultsseem to suggest that r for the full sample case is also two.therefore, taking the results for the subsample period intoaccount, we also set r to two for the full sample period.

230 H. Y amada

3 Further information on data (including the exact series code) is available upon request from the author.4 In fact, observations used in Bahmani-Oskooee and Shabsigh (1996) start from 1973:1. Because the ® rst full quarter of the ¯ oating exchange rate systemis 1973:2 , we use observations from 1973:2 onwards.5 See Hansen and Juselius (1995, p. 28).

Table 1. Johansen’s cointegration rank test

Subsample Fullsample

r Trace L-max Trace L-max Trace (10%) L-max (10%)

0 58.55 26.79 55.76 26.07 43.95 24.731 31.76 22.05 29.69 14.39 26.79 18.602 9.71 8.50 15.29 12.99 13.33 12.073 1.21 1.21 2.31 2.31 2.69 2.69

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Page 4: M2 demand relation and effective exchange rate in Japan: a cointegration analysis

Stationarity test. The results for the cointegration testindicated that the cointegration rank is two. However,both order-two cointegrating vectors do not necessarilyrepresent the long-run equilibrium relation among thevariables. This is because the number of cointegratingrelations increases for each stationary variable included,as stated in Hansen and Juselius (1995, p. 65). If thereare two stationary variables in our system, then bothorder-two cointegrating relations are trivial and there isno long-run equilibrium M2 demand relation. As aconsequence, we conducted stationarity tests on eachvariable in the system using the LRT discussed in Johan-sen and Juselius (1992). For example, for the Call rate,we tested the hypothesis concerning the cointegratingmatrix A in Equation 2 as

A 0 ˆ a11 a21 a31 a410 0 1 0

¡ ¢…3†

Table 2 reports the results of the stationarity test. The`LRT’ and `p-value’ in the table represent the values ofLRT and the p-value of the test. From this table, we seethat the null of stationarity is rejected for all variablesexcept for the Call rate (rt). The p-values of the Call ratefor the subsample and for the full sample are 80.3% and17.8%, respectively. These results indicate that the Callrate is stationary , and therefore one of the cointegratingrelations comes from the stationarity of the Call rate.6

Furthermore, the results imply that the Call rate does notconstitute the long-run equilibrium relation with the M2money demand.

Estimation of V ECM with parameter restriction. Fromthe results indicating the stationarity of the Call rate, weestimated the VECM, by imposing the restrictionsa31 ˆ 0 and a11 ˆ 1 in Equation 3 with the procedurethat is discussed in Johansen and Juselius (1994).

Table 3 shows the results of a serial correlation test forresiduals in VECM (2). `LM(1)’ [̀LM(4)]’ in the table,represents the value of the Lagrange multiplier test for® rst [fourth] order autocorrelation . The table shows thatthe p-values of the tests are more than 20% in all cases, andthat these results are consistent with the speci® cation of themodel. Therefore, we estimated the VECM with these par-ameter restrictions.

Table 4 reports estimates of the long-run equilibrium M2demand relation for both sample periods. The value inparentheses represents the value of the Wald test statisticfor the signi® cance of parameters whose distribution in thelimit is chi-squared with one degree of freedom.7 In thistable, `*’ signi® es that the corresponding parameter is sta-tistically signi® cant at the 1% level. From this table, we® nd that the elasticity of the long-run e� ective exchangerate is statistically signi® cant at the 1% level in both sampleperiods. These results indicate that the e� ective exchangerate is necessary for M2 demand cointegration in Japan.Furthermore, these results imply that the absence of thee� ective exchange rate in their system leads Miyao (1996)to ® nd no empirical evidence supporting M2 demand coin-tegration. From Table 4, we also ® nd that the elasticity ofthe long-run e� ective exchange rate is negative, which iscontrary to Bahmani-Oskooee and Shabsigh (1996). Ourresults indicate that appreciation of the yen leads to adecrease in M2 demand. In addition, we found that esti-mates of the long-run income elasticity are greater than twofor both sample periods.8

In addition to estimating the long-run M2 demand rela-tion, we estimated the loading coe� cient for the long-runM2 demand relation in the M2 error correction model.

M2 demand and e� ective exchange rate in Japan 231

6 We conducted an ADF test for each variable. The null of unit root was not rejected except for the Call rate at the 10% level. The results of the ADF testare available from the author upon request. Miyao (1996 , footnote 4) also reported that for the case of the Call rate, the null of unit root is rejected by theADF test.7 See Hansen and Juselius (1995, p. 43) for further information on this Wald test.8 Bahmani-Oskooee and Shabsigh (1996) reported that the long-run income elasticity is 1%, and argued that this is supportive of the monetarist view. Wethen tested the hypothesis that the long-run income elasticity is equal to unity with the Wald test statistics above. The null hypothesis was rejected at the1% level for both sample periods.

Table 2. Stationarity test

Subsample Full sample

LRT p-value LRT p-value

mt 20.6 0.0% 11.6 0.3%yt 20.2 0.0% 11.3 0.3%rt 0.4 80.3% 3.5 17.8%et 15.1 0.1% 9.6 0.8%

Table 3. Test for serial correlation of residuals

LM(1) p-value LM(4) p-value

Subsample 10.9 82% 20.5 20%Full sample 12.3 72% 13.8 61%

Table 4. Estimation of the long-run equilibriummoney demand relation

Subsamplemt ˆ 2.94 yt 71.03* et

(123.2) (34.0)

Full samplemt = 2.05* yt 70.27* et

(352.3) (16.1)

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Page 5: M2 demand relation and effective exchange rate in Japan: a cointegration analysis

Table 5 shows the results. ®11 represents the (1,1) elementof ¡ in Equation 2. p-values for the signi® cance test of ®11are less than 1% for both sample periods. These resultsindicate the the M2 error correction model contains theerror correction term for the long-run equilibrium M2demand relation. Combined with the fact that the e� ectiveexchange rate elasticity is signi® cant, this result implies thatthe e� ective exchange rate causes M2 demand in Granger’ssense.9

IV. SUMMA R Y A ND DISCUSSION

This paper has re-examined the empirical evidence ofBahmani-Oskooee and Shabsigh (1996), that M2 demandin Japan does not form a cointegrated system unless thee� ective exchange rate is included. We examined quarterlydata not only from 1973:2 to 1990:4, which is the sampleperiod of Bahmani-Oskooee and Shabsigh (1996), but alsofrom 1973:2 to 1997:3.

Our empirical ® ndings may be summarized as follows:

(i) The long-run e� ective exchange rate elasticity is sta-tistically signi® cant at the 1% level in both sampleperiods. These results indicate that the e� ectiveexchange rate is necessary for M2 demand cointe-gration in Japan and imply that the absence of thee� ective exchange rate in their system leads Miyao(1996) to ® nd no empirical evidence supporting M2demand cointegration.

(ii) The long-run e� ective exchange rate elasticity isnegative; this result indicates that appreciation ofthe yen leads to a decrease of M2 demand.

(iii) The loading coe� cient for the long-run equilibriumM2 demand relation in the M2 error correctionmodel is statistically at the 1% level in both sampleperiods. Combined with result (i) above, this resultimplies that the e� ective exchange rate causes M2demand in Granger’ s sense.

Finally, we o� er some comments concerning result (ii).Arango and Nadiri (1981, p. 72) argued that if the domesticcurrency depreciates, then the value of foreign assets ofdomestic residents in their own currency increases, andthat this leads to an increase of the money balance.10 TheJapanese economy experienced a huge devaluation of for-eign assets in yen after the Plaza accord. One possible in-terpretation of result (ii) is that these led to decreases in M2demand.

A CKNOWLEDGEMENT

We are grateful to Professor Hiroshi Shibuya for helpfulsuggestions.

R EFER ENCES

Arango, S. and Nadiri, M. I. (1981) Demand for money in openeconomies, Journal of Monetary Economics, 7, 69± 83.

Bahamani-Oskooee, M. and Shabsigh, G. (1996) The demand formoney in Japan: evidence from cointegration analysis, Japanand the W orld Economy, 8, 1± 10.

Hansen, H. and Juselius, K. (1995) CATS in RATS, Manual ofCointegration Analysis of T ime Series, Estima.

Johansen, S. (1991) Estimation and hypothesis testing of cointe-gration vectors in Gaussian autoregressive models,Econometrica , 59, 1551± 80.

Johansen, S. and Juselius, K. (1992) Testing structural hypothesesin a multivariate cointegration analysis of the PPP and theUIP for UK, Journal of Econometrics, 53, 211± 44.

Johansen, S. and Juselius, K. (1994) Identi® cation of the long-runand the short-run structure: an application to the ISLMmodel, Journal of Econometrics, 63, 7± 36.

McNown, R. and Wallace, M. (1992) Cointegration tests of along-run relation between money demand and the e� ectiveexchange rate, Journal of International Money and Finance,11, 107± 14.

Miyao, R. (1996) Does a cointegrating M2 demand relation reallyexist in Japan? Journal of the Japanese and InternationalEconomies , 10, 169± 80.

Osterwald-Lenum, M. (1992) A note with quantiles of the asymp-totic distribution of the maximum likelihood cointegrationrank test statistics, Oxford Bulletin of Economics andStatistics, 54, 461± 72.

Toda, H. Y. and Yamamoto, T. (1995) Statistical inference invector autoregressions with possibly integrated processes,Journal of Econometrics, 66 , 225± 50.

232 H. Y amada

9 This result, however, could not be con® rmed with the alternative testing procedure proposed by Toda and Yamamoto (1995), even at the 10%signi® cance level for both sample periods. For this reason, this result should be taken with some caution.10 However, they reported that statistical signi® cance of the exchange rate could not be found. See Arango and Nadiri (1981, pp. 76± 9).

Table 5. Estimation of loading coe� cient

Subsample Full sample

Estimates t-value p-value Estimates t-value p-value

y11 0.03 2.82 0.1% 0.05 2.26 0.6%

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