Memo on the Determinants of Central Bank Euro Holdings by Menzie Chinn 1 UC Santa Cruz

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1 Memo on the Determinants of Central Bank Euro Holdings by Menzie Chinn 1 UC Santa Cruz May 30, 1999 (minor revisions June 8, 2000) Summary: Results from regressions using (i) GDP ratios expressed relative to the sum of G-5 GDP; (ii) inflation expressed using 10 year averages and 5 year average exchange rate volatility (nominal trade weighted). Regressions were run using either Logit of shares or Shares as regressand. A shares regression yields better prediction for 1997 DM holdings (3% error vs. 10%) while a logit regression yields better fit for Swiss France (-0.4% error vs. 5.6%) and Japanese yen (-2.5 error vs. -5.4%). A shares regression, with adding constraint imposed, is estimated with SUR. Under a variety of assumptions, the euro share, using 1997 values of right hand side variables, is between , if the UK is included in EMU. The US predicted value is about 0.48, 0.01 more than actual 1997 shares, but about 0.01 less than predicted 1997 value. 1. Data 2 The data -- mostly from the IMF s International Financial Statistics -- in this set of regressions differ from the previous regression in that I express GDP variables as ratios of the sum of 5-country GDP. The 5 countries are: US, UK, Germany (West), France, and Japan. There was some issue of whether Italy should be used instead of the UK, but since the UK had a larger GDP for most of the sample, I stuck with it. 1 chinn@cats.ucsc.edu. Menzie Chinn Thanks to Eswar Prasad of the IMF for providing the holdings data (which are available in hard copy form from the IMF s Annual Report). 1

2 2. Regression Results 2.1 Regression using LOGIT variable on LHS, G-5 shares, and 10 year inflation. Pooled LS // Dependent Variable is LOGT? Date: 05/28/99 Time: 16:27 Sample(adjusted): Included observations: 23 after adjusting endpoints Total panel observations 161 Variable CoefficienStd. Errort-Statistic Prob. C ?RATIOY (?PI10AVG-INDUSPI10A ?SVOL0_ R-squared Mean dependent var Adjusted R-squared S.D. dependent var S.E. of regression Sum squared resid Log likelihood F-statistic Durbin-Watson stat 7265 Prob(F-statistic) FR Residuals GY Residuals JP Residuals NE Residuals SW Residuals UK Residuals US Residuals Figure 1: Residuals from LOGIT regression 2

3 RESIDFRLGT RESIDGYLGT - RESIDJPLGT RESIDNELGT -8 RESIDSWLGT 0 RESIDUKLGT RESIDUSLGT Figure 2: Residuals, from Logit regression predictions converted to shares. obs RESIDFRLGT RESIDGYLGT RESIDJPLGT RESIDNELGT RESIDSWLGT RESIDUKLGT RESIDUSLGT

4 2.2. Results from regression using SHARES Pooled LS // Dependent Variable is?share1 Date: 05/28/99 Time: 16:29 Sample(adjusted): Included observations: 23 after adjusting endpoints Total panel observations 161 Variable CoefficienStd. Errort-Statistic Prob. C ?RATIOY (?PI10AVG-INDUSPI10A ?SVOL0_ R-squared Mean dependent var Adjusted R-squared S.D. dependent var S.E. of regression 2967 Sum squared resid Log likelihood F-statistic Durbin-Watson stat Prob(F-statistic) 0000 FR Residuals GY Residuals JP Residuals NE Residuals SW Residuals UK Residuals US Residuals Figure 3: Residuals from SHARES regression. 4

5 obs RESIDFR RESIDGY RESIDJP RESIDNE RESIDSW RESIDUK RESIDUS Regression Results from Shares Specification Incorporating Adding Up Constraint (OLS) System: SYS01 Estimation Method: Least Squares Date: 05/29/99 Time: 15:05 Sample: Coefficient Std. Errort-Statistic Prob. C(1) C(2) C(3) C(4) Determinant residual covariance 3.97E-24 Equation: FRSHARE1 = C(1) + C(2)*FRRATIOY3 + C(3)*(FRPI10AVG-IN DUSPI10AVG) + C(4)*FRSVOL0_4 R-squared Mean dependent var Adjusted R-squared S.D. dependent var 6582 S.E. of regression 1976 Sum squared resid Durbin-Watson stat Equation: GYSHARE1 = C(1) + C(2)*GYRATIOY3 + C(3)*(GYPI10AVG-I NDUSPI10AVG) + C(4)*GYSVOL0_4 R-squared Mean dependent var Adjusted R-squared S.D. dependent var 3517 S.E. of regression 7794 Sum squared resid Durbin-Watson stat

6 Equation: JPSHARE1 = C(1) + C(2)*JPRATIOY3 + C(3)*(JPPI10AVG-IND USPI10AVG) + C(4)*JPSVOL0_4 R-squared Mean dependent var 4478 Adjusted R-squared S.D. dependent var 0694 S.E. of regression Sum squared resid Durbin-Watson stat 1739 Equation: NESHARE1 = C(1) + C(2)*NERATIOY3 + C(3)*(NEPI10AVG-IN DUSPI10AVG) + C(4)*NESVOL0_4 R-squared Mean dependent var 7826 Adjusted R-squared S.D. dependent var 2516 S.E. of regression Sum squared resid 7331 Durbin-Watson stat Equation: SWSHARE1 = C(1) + C(2)*SWRATIOY3 + C(3)*(SWPI10AVG-I NDUSPI10AVG) + C(4)*SWSVOL0_4 R-squared Mean dependent var Adjusted R-squared S.D. dependent var 5883 S.E. of regression 8785 Sum squared resid 9895 Durbin-Watson stat Equation: UKSHARE1 = C(1) + C(2)*UKRATIOY3 + C(3)*(UKPI10AVG-IN DUSPI10AVG) + C(4)*UKSVOL0_4 R-squared Mean dependent var 4391 Adjusted R-squared S.D. dependent var 6337 S.E. of regression 1678 Sum squared resid Durbin-Watson stat Equation: (1-FRSHARE1-GYSHARE1-JPSHARE1-NESHARE1-SWSHAR E1-UKSHARE1-OTSHARE1-EUSHARE1) = C(1) + C(2)*USRATIOY3 + C(3)*(USPI10AVG-INDUSPI10AVG) + C(4)*USSVOL0_4 R-squared Mean dependent var Adjusted R-squared S.D. dependent var S.E. of regression Sum squared resid Durbin-Watson stat

7 FRSHARE1 Residuals GYSHARE1 Residuals JPSHARE1 Residuals NESHARE1 Residuals SWSHARE1 Residuals UKSHARE1 Residuals (1-FRSHARE1-GYSHARE1-JPSHARE1-NESHARE1-SWSHARE1-UKSHARE1-OTSHARE1-EUSHARE1) Residuals France Germany Japan Netherlands Switzerland UK US obs RESID1 RESID2 RESID3 RESID4 RESID5 RESID6 RESID

8 2.4. Regression Results from Shares Specification Incorporating Adding Up Constraint (SUR) System: SYS01 Estimation Method: Seemingly Unrelated Regression Date: 05/29/99 Time: 15:15 Sample: Coefficient Std. Errort-Statistic Prob. C(1) C(2) C(3) C(4) Determinant residual covariance 6.44E-25 Equation: FRSHARE1 = C(1) + C(2)*FRRATIOY3 + C(3)*(FRPI10AVG-IN DUSPI10AVG) + C(4)*FRSVOL0_4 R-squared Mean dependent var Adjusted R-squared S.D. dependent var 6582 S.E. of regression 9067 Sum squared resid 6289 Durbin-Watson stat Equation: GYSHARE1 = C(1) + C(2)*GYRATIOY3 + C(3)*(GYPI10AVG-I NDUSPI10AVG) + C(4)*GYSVOL0_4 R-squared Mean dependent var Adjusted R-squared S.D. dependent var 3517 S.E. of regression Sum squared resid Durbin-Watson stat Equation: JPSHARE1 = C(1) + C(2)*JPRATIOY3 + C(3)*(JPPI10AVG-IND USPI10AVG) + C(4)*JPSVOL0_4 R-squared Mean dependent var 4478 Adjusted R-squared S.D. dependent var 0694 S.E. of regression 0600 Sum squared resid Durbin-Watson stat Equation: NESHARE1 = C(1) + C(2)*NERATIOY3 + C(3)*(NEPI10AVG-IN DUSPI10AVG) + C(4)*NESVOL0_4 R-squared Mean dependent var 7826 Adjusted R-squared S.D. dependent var 2516 S.E. of regression Sum squared resid 4245 Durbin-Watson stat Equation: SWSHARE1 = C(1) + C(2)*SWRATIOY3 + C(3)*(SWPI10AVG-I NDUSPI10AVG) + C(4)*SWSVOL0_4 8

9 R-squared Mean dependent var Adjusted R-squared S.D. dependent var 5883 S.E. of regression 4109 Sum squared resid Durbin-Watson stat Equation: UKSHARE1 = C(1) + C(2)*UKRATIOY3 + C(3)*(UKPI10AVG-IN DUSPI10AVG) + C(4)*UKSVOL0_4 R-squared Mean dependent var 4391 Adjusted R-squared S.D. dependent var 6337 S.E. of regression Sum squared resid Durbin-Watson stat Equation: (1-FRSHARE1-GYSHARE1-JPSHARE1-NESHARE1-SWSHAR E1-UKSHARE1-OTSHARE1-EUSHARE1) = C(1) + C(2)*USRATIOY3 + C(3)*(USPI10AVG-INDUSPI10AVG) + C(4)*USSVOL0_4 R-squared Mean dependent var Adjusted R-squared S.D. dependent var S.E. of regression 7509 Sum squared resid Durbin-Watson stat FRSHARE1 Residuals GYSHARE1 Residuals JPSHARE1 Residuals NESHARE1 Residuals SWSHARE1 Residuals UKSHARE1 Residuals (1-FRSHARE1-GYSHARE1-JPSHARE1-NESHARE1-SWSHARE1-UKSHARE1-OTSHARE1-EUSHARE1) Residuals

10 obs RESID8 RESID9 RESID10 RESID11 RESID12 RESID13 RESID Simulation Results A simple back-of-the envelope calculation using the estimates from the unconstrained share (not logit) regression (Section 2.2), and expressing EU-11 GDP as the sum of Germany, France, and Italy yields an implied share of the euro holdings of 0.34 (the sum of EU-11 currencies in 1997 was including ECUs). If EU-11 GDP is expressed as the sum of Germany, France, Italy and the UK, then the predicted euro holdings are 0.45 (the sum of EU-11 currencies plus Pound in 1997 was 0.23). Calculations using constrained SUR estimates (Section 2.4 above) are performed using several assumptions. 1. Using original G-5 GDP to normalize each country s GDP, 1.1 and UK not in EMU yields euro share of UK in EMU yields euro share of Using G-5 GDP to be EU-11 (as sum of FR, GY, NE, IT), US, Japan, UK, Switzerland 2.1 and UK not in EMU yields euro share of 0.33, US share of 0.48, Japan share of. 2.2 UK in EMU yields euro share of NOTE: in none of these cases is the adding-up constraint imposed in the simulation part (only in estimation portion). euromem3a_rev.wpd 5/30/99 rev 6/8/00 10