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 0.32-0.34, 0.42-0.45 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 Email: chinn@cats.ucsc.edu. Menzie Chinn 1999. 2 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. 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): 1975 1997 Included observations: 23 after adjusting endpoints Total panel observations 161 Variable CoefficienStd. Errort-Statistic Prob. C -4.568419 0.148201-30.82587 00?RATIOY3 9.810941 0.373211 26.28791 00 (?PI10AVG-INDUSPI10A-17.49353 2.665179-6.563734 00?SVOL0_4-0.865235 1.135151-0.762221 0.4471 R-squared 0.843549 Mean dependent var-3.081129 Adjusted R-squared 0.840560 S.D. dependent var 1.741660 S.E. of regression 0.695444 Sum squared resid 75.93182 Log likelihood 65.75150 F-statistic 282.1706 Durbin-Watson stat 7265 Prob(F-statistic) 0000 0.4 0.2 0.0-0.2-0.4-0.6-0.8-1.0 FR Residuals 1.8 1.6 1.4 1.2 1.0 0.8 GY Residuals 0.0-0.1-0.2-0.3-0.4-0.5 JP Residuals -1.2 98 00 0.6 98 00-0.6 98 00-0.2-0.4-0.6-0.8-1.0-1.2-1.4-1.6 NE Residuals 0.6 0.4 0.2 0.0-0.2-0.4 SW Residuals 1.0 0.8 0.6 0.4 0.2 UK Residuals -1.8 98 00-0.6 98 00 0.0 98 00 0.8 US Residuals 0.6 0.4 0.2 0.0-0.2-0.4-0.6 98 00 Figure 1: Residuals from LOGIT regression 2
0.010 0.14 5 0-5 0.12-0.01-0.010-0.015 RESIDFRLGT RESIDGYLGT - RESIDJPLGT -2 0.012 0-4 -6-8 -0.010-0.012 8 4 0-4 0.016 0.012 8 4-0.014 RESIDNELGT -8 RESIDSWLGT 0 RESIDUKLGT 0.15 - -0.15 RESIDUSLGT Figure 2: Residuals, from Logit regression predictions converted to shares. obs RESIDFRLGT RESIDGYLGT RESIDJPLGT RESIDNELGT RESIDSWLGT RESIDUKLGT RESIDUSLGT 1975-8631 9259-0.014449-3437 8459 0.013175 0.132207 1976-9709 2741-8974 -4558 5905 4284 6538 1977-0.010124 9794-0.012052-5370 3303 3468 5008 1978-0.011594 5444-4804 -6187 1392 2213 0.072917 1979-0.013254 3277-9040 -7150 4153 5481 3490 1980-6077 0.077334-0.010745-5159 7954 0.014989-0.094105 1981-7822 0459-0.015836-7647 2708 7841-5598 1982-9868 5210-0.018232-9053 1605 0.010206 0525 1983-9672 5611 8027-0.012213-4767 0.010185 6788 1984-9571 5369 4466-0.012640-6200 0.012715-6299 1985-7262 0.077325 2273-0.011254-2501 0.010260-3051 1986-8778 1216 4134-0.010273-2094 5988-1977 1987-9319 6275 9572-8570 -0497 2631-6857 1988-8145 0.099485 8333-0.010251 0946 6960-6764 1989-4647 0.138084 0904-8338 -1440 6456-0.099648 1990 3068 0.130933-0.013819-8871 -0643 0.011871-6191 1991 6478 0.118070-9231 -8170-0663 0.015466-0.076796 1992 2425 0.099861-0.015893-0.011656-2196 0.014188 9087 1993-1946 7036-9356 -0.010944-0445 0.012778 3386 1994-1172 0.112411-2912 -0.011420-2581 0.016413 9767 1995-2423 7640-0.016016-0.011923-3386 0.014935 9045 1996-7580 2047 4847-0.012325-4179 0.016958 4021 1997-0.013644 0362 5193-0.010252-4290 0.017201 6698 3
2.2. Results from regression using SHARES Pooled LS // Dependent Variable is?share1 Date: 05/28/99 Time: 16:29 Sample(adjusted): 1975 1997 Included observations: 23 after adjusting endpoints Total panel observations 161 Variable CoefficienStd. Errort-Statistic Prob. C 1773 0.011287 1.928929 55?RATIOY3 1.293514 8425 45.50611 00 (?PI10AVG-INDUSPI10A-0.940792 0.202989-4.634688 00?SVOL0_4-0.768745 6457-8.891638 00 R-squared 0.933823 Mean dependent var 0.120832 Adjusted R-squared 0.932558 S.D. dependent var 0.203960 S.E. of regression 2967 Sum squared resid 0.440471 Log likelihood 471.8002 F-statistic 738.4739 Durbin-Watson stat 0.122243 Prob(F-statistic) 0000 FR Residuals GY Residuals JP Residuals - - -0.07 - - - - 98 00-98 00-98 00 0.03 NE Residuals SW Residuals UK Residuals 0.01-0.01 98 00 98 00 98 00 0.20 US Residuals 0.15-98 00 Figure 3: Residuals from SHARES regression. 4
obs RESIDFR RESIDGY RESIDJP RESIDNE RESIDSW RESIDUK RESIDUS 1975-2059 0673-0.097642 7244 0.075323-3657 0.172221 1976 8277 0.010230-0.090987 9096 0.074301 5666 0.156706 1977 8941 0.011825-1863 4480 1923 2023 0.163572 1978 4516 0.011412 3244 0.010191 0.099428 0.012915 0.130243 1979-6730 -5897 5080 0293 2263 0.038921-8948 1980 0263 6156 5007-0257 4151 8681-7311 1981-8287 -0.013735 1756-4739 8073 8041 0395 1982-7531 0540 6463-8909 0.076019 3855 1129 1983 0342 3369-3083 -0.016492 0.035505 2870 0.033870 1984-4472 -0.018400-3714 -0.015983 0.036307 3200 0.038002 1985-0439 5324-8487 -0.014419 4498 4379 2564 1986-9431 3916-0.074961-0.019941 0.031544 7680 0.011293 1987-5205 8488-3923 -0.019899 0.031566 0.036756-1711 1988-0.071557 0.018673-4112 2052 0.031285 0.032856 1600 1989-8988 7244-0.073181-0.018002 0.039626 0.036534 8495 1990-5359 2800 1353 2070 2618 0.037517 2893 1991-7766 6074-0.075067 2357 3505 0.016404 2912 1992-6271 0.013817-0.090688 2276 4972 0.033793-0710 1993-5071 9970-5685 -0.017628 5756 0.032680 0280 1994-7143 0.034444 5760-0.019291 6347 4688-0.013066 1995-1618 0.039394-0910 -0.012964 0476 9273-3532 1996-8383 0.034138-7169 -0.012728 8036 5611 0.012775 1997-0.076358 0.030273 4113-9758 6199 2077 2752 2.3. Regression Results from Shares Specification Incorporating Adding Up Constraint (OLS) System: SYS01 Estimation Method: Least Squares Date: 05/29/99 Time: 15:05 Sample: 1975 1997 Coefficient Std. Errort-Statistic Prob. C(1) 1788 0.011296 1.928781 56 C(2) 1.293248 8447 45.46173 00 C(3) -0.940941 0.203146-4.631853 00 C(4) -0.768711 6524-8.884409 00 Determinant residual covariance 3.97E-24 Equation: FRSHARE1 = C(1) + C(2)*FRRATIOY3 + C(3)*(FRPI10AVG-IN DUSPI10AVG) + C(4)*FRSVOL0_4 R-squared -75.561122 Mean dependent var 0.014348 Adjusted R-squared -87.649720 S.D. dependent var 6582 S.E. of regression 1976 Sum squared resid 0.072979 Durbin-Watson stat 0.016901 Equation: GYSHARE1 = C(1) + C(2)*GYRATIOY3 + C(3)*(GYPI10AVG-I NDUSPI10AVG) + C(4)*GYSVOL0_4 R-squared -0.206301 Mean dependent var 0.126174 Adjusted R-squared -0.396769 S.D. dependent var 3517 S.E. of regression 7794 Sum squared resid 0.014677 Durbin-Watson stat 0.308861 5
Equation: JPSHARE1 = C(1) + C(2)*JPRATIOY3 + C(3)*(JPPI10AVG-IND USPI10AVG) + C(4)*JPSVOL0_4 R-squared -10.910271 Mean dependent var 4478 Adjusted R-squared -12.790840 S.D. dependent var 0694 S.E. of regression 0.076851 Sum squared resid 0.112215 Durbin-Watson stat 1739 Equation: NESHARE1 = C(1) + C(2)*NERATIOY3 + C(3)*(NEPI10AVG-IN DUSPI10AVG) + C(4)*NESVOL0_4 R-squared -51.624058 Mean dependent var 7826 Adjusted R-squared -59.933119 S.D. dependent var 2516 S.E. of regression 0.019643 Sum squared resid 7331 Durbin-Watson stat 0.077255 Equation: SWSHARE1 = C(1) + C(2)*SWRATIOY3 + C(3)*(SWPI10AVG-I NDUSPI10AVG) + C(4)*SWSVOL0_4 R-squared -117.053700 Mean dependent var 0.016391 Adjusted R-squared-135.693758 S.D. dependent var 5883 S.E. of regression 8785 Sum squared resid 9895 Durbin-Watson stat 0.037057 Equation: UKSHARE1 = C(1) + C(2)*UKRATIOY3 + C(3)*(UKPI10AVG-IN DUSPI10AVG) + C(4)*UKSVOL0_4 R-squared -36.357058 Mean dependent var 4391 Adjusted R-squared -42.255541 S.D. dependent var 6337 S.E. of regression 1678 Sum squared resid 0.033004 Durbin-Watson stat 0.117258 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 0.388065 Mean dependent var 0.602087 Adjusted R-squared 0.291444 S.D. dependent var 0.090822 S.E. of regression 0.076450 Sum squared resid 0.111048 Durbin-Watson stat 0.296377 6
FRSHARE1 Residuals GYSHARE1 Residuals JPSHARE1 Residuals - - -0.07 - - - - - - 0.03 NESHARE1 Residuals SWSHARE1 Residuals UKSHARE1 Residuals 0.01-0.01 (1-FRSHARE1-GYSHARE1-JPSHARE1-NESHARE1-SWSHARE1-UKSHARE1-OTSHARE1-EUSHARE1) Residuals 0.20 0.15 - France Germany Japan Netherlands Switzerland UK US obs RESID1 RESID2 RESID3 RESID4 RESID5 RESID6 RESID7 1975-2052 0680-0.097615 7233 0.075306-3647 0.173341 1976 8269 0.010236-0.090960 9084 0.074282 5675 0.157826 1977 8934 0.011831-1836 4468 1903 2032 0.162694 1978 4510 0.011418 3219 0.010179 0.099406 0.012924 0.131365 1979-6723 -5891 5055 0280 2241 0.038931-9827 1980 0255 6161 4983-0271 4128 8689-7191 1981-8279 -0.013730 1732-4754 8049 8049-0485 1982-7522 0536 6439-8925 0.075995 3863 1245 1983 0332 3365-3059 -0.016507 0.035481 2877 0.033987 1984-4463 -0.018396-3690 -0.015998 0.036284 3207 0.037121 1985-0430 5328-8463 -0.014435 4476 4384 3682 1986-9422 3920-0.074937-0.019957 0.031523 7684 0.012412 1987-5196 8492-3899 -0.019915 0.031546 0.036760-2592 1988-0.071548 0.018677-4087 2068 0.031266 0.032861 0718 1989-8979 7249-0.073155-0.018018 0.039608 0.036539 8378 1990-5351 2807 1327 2085 2601 0.037522 2778 1991-7758 6083-0.075036 2371 3489 0.016409 2800 1992-6264 0.013825-0.090657 2290 4955 0.033797-0596 1993-5065 9978-5655 -0.017642 5739 0.032683 0396 1994-7138 0.034453 5731-0.019304 6330 4693-0.013948 1995-1614 0.039403-0882 -0.012978 0459 9278-4414 1996-8379 0.034147-7140 -0.012742 8019 5615 0.013894 1997-0.076354 0.030282 4086-9771 6182 2081 3631 7
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: 1975 1997 Coefficient Std. Errort-Statistic Prob. C(1) 0.013258 2500 5.303261 00 C(2) 1.238806 0.014516 85.34053 00 C(3) -0.777173 0850-12.77187 00 C(4) -0.645241 0.030027-21.48841 00 Determinant residual covariance 6.44E-25 Equation: FRSHARE1 = C(1) + C(2)*FRRATIOY3 + C(3)*(FRPI10AVG-IN DUSPI10AVG) + C(4)*FRSVOL0_4 R-squared -68.542753 Mean dependent var 0.014348 Adjusted R-squared -79.523188 S.D. dependent var 6582 S.E. of regression 9067 Sum squared resid 6289 Durbin-Watson stat 0.013525 Equation: GYSHARE1 = C(1) + C(2)*GYRATIOY3 + C(3)*(GYPI10AVG-I NDUSPI10AVG) + C(4)*GYSVOL0_4 R-squared -0.627983 Mean dependent var 0.126174 Adjusted R-squared -0.885033 S.D. dependent var 3517 S.E. of regression 0.032288 Sum squared resid 0.019808 Durbin-Watson stat 0.214872 Equation: JPSHARE1 = C(1) + C(2)*JPRATIOY3 + C(3)*(JPPI10AVG-IND USPI10AVG) + C(4)*JPSVOL0_4 R-squared -12.100674 Mean dependent var 4478 Adjusted R-squared -14.169201 S.D. dependent var 0694 S.E. of regression 0600 Sum squared resid 0.123431 Durbin-Watson stat 0.034129 Equation: NESHARE1 = C(1) + C(2)*NERATIOY3 + C(3)*(NEPI10AVG-IN DUSPI10AVG) + C(4)*NESVOL0_4 R-squared -29.471632 Mean dependent var 7826 Adjusted R-squared -34.282942 S.D. dependent var 2516 S.E. of regression 0.014947 Sum squared resid 4245 Durbin-Watson stat 0.093148 Equation: SWSHARE1 = C(1) + C(2)*SWRATIOY3 + C(3)*(SWPI10AVG-I NDUSPI10AVG) + C(4)*SWSVOL0_4 8
R-squared -101.551077 Mean dependent var 0.016391 Adjusted R-squared-117.743353 S.D. dependent var 5883 S.E. of regression 4109 Sum squared resid 0.078090 Durbin-Watson stat 0.030222 Equation: UKSHARE1 = C(1) + C(2)*UKRATIOY3 + C(3)*(UKPI10AVG-IN DUSPI10AVG) + C(4)*UKSVOL0_4 R-squared -18.852665 Mean dependent var 4391 Adjusted R-squared -21.987296 S.D. dependent var 6337 S.E. of regression 0.030383 Sum squared resid 0.017539 Durbin-Watson stat 0.155231 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 0.198227 Mean dependent var 0.602087 Adjusted R-squared 0.071632 S.D. dependent var 0.090822 S.E. of regression 7509 Sum squared resid 0.145498 Durbin-Watson stat 0.220218 FRSHARE1 Residuals GYSHARE1 Residuals JPSHARE1 Residuals - - -0.07 - - - - - - -0.12 0.03 NESHARE1 Residuals SWSHARE1 Residuals UKSHARE1 Residuals 0.01-0.01 0.09 0.07 0.03 0.03 0.01-0.01 (1-FRSHARE1-GYSHARE1-JPSHARE1-NESHARE1-SWSHARE1-UKSHARE1-OTSHARE1-EUSHARE1) Residuals 0.20 0.15 9
obs RESID8 RESID9 RESID10 RESID11 RESID12 RESID13 RESID14 1975-2953 2870-0.099845 5285 9454-8232 0.196395 1976-0121 0.011783-0.093325 6677 8682 0.014861 0.181788 1977 2310 0.013079-5874 2919 0.075053 0.011687 0.186775 1978 8704 0.015914-0410 0.011039 9733 4006 0.156092 1979-7514 1370-2220 3026 0.076014 6111 0.016114 1980-9548 0.014351-5686 3068 0.078545 4478 3804 1981-8217 -4283-3267 -0679 1262 0.034870 0.018747 1982-8383 -0.010353 9219-4095 0.071182 0.039926 6380 1983 0728 2592-9590 -0.010883 0.036625 7357 0426 1984-5426 -9015-5571 -0.010567 0.036840 0080 1956 1985-1541 0.014323-7106 -8891 3973 1187 0.016538 1986-9241 0.013652-0.075473-0.013171 0.032870 0.034909 5713 1987-2351 0.018196-3572 -0.012734 0.032844 5225 0.010187 1988-7314 8597-3883 -0.014806 0.032581 2413 0.012483 1989-4565 6661-0.074622-0.011326 0.038862 5664-0.016570 1990-0076 2666 6030-0.014994 1118 7544 9103 1991-1240 0.035697-0.076180-0.015326 1661 0.010885-0.019830 1992-0283 2271-0.090687-0.015900 0996 5428 0.013167 1993 9360 0.036797-9297 -0.011998 0199 4230 0.015376 1994-0739 1162 9968-0.013571 2028 0.017985 2815 1995 6265 4335-6384 -8452 5347 4794 0.011888 1996-2588 0.038984-0.073299-8472 1577 0.018906 0.032644 1997-0.070175 0.035354-3071 -5902 1677 0.015872-3919 3. 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 0.195 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 0.32 1.2 UK in EMU yields euro share of 0.43 2. 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 0.42. 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