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1 TCER Working Paper Series 量 的 質 的 金 融 緩 和 からの 出 口 における 財 政 負 担 Fiscal Cost to Exit Quantitative Easing: The Case of Japan 藤 木 裕 Hiroshi Fujiki 戸 村 肇 Hajime Tomura 2015 年 9 月 Working Paper J-13 公 益 財 団 法 人 東 京 経 済 研 究 センター 東 京 都 千 代 田 区 飯 田 橋 by Hiroshi Fujiki and Hajime Tomura. All rights reserved. Short sections of text, not to exceed two paragraphs, may be quoted without explicit permission provided that full credit, including notice, is given to the source.
2 概 要 本 稿 の 目 的 は 日 本 銀 行 の 量 的 質 的 金 融 緩 和 政 策 が 達 成 された 暁 の 政 策 運 営 ( 出 口 戦 略 )で 生 じる 財 政 負 担 の 試 算 を 行 うことである ベンチマークシナリオとして 日 本 銀 行 は2016 年 度 に2 %の 物 価 安 定 の 目 標 を 達 成 した 時 点 で マネタリーベース 目 標 を 破 棄 し 長 期 国 債 の 買 入 れを 停 止 するととも に 短 期 金 利 を 引 き 上 げると 仮 定 する その 後 日 本 銀 行 は 超 過 準 備 に 政 策 金 利 並 みの 付 利 を 行 うと ともに 長 期 国 債 の 市 中 売 却 はせず 過 去 に 購 入 した 長 期 国 債 が 満 期 を 迎 えるにつれ 徐 々にバランス シートを 縮 小 させると 仮 定 する この 仮 定 の 下 では 超 過 準 備 がなくなるまでに 約 20 年 が 必 要 である この 間 長 期 国 債 からの 利 息 収 入 が 減 る 一 方 巨 額 の 超 過 準 備 への 利 払 いが 必 要 となるため 日 本 銀 行 の 剰 余 金 も10 年 以 上 マイナスになる ただしこの 試 算 は 景 気 見 通 しに 沿 った 日 本 銀 行 の 収 益 予 測 ではなくあくまでシナリオ 分 析 であることに 注 意 が 必 要 である 他 のシナリオ 分 析 の 結 果 からは ベンチ マークの 仮 定 よりも 物 価 安 定 の 目 標 達 成 が 遅 れるほど あるいは 日 本 銀 行 券 への 需 要 が 減 るほど 日 本 銀 行 の 剰 余 金 のマイナス 幅 が 大 きくなることが 示 される 藤 木 裕 東 京 経 済 研 究 センター (TCER) 及 び 中 央 大 学 商 学 部 八 王 子 市 東 中 野 fujiki@tamacc.chuo-u.ac.jp 戸 村 肇 早 稲 田 大 学 政 治 経 済 学 術 院 新 宿 区 西 早 稲 田 tomura.hajime@gmail.com
3 Abstract This paper simulates the cash flows and balance sheets of the Bank of Japan (BoJ) before and after exiting from Quantitative and Qualitative Monetary Easing (QQE) under various scenarios. The simulations show that the BoJ will record significant accounting losses after exiting QQE. These losses are fiscal costs for the consolidated Japanese government as they represent increased interest expenses to the public and will arise because the BoJ will acquire a large amount of Japanese government bonds at very low interest rates during QQE, whose interest payments will then be insufficient to cover interest expenses on excess reserves after exiting QQE. Moreover, any cumulative accounting losses will ensure the BoJ's net asset position remains negative for a sustained period of time. We also find that the BoJ's accounting losses will increase with the duration of QQE and the interest rate elasticity of banknote demand, and decrease if the BoJ conducts tapering following the ending of QQE. Finally, the effect of tapering will be significantly stronger if there is no safety channel for the long-term interest rate. Hiroshi Fujiki TCER and Chuo University Department of Commerce Higashinakano Hacjhioji Tokyo Japan fujiki@tamacc.chuo-u.ac.jp Hajime Tomura Waseda University Faculty of Political Science and Economics Nishiwaseda Shinzyuku Tokyo tomura.hajime@gmail.com
4 ETF Will Roberds Summer Workshop on Economic Theory 2015 Corresponding author. 1
5 Goodfriend [2000] Fujiki, Okina and Shiratsuka [2001] /kk1505a.pdf 2 2
6 [2003] [2003] [2013] [2015] Carpenter et al.[2015] Del Negro and Sims[2014] 3
7 Reis[2015] 3 Reis[2015] Goodfriend[2014] [2014] Carpenter et al.[2015])
8 Bernanke[2015] [2014] [2014] [2014] (1) (2) (3) 4 [2014] [2014] 5
9 [2014] GDP [2013] [2013] [2008] [2013] [2008] 2 2 [2014] (1) (2) (3) 6
10 D G,t ( B G,t (W G,t ) (S G,t ) t CF G,t = T G,t + J CB,t G G,t R G,t P G,t + N G,t + i ST,t W G,t i ST,t S G,t (1) T G,t : J CB,t : G G,t : R G,t : P G,t : N G,t : i ST,t : W G,t : W G,t+1 W G.t + D G,t+1 D G,t = CF G,t (2) B G,t+1 B G.t = N G,t P G,t (3) 7
11 (B CB,t ) (D B,t ) (S CB,t ) (D G,t ) (C CB,t ) (E CB,t ) D REQ,t D EX,t D REQ,t + D EX,t = D B,t (4) C CB,t ) GDP GDP t C CB,t = µ t GDP t (5) µ t µ t = { (6) GDP ETF J-REIT
12 1990 GDP D REQ,t = τη t GDP t (7) τ η t GDP τ τ = (8) η t µ t { 2.05 η t = 1.53 (9) 6 D G,t D G,t = 0 (10) τ η
13 +R CB,t +P CB,t V CB,t +i ST,t S CB,t (S CB,t+1 S CB,t ) I CB,t ) J CB,t F CB,t T CB,t D EX,t I CB,t [2014] F CB,t F CB,t = 1900 (2013 GDP GDP GDP GDP g (π t ) GDP t = (1 + g)(1 + π t )GDP t 1 (11) 8 F CB,t /12 10
14 GDP g = (12) 0 2 π t = { (13) i ST,t i ST,t = (14) D B,t+1 D B,t = V CB,t R CB,t P CB,t + S CB,t+1 S CB,t i ST,t S CB,t + I CB,t + J CB,t + F CB,t + T CB,t (C CB,t+1 C CB,t ) (15) 2.6 E CB,t = B CB,t + S CB,t D B,t C CB,t (16) 11
15 B CB,t+1 B CB,t = V CB,t P CB,t + A CB,t (17) A CB,t A CB,t 2.7 π CB,t = R CB,t + i ST,t S CB,t I CB,t + A CB,t F CB,t (18) T CB,t = max{0, 0.275π CB,t } (19) J CB,t = max{0, 0.75(π CB,t 1 T CB,t 1 )} (20)
16 2.8 V CB,t + S CB,t+1 S CB,t = P CB,t + R CB,t I CB,t J CB,t F CB,t T CB,t + i ST,t S CB,t + C CB,t+1 C CB,t + D B,t+1 D B,t (21) W G,t+1 W G.t = S G,t+1 S G,t + T G,t + J CB,t + T CB,t G G,t R G,t P G,t + N G,t + i ST,t W G,t i ST,t S G,t (22) W G,t+1 W G.t (S G,t+1 S G,t ) + P G,t P CB,t [N G,t V CB,t (S CB,t+1 S CB,t )] = T G,t G G,t R G,t + i ST,t W G,t i ST,t S G,t + R CB,t I CB,t F CB,t + i ST,t S CB,t + C CB,t+1 C CB,t + D B,t+1 D B,t (23) W G,t+1 W G.t + P G,t P CB,t (N G,t V CB,t ) [(S G,t+1 S G,t ) (S CB,t+1 S CB,t )] = T G,t G G,t (R t R CB,t ) + i ST,t W G,t i ST,t (S G,t S CB,t ) I CB,t F CB,t + C CB,t+1 C CB,t + D B,t+1 D B,t (24) (P G,t P CB,t ) V CB,t P CB,t
17 V CB,t = 12 ( )
18 ( (21) D B,t+1 D B,t V CB,t S CB,t+1 S CB,t S CB,t+1 S CB,t = V CB,t + P CB,t + R CB,t J CB,t T CB,t I CB,t F CB,t + i ST,t S CB,t + C CB,t+1 C CB,t + (25) D B,t+1 D B,t 80 (25) (25) V CB,t = Krishnamurthy-Vissing Jorgense[2011]
19 (21) S CB,t+1 S CB,t = P CB,t P CB,t 1 D B,t+1 D B,t if D B,t+1 D REQ,t+1 = V CB,t + S CB,t+1 S CB,t P CB,t R CB,t + J CB,t + T CB,t +I CB,t + F CB,t i ST,t S CB,t (C CB,t+1 C CB,t ) (26) D B,t+1 D REQ,t+1 D B,t+1 = D REQ,t+1 S CB,t+1 S CB,t = V CB,t + P CB,t + R CB,t J CB,t T CB,t I CB,t F CB,t + i ST,t S CB,t + C CB,t+1 C CB,t + D REQ,t+1 D B,t if D B,t+1 < D REQ,t+1 in Eq. (26) (27) I CB,t GDP
20 3 (2014 ( ROA) Del Negro and Sims[2014] ROA 17
21
22 5.2.1 [2014] [2014] µ t = RC CB,t RGDP t (CALL t ) ln(rc CB,t ) = a0 + a1 ln(rgdp t ) + a2 (CALL t ) + ε 1t ln(rc CB,t ) = b0 + b1 ln(rgdp t ) + b2 ln(call t ) + ε 2t ε 1t ε 2t GDP Elliott,Rothenberg and Stock[1996] Gregory and Hansen [1996] Gregory and Hansen [1996] 2004 Hayashi[2000] b1, b2 Dynamic OLS(DOLS) b1=1.029 b2= DOLS b GDP
23 [2008] [2008] % [2008] [2008] [2008] [2008]
24 5.3 [2014] { { ( ) }} BCB,t i LT,t = i ST,t + min 0.01, min 0, ln ln(0.041) GDP t i LT,t Krishnamurthy and Vissing- Jorgensen [2011] GDP GDP 2014 GDP
25 [2014] [2014] [2014] [2014] (1) (2) (3) [2014] [2014] [2014]
26 Carpenter et al [2015] [2014] [2014]
27 (1) (2) (3) [1] Bernanke, Ben S., Monetary policy in the future, Remarks at the IMF s Rethinking Macro Policy III conference on April 15, 2015, ben-bernanke/posts/2015/04/15-monetary-policy-in-the-future, 24
28 [2] Carpenter, Seth B., Jane E. Ihrig, Elizabeth C. Klee, Daniel W. Quinn, and Alexander H. Boote. The Federal Reserve s Balance Sheet and Earnings: A Primer and Projections. International Journal of Central Banking, 11(2), 2015, [3] Del Negro, Marco, and Christopher A. Sims, When Does a Central Bank s Balance Sheet Require Fiscal Support? November 2014,Federal Reserve Bank of New York, Staff Reports Number 701,Revised: March [4] Elliott, Graham. R., Thomas. J. Rothenberg, and James. H. Stock, Efficient Tests for an Autoregressive Unit Root. Econometrica 64 (4), , [5] Fujiki, Hiroshi, Kunio Okina, and Shigenori Shiratsuka, Monetary Policy under Zero Interest Rate: Viewpoints of Central Bank Economists. Monetary and Economic Studies, 19 (1), Bank of Japan, , [6] Goodfriend, Marvin, Overcoming the Zero Bound on Interest Rate Policy, Journal of Money, Credit and Banking, 32(4), 2000, [7] Goodfriend, Marvin, Monetary Policy as a Carry Trade. Monetary and Economic Studies, 32, Bank of Japan, 2014, [8] Gregory, W. Allan and Bruce E. Hansen, Residual-based Tests for Cointegration in Models with Regime Shifts, Journal of Econometrics, 70, 1996, [9] Hayashi, Fumio, Econometrics, Princeton University Press, [10] Krishnamurthy, Arvind, and Annette Vissing-Jorgensen, The Effects of Quantitative Easing on Interest Rates: Channels and Implications for Policy, Brookings Papers on Economic Activity, 43(2), 2011, [11] Miyao, Ryuzo, Liquidity Traps and the Stability of Money Demand: Is Japan Really Trapped at the Zero Bound? RIEB Discussion Paper No. 127, Research Institute for Economics and Business Administration, Kobe University, [12], Use of Money Supply in the Conduct of Monetary Policy: Re-Examining the Time-Series Evidence, Japanese Economic Review, 56, 2005, pp [13] Nakashima, Kiyotaka, and Makoto Saito, On the Comparison of Alternative Specifications for Money Demand: The Case of Extremely Low Interest Rate Regimes in Japan, Journal of the Japanese and International Economies, 26 (3), 2012, pp [14] Reis,Ricardo, Different Types of Central Bank Insolvency and the Central Role of Seignorage, NBER Working Paper Series, 21226,
29 [15] BP 2013 [16] 2014 [17] koen_2003/ko0310f.htm/ [18] 2014 [19] [20] Weekly Economic Report Market Economics No. 545-s BNP PARIBAS [21] 2005 [22] [23]
30 A 1 C CB,t ) GDP GDP t µ t µ t = C CB,t = µ t GDP t { GDP 9 GDP [2014] GDP [2014] M1 Miyao[2002, 2005] Nakashima and Saito[2012] [2004] C CB,t NGDP t GDP SNA 1968SNA P GDP t GDP SNA 1968SNA CALL t GDP 1959 GDP GDP RC CB,t = C CB,t P GDP t, RGDP t = NGDP t P GDP t ln(rc CB,t ) = a0 + a1 ln(rgdp t ) + a2 (CALL t ) + ε 1t ln(rc CB,t ) = b0 + b1 ln(rgdp t ) + b2 ln(call t ) + ε 2t ε 1t ε 2t 27
31 Miyao[2002, 2005] Nakashima and Saito[2012] 2000 M1 [2004] Miyao[2002] b1=1 [2014] 16 GDP Gregory and Hansen [1996] 3 GDP, GDP GDP ADF ADF P-value ln(rc CB,t ) ln(rgdp t ) CALL t ln(call t ) Stata 13 dfuller Elliott,Rothenberg and Stock[1996] AIC Stata13 dfgls 16 [2008] [2005] [2005]
32 % 5% 10% Stata 13 egranger Gregory and Hansen [1996] Gregory and Hansen [1996] 2004 ADF Zt ( ) ( ) 1% 5% 10% ADF ) -5.59(2004) Zt ) -5.64(2004) Zα ) (2004) Stata 13 ghansen Hayashi[2000] b1, b2 Static OLS(SOLS) Dynamic OLS(DOLS) b1 b2 SOLS DOLS (s.e.) (.043) (.010) DOLS Stata 13 ivreg2 SOLS b1=1.121,b2= SOLS ADF SOLS DOLS DOLS b1=1.029 b2= DOLS b GDP
33 B 2003 [2008] [2008] % 0.9 [2008] [2008] [2008] [2008]
34 Gregory and Hansen [1996] ADF 2009 (2008) (1995) DOLS exp(2*1.4) =
35 1: GDP Inflation rate Short term nominal interest rate Nominal GDP growth rate Fiscal year 32
36 2: Trillion yen Reserves JGBs Net Short term assets Cash Fiscal year 33
37 3: Trillion yen Interest on reserves Interest on JGBs Interest on short term assets Pre tax profit Fiscal year 34
38 4: After tax profit per asset Fiscal year 35
39 5: Trillion yen Fiscal year 36
40 6: Trillion yen Fiscal year 37
41 7: Trillion yen in present value Fiscal year 38
42 8: Trillion yen tau = 2016 tau = 2018 Fiscal year
43 9: Trillion yen tau = 2016 tau = 2018 Fiscal year
44 10: Fitted value based on the real banknote demand function Data Trillion yen Fiscal year 41
45 11: /
46 12:
47 13: (1995) (2008) ( ) Callrate
48 14: Trillion yen Benchmark No interest rate elasticity Return of the banknote demand function Disappearance of cash stash Fiscal year GDP DOLS
49 15: Trillion yen Benchmark No interest rate elasticity Return of the banknote demand function Disappearance of cash stash Fiscal year GDP DOLS
50 16: Trillion yen Benchmark No interest rate elasticity Return of the banknote demand function Disappearance of cash stash Fiscal year GDP DOLS
51 17: Trillion yen Reserves JGBs Net Short term assets Cash Fiscal year 10 48
52 18: Trillion yen Benchmark Adjustment period = 10 yrs Adjustment period = 20 yrs Fiscal year
53 19: Trillion yen Benchmark Adjustment period = 10 yrs Adjustment period = 20 yrs Fiscal year
54 20: Trillion yen Short term nominal interest rate Long term nominal interest rate (benchmark) Long term nominal interest rate (adjustment period = 10 years) Long term nominal interest rate (adjustment period = 20 years) Fiscal year
55 21: Trillion yen With the safety channel Without the safety channel Fiscal year 10 safety channel 52
56 22: Trillion yen With the safety channel Without the safety channel Fiscal year 10 safety channel 53
57 23: With the safety channel Without the safety channel safety channel 54
58 24: [2014] Reserves JGBs Net Short term assets Cash Govt s Reserves (End of) fiscal year 55
59 25: [2014] Inflation rate Short term interest rate Long term interest rate Fiscal year GDP
60 26: [2014] Interest on reserves Interest on JGBs Interest on short term assets Pre tax profit Fiscal year [2014] ETF 57
61 27: [2014] BoJ s profit transfer to the gov t Fiscal year 58
62 28: [2014] Equity Fiscal year 59
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