The Reanchoring Channel of QE

Transcription

1 The Reanchoring Channel of QE The ECB s Asset Purchase Programme and Long-Term Inflation Expectations Philippe Andrade Johannes Breckenfelder Fiorella De Fiore Peter Karadi Oreste Tristani European Central Bank* Bank of Canada Annual Conference, November 2016 *The views expressed are those of the authors, and do not necessarily reflect the official position of the ECB or the Eurosystem.

2 Overview Large-scale asset purchases (LSAP) Key policy tool of all major central banks Substitute for interest rates stuck at their effective lower bound (ZLB)

3 Overview Large-scale asset purchases (LSAP) Key policy tool of all major central banks Substitute for interest rates stuck at their effective lower bound (ZLB) In a frictionless world, LSAP no impact (Curdia and Woodford, 2011)

4 Overview Large-scale asset purchases (LSAP) Key policy tool of all major central banks Substitute for interest rates stuck at their effective lower bound (ZLB) In a frictionless world, LSAP no impact (Curdia and Woodford, 2011) In practice, significant announcement effects (Krishnamurthy and Vissing-Jorgensen, 2011; Altavilla, Carboni and Motto, 2015)

5 Overview Large-scale asset purchases (LSAP) Key policy tool of all major central banks Substitute for interest rates stuck at their effective lower bound (ZLB) In a frictionless world, LSAP no impact (Curdia and Woodford, 2011) In practice, significant announcement effects (Krishnamurthy and Vissing-Jorgensen, 2011; Altavilla, Carboni and Motto, 2015) Our focus: Impact on long-term inflation expectations at the ZLB EA Adverse shocks at the ZLB led to some deanchoring in in EA Initial LSAP announcement in 2015:1 contributed to reanchoring

6 This paper Event-study evidence on ECB s LSAP (APP) announcements on inflation expectations Unconventional easing leads to subsequent rise in 5-year-ahead inflation expectations

7 This paper Event-study evidence on ECB s LSAP (APP) announcements on inflation expectations Unconventional easing leads to subsequent rise in 5-year-ahead inflation expectations DSGE model with Balance-sheet constrained financial intermediaries Binding effective lower bound Imperfect information about CB s target

8 This paper Event-study evidence on ECB s LSAP (APP) announcements on inflation expectations Unconventional easing leads to subsequent rise in 5-year-ahead inflation expectations DSGE model with Balance-sheet constrained financial intermediaries Binding effective lower bound Imperfect information about CB s target Calibrated to the euro area Quantifies the importance of the reanchoring channel of APP Shock w/o policy action: downturn and deanchoring APP stimulates the economy and leads to reanchoring

9 Findings Reanchoring channel is potent Explains 1/3 of the inflation impact of APP Amplified impact on short-term inflation Mechanism (ZLB and financial accelerator): Higher target implies easier policy Leads to higher expected inflation Implies lower real rates now (ZLB, even though earlier liftoff) Raises asset prices, eases financial constraints in a positive feedback loop

10 Findings Reanchoring channel is potent Explains 1/3 of the inflation impact of APP Amplified impact on short-term inflation Mechanism (ZLB and financial accelerator): Higher target implies easier policy Leads to higher expected inflation Implies lower real rates now (ZLB, even though earlier liftoff) Raises asset prices, eases financial constraints in a positive feedback loop Implications Target uncertainty renders policy passivity costly Makes credible policy signals powerful

11 EA event study ECB press conferences January June 2016 Special ECB: IR announcements separate from press conferences Press conferences (36) Robustness: exclude 3 with key FG announcements (June 5, 2014; October 22, 2015; March 10, 2016)

12 EA event study ECB press conferences January June 2016 Special ECB: IR announcements separate from press conferences Press conferences (36) Robustness: exclude 3 with key FG announcements (June 5, 2014; October 22, 2015; March 10, 2016) Measurement of the monetary policy indicator 5-year German bund yield Market price: average of the best bid and ask quotes, from the last 5 Surprise: price change between 10 minutes before, 80 minutes after the start of the press conference Cumulated over each quarter

13 EA event study, cont Inflation expectations 5-year ahead inflation expectations in the SPF Robustness: 5-year inflation swap yields 5-year-ahead

14 EA event study, cont Inflation expectations 5-year ahead inflation expectations in the SPF Robustness: 5-year inflation swap yields 5-year-ahead Methodology: Quarterly regressions EA y t = α + β x t 1 + ε t,

15 Impact on 5-year inflation expectations (1) (2) (3) (4) Post 2013 Pre 2013 APP APP, No FG Change in 5-year-ahead inflation expectations 5-year German yield *** ** *** surprise (-4.392) (1.551) (-3.151) (-3.960) Sample 2013q1-2016q2 2001q1-2012q4 2014q2-2016q2 2014q2-2016q2 Observations R-squared Robust t-statistics in parentheses *** p<0.01, ** p<0.05, * p<0.1 Easing yields to reanchoring Robustness: ILS

16 Overview Quantitative DSGE model Representative family with Households Consumption habits Monopolistically competitive labor market; staggered wage setting Portfolio adjustment costs HH assets Intermediate good producers with working capital constraint Intermediate Capital producers with investment adjustment costs (Q) Capital Monopolistically competitive retailers with staggered price setting Retailers

17 Overview Quantitative DSGE model Representative family with Households Consumption habits Monopolistically competitive labor market; staggered wage setting Portfolio adjustment costs HH assets Intermediate good producers with working capital constraint Intermediate Capital producers with investment adjustment costs (Q) Capital Monopolistically competitive retailers with staggered price setting Retailers Balance sheet constrained financial intermediaries

18 Overview Quantitative DSGE model Representative family with Households Consumption habits Monopolistically competitive labor market; staggered wage setting Portfolio adjustment costs HH assets Intermediate good producers with working capital constraint Intermediate Capital producers with investment adjustment costs (Q) Capital Monopolistically competitive retailers with staggered price setting Retailers Balance sheet constrained financial intermediaries Central bank with uncertain inflation target

19 Financial intermediaries Representative family f bankers, 1 f workers Bankers: start-up fund X, stochastic survival σ

20 Financial intermediaries Representative family f bankers, 1 f workers Bankers: start-up fund X, stochastic survival σ Assets: State-contingent loans (Qt S t ): R kt Long-term government bond (qt B t ): R bt

21 Financial intermediaries Financial intermediaries Collect deposits from HHs: D t Accumulate net worth from retained earnings Nt Invest them into loans and government bonds

22 Financial intermediaries Financial intermediaries Collect deposits from HHs: D t Accumulate net worth from retained earnings Nt Invest them into loans and government bonds Agency problem: bankers can divert the fraction θ of loans and θ of gov t bonds, with 0 1.

23 Implications Details Risk-adjusted aggregate leverage constraint Q t S pt + q t B pt φ t N t where φ t is an endogenous leverage ratio.

24 Implications Details Risk-adjusted aggregate leverage constraint Q t S pt + q t B pt φ t N t where φ t is an endogenous leverage ratio. Arbitrage between corporate and sovereign bonds E t β Ω t+1 (R kt+1 R t+1 ) = E t β Ω t+1 (R bt+1 R t+1 ), where Ω t+1 the FI s discount factor.

25 Implications Details Risk-adjusted aggregate leverage constraint Q t S pt + q t B pt φ t N t where φ t is an endogenous leverage ratio. Arbitrage between corporate and sovereign bonds E t β Ω t+1 (R kt+1 R t+1 ) = E t β Ω t+1 (R bt+1 R t+1 ), where Ω t+1 the FI s discount factor. Aggregate net worth N t = σ [(R kt R t )Q t 1 S pt 1 + (R bt R t )q t 1 B pt 1 +R t N t 1 ] + X

26 Credit Policy Central bank: Less efficient in providing credit τ efficiency cost

27 Credit Policy Central bank: Less efficient in providing credit τ efficiency cost Not balance sheet constrained

28 Credit Policy Central bank: Less efficient in providing credit τ efficiency cost Not balance sheet constrained Asset purchases Gov t: Reducing the supply of long-term assets Private: Direct credit to the private sector

29 Credit Policy, cont. Composition of Assets between banks and central bank S t =S pt + S gt B t =B pt + B gt

30 Credit Policy, cont. Composition of Assets between banks and central bank S t =S pt + S gt B t =B pt + B gt Private Securities Demand Q t S t = φ t N t + Q t S gt + q t (B gt B t )

31 Credit Policy, cont. Composition of Assets between banks and central bank S t =S pt + S gt B t =B pt + B gt Private Securities Demand Q t S t = φ t N t + Q t S gt + q t (B gt B t ) Purchases of gov t bonds have: weaker effects on private vs. gov t securities demand stronger effects on excess returns of private vs. gov t sec.

32 Central Bank LSAP: Ψ t = (Q t S gt + q t B gt )/4Ȳ Follows a second-order autoregressive process

33 Central Bank LSAP: Ψ t = (Q t S gt + q t B gt )/4Ȳ Follows a second-order autoregressive process Interest rate policy with ZLB: i t i t = max(0, i t ) i t =ρ i i t 1 + (1 ρ i ) [πt + κ π (π t πt ) + κ y y t ] + κ π (π t π t 1 ) + κ y (y t y t 1 ) + ε t πt =ρ π πt 1 + ε π t

34 Central Bank LSAP: Ψ t = (Q t S gt + q t B gt )/4Ȳ Follows a second-order autoregressive process Interest rate policy with ZLB: i t i t = max(0, i t ) i t =ρ i i t 1 + (1 ρ i ) [πt + κ π (π t πt ) + κ y y t ] + κ π (π t π t 1 ) + κ y (y t y t 1 ) + ε t πt =ρ π πt 1 + ε π t Conventional and unconventional policies are substitutes Effective lower bound on the interest rate LSAP unconstrained

35 Learning Imperfect information: π t, ε t are unobserved

36 Learning Imperfect information: π t, ε t are unobserved Learning rule, π e t+1 =ρ π eπ e t ξ {s t s e t } s t =i t ςψ t [(1 ρ i )κ π + κ π ] π t [(1 ρ i )κ y + κ y ] y t s e t =Ẽt 1 [s t ]

37 Learning Imperfect information: π t, ε t are unobserved Learning rule, π e t+1 =ρ π eπ e t ξ {s t s e t } s t =i t ςψ t [(1 ρ i )κ π + κ π ] π t [(1 ρ i )κ y + κ y ] y t s e t =Ẽt 1 [s t ] Idea Motivated by constant gain (ξ) learning Agents assume LSAP substitutes IRs at the ZLB, i S t = i t ςψ t

38 Learning Imperfect information: π t, ε t are unobserved Learning rule, π e t+1 =ρ π eπ e t ξ {s t s e t } s t =i t ςψ t [(1 ρ i )κ π + κ π ] π t [(1 ρ i )κ y + κ y ] y t s e t =Ẽt 1 [s t ] Idea Motivated by constant gain (ξ) learning Agents assume LSAP substitutes IRs at the ZLB, i S t = i t ςψ t Reanchoring At ZLB i t = i e t without LSAP, low inflation leads to deanchoring LSAP: Ψt > Ψ e t leads to reanchoring

39 Solution Learning equilibrium Agents optimize, learn about CB target CB sets LSAP policy and interest rates s.t. ZLB All markets clear

40 Solution Learning equilibrium Agents optimize, learn about CB target CB sets LSAP policy and interest rates s.t. ZLB All markets clear First-order appr. solution: impulse response analysis Optimality conditions loglinearized around a non-stochastic steady state Shocks hit in period 1 Inflation target stays unchanged (unknown to agents) ZLB binds endogenously (non-linearity)

41 Solution Learning equilibrium Agents optimize, learn about CB target CB sets LSAP policy and interest rates s.t. ZLB All markets clear First-order appr. solution: impulse response analysis Optimality conditions loglinearized around a non-stochastic steady state Shocks hit in period 1 Inflation target stays unchanged (unknown to agents) ZLB binds endogenously (non-linearity) Algorithm: solution over the impulse response space Each period: Update expectations about the inflation target Forecast perceived responses (including the length ZLB is expected to bind) Consume, work, save, invest, set prices, wages now IR policy is set according to a constant inflation target Repeat each period until steady state reached

42 Calibration Tightness of credit conditions Average credit spreads Private: 2.45% (LT CCB - Eonia) Sovereign: 2.1% (EA 10-year yield - Eonia) FI leverage: 6 Assets over equity of FIs, NFCs in EA SA

43 Calibration Tightness of credit conditions Average credit spreads Private: 2.45% (LT CCB - Eonia) Sovereign: 2.1% (EA 10-year yield - Eonia) FI leverage: 6 Assets over equity of FIs, NFCs in EA SA Learning rule 15bps decline in LT expectations before APP (ξ = 0.062) Similar impact of APP and 1.1% monpol shock (ς = 0.068) Monpol 9bps increase on APP announcement (consistent with SPF change between 2015Q1-Q3)

44 Calibration, cont. Conventional parameters Price- and wage stickiness, consumption habits, investment adjustment costs, policy rule Parameters As estimated in NAWM (Christoffel et al., 2008) Monpol High nominal stickiness

45 Calibration, cont. Conventional parameters Price- and wage stickiness, consumption habits, investment adjustment costs, policy rule Parameters As estimated in NAWM (Christoffel et al., 2008) Monpol High nominal stickiness APP 11% of GDP, maturity: 8, 9% in ten-year equivalents Hump-shaped pattern Calibrated to reach peak in 2 years, exit as bonds mature

46 Results Stylized demand shock Level Persistent shock to savings preference Inflation: 2.4%, Output 7%, 10-year rate -100bps Deanchoring: perceived target 15 bps, expected liftoff: 7 quarters

47 Results Stylized demand shock Level Persistent shock to savings preference Inflation: 2.4%, Output 7%, 10-year rate -100bps Deanchoring: perceived target 15 bps, expected liftoff: 7 quarters APP Impact Peak effects: inflation 40bps, output: 1.1% Important channel: reanchoring (1/3 of inflation effect) Reanchoring Equivalent to a 1.1% monpol shock Monpol

48 Results Stylized demand shock Level Persistent shock to savings preference Inflation: 2.4%, Output 7%, 10-year rate -100bps Deanchoring: perceived target 15 bps, expected liftoff: 7 quarters APP Impact Peak effects: inflation 40bps, output: 1.1% Important channel: reanchoring (1/3 of inflation effect) Reanchoring Equivalent to a 1.1% monpol shock Monpol Raising efficiency Maturity extension (from 8 to 11, +10bps inflation effect) Maturity Forward guidance (+5 bps inflation effect) Forward guidance

49 Other channels Duration channel Figure

50 Other channels Duration channel Figure Stealth recapitalization Recapitalization

51 Reanchoring Channel: Related Literature Event-study evidence on QE Broad asset-price impact (Rogers, Scotti and Wright, 2014; Swanson, 2015) Scarce evidence on impact on long-term inflation expectations Market expectations (Krishnamurthy and Vissing-Jorgensen, 2011; Altavilla, Carboni and Motto, 2015): premium component

52 Reanchoring Channel: Related Literature Event-study evidence on QE Broad asset-price impact (Rogers, Scotti and Wright, 2014; Swanson, 2015) Scarce evidence on impact on long-term inflation expectations Market expectations (Krishnamurthy and Vissing-Jorgensen, 2011; Altavilla, Carboni and Motto, 2015): premium component Information in introducing QE Related to signalling at ZLB (Bhattarai, Eggertsson and Gafarov, 2015) There: QE helps commitment of discretionary CB Here: QE reveals information about policy rule (Gürkaynak, Sack and Swanson, 2005; Gürkaynak, Levin and Swanson, 2010) Complements asset-revaluation channels (Gertler and Karadi, 2013; Del Negro, Eggertsson, Ferrero and Kiyotaki, 2010; Chen, Cúrdia and Ferrero, 2012)

53 Conclusion Inflation-expectation reanchoring: key channel Event-study evidence Quantified in a DSGE macromodel

54 Conclusion Inflation-expectation reanchoring: key channel Event-study evidence Quantified in a DSGE macromodel Policy conclusions Inactivity particularly costly with deanchoring Reanchoring enhances policy effectiveness Duration of targeted assets should be maximized Forward guidance reinforces the effectiveness of APP

55 Euro Area Inflation Expectations Percent Percent year ahead inflation expectations (q-o-q change, one quarter lead) 5-year German rate (intraday changes around press conferences) 5-year ahead inflation expectations (level, right axis) Source: ECB, Survey of Professional Forecasters. 1 Back

56 Euro Area Inflation Expectations Percent Q1 2001Q3 2002Q1 2002Q3 2003Q1 2003Q3 2004Q1 2004Q3 2005Q1 2005Q3 2006Q1 2006Q3 2007Q1 2007Q3 2008Q1 2008Q3 2009Q1 2009Q3 2010Q1 2010Q3 2011Q1 2011Q3 2012Q1 2012Q Percent year ahead inflation expectations (q-o-q change, one quarter lead) 5-year German rate 5-year ahead inflation expectations (level, right axis) Source: ECB, Survey of Professional Forecasters. 1.2 Back

57 Impact on 5x5 inflation-linked swap rates (1) (2) (3) (4) Post 2013 Pre 2013 APP APP, No FG Change in 5x5 inflation-linked swap yields 5-year German yield ** 0.571*** ** ** surprise (-2.754) (4.303) (-2.592) (-2.571) Sample 2013q1-2016q2 2004q1-2012q4 2014q2-2016q2 2014q2-2016q2 Observations R-squared Robust t-statistics in parentheses *** p<0.01, ** p<0.05, * p<0.1 Easing yields to reanchoring Back

58 Impact of an interest rate innovation 0.2 Policy rate 0.3 Inflation 0.6 Output Employment 0.6 % from ss New Area Wide 0 Model 0 Baseline Real interest rate Asset price Consumption Investment % from ss Quarters Quarters Quarters Quarters Back

59 Demand shock and APP % from ss % from ss % from ss % from ss Savings preference Inflation Investment 10 year rate % of GDP 10 5 CB purchases Output Asset Price Perceived Inflation Target Quarters Quarters Quarters No Policy Baseline Quarters Policy rate Consumption Banks Market Capitalization Expected Liftoff Back

60 APP and maturity extension % from no policy Savings preference Inflation % of GDP CB purchases Output 0.5 Policy rate Consumption % impact Investment Asset Price Banks Market Capitalization 20 % impact % impact year rate Quarters Perceived Inflation Target Quarters Baseline Quarters 0 Maturity Extension Expected Liftoff Quarters Back

61 APP with and without reanchoring channel % of GDP % from no policy % from no policy CB purchases Output Asset Price % from no policy Policy rate Quarters Baseline Consumption Banks market valuation Inflation Investment Quarters Quarters No inflation deanchoring 0 10 year rate Back

62 APP and monetary policy shock % from no policy % of GDP % from no policy 10 5 CB purchases Policy rate Asset Price % from no policy Output Consumption year rate Inflation Investment Perceived inflation objective Quarters Quarters Quarters Baseline Monetary policy shock ( 110bps) Back

63 APP and forward guidance 10 CB purchases 0.4 Policy rate 0.8 Inflation % of GDP % impact Baseline Output APP with Forward Guidance 10 year rate Expected Liftoff % impact Quarters Quarters Quarters Quarters Back

64 References I Altavilla, Carlo, Giacomo Carboni, and Roberto Motto (2015) Asset Purchase Programmes and Financial Markets: Evidence from the Euro Area, ECB working paper no Bhattarai, Saroj, Gauti Eggertsson, and Bulat Gafarov (2015) Time Consistency and the Duration of Government Debt: A Signalling Theory of Quantitative Easing, NBER Working Paper 21336, Board of Governors of the Federal Reserve System (U.S.). Chen, Han, Vasco Cúrdia, and Andrea Ferrero (2012) The Macroeconomic Effects of Large-scale Asset Purchase Programmes, The Economic Journal, Vol. 122, pp

65 References II Christoffel, Kai, Guenter Coenen, and Anders Warne (2008) The New Area-Wide Model of the Euro Area: A Micro-Founded Open-Economy Model for Forecasting and Policy Analysis, Working Paper Series 0944, European Central Bank. Curdia, Vasco and Michael Woodford (2011) The Central Bank Balance Sheet as an Instrument of Monetary Policy, Journal of Monetary Economics, Vol. 58, pp Del Negro, Marco, Gauti Eggertsson, Andrea Ferrero, and Nobuhiro Kiyotaki (2010) The Great Escape? A Quantitative Evaluation of the Fed s Non-Standard Policies, unpublished, Federal Reserve Bank of New York. Gertler, Mark and Peter Karadi (2013) QE 1 vs. 2 vs. 3...: A Framework for Analyzing Large-Scale Asset Purchases as a Monetary Policy Tool, International Journal of Central Banking, Vol. 9, pp

66 References III Gürkaynak, Refet S, Andrew Levin, and Eric Swanson (2010) Does Inflation Targeting Anchor Long-Run Inflation Expectations? Evidence from the U.S., UK, and Sweden, Journal of the European Economic Association, Vol. 8, pp Gürkaynak, Refet S, Brian Sack, and Eric Swanson (2005) The Sensitivity of Long-Term Interest Rates to Economic News: Evidence and Implications for Macroeconomic Models, American Economic Review, pp Krishnamurthy, Arvind and Annette Vissing-Jorgensen (2011) The Effects of Quantitative Easing on Interest Rates, Brookings Papers on Economic Activity. Rogers, John H, Chiara Scotti, and Jonathan H Wright (2014) Evaluating asset-market effects of unconventional monetary policy: a multi-country review, Economic Policy, Vol. 29, pp

67 References IV Swanson, Eric T (2015) Measuring the Effects of Unconventional Monetary Policy on Asset Prices, Technical report, National Bureau of Economic Research.

68 Households Maximize utility subject to E t i=0 [ β i ln(c t+i hc t+i 1 ) χ ] 1 + ϕ L1+ϕ t+i C t + D ht+1 = W t L t + Π t + T t + R t D t where D ht : short term debt (deposits and government debt) Πt : payouts to the household from firm ownership net the transfers it gives to the bankers

69 Wage setting Labor supply is a composite of heterogeneous labor services [ 1 N t = 0 ] ε W εw 1 ε W 1 N ft ε W df where N ft is the supply of labor service f. (1)

70 Wage setting Labor supply is a composite of heterogeneous labor services [ 1 N t = 0 ] ε W εw 1 ε W 1 N ft ε W df where N ft is the supply of labor service f. (1) From cost minimization by firms: N ft = ( ) ε W Wft W t N t (2)

71 Wage setting Labor supply is a composite of heterogeneous labor services [ 1 N t = 0 ] ε W εw 1 ε W 1 N ft ε W df where N ft is the supply of labor service f. (1) From cost minimization by firms: N ft = ( ) ε W Wft W t Staggered wage setting a la Calvo Wages can be adjusted with probability 1 γw Indexation with probability γw (Π t) N t (2)

72 Wage Setting Optimal Wage Setting i=0 γ i β i Λ t+i [ W t Π t,t+i P t+i µ W N ϕ ft+i ] N ft+i = 0 (3) with µ W = 1 1 1/ε W.

73 Wage Setting Optimal Wage Setting i=0 γ i β i Λ t+i [ W t Π t,t+i P t+i µ W N ϕ ft+i ] N ft+i = 0 (3) with µ W = 1 1 1/ε W.

74 Wage Setting Optimal Wage Setting i=0 γ i β i Λ t+i [ W t Π t,t+i P t+i µ W N ϕ ft+i ] N ft+i = 0 (3) with µ W = 1 1 1/ε W. From the law of large numbers, W t = [ (1 γ W )(W t ) 1 ε W + γ W (Π γ W i t 1 Π 1 γ W i t ] 1 P t 1 ) 1 ε 1 ε W W (4)

75 Household Asset Holdings Households can directly hold private securities and long-term gov t bonds subject to transactions costs Private: holding costs: 1 2 κ(s ht S h ) 2 for S ht S h. Gov t bonds: holding cost: 1 2 κ(b ht B h ) 2 for B ht B h

76 Household Asset Holdings Households can directly hold private securities and long-term gov t bonds subject to transactions costs Private: holding costs: 1 2 κ(s ht S h ) 2 for S ht S h. Gov t bonds: holding cost: 1 2 κ(b ht B h ) 2 for B ht B h Household asset demands: S ht =S h + E tλ t,t+1 (R kt+1 R t+1 ) κ B ht =B h + E tλ t,t+1 (R bt+1 R t+1 ) κ

77 Household Asset Holdings Households can directly hold private securities and long-term gov t bonds subject to transactions costs Private: holding costs: 1 2 κ(s ht S h ) 2 for S ht S h. Gov t bonds: holding cost: 1 2 κ(b ht B h ) 2 for B ht B h Household asset demands: Elasticity κ S ht =S h + E tλ t,t+1 (R kt+1 R t+1 ) κ B ht =B h + E tλ t,t+1 (R bt+1 R t+1 ) κ the excess returns go to zero as κ 0, the quantities go to their frictionless values as κ.

78 Credit policy with HH asset demand Composition of Assets S t = S pt + S ht + S gt B t = B pt + B ht + B gt

79 Credit policy with HH asset demand Composition of Assets S t = S pt + S ht + S gt Private Asset Demands B t = B pt + B ht + B gt Q t (S t S h ) = φ t N t + Q t S gt + q t [ Bgt (B t B h ) ] + (Q t + 2 q t ) E tλ t,t+1 (R kt+1 R t+1 ) κ

80 Credit policy with HH asset demand, cont. Relative effects of securities versus gov t bond purchases similar to before. Larger effects of purchases with fixed demand. Responses of household asset demands can moderate effects. Overall, need limits to arbitrage for bank and household asset demands.

81 Households Representative family f bankers, 1 f workers Perfect consumption insurance

82 Households Representative family f bankers, 1 f workers Perfect consumption insurance With iid. probability 1 σ, a banker becomes a worker. (Limits bankers ability to save themselves out of the financial constraints)

83 Households Representative family f bankers, 1 f workers Perfect consumption insurance With iid. probability 1 σ, a banker becomes a worker. (Limits bankers ability to save themselves out of the financial constraints) Each period, (1 σ)f workers randomly become bankers

84 Households Representative family f bankers, 1 f workers Perfect consumption insurance With iid. probability 1 σ, a banker becomes a worker. (Limits bankers ability to save themselves out of the financial constraints) Each period, (1 σ)f workers randomly become bankers New banker receives a start-up fund from the family

85 Assets Return on state-contingent debt (capital) R kt+1 = Z t+1 + Q t+1 Q t

86 Assets Return on state-contingent debt (capital) R kt+1 = Z t+1 + Q t+1 Q t Return on long term gov t bonds R bt+1 = Ξ/P t + q t+1 q t

87 Financial Intermediaries Intermediary Balance Sheet Q t s t + q t b t = n t + d t

88 Financial Intermediaries Intermediary Balance Sheet Evolution of net worth Q t s t + q t b t = n t + d t n t = R kt Q t 1 s t 1 + R bt q t 1 b t 1 R t d t 1

89 Financial Intermediaries Intermediary Balance Sheet Evolution of net worth Q t s t + q t b t = n t + d t n t = R kt Q t 1 s t 1 + R bt q t 1 b t 1 R t d t 1 FI s objective V t = E t (1 σ)σ i 1 Λ t,t+i n t+i (5) i=1

90 Limits to Arbitrage Agency problem: banker can divert the fraction θ of loans and θ of gov t bonds, with 0 1.

91 Limits to Arbitrage Agency problem: banker can divert the fraction θ of loans and θ of gov t bonds, with 0 1. Lenders can recover the residual funds and shut the bank down.

92 Limits to Arbitrage Agency problem: banker can divert the fraction θ of loans and θ of gov t bonds, with 0 1. Lenders can recover the residual funds and shut the bank down. Incentive constraint V t θq t s t + θq t b t. (6)

93 Implications Solution Risk-adjusted leverage constraint Q t s t + q t b t = φ t n t where φ t is an endogenous leverage ratio.

94 Implications Solution Risk-adjusted leverage constraint Q t s t + q t b t = φ t n t where φ t is an endogenous leverage ratio. Arbitrage between corporate and sovereign bonds E t β Ω t+1 (R kt+1 R t+1 ) = E t β Ω t+1 (R bt+1 R t+1 ), where Ω t+1 the FI s discount factor.

95 Aggregation Aggregate leverage Q t S pt + q t B pt φ t N t

96 Aggregation Aggregate leverage Aggregate net worth Q t S pt + q t B pt φ t N t N t = σ [(R kt R t )Q t 1 S pt 1 + (R bt R t )q t 1 B pt 1 +R t N t 1 ] + X

97 Resource Constraint and Government Policy Resource constraint Y t = C t + I t + f ( It I t 1 ) I t + G + Φ t where Φ t is the portfolio transactions costs.

98 Resource Constraint and Government Policy Resource constraint Y t = C t + I t + f ( It I t 1 ) I t + G + Φ t where Φ t is the portfolio transactions costs. Central bank balance sheet Q t S gt + q t B gt = D gt

99 Resource Constraint and Government Policy Resource constraint Y t = C t + I t + f ( It I t 1 ) I t + G + Φ t where Φ t is the portfolio transactions costs. Central bank balance sheet Gov t budget constraint Q t S gt + q t B gt = D gt G = T t + (R kt R t τ)s gt 1 + (R bt R t )B gt 1

100 Financial Intermediaries Problem End-of-period value function V t V t 1 (s t 1, b t 1, n t 1 ) = E t 1 Λ t 1,t {(1 σ)n t + σw t (n t )}

101 Financial Intermediaries Problem End-of-period value function V t V t 1 (s t 1, b t 1, n t 1 ) = E t 1 Λ t 1,t {(1 σ)n t + σw t (n t )} Beginning-of-period value function W t subject to [λ t ] W t (n t ) = max s t,b t V t (s t, b t, n t ) V t (s t, b t, n t ) θq t s t + θq t b t

102 Solution Conjecture: linear end-of-period value function V t = µ st Q t s t + µ bt q t b t + ν t n t

103 Solution Conjecture: linear end-of-period value function V t = µ st Q t s t + µ bt q t b t + ν t n t Beginning-of-period Lagrange function (1 + λ t )(µ st Q t s t + µ b q t b t + ν t n t ) λ t (θq t s t + θq t b t )

104 Solution, cont. FONC: s t µ st = λ t 1 + λ t θ FONC: b t µ bt = λ t 1 + λ t θ = µ st FONC: λ t (µ st Q t s t + µ bt q t b t + ν t n t ) (θq t s t + θq t b t ) = 0

105 Solution, cont. Endogenous risk-adjusted leverage constraint: Q t s t + q t b t = φ t n t where φ t is the leverage ratio: ν t φ t = θ µ st

106 Solution, cont. Endogenous risk-adjusted leverage constraint: Q t s t + q t b t = φ t n t where φ t is the leverage ratio: φ t = ν t θ µ st Beginning-of-period value function W t (n t ) =µ st (Q t s t + q t b t ) + ν t n t =(µ st φ t + ν t )n t =θφ t n t

107 Solution, cont. End-of-period value function µ st 1 Q t 1 s t 1 + µ bt 1 q t 1 b t 1 + ν t 1 n t 1 = subject to E t 1 Λ t 1,t {(1 σ)n t + σw t (n t )}, n t = (R kt R t )Q t 1 s t 1 + (R bt R t )q t 1 b t 1 + R t n t 1

108 Solution, cont. End-of-period value function µ st 1 Q t 1 s t 1 + µ bt 1 q t 1 b t 1 + ν t 1 n t 1 = subject to E t 1 Λ t 1,t {(1 σ)n t + σw t (n t )}, n t = (R kt R t )Q t 1 s t 1 + (R bt R t )q t 1 b t 1 + R t n t 1 After substitution µ st 1 Q t 1 s t 1 + µ bt 1 q t 1 b t 1 + ν t 1 n t 1 = E t 1 Λ t 1,t {[(1 σ) + σθφ t ] (R kt R t )Q t 1 s t 1 + (R bt R t )q t 1 b t 1 + R t n t 1 },

109 Solution, cont. Partial marginal values µ st =E t Ωt+1 (R kt+1 R t+1 ) µ bt =E t Ωt+1 (R bt+1 R t+1 ) = µ st ν t =E t Ωt+1 R t+1 Ω t =Λ t,t+1 [1 σ + σθφ t ] where Ω t > 1 is the FI s discount factor.

110 Solution, cont. Partial marginal values µ st =E t Ωt+1 (R kt+1 R t+1 ) µ bt =E t Ωt+1 (R bt+1 R t+1 ) = µ st ν t =E t Ωt+1 R t+1 Ω t =Λ t,t+1 [1 σ + σθφ t ] where Ω t > 1 is the FI s discount factor. End-of-period value function is indeed linear.

111 Capital producers Profit Maximization ( max E t β t Iτ + I Λ t,τ {(Q τ 1)I τ f τ=t I τ 1 ) } (I τ ) (7) where f (1) = f (1) = 0 and f (1) > 0.

112 Capital producers Profit Maximization ( max E t β t Iτ + I Λ t,τ {(Q τ 1)I τ f τ=t I τ 1 ) } (I τ ) (7) where f (1) = f (1) = 0 and f (1) > 0. Q relation for investment: Q t = 1 + f ( ) + I t I t 1 f ( ) E t βλ t,t+1 ( It+1 I t ) 2 f ( ) (8)

113 Intermediate Goods Producer Production Y t = A t (K t ) α L 1 α t (9)

114 Intermediate Goods Producer Production Y t = A t (K t ) α L 1 α t (9) Evolution of firm capital K t+1 = [I t + (1 δ)k t ]

115 Intermediate Goods Producer Production Y t = A t (K t ) α L 1 α t (9) Evolution of firm capital K t+1 = [I t + (1 δ)k t ] Share issue S t = K t+1

116 Intermediate Goods Producers, cont. FONC labor: P mt (1 α) Y t L t = W t, (10) P mt be the price of intermediate goods output Capital rental Z t = P mt α Y t+1 K t+1 δ, the replacement price of used capital is fixed at unity.

117 Retailers and price setting Final output as a composite of retail output [ 1 Y t = where Y ft is output by retailer f. 0 ] ε ε 1 ε 1 Y ft ε df (11)

118 Retailers and price setting Final output as a composite of retail output [ 1 Y t = where Y ft is output by retailer f. 0 ] ε ε 1 ε 1 Y ft ε df (11) From cost minimization by users of final output: ( ) ε Pft Y ft = Y t (12) P t

119 Retailers and price setting Final output as a composite of retail output [ 1 Y t = where Y ft is output by retailer f. 0 ] ε ε 1 ε 1 Y ft ε df (11) From cost minimization by users of final output: ( ) ε Pft Y ft = Y t (12) Staggered price setting a la Calvo Price can be adjusted with probability 1 γ Indexation with probability γ Partially (1 γ P ) to target Π t, Partially (γ P ) to past inflation Π t 1 Π t = Π 1 γ P t Π γ P t 1 P t

120 Price Setting Price Setting Problem max i=0 γ i β i Λ t,t+i [ P t Π t,t+i P t+i P mt+i ] Y ft+i (13)

121 Price Setting Price Setting Problem max i=0 γ i β i Λ t,t+i [ P t Π t,t+i P t+i P mt+i ] Y ft+i (13) Optimal Price Setting i=0 with µ = 1 1 1/ε. γ i β i Λ t,t+i [ P t Π t,t+i P t+i µp mt+i ] Y ft+i = 0 (14)

122 Price Setting Price Setting Problem max i=0 γ i β i Λ t,t+i [ P t Π t,t+i P t+i P mt+i ] Y ft+i (13) Optimal Price Setting i=0 γ i β i Λ t,t+i [ P t Π t,t+i P t+i µp mt+i ] Y ft+i = 0 (14) with µ = 1 1 1/ε. From the law of large numbers, P t = [ (1 γ)(pt ) 1 ε + γ(π γ P t 1 Π 1 γ P t P t 1 ) 1 ε] 1 1 ε (15)

123 Parameters Households β Discount rate h Habit parameter χ Relative utility weight of labor B/Y Steady state Treasury supply K h /K Proportion of direct capital holdings of the HHs B h /B Proportion of long term Treasury holdings of the HHs κ Portfolio adjustment cost ϕ Inverse Frisch elasticity of labor supply ɛ W Elasticity of labor substitution γ W Probability of keeping the wage constant γ W, Wage indexation parameter ρ π p Persistence of a shock to the perceived inflation objective κ Kalman-gain ς Relative weight of APP surprise Financial Intermediaries θ Fraction of capital that can be diverted Proportional advantage in seizure rate of government debt ω Proportional transfer to the entering bankers σ Survival rate of the bankers Intermediate good firms α Capital share δ Depreciation rate Back

124 Parameters, cont. Capital Producing Firms η i Inverse elasticity of net investment to the price of capital Retail Firms ɛ Elasticity of substitution γ P Probability of keeping the price constant γ P, Price indexation parameter Government G Steady state proportion of government expenditures Y ρ i Interest rate smoothing parameter κ π Inflation coefficient in the policy rule κ dπ Inflation growth coefficient in the policy rule κ dy Output growth coefficient in the policy rule ρ i,zlb Interest rate smoothing leaving the lower bound γ ψ Share of private assets in the purchase program Shocks ψ Initial asset purchase shock ρ 1,ψ First AR coefficient of the purchase shock ρ 2,ψ Second AR coefficient of the purchase shock e β Initial savings preference shock (β) ρ β Persistence of the savings preference shock (β) Back

125 Bond yields around announcement and implementation Both announcement and implementation of the PSPP have sizable impact on yields High duration bonds are impacted significantly more Not only purchased bonds show lower yields (no scarcity channel) relative yields (bp) /1/2015 2/1/2015 3/1/2015 4/1/2015 calendar date purchased: d<5 not purchased: d<5 purchased: 5>=d<10 purchased: d>=10 not purchased: 5>=d<10 not purchased: d>=10 Back

126 Impact of purchases on bond yields No significant effect of individual trades on daily yield changes (excludes first two weeks) Three different setups: (i) simple panel, (ii) event study around the first purchase, (iii) black-out period No differential impact of trading intensity (several measures) Stringent controls: time FE, bond FE. Back

127 The impact of the PSPP on euro area banks QE as a form of bank capital relief: the larger the sovereign bonds holdings, the larger the benefits Event study: reaction of each bank s stock price to PSPP announcement. Focus on quoted banks with info on govt bond holdings (as of end-2014). SNL data, 150 banks. 2-day changes: January 21-23; March 4-6 Need to control for: Broader effects on discounted future profits through improvement in macroeconomic conditions Proxy: increase in country s stock price index Impact of flattened yield curve on interest rate margins Proxy 1: change in 10-yrs govt yield Proxy 2: dummy=1 if bank located in EA Support of bank capital relief in Jan Back

128 Equity price reactions between January 21 and 23, 2015 (SNL sample) (1) (2) (3) constant (4.38) (3.81) (3.21) yield (4.61) (2.83) (2.76) SM (2.88) (3.96) (4.54) EA bank (d) (-3.65) (-4.69) exposure 0.06 (2.73) Adj. R No. Obs (White robust t-statistics) Back

129 Signal of lower future policy rates Impact on average expectation from SPF 2015Q1-2015Q3: MRO rate forecasts declined from 11 to 6bps for 2016 and from 43 to 31bps for 2017 What do low interest rates mean? (Andrade et al., 2015) Policy will be more accommodative Outlook worse than thought: Trap will last longer Which one prevailed? Estimate individual pre-crisis interest rate rule; panel regression over 1999Q1-2007Q4 Compare observed individual policy rate forecast with forecasts consistent with individual policy rule On average APP associated with expected future accommodation Back

130 Expected deviations from normal times policy q1 2010q1 2012q1 2014q1 2016q1 1 year ahead 2 years ahead Source: ECB SPF and Own calculations Back

131 Risk of reduced effectiveness of the APP Increased issuance of long-term bonds by national governments would raise investors exposure to duration risk, offsetting the impact of APP. Following announcement of PSPP, average maturity of newly issued eligible bonds relative to maturing bonds rose by approx 2 yrs. Combined effect on duration risk is a reduction, over 2015Q1-Q4: Govt issuance increased supply of 10-yrs equivalent debt by 1.9 percent of GDP. PSPP reduced it by 4.5 percent of GDP. Back

132 Limits to the effectiveness All eligible issuers All maturities total amount (bill.) q2 2014q3 2014q4 2015q1 2015q2 2015q3 2015q average weighted maturity (years) Maturity of at least 2 years Maturity below 2 years total amount (bill.) q2 2014q3 2014q4 2015q1 2015q2 2015q3 2015q average weighted maturity (years) total amount (bill.) q2 2014q3 2014q4 2015q1 2015q2 2015q3 2015q average weighted maturity (years) amount newly issued amount cont. issued amount buybacks amount maturing average maturity of issuances average maturity of redemptions Back