Quantitative Easing and Financial Stability

Transcription

1 Quantitative Easing and Financial Stability Michael Woodford Columbia University Nineteenth Annual Conference Central Bank of Chile November 19-20, 2015 Michael Woodford (Columbia) Financial Stability CB Chile / 34

2 Introduction A notable feature of Fed policy since 2008: several-fold increase in size of balance sheet resulting in massive increase in supply of bank reserves [higher by factor > 250] notable shift in composition of assets as well: toward longer-term Treasuries, MBS Michael Woodford (Columbia) Financial Stability CB Chile / 34

3 Introduction A notable feature of Fed policy since 2008: several-fold increase in size of balance sheet resulting in massive increase in supply of bank reserves [higher by factor > 250] notable shift in composition of assets as well: toward longer-term Treasuries, MBS Goal of this policy: to relax financial conditions (specifically, by reducing term spreads) in order to stimulate aggregate demand, when further short-term interest-rate cuts not feasible Michael Woodford (Columbia) Financial Stability CB Chile / 34

4 Introduction A notable feature of Fed policy since 2008: several-fold increase in size of balance sheet resulting in massive increase in supply of bank reserves [higher by factor > 250] notable shift in composition of assets as well: toward longer-term Treasuries, MBS Goal of this policy: to relax financial conditions (specifically, by reducing term spreads) in order to stimulate aggregate demand, when further short-term interest-rate cuts not feasible But some worry: might there not have been a collateral effect of increased risks to financial stability? Michael Woodford (Columbia) Financial Stability CB Chile / 34

5 Why Might QE Threaten Financial Stability? 1 QE as an alternative way of achieving the same thing as cutting short-term interest rates (Bernanke) increase risk-taking by banks? Michael Woodford (Columbia) Financial Stability CB Chile / 34

6 Why Might QE Threaten Financial Stability? 1 QE as an alternative way of achieving the same thing as cutting short-term interest rates (Bernanke) increase risk-taking by banks? 2 Increasing bank reserves stimulates AD by relaxing constraint on short-term debt issuance by banks (Stein) but constraint needed for financial stability? Michael Woodford (Columbia) Financial Stability CB Chile / 34

7 Why Might QE Threaten Financial Stability? 1 QE as an alternative way of achieving the same thing as cutting short-term interest rates (Bernanke) increase risk-taking by banks? 2 Increasing bank reserves stimulates AD by relaxing constraint on short-term debt issuance by banks (Stein) but constraint needed for financial stability? 3 QE effective because lowers risk premia on longer-term bonds suppressing a signal that is needed to deter unwise risks? Michael Woodford (Columbia) Financial Stability CB Chile / 34

8 Goals Wish to develop a model that allows assessment of how seriously to take these arguments Michael Woodford (Columbia) Financial Stability CB Chile / 34

9 Goals Wish to develop a model that allows assessment of how seriously to take these arguments Model needs to include: real effects of monetary policy endogenous term premia endogenous degree of financial fragility conventional interest-rate policy, CB balance sheet, and restrictions on short-term debt finance by banks as alternative policy levers, the effects of which can be compared Michael Woodford (Columbia) Financial Stability CB Chile / 34

10 Key Ideas Motivating the Model Financial fragility results from excessive reliance on collateralized short-term debt in capital structure of banks Michael Woodford (Columbia) Financial Stability CB Chile / 34

11 Key Ideas Motivating the Model Financial fragility results from excessive reliance on collateralized short-term debt in capital structure of banks Why fragile financial structures are tempting: shortage of safe assets investors will pay a premium for them ( money premium ) Michael Woodford (Columbia) Financial Stability CB Chile / 34

12 Key Ideas Motivating the Model Financial fragility results from excessive reliance on collateralized short-term debt in capital structure of banks Why fragile financial structures are tempting: shortage of safe assets investors will pay a premium for them ( money premium ) Public supply of safe assets should be an important determinant of the strength of incentives for private issuance Michael Woodford (Columbia) Financial Stability CB Chile / 34

13 Modeling Approach Funding risk and possibility of fire sale of assets modeled as in Stein (2012) but embedded in an intertemporal monetary equilibrium model, in order to consider interaction with monetary policy Michael Woodford (Columbia) Financial Stability CB Chile / 34

14 Modeling Approach Funding risk and possibility of fire sale of assets modeled as in Stein (2012) but embedded in an intertemporal monetary equilibrium model, in order to consider interaction with monetary policy Demand for safe assets modeled using a cash-in-advance structure as in Lucas and Stokey (1987) but here interpret the cash that can be used to satisfy CIA constraint as interest-earning short-term safe instruments such as T-bills, CB liabilities (reserves, reverse repos), or asset-backed CP Michael Woodford (Columbia) Financial Stability CB Chile / 34

15 Elements of the Model: Agents Infinite-lived representative household can be thought of as made up of several members with separate budgets within the period, though all funds pooled at end of each period: worker : supplies inputs used to produce all final goods; receives income available to household at end of period shopper : buys regular final goods [both cash goods and credit goods ]; cash must be set aside earlier Michael Woodford (Columbia) Financial Stability CB Chile / 34

16 Elements of the Model: Agents Infinite-lived representative household can be thought of as made up of several members with separate budgets within the period, though all funds pooled at end of each period: worker : supplies inputs used to produce all final goods; receives income available to household at end of period shopper : buys regular final goods [both cash goods and credit goods ]; cash must be set aside earlier investor : buys special final goods, using line of credit set up earlier in period; can also bid for risky durables in fire sale banker : buys risky durables, financed from equity investment by household and issuance of short-term debt Michael Woodford (Columbia) Financial Stability CB Chile / 34

17 Resolution of Within-Period Uncertainty p no crisis 1 no asset collapse period t (state ) ξ t asset trading period t+1 1-p q no asset collapse crisis 1-q asset collapse Michael Woodford (Columbia) Financial Stability CB Chile / 34

18 Elements of the Model: Preferences Preferences of the representative household: E t τ=t β τ t [u(c 1τ, c 2τ ) + ũ(c 3τ ) + γs τ v(y τ ) w(x τ )] where c 1t = consumption of cash goods c 2t = consumption of credit goods c 3t = consumption of special goods s t = services from [intact] old durables Y t = supply of normal goods x t = supply of special goods Michael Woodford (Columbia) Financial Stability CB Chile / 34

19 Elements of the Model: Demand for Liquidity purchases of cash goods subject to a cash-in-advance constraint (as in Lucas-Stokey, 1987) P t c 1t M t Michael Woodford (Columbia) Financial Stability CB Chile / 34

20 Elements of the Model: Demand for Liquidity purchases of cash goods subject to a cash-in-advance constraint (as in Lucas-Stokey, 1987) P t c 1t M t cash balances M t : assets of the buyer that can be transferred to the seller, and have a certain nominal value at end of period Michael Woodford (Columbia) Financial Stability CB Chile / 34

21 Elements of the Model: Demand for Liquidity purchases of cash goods subject to a cash-in-advance constraint (as in Lucas-Stokey, 1987) P t c 1t M t cash balances M t : assets of the buyer that can be transferred to the seller, and have a certain nominal value at end of period cash includes riskless nominal liabilities of the government (Treasury bills) can also be short-term debt issued by bankers, if collateralized to ensure completely riskless but to be acceptable as cash, holders of debt must have right to force liquidation of the collateral, if necessary in order to ensure that banker can pay them in full Michael Woodford (Columbia) Financial Stability CB Chile / 34

22 Elements of the Model: Banks A banker can purchase shares s t of the risky asset, subject to budget constraint Q t s t equity t + D t where Q t = price of asset in initial period-t market, D t = issuance of short-term debt Michael Woodford (Columbia) Financial Stability CB Chile / 34

23 Elements of the Model: Banks A banker can purchase shares s t of the risky asset, subject to budget constraint Q t s t equity t + D t where Q t = price of asset in initial period-t market, D t = issuance of short-term debt Short-term debt can be marketed as riskless only if D t Γ t s t, where Γ t = price of asset in event of fire sale Michael Woodford (Columbia) Financial Stability CB Chile / 34

24 Elements of the Model: Fire Sale Distortions If crisis state occurs, banker must offer st s units of the durable for sale, sufficient to allow redemption of short-term debt: D t Γ t s s t Γ t s t Michael Woodford (Columbia) Financial Stability CB Chile / 34

25 Elements of the Model: Fire Sale Distortions If crisis state occurs, banker must offer st s units of the durable for sale, sufficient to allow redemption of short-term debt: D t Γ t s s t Γ t s t Each investor bids for s d t units of the durables in the fire sale Investor s purchases of special goods must then satisfy P t c 3t + η t Γ t s d t F t where P t is price of special goods, η t is crisis indicator, and credit limit F t has been pre-determined in real terms Michael Woodford (Columbia) Financial Stability CB Chile / 34

26 Elements of the Model: Supply of Durables Investment demand at end of period: household purchases I t units of investment goods on credit, used to produce F (I t ) units of new risky durables, which yield services in period t + 1 durables produced from investment in period t 1 depreciate completely at end of period t Michael Woodford (Columbia) Financial Stability CB Chile / 34

27 Flexible-Price Equilibrium An equilibrium is a collection of household choices {M t, s t,...}, and prices {Q t, Γ t, P t, P t } such that Michael Woodford (Columbia) Financial Stability CB Chile / 34

28 Flexible-Price Equilibrium An equilibrium is a collection of household choices {M t, s t,...}, and prices {Q t, Γ t, P t, P t } such that household choices maximize expected utility subject to the sequence of budget constraints, and Michael Woodford (Columbia) Financial Stability CB Chile / 34

29 Flexible-Price Equilibrium An equilibrium is a collection of household choices {M t, s t,...}, and prices {Q t, Γ t, P t, P t } such that household choices maximize expected utility subject to the sequence of budget constraints, and markets clear: M t = M t + D t s t = F (I t 1 ) s d t = s s t c 1t + c 2t + I t = Y t c 3t = x t Michael Woodford (Columbia) Financial Stability CB Chile / 34

30 Dimensions of Monetary Policy 1 Conventional policy (interest-rate policy): CB chooses R m t+1, the nominal yield on cash over period t + 1, by setting interest on CB liabilities Michael Woodford (Columbia) Financial Stability CB Chile / 34

31 Dimensions of Monetary Policy 1 Conventional policy (interest-rate policy): CB chooses R m t+1, the nominal yield on cash over period t + 1, by setting interest on CB liabilities 2 Balance-sheet policy (quantitative easing): CB chooses m t+1, the real outside supply of cash in period t + 1, through open-market purchases or sales of longer-term bonds Michael Woodford (Columbia) Financial Stability CB Chile / 34

32 Dimensions of Monetary Policy 1 Conventional policy (interest-rate policy): CB chooses R m t+1, the nominal yield on cash over period t + 1, by setting interest on CB liabilities 2 Balance-sheet policy (quantitative easing): CB chooses m t+1, the real outside supply of cash in period t + 1, through open-market purchases or sales of longer-term bonds 3 Macroprudential policy (reserve requirement): CB chooses ξ t+1, effective tax rate on short-term debt issuance by banks[assumed to equal 1 in the above] Michael Woodford (Columbia) Financial Stability CB Chile / 34

33 Dimensions of Monetary Policy 1 Conventional policy (interest-rate policy): CB chooses R m t+1, the nominal yield on cash over period t + 1, by setting interest on CB liabilities 2 Balance-sheet policy (quantitative easing): CB chooses m t+1, the real outside supply of cash in period t + 1, through open-market purchases or sales of longer-term bonds 3 Macroprudential policy (reserve requirement): CB chooses ξ t+1, effective tax rate on short-term debt issuance by banks[assumed to equal 1 in the above] [each of the above variables is set in subperiod 2 of period t] Michael Woodford (Columbia) Financial Stability CB Chile / 34

34 Stationary Equilibrium Consider a stationary policy regime in which: Conventional policy is used to ensure that P t+1 /P t = Π each period [constant inflation target] Michael Woodford (Columbia) Financial Stability CB Chile / 34

35 Stationary Equilibrium Consider a stationary policy regime in which: Conventional policy is used to ensure that P t+1 /P t = Π each period [constant inflation target] Balance-sheet policy maintains m t+1 = m each period Michael Woodford (Columbia) Financial Stability CB Chile / 34

36 Stationary Equilibrium Consider a stationary policy regime in which: Conventional policy is used to ensure that P t+1 /P t = Π each period [constant inflation target] Balance-sheet policy maintains m t+1 = m each period Assume (for now) ξ t+1 = 1 each period [no macropru policy] Michael Woodford (Columbia) Financial Stability CB Chile / 34

37 Stationary Equilibrium Consider a stationary policy regime in which: Conventional policy is used to ensure that P t+1 /P t = Π each period [constant inflation target] Balance-sheet policy maintains m t+1 = m each period Assume (for now) ξ t+1 = 1 each period [no macropru policy] Stationary values of real variables are independent of Π One-parameter family of stationary equilibria indexed by m Michael Woodford (Columbia) Financial Stability CB Chile / 34

38 Stationary Equilibrium Consider a stationary policy regime in which: Conventional policy is used to ensure that P t+1 /P t = Π each period [constant inflation target] Balance-sheet policy maintains m t+1 = m each period Assume (for now) ξ t+1 = 1 each period [no macropru policy] Stationary values of real variables are independent of Π One-parameter family of stationary equilibria indexed by m can alternatively be indexed by stationary value of R m /Π [indicates spread between returns on bonds and cash] higher R m /Π smaller spread more liqudity Michael Woodford (Columbia) Financial Stability CB Chile / 34

39 Stationary Equilibrium Greater scarcity of safe assets (lower m) implies lower real return R m /Π on cash larger money premium smaller share of cash goods in normal goods consumption Michael Woodford (Columbia) Financial Stability CB Chile / 34

40 Stationary Equilibrium Greater scarcity of safe assets (lower m) implies lower real return R m /Π on cash larger money premium smaller share of cash goods in normal goods consumption Michael Woodford (Columbia) Financial Stability CB Chile / 34

41 Stationary Equilibrium Greater scarcity of safe assets (lower m) implies lower real return R m /Π on cash larger money premium smaller share of cash goods in normal goods consumption larger share of short-term debt in banks capital structure increased over-valuation of durables at time of production increased share of durables in normal goods supply Michael Woodford (Columbia) Financial Stability CB Chile / 34

42 Stationary Equilibrium Greater scarcity of safe assets (lower m) implies lower real return R m /Π on cash larger money premium smaller share of cash goods in normal goods consumption larger share of short-term debt in banks capital structure increased over-valuation of durables at time of production increased share of durables in normal goods supply greater under-valuation of durables in fire sale greater under-production of special goods in crisis state Michael Woodford (Columbia) Financial Stability CB Chile / 34

43 Stationary Equilibrium: Numerical Example Qs 2 M Γs D R m Michael Woodford (Columbia) Financial Stability CB Chile / 34

44 Stationary Equilibrium: Numerical Example c1 c2 c n 3 c c 3 4 I R m Michael Woodford (Columbia) Financial Stability CB Chile / 34

45 Stationary Equilibrium: Numerical Example Λ s /(βγ[p + (1 p)q]) ΛΓ/(γq) R m Michael Woodford (Columbia) Financial Stability CB Chile / 34

46 Lessons QE and conventional policy not equivalent in their long-run effects: no real effects of long-run inflation target, while (real) size of CB balance sheet does have long-run real effects Michael Woodford (Columbia) Financial Stability CB Chile / 34

47 Lessons QE and conventional policy not equivalent in their long-run effects: no real effects of long-run inflation target, while (real) size of CB balance sheet does have long-run real effects Larger balance sheet reduces long-run distortions in each of 3 respects: less under-production of cash goods (as share of nondurable normal goods) less over-production of durables less under-production of special goods in crisis state, less over-production in non-crisis state Michael Woodford (Columbia) Financial Stability CB Chile / 34

48 Macroprudential Policy Is QE equivalent to relaxing reserve requirement for private-bank creation of money-like liabilities? Michael Woodford (Columbia) Financial Stability CB Chile / 34

49 Macroprudential Policy Is QE equivalent to relaxing reserve requirement for private-bank creation of money-like liabilities? Effects of variation in reserve requirement: equivalent to varying size of a tax on short-term debt issuance lower ξ t tighter macroprudential policy Michael Woodford (Columbia) Financial Stability CB Chile / 34

50 Macroprudential Policy Is QE equivalent to relaxing reserve requirement for private-bank creation of money-like liabilities? Effects of variation in reserve requirement: equivalent to varying size of a tax on short-term debt issuance lower ξ t tighter macroprudential policy Look first at effects of variation in ξ t on long-run stationary equilibrium fixing Π [maintained by conventional policy] and M/P [maintained by balance-sheet policy] Michael Woodford (Columbia) Financial Stability CB Chile / 34

51 Stationary Equilibrium with Reserve Requirement Qs 2 M Γs D ξ Michael Woodford (Columbia) Financial Stability CB Chile / 34

52 Stationary Equilibrium with Reserve Requirement c1 5 c2 c n c c 3 I ξ Michael Woodford (Columbia) Financial Stability CB Chile / 34

53 Stationary Equilibrium with Reserve Requirement 1.3 Λ s /(βγ[p + (1 p)q]) 1.2 ΛΓ/(γq) ξ Michael Woodford (Columbia) Financial Stability CB Chile / 34

54 Lessons Expansion of CB balance sheet not equivalent to relaxation of macroprudential policy effects more similar to those resulting from a tightening of macro-pru policy because increased outside supply of safe assets reduces incentive for bank issuance of short-term debt, just as tighter macro-pru policy does Michael Woodford (Columbia) Financial Stability CB Chile / 34

55 Lessons Expansion of CB balance sheet not equivalent to relaxation of macroprudential policy effects more similar to those resulting from a tightening of macro-pru policy because increased outside supply of safe assets reduces incentive for bank issuance of short-term debt, just as tighter macro-pru policy does But that association not equivalence, either tighter macro-pru policy reduces 2 types of inefficiency but not all 3 types that are reduced by increased outside supply of safe assets Michael Woodford (Columbia) Financial Stability CB Chile / 34

56 Introducing Nominal Rigidity Contrast between conventional monetary policy and QE is exaggerated when we only consider long-run steady states, in which prices can be treated as perfectly flexible no real effects of conventional policy no effect on financial stability Michael Woodford (Columbia) Financial Stability CB Chile / 34

57 Introducing Nominal Rigidity Contrast between conventional monetary policy and QE is exaggerated when we only consider long-run steady states, in which prices can be treated as perfectly flexible no real effects of conventional policy no effect on financial stability But this is not true when we allow for short-run price stickiness conventional policy can temporarily influence real interest rates and money premium, with implications for banks capital structure decisions and hence financial stability Michael Woodford (Columbia) Financial Stability CB Chile / 34

58 Introducing Nominal Rigidity Simple model with sticky prices: suppose that price P t for normal goods is predetermined: chosen end of period t 1 workers then supply whatever quantity of normal goods are demanded in subperiod 2 of period t price set at level expected to clear market at time that it is set (though may not be market-clearing ex post) Michael Woodford (Columbia) Financial Stability CB Chile / 34

59 Introducing Nominal Rigidity Simple model with sticky prices: suppose that price P t for normal goods is predetermined: chosen end of period t 1 workers then supply whatever quantity of normal goods are demanded in subperiod 2 of period t price set at level expected to clear market at time that it is set (though may not be market-clearing ex post) All other prices ( P t, Q t, Γ t, prices of financial assets) are perfectly flexible Michael Woodford (Columbia) Financial Stability CB Chile / 34

60 Introducing Nominal Rigidity Simple model with sticky prices: suppose that price P t for normal goods is predetermined: chosen end of period t 1 workers then supply whatever quantity of normal goods are demanded in subperiod 2 of period t price set at level expected to clear market at time that it is set (though may not be market-clearing ex post) All other prices ( P t, Q t, Γ t, prices of financial assets) are perfectly flexible Note that if no unexpected shocks other than those associated with crisis and asset collapse, eq m will be same as that analyzed above (since P t is set at level that does clear market) Michael Woodford (Columbia) Financial Stability CB Chile / 34

61 Introducing Nominal Rigidity Simple case analyzed here: one-time shock χ to aggregate demand in some period t for one period only, utility terms are χ [u(c 1t, c 2t ) v(y t )] for some factor 0 < χ < 1 shock is completely unexpected: prior to subperiod 2 of period t (and when P t is set), stationary eq m (constant inflation rate Π, constant values R m, m, ξ) is expected to continue after shock occurs, no further such shocks expected P τ still expected to clear market in all periods τ > t Michael Woodford (Columbia) Financial Stability CB Chile / 34

62 Monetary Policy Responses to a Shock Consider only policies under which conventional policy (sequence {Rτ+1 m } for all τ > t) is used to ensure inflation target P τ /P τ 1 = Π is hit for all τ > t m τ+1 = m, ξ τ+1 = ξ for all τ > t thus consider only effects of possible responses of R m t+1, m t+1, ξ t+1 to shock χ in period t Michael Woodford (Columbia) Financial Stability CB Chile / 34

63 Monetary Policy Responses to a Shock Consider only policies under which conventional policy (sequence {Rτ+1 m } for all τ > t) is used to ensure inflation target P τ /P τ 1 = Π is hit for all τ > t m τ+1 = m, ξ τ+1 = ξ for all τ > t thus consider only effects of possible responses of R m t+1, m t+1, ξ t+1 to shock χ in period t Under this assumption, shock χ and policy responses affect only allocation of resources in period t and financial conditions [asset prices, durables prices, bank capital structure, real cash supply] in period t + 1 allocation of resources in all periods τ > t, and financial conditions in all periods τ > t + 1, are again as in the stationary equilibrium Michael Woodford (Columbia) Financial Stability CB Chile / 34

64 Monetary Policy Responses to a Shock A key measure of financial conditions: expected one-period real return on longer-term bonds: ] 1 + r t+1 b E t+1 [R t+1 b P t = λ t β λ P t+1 where λ t = marginal utility of real income (units of normal goods) at end of period t, λ = steady-state value [the measure of financial conditions that is relevant for aggregate demand for non-durable normal goods] Michael Woodford (Columbia) Financial Stability CB Chile / 34

65 Alternative Monetary Policy Responses: Results All three policies reducing R m t+1 increasing m t+1 increasing ξ t+1 are ways to increase aggregate demand in short run: relax financial conditions (lower λ t lower r b t+1 ) increase demand for credit goods increase investment demand Michael Woodford (Columbia) Financial Stability CB Chile / 34

66 Alternative Monetary Policy Responses: Results All three policies reducing R m t+1 increasing m t+1 increasing ξ t+1 are ways to increase aggregate demand in short run: relax financial conditions (lower λ t lower r b t+1 ) increase demand for credit goods increase investment demand But all also increase risks to financial stability: increase short-term debt issuance by banks increase Q t+1, lower Γ t+1 increase suboptimality of special goods consumption Michael Woodford (Columbia) Financial Stability CB Chile / 34

67 Alternative Monetary Policy Responses: Results However, they can be ordered: for a given size increase in aggregate demand Y t, among the 3 policies, QE (increasing m t+1 ) increases demand for durables and short-term debt issuance by banks the least, interest-rate policy (reducing Rt+1 m ) does so to an intermediate extent, and relaxation of macroprudential policy (raising ξ t+1 ) increases demand for durables and risks to financial stability the most Michael Woodford (Columbia) Financial Stability CB Chile / 34

68 Alternative Monetary Policy Responses: Results However, they can be ordered: for a given size increase in aggregate demand Y t, among the 3 policies, QE (increasing m t+1 ) increases demand for durables and short-term debt issuance by banks the least, interest-rate policy (reducing Rt+1 m ) does so to an intermediate extent, and relaxation of macroprudential policy (raising ξ t+1 ) increases demand for durables and risks to financial stability the most Key difference between QE and interest-rate cut: in case of QE, a given increase in investment demand requires larger r b t+1 reduction, because of greater reduction of money premium larger share of demand increase is non-durable demand Michael Woodford (Columbia) Financial Stability CB Chile / 34

69 Lessons Short-run effects of increased QE do include increased risks to financial stability but less so than if same increase in aggregate demand were achieved by an interest-rate cut, or by relaxing macro-pru policy Michael Woodford (Columbia) Financial Stability CB Chile / 34

70 Lessons Short-run effects of increased QE do include increased risks to financial stability but less so than if same increase in aggregate demand were achieved by an interest-rate cut, or by relaxing macro-pru policy Possible to use QE to stimulate aggregate demand at ZLB, without adverse effects on financial stability: by combining QE with macro-pru tightening Michael Woodford (Columbia) Financial Stability CB Chile / 34

71 Lessons Short-run effects of increased QE do include increased risks to financial stability but less so than if same increase in aggregate demand were achieved by an interest-rate cut, or by relaxing macro-pru policy Possible to use QE to stimulate aggregate demand at ZLB, without adverse effects on financial stability: by combining QE with macro-pru tightening Advantages of this approach to aggregate demand stimulus suggest a role for QE even when ZLB not a constraint on interest-rate policy Michael Woodford (Columbia) Financial Stability CB Chile / 34