Inside Money, Investment, and UnconventionalMonetary Policy
Lukas Altermatt
University of Basel, Department of Economics (WWZ)
November 9, 2017
Workshop on Aggregate and Distributive Effects ofUnconventional Monetary Policies
Gerzensee
Lukas Altermatt Inside Money, Investment, and Unconventional Monetary Policy
Content
1 Introduction
2 Environment
3 Equilibrium
4 Policy
5 Conclusion
Lukas Altermatt Inside Money, Investment, and Unconventional Monetary Policy
Motivation
After the financial crisis, many countries found themselves ina liquidity trap:
Nominal interest rates equal to zeroLow inflation, but not necessarily zeroOpen-market operations have no effect on inflation
Research QuestionHow does an economy end up in a liquidity trap and whichunconventional policies should be used to escape from it?
Lukas Altermatt Inside Money, Investment, and Unconventional Monetary Policy
Existing literature on the liquidity trap
(New-)Keynesian Literature:Krugman et al. (1998), Eggertsson and Woodford (2003,2004),Christiano et al. (2011), Eggertsson and Krugman(2012), Werning (2012), Correia et al. (2013), Guerrieri andLorenzoni (2017), Cochrane (2017)(New-)Monetarist Literature:Williamson (2012, 2016), Rocheteau et al. (2016), Bacchettaet al. (2016)
Lukas Altermatt Inside Money, Investment, and Unconventional Monetary Policy
Motivation
Since the financial crisis, many countries experienced highbase money growth rates:
myf.red/g/cTFB
0
400
800
1,200
1,600
2,000
2,400
2,800
3,200
3,600
4,000
4,400
1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 2012 2014 2016
fred.stlouisfed.orgSource:FederalReserveBankofSt.Louis
St.LouisAdjustedMonetaryBase
Billions
ofD
ollars
Figure: Monetary base in the US.
Lukas Altermatt Inside Money, Investment, and Unconventional Monetary Policy
Motivation
But inflation stayed low:
myf.red/g/erWC
-2
-1
0
1
2
3
4
5
6
1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 2012 2014 2016
fred.stlouisfed.orgSource:U.S.BureauofEconomicAnalysis
PersonalConsumptionExpenditures:Chain-typePriceIndex
PercentChangefromYearAgo
Figure: Headline PCE inflation in the US.
Lukas Altermatt Inside Money, Investment, and Unconventional Monetary Policy
Motivation
In New Monetarist models, inflation is pinned down by thebase money growth rate⇒ We need a model where inflation is decoupled from thebase money growth rate
Lukas Altermatt Inside Money, Investment, and Unconventional Monetary Policy
Modeling approach
A model based on the framework of Lagos and Wright (2005)Illiquid capital from Lagos and Rocheteau (2008)Key innovation: Taking banks’ balance sheets and banks’investment decisions seriouslyAnalyze the effect of different policy measures in anendogenously arising liquidity trap
Lukas Altermatt Inside Money, Investment, and Unconventional Monetary Policy
Preview of results
A liquidity trap can occur because of:
A decrease in the bonds to money ratio (US: 11.22 in 2008 /4.39 in 2014)A fall in return from capitalAn increase in deposits
Lukas Altermatt Inside Money, Investment, and Unconventional Monetary Policy
Preview of results
Effects of different policies in a liquidity trap:
Open-market operations have no real effectsHelicopter money increases inflationIf negative interest rates are imposed, open-market operationshave real effects
Lukas Altermatt Inside Money, Investment, and Unconventional Monetary Policy
Content
1 Introduction
2 Environment
3 Equilibrium
4 Policy
5 Conclusion
Lukas Altermatt Inside Money, Investment, and Unconventional Monetary Policy
The environment
Time is discrete and continues foreverEach period is divided into two subperiods, DM and CMUnit measure each of buyers and sellersUnit measure of banksA monetary authorityA fiscal authority
Lukas Altermatt Inside Money, Investment, and Unconventional Monetary Policy
Fiscal authority
Has to finance some spending gtCan do so either by issuing one-period bonds Bt or by raisinglump-sum taxes τt
Lukas Altermatt Inside Money, Investment, and Unconventional Monetary Policy
Monetary authority
Issues currency M , value of currency φt, rate of inflation πt+1Can issue newly created currency by:
Buying government bondslump-sum transfers to agents
Lukas Altermatt Inside Money, Investment, and Unconventional Monetary Policy
Buyers and sellers
In the CM buyers and sellers can consume and work at linearutility / disutilityIn the DM, buyers and sellers meetSellers can produce a good buyers likeAll sellers accept currency; a share η also accepts depositsBonds and capital can never be used to trade in the DM
Lukas Altermatt Inside Money, Investment, and Unconventional Monetary Policy
Banks
Banks are agents, live for one periodIn each CM, a new set of banks replaces the old onesCan’t produce goodsGet linear utility from consumption during their second CM
Lukas Altermatt Inside Money, Investment, and Unconventional Monetary Policy
Banks: Deposits
Agents can make nominal deposits d at banksEquilibrium interest rate on deposits is id
Banks compete for deposits, taking id as givenBanks are not anonymous and have full commitment,therefore bank deposits are tradable
Lukas Altermatt Inside Money, Investment, and Unconventional Monetary Policy
Banks: Investment
Banks can invest in capital, bonds or currencyCapital is individual to each bank and has the followingproperties:
Return f(k), earned during the following CMf ′(k) > 0, f ′′(k) < 0, and f ′(0) =∞
Lukas Altermatt Inside Money, Investment, and Unconventional Monetary Policy
The banks’ problem
Banks choose:
Deposits dt
Currency share αM
Bond share αB
Lukas Altermatt Inside Money, Investment, and Unconventional Monetary Policy
The banks’ problem
First order condition for dt:
(1− αB − αM )f ′((1− αB − αM )φtηdt)︸ ︷︷ ︸capital
+αB(1 + iB)
1 + πt+1︸ ︷︷ ︸bonds
+αM
1 + πt+1︸ ︷︷ ︸currency
=1 + id
1 + πt+1︸ ︷︷ ︸deposits
Marginal return is set equal to marginal cost
Lukas Altermatt Inside Money, Investment, and Unconventional Monetary Policy
The banks’ problem
First order condition for αM :
f ′((1− αB − αM )φtηdt)︸ ︷︷ ︸capital
≥ 11 + πt+1︸ ︷︷ ︸
currency
With equality if the constraint αM ≥ δ is non-bindingFor everything explained in this presentation, δ = 0 WLOG
Lukas Altermatt Inside Money, Investment, and Unconventional Monetary Policy
The banks’ problem
First order condition for αB:
f ′((1− αB − αM )φtηdt)︸ ︷︷ ︸capital
≥ 1 + iB
1 + πt+1︸ ︷︷ ︸bonds
With equality if the constraint αB ≥ 0 is non-binding
Lukas Altermatt Inside Money, Investment, and Unconventional Monetary Policy
Social optimum
q∗ from u′(q∗) = c′(q∗)k∗ from f ′(k∗) = 1
β
Lukas Altermatt Inside Money, Investment, and Unconventional Monetary Policy
Content
1 Introduction
2 Environment
3 Equilibrium
4 Policy
5 Conclusion
Lukas Altermatt Inside Money, Investment, and Unconventional Monetary Policy
Bond market clearing
Bonds can be held by agents and banksBonds have no liquidity value for agentsAgents hold bonds only if 1 + iB = 1+πt+1
β
Lukas Altermatt Inside Money, Investment, and Unconventional Monetary Policy
Bond market clearing
Banks hold bonds if (1− δ)iB ≥ id
If id = 0, banks are willing to hold bonds even at iB = 0At iB = 0, currency and bonds are perfect substitutes forbanks
Lukas Altermatt Inside Money, Investment, and Unconventional Monetary Policy
Equilibrium investment by banks
𝑘𝑘
𝑓𝑓𝑓(𝑘𝑘)
1β
𝑘𝑘∗
11 + π
𝑘𝑘�
Figure: Marginal return of capital
Lukas Altermatt Inside Money, Investment, and Unconventional Monetary Policy
Equilibrium investment by banks
𝑘𝑘∗
capital
0
deposits
11 + π
1β
marginal return
quantities
capital
currency
bonds
𝑘𝑘∗
deposits
Lukas Altermatt Inside Money, Investment, and Unconventional Monetary Policy
Equilibrium investment by banks
𝑘𝑘∗
ϕ𝑡𝑡(𝐵𝐵𝑡𝑡 − 𝑏𝑏𝑡𝑡𝑀𝑀)
𝑘𝑘∗ + ϕ𝑡𝑡(𝐵𝐵𝑡𝑡 − 𝑏𝑏𝑡𝑡𝑀𝑀)
capital
bonds
0
11 + π
1β
quantities
capital
currency
bonds
𝑘𝑘∗
deposits
deposits
marginal return
Lukas Altermatt Inside Money, Investment, and Unconventional Monetary Policy
Equilibrium investment by banks
𝑘𝑘∗
ϕ𝑡𝑡(𝐵𝐵𝑡𝑡 − 𝑏𝑏𝑡𝑡𝑀𝑀)
𝑘𝑘∗ + ϕ𝑡𝑡(𝐵𝐵𝑡𝑡 − 𝑏𝑏𝑡𝑡𝑀𝑀) �𝑘𝑘 + ϕ𝑡𝑡(𝐵𝐵𝑡𝑡 − 𝑏𝑏𝑡𝑡𝑀𝑀)
�𝑘𝑘 capital
bonds
0
11 + π
1β
quantities
capital
currency
bonds
𝑘𝑘∗
deposits
deposits
marginal return
Lukas Altermatt Inside Money, Investment, and Unconventional Monetary Policy
Equilibrium investment by banks
𝑘𝑘∗
ϕ𝑡𝑡(𝐵𝐵𝑡𝑡 − 𝑏𝑏𝑡𝑡𝑀𝑀)
𝑘𝑘∗ + ϕ𝑡𝑡(𝐵𝐵𝑡𝑡 − 𝑏𝑏𝑡𝑡𝑀𝑀) �𝑘𝑘 + ϕ𝑡𝑡(𝐵𝐵𝑡𝑡 − 𝑏𝑏𝑡𝑡𝑀𝑀)
�𝑘𝑘 capital
bonds
currency
0
11 + π
1β
quantities
capital
currency
bonds
𝑘𝑘∗
deposits
deposits
marginal return
Lukas Altermatt Inside Money, Investment, and Unconventional Monetary Policy
Banks’ demand schedule for deposits
𝑑
𝑖𝑑 deposit demand
0
(1 − δ)(1 + π
β− 1)
Lukas Altermatt Inside Money, Investment, and Unconventional Monetary Policy
Buyers’ supply schedule for deposits
deposit supply
𝑑
𝑖𝑑
𝑑∗ 0
1 + π
β− 1
Lukas Altermatt Inside Money, Investment, and Unconventional Monetary Policy
Equilibrium investment by banks
𝑘𝑘∗
ϕ𝑡𝑡(𝐵𝐵𝑡𝑡 − 𝑏𝑏𝑡𝑡𝑀𝑀)
𝑘𝑘∗ + ϕ𝑡𝑡(𝐵𝐵𝑡𝑡 − 𝑏𝑏𝑡𝑡𝑀𝑀) �𝑘𝑘 + ϕ𝑡𝑡(𝐵𝐵𝑡𝑡 − 𝑏𝑏𝑡𝑡𝑀𝑀)
�𝑘𝑘 capital
bonds
currency
0
11 + π
1β
quantities
capital
currency
bonds
𝑘𝑘∗
deposits
deposits
Focus on this
region
marginal return
Lukas Altermatt Inside Money, Investment, and Unconventional Monetary Policy
Liquidity Trap
deposit supply
𝑑𝑑
𝑖𝑖𝑑𝑑
𝑑𝑑∗
deposit demand
0
1 + πβ
− 1
(1 − δ)(1 + πβ − 1)
Lukas Altermatt Inside Money, Investment, and Unconventional Monetary Policy
Liquidity Trap
deposit supply
𝑑𝑑
𝑖𝑖𝑑𝑑
𝑑𝑑∗
deposit demand
0
1 + πβ − 1
(1 − δ)(1 + πβ
− 1)
banks hold allbonds
Lukas Altermatt Inside Money, Investment, and Unconventional Monetary Policy
Liquidity Trap
deposit supply
𝑑𝑑
𝑖𝑖𝑑𝑑
𝑑𝑑∗
deposit demand
0
1 + πβ − 1
(1 − δ)(1 + πβ
− 1)
banks hold allbondsinterest rate onbonds is zero
Lukas Altermatt Inside Money, Investment, and Unconventional Monetary Policy
Liquidity Trap
deposit supply
𝑑𝑑
𝑖𝑖𝑑𝑑
𝑑𝑑∗
deposit demand
0
1 + πβ − 1
(1 − δ)(1 + πβ
− 1)
banks hold allbondsinterest rate onbonds is zerobanks holdcurrency
Lukas Altermatt Inside Money, Investment, and Unconventional Monetary Policy
Liquidity Trap
deposit supply
𝑑𝑑
𝑖𝑖𝑑𝑑
𝑑𝑑∗
deposit demand
0
1 + πβ − 1
(1 − δ)(1 + πβ
− 1)
banks hold allbondsinterest rate onbonds is zerobanks holdcurrencyq < q∗
Lukas Altermatt Inside Money, Investment, and Unconventional Monetary Policy
Liquidity Trap
deposit supply
𝑑𝑑
𝑖𝑖𝑑𝑑
𝑑𝑑∗
deposit demand
0
1 + πβ − 1
(1 − δ)(1 + πβ
− 1)
banks hold allbondsinterest rate onbonds is zerobanks holdcurrencyq < q∗
k > k∗
Lukas Altermatt Inside Money, Investment, and Unconventional Monetary Policy
Content
1 Introduction
2 Environment
3 Equilibrium
4 Policy
5 Conclusion
Lukas Altermatt Inside Money, Investment, and Unconventional Monetary Policy
Policy in a liquidity trap
Are open market-operations powerless?What is the effect of helicopter money?What happens if negative interest rates are implemented?
Lukas Altermatt Inside Money, Investment, and Unconventional Monetary Policy
Policy
One-time increase in M , announced one period beforeThis policy increases inflation for one period and has realeffects in LW models (see Berentsen and Waller (2011))This increase can come through:
open-market operationslump-sum transfers
Lukas Altermatt Inside Money, Investment, and Unconventional Monetary Policy
Open-market operations
To increase M by open-market operations, available bondsdecrease by the same amount
Lukas Altermatt Inside Money, Investment, and Unconventional Monetary Policy
Open-market operations in a liquidity trap
In a liquidity trap, iB = 0Banks hold all bondsCurrency is a perfect substitute for bondsOpen-market operations have no effect
Lukas Altermatt Inside Money, Investment, and Unconventional Monetary Policy
Helicopter money
Helicopter money is an increase in M through lump-sumtransfersThis policy has no effect on the quantity of bonds circulating
Lukas Altermatt Inside Money, Investment, and Unconventional Monetary Policy
Helicopter money in a liquidity trap
Helicopter money increases currency without affecting bondsThe currency reaches the goods marketInflation increases for one period, hence helicopter money isnon-neutral
Lukas Altermatt Inside Money, Investment, and Unconventional Monetary Policy
How to implement helicopter money
So far, helicopter money modeled as lump-sum transfer toagentsMight not be legally possible for the central bankHelicopter money also works as:
Purchase of goods by central bankTransfer to fiscal authority - but only if debt is not reduced!
Lukas Altermatt Inside Money, Investment, and Unconventional Monetary Policy
Negative interest rates
Negative interest rates are defined as interest paid by banksfor the currency they holdNeither Mt nor Bt available are directly affected by this policy
Lukas Altermatt Inside Money, Investment, and Unconventional Monetary Policy
Negative interest rates
deposit supply
𝑑𝑑
𝑖𝑖𝑑𝑑
𝑑𝑑∗
deposit demand
0
1 + πβ − 1
𝑖𝑖𝑅𝑅
δ𝑖𝑖𝑅𝑅 + (1 − δ)(1 + πβ − 1)
Figure: Demand and supply for deposits with negative interest rates
Lukas Altermatt Inside Money, Investment, and Unconventional Monetary Policy
Negative interest rates in a liquidity trap
With negative interest rates, a liquidity trap cannot existBanks are not willing to hold excess reserves with negativeinterest ratesOpen-market operations always effective with negative interestratesIntroducing negative interest rates reduces investment incapital
Lukas Altermatt Inside Money, Investment, and Unconventional Monetary Policy
Negative interest rates - model shortcomings
Negative interest rates help because they introduce returnspread between bonds and reservesIn reality, bond rates negative at similar rates
Lukas Altermatt Inside Money, Investment, and Unconventional Monetary Policy
Content
1 Introduction
2 Environment
3 Equilibrium
4 Policy
5 Conclusion
Lukas Altermatt Inside Money, Investment, and Unconventional Monetary Policy
Conclusion
A liquidity trap can exist at zero and positive inflation ratesCaused by preference or production parameters, or by ascarcity of bondsOpen-market operations don’t affect inflationHelicopter money increases inflation temporarilyWith negative interest rates on reserves, open-marketoperations become effective again
Lukas Altermatt Inside Money, Investment, and Unconventional Monetary Policy
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Economic Review, 103(4):1172–1211.Eggertsson, G. B. and Krugman, P. R. (2012). Debt, deleveraging, and the liquidity trap: A fisher-minsky-koo
approach. The Quarterly Journal of Economics, 127(3):1469–1513.Eggertsson, G. B. and Woodford, M. (2003). The zero bound on interest rates and optimal monetary policy.
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Journal of Economics, 132(3):1427–1467.Krugman, P. R., Dominguez, K. M., and Rogoff, K. (1998). It’s baaack: Japan’s slump and the return of the
liquidity trap. Brookings Papers on Economic Activity, 1998(2):137–205.Lagos, R. and Rocheteau, G. (2008). Money and capital as competing media of exchange. Journal of Economic
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Economy, 113 (3):463–484.Rocheteau, G., Wright, R., and Xiao, S. X. (2016). Open market operations. mimeo.Werning, I. (2012). Managing a liquidity trap: Monetary and fiscal policy. MIT mimeo.Williamson, S. (2012). Liquidity, monetary policy, and the financial crisis: A new monetarist approach. American
Economic Review, 102 (6):2570–2605.Williamson, S. (2016). Scarce collateral, the term premium, and quantitative easing. Journal of Economic Theory,
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Lukas Altermatt Inside Money, Investment, and Unconventional Monetary Policy