inside money, investment, and unconventional monetary policy · 2017. 11. 20. · lukas altermatt...

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


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?


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)


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.


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.


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


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


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


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


Content

1 Introduction

2 Environment

3 Equilibrium

4 Policy

5 Conclusion


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


Fiscal authority

Has to finance some spending gtCan do so either by issuing one-period bonds Bt or by raisinglump-sum taxes τt


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


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


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


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


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) =∞


The banks’ problem

Banks choose:

Deposits dt

Currency share αM

Bond share αB



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



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



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


Social optimum

q∗ from u′(q∗) = c′(q∗)k∗ from f ′(k∗) = 1

β


Content

1 Introduction

2 Environment

3 Equilibrium

4 Policy

5 Conclusion


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


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


Equilibrium investment by banks

𝑘𝑘

𝑓𝑓𝑓(𝑘𝑘)

1β

𝑘𝑘∗

11 + π

𝑘𝑘�

Figure: Marginal return of capital



𝑘𝑘∗

capital

0

deposits

11 + π

1β

marginal return

quantities

capital

currency

bonds

𝑘𝑘∗

deposits



𝑘𝑘∗

ϕ𝑡𝑡(𝐵𝐵𝑡𝑡 − 𝑏𝑏𝑡𝑡𝑀𝑀)

𝑘𝑘∗ + ϕ𝑡𝑡(𝐵𝐵𝑡𝑡 − 𝑏𝑏𝑡𝑡𝑀𝑀)

capital

bonds

0

11 + π

1β

quantities

capital

currency

bonds

𝑘𝑘∗

deposits

deposits

marginal return



𝑘𝑘∗


𝑘𝑘∗ + ϕ𝑡𝑡(𝐵𝐵𝑡𝑡 − 𝑏𝑏𝑡𝑡𝑀𝑀) �𝑘𝑘 + ϕ𝑡𝑡(𝐵𝐵𝑡𝑡 − 𝑏𝑏𝑡𝑡𝑀𝑀)

�𝑘𝑘 capital

bonds

0

11 + π

1β

quantities

capital

currency

bonds

𝑘𝑘∗

deposits

deposits

marginal return



𝑘𝑘∗



�𝑘𝑘 capital

bonds

currency

0

11 + π

1β

quantities

capital

currency

bonds

𝑘𝑘∗

deposits

deposits

marginal return


Banks’ demand schedule for deposits

𝑑

𝑖𝑑 deposit demand

0

(1 − δ)(1 + π

β− 1)


Buyers’ supply schedule for deposits

deposit supply

𝑑

𝑖𝑑

𝑑∗ 0

1 + π

β− 1



𝑘𝑘∗



�𝑘𝑘 capital

bonds

currency

0

11 + π

1β

quantities

capital

currency

bonds

𝑘𝑘∗

deposits

deposits

Focus on this

region

marginal return


Liquidity Trap

deposit supply

𝑑𝑑

𝑖𝑖𝑑𝑑

𝑑𝑑∗

deposit demand

0

1 + πβ

− 1

(1 − δ)(1 + πβ − 1)


Liquidity Trap

deposit supply

𝑑𝑑

𝑖𝑖𝑑𝑑

𝑑𝑑∗

deposit demand

0

1 + πβ − 1

(1 − δ)(1 + πβ

− 1)

banks hold allbonds


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


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


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∗


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∗


Content

1 Introduction

2 Environment

3 Equilibrium

4 Policy

5 Conclusion


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?


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


Open-market operations

To increase M by open-market operations, available bondsdecrease by the same amount


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


Helicopter money

Helicopter money is an increase in M through lump-sumtransfersThis policy has no effect on the quantity of bonds circulating


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


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!


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


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


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


Negative interest rates - model shortcomings

Negative interest rates help because they introduce returnspread between bonds and reservesIn reality, bond rates negative at similar rates


Content

1 Introduction

2 Environment

3 Equilibrium

4 Policy

5 Conclusion


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


ReferencesBacchetta, P., Benhima, K., and Kalantzis, Y. (2016). Money and capital in a persistent liquidity trap. CEPR

Discussion Paper No. DP11369.Berentsen, A. and Waller, C. (2011). Prive level targeting and stabilization policy. Journal of Money, Credit and

Banking, 43(2):559–580.Christiano, L., Eichenbaum, M., and Rebelo, S. (2011). When is the government spending multiplier large?

Journal of Political Economy, 119(1):78–121.Cochrane, J. H. (2017). The new-keynesian liquidity trap. Journal of Monetary Economics, 92:47–63.Correia, I., Farhi, E., Nicolini, J. P., and Teles, P. (2013). Unconventional fiscal policy at the zero bound. American

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.

Brookings Papers on Economic Activity, pages 139–233.Eggertsson, G. B. and Woodford, M. (2004). Policy options in a liquidity trap. American Economic Review,

94(2):76–79.Guerrieri, V. and Lorenzoni, G. (2017). Credit crises, precautionary savings, and the liquidity trap. The Quarterly

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

Theory, 142:247 Ű 258.Lagos, R. and Wright, R. (2005). A unified framework for monetary theory and policy analysis. Journal of Political

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,

164:136–165.


inside money, investment, and unconventional monetary policy · 2017. 11. 20. · lukas altermatt...

Documents