Advanced Macroeconomics An Easy Guide Recent debates in monetary policy

CHAPTER 21 Recent debates in monetary policy In the last two chapters we presented the basic analytics of monetary policy in the long and in the short run , For the short run , we developed a simple New model that can parsimoniously make sense of policy as it has been understood and practised over the last few decades . Before the 2008 crisis , most central banks , and quite a few market central banks as well , carried out monetary policy by targeting a interest rate . In turn , movements in this interest rate were typically guided by the desire to keep close to a target this was the popular policy of targeting . This consensus led to a dramatic decrease in , to the point of near extinction in most economies , over the last two or three decades . But this benign consensus was shaken by the Great Financial Crisis of . First , there was criticism that policy had failed to prevent ( and perhaps contributed to unleashing ) the crisis . Soon , all of the world major central banks were moving fast and courageously into uncharted terrain , cutting interest rates sharply and all the way to zero . A and key issue , therefore , was whether the conventional tools of policy had been rendered ineffective by the zero lower bound , In response to the crisis , and in a change that persists until today , central banks adopted all kinds of unconventional or unorthodox monetary policies . They have used central bank reserves to buy bonds and markets with liquidity , in a policy typically called quantitative easing , And they have also used their own reserves to buy private sector credit instruments ( in effect lending directly to the private sector ) in a policy often referred to as credit easing . Interest rate policy has also become more complex . Central banks have gone beyond controlling the contemporary short rate , and to announcing the future path of short rates ( for a period of time that could last months or years ) in an attempt at expectations a policy known as forward , Last but not least , monetary authorities have also begun paying interest on their own reserves which , to the extent that there is a gap between this rate and the market rate of interest ( say , on bonds ) gives central bankers an additional policy tool . These policies can be on several grounds , One is the traditional control of updated in recent years to include avoidance of as well . Another is control of aggregate demand and output , especially when the zero lower bound on the nominal interest limits the ness of traditional monetary policy . A third reason for unconventional policies is stability if How to cite this book chapter , and , A . 2021 . Advanced An Easy Guide . 21 . Recent debates in monetary policy , London Press . DOI License .

324 RECENT DEBATES IN MONETARY POLICY spikes in spreads , for instance , threaten the health of banks and other intermediaries ( this is exactly what happened in ) then monetary policy may need to act directly on those spreads to guarantee stability and avoid runs and the risk of bankruptcy . Do these policies work , in the sense of attaining some or all of these objectives ?

How do they work ?

Why do they work ?

What does their effectiveness ( or lack of effectiveness ) hinge on ?

A massive academic literature on these questions has emerged during the last decade . Approaches vary , but the most common line of attack has been to append a sector to the standard New model ( yes , hard to believe , but , until the crisis , was largely absent from most macro models ) and then explore the implications . This change brings at least two . First , can itself be a source of disturbances , as it occurred in and had also occurred in many earlier crises in emerging markets . Second , the enlarged model can be used to study how monetary policy can respond to both and conventional disturbances , with the sector also playing the role of potential of those shocks . Here we can not summarise that literature in any detail ( but do look at and ( 2003 ) and ( 2011 ) and the survey by et al . 2013 ) for a taste ) What we do is extend our standard model of earlier sections and chapters to include a role for liquidity and , and we use the resulting model to study a few ( not all ) varieties of unconventional monetary policy . The issues surrounding conventional and unconventional monetary policies have taken on new urgency because of the crisis . In the course of 2020 , central banks again resorted to interest , cutting it all the way to the zero lower bound , coupled with quantitative easing and credit easing that are even more massive than those used over a decade ago . And in contrast to the Great Crisis , when only central banks experimented with unconventional policies , this time around many central banks have dabbled as well , So understanding how those policies work has key and urgent policy relevance and that is the purpose of this chapter , The liquidity trap and the zero lower bound Hicks , in the famous paper where he introduced the model , Hicks ( 1937 ) showed how monetary policy in occasions might become ineffective . These liquidity traps as he called them , occurred when the interest rate fell to zero and could not be pushed further down . In this section we model this liquidity trap in our New framework . Until not too long ago , economists viewed the liquidity trap as the stuff of textbooks , not reality . But then in the got stuck in a situation of very low or negative and no growth . No matter what the authorities tried , nothing seemed to work . In 1998 , Paul pointed out that here we are with what surely looks a lot like a liquidity trap in the worlds economy . And then he proceeded to show that such a trap could happen not just in the static model , but in a more sophisticated , dynamic New model . Of course , the experience of was not the only one in which a liquidity trap took center stage . During the world crisis of , the worlds major central banks cut their interests to zero or thereabouts , and found that policy alone was not to contain the collapse of output . The same , perhaps with greater intensity and speed , has occurred during the crisis of ,

RECENT IN MONETARY POLICY 325 with monetary authorities cutting rates to zero and searching for other policy tools to contain the destruction of jobs and the drop in activity So , the issues surrounding the zero lower bound and liquidity traps are a central concern of today , To study such traps formally , let us return to the canonical New model of Chapter 15 it , i , where , recall , Ir , is , is the output gap , is the nominal interest rate , is the natural or interest rate , which depends on both preferences ( the discount rate and the elasticity ) and trend productivity growth ( To close the model , instead of simply assuming a mechanic policy rule ( of the Taylor type or some other type , as we did in Chapter 15 ) we consider alternative paths for the interest rate in response to an exogenous shock , 2011 ) in an and elegant analysis of the liquidity trap , studies formal by the , both under rules and under discretion . Here we take a somewhat more informal approach , which draws from his analysis and delivers some of the same policy Define a liquidity trap as a situation in which the zero lower bound is binding and monetary policy is powerless to stabilise and output , To fix ideas , consider the following shock ( for . Starting from , at time the natural rate of interest unexpectedly goes down to , and it remains there until time , when it returns to and stays there forever . The key difference between this shock and that studied in Chapter 15 in the context of the same model , is that now the natural rate of interest is negative for an interval of time . Recall that this rate depends on preferences and on trend growth in the natural rate of output . So if this productivity growth becomes sufficiently negative , If could be negative as well . Notice that the combination of productivity and a negative natural rate of interest to what Summers ( 2018 ) has labelled secular stagnation . The point is important , because , if secular stagnation , by Summers precisely as a situation in which the natural rate of interest falls below zero for a very long time ( secular comes from the Latin , meaning century ) then economies will often themselves in a liquidity trap . The other novel component of the analysis here , compared to Chapter 15 , is that now we explicitly impose the zero lower bound on the nominal interest rate , and require that i , OW . If the central bank acts with discretion , choosing its preferred action at each instant , the zero lower bound will become binding as it responds to the shock . To see this , let us first ask what the central bank will do once the shock is over at time Recall the canonical New model displays , what and Gali ( 2007 ) called the divine coincidence there is no between keeping low and stabilising output , If i , then Ir , is an equilibrium , So starting at time , any central bank that is happiest when both and the output gap are at zero will engineer exactly that outcome , ensuring Ir , VI In terms of the phase diagram in Figure , we assume that initially ( before the shock ) i , so that It , OW . Therefore , the initial steady state was at point A , and to that point exactly the system must return at time , What happens between dates and ?

Trying to prevent a recession and the 326 RECENT DEBATES IN MONETARY POLICY Figure Monetary policy in the corresponding , the central bank wi cut the nominal interest all the way to zero . That will mean that between dates and , dynamics correspond to the system with steady state at point , but because of the zero lower bound , policy can not take the economy all the way back to the situation and keep Ir , always . So , on impact the system jumps to point , and both and the output gap remain negative ( and depression or at least recession take hold ) in the aftermath of the shock and until date . Both ( 1998 ) and ( 2011 ) emphasise that the problem is the central banks lack of credibility keeping the economy at , is optimal starting at time , and so people in this economy will pay no attention to announcements by the central bank that claim something else . In technical language , the monetary authority suffers from a time inconsistency problem of the kind identified by and Prescott ( 1977 ) and ( 1978 ) see Chapter 20 ) from the point of view of any time before time , engineering some after optimal . But when time , zero and a zero output gap become optimal . What is to be done ?

This is ( 1998 ) answer The way to make monetary policy effective , then , is for the Central Bank to credibly promise to be irresponsible to make a persuasive case that it will permit to occur , thereby producing the negative real interest rates the economy needs . In fact , there are simple paths for the nominal interest rate that , if the central bank could commit to them , would deliver a better result . Consider a plan , for instance , that keeps and the output gap constant at , Since ' If , it follows that it , and , Although this policy is not fully optimal , it may well ( depending on the social welfare function and on parameter values ) deliver higher welfare than the policy of ' forever , which causes recession and between

RECENT IN MONETARY POLICY 327 and And note that as prices become less sticky ( in the limit , as goes to ) the output gap goes to zero , so this policy ensures no recession ( and no boom either ) Notice , strikingly , that this policy just like the one described in the phase diagram above also involves keeping the nominal interest stuck against the zero lower bound during the whole duration of the adverse shock , between times and So if the policy is the same over that time interval , why are results ?

Why is there no recession as a result of the shock ?

Crucially , the difference arises because now people expect there will be and a positive output gap after time , and this pushes up before ( recall from Chapter 15 that today increases with the present discounted value of the output gaps into the future ) reducing the real interest rate and pushing up consumption demand and economic activity . Of course , the alternative policy path just considered is just one such path that avoids recession , but not necessarily the optimal path , 2011 ) and , before that , and ( 2003 ) characterised the fully optimal policies needed to get out of a liquidity trap . Details vary , but the main message is clear during the shock , the central bank needs to be able to persuade people ( to , in the language of theory ) it will create after the shock is over . What can central banks do to acquire the credibility to become irresponsible ?

One possibility is that they try to expectations through what has become known as ward guidance . One example , is the Feds repeated assertion that it anticipates that weak economic conditions are likely to warrant exceptionally low levels of the federal funds rate for some time . natively , central bankers can stress that they will remain vigilant and do whatever it takes to avoid a deep recession . For instance , on 28 February 2020 , when the Covid 19 pandemic was breaking out , Fed Chairman Powell issued this brief statement The fundamentals of the US , economy remain strong . However , the poses evolving risks to economic activity The Federal Reserve is closely monitoring developments and their implications for the economic outlook . We will use our tools and act as appropriate to support the economy When put this way , the problem seems relatively simple to solve the needs only to use these tools to obtain a similar result to what it would obtain by simply playing around with the term nominal interest rate , as in normal times . Unfortunately , this is not that easy precisely because of the crucial role played by expectations and credibility The crucial point is that the central bankers need to convince the public that it will pursue expansionary policies in the future , even if runs above target , and this runs counter to their accumulated credibility as hawkish and committed , Recent thinking on these issues and on other policy alternatives available to when against the zero lower bound is in ( 2016 ) He argues that , when it comes to forward guidance , what is needed are explicit criteria or rules about what would lead the central bank to change policy in the future criteria that would facilitate commitment to being irresponsible , One way to do that is to make policy the central bank commits to keep a tain path for interest rates unless certain criteria , in terms of a certain target for the output gap or unemployment or nominal , for instance , are met . The Fed has actually moved recently towards that approach , stating that current low rates will be maintained unless unemployment falls below a certain level , or rises above a certain level . The recent targeting shift by the Bank of can also be interpreted in line with this approach . Another way forward is to move from an target to a price level target ( see and ( 2003 ) and and ( 2004 ) The of a target over an

328 RECENT DEBATES IN MONETARY POLICY target to is that it meets enhanced pressure with an commitment to pursue expansionary policy in the future ( even if the target price level is unchanged ) An target , on the other hand , lets bygones be bygones a drop in prices today does not affect the course of policy in the future , since , under targeting , the central bank is focused only on the current rate of change in prices . Thus , targeting does not induce the same kind of adjustment of expectations about the future course of policy as does targeting ?

And if a rethinking of the traditional targeting framework is called for , another rule that has gained adherents recently is the or nominal level targeting ( see Sumner ( 2014 ) and ( 2019 ) In targeting nominal the central bank could commit to for falls in output by allowing for higher . The underlying point is that would provide a better indicator , compared to alone , of the kind of policy intervention that is needed . Reserves and the central bank balance sheet As we mentioned , the Great Financial Crisis introduced a wealth of new considerations for monetary policy . In this section we develop a model of quantitative easing where the Central Bank pays money on its reserves , adding a new variable to the policy tool which was not present in our traditional models where the rate of return on all Central Bank liabilities was at zero . We will see this introduces a number of new issues , While the modelling does not make this necessarily explicit , underlying the new paradigm is the understanding that there is a sector that liquidity . Thus , before going into the full problem , we lay out a more pedestrian approach to illustrate some of the issues , Introducing the sector To introduce these new issues we can start from a simple type of model , as in the lower panel of Figure If there are intermediaries , there must be multiple interest rates one that is paid to savers ( i ) and another that is charged from borrowers ( i ) Otherwise , of course , how would those intermediaries make any money ?

This market , depicting the supply of loans and the demand for loans , is shown in the upper panel of Figure . The IS curve below is drawn for a given level of spread . As a result , the role of intermediation introduces a new channel for the and of economic shocks . For instance , suppose a high level of economic activity affects asset prices , and hence the net worth of intermediaries and borrowers . This will allow for additional rowing at any level of spread ( a shift of the curve to the right ) This makes the IS curve than what it would otherwise be the same change in income would be associated with a smaller change in the interest rate paid to savers , This the effects on output of any shift in the curves . Even more interestingly , this lets us consider the of direct shocks to intermediation beyond the of other shocks , An upward shift of the curve ( less credit available for any level of spread ) means a downward shift to the IS curve a larger equilibrium spread translated into less est being paid to savers . This shock , illustrated in Figure , leads ( in the absence of monetary policy compensating for the negative shock ) to an output contraction with falling interest rates , Anything that impairs the capital of intermediaries ( say , a collapse in the prices of

RECENT DEBATES IN MONETARY POLICY 329 Figure Effects of a disruption of credit supply A A tightening of credit supply ( Interest rate spread ( between savers and borrowers ) Volume of lending Impact on the IS curve Interest rate Aggregate income securities they hold ) or that tighten leverage constraints ( say , they are required to post more eral when raising funds because the market is suspicious of their solvency ) will correspond to such an upward shift of the curve . If the IS curve is shifted far enough to the left , monetary policy may be constrained by the zero lower bound on interest rates Does all of that sound familiar ?

Needless to say , a simple type of framework leaves all sorts of questions open in terms of the behind the curves we ve been around with . To that point we now turn .

330 RECENT DEBATES IN MONETARY POLICY A model of quantitative easing Now we focus on the role of the central bank balance and , more , on the role of central bank reserves in the conduct of unconventional monetary policy . This emphasis has a practical motivation . As Figure makes clear , the Federal Reserve ( and other central banks ) have issued reserves to purchase government bonds , bonds and other kinds of papers , dramatically enlarging the size of central bank balance sheets . The assets in Figure 213 have been mostly with overnight interest paying voluntarily held deposits by institutions at the central bank . We call these deposits reserves for short . As Reis ( 2016 ) emphasises , reserves have two unique features that justify this focus . First , the bank is the monopoly issuer of reserves . As a monopoly issuer , it can choose the interest to pay on these reserves . Second , only banks can hold reserves . This implies that the aggregate amount of reserves in the overall banking system is determined by the central bank . The liability side of a central bank balance sheet has two main components currency ( think of it as bank notes ) and reserves . Together , currency and reserves add up to the monetary base . The central bank perfectly controls their sum , even if it does not control the breakdown between the two components of the monetary base . These two properties of the central bank imply that the central bank , can in principle , choose both the quantity of the monetary base and the nominal interest rate paid on reserves . Whether it can also control the quantity of reserves , and do so independently of the interest rate that it pays , depends on the demand for reserves by . Figure Assets held by FED , BOE and 1000 800 600 400 200 2005 2010 2015 2020 Year BOE Total Assets Index ( 2006 03 100 )

RECENT IN MONETARY POLICY Before the 2008 crisis , central banks typically adjusted the volume of reserves to nominal interest rates in interbank markets . The zero lower bound made this policy infeasible during the crisis . many central banks adopted a new process for monetary policy they set the interest rate on reserves , and maintained a high level of reserves by paying an interest rate that is close to market rates ( on bonds , say ) In turn , changes in the reserve rate quickly feed into changes in interbank and other short rates . Let , be the real value of a central means of payment . You can think of it as central bank reserves . But following and ( 2020 ) and et al . 2019 ) you can also think of it as a digital currency issued by the monetary authority and held directly by households . In either case , the key feature of ) is that it provides liquidity services it enables parties to engage in buying , selling , and settling of balances . In what follows , we will refer to ) using the acronym ( means of payment , not be confused with our earlier use of for monetary policy ) but do keep in mind both feasible interpretations . Later in this chapter we will show that the model developed here can also be extended ( or reinterpreted , really ) to study a more conventional situation in which only commercial banks have access to accounts at the central bank and households only hold deposits at commercial banks . The simplest way to model demand for is to include it in the utility function of the household , I where is the elasticity of substitution in consumption , and is a weight with at that lies between and . The representative household the present counted value of this utility subject to the following budget constraint ) if ) where , is the real value of a nominal ( bond , issued either by the ment or by the private sector , if is the nominal interest rate paid by the bond , and if is the nominal interest rate paid by the central bank to holders of , Income ) comprises household income and government transfers . In accordance with our discussion above , the monetary authority controls this interest rate and the supply of . Since we do not want to go into the supply side of the model in any detail here , we simply include a generic formulation income , which should include wage income but could have other components as well . Government transfers must be included because governments may wish to rebate to agents any seigniorage collected from currency holders . Let total assets be A ) Then we can write the budget constraint as A ) if ) A ) if ' In the households problem , A I is a state variable and ) and , are the control variables . First order conditions are ( i )

332 RECENT DEBATES IN MONETARY POLICY where A , is the shadow value of household assets ( the variable in the problem ) These conditions are standard for the Ramsey problem , augmented here by the presence of the . It follows from ( and ( in logs , denoted by small case letters , the demand function for is , where A , log ) if 17 ) So , intuitively , demand for is proportional to consumption and decreasing in the opportunity cost ( if if ) of holding . Notice that this demand function does not involve satiation as if if goes to zero , does not remain bounded . From a technical point of view , it means that we can not consider here a policy of if ' The appendix shows that in logs , the equation is a , A , Differentiating ( with respect to time yields a , To close the model we need two more equations . One is the law of motion for real holdings , also in logs 51 , where is the rate of growth of the nominal stock of . Intuitively , the real stock rises with and falls with . So ) and if are the two policy levers , with if endogenous ( From ( and ( 2115 ) it follows that a , This equation and the equation ( 2113 ) can be combined to yield ' if ) A I a ' ix ) Now , given the ofA , in ( 2112 ) if ( a ) eA if , which can trivially be included in ( A ! Recall next that because the economy is closed all output is consumed , so it , If we again , as the output gap , the equation becomes , if , A , where , as in previous sections , the natural rate of interest is , and is the exogenous rate of growth of the natural rate of output )

RECENT IN MONETARY POLICY 333 Next , with , the demand function ( becomes , A , which , in deviations from steady state , is , A , We close the model with the Phillips curve , using the same formulation as in this chapter and earlier it , pit , Replacing ( 2122 ) in ( we get , A , That completes the model , which can be reduced to a system of three differential equations in unknowns , and A , whose general solution is quite complex . But there is one case , that of log utility , which lends itself to a simple and purely graphical solution . On that case we focus next . then ( to A , This is an unstable differential equation in A , and exogenous parameters or policy variables . Thus , when there is a permanent shock , A , jumps to the steady state . This equation does not depend on other endogenous variables ( or if ) so it can be solved separately from the rest of the model . The evolution over time of A , depends on itself and the policy parameters if and ) Now the Phillips curve and the law of motion for are a system of two differential equations in two unknowns , Ir , and , with ( A , exogenously given , In matrix form the system is ' A , 2126 where , It is straightforward to see that Det ( and ( It follows that one of the of is positive and the other is negative . Since it , is a jumpy variable and , is a sticky or state variable , we conclude that the system is stable , as seen in Figure . Before considering the effects of shocks on the dynamics of this system , let us ask why this model ?

What does it add to the standard formulation ?

The first is realism , Since the Great Financial Crisis , many central banks have begun using the interest paid on reserves as an instrument of monetary policy . This policy alternative is not something one can study in conventional models . Second , and more important , not only different interest rates , but the size and composition of the central bank balance sheet now matter . Changes in the speed of creation and open market operations involving can affect both and output . For a more general discussion of the role of the central banks balance sheet , see and ( 2011 ) Third , a technical but point this model does not suffer from the problem of of equilibrium that plagues models with an exogenous nominal interest rate , as we saw in Chapter 15 . For further discussion , see Hall and Reis ( 2016 ) and and ( 2020 )

334 RECENT DEBATES IN MONETARY POLICY Figure A model of central bank reserves II it Figure Reducing the rate on reserves Effects of monetary policy shocks Consider first the effects of an unexpected and permanent reduction in if , one of the two policy tools the central bank has . Suppose that at time ?

moves from id to , where id . We show this in Figure . Recall that in steady state the market rate of interest on bonds is pinned down by i . So , as if falls , A , the steady state gap between the two interest rates rises . We saw that in response to a permanent policy shock , A , will immediately jump to its new ( higher , in this case ) steady state level . This means that we can look at the dynamics of and independently of A ,

RECENT IN MONETARY POLICY 335 The other thing to notice is that as the steady state gap ( i ' goes up , steady state demand for falls . In the phase diagram in Figure , this is in the fact that the it schedule moves to the left , and the new steady state is at point , On impact , the system jumps up to point , with temporarily high . Thereafter , both and real stocks of fall toward their new steady state levels . What happens to consumption and output ?

The cut in if makes people want to hold less , but the stock of can not fall immediately What the market for is a an upward jump in consumption ( and output , given that prices are sticky ) The temporary boom causes an increase in above the rate of nominal growth , which over time erodes the real value of the stock of outstanding , until the system settles onto its new steady state , In summary the permanent cut in the interest rate paid on causes a temporary boom . rises and then gradually falls and so does output . All of this happens without modifying the pace of nominal growth . So , changes in the interest rate paid on central bank reserves ( or on a digital means of payment ) do serve as tool of monetary policy , with real effects , Consider next the effects of an unexpected and permanent increase in , the other tool the central bank has at its disposal . Suppose that at time , policy moves from to , where . Recall again that in steady state the market rate of interest on bonds is pinned down by . So , as rises and id remains constant , the steady state gap between the two interest rates will go up , But A , will jump right away to , so again we can look at the dynamics of the system independently of A , As the steady state gap ( i id ) rises , steady state demand for goes down , In the phase diagram in Figure , this is in the fact that the it schedule moves to the left . But now the schedule also shifts ( upward ) so that the new steady state is at point On impact , the system jumps up to point , with overshooting its new , higher , steady state level . Thereafter , both and the real stock of fall toward their new steady state levels , Figure Increasing money growth

336 RECENT DEBATES IN MONETARY POLICY Figure The dynamics of the interest rate spread A , Note that the overshoot is necessary to erode the real value of , since in the new steady state agents will demand less of it , As in the previous case , rises since consumption and output are temporarily above their steady state levels . Finally , consider the effects of a temporary drop in if , the interest rate paid on . To fix ideas , consider the following unexpected shock occurring at time 41 To sort out what happens it helps to begin by asking what is the trajectory of A , It rises on impact , but it does not go all the way up to A , the level it would take on if the change were permanent , The differential At falls thereafter , so that it can jump at when if goes back to its initial level , ensuring that A , is back to its initial steady state level A an instant after ( in contrast to the policy variable , can not jump ) Let , be the value ofA , once the unexpected shock happens at . It must be the case , by the arguments above , that A A , You can see this evolution in the phase diagram in Figure , where we show the ( version of ) the At schedule . What are the implications for the dynamic behaviour of and the real stock of ?

We can study that graphically in Figure below . If the policy change were permanent , the it schedule would have moved all the way to , giving rise to a steady state at But the fact that A offsets some of that leftward movement , So , the it schedule moves to , creating a temporary ( for an instant ) steady state at Ask what would happen if A , were to remain at until time would jump up on impact . But it can not go beyond point , because if it did the system would diverge to the northwest afterwards . So , would jump to a point like After the jump , the economy would begin to move following the arrows that correspond to the system with steady state at .

RECENT DEBATES IN MONETARY POLICY 337 Figure A temporary decline in the rate on reserves ! Of course , an instant after , and because ofthe movement in A , the locus it begins to shift to the right . But this does not affect the qualitative nature of the adjustment path , because the system always lies to the right of the shifting it locus , and thus obeys the same laws of motion as it did an instant earlier . The evolution of and real is guided by the need that , at , the system must be on the saddle path leading to the initial steady state at point You can see from the phase diagram that after the initial jump up , falls between times and , and rises thereafter . The real value of drops initially due to the high , but then gradually recovers as Ir , falls below . One can show also that output goes through a boom between times and , takes a discrete drop at when the interest rate if rises again , and recovers gradually until returning to its initial steady state level . Policy implications and extensions Quantitative easing We emphasised above that in this model the monetary authority has access to two policy levers an interest rate ( id ) and a quantity tool ( potentially , two interest rates , if the central bank chooses to engage in open market operations and use changes in quantities to target il . So we have gone beyond the realm of conventional policy , in which control of the single interest rate on bonds is the only We saw earlier that a dilemma arises when the nominal interest rate is against the zero lower bound . Can we use the model we have just built to study that conundrum ?

Is there a policy that can stabilise output and when the lower bound binds ?

The answer is yes ( subject to parameter values ) and in what follows we explain how and why . To fix ideas , let us go back to the situation studied earlier in this chapter , in which , because of lagging productivity growth , the natural rate of interest drops . Suppose initially , if

338 RECENT DEBATES IN MONETARY POLICY and it . Then the following shock hits for 2129 for ta ( So starting from , at time the natural rate of interest unexpectedly drops down to and it remains there until time , when it returns to and stays there forever . Notice that ' during the duration ofthe shock the curve ( 2120 ) becomes , if Ir , 2130 ) So , Ir , would require if . But this is impossible if the zero lower bound is binding and hence if must be , Our conclusion , therefore , is that for monetary policy to get around the zero lower bound problem we must focus on the case in which ' This is the case in which the utility function is not separable in consumption and liquidity ( so that that changes in the opportunity cost of holding liquidity have an impact on the time profile of consumption and aggregate demand . If we go back to the case in which , during the duration of shock the curve ( 2120 ) becomes , a ( if , A , 2131 ) It follows from ( that , and Ir , if and only if ' ot ' eA A , 2132 ) where we have used if ( a ' eAr ii . For simplicity , focus on the case . In that case , the of this equation is positive ( recall ) so the interest gap A , must rise gradually during the period of the shock , At this point we have to take a stance on a question does the zero lower bound apply to if as well ?

If we interpret , narrowly , as reserves commercial banks hold at the central bank , the answer may be negative it is not hard to think of liquidity or safety reasons why banks would want to hold reserves at the central bank even if they have to pay a cost to do so . But if we interpret if more broadly as a digital currency , then the answer could be yes , because if the nominal interest rate on reserves is negative , households could prefer to hold their liquidity under the mattress and look for substitutes as a means of payment . This is the standard argument for the zero lower bound . To avoid wading into this controversy , in this section we assume if . Moreover , and to keep things very simple , we assume the central bank keeps if at its steady state level of zero throughout . In that case , the equation for the evolution of A , reduces to ' a ) A ( I ( Next , recall the liquidity demand function , A , which implies that if consumption is to be constant during the period of the shock , then , That is to say , the interest gap can be rising only if the ( real ) stock of is falling . But since we are also requiring zero during that period , real decline is the same as nominal decline , implying , So now we know what the time of and , must be between times and What about the initial and terminal conditions ?

Suppose we require is . so that the interest rate on bonds will RECENT IN MONETARY POLICY 339 be exactly at its steady state level at time Since if is constant at zero and A , must be falling , it follows that if must be rising during the length of the shock . So if must have jumped down at time , which in turn means , must have jumped up at the same time . In summary if ' a policy that keeps output at full employment and at zero , in spite of the shock to the natural interest rate , involves a ) discretely increasing the nominal and real stock of at the time of the shock , causing the interest rate on bonds to fall on impact in response to the shock , in what resembles QE ) allowing the nominal and real stock of to fall gradually during the period of the shock , in what resembles the unwinding of QE ) once the shock is over , ensuring policy variables return to ( or remain at ) their steady state settings and if for all The intuition for why this policy can keep the economy at full employment is as follows . With two goods ( in this case , consumption and liquidity services ) entering the utility function , what matters for the optimal of expenditure is not simply the real interest rate in units of consumption , but in units of the bundle , that includes both the consumption good and the real value of . Because the nominal rate on bonds can not fall below zero , what brings the real interest rate down to the full employment level is the behaviour of the relative price A , When , A , has to rise to achieve the desired effect . If , on the contrary , we assumed ' then A , would have to fall over time the period of the In the case ' the gradual increase in A , follows an initial drop in the same variable , caused by a discrete increase in the nominal and real stock of . This quantitative easing , if feasible , manages to keep the economy at full employment and zero in spite of the shock to the natural rate of interest and the existence of a zero lower bound for both nominal interest rates . Money An objection to the arguments so far in this chapter is that digital currencies do not yet exist , so households do not have accounts at the central bank . In today world , the only users of central bank reserves are commercial banks . But most households do use bank deposits for transactions , This does not mean that our previous analysis is useless . On the contrary , with relatively small , it is straightforward to introduce a banking system into the model . et al . 2019 ) carry out the complete analysis . Here , we just sketch the main building blocks , A commercial bank balance sheet has deposits and bank equity on the liability side , and central bank reserves and other assets ( loans to , government bonds ) on the asset side . Banks are typically they can issue deposits only if they have enough collateral where central bank reserves and government bonds are good collateral . So now , can stand for ( the log of ) the real value of deposits held in the representative commercial bank , and if is the interest rate paid on those deposits . Because deposits provide liquidity services , if can be smaller than the interest rate on bonds , if , The central bank does not control if or if directly . But banks do keep reserves at the central bank , and this gives the monetary authority indirect control over market rates . Denote by if the interest rate paid on central bank reserves , It is straightforward to show ( see et al . 2019 ) for details ) that optimal behaviour by banks leads to ( if ) if ) where if if banks are have monopoly Whenever , if ( if so that the rate on deposits and on central bank reserves are linked , with

340 RECENT DEBATES IN MONETARY POLICY the former always above the latter . The central bank can affect the rate on deposits by adjusting both the quantity of reserves and the interest rate paid on them . Demand for deposits , as in the previous subsection , depends on the opportunity cost of holding deposits , 2135 ) Using the equation above we have , i ( With this expression in conjunction with the dynamic curve , the , and the corresponding policy rules , we have a macro model almost identical to that of the earlier sections , and which can be used to analyse the effects of exogenous shocks and policy changes , Aside from realism , this extended version has one other advantage shocks to conditions can now become another source of business cycle variation that needs to be counteracted by ( and perhaps ) policy . The parameter if , conditions in the markets , the quality of the collateral , the extent of competition , enter as shifters in the expression for deposit demand . To ideas , consider what happens if we continue with the policy arrangement of the subsection , with if and the interest rate on reserves ( now labelled if ) exogenously given . Then , and since , is a sticky variable that can not jump in response to shocks , an unexpected change in if would imply a change in consumption , and , therefore , in aggregate demand and output , So , in the presence of shocks to market conditions , monetary have to consider whether and how they want to respond to such shocks . So far the focus of this chapter has been on unconventional policies that involve changing the quantity of reserves by having the central bank carry out open market operations involving safe assets like government bonds . But at the zero lower bound , and if the interest rate on reserves is brought down to the level of the interest rate on bonds ( a case of liquidity satiation , not considered above ) then from the point of view of the private sector ( of a commercial bank , say ) central bank reserves and , liquid government bonds become identical they are both issued by the state ( or the consolidated government , if you wish ) paying the same rate of interest . So , operations that involve swapping one for the other can not have any real effects . That is why , in the face of markets and distortions , over the last decade and particularly since the Great Financial Crisis , central banks have turned to issuing reserves to purchase other kinds of assets , from corporate bonds to loans on banks balance sheets , in effect lending directly to the private sector . As mentioned at the outset , these are usually labelled credit easing policies , in contrast to the quantitative easing policies that only involve conventional open market operations . Credit easing can be incorporated into a simple model like the one we have been studying in this chapter , or also into more sophisticated models such as those of and ( 2011 ) and et al . 2019 ) There are many obvious reasons why such policies can have real effects one is that they can get credit again when the pipes of the system become clogged or frozen in a crisis . A related reason is that in this context policy can not only address aggregate demand , but also help alleviate supply constraints if , for instance , lack of credit keeps from having the necessary working capital to operate at the optimal levels of Output . This all begs the question of what

RECENT IN MONETARY POLICY policy rules ought to look like in such circumstances , a fascinating subject we can not address here , but about which there is a growing literature beginning with the 2009 lecture at in which Ben , then Fed Chair , explained the Fed approach to the crisis , which stressed credit easing policies ( 2009 ) Appendix The , 21110 ) repeated here for convenience , are ?

a ) i ) I ( where we have , Combining the two , we have demand for , which in logs is , A , where A , Next , differentiating ( with respect to time and then combining with ( yields a . Or , in logs ( Using demand for from ( in the ( yields ( Or , in logs , a ) A ,

342 RECENT DEBATES IN MONETARY POLICY Differentiating ( with respect to time yields , a , a ) A , Replacing the expression for , from ( 2146 ) in ( we obtain the equation ( used in the text a , A , which can be also written , perhaps more intuitively , as . a , if ( A , This way of writing it emphasises that the relevant real interest rate now includes the term ( a ) A , which corrects for changes in the relative price of the two items that enter the sumption function . Notes On monetary policy during the pandemic , see ( 2020 ) A good review ofthe discussion can be found in ( 2017 ) A technical in Chapter 15 we claimed that , in the absence of an activist interest rule , the canonical equation New model does not have a unique equilibrium . So why have no multiplicity issues cropped up in the analysis here ?

Because , to draw the phase diagram the way we did we assumed the central bank would do whatever it takes to keep it , starting at ( including , perhaps , the adoption of an activist rule starting at that time ) That is enough to pin down uniquely the evolution of the system before because it must be exactly at the origin ( Ir , at See ( 2011 ) for the formal behind this argument . Recall from Chapter 14 that 41211 , and of is the expected length ofa price quotation in the ( 1983 ) model . So as prices become perfectly , goes to For details , see the discussion by on the paper by and ( 2003 ) See ( 2010 ) from which this discussion is taken . In particular , on whether banks demand for liquidity has been satiated or not . See the discussion in Reis ( 2016 ) We will see later that , under some simple extensions , can also be thought of as deposits issued by commercial banks . But let us stick with the digital currency interpretation for the time being . You may be wondering where currency is in all of this . We have not modelled it explicitly , but we could as long as it is an imperfect substitute for ( meaning they are both held in equilibrium even though they have different yields zero in nominal terms in the case of currency ) According to Reis ( 2016 ) this is more or less what the Federal Reserve has tried to do since the Great Financial Crisis of , thereby the demand for liquidity This very helpful way of solving a model ofthis type is due to and ( 1996 ) Notice , however , that all the analysis so far ( and what follows as well ) assumes id . That is , there is an opportunity cost of holding reserves ( or , if you prefer ) and therefore liquidity demand by banks ( or households , again , if you prefer ) is not satiated . The situation is different when the interest rate on reserves is the same as the interest rate on government bonds . Reserves are a liability issued by one branch of government the central bank . Bonds or bills are a liability issued by another

RECENT IN MONETARY POLICY 343 branch of government the Treasury . The issuer is the same , and therefore these securities ought to have the same ( or very similar ) risk characteristics . If they also pay the same interest rate , then they become perfect substitutes in the portfolios of private agents , An operation involving exchanging reserves for bonds , or , would have no reason to deliver real effects . A irrelevance result would kick , However , there may be some special circumstances ( or crisis , for instance ) in which this equivalence breaks down , See the discussion in Reis ( 2016 ) QE involves issuing reserves to purchase bonds , and that is exactly what is going on here . Notice this policy is not unique . There are other paths for and if that could keep output and constant . We have just chosen a particularly simple one . Notice also that in the sequence we described , the interest gap A , jumps down on impact and then rises gradually until it reaches its steady level at time , but this trajectory is feasible as long as the shock does not last too long ( is not too large ) and the shock is not too deep is not too negative ) The constraints come from the fact that on impact A , drops but can never reach zero ( because in that case demand for would become unbounded ) In other words , the central bank is not free to pick any initial condition for A , in order to ensure that , given the speed with which it must rise , it will hit the right terminal condition at time Part of the problem comes from the fact that we have assumed that the rate in the initial steady state is zero , so the initial nominal interest rate on bonds is equal to the natural rate of interest , But , in practice , most central banks target at percent per year , which gives A , more room to drop , so that central bankers can freely engage in the kind of policy we have described . Moreover , in the aftermath of the global crisis there were suggestions to raise targets higher , to give central banks even more room in case of trouble . 15 ( 1983 ) was the to make this point , 16 By contrast , in the absence of and with perfect competition , and if if , so that the interest rate on deposits is equal to the rate paid on central bank reserves . 13 References , 2019 ) Facts , fears , and functionality of level targeting A guide to a popular framework for monetary policy . Research Paper . 2009 ) The crisis and the policy response . Stamp Lecture , London School of , 13 , 2009 . Gali , I , 2007 ) Real wage and the New model . journal of Money , Credit and Banking , 39 , 2013 ) with A survey Advances in Economics and Econometrics . A . 1978 ) On the time consistency of optimal policy in a monetary economy . 141 1428 . A , 1983 ) Staggered prices in a framework , Journal of Monetary , 12 ( A . A , 1996 ) and money . The Economic Journal , 106 ( 439 ) 2011 ) The balance sheet as an instrument of icy journal Economics , 58 (

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