Quantitative Easing at the Zero-Lower Bound

Transcription

1 Quantitative Easing at the Zero-Lower Bound In Light of Recent Developments Enrique Martínez-García Federal Reserve Bank of Dallas and Adjunct at Southern Methodist University Dallas, January 30, 205 Abstract Quantitative easing can have e ects on prices when short-term interest rates are at the zero-lower bound if it a ects future money supply (rather than today s money supply). Therefore, assuming some form of monetary non-neutrality (e.g., in the context of a standard sticky-price model), quantitative easing can also have real e ects. In turn, if quantitative easing s impact on the supply of money is expected to be reversed before short-term interest rates lift-o, its e ect on prices and output might be muted. Echoing the arguments of Krugman (998) and Koenig (20) in regards to the conduct of monetary policy in a liquidity (or de ationary) trap, I argue that expectations about the future policy of the central bank (and its ability to commit to that policy path) are crucial. A permanent increase in the money supply may help build the credibility of the central bank to act "irresponsibly" in the words of Krugman (998) when in a liquidity trap. A credible commitment to such a policy can then keep long-term in ation expectations anchored (away from a de ationary steady state) and lead to increases in current prices (and wages) with e ects on economic activity today. JEL Classi cation: E3, E43, E5, E52 KEY WORDS: Liquidity Trap, Zero-Lower Bound, Quantitative Easing, Long-Term In ation Expectations Enrique Martínez-García, Federal Reserve Bank of Dallas. Correspondence: 2200 N. Pearl Street, Dallas, TX Phone: + (24) Fax: + (24) enrique.martinez-garcia@dal.frb.org. Webpage: I acknowledge the excellent research assistance provided in parts of this document by Valerie Grossman and Bradley Graves. I thank the feedback and suggestions of Valerie Grossman, Christo er Koch and Mark Wynne. All remaining errors are mine alone.

2 Introduction There have undoubtedly been signi cant e orts in the U.S. as well as among other major advanced countries to provide su cient stimulus to maintain in ation close to its intended target. The chart below illustrates the extent to which central bank s balance sheets have expanded in the aftermath of the 2008 global recession, as nominal interest rates fell to zero. However, the major advanced economies have experienced a prolonged period of below-target in ation. This persistent period of low in ation creates a risk to the credibility of monetary policy. For monetary policy to be e ective, it is key that in ation expectations remain well-anchored. However, this is more of a challenge as the fall of interest rates close to zero has raised the specter of a "liquidity trap." Persistent deviations from the target may weaken the credibility of the central bank, and this appears to be showing in market-based in ation expectations as shown in the chart below. Here, I have plotted the behavior of one market-based measure of longer-term in ation expectations the 5 year, 5 year ahead

3 in ation swap rate for the U.S., the U.K., the euro area and Japan. In the remainder of the paper, I argue that interest rates near or at the zero lower bound do not necessarily imply an economy has fallen into a "liquidity trap" so long as long-term in ation expectations remain wellanchored. I go on to argue that the central bank has tools to avoid such a liquidity trap. I consider a situation whereby a series of shocks pushes the economy against the zero lower bound and argue that quantitative easing in the form of an expansion of the central bank s balance sheet and the money supply can be an e ective instrument to provide short-term stimulus for the economy. The challenges for quantitative easing are that it must be permanent (or long-term) and credible to be e ective, and it must remain consistent with a non-de ationary steady state after interest rates lift o (in order to keep long-term in ation expectations well-anchored). I conclude by noting the importance of timing. My theoretical analysis suggests that it is preferable not to diminish the level of stimulus through quantitative easing until after interest rates start to rise. I am concerned that some of the declines seen since the second-half of 204 in market-based in ation expectations may be factoring in the perception that the September FOMC decision to stop bond purchases came "too early" and that this is not providing enough monetary support to credibly maintain in ation expectations anchored as before. I speculate that there might be some spillover e ects too. Finally, I suggest that if such were the case, it is important to investigate what further policy options the central bank has to ensure that in ation expectations remain well-anchored in the long run and that monetary policy does not become too tight in the short run. 2

4 2 Liquidity Traps and the Zero Lower Bound I refer to a liquidity trap (or more accurately a de ationary trap) as an scenario when the nominal interest rate is zero and low in ation or outright de ation are built into in ation expectations. This is a problem that arises with interest rate rule-based policies where multiple steady states cannot be ruled out and becomes a problem for policymakers intent on conducting expansive monetary policy to stimulate the economy. I illustrate this liquidity trap scenario drawing from the model of Benhabib, Schmitt-Grohé and Uribe (200). Benhabib, Schmitt-Grohé and Uribe (200) show that the basic steady-state relation that implies multiple equilibria with interest rate rules is common to a wide range of monetary models with representative agents and with an in nite horizon, and it holds irrespective of whether prices are exible or sticky or whether money enters the model through the utility function, the production function, a cash-in-advance constraint, or even in the cashless limit. In general, explosive de ationary paths can be ruled out even with the zero lower bound on nominal interest rates, as under most forms of the Taylor rule, accommodating explosive de ation becomes inconsistent with the zero bound constraint. However, the point of Benhabib, Schmitt- Grohé and Uribe (200) is that bounded de ation cannot be ruled out that, in fact, the economy can end in a liquidity trap. To motivate the idea of Benhabib, Schmitt-Grohé and Uribe (200), I start with the standard Euler equation on consumption, i.e., ( + i t ) u c;t g (x t ) () + u c;t+ where t+ Pt+ de nes in ation, i t is the short-term nominal interest rate and x t is a vector of other endogenous variables. The Euler equation can be approximated in logs as i t t+ + ln (g (x t )) : (2) I also specify a fairly standard Taylor (993)-type monetary policy rule which I describe simply as follows: i t ln (h (x t )) + + ( t ) ; > : (3) Finally, let me consider for simplicity of exposition a exible price setting where there are no price distortions and assume that all real variables are at their steady state (by assuming that x t x). Then, one can look at the dynamics of the nominal variables towards the steady state with the following di erence equation for in ation which combines (2) and (3): t+ + ( t ) + ln We can redi ne the in ation dynamics equation as follows: h (x) : (4) g (x) where, for convenience, I use the following notation: + g (x t ). Hence, with i t 0 it must follow that t+ t+ + ( t ) ; (5) ln( h(x) g(x) ). Note that in steady state ln (g (x)) < 0 and this puts a lower 3

5 bound on de ation in steady state. With all these ingredients, two steady states emerge characterized by the dynamics illustrated in the gure below. is an unstable steady state (a saddle point), while is stable and associated with i 0 (a liquidity trap). The two policy take-aways from this example and the extensive literature that has built on the idea of multiple equilibria are that: (a) Long-term in ation expectations should be tied to the in the long run. If drifts in expectations are left unchecked, then they may naturally drift downwards toward the de ationary steady state (the liquidity trap < 0). This should be a concern for policymakers when indications start to appear that in ation expectations are indeed drifting downwards. (b) The fact that the de ationary steady state tends to be stable suggests a stronger hurdle for policy to bring the economy back to. Sometimes the case of Japan has been described as one where policy failures have led the country to a liquidity trap where in ation expectations have incorporated de ation. In my remarks, I would not have much to say about the course for monetary policy in this scenario. In turn, I will focus on a di erent scenario that seems more relevant for the U.S. and other advanced economies (and here I have in mind both the euro area and the U.K.). This is a scenario whereby the economy starts at the steady state > 0 but gets hit by a number of shocks that push nominal interest rates against the zero lower bound. I will generalize the stylized framework presented in this section somewhat to be able to discuss the role of quantitative easing 4

6 as a tool to prevent very low interest rates from pushing the economy into a liquidity trap. 3 Quantitative Easing at the Zero Lower Bound Often we hear references to the e ect that near-zero interest rates are an indication of a country falling into a "liquidity trap" or a "de ationary trap." In the sense that I have described before, a de ationary trap truly arises whenever long-term in ation expectations settle on the de ationary steady state < 0. In other words, nominal interest rates can fall to near zero and not lead to a de ationary trap (liquidity trap) of the type I identi ed here so long as the central bank can act to keep long-run in ation expectations anchored at the steady state. One can look at forward guidance as one of the policy frameworks that could conceivably deliver that so long as it is credible and serves to assuage the concerns of economic agents that in ation will drift permanently low in the future. There are other policy options that one can consider, but here I will emphasize only one: quantitative easing (through changes in the money supply). Even though interest rates might be stuck at or close to zero, the central bank can still provide monetary accommodation by increasing the money supply. I refer to such actions as quantitative easing or QE in the reminder of the paper. But will quantitative easing work by manipulating the money supply, and if so, why and how? Answering these questions is crucial in thinking about questions such as the appropriate exit strategies and the timing of events. At the height of the 2008 global nancial crisis, markets "froze" to a great extent. The actions of the central banks at the time were meant to address a crisis of con dence in nancial markets, help out rms with "bad assets," etc. However, I will not address any of it explicitly here. In turn, I focus on the role of quantitative easing and its e ectiveness in keeping the economy away from a liquidity trap even when hit with a series of shocks that can push nominal rates close to zero. My remarks build on the work of Auerback and Obstfeld (2005) to suggest that quantitative easing may prevent the economy from falling into a liquidity trap even when interest rates are at or near zero for an extended period of time. The key insight here is that the money supply can help anchor in ation expectations in the long run when interest rates begin to rise but may also have stimulative e ects in the short run. Both aspects of the policy must be taken into account accordingly. Toy Model of the Economy Assume a representative agent, in nite-horizon model with a cash-inadvance constraint. I shall maintain for simplicity the assumption that prices are fully exible, but allowing for the possibility of time variation in the intertemporal discount factor. Time-variation in the intertemporal discount factor is a standard short-hand that permits us to think of a scenario whereby nominal interest rates can be driven down to the zero lower bound. Household utility is given by U 0 X t0 Y t s0 s U (C t ; L t ) ; (6) where s > is possible for a number of quarters. The problem would still be well-de ned so long as Y t lim t! s 0. The speci cation of the utility function is U (C t ; L t ) ln C t k t L t, where C t is s0 aggregate consumption, L t is aggregate labor and k t is a labor supply shifter. Households hold government 5

7 debt, B t, and money, M t. The total real wealth (at the beginning of the period) V t is de ned as, V t B t + M t ; (7) where is the price level at time t. The households budget constraint can simply be written as, V t+ B t ( + i t ) + M t + D t + w tl t T t C t ; (8) where T t is a lump-sum transfer, w t is the nominal wage, and D t are nominal dividends. The nominal interest rate i t is constrained at zero, i.e., i t 0: (9) while real interest rates are de ned as + r t +it. Using the de nition of the real wealth and the real interest rate, the budget constraint can be re-expressed as V t+ V t ( + r t ) i t M t + D + w tl t T t C t : (0) Let me impose a CIA constraint together with a tax on consumption, t, which has to be paid with cash, M t ( + t ) C t : () The CIA constraint is binding when i t > 0, and non-binding when i t 0 (at the zero lower bound). The complementary slackness condition of this problem can be expressed as follows: i t M t i t ( + t ) C t : (2) Inserted into the budget constraint, I obtain the following expression: V t+ V t ( + r t ) + D t + w tl t T t ( + i t + t i t ) C t : (3) If total real tax payments on consumption are transferred to the household without other uses by the government, i.e., T t t C t, then it follows that V t+ V t ( + r t ) + D t + w tl t ( + i t ) ( + t ) C t : (4) The optimal behavior of households can be characterized with the following rst-order conditions from the household optimization problem: C t t ( + i t ) ( + t ) ; (5) k t w t t ; (6) t t+ t+ ( + r t+ ) : (7) 6

8 This results in the following set of equilibrium conditions, C t ( + i t ) ( + t ) C t Monetary Policy at the Zero Lower Bound w t k t ( + i t ) ( + t ) (8) t+ C t+ ( + i t+ ) ( + t+ ) ( + r t+) C t+ ( + i t ) ( + t ) C t+ t ( + i t+ ) ( + t+ ) ( + r t+) C t+ ( + t ) C t+ ( + i t ) t + ( + t+ ) : (9) Assume that some shock(s) has made the CIA constraint non-binding (say " 0 ), such that the economy starts with i 0 0. s cannot be permanently above or the problem would not be well-de ned, so there must be a nite time after which nominal interest rates would have to start rising again. Assume that at some point in time T > 0, the nominal interest rate becomes positive again, i.e. i T > 0. In other words, at some future date the zero lower bound will not be binding again but then the CIA constraint will be binding. Assume a constant consumption tax ( t ), and combine (8) and (9): C t+ C t+ ( + i t ) ; t + w t+ k t ( + i t ) w t k t+ ( + i t+ ) + ( + i t ) ; t+ + w t+ k t w t k t+ ( + i t+ ) t+ : The following equilibrium condition arises from these equations: w t+ k t+ ( + i t+ ) t+ w t k t : (20) For tractability, let me make a more heroic assumption and assume that T is known. So, as long as the economy is at the zero lower bound, for t < T w t+ k t+, it would follow that t+ w t k t : (2) When the economy is out of the zero lower bound, for t > T, it would follow that C t+ C t+ ( + i t ) ; (22) t + which combined with the binding CIA constraint M t ( + ) C t, this implies that M t+ M t+ ( + i t ) : (23) t + Inserted into (20), it follows that w t k t t t+ M t+ M t w t k t : (24) 7

9 Hence, out of the zero lower bound, nominal wage growth (and ultimately price growth) in this framework is determined by nominal money growth. For t T we have the following implication: and thus by the CIA constraint, which binds in T, I can infer that C T C T T P T P T ; (25) Thus, by the labor supply equation at T, where i T 0, I get that M T C T ( + ) T P T : (26) M T k T w T T ; (27) or simply, w T k T M T T : (28) This "terminal condition" shows that wages (and prices) just prior to getting out of the zero lower bound would be determined by the money supply at time T. This "terminal condition" can be resolved by backward induction to give me period 0 wages (and prices): w YT 0 k MT s ; t T : (29) 0 s T This is the key implication of the model to assess the role of quantitative easing as it ties the money supply at the time interest rates start rising to wages today and for as long as nominal interest rates remain at the zero lower bound. 8

10 4 Concluding Remarks: Policy Implications First. This simple model I have presented here shows that a temporary increase in the money supply at t 0 will have no e ect unless it a ects the future money supply. The implication here is that quantitative easing can have e ects on prices today, if it changes future money supply not today s money supply. A permanent increase in the money supply will permanently increase all prices and wages in the same proportion in this context. Current money is neutral in the model: it does not a ect any real variable. In a sticky-price version of the model, such an ability to a ect aggregate prices (the price level) will have positive output e ects in the short-run. Crucial here are expectations about future policy (and thus the ability of the central bank to commit). If quantitative easing is expected to be reversed, it may have no e ects on prices and therefore it may not have real e ects on output either. My view is that something along these lines could explain why the actions of the ECB appear less successful than those of the Federal Reserve or the Bank of England. Second. Quantitative easing understood as an expansion of the money supply should be viewed as credible and should be sustained over time for it to have real e ects in the short run. In that case, it can help raise wages (and prices) even at the zero-lower bound to stimulate the economy. In a richer model, this would be re ected in higher in ation expectations and lower real rates. Over the long term, however, interest rates should eventually increase again. The challenge is to determine what should be the optimal expansion of the money supply to ensure that as nominal interest rates lift-o and the Taylor rule comes back, the economy is still credibly anchored around the non-de ationary steady state. I believe that the stable long-term in ation expectations is an indication that the markets perceive the level of accommodation provided in these countries as consistent with a non-de ationary scenario. Third. The implication of the model would be to let interest rates rise before limiting the expansion of the money supply. My concern is that the September FOMC decision may have come "too early" in the U.S. I do not discount other explanations, but I draw attention here to the risk that the decline in long-term in ation expectations seen in the U.S. recently may in fact re ect a loss of credibility of the Fed s policies because the perceived unwinding of quantitative easing came before interest rates started to get back to normal (that is, away from the zero lower bound). Within the simple model presented here, this may have contractionary e ects through lower long-term in ation expectations and may depress current prices. In this sense, the decline in long-term in ation expectations is worrisome. Finally, although the model does not have an international dimension, I think it is plausible that the patterns we see in the data are partly due to spillovers operating through standard trade and nancial linkages or simply through a domino e ect. Although this is a very stylized representation of the economy and of the implications from quantitative easing, my analysis suggests that: (a) Monitoring the developments in in ation expectations (especially long-run in ation expectations) both domestically as well as abroad is warranted. (b) Policy-makers must considering policy option alternatives to keep long-term in ation expectations credibly anchored and avoid unnecessary tightening in the short-run (through lower wages and in ation expectations). In particular, this is all the more relevant if further quantitative easing until interest rates start rising is o the table now. 9

11 References [] Auerbach, Alan J., and Maurice Obstfeld (2005): "The Case for Open-Market Purchases in a Liquidity Trap." American Economic Review, Vol. 95 (), pp [2] Benhabib, Jess, Stephanie Schmitt-Grohé, and Martín Uribe (200): "The Perils of Taylor Rules." Journal of Economic Theory, Vol. 96 (-2), pp [3] Grossman, Valerie, Adrienne Mack, and E. Martínez-García (204): "A Contribution to the Chronology of Turning Points in Global Economic Activity ( )." Globalization and Monetary Policy Institute Working Paper no. 69, January 204. [4] Koenig, Evan (20): "An IS-LM Analysis of the Zero-Bound Problem." Federal Reserve Bank of Dallas Sta Paper No. 3. [5] Krugman, Paul R. (998): "It s Baaack: Japan s Slump and the Return of the Liquidity Trap." Brookings Papers on Economic Activity, Vol. 2, pp [6] John B. Taylor (993): "Discretion Versus Rules in Practice." Carnegie-Rochester Conference Series on Public Policy, Vol. 39, pp