Parallel Digital Currencies and Sticky Prices

Aperennial topic of discussion among scholars and policymakers is how best to think about a benchmark for macroeconomics as it applies to monetary policy. Should the benchmark for policy analysis be the open economy with international interest rate linkages and flexible exchange rates (after all, major economies are in fact open with flexible exchange rates), or should it be the closed economy in which such linkages and exchange rate adjustments are assumed away? Of course, few if any policy makers would seek to guide policy by ignoring capital flows and exchange rates, but in many cases it appears as though the starting point for analysis is the closed‐economy macro model, these days a variant of the dynamic new Keynesian model. Those who start from a closed‐economy framework often have questions about how “openness” influences the analysis. How does the neutral real interest depend on “global” developments? Is the Phillips curve trade‐off between inflation and domestic output better or worse in the open versus the closed economy? Is “potential GDP” a function of global developments, or only of domestic resources available and domestic productivity? Perhaps most important, how—if at all—does openness influence the optimalmonetary policy rule? Is a Taylor rule the rightmonetary policy for an open economy? In 2002 Jordi Gali, Mark Gertler, and I published a paper in the Journal of Monetary Economics that developed a benchmark (at least in ourway of thinking) dynamic two‐country optimizing macro model of optimal monetary policies in the open economy. Our focus in that paper was deriving optimal policy rules in the two‐country model and assessing the gains from international monetary policy cooperation. In that paper, we emphasized the following implications of the model:

The rise of digital currencies may result in domestic parallel currencies. Their exchange rate shocks will present a new challenge for monetary policy. We analyze these issues in a New Keynesian framework, where firms can set prices in one of the available currencies. Price rigidity translates a one-time appreciation of a parallel currency into persistent redistribution towards the dollar sector output and inflation. The persistence lasts longer if the central bank targets "dollar"sector inflation, rather than inflation across all currency sectors. An increase in dollar price rigidity may lead to a decrease rather than an increase of the non-dollar sector.

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In this paper I search for an optimal con�gurations of parameters for variants of the Taylor rule by using an Accurate Second-Order Welfare based method within a fully microfounded Dynamic Stochastic model, with price rigidities, without capital accu- mulation. Money is inserted via a transaction cost function, price rigidities are modelled via quadratic cost of price adjustment. A version of the model with distortionary taxation is also explicitly tested. The model is solved up to Second Order solution. Optimal rules are obtained by maximizing a conditional welfare measure, di¤erently from what has been done in the current literature. Optimal monetary policy functions turn out to be characterized by in�ation targeting parameter lower than in empirical studies. In general, the optimal values for moentary policy parameters depend from the degree of nominal rigidities and from the role of �scal policy. When nominal rigidities are higher, optimal monetary policy becomes more aggressive towards in�ation. With a tigther �scal policy, optimal monetary policy turns out to be less in�ation-aggressive. Moreover, the results show that relying conditional welfare mea- sure avoids the problems related with �rst-order or unconditional welfare measures. Impulse Response functions based on second order model solution show a non-a¢ ne pattern when the economy is hit by shocks of di¤erent magnitude.

Previous articleNext article FreeCommentMarc P. GiannoniMarc P. GiannoniFederal Reserve Bank of Dallas Search for more articles by this author Federal Reserve Bank of DallasPDFPDF PLUSFull Text Add to favoritesDownload CitationTrack CitationsPermissionsReprints Share onFacebookTwitterLinked InRedditEmailQR Code SectionsMoreI. IntroductionSince Phillips (1958), economists have sought to estimate a Phillips curve relationship or a positive relation between inflation, πt, and a measure of the output gap, xt. Although historically such a relationship could be easily detected, the Phillips curve appears to have flattened in the United States more recently. Some authors have suggested that inflation does not depend on slack, that it is largely exogenous. This raises the key question: What changed? The answer to that question is critical for much of macroeconomics and in particular for monetary policy. With most central banks around the world seeking to stabilize inflation around a target level (e.g., 2% in the United States), it is crucial to understand the determinants of inflation and to know whether monetary policy can still affect inflation.Several potential explanations have been provided for the flattening of the Phillips curve. Some have suggested that structural changes in the economy in recent decades have played a significant role (e.g., Duca 2019). In many of models of sticky prices, more rigid prices than in the past or increases in market concentration and pricing power (De Loecker and Eeckhout 2017) could also result in a flattening of the Phillips curve. McLeay and Tenreyro argue instead that monetary policy itself is responsible for the flattening of the Phillips curve. The explanation is simple: If the central bank conducts optimal monetary policy, seeking to minimize deviations of inflation from target and output from potential output, then it should set its policy instruments to increase inflation when output is below potential and vice versa. It follows that optimal policy causes a negative correlation between inflation and the output gap. That negative correlation blurs in turn the positive correlation implied by the Phillips curve, so that in equilibrium, the correlation between inflation and the output gap may be positive, negative, or null, depending on the variability of shocks perturbing either the Phillips curve or the optimal policy relationship. The authors make the point very clearly through a sharp and elegant analysis, in the context of a simple New Keynesian model.After exposing the identification problem in estimating the slope of a Phillips curve, McLeay and Tenreyro propose strategies to estimate the Phillips curve and present evidence of a robust Phillips curve in the United States. This is a very nice and transparent paper that should be read by all of those who are interested in understanding and estimating the Phillips curve.In the remainder of this discussion, I will briefly review the authors’ story in the historical context and will quibble in Section III with the authors’ proposed identification of the Phillips curve, focusing in particular on the role of expectations.II. The StoryA key point of the paper is that one should distinguish between (i) a reduced-form Phillips curve, that is, an empirical relationship between inflation and a measure of the output gap, and (ii) a structural Phillips curve, that is, the underlying relationship between inflation, the output gap, inflation expectations, and possibly other factors, resulting from the firms’ optimal setting of their prices. In the debate about the flattening of the Phillips curve, the two concepts are often mixed, as the structural Phillips curve may be difficult to identify. As the authors make clear, optimal policy can lead to a flattening or even a negative relationship between inflation and the output gap in the reduced-form Phillips curve, even though there is a well-defined positively sloped underlying structural Phillips curve. The authors’ result does not rely on assuming that the policy maker conducts optimal policy under discretion and that it has a quadratic objective function. Consider the standard (structural) New Keynesian Phillips curve (eq. [1] in the paper) that characterizes the trade-off between inflation, πt, and the output gap, xt, faced by the central bank:(1)πt=βEtπt+1+κxt+ut,with a slope κ that is positive by assumption. In the face of “cost-push shocks,” ut, it is generally not possible to stabilize both inflation and the output gap. Suppose that the central bank can control the output gap, for example, via a short-term policy rate; that it observes ut and that it seeks to stabilize inflation at its target (πt=0) as in the case of a pure inflation-targeting regime. Optimal policy would then imply that the output gap respond negatively to the cost-push shockxt=−κ−1utso that, in equilibrium, inflation and hence inflation expectations are completely stabilized around the inflation target:πt=0,Etπt+1=0,as illustrated by the x-axis in figure 1 (which is adapted from figure 3 in the paper). The implication of this policy is that inflation would be uncorrelated swith the output gap. In other words, even though the underlying structural Phillips curve implies a positive relationship between inflation and the output gap, inflation targeting gives rise to a flat reduced-form Phillips curve relationship, with inflation apparently unrelated to the output gap.Fig. 1. Structural Phillips curve and optimal policyView Large ImageDownload PowerPointIn the case that the central bank cares both about inflation and output gap deviations from target, as the authors point out, optimal policy under discretion gives rise to a negative relationship between inflation and the output gap. Indeed, when the central bank seeks to minimize the loss function:(2)E0∑t=0∞βt[πt2+λxt2],subject to the behavior of the private sector represented by the structural Phillips curve (eq. [1]), optimal policy under discretion, that is, taking private sector expectations Etπt+j, Etxt+j as given, results in the optimal targeting rule:(3)πt=−λκxt,which states that the central bank seeks to increase inflation when output is below potential and vice versa, as illustrated by the downward-sloping gray line in figure 1. As exogenous shocks ut shift the Phillips curve but not the optimal policy relation (eq. [2]), equilibrium realizations of inflation and the output gap draw not the Phillips curve but rather the optimal target criterion (eq. [2]). In equilibrium, πt, xt depend only on utπt=λκ2+λ(1−βρ)ut,xt=−κκ2+λ(1−βρ)ut,where ρ is the degree of serial correlation in ut so that the covariance between inflation and the output gapcov(πt,xt)=−λκ(κ2+λ(1−βρ))2var(ut)<0is necessarily, and the correlation corr(πt,xt)=−1.A. Targeting Rule versus Taylor RuleSome readers may find a target criterion of the form (eq. [3]) to be unrealistic. We should however note that its characterization of monetary policy is not too different from that under a conventional Taylor rule. Indeed, the optimal target criterion (eq. [3]) implies that the policy rate it is set so as to satisfy πt+(λ/κ)xt=0. The policy rate can thus be related to inflation and the output gap according to a conventional Taylor-type rule:it=ϕ(πt+λκxt)with a large coefficient ϕ(→∞). If, in addition, policy makers care to also stabilize other variables such as the interest rate, then the optimal policy response to inflation and the output gap would likely be of a similar form but with a smaller coefficient 0<ϕ<∞, and the optimal interest rate would in addition respond to these other variables (e.g., the lagged interest rate).B. Historical ContextAs the authors recognize, the flattening or disappearance of an empirical relationship such as the reduced-form Phillips curve as a consequence of a successful monetary policy is an old idea that goes back at least to Kareken and Solow (1963), who emphasized that if monetary policy succeeds at offsetting all shocks that affect income, then we would observe fluctuations in money growth and a perfectly steady path for income. Similar ideas have been reinforced and generalized by many authors since then, most prominently with Goodhart’s “law” (1981)1 and the Lucas (1976) critique,2 and it is still mentioned in recent work (e.g., Hooper, Mishkin, and Sufi 2019). Unfortunately, it appears that much of the profession is quick to forget these powerful lessons when the empirical relationship between two key macroeconomic variables appears to have weakened, and so it is important that McLeay and Tenreyro remind us of this. As we learned from Lucas (1976), these lessons do not apply merely to relationships between two macroeconomic variables; they can be more pervasive. For instance, when Boivin and Giannoni (2006) documented the fact that impulse response functions of inflation and output to an unexpected 25 basis points change in the federal funds rate had become more muted in the post-1980 period, compared with the 1960–80 period, they asked whether this was due to a structural change in the economy (such as a flattening of the structural Phillips curve or a diminished sensitivity of economic activity to interest rate changes) or to a change in policy itself; they found that a more aggressive stance of policy toward inflation stabilization in the post-1980 period could explain most if not all of the change in estimated impulse response functions.III. Identifying the Structural Phillips CurveAside from making it very clear that one should not conclude that the Phillips curve has disappeared based on correlations between inflation and the output gap, or simple regressions, McLeay and Tenreyro describe in simple terms the identification problem, propose ways to address it, and provide evidence that there is a structural Phillips curve with positive slope between inflation and the output gap. As figure 1 illustrates, cost-push shocks ut help trace the policy rule, not the Phillips curve. If the policy rule is itself subject to disturbances et so that it becomes(4)πt=−λκxt−et,then fluctuations in et may help trace the structural Phillips curve. The identification problem arises when we face shocks to both the policy (targeting) rule and the Phillips curve.Focusing on equations (1) and (4) provides a transparent way of characterizing the identification problem, in a near-static environment (for given inflation expectations), in which the Phillips curve implies a positive contemporaneous relation between πt and xt, whereas policy implies a negative contemporaneous relation between these two variables. If only we could control for the cost-push shocks ut, then shocks to the policy rule (represented by the downward-sloping gray line in fig. 1) would trace out the structural Phillips curve. Similarly, the identification problem can be partly addressed in the case of regional Phillips curve subject to region-specific cost-push shocks, but with monetary policy responding to aggregate economic conditions, as McLeay and Tenreyro as well as other recent studies have proposed (Hooper et al. 2019).A. Difficulties with Identification via Disturbances to the Optimal Target CriterionAlthough the authors make a strong case for identifying the Phillips curve using equations (1) and (4), I am concerned that it may not be as easy to identify the Phillips curve in more complicated setups, in particular when the policy rule disturbances et are not exogenous and depend on other variables, including variables affecting the residuals ut themselves, or if the residuals ut capture more than exogenous cost-push shocks, indeed if they depend on variables that also shift the policy rule.To illustrate this point, I consider a few examples:• Take again the simple Phillips curve (eq. [1]) and the objective function (eq. [2]), but assume that optimal policy is conducted under commitment. Then, as pointed out by McLeay and Tenreyro, optimal policy can be represented by an optimal target criterion of the form (eq. [4]) with et=−(λ/κ)xt−1. If the cost-push shock is serially correlated, then et and ut are correlated. A suitable instrument is thus needed.• Assume instead that inflation involves some inertia as modeled, for example, in Christiano, Eichenbaum, and Evans (2005), and as appears realistic in the data. Then, as shown in Giannoni and Woodford (2004, eq. [12]), lagged inflation appears both in the Phillips curve (eq. [1]) and in the optimal target criterion (eq. [4]), so that et and ut would both be functions of lagged inflation.• When the representative household faces habit persistence in expenditures, then again, as shown in Giannoni and Woodford (2004, eq. [47] and eq. [53]), both the Phillips curve and the optimal target criterion involve the lagged output gap, so that ut and et in equations (1) and (4) would be both functions of xt−1 and hence would be correlated.• Suppose, alternatively, that the policy maker faces a Phillips curve of the form (eq. [1]) but cares about interest rate variability in addition to the two other terms entering the objective function (eq. [2]). Then, the optimal target criterion involves a relationship between current and forecasts of inflation, output gaps, as well as lags of the output gap and interest rates (see Giannoni and Woodford 2004; eq. [22]). Again, that would imply that the terms ut and et in equations (1) and (4) would be correlated.Similar concerns arise when the model involves both price and wage stickiness, so that a Phillips curve arises for price and for wage inflation; when monetary policy actions have delayed effects on macroeconomic variables, so that optimal policy depends on expectations of future inflation and output gaps; and so on.B. Identifying the Phillips Curve: Static versus DynamicAlthough McLeay and Tenreyro make an important conceptual point and provide a very intuitive way of characterizing the difficulty in identifying the Phillips curve in a near-static framework, I am skeptical that one can fully recover the Phillips curve without taking a stronger stance on dynamic relationships linking the key macroeconomic variables. The simple New Keynesian Phillips curve considered is an invaluable tool to develop intuition, but much of the empirical literature suggests that inflation responds to measures of slack in a more inertial fashion. Similarly, whereas the simple model considered assumes that policy makers can instantaneously affect economic activity and the output gap, empirical evidence suggests the effects are more sluggish. (If not, it would be difficult to explain why inflation has been below its target and economic activity has been below estimates of its potential for so many years following the Great Recession.) This implies that the dynamic relationship between inflation and the output gap is more complex than described by the simple New Keynesian model and that it is important to properly model these dynamics to identify a Phillips curve.Estimated dynamic stochastic general equilibrium (DSGE) models are a valuable tool to characterize the joint dynamics of key macroeconomic variables and thus of the complex interactions between the Phillips curve and policy. In such dynamic models, inflation expectations play a key role, and a monetary policy aimed at stabilizing inflation and hence inflation expectations does also imply a flattening of the reduced-form Phillips curve. A potential downside of such fully specified models is that they are necessarily misspecified. A key question, then, is whether such models can explain important recent episodes. In particular, Del Negro, Giannoni, and Schorfheide (2015) study whether a standard DSGE model along the lines of Christiano et al. (2005) and Smets and Wouters (2007) augmented with financial frictions and estimated with data up to 2008Q3 can explain the US macroeconomic behavior during and after the Great Recession. They find that as soon as credit spreads jump in the fall of 2008, the model successfully predicts the sharp contraction in activity and the modest and protracted decline in inflation, as shown in figure 2. They also find that data on credit spreads and inflation expectations, in addition to the standard data series used by, for example, Smets and Wouters (2007), are important in properly characterizing the state of the economy.Fig. 2. Dynamic stochastic general equilibrium (DSGE) model forecast of gross domestic product (GDP) growth, the output gap, and GDP deflator inflation, based on the model in Del Negro et al. (2015). Out-of-sample forecast starting in 2008Q4 (dotted lines); data used in estimation (solid lines); and ex post realization of the data (dashed lines).View Large ImageDownload PowerPointTo understand why inflation does not collapse given the sharp drop in output, it is useful to consider a simplified version of the forward-looking Phillips curve considered in the model. That simplified Phillips curve, which is similar to equation (1)—except that xt is replaced with real marginal costs—implies that inflation does not depend only on the current gap (or marginal cost), but on the entire path of future gaps:πt=∑j=0∞βjEt[κxt+j︸gaps+ut+j︸mark-up shocks].It follows that inflation and inflation expectations in the model remain well anchored, despite the sharp collapse in output, because monetary policy is expected to be aggressive enough to close the gaps in the future.Similarly to McLeay and Tenreyro, although the model includes a structural Phillips curve that involves a positive relationship between inflation and the output gap, inflation was predicted to move relatively little in the face of the output collapse. However, in contrast to McLeay and Tenreyro, according to the DSGE model, it was not the contemporaneous monetary stimulus (at the end of 2008 and in early 2009) that helped stabilize inflation; indeed, short-term nominal rates were constrained by the zero lower bound at that time. Instead, the expectation of future stimulus induced expectations of closing output gaps in the future and hence helped keep inflation near its target.IV. ConclusionMcLeay and Tenreyro have written a very nice paper that clearly and elegantly exposes the identification problem in estimating the slope of a Phillips curve when policy makers seek to stabilize inflation and/or the output gap. They propose interesting strategies to estimate the Phillips curve and present evidence of a robust Phillips curve in the United States. The simplicity of the framework considered allows the authors to provide numerous insights. I have expressed some reservations about the ability to generalize the results beyond the current framework, in particular when one faces more complex dynamic interactions between inflation, inflation expectations, activity, and policy. In more complicated environments, I suspect that DSGE model estimation remains necessary to better characterize the joint dynamics of macro variables, and the role of expectations.Endnotes. Author email address: Giannoni ([email protected]). The views expressed in this discussion are those of the author and do not necessarily represent those of the Federal Reserve Bank of Dallas or the Federal Reserve System. For acknowledgments, sources of research support, and disclosure of the author’s material financial relationships, if any, please see https://www.nber.org/chapters/c14246.ack.1. Goodhart (1981, 116): “Any observed statistical regularity will tend to collapse once pressure is placed upon it for control purposes.”2. Lucas (1976, 40–41): “A change in policy [parameters] affects the behavior of the system in two ways: first by altering the time series behavior of [policy variables]; second by leading to modification of the behavioral parameters … governing the rest of the system… . It follows that any change in policy will systematically alter the structure of econometric models.”ReferencesBoivin, J., and M. P. Giannoni. 2006. “Has Monetary Policy Become More Effective?” Review of Economics and Statistics 88 (3): 445–62.First citation in articleCrossrefGoogle ScholarChristiano, L. J., M. Eichenbaum, and C. Evans. 2005. “Nominal Rigidities and the Dynamic Effect of a Shock to Monetary Policy.” Journal of Political Economy 113 (1): 1–45.First citation in articleLinkGoogle ScholarDe Loecker, J., and J. Eeckhout. 2017. “The Rise of Market Power and the Macroeconomic Implications.” Working Paper no. 23687, NBER, Cambridge, MA.First citation in articleGoogle ScholarDel Negro, M., M. P. Giannoni, and F. Schorfheide. 2015. “Inflation in the Great Recession and New Keynesian Models.” American Economic Journal: Macroeconomics 7 (1): 168–96. https://doi.org/10.1257/mac.20140097.First citation in articleCrossrefGoogle ScholarDuca, J. V. 2019. “Inflation and the Gig Economy: Have the Rise of Online Retailing and Self-Employment Disrupted the Phillips Curve?” Dallas Fed Working Paper no. 1814. https://doi.org/10.24149/wp1814.First citation in articleGoogle ScholarGiannoni, M. P., and M. Woodford. 2004. “Optimal Inflation Targeting Rules.” In The Inflation-Targeting Debate, ed. B. Bernanke and M. Woodford, 93–162. Chicago: University of Chicago Press.First citation in articleGoogle ScholarGoodhart, C. 1981. “Problems of Monetary Management: The U.K. Experience.” In Inflation, Depression, and Economic Policy in the West, ed. Anthony S. Courakis, 111–46. Totowa, NJ: Barnes & Noble.First citation in articleGoogle ScholarHooper, P., F. S. Mishkin, and A. Sufi. 2019. “Prospects for Inflation in a High Pressure Economy: Is the Phillips Curve Dead or Is It Just Hibernating?” Working Paper no. 25792, NBER, Cambridge, MA.First citation in articleGoogle ScholarKareken, John H., and Robert M. Solow. 1963. “Lags in Monetary Policy.” In Stabilization Policies, ed. E. Cary Brown, 14–96. New York: Prentice Hall.First citation in articleGoogle ScholarLucas, R. E., Jr. 1976. “Econometric Policy Evaluation: A Critique.” Carnegie-Rochester Conference Series on Public Policy 1:19–46.First citation in articleCrossrefGoogle ScholarPhillips, A. W. 1958. “The Relation between Unemployment and the Rate of Change of Money Wage Rates in the United Kingdom, 1861–1957.” Economica 25 (100): 283–99. https://doi.org/10.2307/2550759.First citation in articleGoogle ScholarSmets, F., and R. Wouters. 2007. “Shocks and Frictions in US Business Cycles: A Bayesian DSGE Approach.” American Economic Review 97 (3): 586–606. https://doi.org/10.1257/aer.97.3.586.First citation in articleCrossrefGoogle Scholar Previous articleNext article DetailsFiguresReferencesCited by NBER Macroeconomics Annual Volume 342019 Sponsored by the National Bureau of Economic Research (NBER) Article DOIhttps://doi.org/10.1086/707182 © 2020 by National Bureau of Economic Research. All rights reserved.PDF download Crossref reports no articles citing this article.

Optimal monetary policy with the cost channel

IntroductionRecent Developments in Monetary Macroeconomics David Altig The contents of this volume hardly require explanation beyond its title: "Recent Developments in Monetary Macroeconomics." Our intent for the conference was to collect a set of papers reflecting the cutting edge of applied monetary macroeconomics. As befitting such an ambitious-sounding goal, the contributions are wide ranging. For purposes of this brief introduction, however, we might organize the papers as answers to three questions. (1) What is the "optimal" Taylor rule? (2) Are "New Keynesian" or "New Neoclassical Synthesis" models the final word on the monetary transmission mechanism? (3) Is there a role for money in the conduct of monetary policy? What is the "Optimal" Taylor Rule The inclusion of the Taylor rule issue is almost a prerequisite for any collection of papers purporting to survey recent developments in monetary macroeconomics. In policy discussions, the Taylor rule is ubiquitous, and it is currently the choice among alternative specifications of central bank behavior. More precisely, perhaps, the general form of the Taylor rule is the choice, as it has come to represent the general class of equations that relate the federal funds rate to some measure of an output gap and inflation rate. There is substantially less unanimity about whether output gaps and inflation rates should be past, present, or (expected) future values, whether past values of the funds rate need to be included, and what are the appropriate magnitudes of the responses to each of these measures. Marc Giannoni and Michael Woodford offer the natural approach to addressing the dispute: find the representation that is optimal within the framework being employed for policy analysis. The model in question here is essentially a derivative of the "New Neoclassical Synthesis" class of models that are currently the workhorses of most monetary policy analyses among academic and central bank staffs alike. Their approach to discovering the optimal policy within this structure has the flavor of [End Page 1039] the "Ramsey problem" familiar from optimal tax policy, although with the strong requirement that the derived policy rule be "robustly optimal": it must support the optimal equilibrium no matter what the distribution of disturbances the model policymakers face. Giannoni and Woodford offer two essential lessons. First, whether optimal policy incorporates forecasts of future price-level growth or output gaps depend critically on the dynamics of the inflation rate. If the adjustment of the price-level to shocks is inertial, then optimal policy necessarily depends on forecasts of future inflation. Second, the response of the funds rate to its own past is inertial. In fact, it is super-inertial, meaning that (all else equal), the contemporaneous funds rate responds more than one-for-one with the lagged value of the funds rate (and lagged changes in the rate). The proposition that monetary authorities ought to aggressively respond to lagged values of the funds rate also arises in the papers by Jess Benhabib, Stephanie Schmitt-Grohé, and Martín Uribe, and George Evans and Seppo Honkapohja. In the latter case, the authors consolidate and expand on their well-known work on learning dynamics. A central contribution of the work presented in this article is the notion that convergence to a unique rational expectations equilibrium under learning, as well as the stability of that equilibrium, serves as basis for the choice (or rejection) of an optimal policy formulation. An apparent lesson from Evans and Honkapohja's analysis is that the learnability criterion prescribes a policy rule that differs in some important ways from the conventional wisdom coming from analyses that invoke the Taylor rule in a pure rational expectations environment. In particular, they conclude that the optimal policy rule in the environment they consider requires the monetary authority to respond directly to private-sector expectations. The environment they consider is essentially the same as in Giannoni and Woodford, with the exception of the central bank's assumed loss function: Giannoni and Woodford assume a preference for interest rate smoothing, Evans and Honkapohja do not. In his comments, John Duffy points out that the introduction of interest-smoothing motive yields an optimal policy rule under learning that is much closer to the conventional view. In particular, it does not require...

Optimal monetary policy in a currency union with interest rate spreads

Debt Stabilization Bias and the Taylor Principle: Optimal Policy in a New Keynesian Model with Government Debt and Inflation Persistence

We analyse optimal monetary and fiscal policy in a New-Keynesian model with public debt and inflation persistence. Leith and Wren-Lewis (2007) have shown that optimal discretionary policy is subject to a 'debt stabilization bias' which requires debt to be returned to its pre-shock level. This finding has two important implications for optimal discretionary policy. Firstly, as Leith and Wren-Lewis have shown, optimal monetary policy in an economy with high steady-state debt cuts the interest rate in response to a cost-push shock - and therefore violates the Taylor principle. We show that this striking result is not true with high degrees of inflation persistence. Secondly, we show that optimal fiscal policy is more active under discretion than commitment at all degrees of inflation persistence and all levels of debt.

We consider optimal monetary policy in a model that integrates credit frictions in the standard New Keynesian model with sticky prices and wages as well as adjustment costs of capital. Different from traditional models with credit frictions, such as those by Carlstrom and Fuerst (Econ Theory 12:583–597, 1998), our model is able to generate an anti-cyclical external finance premium as observed empirically in the U.S. economy. Monetary policy is characterized by a Taylor rule according to which the nominal interest rate is set as a function of the deviation of the inflation rate from its target rate, the output gap, and Tobin’s q. The latter is measured by the relative price of newly installed capital. We show that monetary policy should optimally decrease interest rates with higher capital prices. However, the consideration of Tobin’s q implies only small welfare effects. These results are robust with respect to a more general Epstein and Zin (Econometrica 57:937–969, 1989) welfare specification and to exogenous shifts to both the atemporal marginal rate of substitution between consumption and leisure as well as the households’ discounting behavior.

Previous articleNext article FreeCommentBennett T. McCallumBennett T. McCallumCarnegie Mellon University and NBER Search for more articles by this author Carnegie Mellon University and NBERPDFPDF PLUSFull Text Add to favoritesDownload CitationTrack CitationsPermissionsReprints Share onFacebookTwitterLinked InRedditEmailQR Code SectionsMoreI. IntroductionThis is an interesting and challenging paper, in which Atkeson and Kehoe put forth a very strong critique of current mainstream monetary policy analysis. Monetary economists have, of course, been rather pleased with the development of their subject over the past 10–15 years, current U.S. policy difficulties notwithstanding. Indeed, the tone of a prominent recent expository paper by my colleague, Marvin Goodfriend, is somewhat triumphal in spirit.1 The spirit of the Atkeson and Kehoe paper, by contrast, is conveyed by a recent publication of theirs, together with coauthor Fernando Alvarez, which bears the title “If Exchange Rates Are Random Walks, Then Almost Everything We Say about Monetary Policy Is Wrong” (Alvarez, Atkeson, and Kehoe 2007). That paper focuses on exchange rate failures, whereas the current one stresses the term structure of interest rates, but the line of argument is basically the same.The title of the 2007 paper leads me rather naturally to ask myself what it is that I would say in answer to the implied question, “What important things do monetary economists really know—or at least believe—about monetary policy?” My own answer to that question would go along the following lines: (i) We believe that if the monetary authority keeps monetary policy expansionary for a substantial length of time, the main effect will be to generate a higher inflation rate than would have prevailed otherwise, with little or no overall effect on aggregate production and employment. (ii) Nominal interest rates will be higher, also, with real rates being affected very little. (iii) If, however, the monetary authority changes policy unexpectedly and abruptly in an expansionary direction, there will most likely be an expansion in aggregate output and employment—but it will be only temporary. (iv) If these changes are in the direction of tighter policy, the signs of the above‐mentioned effects will be reversed. (v) In particular, the monetary authority has the power to generate a recession, in which output and then the inflation rate will fall. (vi) The precise nature of the mechanism that generates the real effects of monetary policy changes of this type is not very well understood. Then, if my questioner had not wandered away in boredom, I would want to add something like the following: (vii) The foregoing points refer to an expansionary or contractionary monetary policy stance—loose or tight—but how is this measured? Well, a sustained high growth rate of the stock of base money will (under most institutional arrangements) be expansionary, but matters are a little less clear‐cut when the central bank actually carries out its policy by manipulating overnight interest rates. Nevertheless, there are ways in which we can characterize tighter versus looser policy in terms of interest rate rules by reference to the implied target inflation rate, the strength of responses to deviations from target, and so forth.Now, I suspect that Atkeson and Kehoe probably do not disagree with most of these statements as to what monetary economists know (or believe), even on a substantive basis.2 But their title of the current paper, as distinct from the 2007 item, refers to a need for a new approach to monetary policy analysis. So let us turn to a consideration of what today’s mainstream approach is. As it happens there is a short statement of that type, in a paper of mine, that gives the following description. The approach is one in which “the researcher specifies a quantitative macroeconomic model that is intended to be structural (invariant to policy changes) and consistent with both theory and data. Then, by stochastic simulation or analytical means, he determines how crucial variables (such as inflation and the output gap) behave on average under various alternative policy rules. Usually, rational expectations (RE) is assumed in both stages. Evaluation of the different outcomes can be accomplished by means of an optimal control exercise, or by reference to an explicit loss function, or left to the judgment (i.e., loss function) of the implied policymaker” (McCallum 2001, 258). Here, too, I doubt that Atkeson and Kehoe have any major disagreement with this general approach. What they do disagree with, if I understand at all, is the model that is typically used in recent work and taken to be structural.3In a sense my last statement could be regarded as merely quibbling over their title. But the point seems to be one of some importance: if Atkeson and Kehoe can generate an optimizing model that incorporates reliable, quantitative estimates reflecting time‐varying “risk” (i.e., state‐dependent variances and covariances) and endogenously explains inflation and output fluctuations, then monetary economists would presumably be happy to incorporate such features in their models—and would not consider this to reflect any basically new approach. Be that as it may, in what follows I will briefly review their featured empirical regularities, discuss issues concerning their suggested modeling strategy, and provide a brief conclusion.1See “How the World Achieved Consensus on Monetary Policy” (Goodfriend 2007).2They would probably grumble, justifiably, about the vagueness of point vii.3McCallum (2001, 258) goes on to say: “There is also considerable agreement about the general, broad structure of the macroeconomic model to be used.” Atkeson and Kehoe clearly would not share in this agreement.II. Empirical RegularitiesAtkeson and Kehoe begin, in Section I, with “four key regularities regarding the dynamics of interest rates and risk that we use to guide our construction” of a model and its pricing kernel. The first two pertain to a principal components analysis of a collection of interest rates, specifically, a 3‐month T‐bill rate and zero‐coupon yields on U.S. Treasury securities with k‐year maturities for $$k=1,$$ 2, …, 13. Time series observations are monthly over 1946.12–2007.12. The first regularity is that “the first principal component accounts for over 90% of the variance of the short rate [i.e., the 3‐month rate].” The second regularity is that “the second principal component is very similar to the yield spread between the short rate and the long [i.e., 13‐year] rate.” Having demonstrated these facts—and also that the first component is correlated even more strongly with the long rate—the authors henceforth use just the short and long rates.More substantively (and more questionably), the third and fourth regularities pertain to expected excess returns in the context of term structure and international exchange rate contexts. Specifically, movements in yield spreads and exchange rate premia are “associated with movements in risk.” The way in which these regularities might be regarded by some readers as questionable is that, in many studies, “risk” is operationally the name that is given to differentials in expected returns that the analyst’s model is not able to explain.Later in the paper, in Section V.A, Atkeson and Kehoe plot short‐rate and long‐rate time series for the United States over an extended period from 1836 through 2007. In addition, they include analogous plots for the United Kingdom, France, Germany, and the Netherlands. In all of these, the fluctuations of the long rate represent “a much smaller fraction of overall fluctuations in the short rate than they are in the postwar period.” Thus, they state: “A central question in the analysis of monetary policy at the secular level then is, What institutional changes led to this pattern?” In the preliminary version of this comment, I responded to a more pointed and strongly emphasized version of this query by stating that, to me, it is no surprise that expectations of future interest rates became unanchored during the post–World War II period, because, to again quote myself,[the] collapse of the Bretton Woods system created, for the first time in history, a situation in which the world’s leading central banks were responsible for conducting monetary policy without an externally imposed monetary standard (often termed a “nominal anchor”). Previously, central banks had normally operated under the constraint of some metallic standard (e.g., a gold or silver standard), with wartime departures being understood to be temporary, i.e., of limited duration. Some readers might not think of the Bretton Woods system as one incorporating a metallic standard, but by design it certainly was, since the values of all other currencies were pegged to the U.S. dollar and the latter was pegged to gold at $35 per ounce. (McCallum 1999, 175–76)All in all, it seems that there is no difficulty in understanding why an altered monetary policy regime generated different expectations regarding inflation and therefore future short interest rates in the post–World War II era. The variability in long rates during the 1960s developed as market participants began to see that the United States was not going to be bound by its commitment to maintain the $35 per ounce price of gold. Then the variability jumps up around the time of the Bretton Woods collapse in 1971—see Atkeson and Kehoe’s figures 6A–6E—and continues to rise into the Volcker disinflation that was painful (with extremely high nominal interest rates) but that ultimately succeeded in restoring some semblance of a nominal anchor.What about the return to stability that may have occurred around 1990? That year is, of course, the year in which the first central bank (New Zealand) officially adopted a monetary policy regime of “inflation targeting” (IT). At that time, this was taken to mean a policy whose only objective was a low and stable inflation rate. Since then, the IT term has come to be applied to regimes that give more weight to output/employment stabilization, but most monetary economists understand it as continuing to emphasize, as the primary goal, inflation control. So again the timing is about right for the possible recovery of anchored expectations that the first empirical regularity is said to reflect.To this general line of argument, Atkeson and Kehoe object: “But this answer is, at best, superficial. In the prewar era, countries chose to be on the gold standard most of the time and chose to leave it when it suited their purposes. Thus, the relevant questions are, rather, What deeper forces led agents to have confidence that their governments would choose stable policy over the long term? And what forces led them to lose this confidence after World War II? Only if we can quantitatively account for this history can we give advice on how to avoid another great inflation.”In this regard it must be said that I consider an explanation of the evolution of beliefs regarding the monetary standard, held by citizens of the United States, Great Britain, Germany, and so forth, to be somewhat beyond the scope of monetary policy analysts. To think about this issue, one must recognize that historically “the gold standard” required not just that the monetary authority would stand ready to exchange gold and currency at a specified rate but also that this rate should be unchanged “forever.” That arrangement made it such that severe inflation would not occur—even the major historical gold discoveries did not generate sustained inflation on the order of 10% per year—but it did generate more cyclical instability of real variables than we have had in the postwar era. Could policy of that type win popular support in today’s environment in the United States? If not, which would be my answer, then we need an entire unified social science to provide an explanation at “a deeper level.” And such an explanation—which would need to emphasize enormous developments in the media, extensions of suffrage, evolution of religious beliefs, attitudes toward the role of government, and so on—would not be of much help to central bankers. Let us turn then to monetary policy analysis considered more narrowly.III. Basic AnalysisThe heart of Atkeson and Kehoe’s paper is a recommended response to the third and fourth of the regularities mentioned above, that is, that measured excess returns on multiperiod bonds fluctuate strongly with yield spreads for bonds of different maturities and for international exchange rates. These regularities are translated by Atkeson and Kehoe into an argument that the consumption Euler equation, some version of which (often termed an expectational IS equation) is one basic ingredient of current macro‐monetary models, performs very poorly empirically. This is, of course, true for the simplest versions, but that problem has been widely recognized by monetary economists. A nice overview of empirical weaknesses of so‐called New Keynesian models was provided some years ago in a working paper by Richard Dennis (2003), which is briefly and nontechnically summarized in Dennis (2004). (The weaknesses discussed there relate to the Calvo‐style price adjustment relation, as well as the consumption Euler equation.) Dennis distinguishes between the bare‐bones “canonical model” and a “hybrid” version that adds habit formation in consumption behavior to the basic consumption‐saving relationship and also adds a somewhat dubious dependence on lagged inflation to the basic Calvo price adjustment relation. He recognizes, following Estrella and Fuhrer (2002), that “the problem with the canonical model is that the behavior of output, consumption, prices, and interest rates suggested by the model are fundamentally at odds with observed data” (Dennis 2004, 1). The hybrid model performs better, in terms of matching quarterly data, but “there are a number of areas where the hybrid model’s responses differ importantly from” impulse responses of an identified vector autoregression (VAR; Dennis 2004, 3).The point here is that monetary economists are quite aware that current models, even with elaborations of the type utilized by Christiano, Eichenbaum, and Evans (2005) or Smets and Wouters (2007), have empirical weaknesses, and they have been active in trying to eliminate these problems by improved specification. One pertinent and recent example concerns the discouraging results reported by Canzoneri, Cumby, and Diba (2007), that is, that inclusion of habit formation in consumption behavior unrealistically increases the variability of interest rates.4 Subsequent results by Collard and Dellas (2007) indicate, however, that this deterioration obtains when the household utility function is taken to be additively separable in consumption and leisure. If instead consumption and leisure enter the function in a Cobb‐Douglas manner, then inclusion of habit results in an improved—not worsened—match of the model’s interest rate variability to that of the data.I might also remark that Atkeson and Kehoe’s way of considering the empirical failure of the Euler equation seems questionable. Specifically, they discuss the relationship in a manner that would be appropriate if the role of this equation were to explain movements in nominal interest rates of various maturities. In fact, however, the role of this equation in standard monetary policy models is to explain consumption in response to (real) interest rates and expected future consumption (and, in habit specifications, lagged consumption). No mention of the adequacy or inadequacy of the standard model’s properties with regard to consumption is provided.5Be that as it may, it is essential to consider the analytical heart of Atkeson and Kehoe's paper, which is their presentation of “a simple model of the pricing kernel that is consistent with these [observed] dynamics” pertaining to interest rates. For the one‐period nominal interest rate, it in their notation, the pricing kernel mt+1 is an unobservable random variable that is generated by a stochastic process such that the interest rate it can be determined by a relation of the form $$i_{t}=-\mathrm{log}\,E_{t}\mathrm{exp}\,( m_{t+1}) .$$ Assuming conditional lognormality, then, we have (1)it=−Emt+1−0.5Vartmt+1. Except for lognormality, the content of their model for it is then the specification of the stochastic process generating mt+1. They take it to be (2)−mt+1=δ+z1t+σ1ε1t+1=1−λ2/2z2t+z2t0.5λε2t+1+σ3ε3t+1, where $$\varepsilon _{1t},$$ $$\varepsilon _{2t},$$ and $$\varepsilon _{3t}$$ are independent, standard normal, white‐noise innovations and where (3)z1t+1=z1t+σ1ε1t+1. (4)z2t+1=1−φθ+φz2t+z2t0.5σ2ε2t+1. These processes are chosen with an eye to their implications for the term structure via the relation (5)1=Etexpmt+1+pt+1k−1, which characterizes an absence of arbitrage possibilities for k‐period bonds with prices, $$p^{k-1}_{t+1}$$. From these prices the analyst can calculate term structure measures.Finally, Atkeson and Kehoe calibrate the model by assuming that $$\lambda =\sqrt{2}$$, $$\varphi =0.99,$$ and $$\sigma _{2}=0\mathrm{.}\,017$$. This specification suffices, they report, to generate interest rates of different maturities such that the term structure features long and short rates that possess properties that have the general characteristics found in their exploration of monthly data for rates of various maturities in the U.S. data.How does this model compare in specification with the standard three‐equation framework used in recent years to model one‐period interest rates, consumption (and/or output), and inflation by Clarida, Gali, and Gertler (1999), McCallum (2001), Woodford (2003, 238–47), and dozens of other monetary economists? That framework, as is well known, consists of (i) a consumption Euler equation (aka expectational IS relation), (ii) a price adjustment relation (usually of the Calvo variety), and (iii) a monetary policy rule that specifies adjustments of the one‐period nominal policy rate it to its determinants, which include the steady state real interest rate, the central bank’s inflation target, departures of inflation from target, and departures of output from its natural (flexible price) rate. (The lagged rate it‐1 is often included as well to represent smoothing.) This framework implicitly adopts the expectations theory of the term structure, which is known to be inconsistent with the data. Notable examples of larger models that include more variables and equations but that have the same basic underlying logic are provided by Christiano et al. (2005) and Smets and Wouters (2007).One aspect of the comparison is that the Atkeson‐Kehoe model, since it pertains to an “endowment economy,” implicitly assumes that price level adjustments are complete within each period so that output is always equal to its (exogenous) natural rate, flexible price value. Only a degenerate version of the Calvo equation component of the standard model is therefore present. That removes one endogenous variable, output/consumption. For some purposes, a flexible price model can be useful for monetary policy principles, as in Woodford (2003, chap. 2). But Atkeson and Kehoe also treat inflation as exogenous. Thus, there is no possibility remaining for conducting monetary policy analysis, and it is not determined by central bank behavior. Those features are consistent with their expressed view that the central bank “simply responds to exogenous changes in real risk—specifically, to exogenous changes in the conditional variance of the real pricing kernel—with the aim of maintaining inflation close to a target level.” But this seems highly unsatisfactory. It is probably true that a substantial portion of the meeting‐to‐meeting variations in the federal funds rate in the United States represents adjustments that are responses to changes in real rates that are brought about by changes in tastes, technology, shocks from abroad, and even perhaps some random behavioral errors by private agents. In fact, this is implied by much of the analysis that represents today’s mainstream monetary policy analysis—see, for example, Woodford (2003, and But the modeling approach suggested by Atkeson and Kehoe that the its for a random that is it no in a no is provided that their model would do a of matching data on much less two variables as endogenous and by central bank by a policy rule for a variable, the model is not in for monetary et al. (2007) paper is by Atkeson and and Kehoe to believe that standard have Euler equations that include no term reflecting and Kehoe are to say that the Euler equation specification in many monetary models does not well empirically. In addition, their specification of stochastic processes for the and variables that yield a pricing kernel that term structure features that the data in important ways is and They in that models in which conditional variances of returns are variable provide an possibility for improved model specification. This is not of course, and does not of inflation and output as exogenous or to a model that leads to their highly about the nature of monetary policy in the United States (and, other and currency is a of the monetary policy that term structure that pricing with time‐varying risk premia in models along with endogenous price and monetary policy rules. Some leading examples are provided by and and et al. (2007), and These have beyond Atkeson and Kehoe in to models that the term structure regularities maintaining a framework for monetary policy analysis. the approach time‐varying conditional is not the only one of as the Collard and Dellas (2007) example In I by of the Atkeson and Kehoe critique of some features of today’s New Keynesian monetary policy models, but I their current to be in essential their of U.S. monetary policy to be and their critique of current monetary policy analysis to be a brief see Atkeson, and 2007. “If Exchange Rates Are Random Walks, Then Almost Everything We Say about Monetary Policy Is and in Cumby, and T. 2007. and of Monetary in Eichenbaum, and and the of a to Monetary of in Gali, and of Monetary A New Keynesian of in and 2007. and Monetary paper, of in Keynesian Empirical of in Keynesian and to the of in and of a of in and 2007. with of in and McCallum and the of of Monetary in 2007. “How the World Achieved Consensus on Monetary of in T. in Monetary Policy The of and of in of in Monetary Policy to and in 2007. and Monetary paper, of University of in and in and 2007. and in A in and of a of Monetary University in Previous articleNext article by NBER by the of on this by the of no articles this

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