The Risk-Adjusted Monetary Policy Rule

Finance and Economics Discussion Series Divisions of Research & Statistics and Monetary Affairs Federal Reserve Board, Washington, D.C. The Risk-Adjusted Monetary Policy Rule Taisuke Nakata and Sebastian Schmidt 2016-061 Please cite this paper as: Nakata, Taisuke, and Sebastian Schmidt (2016). “The Risk-Adjusted Monetary Policy Rule,” Finance and Economics Discussion Series 2016-061. Washington: Board of Governors of the Federal Reserve System, http://dx.doi.org/10.17016/FEDS.2016.061. NOTE: Staff working papers in the Finance and Economics Discussion Series (FEDS) are preliminary materials circulated to stimulate discussion and critical comment. The analysis and conclusions set forth are those of the authors and do not indicate concurrence by other members of the research staff or the Board of Governors. References in publications to the Finance and Economics Discussion Series (other than acknowledgement) should be cleared with the author(s) to protect the tentative character of these papers.

The Risk-Adjusted Monetary Policy Rule∗ Taisuke Nakata† Sebastian Schmidt‡ Federal Reserve Board European Central Bank First Draft: July 2016 Abstract Macroeconomists are increasingly using nonlinear models to account for the effects of risk in the analysis of business cycles. In the monetary business cycle models widely used at central banks, an explicit recognition of risk generates a wedge between the inflation-target parameter in the monetary policy rule and the risky steady state (RSS) of inflation—the rate to which inflation will eventually converge—which can be undesirable in some practical applications. We propose a simple modification to the standard monetary policy rule to eliminate the wedge. In the proposed risk-adjusted policy rule, the intercept of the rule ismodifiedsothattheRSSofinflationequalstheinflation-targetparameterinthepolicyrule. JEL: E32, E52 Keywords: Effective Lower Bound, Inflation Targeting, Monetary Policy Rule, Risk, Risky Steady State. ∗WewouldliketothankMikeKiley,MatthiasPaustian,JohnRoberts,HiroatsuTanaka,BobTetlow,and seminar participants at the Board of Governors of the Federal Reserve System for helpful discussions. Paul Yoo provided excellent research assistance. The views expressed in this note, and all errors and omissions, should be regarded as those solely of the author and are not necessarily those of the Federal Reserve Board of Governors, the Federal Reserve System, or the European Central Bank. †Division of Research and Statistics, Federal Reserve Board, 20th Street and Constitution Avenue N.W. Washington, DC 20551; Email: taisuke.nakata@frb.gov ‡European Central Bank, Monetary Policy Research Division, 60640 Frankfurt, Germany; Email: sebastian.schmidt@ecb.int. 1

1 Introduction Macroeconomists are increasingly using nonlinear stochastic models to account for the effects of risk in the analyses of business cycles. In nonlinear models, an explicit recognition of risk creates a discrepancy between the deterministic steady state (DSS) and risky steady state (RSS).1 In monetary business cycle models, this discrepancy implies a wedge between the inflation-target parameter in the monetary policy rule and the RSS of inflation—the rate to which inflation will eventually converge once all headwinds and tailwinds dissipate. Unless it is explicitly taken account of, this wedge means that inflation persistently deviates from the central bank’s inflation objective, which can be undesirable depending on the purpose of the analysis. In this paper, we propose a simple modification to the standard policy rule—the riskadjusted policy rule—to eliminate the wedge. In the proposed modification, the intercept of the policy rule is adjusted so that the RSS of inflation equals the inflation-target parameter in the policy rule. We show that this modification is mathematically equivalent to adjusting the value assigned to the inflation-target parameter in the standard policy rule, but has the advantage that the inflation-target parameter can be interpreted structurally as the central bank’s inflation objective. This paper is organized as follows. In section 2, we illustrate the wedge between the inflation-target parameter in the policy rule and the RSS of inflation that arises in nonlinear stochastic economies with standard monetary policy rules, using as a laboratory a model with an occasionally binding effective lower bound (ELB) constraint on nominal interest rates. In section 3, we describe a risk-adjusted policy rule that eliminates this wedge with an appropriateinterceptadjustment. Section4putsthepaperintobroadercontextbyrelatingit tothediscussionofhowtointerpretthecentralbank’sinflationobjectiveandbyhighlighting other applications where our risk-adjusted policy rule is useful. Section 5 concludes. 2 A wedge We use an empirical model considered in Hills, Nakata, and Schmidt (2016b) to illustrate the wedge between the RSS of inflation and the inflation-target parameter in the policy rule on the one hand and our proposed approach to eliminating it on the other. Our model is a standard sticky-price model with an occasionally binding ELB constraint on nominal interest rates, consumption habits, sticky wages, and a non-stationary TFP process. While themodelismorecomplicated than necessarytoillustratethewedge, as wellasourproposed approach to eliminating it, we believe that the use of an empirically plausible model is useful in highlighting the quantitative relevance of the wedge. The details of the model and the calibration are relegated to the Appendix.2 The policy rule in the model is given by a standard Taylor rule truncated below at the ELB: 1The DSS of a model is the steady state associated with the version of the model without uncertainty. The RSS of a model is a point to which the economy eventually converges when all headwinds and tailwinds dissipate. For a formal definition, see Coeurdacier, Rey, and Winant (2011) and Hills, Nakata, and Schmidt (2016b). In linear models, the DSS and RSS coincide because certainty equivalence holds. 2Weuseaversionofthebaselineempiricalmodelaugmentedwithtotalfactorproductivity(TFP)shocks that is discussed in Appendix E of Hills, Nakata, and Schmidt (2016b). The same model is used in Hills, Nakata, and Schmidt (2016a), a nontechnical summary of Hills, Nakata, and Schmidt (2016b). 2

R = max[R ,R∗], t ELB t where R is the short-term nominal interest rate, R is the ELB, and R∗ is the notional t ELB t short-term nominal interest rate. The notional rate is given by (cid:18) R∗ (cid:19)ρR (cid:18) Πp (cid:19)(1−ρR)φπ (cid:32) Y˜ (cid:33)(1−ρR)φy R∗ = R t−1 t t , (1) t DSS R DSS Πtarg Y˜ DSS where Πp is the rate of price inflation, Y˜ is detrended output (i.e., output divided by the t t level of TFP), and Πtarg is the inflation-target parameter. The DSS of inflation equals Πtarg. R is the deterministic steady state of R and is a function of structural parameters: DSS t aχcΠtarg R = , (2) DSS β where a is the trend growth rate of technology, β is the discount rate of the household, and χ is the inverse intertemporal elasticity of substitution for consumption goods. We will refer c toR astheinterceptofthestandardpolicyrule, asthistermshowsupastheinterceptin DSS the linearized version of the standard policy rule. The intercept term is given by equation (2) in the monetary policy rule in almost all DSGE (Dynamic Stochastic General Equilibrium) models.3 Y˜ is the deterministic steady state of Y˜ and is a function of structural parameters: DSS t (cid:18) (cid:19) 1 Y˜ = (θ p −1)(θ w −1) χc+χn , DSS θ θ p w where θ is the elasticity of substitution among intermediate goods, θ is the elasticity of p w substitution among intermediate labor inputs, and χ is the inverse labor supply elasticity. n Note that Y˜ does not depend on the inflation-target parameter because firms’ price- DSS adjustmentcostsareassumedtodependonthedeviationofinflationfromtheinflation-target parameter in our model. Hills, Nakata, and Schmidt (2016b) show that the RSS inflation of this model is nontrivially below Πtarg, as the tail risk in future marginal costs induced by the possibility of hitting the ELB constraint exerts downward pressures on inflation. Table 1a shows the risky and deterministic steady state values of inflation, the output gap, and the policy rate from their empirical model in which Πtarg is set to 2 percent, the target rate of inflation in many advanced economies. Inflation falls 29 basis points below the target rate of inflation at the RSS. Note that the wedge between the RSS of inflation and the inflation-target parameter is non-trivial even in the model without the ELB, indicating the pervasiveness of the wedge in nonlinear economies. To provide an alternative look at this undershooting result, we plot the modal projections ofthepolicyrate,inflation,andtheoutputgapfromthemodelafteracombinationofdemand and TFP shocks push down the policy rate to the ELB. The magnitudes of the two shocks are chosen so that inflation is 50 basis points and the output gap is minus 7 percent at time one. The model projects inflation to return to a level below 2 percent. If an economist wants 3Toourknowledge,allpublishedpapersonmonetaryDSGEmodelsspecifytheinterceptofthemonetary policy rule in this way. 3

Table 1: The Risky Steady State in a Model with ELB (a) With the Standard Policy Rule Inflation Output Gap Policy Rate Deterministic steady state 2 0 3.75 Risky steady state 1.71 0.32 3.04 (Wedge) (−0.29) (0.32) (−0.71) E[·] 1.66 0.29 3.17 Prob(R = R ) 16% t ELB Risky steady state w/o the ELB 1.88 0.04 3.37 (Wedge) (−0.12) (0.04) (−0.38) (b) With the Risk-Adjusted Policy Rule Inflation Output Gap Policy Rate Risky steady state 2 0.22 3.39 E[·] 1.97 0.24 3.50 Adjusted Intercept 3.17 Prob(R = R ) 11.9% t ELB to conduct policy analyses using a model in which inflation eventually returns to the central bank’s inflation objective, she or he needs to find a sensible way to modify the policy rule to avoid this permanent undershooting of the inflation objective. Figure 1: Modal Forecasts from a Model with ELB Policy Rate (Annualized %) Inflation (Annualized %) Output Gap (%) 4 2 3 3 0 1.5 2 −3 1 1 −6 Standard Rule Risk−Adjusted Rule 0 0.5 −9 0 5 10 15 20 25 30 35 40 0 5 10 15 20 25 30 35 40 0 5 10 15 20 25 30 35 40 Quarter Quarter Quarter †The thin black horizontal line in the left panel at 3.75 is the deterministic steady state of the policy rate. 3 The risk-adjusted policy rule 3.1 The proposed rule We propose to eliminate the wedge between the inflation-target parameter and the RSS of inflation by adjusting the intercept of the policy rule. Let the intercept-adjusted policy 4

rule be given by R∗ = S aχcΠtarg (cid:32) R t ∗ −1 (cid:33)ρR(cid:18) Πp t (cid:19)(1−ρR)φπ (cid:32) Y˜ t (cid:33)(1−ρR)φy , (3) t R β S aχcΠtarg Πtarg Y˜ R β DSS where S that appears in front of aχcΠtarg is the intercept adjustment term and S aχcΠtarg R β R β is the adjusted intercept.4 We call S an intercept-adjustment term because this term would R show up as the intercept in the linearized version of the policy rule. A key feature of equation (3) is that the presence of the intercept-adjustment parameter breaks the standard link between the intercept and the model’s structural parameters. When the standard policy rule is specified in the context of structural models, the intercept is a function of the model’s structural parameters—a, β, χ , and Πtarg in our model—as seen in c equations(1)and(2). Thus,underthestandardpolicyrule,oneneedstoadjustatleastoneof the structural parameters of the model to change the intercept. Under the intercept-adjusted policy rule, the intercept of the rule is a free parameter of the model. Our proposal is to use the intercept-adjusted policy rule with the value for S chosen R so that the RSS inflation and the inflation-target parameter coincide. We will refer to the intercept-adjusted policy rule with S so chosen as the risk-adjusted policy rule. The size of R the intercept adjustment that equates the RSS of inflation to the inflation-target parameter depends on the specifics of the model and needs to be found numerically. Figure 2 shows how the RSS of inflation changes with the adjusted intercept in the model of Hills, Nakata, and Schmidt (2016b). Since the RSS of inflation is below 2 percent under the standard policy rule, the necessary adjustment would be to lower the intercept, as a lower intercept implies, all else being equal, a more accommodative policy stance, generating upward pressures on inflation. According to the figure, lowering the intercept by about 60 basis point (from 3.75 to 3.17 percent) leads to the RSS inflation of 2 percent. Table 1b reports the RSS of the model with ELB and the risk-adjusted policy rule. By construction, under the risk-adjusted policy rule, the RSS of inflation is 2 percent. Even though the intercept in the policy rule is lower in the risk-adjusted policy rule than in the standard policy rule, the RSS policy rate is higher—3.04 versus 3.39 percent—reflecting a higher RSS inflation. The RSS output gap is positive, but it is a bit lower under the riskadjusted policy rule than under the standard policy rule. The lower RSS output gap is due to the lower frequency of being at the ELB (11.9 percent under the risk-adjusted rule versus 16 percent under the standard rule), which in turn is due to the higher RSS policy rate. Note that the RSS policy rate is higher than the intercept of the policy rule (3.39 percent versus 3.17 percent) because the output gap is positive at the RSS. To visualize the difference in 4Anequivalentpolicyruleunderwhichthepolicyraterespondstothedeviationofthedetrendedoutput from its risky steady state counterpart is aχcΠtarg (cid:32) R∗ (cid:33)ρR(cid:18) Πp (cid:19)(1−ρR)φπ(cid:18) Y˜ (cid:19)(1−ρR)φy R∗ =Sˆ t−1 t t , t R β Sˆ aχcΠtarg Πtarg Y˜ R β RSS where (cid:18) Y˜ (cid:19)−φy Sˆ =S DSS . R R Y˜ RSS This representation of the policy rule may first seem appealing as the output deviation term is zero at the RSS by construction. However, this representation is not practically useful for modelers as the RSS output level is not known to the modelers before the model is solved. 5

Figure 2: The Risky Steady State Inflation and the Adjusted Intercept 2.1 2 1.9 1.8 1.7 1.6 1.5 3 3.25 3.5 3.75 4 Adjusted Intercept (S R ) R DSS noitalfnI SSR 3.17 Notes: ThefigureshowshowtheRSSinflationvarieswiththeadjustedintercept. BoththeRSSinflationand the adjusted intercept are expressed in annualized percent. the RSS between the models with standard and risk-adjusted rules, solid red lines in figure 1 show the modal projections of the policy rate, inflation, and the output gap from the model with the risk-adjusted policy rule where the magnitudes of the shocks are chosen so that inflation is 50 basis points at time one and the output gap is minus 7 percent. Tobetterunderstandhowourproposedmethodworks,itisusefultographicallyillustrate how the intercept adjustment affects the RSS of inflation and the policy rate. Figure 3 plots the standard Fisher relation, the risk-adjusted Fisher relation, the standard policy rule, and the risk-adjusted policy rule. The risky (deterministic) steady state of the model with the standardpolicyruleisgivenbytheintersectionoftherisk-adjusted(standard)Fisherrelation andthestandardpolicyrule. TheRSSofthemodelwiththerisk-adjustedpolicyruleisgiven by the intersection of the risk-adjusted Fisher relation and the risk-adjusted policy rule. According to the figure, and as discussed in detail in Hills, Nakata, and Schmidt (2016b), the presence of risk lowers the line representing the Fisher relation, pushing down the steadystate inflation rate in the absence of an adjustment in the policy rule. The risk adjustment in the policy rule lowers the policy rate corresponding to a given inflation rate, pushing up RSS inflation back to the level consistent with the inflation-target parameter. 3.2 Comparison with the inflation-target parameter adjustment The intercept adjustment in equation (3) is mathematically equivalent to an adjustment in the value assigned to the inflation-target parameter in the standard policy rule. Let ΠCB be the value of the central bank’s inflation objective. The standard policy rule with an adjusted value for the inflation-target parameter is given by R∗ = aχcS Π ΠCB (cid:32) R t ∗ −1 (cid:33)ρR(cid:18) Πp t (cid:19)(1−ρR)φπ (cid:32) Y˜ t (cid:33)(1−ρR)φy , t β aχcSΠΠCB S Π ΠCB Y˜ DSS β 6

Figure 3: The Risk-Adjusted Fisher Relation and the Risk-Adjusted Taylor Rule R DSS Risk−Adjusted Standard Fisher Relation Fisher Relation RSS* RSS Risk−Adjusted 1 Taylor Rule Standard Taylor Rule Π 2 †DSS stands for “deterministic steady state,” and RSS stands for “risky steady state.” where S is the inflation-target adjustment term and S ΠCB is the adjusted value assigned Π Π to the inflation-target parameter. This approach has a precedent. With the interpretation thatthemodel’sunconditionalaverageofinflationcorrespondstothecentralbank’sinflation objective, Reifschneider and Williams (2000) proposed an upward adjustment in the value assigned to the inflation-target parameter in the standard policy rule so that the model’s unconditional average of inflation is 2 percent, which is the Federal Reserve’s inflation objective. To see the equivalence between the intercept-adjusted policy rule with Πtarg = ΠCB and the standard policy rule with an adjusted value assigned to the inflation-target parameter (Πtarg = S ΠCB), notice that there is one-to-one mapping between the intercept-adjustment Π term and the inflation-target adjustment term:5 S = S1−φπ. (4) R Π When the Taylor principle is satisfied (i.e., φ > 1), this relationship implies that an ad- π justment to lower the intercept (i.e., a lower S ) is equivalent to an adjustment to increase R the inflation-target parameter (i.e., a higher S ).6 Figure 4 shows this mapping between the Π 5Note that this mapping holds when price-adjustment costs depend on the deviation of inflation from the inflation-target parameter and Y˜ does not depend on the inflation-target parameter, S Πtarg. This DSS Π condition holds true for our model. In models in which Y˜ depends on the value assigned to the inflation- DSS target parameter, the mapping is given by S = S1−φπ (cid:16) Y˜ DSS(SΠΠCB) (cid:17)−φy , where Y˜ (·) is a function R Π Y˜ DSS(ΠCB) DSS mapping the inflation-target parameter to the steady state output. 6In a log-linearized policy rule, this mapping becomes s r ∼=(1−φ π )s π , where s :=log(S ) and s :=log(S ). See the appendix for more details on the risk-adjusted policy rule in r R π Π linear form. 7

adjusted intercept and the adjusted inflation-target parameter in our model.7 Figure 4: Mapping Between the Adjusted Intercept and the Adjusted Inflation-Target Parameter 2.3 2.23 2.2 2.1 2 1.9 3 3.17 3.25 3.5 3.75 4 Adjusted Intercept (S R ) R DSS )BCΠ S( tegraT noitalfnI detsujdA Π Note: Thefigureshowsthemappingbetweentheadjustedinterceptandtheadjustedinflation-targetparameter. Both the adjusted intercept and the adjusted inflation-target parameter are expressed in annualized percent. Asaresultofthemathematicalequivalencebetweentheintercept-adjustedpolicyruleand the standard policy rule with an adjusted value assigned to the inflation-target parameter, there are two ways in which modelers can arrive at the right size of the intercept adjustment for the risk-adjusted policy rule. One is to solve the model with the intercept-adjusted policy rule and iterate on S until the RSS of inflation equals the desirable inflation objective. R The other is to solve the model with the standard policy rule, iterate on S until the RSS of Π inflationequalsthedesirableinflationobjective, andtranslatetheinflation-targetadjustment into the intercept adjustment using equation (4). An advantage of the risk-adjusted policy rule over the standard policy rule with an adjusted value assigned to the inflation-target parameter is that the former allows for a simple structural interpretation of the inflation-target parameter. In the risk-adjusted policy rule, the inflation-target parameter can be naturally interpreted as the central bank’s inflation objectivebecausetheRSSofinflationcoincideswiththevalueoftheinflation-targetparameter. In the standard policy rule, the RSS of inflation is different from the value assigned to the inflation-target parameter unless the model is linear, complicating the interpretation of the inflation-target parameter. In our model, assigning the value of 2.23 percent to the inflationtarget parameter achieves the RSS inflation of 2 percent, as seen in figure 4. However, in this setup, the value assigned to the inflation-target parameter is simply a number that allows the model to generate the RSS of inflation so that it is consistent with the central bank’s inflation objective and does not have any structural interpretation. The desirability of being able to interpret the inflation-target parameter as the central bank’s inflation objective depends on the purpose of the analysis. In many estimation exer- 7In our model, φ =3.5. π 8

cises using U.S. data, the estimated value for the inflation-target parameter can substantially differfrom2percent, dependingonthesampleusedforestimation. Thediscrepancybetween the estimated value and the Federal Reserve’s target rate of 2 percent may not pose any issue if the goal of estimation is only to fit the data and understand the past. However, if the goal of the analysis is to think about the implications of alternative policy rulesfortheeconomicoutlookandifsuchanalysesareusedtoinformpolicymakers, itistypically useful—from the perspective of communication between modelers and policymakers—if the inflation-target parameter in the policy rule can be simply interpreted as the central bank’s inflation objective. For example, in the EDO Model—short for Estimated Dynamic Optimization-based Model—which is used at the Board of Governors of the Federal Reserve System for various policy analyses, the inflation-target parameter in the policy rule is set to 2 percent, the Federal Reserve’s target rate of inflation, to allow for a simple interpretation of the inflation-target parameter (Chung, Kiley, and Laforte (2010)).8 Similarly, in the New Area-Wide Model of the Euro Area, the DSGE model used for policy analyses at the European Central Bank, the inflation-target parameter is interpreted as the monetary authority’s long-run inflation objective and is set to 1.9 percent, which is “consistent with the ECB’s quantitative definition of price stability of inflation below, but close to 2 percent” (Christoffel, Coenen, and Warne (2008)).9 4 Discussion 4.1 Interpreting the central bank’s inflation objective Throughout the paper, we interpret the central bank’s inflation objective as specifying the desired level of the RSS inflation. Under this interpretation, the dynamics of inflation are consistent with the central bank’s inflation objective of x percent if the RSS of inflation is x percent. Accordingly,ourfocusinSection3wasonhowtomodifythepolicyruletoeliminate the wedge between the RSS inflation and the central bank’s inflation objective. However, some have interpreted the central bank’s inflation objective as specifying the average rate of inflation over a long period of time. Under this alternative interpretation, the dynamics of inflation are consistent with the central bank’s inflation objective of x percent if the unconditional average of inflation is x percent. The paper by Reifschneider and Williams (2000) is a prominent example adopting this interpretation. In our model, the unconditional average of inflation is also below the target rate of 2 percent, as shown in table 1a. Thus, the need for adjusting the policy rule can also arise under this alternative interpretation of the central bank’s inflation objective. Our intercept-adjustment procedure can be easily modified if modelers take this alternative interpretation and want to set the unconditional average of inflation, as opposed to 8Chung,Kiley,andLaforte(2010)explaintheircalibrationchoicebysaying,“someimportantdeterminants of steady-state behavior were calibrated to yield growth rates of GDP and associated price indexes that correspondedto“conventional”wisdominpolicycircles,eventhoughslightdeviationsfromsuchvalueswould have been preferred (in a “statistically significant” way) to our calibrated values.” 9These models are used for policy analyses in the context of the ELB on nominal interest rates (see, for instance, Chung, Laforte, Reifschneider, and Williams (2012) and Coenen and Warne (2014)). Due to the computational difficulty of globally solving large-scale DSGE models, the models are currently solved and simulated using solution methods that rely on the assumption that certainty equivalence holds (“perfectforesight”assumption). Asaresultofthisassumption,theriskysteadystatecoincideswiththedeterministic steady state in these applications. 9

the RSS of inflation, to the central bank’s inflation objective. Specifically, modelers would need to search for the size of the intercept adjustment such that the unconditional average of inflation, instead of the RSS inflation, equals the central bank’s inflation objective. In our example, the intercept that achieves the unconditional average of inflation of 2 percent is lower than the intercept that achieves the RSS inflation of 2 percent, because the unconditional average of inflation is lower than the RSS inflation in the model with the standard policy rule, as shown in table 1a. While our intercept-adjustment procedure is useful regardless of the interpretation of the central bank’s inflation objective adopted by modelers, it is perhaps appropriate to explain why it is more plausible to interpret the central bank’s inflation objective as specifying the desired level of the RSS inflation than as specifying the desired unconditional average of inflation. The interpretation that the central bank’s inflation objective specifies the desired unconditionalaverageofinflationisinconsistentwiththeinflationprojectionsbyU.S.policymakers in the following sense. In the United States, both core and overall PCE inflation rates averaged non-trivially below 2 percent over the last decade or so. Thus, to achieve the average inflation rate of 2 percent over a long period of time, policymakers will need to overshoot the target rate non-trivially and persistently in the future. However, according to recent releases of the Summary of Economic Projections (SEP), U.S. policymakers expect inflation to return to 2 percent in the long-run without any overshooting.10 As shown in figure 1, in the aftermath of a recession, the model’s inflation projection monotonically increases with forecast horizon and eventually converges to the RSS inflation. Thus, the eventual return of the inflation projection to 2 percent without any overshooting in the SPE is consistent with the interpretation that the central bank’s inflation objective specifies the desired level of the RSS inflation. Inasimilarvein,Draghi(2016)statesthat“IntheECB’scase,ouraimistokeepinflation below but close to 2 percent over the medium term. Today, this means raising inflation back towards 2 percent.” Thus, even though inflation in the euro area, as measured by the HICP, averaged below 2 percent over recent years, ECB policymakers do not seem to interpret their mandate to be consistent with aiming for a transitory overshooting of inflation rates close to 2 percent. 4.2 Other applications While we used a model with an occasionally binding ELB constraint to illustrate our proposed modification to the monetary policy rule, our proposal is useful in a wide variety of nonlinear models. As briefly discussed in section 2, the difference between the DSS and RSS are nontrivial in our model even without the ELB constraint. In our experience, the difference between the DSS and RSS can be quite large in New Keynesian models with recursive preferences often used to analyze the dynamics of term premiums or the effects of uncertainty shocks. Our proposed intercept-adjustment will be useful in such applications even if the model abstracts from the ELB constraint. In addition to the ELB constraint on nominal interest rates, researchers are increasingly interested in the implications of other inequality constraints in macroeconomic models. For 10See, for example, the Summary of Economic Projections released on June 15, 2016 (available at www. federalreserve.gov/monetarypolicy/files/fomcprojtabl20160615.pdf). 10

example, since the Great Recession, the literature on financial frictions has been developing rapidly, examining the implications of occasionally binding borrowing constraints on the household or leverage constraints on banks. Our risk-adjusted policy rule is likely to be useful in models featuring these other inequality constraints. 4.3 Contrast with linear models Theissuedescribedinthispaperhasnotreceivedmuchattentionbecauselinearmonetary DSGE models have been predominant tools for model-based analyses of monetary policy. In linear monetary DSGE models, the inflation-target parameter in the policy rule coincides with the RSS of inflation and the unconditional average of inflation. Researchers typically set the inflation-target parameter to the central bank’s inflation objective, and because of this coincidence, there is less need to think about conceptual differences among these objects. Our analysis highlights the importance and difficulty of understanding conceptual differences among the central bank’s objective, the inflation-target parameter, and the RSS and the unconditional average of inflation, as nonlinear models become more widely used in the analyses of monetary policy. 5 Conclusion We have proposed a simple method to close the wedge between the inflation-target parameter in the policy rule and the RSS of inflation in nonlinear stochastic monetary DSGE models. The proposed method is to numerically find the right adjustment in the intercept of the risk-adjusted policy rule. While this method is mathematically equivalent to adjusting the inflation-target parameter in the standard policy rule, it has the advantage that it allows modelers to align the inflation-target parameter in the policy rule with the central bank’s inflation objective. The Great Recession has provided macroeconomists with a new set of challenging questions. Properly addressing some of these questions requires macroeconomists to go beyond linear models. While we use a model with an occasionally binding ELB constraint as a laboratory to illustrate our proposed method, we expect our method to be useful in a broad set of nonlinear models. References Christoffel, K., G. Coenen, and A. Warne (2008): “The New Area-Wide Model of the Euro Area: AMicro-FoundedOpen-EconomyModelforForecastingandPolicyAnalysis,”ECBWorking Paper Series 944, European Central Bank. Chung, H., M. Kiley, and J.-P. Laforte (2010): “Documentation of the Estimated, Dynamic, Optimization-based (EDO) Model of the U.S. Economy: 2010 Version,” Finance and economics discussion series, Board of Governors of the Federal Reserve System (U.S.). Chung, H., J.-P. Laforte, D. Reifschneider, and J. C. Williams (2012): “Have We Underestimated the Likelihood and Severity of Zero Lower Bound Events?,” Journal of Money, Credit and Banking, 44(s1), 47–82. Coenen, G., and A. Warne (2014): “Risks to Price Stability, the Zero Lower Bound and Forward Guidance: A Real-Time Assessment,” International Journal of Central Banking, 10(2), 7–54. 11

Coeurdacier,N.,H.Rey,andP.Winant(2011): “TheRiskySteadyState,”AmericanEconomic Review, 101(3), 398–401. Draghi, M. (2016): “Delivering a Symmetric Mandate with Asymmetric Tools: Monetary Policy in a Context of Low Interest Rates,” Remarks at the Ceremony to Mark the 200th Anniversary of the Oesterreichische Nationalbank, Vienna. Hills, T. S., T. Nakata, and S. Schmidt(2016a): “TheRiskyofReturningtotheEffectiveLower Bound: An Implication for Inflation Dynamics after Lift-Off,” Feds notes, Board of Governors of the Federal Reserve System (U.S.). (2016b): “The Risky Steady State and the Interest Rate Lower Bound,” Finance and Economics Discussion Series 2016-009, Board of Governors of the Federal Reserve System (U.S.). Reifschneider, D., and J. C. Williams (2000): “Three Lessons for Monetary Policy in a Low- Inflation Era,” Journal of Money, Credit and Banking, 32(4), 936–966. 12

For Online Publication: Technical Appendix A The Risk-Adjusted Policy Rule in Linear Form By taking the log of the standard policy rule, we obtain the following linear policy rule: r∗ = (cid:2) χ log(a)+πtarg −log(β) (cid:3) t c +ρ (cid:0) r∗ − (cid:2) χ log(a)+πtarg −log(β) (cid:3)(cid:1) R t−1 c +(1−ρ )φ (πp−πtarg) R π t +(1−ρ )φ y˜, R y t where x := log(X) for x ∈ [r∗,π ,πtarg] and y˜ := log(Y˜)−log(Y˜ ). t t t t DSS The intercept-adjusted policy rule in linear form is given by r∗ = (cid:2) s +χ log(a)+πtarg −log(β) (cid:3) t r c +ρ (cid:0) r∗ − (cid:2) s +χ log(a)+πtarg −log(β) (cid:3)(cid:1) R t−1 R c +(1−ρ )φ (πp−πtarg) R π t +(1−ρ )φ y˜, R y t where s := log(S ). r R Thestandardpolicyrulewithanadjustedvalueassignedtotheinflation-targetparameter in linear form is given by r∗ = (cid:2) χ log(a)+s +πCB −log(β) (cid:3) t c π +ρ (cid:0) r∗ − (cid:2) s +χ log(a)+s +πCB −log(β) (cid:3)(cid:1) R t−1 R c π +(1−ρ )φ (πp−(s +πCB)) R π t π +(1−ρ )φ y˜, R y t where ΠCB is the central bank’s inflation objective, πCB := log(ΠCB), and s := log(S ). π Π The mapping between s and s is given by r π s = (1−φ )s . r π π Let Πadj (andπadj := log(Πadj)) denotethe adjustedvalue assigned tothe inflation-target parameter. That is, Πadj := S ΠCB. Π Then, s = πadj −πCB π and the mapping of the intercept adjustment and the inflation-target adjustment can be written as s = (1−φ )(πadj −πCB) r π 13

B Details of the Model This section describes an extension of the stylized model with a representative household, a final good producer, a continuum of intermediate goods producers with unit measure, and the government. B.1 Household markets B.1.1 Labor packer The labor packer buys labor N from households at their monopolistic wage W and h,t h,t resells the packaged labor N to intermediate goods producers at W . The problem can be t t written as (cid:90) 1 max W N − W N df t t h,t h,t N h,t ,h∈[0,1] 0 subject to the following CES technology (cid:20)(cid:90) 1 θw−1 (cid:21) θw θw −1 N = N θw dh . t h,t 0 The first order condition implies a labor demand schedule (cid:20) W (cid:21)−θw N = h,t N .11 h,t t W t θw is the wage markup parameter. B.1.2 Household The representative household chooses its consumption level, amount of labor, and bond holdings so as to maximize the expected discounted sum of utility in future periods. As is common in the literature, the household enjoys consumption and dislikes labor. Assuming that period utility is separable, the household problem can be defined by max E (cid:88) ∞ βt−1 (cid:34) (cid:89) t−1 δ (cid:35)(cid:34) (C h,t −ζC t a −1 )1−χc −A1−χc N h 1 , + t χn (cid:35) C h,t ,w h,t ,B h,t 1 t=1 s=0 s 1−χ c t 1+χ n subject to the budget constraint (cid:34) (cid:35)2 ϕ W P C +R−1B ≤ W N −W w h,t −1 N +B +P Φ −P T t h,t t h,t h,t h,t t 2 aW (cid:0) Π¯w (cid:1)1−ιw (cid:0) Πw (cid:1)ιw t h,t−1 t t t t h,t−1 t−1 or equivalently (cid:34) (cid:35)2 B ϕ w Πp B C + h,t ≤ w N −w w h,t t −1 N + h,t−1 +Φ −T h,t R t P t h,t h,t t 2 aw h,t−1 (cid:0) Π¯w (cid:1)1−ιw (cid:0) Πw (cid:1)ιw t P t t t t−1 11This implies that the labor packer will set the wage of the packaged labor to W = (cid:104)(cid:82)1W1−θw dh (cid:105) 1− 1 θw . t 0 h,t 14

and subject to the labor demand schedule (cid:20) W (cid:21)−θw h,t N = N . h,t t W t –or equivalently (cid:20) w (cid:21)−θw h,t N = N . h,t t w t where C is the household’s consumption, N is the labor supplied by the household, P is h,t h,t t thepriceoftheconsumptiongood,W (w )isthenominal(real)wagesetbythehousehold, h,t h,t W (w ) is the market nominal (real) wage, Φ is the profit share (dividends) of the household t t t from the intermediate goods producers, B is a one-period risk free bond that pays one unit h,t ofmoneyatperiodt+1, T arelump-sumtaxesortransfers, andR−1 isthepriceofthebond. t t Ca represents the aggregate consumption level from the previous period that the household t−1 takes as given. The parameter 0 ≤ ζ < 1 measures how important these external habits are to the household. Because we are including wage indexation, measured by the parameter ι , we assume the household takes as given the previous period wage inflation, Πw , where w t−1 Πw = Wt = wtPt = wt Πp. Π¯w is the target rate of wage inflation, which is set to t aWt−1 awt−1Pt−1 awt−1 t equal to Π¯p, the inflation-target parameter in the policy rule. The discount rate at time t is given by βδ where δ is the discount factor shock altering t t the weight of future utility at time t+1 relative to the period utility at time t. δ is assumed t to follow an AR(1) process: δ = (1−ρ )+ρ δ +(cid:15)δ ∀t ≥ 2 t δ δ t−1 t and δ is given. The innovation (cid:15)δ is normally distributed with mean zero and standard 1 t deviation σ . It may therefore be interpreted that an increase in δ is a preference imposed δ t by the household to increase the relative valuation of the future utility flows, resulting in decreased consumption today (when considered in the absence of changes in the nominal interest rate). A is a non-stationary total factor productivity shock that also augments labor in the t utility function in order to accommodate the necessary stationarization of the model later on. See the next section for more details on this process. B.2 Producers B.2.1 Final good producer The final good producer purchases the intermediate goods Y at the intermediate price f,t P and aggregates them using CES technology to produce and sell the final good Y to the f,t t household and government at price P . Its problem is then summarized as t (cid:90) 1 max P Y − P Y di t t f,t f,t Y f,t ,f∈[0,1] 0 15

subject to the CES production function (cid:20)(cid:90) 1 θp−1 (cid:21) θp θ − p 1 Y = Y θp di . t f,t 0 θp is the price markup parameter. B.2.2 Intermediate goods producers There is a continuum of intermediate goods producers indexed by f ∈ [0,1]. Intermediate goods producers use labor to produce the imperfectly substitutable intermediate goods according to a linear production function (Y = A N ) and then sell the product to the final f,t t f,t good producer. Each firm maximizes its expected discounted sum of future profits12 by setting the price of its own good. Any price changes are subject to quadratic adjustment costs. ϕ will represent an obstruction of price adjustment, the firm indexes for prices—measured p by ι —and takes as given previous period inflation Πp , and Π¯p is the inflation-target pap t−1 rameter. ∞ (cid:34)t−1 (cid:35) (cid:34) (cid:35) maxE (cid:88) βt−1 (cid:89) δ λ P Y −W N −P ϕ p [ P f,t −1] 2 Y P f,t 1 t=1 s=0 s t f,t f,t t f,t t 2 (cid:0) Π¯p (cid:1)1−ιp (cid:0) Πp t−1 (cid:1)ιpP f,t−1 t such that (cid:20) P (cid:21)−θp Y = f,t Y .13 f,t t P t (cid:104) (cid:105) λ istheLagrangemultiplieronthehousehold’sbudgetconstraintattimetandβt−1 (cid:81)t−1 δ λ t s=0 s t is the marginal value of an additional profit to the household. The positive time zero price is the same across firms (i.e. P = P > 0). i,0 0 A represents total factor productivity which follows a random walk with drift: t ln(A ) = ln(a)+ln(A )+a . t t−1 t a is the unconditional rate of growth of productivity. a is a productivity shock following an t AR(1) process: ln(a ) = ρ ln(a )+(cid:15)A. t a t−1 t where (cid:15)A is normally distributed with mean zero and standard deviation σ . This growth t A factor will imply that some of the variables will acquire a unit root, meaning the model will have to be stationarized. Monetary policy will also have to accommodate this growth factor as well. 12NOTE: Each period, as it is written below, is in nominal terms. However, we want each period’s profits in real terms so the profits in each period must be divided by that period’s price level P which we take care t of further along in the document. 13This expression is derived from the profit maximizing input demand schedule when solving for the final goodproducer’sproblemabove. PluggingthisexpressionbackintotheCESproductionfunctionimpliesthat the final good producer will set the price of the final good P = (cid:104)(cid:82)1P1−θp di (cid:105) 1− 1 θp . t 0 f,t 16

B.3 Government policies It is assumed that the monetary authority determines nominal interest rates according to a truncated notional inertial Taylor rule augmented by a speed limit component. R = max[1,R∗] t t where R∗ (cid:18) R∗ (cid:19)ρR (cid:18) Πp (cid:19)(1−ρR)φπ (cid:18) Y (cid:19)(1−ρR)φy t = t−1 t t R DSS R DSS Πtarg A t Y˜ DSS where Πp = Pt is the inflation rate between periods t − 1 and t and R = Πtargaχc t Pt−1 DSS β (see the section on stationarization to see why). Y˜ is the deterministic steady state of DSS stationarized output, and Πtarg is the inflation-target parameter. B.4 Market clearing conditions The market clearing conditions for the final good, labor and government bond are given by (cid:34) (cid:35)2 (cid:90) 1 ϕ P p f,t Y = C + −1 Y df +... t t 0 2 (cid:0) Π¯p (cid:1)1−ιp (cid:0) Πp t−1 (cid:1)ιpP f,t−1 t (cid:34) (cid:35)2 (cid:90) 1 ϕ w Πp ...+ w w h,t t −1 N dh 0 t 2 aw h,t−1 (cid:0) Π¯w (cid:1)1−ιw (cid:0) Πw (cid:1)ιw t t−1 (cid:90) 1 N = N di t f,t 0 (cid:90) 1 Ca = C = C dh t t h,t 0 and (cid:90) 1 B = B dh = 0. t h,t 0 B.5 An equilibrium Given P and stochastic processes for δ , an equilibrium consists of allocations {C , N , 0 t t t N , Y , Y , G }∞ , prices {W ,P ,P }∞ , and a policy instrument {R }∞ such that f,t t f,t t t=1 t t f,t t=1 t t=1 (i) allocations solve the problem of the household given prices and policies ∂C : (C −ζCa )−χc −λ = 0 h,t h,t t−1 t 17

N1+χn (cid:18) w (cid:19)−θw(1+χn)−1 ∂w : θwA1−χc t h,t h,t t w w t t (cid:18) w (cid:19)−θw +(1−θw)λ h,t N t t w t (cid:32) (cid:33) w Πp Πp −λ w ϕ h,t t −1 N t t t w aw h,t−1 (cid:0) Π¯w (cid:1)1−ιw (cid:0) Πw t−1 (cid:1)ιw t aw h,t−1 (cid:0) Π¯w (cid:1)1−ιw (cid:0) Πw t−1 (cid:1)ιw (cid:32) (cid:33) w Πp w Πp +βδ E λ w ϕ h,t+1 t+1 −1 N h,t+1 t+1 = 0 t t t+1 t+1 w aw h,t (cid:0) Π¯w (cid:1)1−ιw(Πw t )ιw t+1 aw h 2 ,t (cid:0) Π¯w (cid:1)1−ιw(Πw t )ιw λ λ t t+1 ∂B : − +βδ E = 0 h,t t t R P P t t t+1 (ii) P solves the problem of firm i f,t By making the appropriate substitution (the intermediate goods producer’s constraints in place of Y and subsequently in for N ) and by dividing each period’s profits by that f,t f,t period’s price level P so as to put profits in real terms (and thus make profits across periods t comparable) we get the following: Y (cid:104) P (cid:32) P (cid:33) (cid:18) P (cid:19)−θp ∂P : λ t t ϕ f,t −1 −(1−θp) f,t f,t t P t (cid:0) Π¯p (cid:1)1−ιp (cid:0) Πp t−1 (cid:1)ιpP f,t−1 p (cid:0) Π¯p (cid:1)1−ιp (cid:0) Πp t−1 (cid:1)ιpP f,t−1 P t w (cid:18) P (cid:19)1+θp (cid:105) λ Y (cid:34) (cid:32) P (cid:33) P (cid:35) −θp t t = βδ E t+1 t+1 P ϕ f,t+1 −1 f,t+1 A t P f,t t t P t+1 t+1 p (cid:0) Π¯p (cid:1)1−ιp(Πp t ) ιpP f,t (cid:0) Π¯p (cid:1)1−ιp(Πp t ) ιpP f 2 ,t (iii) P = P ∀i (cid:54)= j f,t j,t (cid:34) (cid:32) (cid:33) (cid:35) Y Πp Πp w t ϕ t −1 t −(1−θp)−θp t = ... λ− t 1 p (cid:0) Π¯p (cid:1)1−ιp (cid:0) Πp t−1 (cid:1)ιp (cid:0) Π¯p (cid:1)1−ιp (cid:0) Πp t−1 (cid:1)ιp A t (cid:32) (cid:33) Y Πp Πp ... = βδ E t+1 ϕ t+1 −1 t+1 t t λ−1 p (cid:0) Π¯p (cid:1)1−ιp(Πp) ιp (cid:0) Π¯p (cid:1)1−ιp(Πp) ιp t+1 t t (iv) R follows a specified rule t and (v) all markets clear. Combining all of the results derived from the conditions and exercises in (i)-(v), a symmetric equilibrium can be characterized recursively by {C ,N ,Y ,w ,Πp,R }∞ satisfying t t t t t t t=1 the following equilibrium conditions: λ = βδ R E λ (cid:0) Πp (cid:1)−1 t t t t t+1 t+1 λ = (C −ζC )−χc t t t−1 18

(cid:34) (cid:32) (cid:33) (cid:35) N Πw Πw A1−χcNχn t ϕ t −1 t −(1−θw)−θw t t = ... λ− t 1 w (cid:0) Π¯w (cid:1)1−ιw (cid:0) Πw t−1 (cid:1)ιw (cid:0) Π¯w (cid:1)1−ιw (cid:0) Πw t−1 (cid:1)ιw λ t w t (cid:32) (cid:33) N Πw Πw w ... = βδ E t+1 ϕ t+1 −1 t+1 t+1 t t λ− t+ 1 1 w (cid:0) Π¯w (cid:1)1−ιw(Πw t )ιw (cid:0) Π¯w (cid:1)1−ιw(Πw t )ιw w t w Πw = t Πp t aw t t−1 (cid:34) (cid:32) (cid:33) (cid:35) Y Πp Πp w t ϕ t −1 t −(1−θp)−θp t = ... λ− t 1 p (cid:0) Π¯p (cid:1)1−ιp (cid:0) Πp t−1 (cid:1)ιp (cid:0) Π¯p (cid:1)1−ιp (cid:0) Πp t−1 (cid:1)ιp A t (cid:32) (cid:33) Y Πp Πp ... = βδ E t+1 ϕ t+1 −1 t+1 t t λ−1 p (cid:0) Π¯p (cid:1)1−ιp(Πp) ιp (cid:0) Π¯p (cid:1)1−ιp(Πp) ιp t+1 t t (cid:34) (cid:35)2 (cid:34) (cid:35)2 ϕ Πp ϕ Πw Y = C + p t −1 Y + w t −1 w N t t 2 (cid:0) Π¯p (cid:1)1−ιp (cid:0) Πp (cid:1)ιp t 2 (cid:0) Π¯w (cid:1)1−ιw (cid:0) Πw (cid:1)ιw t t t−1 t−1 Y = A N t t t R = max[1,R∗] t t where R∗ (cid:18)R∗ (cid:19)ρR (cid:18) Πp(cid:19)(1−ρR)φπ (cid:18) Y (cid:19)(1−ρR)φy t = t−1 t t R¯ R¯ Π¯p A Y¯ t and given the following processes (∀t ≥ 2): δ = (1−ρ )+ρ δ +(cid:15)δ t δ δ t−1 t and ln(A ) = ln(a)+ln(A )+a . t t−1 t ln(a ) = ρ ln(a )+(cid:15)A. t a t−1 t B.6 A stationary equilibrium LetY˜ = Yt,C˜ = Ct,w˜ = wt,andλ˜ = λt bethestationaryrepresentationsofoutput, t At t At t At t A−χc t consumption, real wage, and marginal utility of consumption respectively. The stationary symmetric equilibrium can now be characterized by the following system of equations. λ˜ = β δ R E λ˜ (cid:0) Πp (cid:1)−1 exp(−χ (cid:15)A ) t aχc t t t t+1 t+1 c t+1 ζ λ˜ = (C˜ −ζ˜C˜ exp(−(cid:15)A))−χc, ζ˜= t t t−1 t a (cid:34) (cid:32) (cid:33) (cid:35) N w˜ Πw Πw Nχn t t ϕ t −1 t −(1−θw)−θw t = ... λ˜− t 1 w (cid:0) Π¯w (cid:1)1−ιw (cid:0) Πw t−1 (cid:1)ιw (cid:0) Π¯w (cid:1)1−ιw (cid:0) Πw t−1 (cid:1)ιw λ˜ t w˜ t (cid:32) (cid:33) ... = βϕ w δ E N t+1 w˜ t+1 Πw t+1 −1 Πw t+1 exp (cid:0) (1−χ )(cid:15)A (cid:1) aχc−1 t t λ−1 (cid:0) Π¯w (cid:1)1−ιw(Πw)ιw (cid:0) Π¯w (cid:1)1−ιw(Πw)ιw c t+1 t+1 t t 19

Πw = w˜ t Πpexp (cid:0) (cid:15)A(cid:1) t w˜ t t t−1 (cid:34) (cid:32) (cid:33) (cid:35) Y˜ Πp Πp t ϕ t −1 t −(1−θp)−θpw˜ = ... λ˜−1 p (cid:0) Π¯p (cid:1)1−ιp (cid:0) Πp (cid:1)ιp (cid:0) Π¯p (cid:1)1−ιp (cid:0) Πp (cid:1)ιp t t t−1 t−1 (cid:32) (cid:33) ... = βϕ p δ E Y˜ t+1 Πp t+1 −1 Πp t+1 exp (cid:0) (1−χ )(cid:15)A (cid:1) aχc−1 t t λ˜−1 (cid:0) Π¯p (cid:1)1−ιp(Πp) ιp (cid:0) Π¯p (cid:1)1−ιp(Πp) ιp c t+1 t+1 t t (cid:34) (cid:35)2 (cid:34) (cid:35)2 ϕ Πp ϕ Πw Y˜ = C˜ + p t −1 Y˜ + w t −1 w˜ N t t 2 (cid:0) Π¯p (cid:1)1−ιp (cid:0) Πp (cid:1)ιp t 2 (cid:0) Π¯w (cid:1)1−ιw (cid:0) Πw (cid:1)ιw t t t−1 t−1 Y˜ = N t t and R = max[1,R∗] t t where R∗ (cid:18) R∗ (cid:19)ρR (cid:18) Πp (cid:19)(1−ρR)φπ (cid:18) Y (cid:19)(1−ρR)φy t = t−1 t t R DSS R DSS Πtarg A t Y˜ DSS and given the following processes (∀t ≥ 2): δ = (1−ρ )+δ +(cid:15)δ t δ t−1 t and B.7 Stationary deterministic steady-state values For each variable, X , we denote its corresponding stationary deterministic steady-state t value as X¯. The following is a list of analytical expressions for the stationary steady states for each of the variables of the model. Πp = Πtarg DSS Πw = Πp DSS DSS aχcΠp R = DSS DSS β θ −1 p w˜ = DSS θ p   1 χc+χn w˜ (θ −1) C˜ DSS =  θ DS (cid:16) S 1− w ζ˜ (cid:17)χc  w λ˜ = (cid:104)(cid:16) 1−ζ˜ (cid:17) C˜ (cid:105)−χc DSS DSS N˜ = Y˜ = C˜ DSS DSS DSS 20

B.8 Parameter values Table 2: Parameter Values for the Empirical Model Parameter Description Parameter Value β Discount rate 0.99875 a Trend growth rate of productivity 1.25 400 χ Inverse intertemporal elasticity of substitution for C 1.0 c t ζ Degree of consumption habits 0.5 χ Inverse labor supply elasticity 0.5 n θ Elasticity of substitution among intermediate goods 11 p θ Elasticity of substitution among intermediate labor inputs 4 w ϕ Price adjustment cost 700 p ϕ Wage adjustment cost 300 w ι Price indexation parameter 0 p ι Wage indexation parameter 0 w Interest-rate feedback rule 400(Π¯p−1) (Annualized) target rate of inflation 2.0 ρ Interest-rate smoothing parameter in the Taylor rule 0.8 R φ Coefficient on inflation in the Taylor rule 3.5 π φ Coefficient on the output gap in the Taylor rule 0.25 y 400(R −1) (Annualized) effective lower bound 0.13 ELB Shocks ρ AR(1) coefficient for the discount factor shock 0.85 d σ The standard deviation of shocks to the discount factor 0.66 (cid:15),δ 100 σ The standard deviation of TFP shocks 0.16 (cid:15),a 100 21