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FEDERAL RESERVE BANK OF CLEVELAND pd papers NUMBER 17 By Charles T. Carlstrom and Timothy S. Fuerst POLICY DISCUSSION PAPER Inertial Taylor Rules: The Beneﬁt of Signaling Future Policy APRIL 2007 POLICY DISCUSSION PAPERS FEDERAL RESERVE BANK OF CLEVELAND Inertial Taylor Rules: The Beneﬁt of Signaling Future Policy By Charles T. Carlstrom and Timothy S. Fuerst We trace the consequences of an energy shock on the economy under two different monetary policy rules: a standard Taylor rule where the Fed responds to inﬂation and the output gap; and a Taylor rule with inertia where the Fed moves slowly to the rate predicted by the standard rule. We show that with both sticky wages and sticky prices, the outcome of an inertial Taylor rule is superior to that of the standard rule, in the sense that inﬂation is lower and output is higher following an adverse energy shock. However, if prices alone are sticky, things are less clear and the standard rule delivers substantially less inﬂation than the inertial rule in the short run. Charles T. Carlstrom is a senior economic advisor at the Federal Reserve Bank of Cleveland. Timothy S. Fuerst is a professor at Bowling Green State University and a research associate at the Bank. Materials may be reprinted, provided that the source is credited. Please send copies of reprinted materials to the editor. POLICY DISCUSSION PAPERS Policy Discussion Papers are published by the Research Department of the Federal Reserve Bank of Cleveland.To receive copies or to be placed on the mailing list, e-mail your request to firstname.lastname@example.org or fax it to 216-579-3050. Please send your questions comments, and suggestions to us at email@example.com. Policy Discussion Papers are available on the Cleveland Fed’s site on the World Wide Web: www.clevelandfed.org/Research. Views stated in Policy Discussion Papers are those of the authors and not necessarily those of the Federal Reserve Bank of Cleveland or of the Board of Governors of the Federal Reserve System. ISSN 1528-4344 FEDERAL RESERVE BANK OF CLEVELAND Introduction Before exiting an expressway, a cautious driver always signals his intention by switching on his turn signal well in advance of turning because he understands that other drivers’ behavior will be affected by what they expect him do. This commonplace behavior may speak metaphorically to central bank policy: If market participants are forwardlooking, then it may be important for the central bank to signal future policy moves. Starting in June 2004, the FOMC changed its language to indicate that existing policy accommodation would be removed at a “measured pace,” strongly signaling the direction of future Fed policy. But why adjust partway by signaling future policy instead of going all the way more quickly? Likewise, why increase the federal funds rate 25 basis points at each of 10 policy meetings, instead of making ﬁve moves of 50 basis points, or, for that matter, one move of 250 basis points? What are the advantages of a measured pace? One way to describe Fed policy is with a simple Taylor rule, according to which monetary policy responds to inﬂation and the output gap. Clearly, the Fed does not automatically adjust policy according to the prescriptions of the rule. Nevertheless, there is substantial empirical evidence that broad movements in the funds rate are well tracked by a simple Taylor rule. But this evidence also suggests that the Fed adjusts the funds rate much more slowly than the simple Taylor rule prescribes. That is, although funds rate movements are typically in the direction suggested by the rule, these movements are only partial; thus, it takes a series of policy moves to reach the level a simple Taylor rule suggests. This type of Taylor rule is said to be inertial because it changes slowly, and today’s funds rate depends on yesterday’s funds rate. One way to think about an inertial Taylor rule is that policy consists of both the funds rate today and the expected path of the funds rate. Without inertia, policy moves more immediately and does not indicate where the funds rate is likely to head.1 This Policy Discussion Paper shows, in the context of a standard, quantitative, dynamic newKeynesian model, that it is beneﬁcial for policy accommodation to be removed slowly instead of in one—or a few—large moves.That is, an inertial Taylor rule frequently deliv- 1 Of course, even with a noninertial Taylor rule, one will anticipate future funds rate movements to the extent that future inﬂation and the output gap are forecasted. ers a better outcome than a noninertial rule. In particular, we trace the consequences of an energy shock on the economy under two different monetary policy rules: a standard Taylor rule where the Fed responds to inﬂation and the output gap; and a Taylor rule with inertia where the Fed moves slowly to the rate predicted by the standard rule.We show that with both sticky wages and sticky prices, the outcome of a partial-adjustment Taylor rule is superior to that of the standard rule, in the sense that inﬂation is lower and output is higher following an adverse energy shock. However, if prices alone are sticky, things are less clear and the standard rule delivers substantially less inﬂation than the inertial rule in the short run. 1 POLICY DISCUSSION PAPERS NUMBER 17, APRIL 2007 The Taylor Rule The Taylor rule has had a big impact in both monetary policy circles and academic economic research. Figure 1 suggests why.The rule seems to track broad policy moves since 1987 very successfully, which seems remarkable because the rule is so simple: It is set according to only four components: The ﬁrst is the Fed’s long-term inﬂation target and the second is the “natural” or long-term real (inﬂation-adjusted) federal funds interest rate. The sum of these ﬁrst two factors determines the long-run (nominal) federal funds rate, which amounted to 4 percent annually in Taylor’s original rule. The two remaining factors, current output and inﬂation rates, address the way policy should respond to changing circumstances in the short run. The Taylor rule prescribes that the Fed “lean against the wind” when setting interest rates; that is, it should raise rates when current output surpasses potential. It prescribes a similar response to inﬂation—raise interest rates when the inﬂation rate over the past year exceeds its long-term target. But mere leaning is not enough when it comes to inﬂation. Taylor cautioned that interest rates must rise by more than the increase in inﬂation. Given that nominal interest rates naturally increase one-for-one with movements in anticipated inﬂation, just FIGURE 1 INERTIAL AND NONINERTIAL TAYLOR RULE Percent 11 Partial-adjustment Taylor rule c,d 9 Target Taylor rule a,d Effective federal funds rate b 7 5 3 1 -1 1989 1991 1993 1995 1997 1999 2001 2003 2005 a. Target or noninertial Taylor rule is adapted from John B. Taylor, “Discretion versus Policy Rules in Practice,” Carnegie-Rochester Conference Series on Public Policy, vol. 39 (1993), pp. 195–214. b. Effective federal funds rate on the last day of each quarter. c. Partial-adjustment or inertial Taylor rule is the weighted average of the last quarter’s federal funds rate and the target Taylor rule. d. The exact form of both Taylor rules comes from Sharon Kozicki “How Useful Are Taylor Rules for Monetary Policy?” Federal Reserve Bank of Kansas City, Economic Review, vol. 84 no. 2, 5–33. Sources: U.S. Department of Commerce, Bureau of Economic Analysis; Congressional Budget Ofﬁce; Board of Governors of the Federal Reserve System, “Selected Interest Rates,” and Federal Reserve Statistical Releases, H.15; and Bloomberg Financial Information Services. 2 FEDERAL RESERVE BANK OF CLEVELAND increasing the funds rate one-for-one with inﬂation is like treading water. Therefore, the Fed must increase the real funds rate with inﬂation to make any headway. This morethan-proportional response of the nominal funds rate to inﬂation, known as the Taylor principle, therefore prescribes that the real federal funds rate should be made greater than the natural rate of interest whenever inﬂation is above target. In the simplest form of the rule, Taylor argued that the Fed should increase the real funds rate by half a percentage point for every percentage point that inﬂation is above target or output is above potential. This implies that the nominal funds rate should increase by 1.5 percent for every percentage point increase in inﬂation. (Likewise, the Fed should decrease the real funds rate by the same amount for deviations below either target or potential.) Thus, Taylor felt that monetary policy (in terms of the real funds rate) should respond equally (in terms of the real interest rate) to inﬂation and output deviations. But the exact weights are not crucial. Empirical evidence suggests that the Fed has responded to output-gap deviations (at least since 1983) a little less than Taylor had assumed: it* = 2.32 + 1.44 * (π t − π * ) + 0.15* output gapt . Figure 1 plots this rule, which goes for long periods below or above the actual funds rate. One reason for these long misses is that the FOMC does not change the funds rate as often or as dramatically as the simple Taylor rule suggests. Instead, the actual funds rate exhibits a lot of inertia, suggesting that an inertial Taylor rule might be a better ﬁt. Here the Fed also looks at the past funds rate in setting its target.The partial-adjustment (or inertial) Taylor rule is given by itPA = 0.76 * it −1 + 00.24* it* , where it–1 is last quarter’s funds rate (measured by the federal funds rate on the last day of the quarter) and i* is the target rate (the rate suggested by the Taylor rule without inertia). Figure 1 also plots this inertial rule. The baseline rule without inertia is basically a longer-run target that provides guidance for where the funds rate will eventually end up. This formulation assumes that instead of moving there immediately, the Fed moves only 24 percent of the way there each quarter.Figure 1 clearly shows that this partial-adjustment Taylor rule tracks the actual funds rate very closely.Another way of thinking about the partialadjustment formulation is that instead of reacting to today’s inﬂation and output gap, the FOMC reacts to a weighted average of today’s and all past inﬂation and output gaps. The discussion that follows shows that with sticky prices and sticky wages, a partial-adjustment Taylor rule delivers better inﬂation and output outcomes than the traditional Taylor rule. This is shown in the context of an oil shock that reduces output and increases inﬂation. 3 POLICY DISCUSSION PAPERS NUMBER 17, APRIL 2007 Oil Prices and Monetary Policy: A CGE Model To ascertain whether an inertial or noninertial Taylor rule is better, we need a calibrated computable general-equilibrium (CGE) model. Here we sketch the model used for our simulations; we describe it more fully in the appendix, along with our calibration of its parameters. Oil is an important input in manufacturing (and, perhaps to a lesser extent, in services). Oil price increases will therefore reduce output and (for a given monetary policy) increase prices.The rise in prices is not instantaneous, however; the evidence suggests that prices are sticky and adjust slowly and that wages are sticky as well. Both these forms of nominal stickiness imply that output will not respond efﬁciently and will differ from its ﬁrst-best level (or potential). That is, if both prices and wages were perfectly ﬂexible, the output gap would be zero. A key issue in the analysis is, of course, the statement of monetary policy. For the benchmark simulation, we assume that policy is given by the noninertial Taylor type described in the previous section. For the inertial rule, we assume that policy adjusts only 24 percent of the way to the rate predicted by the basic Taylor rule (this is the partialadjustment rate suggested by Kozicki, 1999). Model Simulations Model simulations suggest that there may be an advantage in adjusting the funds rate slowly. Figure 2 answers the hypothetical questions, “Holding everything else constant, how would inﬂation, interest rates, and output be expected to behave following a onetime 30 percent increase in oil prices? How would these variables behave if the Fed followed a noninertial Taylor rule versus an inertial Taylor rule?” All variables are plotted as log deviations from trend. (For the funds rate and inﬂation, these are linear deviations from trend.) With both rules, the oil shock tends to increase inﬂation. The Taylor rule suggests that policymakers raise the nominal interest rate to keep inﬂation from increasing even more. But with inertia, this increase is smaller and spread out over time. Therefore, the difference between an inertial rule and noninertial rule is that the latter increases rates less today with a promise of future increases. This promise to increase rates in the future is extremely important. With inertia, the nominal funds rate lags behind the rule without inertia and peaks at a much lower level as well. The promise of future rate increases keeps inﬂation lower than the noninertial rule as well. Surprisingly, the funds rate with inertia is always lower than the noninertial Taylor rule, yet inﬂation too is always lower. This is because the stance of monetary policy is not given by the nominal funds rate but by the real, inﬂation-adjusted funds rate. More precisely, the policy stance is given by how much the real, inﬂation-adjusted 4 FEDERAL RESERVE BANK OF CLEVELAND funds rate deviates from the Wicksellian interest rate (the real interest rate that would prevail in the economy if there were no price or wage stickiness or, equivalently, if the output gap were always equal to zero). By construction, therefore, the Wicksellian rate is the same for both the inertial and noninertial rules. In the quarters immediately following an oil price increase, policy is much easier (the real rate is lower) for the inertial rule. However, this does not translate into more inﬂation today because in later periods, policy is expected to be tighter for the inertial rule.A long period in the distant future when policy is expected to be tighter more than compensates (in terms of inﬂation outcomes) for the shorter period of time when policy was substantially easier. The true stance of monetary policy, therefore, is given not only by the real interest rate but also by the real rate’s future path. Although inversely related, the behavior of the output gap mirrors that of the real interest rate. In the beginning, the real interest rate is lower, making policy less restrictive than it is for the noninertial rule. Not surprisingly, output is higher and thus the output gap for the inertial rules during these periods. In subsequent periods, things are reversed.The output gap is composed of two distortions, one arising from sticky prices and the other from sticky wages.The output gap from sticky prices is nearly identical for the two rules (although a little lower for the inertial rule). It is the gap arising from sticky wages that drives the differences in the total output gap. Inﬂation is a little lower in the inertial model because output and the output gap resulting from sticky prices is a little lower.Another way of thinking about inﬂation is that it is the present discounted value of all future marginal costs (the inverse of a markup). Current prices are determined by marginal cost, as it is today and is expected be in the future. A larger markup (lower marginal cost) means that output is further below its efﬁcient level, a negative output gap. Like marginal cost for sticky prices, the monopoly distortion in labor markets measures the difference between the household’s marginal rate of substitution and the real wage. A value of unity would mean no distortion, whereas a smaller value would imply a larger distortion and thus less output and the output gap. Analogous to inﬂation, wage inﬂation is the present discounted value of all these future deviations. This distortion is what drives the differences in the output gap between the inertial and noninertial Taylor rule simulations. Nominal wage inﬂation driven by differences in real wage growth is always lower in the inertial model. The fact that wage inﬂation is always lower with inertia implies that in a present discounted sense, output is further below potential than it is in the model without inertia. 5 POLICY DISCUSSION PAPERS FIGURE 2 NUMBER 17, APRIL 2007 RESPONSE TO AN OIL SHOCK (STICKY PRICES AND STICKY WAGES)* Deviation from trend, percent 0.9 0.8 0.7 0.6 0.5 0.4 Inflation (standard rule) 0.3 0.2 0.1 Inflation (inertial rule) 0.0 0 2 4 6 8 10 Quarter 12 14 16 18 20 Deviation from trend, percent 0.9 0.8 Nominal interest rate (standard rule) 0.7 0.6 0.5 0.4 0.3 0.2 Nominal interest rate (inertial rule) 0.1 0.0 0 2 4 6 8 10 12 14 16 18 20 16 18 20 Quarter Deviation from trend, percent 0.4 Real rate (standard rule) 0.3 Real rate (inertial rule) 0.2 0.1 0.0 -0.1 -0.2 -0.3 Wicksellian rate -0.4 -0.5 0 2 4 6 8 10 Quarter 6 12 14 FEDERAL RESERVE BANK OF CLEVELAND FIGURE 2 RESPONSE TO AN OIL SHOCK (STICKY PRICES AND STICKY WAGES)* (CONTINUED) Deviation from trend, percent 1.0 Gap (standard rule) 0.5 0.0 -0.5 Gap (inertial rule) -1.0 -1.5 -2.0 -2.5 -3.0 0 2 4 6 8 10 12 14 16 18 20 14 16 18 20 Quarter Deviation from trend, percent 1.4 Marginal cost (inertial rule) 1.2 1.0 0.8 0.6 0.4 Marginal cost (standard rule) 0.2 0.0 0 2 4 6 8 10 12 Quarter Deviation from trend, percent 1 Labor distortion (standard rule) 0 Labor distortion (inertial rule) -1 -2 -3 -4 -5 0 2 4 6 8 10 12 14 16 18 20 Quarter 7 POLICY DISCUSSION PAPERS FIGURE 2 NUMBER 17, APRIL 2007 RESPONSE TO AN OIL SHOCK (STICKY PRICES AND STICKY WAGES)* (CONTINUED) Deviation from trend, percent 0.16 Wage inflation (standard rule) 0.12 0.08 Wage inflation (inertial rule) 0.04 0.00 -0.04 0 2 4 6 8 10 12 14 16 18 20 Quarter *Simulations are hypothetical responses to a 30 percent oil price shock, given that future oil prices behave as they have in the past. Sources: U.S. Department of Commerce, Bureau of Economic Analysis; U.S. Department of Labor, Bureau of Labor Statistics; Board of Governors of the Federal Reserve System, “Selected Interest Rates,”Federal Reserve Statistical Releases H.15; and authors’ calculations. The differences between the output gap driven by sticky prices and that driven by sticky wages suggests that the latter may be crucial to the result that inertia appears to deliver better outcomes. A model with just sticky prices bears this out. Figure 3 graphs the outcomes for the model with only sticky prices. Inﬂation was everywhere lower for the inertial Taylor rule in the model with both sticky prices and sticky wages. But with only sticky prices, inﬂation is initially much higher for the inertial Taylor rule. Output and the output gap are initially higher as well. Because of the large inﬂation jump, nominal interest rates in the ﬁrst few quarters after the energy shock are just as high for the inertial rule as for the noninertial. The importance of inertial Taylor rules is reminiscent of the beneﬁts of forward-looking language in FOMC policy statements.With forward-looking language, the Fed moves today and signals where they intend to move in the future. Likewise, by inﬂuencing expectations, monetary policy operates off of both short- and long-term rates.An inertial Taylor rule basically states where the Fed moves today and where they are expected to move in the future. 8 FEDERAL RESERVE BANK OF CLEVELAND FIGURE 3 RESPONSE TO AN OIL SHOCK (STICKY PRICES ONLY)* Deviation from trend, percent 0.35 0.30 0.25 Inflation (standard rule) 0.20 0.15 0.10 Inflation (inertial rule) 0.05 0.00 0 2 4 6 8 10 12 14 16 18 20 Quarter Deviation from trend, percent 0.40 0.35 Nominal interest rate (standard rule) 0.30 0.25 0.20 Nominal interest rate (inertial rule) 0.15 0.10 0.05 0.00 0 2 4 6 8 10 12 14 16 18 20 12 14 16 18 20 Quarter Deviation from trend, percent 0.2 Real rate (standard rule) 0.1 Real rate (inertial rule) 0.0 -0.1 -0.2 -0.3 Wicksellian rate -0.4 -0.5 0 2 4 6 8 10 Quarter 9 POLICY DISCUSSION PAPERS FIGURE 3 NUMBER 17, APRIL 2007 RESPONSE TO AN OIL SHOCK (STICKY PRICES ONLY)* (CONTINUED) Deviation from trend, percent 0.6 0.4 Gap (inertial rule) 0.2 0.0 -0.2 -0.4 Gap (standard rule) -0.6 -0.8 0 2 4 6 8 10 12 14 16 18 20 Quarter *Simulations are hypothetical responses to a 30 percent oil price shock, given that future oil prices behave as they have in the past. Sources: U.S. Department of Commerce, Bureau of Economic Analysis; U.S. Department of Labor, Bureau of Labor Statistics; Board of Governors of the Federal Reserve System, “Selected Interest Rates,” Federal Reserve Statistical Releases, H.15; and authors’ calculations. Conclusion This paper has shown that in a standard model with sticky wages and sticky prices, a Taylor rule with inertia delivers better outcomes than the standard rule without inertia.This result, however, depends on the stickiness of wages relative to prices. Recent work by Christiano, Eichenbaum, and Evans suggests the importance of sticky wages in explaining business cycle ﬂuctuations. This lends support to the notion that the Fed implicitly follows an inertial Taylor rule because it delivers lower interest rates and inﬂation without worsening output signiﬁcantly. In fact, for the ﬁrst several quarters following the oil price increase, output is also higher for the inertial rule. 10 FEDERAL RESERVE BANK OF CLEVELAND Appendix The Model Apart from adding oil to the production technology, the underlying model is fairly standard. See Woodford (2003) and Walsh (2003) for details. The theoretical model described here consists of households and ﬁrms; we present the decision problems of each in turn. Households Households are inﬁnitely lived, discounting the future at rate β . Their period-by-period utility function is given by U ( Ct , Lt , Mt +1 C 1−σ L1+γ M ) ≡ t − t + V ( t +1 ), Pt Pt 1−σ 1+ γ where σ < 0, γ > 0, V is increasing and concave, Ct denotes consumption, Lt denotes M labor, and t +1 denotes real cash balances that can facilitate time-t transactions. The Pt household begins period t with Mt cash balances and Bt – 1 one-period nominal bonds that pay Rt – 1 gross interest. With wt denoting the real wage, Pt the price level, and Xt the time-t monetary injection, the household’s intertemporal budget constraint is given by Pt Ct + Bt + Mt +1 ≤ Mt + Rt −1 Bt −1 + Pt wt Lt + Xt . The household’s portfolio choice is given by V ′( Mt +1 / Pt ) Rt − 1 = Rt Ct−σ Ct−σ = Rt β Ct−+σ / π t +1 . 1 Following Erceg, Henderson, and Levin (2000), we assume that households are monopolistic suppliers of labor and that nominal wages are adjusted as in Calvo (1983). In this case, labor supply behavior is given by Ctσ Lγ = Zht Wt . t It is easy to see that the wage elasticity of labor demand in this model is 1/ γ . The variable Zht in this labor demand equation is the monopoly distortion as it measures the difference between the household’s marginal rate of substitution and the real wage. In the case of perfectly ﬂexible but monopolistic wages, Zht = Zh is constant and less than unity. The smaller Zh is, the greater is the monopoly power. In the case of sticky 11 POLICY DISCUSSION PAPERS NUMBER 17, APRIL 2007 nominal wages, Zht is variable and moves in response to the real and nominal shocks hitting the economy. Erceg et al. (2000) demonstrate that in log deviations, nominal wage adjustment is given by π tw = λ w zht + βπ tw , +1 w where π t is time-t net nominal wage growth, and zht denotes the log deviation from the steady state. Firms The ﬁrms in the model utilize labor services, Lt, from households, and energy, Et, from external sources to produce the ﬁnal good using the CES technology: 1 /(1− ρ ) Y = f ( L, E ) ≡ ⎡(1 − a ) L1− ρ + aE 1− ρ ⎤ ⎣ ⎦ . w The real energy price is equal to π t so that a ﬁrm’s nominal proﬁts are given by profits = Pt (Yt − wt Lt − pte Et ). The ﬁrm is a monopolistic producer of these goods, implying that labor will be paid below its marginal product. Let Zt denote marginal cost so that we have wt = Zt fL ( t ) pte = Zt f E ( t ). The variable Zt is the monopoly distortion as it measures how far the ﬁrm’s marginal products differ from the real factor prices. In the case of perfectly ﬂexible but monopolistic prices, Zt = Z is constant and less than unity. The smaller Z is, the greater is the monopoly power. In the case of sticky prices, Zt is variable and moves in response to the real and nominal shocks hitting the economy. Yun (1996) demonstrates that in log deviations, nominal price adjustment is given by π t = λ zt + βπ t +1 , where π t is time-t nominal price growth (as a deviation from steady-state nominal price growth) and zt denotes the log deviation from the steady state. 12 FEDERAL RESERVE BANK OF CLEVELAND Equilibrium and Policy There are four markets in this theoretical model: labor, goods, bonds, and money. The respective market-clearing conditions include Ct = Yt = pte Et and Bt = 0. The money market clears with the household holding the per capita money supply intertemporally. Calibration Before proceeding with the analysis, we need to set parameter values consistent with empirical estimates for a quarterly model. Preference parameters are given by β = 0.99 (implying a 4 percent annual steady-state real rate of return), σ = 2, and γ = 3. The latter values are consistent with micro evidence of fairly inelastic savings and labor supply behavior. Since monetary policy is given by an interest rate targeting procedure, the nature of money’s utility is irrelevant. Finally, we assume that prices and nominal wage levels can be adjusted on average every 2.9 quarters. Given the other preference parameters, this implies λ = 0.19 and λ w = 0.0146. For the model with sticky prices only λ w = 1000. As for ﬁrms, the elasticity of substitution between oil and labor is equal to 1/ ρ . Consistent with empirical estimates, we set this elasticity to 0.59, or ρ = 1.7. See Kim and Loungani (1992). The share parameter, a, is set to 0.02.This implies a share of energy in total output of 6 percent (consistent with its share in 1989). The (logged) real price of oil is given by an exogenous AR(2) process: pte = a1 pte−1 + a2 pte−2 + ε t . Estimating this process yields a1 = 1.12 and a2 = –15. Finally, recall that monetary policy in the baseline experiment is given by Rt = (1 − ρ ) Rss + ρ Rt −1 + (1 − ρ )(τπ t + τ y yt ). Empirical evidence presented in Kozicki (2002) suggests that since 1983, the coefﬁcients in this monetary policy rule are τ = 1.44 and τ y = 0.14. For the noninertial Taylor rule, ρ = 0, whereas for the inertial Taylor rule, ρ = 0.76. 13 POLICY DISCUSSION PAPERS NUMBER 17, APRIL 2007 References Calvo, G., 1983.“Staggered Prices in a Utility-Maximizing Framework,” Journal of Monetary Economics 12:383–98. Christiano, L.J., M. Eichenbaum, and C.L. Evans, 2005,“Nominal Rigidities and the Dynamic Effects of a Shock to Monetary Policy,” Journal of Political Economy, 113 (1): 1–45. Carlstrom, C.T, and T. S. Fuerst, (forthcoming). “Oil Prices, Monetary Policy, and Expectations,” Journal of Money, Credit, and Banking. Erceg, C.J., D.W. Henderson, and A.T. Levin, 2000. “Optimal Monetary Policy with Staggered Wage and Price Contracts,” Journal of Monetary Economics 46: 281–313. Kozicki, S., 1999.“How Useful Are Taylor Rules for Monetary Policy?” Federal Reserve Bank of Kansas City Economic Review, Second Quarter:533. Kim, I., and P. Loungani, P. 1992,“The Role of Energy in Real Business Cycle Models,” Journal of Monetary Economics 29 (2), 173–89. Taylor, J.B., 1993.“Discretion versus Policy Rules in Practice,” Carnegie-Rochester Conference Series on Public Policy 39:195–214. Walsh, C., 2003. Monetary Theory and Policy, MIT Press. Woodford, M., 2003. Interest and Prices, Princeton University Press. Yun, T., 1996. “Nominal Price Rigidity, Money Supply Endogeneity, and Business Cycles,” Journal of Monetary Economics 37(2):345–70. 14