FirmSpecific Labor, Trend Inflation, and Equilibrium Stability. Takushi Kurozumi and Willem Van Zandweghe December 2012 RWP 1209


 Rodney Wright
 1 years ago
 Views:
Transcription
1 FirmSpecific Labor, Trend Inflation, and Equilibrium Stability Takushi Kurozumi and Willem Van Zandweghe December 212 RWP 129
2 FirmSpecific Labor, Trend Inflation, and Equilibrium Stability Takushi Kurozumi Willem Van Zandweghe December 212 Abstract In a Calvo sticky price model based on micro evidence that each period a fraction of prices is kept unchanged, we examine implications of firmspecific labor for determinacy and expectational stability (Estability) of rational expectations equilibrium under interest rate policy. Firmspecific labor causes higher trend inflation to be more likely to induce not only indeterminacy but also Einstability. The latter is in contrast with the result of E stability in the case of homogeneous labor analyzed in recent research. Moreover, under the same calibration of structural model parameters, indeterminacy and Einstability are much more likely in the case of firmspecific labor than in the case of homogeneous labor. The recent argument a decline in trend inflation along with the Fed s change from a passive to an active policy response to inflation explains much of the U.S. economy s shift from indeterminacy during the Great Inflation era to determinacy during the Great Moderation era depends crucially on the assumption of firmspecific labor. JEL Classification: E31, E52 Keywords: Firmspecific labor, Trend inflation, Sticky prices, Determinacy, Expectational stability The authors are grateful for comments and discussions to Olivier Coibion, Andrew Foerster, and participants at the Federal Reserve Bank of Kansas City and the Midwest Macroeconomics Meetings 212. The views expressed herein are those of the authors and should not be interpreted as those of the Bank of Japan, the Federal Reserve Bank of Kansas City or the Federal Reserve System. Bank of Japan, Nihonbashi Hongokucho, Chuoku, Tokyo , Japan. Tel.: ; fax: address: Federal Reserve Bank of Kansas City, 1 Memorial Drive, Kansas City, MO 64198, USA. Tel.: ; fax: address: 1
3 1 Introduction Recent literature has studied implications of positive trend inflation rates for macroeconomic stability using sticky price models based on micro evidence that each period a fraction of prices is kept unchanged. Ascari and Ropele (29), Hornstein and Wolman (25), and Kiley (27) analyze determinacy of equilibrium under the Taylor (1993) rule and show that higher trend inflation is more likely to induce indeterminacy. Moreover, Coibion and Gorodnichenko (211) argue that a decline in trend inflation along with an increase in the Fed s policy response to inflation accounts for much of the U.S. economy s shift from indeterminacy during the Great Inflation era to determinacy during the Great Moderation era, against Clarida et al. (2) and Lubik and Schorfheide (24) who all attribute this shift solely to the Fed s change from a passive to an active policy response to inflation. 1 In a Calvo (1983) sticky price model, Ascari and Ropele (29) consider homogeneous labor, whereas Coibion and Gorodnichenko (211) introduce firmspecific labor. 2 This difference in the specification of labor yields two differences in inflation dynamics represented by a general formulation of the New Keynesian Phillips curve (NKPC). First, like firmspecific capital analyzed in Altig et al. (211), Eichenbaum and Fisher (27), Sveen and Weinke (25, 27) and Woodford (25), firmspecific labor introduces strategic complementarity or real rigidity. 3 As a consequence, the longrun inflation elasticity of output implied by the NKPC is smaller in the case of firmspecific labor than in the case of homogeneous labor, when the trend inflation rate is greater than a certain threshold that is positive but close to zero. 4 Second, price distortion 1 Boivin and Giannoni (26) show, using counterfactual simulations, that the shift to the Great Moderation cannot be explained solely, or even primarily, by a change in shocks to the U.S. economy, and conclude that in order to explain this shift, it is crucial for the U.S. monetary policy to have changed the way it has, along with the shocks. Kimura and Kurozumi (21) offer theoretical support for the good policy hypothesis about the shift to the Great Moderation using a Calvo model with endogenous price stickiness. Specifically, they show that a more aggressive monetary policy response to inflation makes firms less likely to reset prices and gives the resulting New Keynesian Phillips curve a flatter slope and a smaller disturbance, as observed during the Great Moderation era, and that such a policy response can stabilize both inflation and the output gap by exploiting the feedback effects of this policy response on firms pricesetting. 2 Hornstein and Wolman (25) and Kiley (27) use a Taylor (198) sticky price model. 3 See also Levin et al. (27) for implications of strategic complementarity for sticky price models. 4 By contrast, when the trend inflation rate is lower than this threshold (e.g., the zero trend inflation rate), the longrun inflation elasticity of output is larger in the case of firmspecific labor. 2
4 has an influence on the inflation dynamics in the case of homogeneous labor as long as the elasticity of labor supply is finite and the trend inflation rate is nonzero, but not in the case of firmspecific labor. Thus, when labor is homogeneous, the law of motion of price distortion adds lagged price distortion to the set of relevant model state variables. Despite these differences, the existing literature lacks a comparison of sticky price models with homogeneous labor and with firmspecific labor in terms of equilibrium determinacy or macroeconomic stability. The present paper fills this gap using a Calvo sticky price model with firmspecific labor based on Coibion and Gorodnichenko (28, 211) and its associated model with homogeneous labor, which is a stochastic version of the baseline model of Ascari and Ropele (29). We also examine expectational stability (Estability) of fundamental rational expectations equilibrium (REE) in the model with firmspecific labor, and compare it with that in the model with homogeneous labor. 5 As McCallum (27) indicates, Estability is very closely linked with leastsquares learnability (i.e., stability under leastsquares learning) and this learnability is arguably a necessary property for an REE to be plausible as equilibrium for the model at hand. In a broad class of linear models with expectations (including the loglinearized model of the present paper), a nonexplosive fundamental REE is leastsquares learnable if it is E stable; otherwise, it is not leastsquares learnable (Evans and Honkapohja, 21). Therefore, Estability is an essential condition for an REE to be regarded as plausible. We establish the necessary and sufficient conditions for determinacy of REE and for E stability of fundamental REE when labor is firmspecific. Using these analytical conditions and a plausible calibration of structural model parameters, we show that firmspecific labor causes higher trend inflation to be more likely to induce not only indeterminacy of REE but also Einstability of fundamental REE. Moreover, we find that under the same calibration, indeterminacy and Einstability are much more likely in the case of firmspecific labor than in the case of homogeneous labor. When labor is firmspecific, higher trend inflation is more likely to generate indeterminacy, as shown in Coibion and Gorodnichenko (211). This result is qualitatively consistent with that of Ascari and Ropele (29) who study the case of homogeneous labor, but firmspecific labor is much more likely to cause indeterminacy under the same calibration of structural 5 The term fundamental refers to Evans and Honkapohja s (21) minimalstatevariable (MSV) solutions to linear rational expectations models to distinguish them from McCallum s (1983) original MSV solution. 3
5 model parameters. 6 This is because firmspecific labor introduces strategic complementarity, which is a source of indeterminacy as is the case with firmspecific capital analyzed in Sveen and Weinke (25, 27). Specifically, two key conditions for determinacy are less likely to be satisfied in the model with firmspecific labor under the same calibration. One condition is the longrun version of the Taylor principle: in the long run the interest rate should be raised by more than the increase in inflation. This Taylor principle is less likely to be met as the longrun inflation elasticity of output is smaller. When the trend inflation rate is greater than a certain threshold that is positive but close to zero, the strategic complementarity incorporated by firmspecific labor makes the elasticity smaller and thereby causes the longrun version of the Taylor principle to be less likely to be satisfied. As a consequence, a large policy response to current or expected future output induces indeterminacy in the case of firmspecific labor, even if such a response may ensure determinacy under the same calibration in the case of homogeneous labor. The other condition for determinacy causes a small policy response to current or expected future output to induce indeterminacy under positive trend inflation rates. This condition is also less likely to be met in the case of firmspecific labor than in the case of homogeneous labor, when the same calibration is used in these two cases. Our result of Einstability in the case of firmspecific labor is in contrast with the result of Estability in the case of homogeneous labor. In the latter case, Estability of fundamental REE is likely even when trend inflation is high, as shown in Kurozumi (211). This difference is due to two factors. First, the longrun version of the Taylor principle is a necessary condition for E stability of fundamental REE as well. Therefore, as with the result regarding determinacy, the different result regarding Estability arises because the longrun version of the Taylor principle is less likely to be satisfied in the case of firmspecific labor than in the case of homogeneous labor. Second, when labor is homogeneous, the NKPC depends on price distortion as long as the elasticity of labor supply is finite and the trend inflation rate is nonzero, and hence the law of motion of price distortion adds lagged price distortion to the set of relevant model state 6 Kurozumi (29) shows that the indeterminacy result of Ascari and Ropele (29) is overturned when price stickiness is endogenously determined in a Calvo model along the lines of the literature such as Ball et al. (1988), Romer (199), Kiley (2), Devereux and Yetman (22), and Levin and Yun (27). This is because the longrun inflation elasticity of output implied by the NKPC declines substantially with higher trend inflation in the case of exogenously given price stickiness, whereas in the case of endogenous price stickiness the decline in the elasticity is mitigated as higher trend inflation leads to a higher probability of price adjustment. 4
6 variables. However, this is not the case when labor is firmspecific. For the REE in question, E stability examines whether an associated equilibrium in which agents form expectations under adaptive learning reaches over time the REE. For such expectation formation, lagged price distortion is useful information in the model with homogeneous labor. Particularly, it helps agents form inflation expectations, since price distortion affects inflation dynamics. Therefore, Estability is likely in the case of homogeneous labor. By contrast, in the case of firmspecific labor, price distortion is absent in the set of relevant model state variables and hence higher trend inflation is much more likely to induce Einstability. 7 Our results demonstrate that indeterminacy and Einstability are much more likely in the model with firmspecific labor than in the model with homogeneous labor. Specifically, the argument of Coibion and Gorodnichenko (211) who use the former model to show that a decline in trend inflation plays a key role in the U.S. economy s shift from indeterminacy during the Great Inflation era to determinacy during the Great Moderation era depends crucially on the assumption of firmspecific labor. 8 The remainder of the paper proceeds as follows. Section 2 presents a Calvo sticky price model with firmspecific labor. In this model, Section 3 derives conditions for equilibrium determinacy and for Estability of fundamental REE and investigates implications of these conditions. Section 4 compares the results regarding determinacy and Estability with those in the case of homogeneous labor. Finally, Section 5 concludes. 7 Kobayashi and Muto (211) use a Calvo sticky price model with homogeneous labor based on Sbordone (27) and Cogley and Sbordone (28), but their model follows Sbordone (27) to assume that real marginal cost does not depend on price distortion. Due to this assumption, price distortion does not appear in their NKPC and hence it is absent in the set of relevant model state variables. Consequently, they reach the conclusion that when trend inflation is high, Einstability is likely. This is qualitatively consistent with our result of Einstability obtained in the case of firmspecific labor. 8 Ascari et al. (211) show, conducting counterfactual exercises, that the impact of variations in trend inflation on the likelihood of equilibrium indeterminacy is both modest and limited to the second half of the 197s, suggesting that the Fed s change from a passive to an active policy response to inflation is likely to have been the main driver leading the U.S. economy to a unique equilibrium during the Great Moderation era. 5
7 2 A Calvo sticky price model with firmspecific labor The model is a Calvo sticky price model based on Coibion and Gorodnichenko (28, 211). In the model economy there are a representative household, a finalgood firm, a continuum of intermediategood firms, and a monetary authority. Key features of the model are that the household s members supply labor specific to intermediategood firms, while each period a fraction of intermediategood firms keeps prices of their differentiated products unchanged. The behavior of each economic agent is described in turn. 2.1 Household The representative household consumes C t final goods, supplies {N t (i)} labor specific to each intermediategood firm i [, 1], and purchases S t oneperiod riskless bonds so as to maximize the utility function E β [ln t 1 C t 1 + 1/η t= 1 ] (N t (i)) 1+1/η di exp(ε t ) subject to the budget constraint P t C t + S t = 1 W t (i)n t (i) di + R t 1 S t 1 + T t, where E t is the rational expectation operator conditional on information available in period t, β (, 1) is the subjective discount factor, η is the elasticity of labor supply, ε t is a preference shock governed by a firstorder autoregression process with a persistence parameter ρ [, 1), P t is the price of final goods, W t (i) is the wage paid by intermediategood firm i, R t is the gross interest rate on bonds, and T t consists of lumpsum transfers and firm profits. Combining firstorder conditions for utility maximization with respect to consumption, labor supply, and bond holdings yields where Π t = P t /P t 1 denotes gross inflation. W t (i) = C t (N t (i)) 1/η, (1) P t ( ) Ct exp(ε t+1 ) R t 1 = βe t, (2) C t+1 exp(ε t ) Π t+1 6
8 2.2 Firms The representative finalgood firm produces homogeneous goods Y t under perfect competition by choosing a combination of intermediate inputs {Y t (i)} so as to maximize profit P t Y t subject to the CES production technology 1 P t (i)y t (i) dj [ 1 θ/(θ 1) Y t = (Y t (i)) di] (θ 1)/θ, where P t (i) is the price of intermediate good i and θ > 1 is the price elasticity of demand for each intermediate good. The firstorder condition for profit maximization yields the finalgood firm s demand for intermediate good i, while perfect competition in the finalgood market leads to The finalgood market clearing condition is given by ( ) Pt (i) θ Y t (i) = Y t, (3) P t [ 1 1/(1 θ) P t = (P t (i)) di] 1 θ. (4) Y t = C t. (5) Each intermediategood firm i produces one kind of differentiated goods Y t (i) under monopolistic competition. Firm i s production function is given by Y t (i) = A t (N t (i)) α, (6) where α (, 1] is the labor elasticity of output and the technology A t follows the process ln A t = g + ln A t 1, (7) where g is the rate of technological change. The firstorder condition for minimization of production cost determines firm i s marginal cost MC t (i) = W t(i)n t (i). (8) αy t (i) 7
9 In the face of the finalgood firm s demand (3) and marginal cost (8), intermediategood firms set prices of their products on a staggered basis as in Calvo (1983). Each period a fraction λ (, 1) of firms keeps previousperiod prices unchanged, while the remaining fraction 1 λ of firms sets the price B t (i) so as to maximize the profit function E t j= ( ) λ j Bt (i) θ Q t,t+j Y t+j (B t (i) MC t+j(i)), P t+j where Q t,t+j = β j P t C t exp(ε t+j )/[P t+j C t+j exp(ε t )] is the stochastic discount factor for a unit of money between period t and period t + j. For this profit function to be welldefined, the following assumption is imposed throughout the paper. Assumption 1 The two inequalities λ Π θ 1 < 1 and βλ Π θ(1+1/η)/α < 1 hold, where Π is gross trend (or steadystate) inflation. Moreover, the trend inflation rate is nonnegative, i.e., Π 1. Using eqs. (1), (3), (5), (6), and (8), the firstorder condition for staggered pricesetting leads to { ( ) [ 1 θ E t (βλ) j Bt exp(ε t+j ) θ ( ) ] 1 Y θ γ } t+j Bt =, (9) P t+j θ 1 α A t+j P t+j j= where B t is the price set by firms that reoptimize prices in period t and the composite parameter γ is given by γ = (1 + 1/η)/α. Moreover, the final goods price equation (4) can be reduced to (P t ) 1 θ = (1 λ)(b t ) 1 θ + λ(p t 1 ) 1 θ. (1) 2.3 Monetary authority The monetary authority conducts interest rate policy according to a Taylor (1993) rule. This rule adjusts the interest rate R t in response to deviations of either contemporaneous or expected future inflation and output from their trend levels ln R t = ln R + ϕ π (ln E t Π t+i ln Π) + ϕ y [ln E t (Y t+i /A t+i ) ln y], i =, 1, (11) where R is the gross steadystate interest rate, y is the steadystate level of detrended output y t = Y t /A t, and ϕ π, ϕ y are the degrees of policy responses to inflation and output. The interest rate policy is referred to as outcomebased if i = and forecastbased if i = 1. 8
10 2.4 Loglinearized equilibrium conditions Under Assumption 1, detrending and loglinearizing the equilibrium conditions (2), (5), (9), (1), and (11) leads to ŷ t = E t ŷ t+1 ( ˆR t E t ˆΠt+1 ) + ε t E t ε t+1, (12) ˆΠ t βλ Π θγ E t ˆΠt+1 = β(e t ˆΠt+1 βλ Π θγ E t ˆΠt+2 ) + β( Π 1+θ(γ 1) 1)(1 λ Π θ 1 ) [θγe t ˆΠt+1 (ε t E t ε t+1 )] 1 + θ(γ 1) + γ(1 λ Π θ 1 )(1 βλ Π θγ ) λ Π θ 1 (ŷ t βλ [1 + θ(γ 1)] Π θ 1 E t ŷ t+1 ), (13) ˆR t = ϕ π E t ˆΠt+i + ϕ y E t ŷ t+i, i =, 1, (14) where all hatted variables represent logdeviations from steadystate values. Eq. (13) presents a general formulation of the NKPC, since under the zero trend inflation rate (i.e., Π = 1), this equation is rewritten as ˆΠ t βλe t ˆΠt+1 = β(e t ˆΠt+1 βλe t ˆΠt+2 ) + which can be reduced to 2.5 Calibration ˆΠ t = βe t ˆΠt+1 + γ(1 λ)(1 βλ) (ŷ t βλe t ŷ t+1 ), λ[1 + θ(γ 1)] γ(1 λ)(1 βλ) ŷ t. λ[1 + θ(γ 1)] The ensuing analysis uses a plausible calibration of structural model parameters to illustrate conditions for determinacy and Estability. The benchmark calibration for the quarterly model is summarized in Table 1. In line with Coibion and Gorodnichenko (211), we set the subjective discount factor at β =.99, the elasticity of labor supply at η = 1, the price elasticity of demand for differentiated intermediate goods at θ = 1, the labor elasticity of output at α = 1, and the probability of no price adjustment at λ =.55. Then, we have γ = (1 + 1/η)/α = 2. We also choose the persistence of preference shocks at ρ =.35 similarly to Woodford (23). Note that to meet Assumption 1 under this calibration, the annualized trend inflation rate needs to be less than 12 percent. 9
11 3 Analysis of determinacy and Estability This section establishes the necessary and sufficient conditions for determinacy of REE and for Estability of fundamental REE in the model presented in the preceding section, and then investigates implications of these conditions using the calibration of model parameters presented in Table Determinacy conditions For the analysis of equilibrium determinacy, the loglinearized equilibrium conditions (12) (14) can be reduced to a system of the form x t = AE t x t+1 + Bε t, (15) where x t = [ ˆΠ t ŷ t E t ˆΠt+1 ] and the coefficient matrix A is given in Appendix A. 9 In this system all variables in x t are nonpredetermined. Hence, the REE is determinate if and only if all eigenvalues of the matrix A are inside the unit circle. Thus, the next two propositions can be obtained. Proposition 1 Suppose that the interest rate policy is outcomebased, that is, i = in eq. (14), and Assumption 1 holds. Then, the REE is determinate if and only if the next two inequalities are satisfied. ϕ π + ϕ y ϵ y > 1, (16) F (ϕ π, ϕ y, Π; β, η, θ, α, λ) <, (17) where ϵ y is given by ϵ y = λ Π θ 1 {(1 β)(1 βλ Π θγ )[1 + θ(γ 1)] βθγ( Π 1+θ(γ 1) 1)(1 λ Π θ 1 )} γ(1 λ Π θ 1 )(1 βλ Π θ 1 )(1 βλ Π θγ ) and F ( ) is given in Appendix B. Proof See Appendix B. Proposition 2 Suppose that the interest rate policy is forecastbased, that is, i = 1 in eq. (14), and Assumption 1 holds. Then, the REE is determinate if and only if the condition (16) and 9 The form of the coefficient vector B is omitted, since it is not needed in what follows. 1
12 the next two inequalities are satisfied. ϕ π + (ϕ y 2)ω < 1, (18) G(ϕ π, ϕ y, Π; β, η, θ, α, λ) <, (19) where ω is given by ω = λ Π θ 1 (1 + β)(1 + βλ Π θγ )[1 + θ(γ 1)] + βθγ( Π 1+θ(γ 1) 1)(1 λ Π θ 1 ) γ(1 + βλ Π θ 1 )(1 λ Π θ 1 )(1 βλ Π θγ ) > and G( ) is given in Appendix C. Proof See Appendix C. The condition (16) can be interpreted as the longrun version of the Taylor principle. The NKPC (13) implies that each percentage point of permanently higher inflation yields ϵ y percentage points of permanently higher output. Hence, ϵ y represents the longrun inflation elasticity of output. Then, ϕ π + ϕ y ϵ y shows the permanent increase in the interest rate by the interest rate policy (14) in response to each unit permanent increase in inflation. Therefore, the condition (16) suggests that in the long run the interest rate should be raised by more than the increase in inflation. Note that the longrun version of the Taylor principle (16) is less likely to be satisfied for the interest rate policy coefficients ϕ π, ϕ y as the longrun inflation elasticity of output ϵ y is smaller. 3.2 Estability conditions We turn next to the analysis of Estability of fundamental REE. Following the literature on learning in macroeconomics (e.g., Bullard and Mitra, 22; Evans and Honkapohja, 21), we use the socalled Euler equation approach suggested by Honkapohja et al. (211): the rational expectation operator E t is replaced with a possibly nonrational expectation operator Ê t in the system of eqs. (12) (14). Then, the system can be reduced to z t = CÊtz t+1 + D[1 ]Êtz t+2 + F ε t, (2) where z t = [ˆΠ t ŷ t ] and the coefficient matrices C, D are given in Appendix A. 1 In this system, fundamental REE is given by z t = c + Γε t = (I ρc ρ 2 D[1 ]) 1 F ε t, (21) 1 The form of the coefficient vector F is omitted, since it is not needed in what follows. 11
13 where I denotes a conformable identity matrix. Following Section 1.3 of Evans and Honkapohja (21), we investigate Estability of the fundamental REE (21). Corresponding to this REE, all agents are assumed to be endowed with a perceived law of motion (PLM) of z t z t = c + Γε t. (22) Using forecasts from this PLM to substitute Êtz t+1 and Êtz t+2 out of the system (2) leads to the actual law of motion (ALM) of z t z t = (C + D[1 ])c + [ρ(c + ρd[1 ])Γ + F ]ε t. (23) Then, the mapping T from the PLM (22) to the ALM (23) can be defined by T (c, Γ) = ((C + D[1 ])c, ρ(c + ρd[1 ])Γ + F ). For the fundamental REE ( c, Γ) to be Estable, the matrix differential equation d dτ (c, Γ z) = T (c, Γ) (c, Γ) must have local asymptotic stability at the REE, where τ denotes a notional time. Hence, the fundamental REE ( c, Γ) is Estable if and only if all eigenvalues of two matrices, DT c ( c, Γ) = C + D[1 ] and DT Γ ( c, Γ) = ρ(c + ρd[1 ]), have real parts less than unity. Thus the following two propositions can be obtained. Proposition 3 Suppose that the interest rate policy is outcomebased, that is, i = in eq. (14), and Assumption 1 holds. Then, the fundamental REE is Estable if and only if the longrun version of the Taylor principle (16) and the next two inequalities are satisfied. ϕ π + λ Π θ 1 {[2 β βλ Π θγ (1 β)][1 + θ(γ 1)] βθγ( Π 1+θ(γ 1) 1)(1 λ Π θ 1 )} γ(1 λ Π θ 1 )(2 βλ Π θ 1 )(1 βλ Π θγ (ϕ y + 1) ) > γ(1 λ Π θ 1 )(1 βλ Π θγ ) + λ Π θ 1 [1 + θ(γ 1)] γ(1 λ Π θ 1 )(2 βλ Π θ 1 )(1 βλ Π θγ, (24) ) ϕ π + λ Π θ 1 {(1 ρβ)(1 ρβλ Π θγ )[1 + θ(γ 1)] ρβθγ( Π 1+θ(γ 1) 1)(1 λ Π θ 1 )} γ(1 λ Π θ 1 )(1 ρβλ Π θ 1 )(1 βλ Π θγ (ϕ y + 1 ρ) ) > ρ. (25) Proof See Appendix D. 12
14 Proposition 4 Suppose that the interest rate policy is forecastbased, that is, i = 1 in eq. (14), and Assumption 1 holds. Then, the fundamental REE is Estable if and only if the longrun version of the Taylor principle (16) and the next two inequalities are satisfied. ϕ π + λ Π θ 1 [1 + θ(γ 1)] γ(1 λ Π θ 1 )(1 βλ Π θγ ) (ϕ y + 1 β) > 1 + βλ Π θ 1 {θγ ( Π1+θ(γ 1) 1 ) (1 λ Π θ 1 ) + (1 β)λ Π θγ [1 + θ(γ 1)]} γ(1 λ Π θ 1 )(1 βλ Π θγ, (26) ) ϕ π + λ Π θ 1 {(1 ρβ)(1 ρβλ Π θγ )[1 + θ(γ 1)] ρβθγ( Π 1+θ(γ 1) 1)(1 λ Π θ 1 )} γ(1 λ Π θ 1 )(1 ρβλ Π θ 1 )(1 βλ Π θγ ) ( ϕ y + 1 ρ ) ρ > 1. (27) Proof See Appendix E. 3.3 Implications of determinacy and Estability conditions We now illustrate the conditions for determinacy and for Estability given in Propositions 1 to 4 using the calibration of model parameters presented in Table 1. For the outcomebased interest rate policy (i.e., i = in eq. (14)), Fig. 1 shows regions of the policy coefficients (ϕ π, ϕ y ) that guarantee determinacy of REE or Estability of fundamental REE in the cases of the annualized trend inflation rate of two, four, six, and eight percent. Fig. 2 displays similar regions for the forecastbased interest rate policy (i.e., i = 1 in eq. (14)). Note that the coefficients estimated by Taylor (1993) are (ϕ π, ϕ y ) = (1.5,.5/4) = (1.5,.125) which is marked by in each panel of these figures and thus it is reasonable to consider the range of ϕ π = 4.5 and ϕ y =.375. These two figures demonstrate that higher trend inflation is more likely to induce not only indeterminacy but also Einstability. Indeed, Taylor s estimates generate indeterminacy and Einstability once the annualized trend inflation rate is equal to or greater than four percent. Moreover, higher trend inflation is more likely to generate indeterminacy rather than Einstability, especially when the policy response to output is small. Indeed, in the case of the outcomebased policy with no response to output (i.e., ϕ y = ), determinacy requires a very active policy response to inflation under the annualized trend inflation rate of four percent, whereas Estability requires a mildly active one. The forecastbased policy with no response to expected future output induces indeterminacy for any trend inflation rate considered unless the policy response to expected future inflation is extremely strong, whereas it ensures Estability in the cases of the annualized 13
15 trend inflation rate of two and four percent as long as the policy response to expected future inflation is strong enough. When trend inflation increases, the longrun inflation elasticity of output ϵ y declines, as can be seen in Fig. 3. Therefore, the longrun version of the Taylor principle (16) is less likely to be satisfied for the interest rate policy coefficients ϕ π, ϕ y, as noted above. For instance, the coefficients estimated by Taylor (1993) (i.e. (ϕ π, ϕ y ) = (1.5,.125)) no longer satisfy the longrun version of the Taylor principle once the annualized trend inflation rate is equal to or greater than four percent. Moreover, when the trend inflation rate is greater than a certain threshold that makes the numerator of the longrun inflation elasticity of output ϵ y equal to zero (i.e.,.2 percent in annualized rate terms), the elasticity becomes negative. As a consequence, a large policy response to output induces indeterminacy and Einstability. A small policy response to output also makes indeterminacy and Einstability more likely under higher trend inflation. The indeterminacy region of the interest rate policy coefficients expands with higher trend inflation, because the condition (17) is less likely to be satisfied in the case of the outcomebased policy and the condition (19) is less likely to be met in the case of the forecastbased policy. 11 The Einstability region expands with higher trend inflation, because the condition (24) is less likely to be satisfied in the case of the outcomebased policy and the condition (26) is less likely to be met in the case of the forecastbased policy. 4 Comparison with the case of homogeneous labor This section compares the cases of firmspecific labor and homogeneous labor in terms of determinacy of REE and Estability of fundamental REE. When labor is homogeneous, the utility function of the representative household is and the budget constraint is ) E β (ln t 1 C t 1 + 1/η N 1+1/η t exp(ε t ), t= P t C t + S t = W t N t + R t 1 S t 1 + T t, 11 In addition to the longrun version of the Taylor principle (16), the condition (18) imposes an upper bound on the size of the policy response to expected future output that ensures determinacy. However, this upper bound is substantially larger than the maximum value of the policy coefficient considered in Fig
16 where N t is the supply of homogeneous labor and W t is its wage. Combining firstorder conditions for utility maximization with respect to consumption and labor supply yields W t P t = C t N 1/η t. (28) The firstorder condition for intermediategood firm i s minimization of production cost determines this firm s marginal cost MC t (i) = W tn t (i) αy t (i). (29) The labor market clearing condition is given by N t = 1 N t(i) di. Using this equation and eqs. (3), (5), (6), (28), and (29), the firstorder condition for staggered pricesetting leads to [ ( ) 1 θ E t (βλ) j Bt exp(ε t+j ) θ ( ) 1 γ ( ) ] θ/α Yt+j Bt d 1/η t+j =, (3) θ 1 α j= P t+j A t+j P t+j where d t = 1 (P t(i)/p t ) θ/α di denotes price distortion and evolves according to P θ/α t d t = (1 λ)b θ/α t + λp θ/α t 1 d t 1. (31) Under Assumption 1, detrending and loglinearizing the equilibrium conditions (1), (3), and (31) leads to ˆΠ t βλ Π θ/α E t ˆΠt+1 = β(e t ˆΠt+1 βλ Π θ/α E t ˆΠt+2 ) + β( Π 1+θ(1/α 1) 1)(1 λ Π θ 1 ) [θ/αe t ˆΠt+1 (ε t E t ε t+1 )] 1 + θ(1/α 1) + γ(1 λ Π θ 1 )(1 βλ Π θ/α ) λ Π θ 1 (ŷ t βλ [1 + θ(1/α 1)] Π θ 1 E t ŷ t+1 ) + (1/η)(1 λ Π θ 1 )(1 βλ Π θ/α ) λ Π θ 1 ( [1 + θ(1/α 1)] ˆd t βλ Π θ 1 E t ˆdt+1 ), (32) ˆd t = λ Π θ 1 ( Π 1+θ(1/α 1) 1)θ/α 1 λ Π θ 1 ˆΠt + λ Π θ/α ˆdt 1. (33) In line with Ascari and Ropele (29) and Kurozumi (211), the NKPC (32) now depends on price distortion and therefore eq. (33) adds lagged price distortion ˆd t 1 to the set of relevant state variables of the model with homogeneous labor, as long as the elasticity of labor supply is finite (i.e., η < ) and the trend inflation rate is nonzero (i.e., Π 1). Consequently, it seems impossible to analytically investigate determinacy and Estability and we examine them numerically. 15
17 We now compare the models with firmspecific labor and with homogeneous labor in terms of determinacy of REE and Estability of fundamental REE under the outcomebased interest rate policy (i.e., i = in eq. (14)). Fig. 4 illustrates regions of the outcomebased policy coefficients (ϕ π, ϕ y ) that guarantee determinacy of REE or Estability of fundamental REE in the model with homogeneous labor when the annualized trend inflation rate is two, four, six, or eight percent, using the calibration of parameters presented in Table 1. This figure shows that for moderate rates of trend inflation (e.g., two, four, and six percent), both determinacy and Estability are ensured as long as the policy coefficients satisfy the longrun version of the Taylor principle which is of the same form as the one (16) except that the longrun inflation elasticity of output is now given by 12 (1 β)(1 λ λ Π Π θ/α )(1 βλ Π θ/α )[1 + θ(1/α 1)] θ 1 θ/α( Π 1+θ(1/α 1) 1)[β(1 λ Π θ 1 )(1 λ Π θ/α ) + 1/η(1 βλ Π θ 1 )(1 βλ Π θ/α )] ϵ y = γ(1 λ Π θ 1 )(1 λ Π θ/α )(1 βλ Π θ 1 )(1 βλ Π θ/α. ) When trend inflation is high (e.g., eight percent), determinacy and Estability are ensured basically as long as the longrun version of the Taylor principle is met, except for a very small region of the policy coefficients that induce indeterminacy of REE but generate Estable fundamental REE. For instance, in the case of no policy response to output (i.e., ϕ y = ), a policy response to inflation ϕ π in the interval (1.1, 1.17) induces indeterminacy and E stability. Therefore, regardless of the rate of trend inflation, the interest rate does not need to be adjusted much more than oneforone with current inflation to satisfy the longrun version of the Taylor principle under the calibration. Hence, a low rate of trend inflation is not required to ensure determinacy and Estability under the calibration, as long as the policy rate is adjusted oneforone or slightly more strongly with contemporaneous inflation. For instance, Taylor (1993) s estimates (i.e. ϕ π, ϕ y ) = (1.5,.125)) satisfy the longrun version of the Taylor principle even at high trend inflation rates. The comparison of Figs. 1 and 4 thus demonstrates that under the same calibration of structural model parameters, the outcomebased interest rate policy is much more likely to guarantee determinacy of REE and Estability of fundamental REE in the model with homogeneous labor than in the model with firmspecific labor. We turn next to the forecastbased interest rate policy (i.e., i = 1 in eq. (14)). Fig Note that in the case of an infinite elasticity of labor supply (i.e., η = ), the NKPC coincides in the models with firmspecific labor and with homogeneous labor, and hence not only the longrun inflation elasticity of output but also the longrun version of the Taylor principle is the same in these two models. 16
18 illustrates regions of the forecastbased policy coefficients (ϕ π, ϕ y ) that ensure determinacy of REE or Estability of fundamental REE in the model with homogeneous labor when the annualized trend inflation rate is two, four, six, or eight percent, using the calibration of parameters presented in Table 1. The comparison of Figs. 2 and 5 demonstrates that under the same calibration of structural model parameters, the forecastbased interest rate policy is much more likely to guarantee determinacy of REE and Estability of fundamental REE in the model with homogeneous labor than in the model with firmspecific labor, as is the case with the outcomebased interest rate policy. To satisfy the longrun version of the Taylor principle in the model with homogeneous labor, the interest rate does not need to be adjusted much more than oneforone with expected future inflation, even at high rates of trend inflation. Hence, this Taylor principle is much more likely to be satisfied in the model with homogeneous labor than in the model with firmspecific labor. In addition to the longrun version of the Taylor principle, ensuring Estability requires a sufficiently aggressive policy response to expected future output, while ensuring determinacy requires a more aggressive one. As a result, while the coefficients estimated by Taylor (1993) satisfy the longrun version of the Taylor principle even at high trend inflation rates, they do not ensure determinacy at high trend inflation rates because of an insufficiently strong response to expected future output. Nonetheless, under the calibration, these lower bounds on the policy response to expected future output are less likely to be binding in the model with homogeneous labor than in the model with firmspecific labor. The above results demonstrate that under the same calibration of structural model parameters, indeterminacy and Einstability are much more likely in the model with firmspecific labor than in the model with homogeneous labor analyzed in the recent literature such as Ascari and Ropele (29) and Kurozumi (211). Indeterminacy is much more likely in the model with firmspecific labor because this specification of labor introduces strategic complementarity or real rigidity, which causes indeterminacy like firmspecific capital analyzed in Sveen and Weinke (25, 27). As shown in Fig. 3, when the trend inflation rate is greater than a certain threshold (i.e.,.2 percent in annualized rate terms), the strategic complementarity makes the longrun inflation elasticity of output ϵ y take a smaller negative value and thereby causes the longrun version of the Taylor principle to be less likely to be satisfied. As a consequence, a large policy response to output induces indeterminacy in the model with firmspecific labor, even if such a response may ensure determinacy under the same calibration in the model with homogeneous labor. 17
19 Another condition for determinacy causes a small policy response to contemporaneous or expected future output to induce indeterminacy under positive trend inflation rates. This condition is also less likely to be met in the model with firmspecific labor than in the model with homogeneous labor, when the same calibration is used in these two models. Indeed, in the model with homogeneous labor, it is satisfied under the outcomebased interest rate policy for any trend inflation rate considered. When the interest rate policy is forecastbased, the minimum policy response to expected future output required to ensure determinacy increases substantially with higher trend inflation in the model with homogeneous labor, but it increases even more steeply with higher trend inflation in the model with firmspecific labor. Einstability is much more likely in the model with firmspecific labor than in the model with homogeneous labor for two reasons. First, the longrun version of the Taylor principle is a necessary condition for Estability of fundamental REE as well. This Taylor principle is, as noted above, less likely to be satisfied in the model with firmspecific labor than in the model with homogeneous labor. Second, the NKPC depends on price distortion in the model with homogeneous labor as long as the elasticity of labor supply is finite and the trend inflation rate is nonzero, but not in the model with firmspecific labor. Then, in the former model, the law of motion of price distortion adds lagged price distortion to the set of relevant state variables. For the REE in question, Estability examines whether an associated equilibrium in which agents form expectations under adaptive learning reaches over time the REE. For such expectation formation, lagged price distortion is useful information in the model with homogeneous labor. Particularly, it helps agents form inflation expectations, since price distortion affects inflation dynamics. Therefore, Estability is likely in the model with homogeneous labor. By contrast, price distortion is absent in the set of relevant state variables of the model with firmspecific labor, and hence higher trend inflation is more likely to induce Einstability. We have demonstrated that indeterminacy and Einstability are much more likely in the model with firmspecific labor than in the model with homogeneous labor. It follows that the argument of Coibion and Gorodnichenko (211) who use the former model to show that a decline in trend inflation plays a key role in the U.S. economy s shift from indeterminacy during the Great Inflation era to determinacy during the Great Moderation era depends crucially on the assumption of firmspecific labor. Under the calibration of parameters presented in Table 1, which is also chosen by Coibion and Gorodnichenko, the model with homogeneous labor argues for Clarida et al. (2) and Lubik and Schorfheide (24), who all attribute the 18
20 U.S. economy s shift to the Great Moderation solely to the Fed s change from a passive to an active policy response to inflation. 5 Concluding remarks In a Calvo sticky price model based on micro evidence that each period a fraction of prices is kept unchanged, this paper has examined implications of firmspecific labor for determinacy and Estability of REE under interest rate policy. It has shown that firmspecific labor causes higher trend inflation to be more likely to induce not only indeterminacy of REE but also Einstability of fundamental REE. The latter is in contrast with the result of Estability in the case of homogeneous labor analyzed in recent research. Moreover, we have demonstrated that under the same calibration of structural model parameters, indeterminacy and Einstability are much more likely in the case of firmspecific labor than in the case of homogeneous labor. This shows that Coibion and Gorodnichenko s (211) argument a decline in trend inflation along with the Fed s change from a passive to an active policy response to inflation explains much of the U.S. economy s shift from indeterminacy during the Great Inflation era to determinacy during the Great Moderation era depends crucially on the assumption of firmspecific labor. Thus, future work will estimate the models with firmspecific labor and with homogeneous labor using the method of Lubik and Schorfheide (24) to empirically address the question of whether a decline in trend inflation is a cause of such a shift from indeterminacy to determinacy in the U.S. economy. 19
A Pitfall of Expectational Stability Analysis
A Pitfall of Expectational Stability Analysis Takushi Kurozumi Willem Van Zandweghe October 2, 214 Abstract A pitfall of expectational stability (Estability) analysis can arise in models with multiperiod
More informationThe Basic New Keynesian Model
The Basic New Keynesian Model January 11 th 2012 Lecture notes by Drago Bergholt, Norwegian Business School Drago.Bergholt@bi.no I Contents 1. Introduction... 1 1.1 Prologue... 1 1.2 The New Keynesian
More informationAdvanced Macroeconomics II (second half)
Barcelona Graduate School of Economics Universitat Pompeu Fabra Master in Economics Spring 2012 Professor Jordi Galí (23.413, jgali@crei.cat) Advanced Macroeconomics II (second half) The lectures will
More informationLongTerm Debt Pricing and Monetary Policy Transmission under Imperfect Knowledge
LongTerm Debt Pricing and Monetary Policy Transmission under Imperfect Knowledge Stefano Eusepi, Marc Giannoni and Bruce Preston The views expressed are those of the authors and are not necessarily re
More informationCan the learnability criterion ensure determinacy in New Keynesian Models?
Can the learnability criterion ensure determinacy in New Keynesian Models? Patrick Minford Cardiff Business School and CEPR, United Kingdom Naveen Srinivasan Indira Gandhi Institute of Development Research,
More informationThe Optimal Inflation Rate in New Keynesian Models: Should Central Banks Raise Their Inflation Targets in Light of the Zero Lower Bound?
The Optimal Inflation Rate in New Keynesian Models: Should Central Banks Raise Their Inflation Targets in Light of the Zero Lower Bound? OLIVIER COIBION College of William and Mary and NBER YURIY GORODNICHENKO
More informationWelfare Costs of Inflation in a Menu Cost Model
Welfare Costs of Inflation in a Menu Cost Model Ariel Burstein and Christian Hellwig January 2008 Recent years have seen substantial progress in our understanding of pricing decisions at the micro level.
More informationReal Business Cycle Theory. Marco Di Pietro Advanced () Monetary Economics and Policy 1 / 35
Real Business Cycle Theory Marco Di Pietro Advanced () Monetary Economics and Policy 1 / 35 Introduction to DSGE models Dynamic Stochastic General Equilibrium (DSGE) models have become the main tool for
More informationIfo Institute for Economic Research at the University of Munich. 6. The New Keynesian Model
6. The New Keynesian Model 1 6.1 The Baseline Model 2 Basic Concepts of the New Keynesian Model Markets are imperfect: Price and wage adjustments: contract duration, adjustment costs, imperfect expectations
More informationECON20310 LECTURE SYNOPSIS REAL BUSINESS CYCLE
ECON20310 LECTURE SYNOPSIS REAL BUSINESS CYCLE YUAN TIAN This synopsis is designed merely for keep a record of the materials covered in lectures. Please refer to your own lecture notes for all proofs.
More informationMoney and Public Finance
Money and Public Finance By Mr. Letlet August 1 In this anxious market environment, people lose their rationality with some even spreading false information to create trading opportunities. The tales about
More informationDiscussion of Capital Injection, Monetary Policy, and Financial Accelerators
Discussion of Capital Injection, Monetary Policy, and Financial Accelerators Karl Walentin Sveriges Riksbank 1. Background This paper is part of the large literature that takes as its starting point the
More informationThe Alleged Instability of Nominal Income Targeting. Bennett T. McCallum Carnegie Mellon University and National Bureau of Economic Research
G97/6 The Alleged Instability of Nominal Income Targeting Bennett T. McCallum Carnegie Mellon University and National Bureau of Economic Research JEL No. E52 E32 E30 Preliminary August 1997 G97/6 1 The
More informationECON 5110 Class Notes Overview of New Keynesian Economics
ECON 5110 Class Notes Overview of New Keynesian Economics 1 Introduction The primary distinction between Keynesian and classical macroeconomics is the flexibility of prices and wages. In classical models
More informationWorking Capital Requirement and the Unemployment Volatility Puzzle
Working Capital Requirement and the Unemployment Volatility Puzzle Tsuting Tim Lin Gettysburg College July, 3 Abstract Shimer (5) argues that a searchandmatching model of the labor market in which wage
More informationThe Taylor Rule and Optimal Monetary Policy
The Taylor Rule and Optimal Monetary Policy Michael Woodford Princeton University January 2001. I would like to thank Jim Bullard, Julio Rotemberg, John Taylor and John Williams for helpful comments, Argia
More informationVI. Real Business Cycles Models
VI. Real Business Cycles Models Introduction Business cycle research studies the causes and consequences of the recurrent expansions and contractions in aggregate economic activity that occur in most industrialized
More informationTrend In ation, Nonlinearities and Firms PriceSetting: Rotemberg vs. Calvo
Trend In ation, Nonlinearities and Firms PriceSetting: Rotemberg vs. Calvo Guido Ascari University of Pavia and IfW Lorenza Rossi University of Pavia Abstract There is widespread agreement that the two
More informationComments on \Do We Really Know that Oil Caused the Great Stag ation? A Monetary Alternative", by Robert Barsky and Lutz Kilian
Comments on \Do We Really Know that Oil Caused the Great Stag ation? A Monetary Alternative", by Robert Barsky and Lutz Kilian Olivier Blanchard July 2001 Revisionist history is always fun. But it is not
More informationMA Advanced Macroeconomics: 7. The Real Business Cycle Model
MA Advanced Macroeconomics: 7. The Real Business Cycle Model Karl Whelan School of Economics, UCD Spring 2015 Karl Whelan (UCD) Real Business Cycles Spring 2015 1 / 38 Working Through A DSGE Model We have
More informationInstability of Sunspot Equilibria in Real Business Cycle Models Under Adaptive Learning
Instability of Sunspot Equilibria in Real Business Cycle Models Under Adaptive Learning John Duffy Department of Economics University of Pittsburgh 230 S. Bouquet Street Pittsburgh, PA 15260 USA E mail:
More information11.2 Monetary Policy and the Term Structure of Interest Rates
518 Chapter 11 INFLATION AND MONETARY POLICY Thus, the monetary policy that is consistent with a permanent drop in inflation is a sudden upward jump in the money supply, followed by low growth. And, in
More informationSIMPLE GUIDELINES FOR INTEREST RATE POLICY*
SIMPLE GUIDELINES FOR INTEREST RATE POLICY* José Maria Brandão de Brito** Pedro Teles*** 1. INTRODUCTION Those of us working at research departments in central banks are regularly questioned on the right
More informationKeynesian Macroeconomic Theory
2 Keynesian Macroeconomic Theory 2.1. The Keynesian Consumption Function 2.2. The Complete Keynesian Model 2.3. The KeynesianCross Model 2.4. The ISLM Model 2.5. The Keynesian ADAS Model 2.6. Conclusion
More informationThe Term Structure of Interest Rates and the Monetary Transmission Mechanism
The Term Structure of Interest Rates and the Monetary Transmission Mechanism Massimiliano Marzo Ulf Söderström Paolo Zagaglia November 6, 7 Preliminary and Incomplete Please do not circulate without the
More informationCapital Constraints, Lending over the Cycle and the Precautionary Motive: A Quantitative Exploration (Working Paper)
Capital Constraints, Lending over the Cycle and the Precautionary Motive: A Quantitative Exploration (Working Paper) Angus Armstrong and Monique Ebell National Institute of Economic and Social Research
More informationMonetary Policy and Longterm Interest Rates
Monetary Policy and Longterm Interest Rates Shu Wu The University of Kansas First Draft: July 2004 This version: March 2005 Abstract This paper documents some new empirical results about the monetary
More informationFirmSpecific Labor and FirmSpecific Capital: Implications for the EuroData New Phillips Curve
FirmSpecific Labor and FirmSpecific Capital: Implications for the EuroData New Phillips Curve Julien Matheron Banque de France, Research Division Standard GMM estimates of the New Phillips curve on
More informationDebt Maturity Management, Monetary and Fiscal Policy Interactions
Debt Maturity Management, Monetary and Fiscal Policy Interactions Hao Jin April 22, 23 Abstract This paper examines the interactions of debt maturity management, monetary and fiscal policy in a DSGE model.
More informationDownward Nominal Wage Rigidities Bend the Phillips Curve
FEDERAL RESERVE BANK OF SAN FRANCISCO WORKING PAPER SERIES Downward Nominal Wage Rigidities Bend the Phillips Curve Mary C. Daly Federal Reserve Bank of San Francisco Bart Hobijn Federal Reserve Bank of
More informationReal Business Cycles. Federal Reserve Bank of Minneapolis Research Department Staff Report 370. February 2006. Ellen R. McGrattan
Federal Reserve Bank of Minneapolis Research Department Staff Report 370 February 2006 Real Business Cycles Ellen R. McGrattan Federal Reserve Bank of Minneapolis and University of Minnesota Abstract:
More informationReal Business Cycle Models
Phd Macro, 2007 (Karl Whelan) 1 Real Business Cycle Models The Real Business Cycle (RBC) model introduced in a famous 1982 paper by Finn Kydland and Edward Prescott is the original DSGE model. 1 The early
More informationEcon 303: Intermediate Macroeconomics I Dr. Sauer Sample Questions for Exam #3
Econ 303: Intermediate Macroeconomics I Dr. Sauer Sample Questions for Exam #3 1. When firms experience unplanned inventory accumulation, they typically: A) build new plants. B) lay off workers and reduce
More informationThe RBC methodology also comes down to two principles:
Chapter 5 Real business cycles 5.1 Real business cycles The most well known paper in the Real Business Cycles (RBC) literature is Kydland and Prescott (1982). That paper introduces both a specific theory
More informationInstability of Sunspot Equilibria in Real Business Cycle Models Under Adaptive Learning
Instability of Sunspot Equilibria in Real Business Cycle Models Under Adaptive Learning John Duffy Department of Economics University of Pittsburgh 230 S. Bouquet Street Pittsburgh, PA 15260 USA E mail:
More informationDepartment of Economics
Department of Economics Inflation Persistence and the Phillips Curve Revisited Marika Karanassou and Dennis J. Snower Working Paper No. 586 February 2007 ISSN 14730278 Inflation Persistence and the Phillips
More informationConventional and Unconventional Monetary Policy
Conventional and Unconventional Monetary Policy Vasco Cúrdia Federal Reserve Bank of New York Michael Woodford Columbia University September 3, 29 Abstract We extend a standard New Keynesian model to incorporate
More informationECONOMIC QUESTIONS FOR THE MASTER'S EXAM
ECONOMIC QUESTIONS FOR THE MASTER'S EXAM Introduction 1. What is economics? Discuss the purpose and method of work of economists. Consider observation, induction, deduction and scientific criticism. 2.
More informationFiscal Stimulus Improves Solvency in a Depressed Economy
Fiscal Stimulus Improves Solvency in a Depressed Economy Dennis Leech Economics Department and Centre for Competitive Advantage in the Global Economy University of Warwick d.leech@warwick.ac.uk Published
More informationSurprising Comparative Properties of Monetary Models: Results from a New Model Database
JOHN B. TAYLOR, VOLKER WIELAND Surprising Comparative Properties of Monetary Models: Results from a New Model Database Institute for Monetary and Financial Stability GOETHE UNIVERSITY FRANKFURT AM MAIN
More informationMarkups and FirmLevel Export Status: Appendix
Markups and FirmLevel Export Status: Appendix De Loecker Jan  Warzynski Frederic Princeton University, NBER and CEPR  Aarhus School of Business Forthcoming American Economic Review Abstract This is
More informationIn recent years, Federal Reserve (Fed) policymakers have come to rely
LongTerm Interest Rates and Inflation: A Fisherian Approach Peter N. Ireland In recent years, Federal Reserve (Fed) policymakers have come to rely on longterm bond yields to measure the public s longterm
More informationSticky prices in theory and practice
Sticky prices in theory and practice Bengt Assarsson 20080911 Are prices sticky? Aggregate price rigidity Sticky prices is the distinguishing feature of Keynesian models. The new classical economists
More informationChapter 11. Keynesianism: The Macroeconomics of Wage and Price Rigidity. 2008 Pearson AddisonWesley. All rights reserved
Chapter 11 Keynesianism: The Macroeconomics of Wage and Price Rigidity Chapter Outline RealWage Rigidity Price Stickiness Monetary and Fiscal Policy in the Keynesian Model The Keynesian Theory of Business
More informationUniversidad de Montevideo Macroeconomia II. The RamseyCassKoopmans Model
Universidad de Montevideo Macroeconomia II Danilo R. Trupkin Class Notes (very preliminar) The RamseyCassKoopmans Model 1 Introduction One shortcoming of the Solow model is that the saving rate is exogenous
More informationOptimal InterestRate Smoothing
Optimal InterestRate Smoothing Michael Woodford Department of Economics Princeton University Princeton, NJ 08544 USA June 2002 Abstract This paper considers the desirability of the observed tendency of
More informationCalibration of Normalised CES Production Functions in Dynamic Models
Discussion Paper No. 06078 Calibration of Normalised CES Production Functions in Dynamic Models Rainer Klump and Marianne Saam Discussion Paper No. 06078 Calibration of Normalised CES Production Functions
More informationCollateral Constraints and StateContingent Contracts
Collateral Constraints and StateContingent Contracts Mikhail Dmitriev and Jonathan Hoddenbagh First Draft: April 24 It is commonly assumed that binding collateral constraints amplify the impact of aggregate
More informationEconomics Department Discussion Papers Series ISSN 1473 3307
Economics Department Discussion Papers Series ISSN 1473 337 Evaluating the Role of FirmSpecific Capital in New Keynesian Models. Joao Madeira Paper number 12/4 URL: http://businessschool.exeter.ac.uk/economics/papers/
More informationFourth Edition. University of California, Berkeley
Fourth Edition University of California, Berkeley Introduction Chapter 1 Chapter 2 Chapter 3 Chapter 4 Chapter 5 Chapter 6 Chapter 7 Chapter 8 Chapter 9 Chapter 10 Chapter 11 Chapter 12 Epilogue References
More informationThe Effect on Housing Prices of Changes in Mortgage Rates and Taxes
Preliminary. Comments welcome. The Effect on Housing Prices of Changes in Mortgage Rates and Taxes Lars E.O. Svensson SIFR The Institute for Financial Research, Swedish House of Finance, Stockholm School
More informationSerie documentos de trabajo
Serie documentos de trabajo INVESTMENT AND INTEREST RATE POLICY IN THE OPEN ECONOMY Stephen McKnight El Colegio de México DOCUMENTO DE TRABAJO Núm. II 2011 Investment and Interest Rate Policy in the Open
More informationInflation dynamics, marginal cost, and the output gap: Evidence from three countries
Inflation dynamics, marginal cost, and the output gap: Evidence from three countries Katharine S. Neiss a,* and Edward Nelson b,* a Monetary Analysis, Bank of England, London EC2R 8AH, U.K. b Monetary
More informationWhy Does Consumption Lead the Business Cycle?
Why Does Consumption Lead the Business Cycle? Yi Wen Department of Economics Cornell University, Ithaca, N.Y. yw57@cornell.edu Abstract Consumption in the US leads output at the business cycle frequency.
More informationTHERE HAS BEEN a great resurgence
Journal of Economic Literature Vol. XXXVII (December 1999), pp. 1661 1707 Clarida, Galí, Gertler: The Science of Monetary Policy The Science of Monetary Policy: A New Keynesian Perspective Richard Clarida,
More informationMonetary Policy and Exchange Rate Volatility in a Small Open Economy
Review of Economic Studies (25) 72, 77 734 346527/5/2977$2. c 25 The Review of Economic Studies Limited Monetary Policy and Exchange Rate Volatility in a Small Open Economy JORDI GALÍ CREI, UPF, CEPR
More informationTotal Factor Productivity
Total Factor Productivity Diego Comin NewYorkUniversityandNBER August 2006 Abstract Total Factor Productivity (TFP) is the portion of output not explained by the amount of inputs used in production. The
More informationFederal Reserve Bank of New York Staff Reports
Federal Reserve Bank of New York Staff Reports Deficits, Public Debt Dynamics, and Tax and Spending Multipliers Matthew Denes Gauti B. Eggertsson Sophia Gilbukh Staff Report No. 551 February 2012 This
More informationShould the Central Bank Be Concerned About Housing Prices?
FEDERAL RESERVE BANK OF SAN FRANCISCO WORKING PAPER SERIES Should the Central Bank Be Concerned About Housing Prices? Karsten Jeske Mellon Capital Management Zheng Liu Federal Reserve Bank of San Francisco
More informationFederal Reserve Bank of New York Staff Reports
Federal Reserve Bank of New York Staff Reports Do Expected Future Marginal Costs Drive Inflation Dynamics? Argia M. Sbordone Staff Report no. 204 March 2005 This paper presents preliminary findings and
More informationINVESTMENT PLANNING COSTS AND THE EFFECTS OF FISCAL AND MONETARY POLICY. Susanto Basu and Miles S. Kimball. University of Michigan and NBER
INVESTMENT PLANNING COSTS AND THE EFFECTS OF FISCAL AND MONETARY POLICY Susanto Basu and Miles S. Kimball University of Michigan and NBER MAIN RESULTS. Show that a model with capital accumulation and sticky
More informationA Classical Monetary Model  Money in the Utility Function
A Classical Monetary Model  Money in the Utility Function Jarek Hurnik Department of Economics Lecture III Jarek Hurnik (Department of Economics) Monetary Economics 2012 1 / 24 Basic Facts So far, the
More informationDECONSTRUCTING THE SUCCESS OF REAL BUSINESS CYCLES
DECONSTRUCTING THE SUCCESS OF REAL BUSINESS CYCLES EMI NAKAMURA* The empirical success of Real Business Cycle (RBC) models is often judged by their ability to explain the behavior of a multitude of real
More informationGains from Trade: The Role of Composition
Gains from Trade: The Role of Composition Wyatt Brooks University of Notre Dame Pau Pujolas McMaster University February, 2015 Abstract In this paper we use production and trade data to measure gains from
More informationCash in advance model
Chapter 4 Cash in advance model 4.1 Motivation In this lecture we will look at ways of introducing money into a neoclassical model and how these methods can be developed in an effort to try and explain
More informationGENERAL EQUILIBRIUM WITH BANKS AND THE FACTORINTENSITY CONDITION
GENERAL EQUILIBRIUM WITH BANKS AND THE FACTORINTENSITY CONDITION Emanuel R. Leão Pedro R. Leão Junho 2008 WP nº 2008/63 DOCUMENTO DE TRABALHO WORKING PAPER General Equilibrium with Banks and the FactorIntensity
More informationMonetary Business Cycle Accounting
Monetary Business Cycle Accounting Roman Šustek Bank of England March 3, 2009 Abstract This paper investigates the quantitative importance of various types of frictions for inflation and nominal interest
More informationTopic 7: The NewKeynesian Phillips Curve
EC4010 Notes, 2005 (Karl Whelan) 1 Topic 7: The NewKeynesian Phillips Curve The Phillips curve has been a central topic in macroeconomis since the 1950s and its successes and failures have been a major
More informationMACROECONOMIC ANALYSIS OF VARIOUS PROPOSALS TO PROVIDE $500 BILLION IN TAX RELIEF
MACROECONOMIC ANALYSIS OF VARIOUS PROPOSALS TO PROVIDE $500 BILLION IN TAX RELIEF Prepared by the Staff of the JOINT COMMITTEE ON TAXATION March 1, 2005 JCX405 CONTENTS INTRODUCTION... 1 EXECUTIVE SUMMARY...
More informationDo Higher Interest Rates Raise or Lower Inflation?
Do Higher Interest Rates Raise or Lower Inflation? John H. Cochrane October 24, 25 Abstract The standard newkeynesian model accounts well for the fact that inflation has been stable at a zero interest
More information6. Budget Deficits and Fiscal Policy
Prof. Dr. Thomas Steger Advanced Macroeconomics II Lecture SS 2012 6. Budget Deficits and Fiscal Policy Introduction Ricardian equivalence Distorting taxes Debt crises Introduction (1) Ricardian equivalence
More information12.1 Introduction. 12.2 The MP Curve: Monetary Policy and the Interest Rates 1/24/2013. Monetary Policy and the Phillips Curve
Chapter 12 Monetary Policy and the Phillips Curve By Charles I. Jones Media Slides Created By Dave Brown Penn State University The shortrun model summary: Through the MP curve the nominal interest rate
More informationMacroeconomic Analysis without the Rational Expectations Hypothesis
Macroeconomic Analysis without the Rational Expectations Hypothesis Michael Woodford Columbia University August 16, 2013 Abstract This paper reviews a variety of alternative approaches to the specification
More informationIn#ation dynamics: A structural econometric analysis
Journal of Monetary Economics 44 (1999) 195}222 In#ation dynamics: A structural econometric analysis Jordi GalmH, Mark Gertler * Universitat Pompeu Fabra, Barcelona, Spain Department of Economics, New
More informationA Simple Model of Price Dispersion *
Federal Reserve Bank of Dallas Globalization and Monetary Policy Institute Working Paper No. 112 http://www.dallasfed.org/assets/documents/institute/wpapers/2012/0112.pdf A Simple Model of Price Dispersion
More informationExchange rate versus inflation targeting: a theory of output fluctuations in traded and nontraded sectors
J. Int. Trade & Economic Development 13:3 265 285 Exchange rate versus inflation targeting: a theory of output fluctuations in traded and nontraded sectors Øistein Røisland { and Ragnar Torvik {{ { Norges
More informationCHAPTER 11. AN OVEVIEW OF THE BANK OF ENGLAND QUARTERLY MODEL OF THE (BEQM)
1 CHAPTER 11. AN OVEVIEW OF THE BANK OF ENGLAND QUARTERLY MODEL OF THE (BEQM) This model is the main tool in the suite of models employed by the staff and the Monetary Policy Committee (MPC) in the construction
More informationMacroeconomic Effects of Financial Shocks Online Appendix
Macroeconomic Effects of Financial Shocks Online Appendix By Urban Jermann and Vincenzo Quadrini Data sources Financial data is from the Flow of Funds Accounts of the Federal Reserve Board. We report the
More informationThe Budget Deficit, Public Debt and Endogenous Growth
The Budget Deficit, Public Debt and Endogenous Growth Michael Bräuninger October 2002 Abstract This paper analyzes the effects of public debt on endogenous growth in an overlapping generations model. The
More informationCARLETON ECONOMIC PAPERS
CEP 1414 Employment Gains from MinimumWage Hikes under Perfect Competition: A Simple GeneralEquilibrium Analysis Richard A. Brecher and Till Gross Carleton University November 2014 CARLETON ECONOMIC
More informationOptimal fiscal policy under commitment
Abstract Optimal Fiscal and Monetary Policy with Commitment Mikhail Golosov and Aleh Tsyvinski 1 May 31, 2006 Forthcoming in New Palgrave Dictionary of Economics and Law Optimal fiscal and monetary policy
More informationOn the long run relationship between gold and silver prices A note
Global Finance Journal 12 (2001) 299 303 On the long run relationship between gold and silver prices A note C. Ciner* Northeastern University College of Business Administration, Boston, MA 021155000,
More informationSuggested Answers for Mankiw Questions for Review & Problems
Suggested Answers for Mankiw & Problems The answers here will not have graphs, I encourage to refer to the text for graphs. There is a some math, however I don t expect you to replicate these in your exam,
More informationCH 10  REVIEW QUESTIONS
CH 10  REVIEW QUESTIONS 1. The shortrun aggregate supply curve is horizontal at: A) a level of output determined by aggregate demand. B) the natural level of output. C) the level of output at which the
More informationNominal Rigidities and the Dynamic Effects of a Shock to Monetary Policy. Lawrence J. Christiano and Martin Eichenbaum
Nominal Rigidities and the Dynamic Effects of a Shock to Monetary Policy Lawrence J. Christiano and Martin Eichenbaum Northwestern University, National Bureau of Economic Research, and Federal Reserve
More informationEconomic Brief. Calculating the Natural Rate of Interest: A Comparison of Two Alternative Approaches
Economic Brief October 015, EB1510 Calculating the Natural Rate of Interest: A Comparison of Two Alternative Approaches By Thomas A. Lubik and Christian Matthes The natural rate of interest is a key concept
More informationCurrent Accounts in Open Economies Obstfeld and Rogoff, Chapter 2
Current Accounts in Open Economies Obstfeld and Rogoff, Chapter 2 1 Consumption with many periods 1.1 Finite horizon of T Optimization problem maximize U t = u (c t ) + β (c t+1 ) + β 2 u (c t+2 ) +...
More informationShould Central Banks Respond to Movements in Asset Prices? By Ben S. Bernanke and Mark Gertler *
Should Central Banks Respond to Movements in Asset Prices? By Ben S. Bernanke and Mark Gertler * In recent decades, asset booms and busts have been important factors in macroeconomic fluctuations in both
More informationFriedman Redux: Restricting Monetary Policy Rules to Support Flexible Exchange Rates
Friedman Redux: Restricting Monetary Policy Rules to Support Flexible Exchange Rates Michael B. Devereux Department of Economics, University of British Columbia and CEPR Kang Shi Department of Economics,
More informationMonetary Economic Growth Theory under Perfect and Monopolistic Competitions
DBJ Discussion Paper Series, No.1302 Monetary Economic Growth Theory under Perfect and Monopolistic Competitions Masayuki Otaki (Institute of Social Science, University of Tokyo) Masaoki Tamura (Innovation
More informationMonetary Policy and Exchange Rate Volatility in asmallopeneconomy
Monetary Policy and Exchange Rate Volatility in asmallopeneconomy Jordi Galí Tommaso Monacelli July 27, 24 Abstract We lay out a small open economy version of the Calvo sticky price model, and show how
More informationNormalization and Mixed Degrees of Integration in Cointegrated Time Series Systems
Normalization and Mixed Degrees of Integration in Cointegrated Time Series Systems Robert J. Rossana Department of Economics, 04 F/AB, Wayne State University, Detroit MI 480 EMail: r.j.rossana@wayne.edu
More informationConditional guidance as a response to supply uncertainty
1 Conditional guidance as a response to supply uncertainty Appendix to the speech given by Ben Broadbent, External Member of the Monetary Policy Committee, Bank of England At the London Business School,
More informationFORECASTING DEPOSIT GROWTH: Forecasting BIF and SAIF Assessable and Insured Deposits
Technical Paper Series Congressional Budget Office Washington, DC FORECASTING DEPOSIT GROWTH: Forecasting BIF and SAIF Assessable and Insured Deposits Albert D. Metz Microeconomic and Financial Studies
More informationNew Keynesian Dynamics in a Low Interest Rate Environment.
New Keynesian Dynamics in a Low Interest Rate Environment. R. Anton Braun University of Tokyo Lena Mareen Körber German Institute for Economic Research July 14, 2010 Abstract Recent research has found
More informationIntermediate Macroeconomics: The Real Business Cycle Model
Intermediate Macroeconomics: The Real Business Cycle Model Eric Sims University of Notre Dame Fall 2012 1 Introduction Having developed an operational model of the economy, we want to ask ourselves the
More informationWORKING PAPER SERIES UNDERSTANDING THE DYNAMICS OF LABOR SHARES AND INFLATION NO 784 / JULY 2007. by Martina Lawless and Karl Whelan
/CEPR LABOUR MARKET WORKSHOP ON WAGE AND LABOUR COST DYNAMICS WORKING PAPER SERIES NO 784 / JULY 2007 UNDERSTANDING THE DYNAMICS OF LABOR SHARES AND INFLATION by Martina Lawless and Karl Whelan WORKING
More informationInternational Debt Deleveraging
International Debt Deleveraging Luca Fornaro CREI and Universitat Pompeu Fabra 12 th Macroeconomic Policy Research Workshop Budapest, September 213 1 Motivating facts: Household debt/gdp Household debt/gdp
More informationMoney and Capital in an OLG Model
Money and Capital in an OLG Model D. Andolfatto June 2011 Environment Time is discrete and the horizon is infinite ( =1 2 ) At the beginning of time, there is an initial old population that lives (participates)
More informationImport Prices and Inflation
Import Prices and Inflation James D. Hamilton Department of Economics, University of California, San Diego Understanding the consequences of international developments for domestic inflation is an extremely
More information