Sectoral price rigidity and aggregate dynamics

European Economic Review 65 (2014) 1–22

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Sectoral price rigidity and aggregate dynamics Hafedh Bouakez a,n, Emanuela Cardia b, Francisco Ruge-Murcia b a b

HEC Montréal and CIRPÉE, Canada Department of Economics and CIREQ, University of Montréal, Canada

a r t i c l e i n f o

abstract

Article history: Received 15 August 2012 Accepted 30 September 2013 Available online 18 October 2013

This paper studies the business cycle implications of sectoral heterogeneity in price rigidity using a highly disaggregated multi-sector model. The model is estimated by the Simulated Method of Moments using a mix of aggregate and sectoral U.S. data. The frequencies of price changes implied by our estimates are consistent with those reported in micro-based studies. We show that heterogeneity in price rigidity is the primary factor explaining the heterogeneity in the responses of sectoral output and inflation to a monetary policy shock. We also find that ignoring sectoral heterogeneity in price rigidity leads to the mismeasurement of the relative importance of aggregate and sector-specific shocks in aggregate and sectoral fluctuations. & 2013 Elsevier B.V. All rights reserved.

JEL classification: E3 E4 E5 Keywords: Multi-sector models Price stickiness Simulated method of moments Sectoral shocks Monetary policy

1. Introduction There is now abundant evidence from studies based on micro data that the frequency of price adjustments differs greatly across goods.1 Accordingly, the last few years have witnessed the emergence of an important literature that extends standard sticky-price models by relaxing the assumption of identical price rigidity across firms and sectors. The findings from this literature highlight the importance of this source of heterogeneity in accounting for the behavior of aggregate output and inflation. For instance, Carvalho (2006), Nakamura and Steinsson (2010), Vavra (2010), and Dixon and Kara (2011) find that monetary policy shocks have larger and more persistent effects on aggregate output in a model with heterogeneous price rigidity than in a model with identical rigidity, holding constant the average frequency of price changes. Carvalho and Schwartzman (2008) show that similar effects carry over to a larger class of sticky price and sticky information models.2 Álvarez and Burriel (2001) and Dixon and Kara (2010) find that allowing for a distribution of contract duration and for different types of price setting across firms increases aggregate inflation persistence, bringing it closer to what is observed in the data.3

n

Corresponding author. Tel.: þ1514 340 7003. E-mail address: [email protected] (H. Bouakez). 1 See Bils and Klenow (2004), Klenow and Kryvtson (2008), Nakamura and Steinsson (2008), Gagnon (2009), and Eichenbaum et al. (2011) for final goods; and Carlton (1986) for intermediate goods. 2 Also, see Carvalho and Nechio (2011) who find that heterogeneity in price rigidity induces larger and more persistent movements in the real exchange rate compared with identical price rigidity. 3 On the other hand, Sheedy (2007) shows that adding heterogeneity in the frequency of price changes to an otherwise standard Calvo model reduces intrinsic inflation persistence. Kehoe and Midrigan (2010) build a New Keynesian model that distinguishes between temporary and regular price changes, and find that even if prices change frequently at the micro level, there is a significant degree of low-frequency price stickiness that induces stickiness at the 0014-2921/$ - see front matter & 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.euroecorev.2013.09.009

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H. Bouakez et al. / European Economic Review 65 (2014) 1–22

While this literature provides useful insights on the role of heterogeneous price rigidity in understanding the responses of aggregate prices and quantities to monetary policy shocks, two important questions remain unanswered: (i) the extent to which heterogeneity in price rigidity accounts for differences in sectoral sensitivities to monetary policy shocks, and (ii) the implications of heterogeneity in price rigidity for the relative contribution of structural shocks to aggregate and sectoral fluctuations at business cycle frequencies. Addressing these questions requires a multi-sector model with a realistic production structure in terms of intersectoral linkages and multiple sources of sectoral heterogeneity, including sectoral productivity shocks. This paper aims to answer these questions using a highly disaggregated version of the multi-sector model developed by Bouakez et al. (2009). In that earlier paper, we were concerned with the role of input–output interactions in the transmission of monetary policy shocks and, for empirical purposes, focused on six broad sectors of the U.S. economy.4 Since a fine level of disaggregation is essential to generate the cross-sectional variation needed to address the questions of interest, we estimate and analyze a 30-sector model of the US economy, where the sectors roughly correspond to the two-digit level of the Standard Industry Classification (SIC). Production sectors in the model economy differ in price rigidity, factor intensities, and productivity shocks, and are interconnected through a roundabout production structure whereby they provide materials and investment inputs to each other following the actual Input–Output Matrix and Capital Flow Table of the U.S. economy. The model parameters are estimated by the Simulated Method of Moments (SMM) using a mix of sectoral and aggregate U.S. data.5 Estimation results show that there is considerable heterogeneity in price rigidity across sectors, and that the hypothesis that price rigidity is the same in all sectors is strongly rejected by the data. Importantly, the frequencies of price changes implied by our estimates are generally consistent with micro-based estimates, and the price duration implied by our median estimate (2.4 quarters) is well within the range of durations reported in micro studies. The empirical success of standard sticky-price models generally hinges on assuming long price durations, ranging from 4 to 10 quarters, which are now considered implausible in light of the recent micro evidence on price stickiness.6 Thus, a first important contribution of this study is to demonstrate that modeling explicitly sectoral heterogeneity can help reconcile New Keynesian models with the micro data on price rigidity. Using the estimated model, we establish the following results. First, there is substantial heterogeneity in the responses of sectoral inflation and output to a monetary policy shock. In the case of sectoral inflation, this heterogeneity is primarily due to the heterogeneity in the degree of price rigidity, whereas the cross-sectional variation in sectoral output responses is both due to the heterogeneity in price rigidity and to whether or not the sectors produce capital goods. Capital-good sectors adjust their output by more than nondurable-goods sector and this is so regardless of whether their prices are flexible or rigid. This result reflects the sparsity of the actual Capital-Flow Table whereby the production of capital goods is concentrated in a small number of sectors. Second, we show that modeling heterogeneity in price rigidity has crucial implications regarding the relative importance of the various shocks in accounting for aggregate fluctuations. Some studies have examined this question in the context of real business cycle (RBC) models with flexible prices and found that sector-specific shocks are an important source of aggregate volatility (e.g., Long and Plosser, 1983; Horvath, 1998, 2000; and Conley and Dupor, 2003). Other papers, such as those by Long and Plosser (1987) and Foester et al. (2011), have used factor models to show that aggregate shocks are the main drivers of aggregate fluctuations.7 A benchmark version of our multi-sector model with identical price rigidity in all sectors attributes most (97%) of the unconditional variance of output to sectoral productivity shocks and less than 1% to the monetary policy shock, as in the RBC literature discussed above. However, allowing for heterogeneity in price rigidity across sectors overturns this prediction, attributing about 72% of the unconditional variance of output to aggregate shocks and only about 28% to sectoral shocks. Among the latter, oil shocks explain roughly 10% of output fluctuations, consistent with recent evidence reported by Lippi and Nobili (2012). It is worth emphasizing, however, that these results crucially depend on the remaining sources of sectoral heterogeneity being taken into account and modeled in a realistic manner. More specifically, counterfactual experiments reveal that versions of the model that assume identical processes for the sectoral shocks, identical consumption weights and production-function parameters across sectors, or a symmetric input–output table, largely overestimate the contribution of sectoral shocks to the variance of aggregate output. In particular, under a symmetric input–output table, the fraction of output variability accounted for by oil shocks rises from 10 to about 30%. While heterogeneity in price rigidity downplays the role of sectoral shocks in aggregate fluctuations, it amplifies the relative importance of monetary policy shocks for aggregate output. The fraction of output variability attributed to these

(footnote continued) aggregate level. Altissimo et al. (2009) argue that heterogeneity can increase inflation persistence due to the averaging of industry-specific inflation rates with different persistence levels. 4 Other papers that study the role of input–output interactions include Carvalho (2006), Shamloo and Silverman (2010), Bouakez et al. (2011), and Carvalho and Lee (2011). 5 In a closely related paper, Carvalho and Lee (2011) estimate a multisector model with heterogenous price setting across sectors, input–output production linkages, and sector-specific shocks. Compared with our work, the main objective of their paper is to account for the differential responses of prices to aggregate and sectoral shocks. 6 See, among others, Gali and Gertler (1999), Kim (2000), Ireland (2001, 2003), Smets and Wouters (2003), Christiano et al. (2005), and Bouakez et al. (2005). 7 Also, see Dupor (1999), who argues that under certain assumptions about the structure of the input–output matrix, the effects of sectoral shocks cancel each other out by the law of large numbers.

H. Bouakez et al. / European Economic Review 65 (2014) 1–22

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shocks rises from less than 1% in the model with identical price rigidity to roughly 20% in the model with heterogenous price rigidity. The latter fraction is in agreement with the estimate reported, for example, by Shapiro and Watson (1988), who find that nominal shocks account for 28% of output variation.8 Third, heterogeneity in price rigidity is also found to affect the relative importance of the different shocks in accounting for sectoral fluctuations. A key result of our analysis is that although sector-specific shocks play a limited role in accounting for aggregate output fluctuations, they explain the largest fraction of the variability of sectoral output and inflation. In the case of output, this fraction becomes even larger when the sectors are assumed to have equally rigid prices. In other words, ignoring sectoral heterogeneity in price rigidity leads to an overstatement of the importance of sector-specific shocks in accounting for the variability of sectoral output. On the other hand, heterogeneity in price rigidity has little effect on the variance decomposition of sectoral inflation. The result that sector-specific shocks account for a significant fraction of sectoral inflation variability suggests that sectoral shocks are an important cause of the price changes observed at the micro level and that the observed volatility in sectoral inflation rates need not imply that money is neutral. Boivin et al. (2007) and Mackowiak et al. (2009) examine this question using factor models where the idiosyncratic component is basically a residual term. Instead, our structural analysis puts an economic label on the source of sector-specific shocks and traces out their effects through a fully specified economy. For example, our analysis shows that shocks to agriculture and oil production have large effects on other sectors as a result of input–output interactions. The paper is organized as follows. Section 2 presents the model. Since the analytical framework used to study the sectoral data is that developed in our previous work (Bouakez et al., 2009) and in order to save space, we present here only the outline of the model and refer the reader to that article for a more detailed discussion. Section 3 discusses our estimation strategy and a number of econometric issues. Section 4 reports parameter estimates and examines the microeconomic implications of the model. Section 5 studies the implications of sectoral heterogeneity in price rigidity. Finally, Section 6 summarizes the main conclusions and results from our analysis. 2. A multi-sector model with heterogenous production sectors The economy consists of firms that belong to either of a finite number of sectors, infinitely-lived final consumers, and a monetary authority. 2.1. Production and intermediate consumption Production is carried out by continua of firms in each of J sectors. Firms in the same sector are identical except for the fact that their goods are differentiated and, consequently, they have monopolistically competitive power. Firms in different sectors have different production functions, use different combinations of materials and investment inputs, and face different nominal price frictions. Firm l in sector j produces output yljt using the technology yljt ¼ ðzjt nljt Þν ðkt Þα ðH ljt Þγ ; j

lj

j

j

ð1Þ

j zt

nljt

where is a sector-specific productivity shock, is the labor, The sectoral productivity shock follows the process

lj kt

lj

is the capital, Ht is the materials inputs, and ν þ α þ γ ¼ 1. j

j

j

lnðzjt Þ ¼ ρzj lnðzjt  1 Þ þ εzj ;t ; where ρzj A ð  1; 1Þ and the innovation εzj ;t is identically and independently distributed (i.i.d.) with mean zero and variance s2zj . Idiosyncratic productivity shocks are also assumed by, among others, Golosov and Lucas (2007), Gertler and Leahy (2008) and Midrigan (2011). In those models all shocks are drawn from the same distribution, while in our model the shock distribution depends on the sector the firm belongs to. Materials inputs are a composite of goods produced by all firms in all sectors: !θ=ðθ  1Þ Z J

 ζ ij

H ljt ¼ ∏ ζ ij i¼1

ðhi;t Þζij lj

1

lj

with hi;t ¼

0

ðhmi;t Þðθ  1Þ=θ dm lj

;

ð2Þ

lj

where ζ ij Z 0 is a weight that satisfies ∑Ji ¼ 1 ζ ij ¼ 1, hmi;t is the quantity of good produced by firm m in sector i that is purchased by firm l in sector j as materials input, and θ 41 is the elasticity of substitution between goods produced in the same sector. The capital stock is directly owned by firms and follows the law of motion lj

lj

kt þ 1 ¼ ð1 δÞkt þ X ljt ;

ð3Þ

8 Previous literature that discusses the role of heterogeneity in price rigidity as an amplification mechanism of the effects of monetary policy shocks on aggregate output considers more restricted environments than the one developed in this paper. For example, Carvalho (2006) abstracts from capital accumulation and materials inputs, and Nakamura and Steinsson (2008) model materials inputs symmetrically, meaning that firms in a given sector use equal proportions of all goods. In addition, this literature typically calibrates the parameters using the micro data and evaluates the model in terms of their macro predictions only. Instead, this paper delivers independent estimates of the structural parameters and evaluates the model both in terms of its aggregate and sectoral predictions.

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H. Bouakez et al. / European Economic Review 65 (2014) 1–22 lj

where δ A ð0; 1Þ is the depreciation rate and Xt is an investment technology that combines different goods into units of capital. In particular !θ=ðθ  1Þ Z J

 κ ij

X ljt ¼ ∏ κij i¼1

ðxlji;t Þκij

1

with xlji;t ¼

0

ðxljmi;t Þðθ  1Þ=θ dm

;

ð4Þ

where κij Z0 is a weight that satisfies ∑Ji ¼ 1 κij ¼ 1, and xljmi;t is the quantity of good produced by firm m in sector i that is lj

lj

j

J i ζ ij and purchased by firm l in sector j for investment purposes. The prices of the composites Ht and Xt are Q H t ¼ ∏i ¼ 1 ðpt Þ j

Q Xt ¼ ∏Ji ¼ 1 ðpit Þκij , respectively, where !1=ð1  θÞ Z 1

pit ¼

0

1θ ðpmi dm t Þ

;

ð5Þ

mi

and pt is the price of the good produced by firm m in sector i. Firms face convex costs when adjusting their capital stock and nominal price. Capital-adjustment costs are proportional to the current capital stock and take the quadratic form lj

lj

lj

Γ ljt ¼ ΓðX ljt ; kt Þ ¼ ðχ=2ÞðX ljt =kt δÞ2 kt ;

ð6Þ

where χ Z0 is a constant parameter. Similarly, the real per-unit cost of changing the nominal price is Φljt ¼ Φðpljt ; pljt 1 Þ ¼ ðϕj =2Þðpljt =ðπpljt 1 Þ  1Þ2 ;

ð7Þ

lj pt

j

is the price of the good produced by firm l in sector j, ϕ Z 0 is a sector-specific parameter, and π is the steady-state where aggregate inflation rate. The quadratic adjustment-cost model for nominal prices is due to Rotemberg (1982).9 In the special case where ϕj ¼ 0, the prices of goods produced in sector j are flexible. In this model, there are neither temporary sales nor volume discounts. Also, since the price elasticity of demand does not depend on the use given to the goods by the buyer, firms charge the same price to all consumers regardless of whether their output is used as investment goods, consumption goods, or materials input. The firm's problem is to maximize 1

Eτ ∑ βt  τ ðΛτ =Λt Þðdt =P t Þ; lj

ð8Þ

t¼τ

lj

where dt are nominal profits, Pt is the aggregate price index (to be defined below), β A ð0; 1Þ is a discount factor and Λt is the consumers' marginal utility of wealth. Nominal profits are ! J Z 1 J Z 1 J Z 1 J Z 1 lj mi lj lj lj lj mi dt ¼ pt c t þ ∑ xlj;t dm þ ∑ hlj;t dm  wljt nljt  ∑ pmi pmi t xmi;t dm  ∑ t hmi;t dm i¼1

i¼1

0

J

j

 Γ ljt Q Xt  Φljt pljt cljt þ ∑

i¼1

lj

Z

1

0

i¼1

0

J

xmi lj;t dm þ ∑

i¼1

Z

1 0

!

i¼1

0

mi

hlj;t dm ;

lj

0

ð9Þ mi

where ct is final consumption, wt is the nominal wage, and xmi lj;t and hlj;t are respectively the quantities sold to firm m in sector i as materials input and investment goods. Profit maximization delivers the following demand functions for materials and investment inputs: j

i θ i xljmi;t ¼ κij ðpmi ðpt =Q Xt Þ  1 X ljt ; t =pt Þ j

 1 lj i θ i hmi;t ¼ ζ ij ðpmi ðpt =Q H Ht : t =pt Þ t Þ lj

2.2. Final consumption Consumers are identical, infinitely lived, and their number is constant and normalized to 1. The representative consumer maximizes 1

Eτ ∑ βt  τ ðlogðC t Þ þυt logðM t =P t Þ þ ηt ψ logð1  Nt ÞÞ; t¼τ

ð10Þ

where Ct is consumption, Mt is the nominal money stock, Nt is hours worked, ψ 4 0 is a weight, and υt and ηt are preference shocks. These shocks respectively disturb the intratemporal first-order conditions that determine money demand and labor 9 We use this model rather than the Calvo model because aggregation is simpler: there are no price cohorts and the equilibrium is, therefore, symmetric within sectors. In Section 4.1, we exploit the functional equivalence between the sectoral Phillips curves implied by both models to help interpret our empirical estimates of ϕj .

H. Bouakez et al. / European Economic Review 65 (2014) 1–22

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supply, and follow the processes lnðυt Þ ¼ ρυ lnðυt  1 Þ þ ευ;t ; lnðηt Þ ¼ ρη lnðηt  1 Þ þ εη;t ; where ρυ ; ρη A ð  1; 1Þ and the innovations ευ;t and εη;t are i.i.d. with mean zero and variances s2υ and s2η , respectively. Consumption is an aggregate of all available goods: !θ=ðθ  1Þ Z 1 J j j ðcljt Þðθ  1Þ=θ dl ; ð11Þ C t ¼ ∏ ðξj Þ  ξ ðcjt Þξ with cjt ¼ j¼1

0

lj

∑Jj ¼ 1 ξj

j

¼ 1, and ct is the final consumption of the good produced by firm l in sector j. where ξ Z 0 is a weight that satisfies Hours worked are an aggregate of the hours supplied to each firm in each sector (Horvath, 2000): !ς=ðς þ 1Þ Z 1 J Nt ¼ ∑ ðnjt Þðς þ 1Þ=ς with njt ¼ nljt dl; ð12Þ j¼1

0

j nt

lj

where ς 4 0 is a constant parameter, is the number of hours worked in sector j, and nt is the number of hours worked in firm l in sector j. This specification captures the idea that labor is imperfectly mobile across sectors and permits different wages and hours in different sectors, as found in the data. The aggregate price index is defined as !1=ð1  θÞ Z J

j

P t ¼ ∏ ðpjt Þξ ; j¼1

where pjt ¼

1

0

ðpljt Þ1  θ dl

:

ð13Þ

The consumer's budget constraint (in real terms) is J Z 1 J Z 1 ðpljt cljt =P t Þ dlþ bt þ mt þ ∑ ðaljt sljt =P t Þ dl ∑ j¼1

0

J

¼ ∑

j¼1

j¼1

Z

1 0

0

ðwljt nljt =P t Þ dl þRt  1 bt  1 =π t þ mt  1 =π t

J

þ ∑

j¼1

Z

1 0

lj

ððdt þ aljt Þsljt 1 =P t Þ dl þ Υ t =P t ;

where bt is the real value of nominal bond holdings, mt ¼ M t =P t is real money balances, Rt is the gross nominal interest rate on bonds that mature at time tþ1, πt is the gross inflation rate, Υ t is a government lump-sum transfer, sjt  1 are shares in a j j sectoral mutual fund, and at and dt are, respectively, the price of a share in, and the dividend paid by, mutual fund j. The consumer's utility maximization determines the demand for the good produced by firm l in sector j: cljt ¼ ξj ðpljt =pjt Þ  θ ðpjt =P t Þ  1 C t :

ð14Þ

2.3. Fiscal and monetary policy Fiscal policy consists of lump-sum transfers to consumers each period, which are financed by printing additional money. Thus, the government budget constraint is Υ t =P t ¼ mt  mt  1 =π t ;

ð15Þ

where the term in the right-hand side is seigniorage revenue at time t. Following Ireland (2003), we consider a general specification of monetary policy where the instrument is a flexible linear combination of the rate of nominal interest and the rate of money growth, and it is adjusted in response to inflation, output, and past money growth deviations from their steady-state values. That is λμ′ ðμt =μÞ  λr ðr t =rÞ ¼ λπ ðπ t =πÞ þ λy ðyt =yÞ þ λμ ðμt  1 =μÞ þ ϑt ;

ð16Þ

where μt is the rate of money growth, yt is real output, λr, λμ′ , λμ , λy, and λπ are policy parameters, and ϑt is an i.i.d. monetary policy shock with mean zero and variance s2ϑ . This specification of monetary policy includes as especial cases several policy rules used in the earlier literature. For example, (16) is a Taylor rule when λμ ¼ λμ′ ¼ 0, an endogenous money growth rule when λr ¼ 0, and an exogenous money growth rule when λr ; λy ; λπ ¼ 0. 2.4. Aggregation and equilibrium In equilibrium, net private bond holdings equal zero because consumers are identical, the total share holdings in sector j add up to one, and firms in the same sector are identical. Appendix A shows that J

J

j¼1

j¼1

j

J

Y t ¼ ∑ Y jt ¼ P t C t þ ∑ Q Xt X jt þ ∑ Ajt : j¼1

ð17Þ

That is, aggregate output (Yt) equals private consumption plus investment and the sum of all adjustment costs in all sectors, and is measured as the sum of sectoral values added, just as in the U.S. National Income and Product Accounts.

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H. Bouakez et al. / European Economic Review 65 (2014) 1–22

Table 1 Sectors and production functions. Sector

Agriculture Metal mining Coal mining Oil and gas extraction Nonmetallic mining Construction Food products Tobacco products Textile mill products Apparel Lumber and wood Furniture and fixtures Paper Printing and publishing Chemicals Oil refining Rubber and plastics Leather Stone, clay and glass Primary metal Fabricated metal Nonelectric machinery Electric machinery Transportation equip. Instruments Misc. manufacturing Transport and utilities Trade FIRE Other services

SIC codes

1–9 10 12 13 14 15–17 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40–49 50–59 60–67 70–87

Weights ξj

0.02 0.01 0.01 0.01 0.01 0.01 0.12 0.01 0.01 0.04 0.01 0.02 0.02 0.01 0.03 0.03 0.01 0.01 0.01 0.01 0.01 0.01 0.02 0.05 0.01 0.01 0.21 0.25 0.01 0.01

νj

γj

αj

Estimate

s.e

Estimate

s.e

Estimate

s.e

0.261n 0.328n 0.432n 0.176n 0.314n 0.394n 0.161n 0.146n 0.229n 0.325n 0.247n 0.365n 0.261n 0.398n 0.237n 0.091n 0.323n 0.326n 0.369n 0.229n 0.346n 0.361n 0.350n 0.283n 0.460n 0.327n 0.314n 0.500n 0.283n 0.427n

0.006 0.011 0.009 0.004 0.004 0.004 0.002 0.005 0.004 0.005 0.004 0.003 0.002 0.004 0.003 0.005 0.002 0.005 0.004 0.003 0.002 0.004 0.005 0.004 0.006 0.005 0.005 0.005 0.004 0.002

0.142n 0.306n 0.194n 0.456n 0.254n 0.052n 0.084n 0.290n 0.067n 0.060n 0.100n 0.079n 0.136n 0.124n 0.183n 0.103n 0.091n 0.089n 0.125n 0.084n 0.104n 0.112n 0.127n 0.080n 0.100n 0.117n 0.248n 0.148n 0.356n 0.195n

0.005 0.015 0.008 0.009 0.006 0.001 0.005 0.018 0.002 0.003 0.003 0.002 0.003 0.003 0.004 0.004 0.002 0.007 0.004 0.002 0.003 0.002 0.006 0.004 0.003 0.007 0.004 0.002 0.006 0.005

0.597n 0.366n 0.374n 0.368n 0.432n 0.554n 0.755n 0.564n 0.704n 0.615n 0.653n 0.557n 0.603n 0.478n 0.581n 0.806n 0.586n 0.585n 0.507n 0.687n 0.549n 0.527n 0.523n 0.637n 0.440n 0.555n 0.437n 0.352n 0.361n 0.378n

0.006 0.024 0.010 0.011 0.009 0.005 0.006 0.021 0.005 0.007 0.003 0.003 0.003 0.006 0.006 0.008 0.002 0.003 0.002 0.004 0.003 0.003 0.003 0.003 0.005 0.006 0.009 0.007 0.005 0.006

Note: The consumption weights were taken from Horvath (2000, p. 87). FIRE stands for finance, insurance and real estate. s.e. denotes standard error. n denotes significance at the 5% level.

The equilibrium of the model is symmetric within sectors but asymmetric between sectors. Thus, relative sectoral prices are not all equal to one and real wages and allocations are different across sectors. The model is solved numerically by log-linearizing its equilibrium conditions around the deterministic steady state and applying standard techniques to solve the resulting system of stochastic linear difference equations. 3. Estimation issues 3.1. Disaggregation level The multi-sector model is used to study a highly disaggregated version of the U.S. economy with 30 sectors that roughly correspond to the two-digit Standard Industrial Classification (SIC). The sectors are listed in Table 1 along with the Major Group categories that they include. Agriculture includes the production of crops and livestock, agriculture-related services, and forestry. Construction includes building and heavy construction and special trade contractors. The four mining sectors are Major Groups 10 and 12 to 14. The 20 manufacturing sectors are Major Groups 20–39. Transport and utilities includes all forms of passenger and freight transportation, communications, and electric, gas and sanitary services. Trade includes both wholesale and retail trade. FIRE is finance, insurance and real estate. Finally, other services include personal, business, recreation, repair, health, legal, educational and social services as well as lodging. At this level of disaggregation, agriculture, mining, and construction all include some service industries. For example, oil and gas extraction includes drilling and exploration services. 3.2. Estimation strategy The model is estimated by the Simulated Method of Moments (SMM) using sectoral and aggregate U.S. time series at the quarterly frequency for the period 1964Q1–2002Q4.10 The sample starts in 1964 because data on wages in the service sector 10 In this application, the length of the simulated series relative to the sample size is five and the weighting matrix is the inverse of the matrix with the long-run variance of the moments along the main diagonal and zeros in the off-diagonal elements. The latter is computed using the Newey–West estimator

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are available only after this date, and ends in 2002 because thereafter the Bureau of Labor Statistics (BLS) stopped reporting sectoral data under the SIC codes. The sectoral data are quarterly series of real wages and PPI (Producer Price Index) inflation rates. The raw data were taken from the BLS web site (www.bls.gov). Unfortunately, these data are not available for all 30 sectors in our model. We use sectoral wages for construction, all manufacturing sectors (except electric machinery and instruments for which the data are not available for the complete sample period) and all services sectors. Sectoral wages are constructed by dividing the monthly observations of average weekly earning of production workers by the Consumer Price Index (CPI) and averaging over the 3 months of each quarter. We use sectoral inflation for the 14 sectors listed in Table 2 for which it is possible to match commodity-based PPIs with their respective sector. Matching commodity-based PPIs with sectors allows us to address the fact that the BLS only started to construct industry-level PPIs in the mid-1980s. We assess the quality of the match by computing the correlation between the inflation rates constructed using commodity-based and industry-level PPIs for the periods where both index types are available. These correlations are reported in Table 2 and vary between 0.59 for oil and natural gas and almost 1 for tobacco products.11 Notice that although the data set on sectoral prices and wages is incomplete, sector specific parameters will be identified by our structural estimation approach because these parameters also affect observable aggregate and other sectoral variables through general equilibrium effects. Since the raw data are seasonally unadjusted, we control for seasonal effects by regressing each series on seasonal dummies and purging the seasonal components. The aggregate data are quarterly series of the rate of inflation, the rate of money growth, the rate of nominal interest, per-capita real money balances, per-capita investment and per-capita consumption. With the exceptions noted below, the raw data were taken from the Federal Reserve Economic Database (FRED) available from the Federal Reserve Bank of St-Louis Web site (www.stls.frb.org). The inflation rate is the percentage change in the CPI. The rate of nominal money growth is the percentage change in M2. The nominal interest rate is the 3-month Treasury Bill rate. Real money balances are the ratio of M2 per capita to the CPI. Real investment and real consumption are, respectively, gross private domestic investment and total personal consumption expenditures divided by the CPI. The raw investment and consumption series were taken from the National Income and Product Accounts (NIPA) available at the Web site of the Bureau of Economic Analysis (www.bea.gov). Real money balances, investment and consumption are computed in per-capita terms in order to make the data compatible with the model, where there is no population growth. The population series corresponds to the quarterly average of the mid-month U.S. population estimated by the BEA. Except for the nominal interest rate, all aggregate data are seasonally adjusted at the source. Since the variables in the model are expressed in percentage deviations from the steady state, all series were logged and quadratically detrended. As pointed out by Ireland (2003), the monetary policy rule (16) requires a normalization to pin down the level of the coefficients. Since Ireland (p. 1635) reports values of λμ′ close to 1 (i.e., 0.98 and 1.30) for two different sub-samples, we normalize λμ′ ¼ 1. In preliminary work, we attempted to estimate versions of the rule with a non-zero interest rate coefficient but found that the optimization algorithm would wander into the area of the parameter space where the solution is not stable. For this reason, we focus on a version of (16) where λr ¼ 0. Thus, the estimated monetary policy rule is ðμt =μÞ ¼ λy ðyt =yÞ þ λπ ðπ t =πÞ þ λμ ðμt  1 =μÞ þϑt ; which corresponds to the especial case of (16) where money growth endogenously responds to inflation and output deviations from their steady state values. Below, we also examine the robustness of our results to using the (calibrated) Taylor rule ðr t =rÞ ¼ 1:5ðπ t =πÞ þ 0:125ðyt =yÞ þ ϑt ;

ð18Þ

where the coefficients of inflation and output are those in Taylor (1993) and sϑ ¼ 0:015 was computed using the residuals from (18) in our sample. In summary, the moments used to estimate the model are the variances and first-order autocovariances of the following 43 series: per-capita consumption, per-capita investment, per-capita real money balances, the rate of nominal interest, the rate of money growth, the rate of CPI inflation, the rates of PPI inflation in agriculture, coal mining, oil and gas extraction, nonmetallic mining, food products, tobacco products, lumber and wood, furniture and fixtures, paper, chemicals, oil refining, rubber and plastics, leather, and stone, clay and glass; and the real wages in construction, all 20 manufacturing sectors (except for electric machinery and for instruments) and all four service sectors. These 86 moments are used to identify 30 sectoral price rigidities, the capital adjustment cost parameter, the coefficients of the monetary rule, and the parameters of the productivity, labor supply, money demand, and monetary policy shocks. Estimating both parameters (i.e, mean and standard deviation) of the productivity-shock processes for all sectors would mean estimating 60 parameters. Hence, in order to economize degrees of freedom and sharpen identification, we limit shock heterogeneity to the Division (footnote continued) with a Barlett kernel and Newey–West fixed bandwidth, that is, the integer of 4ðT=100Þ2=9 where T is the sample size. For the model simulation innovations are drawn from Normal distributions. See Ruge-Murcia (2007) for a detailed explanation of the application of SMM to the estimation of DSGE models and Monte-Carlo evidence on its small-sample properties. 11 We were unable to compute this correlation for agriculture because no industry-level PPI is available. In preliminary work, we considered using the commodity-based PPI for metals but the correlation with its industry-level equivalent was only 0.15.

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Table 2 Correlation between commodity-based and industry-level inflation. Sector

Correlation

Agriculture Coal mining Oil and gas extraction Nonmetallic mining Food products Tobacco products Lumber and wood Furniture and fixtures Paper Chemicals Oil refining Rubber and plastics Leather Stone, clay and glass

n.a. 0.940n 0.586n 0.687n 0.857n 0.998n 0.981n 0.753n 0.964n 0.923n 0.998n 0.963n 0.646n 0.881n

Notes: The statistic used to test the null that the pffiffiffiffiffiffiffiffiffiffi ffi phypothesis ffiffiffiffiffiffiffiffiffiffiffi correlation is zero is computed as R T  2= 1  R where R is the correlation coefficient and T is the sample size. Under the null, this statistic follows a tdistribution with T  2 degrees of freedom (see Hogg and Craig, 1978, pp. 300–301). The sample period used to compute these correlations is 1986Q2–2002Q4 for coal, oil and natural gas, and oil refining, and 1985Q2–2002Q4 for the other sectors. We were unable to compute the correlation for agriculture because no industry-level PPI is produced for this sector by the BLS. n denotes significance at the 5% level.

level of the SIC. Thus, we assume one distribution each for agriculture (Division A), all mining sectors (Division B), construction (Division C), all manufacturing sectors (Division D), and all services sectors (Divisions E through I). This means that we estimate the parameters of five rather than of 30 shock distributions. Since draws are independent, however, shock realizations will be different in different sectors, whether they are in the same Division or not. Since finding the steady state of the model requires solving a large system of nonlinear equations, estimation is computationally intensive. Thus, in order to simplify matters, we calibrate the parameters that determine the steady state. The discount rate ðβÞ is set to 0.997, which is the sample average of the inverse of the gross ex-post real interest rate for the period 1964Q2–2002Q4. The depreciation rate is set to δ ¼ 0:02. The elasticity of substitution between goods produced in the same sector ðθÞ is set to 8. This value is in the middle of the range used in the literature, and implies an average markup over marginal cost of approximately 15%. The parameter that determines the elasticity of substitution between hours worked in different sectors is set to 1 (Horvath, 2000). The consumption weights ðξj Þ are the average expenditure shares in NIPA from 1959 to 1995 and were taken from Horvath (2000, p. 87).12 These weights are reported in Table 1. The input weights ζij and κ ij are equal to the share of sector i in the materials and investment input expenditures by sector j, respectively. These shares are computed using data from the 1992 U.S. Input–Output (I–O) accounts.13 More precisely, the ζijs are computed using the Use Table, which contains the value of each input used by each U.S. industry, while the κijs are computed using the Capital Flow Table, which reports the purchases of new structures, equipment and software allocated by using industry. The production function parameters are calibrated on the basis of estimates obtained using the sectoral data on input expenditures compiled by Dale Jorgenson.14 The estimates are reported in Table 1 and indicate substantial heterogeneity in capital, labor and materials intensities across sectors. Services sectors, especially trade, tend to be labor intensive but so are construction, coal mining and some manufacturing sectors like instruments, and printing and publishing. Mining sectors are generally the most capital intensive of the economy, while construction is the least capital intensive. Materials intensity tends to be relatively low in services and mining compared with manufacturing, construction and agriculture. Some manufacturing sectors like oil refining, food products, textile mill products, and lumber and wood are extremely intensive in materials. This heterogeneity in production function parameters is statistically significant in that tests of the null hypothesis that νj , γj and αj are equal in all sectors are strongly rejected by the data. Before proceeding further, we examine the extent to which the model fits aggregate moments not used in the estimation of the model. Table 3 reports selected historical moments of U.S. aggregate time series and those predicted by the model.

12 Our sector definitions differ from Horvath's in that we respectively combine into one sector: agricultural products and agricultural services; motor vehicles and transportation equipment; and transportation services, communications, electric and gas utilities, and water and sanitary services. 13 I–O tables do evolve over time, for example as a result of technological innovation, but the change is relatively moderate at the level of disaggregation used here. We carried out a small number of sensitivity experiments and found our results to be robust to small perturbations around the values used. 14 See Appendix B for a description of the methodology used to construct these estimates.

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Table 3 Actual and predicted moments. Moment

U.S. Data

Var(Ct)/Var(Yt) Var(Xt)/Var(Yt) CorrðC t ; Y t Þ CorrðX t ; Y t Þ Corrðmt ; Y t Þ Corrðπ t ; Y t Þ Corrðr t ; Y t Þ Corrðμt ; Y t Þ

0.63 7.12 0.88 0.83 0.67 0.23  0.00 0.07

Model with heterogeneous price rigidity 0.62 4.06 0.96 0.92 0.80 0.16  0.31 0.42

Note: U.S. series were logged and quadratically detrended.

All in all, the model's predictions in terms of relative volatility and comovement with output are consistent with the data. The only two exceptions are money growth and the nominal interest rate, which are found to be countercyclical in the model whereas they are essentially acyclical in the data. 4. Parameter estimates In this section, we report SMM estimates of the structural parameters of the model and compare our estimates of sectoral price rigidity and productivity with those based on micro data.15 4.1. Sectoral price rigidity SMM estimates of the price rigidity parameters are reported in Table 4. The magnitude of this parameter varies greatly across sectors and the null hypothesis that its true value is the same in all sectors is strongly rejected by the data (p-value o0:001). Hence, heterogeneity in price rigidity is quantitatively important and statistically significant. The median price rigidity parameter is 22.6, which implies a median price duration of 2.4 quarters (see below). This estimate is in the range of median price durations reported in micro-based studies. For example, the median price duration varies between 1.4 and 1.8 quarters in Bils and Klenow (2004), between 1.2 and 2.4 in Klenow and Kryvtson (2008), and between 1.4 and 3.6 quarters in Nakamura and Steinsson (2008). In turn, all of these estimates are smaller than those obtained using aggregate data alone. For example, Gali and Gertler (1999), Smets and Wouters (2003), and Bouakez et al. (2005) respectively report “aggregate” price durations of 5.9, 10.5, and 6.5 quarters. Large price rigidity estimates contribute to the empirical success of one-sector New Keynesian DSGE models, but those estimates are now regarded by some as implausible in light of the recent micro evidence on price rigidity. Instead, our heterogenous multi-sector DSGE model delivers price durations in line with micro data but substantial monetary policy effects (see Section 5). In this sense, our model helps reconcile New Keynesian models with the micro data. For 9 of the 30 sectors, the estimate of the price rigidity parameter is the lowest possible value of zero, meaning that prices are perfectly flexible in these sectors. In addition, for other 4 sectors the estimate is quantitatively small and the hypothesis that its true value is zero cannot be rejected at the 5% level. Thus, at this level of disaggregation, a large number of sectors (13 out of 30) in the U.S. economy are flexible-price sectors. These sectors include producers of primary goods (agriculture and mining), manufactured commodities (for example, tobacco, chemical and petroleum products) and some capital goods (for example, electric and nonelectric machinery, and instruments). Conversely, the hypothesis that prices are flexible can be rejected for 17 sectors, but the magnitude of ϕ is especially large in primary metal, apparel, nonmetallic mining, trade, food and leather goods. Importantly, two sectors (trade, and transport and utilities) are services that account for a substantial part of the Consumer Price Index. Hence, these results suggest that price rigidity in the U.S. economy is mostly concentrated in services. It is important to note that oil production and transformation takes place in two flexible-price sectors: oil and gas extraction (SIC 13) and oil refining (SIC 29), whose expenditures on materials from SIC 13 are 60% of its total. In turn, 15 Some insights about identification can be gained by examining the Jacobian matrix of the moment conditions, which reveals the following. First, the identification of the parameters of sectoral productivity shocks is typically driven by the moments of sectoral inflation or earnings. For example, the variance of sectoral inflation in agriculture is crucial to identify the variance of productivity shocks to agriculture. However, in the case construction the moments of aggregate investment appear to be important as well. Second, the moments of aggregate investment are key to identify the capital adjustment cost parameter, as one would expect. Third, the moments of aggregate and oil inflation are helpful in identifying the parameters of the monetary policy rule. Fourth, sectoral price rigidity is usually identified from the moments of sectoral inflation or earnings, but we found cases (e.g., oil refining) where the key moments were those of a large supplier or customer. Finally, the moments of aggregate inflation are important for the identification of the price rigidity parameters in two large service sectors, namely trade, and transport and utilities. In interpreting these observations, however, it is important to keep in mind that all moments generally contribute to the identification of all parameters through general equilibrium effects.

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Table 4 Sectoral price rigidities. Sector

ϕj

Duration in Micro Data NS

A. Heterogeneous rigidity Agriculture Metal mining Coal mining Oil and gas extraction Nonmetallic mining Construction Food products Tobacco products Textile mill products Apparel Lumber and wood Furniture and fixtures Paper Printing and publishing Chemicals Oil refining Rubber and plastics Leather Stone, clay and glass Primary metal Fabricated metal Nonelectric machinery Electric machinery Transportation equip. Instruments Misc. manufacturing Transport and utilities Trade FIRE Other services Correlation B. Identical rigidity All sectors n

BK

Estimate

s.e.

Implied probability

Implied duration

PPI

CPI Regular

CPI Final

0.0 1.82 362.57n 0.0 1164.09n 389.49n 601.65n 0.0 42.86n 1061.97n 302.55n 134.75n 3.23 52.72n 0.155 0.398 8.69n 537.96n 35.74n 2389.9n 0.0 0.0 0.0 119.83n 0.0 9.55n 263.55n 703.53n 0.0 0.0

– 3.05 2.93 – 3.61 2.81 1.87 – 3.65 3.66 2.50 4.00 1.99 1.78 1.01 0.88 2.44 2.10 1.55 2.34 – – – 2.00 – 3.28 7.19 4.14 – –

0.0 0.176 0.872 0.0 0.927 0.876 0.899 0.0 0.670 0.923 0.860 0.798 0.256 0.697 0.021 0.051 0.419 0.894 0.645 0.949 0.0 0.0 0.0 0.787 0.0 0.436 0.851 0.906 0.0 0.0

1.00 1.21 7.79 1.00 13.65 8.05 9.91 1.00 3.03 13.05 7.15 4.94 1.34 3.30 1.02 1.05 1.72 9.39 2.82 19.49 1.00 1.00 1.00 4.69 1.00 1.77 6.71 10.68 1.00 1.00

0.38

1.91

1.32

1.20

1.25

3.21 1.34

1.55 0.88

1.11 1.40

9.01 7.58 5.85 3.55

10.18

0.87

0.91

6.29

1.35

1.29

6.55 4.25 0.26

4.94 2.23 0.24

5.39 2.08 0.20

9.62

1.12

1.13

5.45 4.59 3.02 6.05 9.14 1.67 6.70

1.98 1.59 2.61 2.03 2.43 1.66 6.40

5.81 0.43

5.63 0.06

1.31 1.35 0.80 3.11 1.76 2.11 3.65 2.00 4.10  0.09

2.95 0.68 8.33 5.21 5.46

0.74 2.02

0.43 5.464

0.731

0.340

CPI Final

1.516

denotes significance at the 5% level.

materials from SIC 29 constitute an important part of material expenditures by mining sectors (e.g., 4% by metal mining), construction (3%)and transportation and utilities (6%), the latter two of which are sticky-price sectors. We now compare our macro estimates of sectoral price rigidity with estimates computed by Bils and Klenow (2004) and Nakamura and Steinsson (2008) using U.S. micro data. In order to make this comparison we exploit the observational equivalence between the Phillips curves in the (log-linearized) Rotemberg and Calvo models and compute the Calvo probabilities and average price durations implied by our estimates (see Appendix C). These implied probabilities and durations are reported in Table 4. Durations constructed from the micro-based estimates are also reported in Table 4. The mean durations for producer prices were computed as the inverse of the monthly frequencies of price changes for Major Industries reported by Nakamura and Steinsson (see their Table 7), divided by 3 to express them in quarters.16 The mean durations of consumer prices were estimated as follows. First, each Entry Level Item (ELI) category in the micro data was matched to one of our sector definitions. Then, sectoral price durations were computed as the weighted average of the durations of ELIs in that sector. The raw ELI durations are those reported by Bils and Klenow (2004) and Nakamura and Steinsson (2008), and the weights are proportional to those given to each ELI in the CPI.17 In total, we constructed four sets of micro estimates respectively

16 Nakamura and Steinsson use different sector definitions from ours, so we match the sectors closest in nature. However, they respectively combine primary and fabricated metal, and electric and nonelectric machinery into single categories. Given the ambiguity in matching these sectors, we have dropped them from Table 4. 17 There were some ELIs for which there was no obvious sectoral match and, consequently, were excluded from the analysis. These were 8 out of 272 ELIs in Nakamura and Steinsson, and 26 out of 350 in Bils and Klenow. Another issue is that the number of ELIs per sector varies considerably. For example,

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based on PPI prices, regular CPI prices and final CPI prices from Nakamura and Steinsson, and final CPI prices from Bils and Klenow. Final CPI prices include the effect of sales. Notice that macro estimates are better correlated with micro estimates based on PPI and regular CPI prices than with those based on final CPI prices that include sales. The correlation between macro estimates and micro estimates based on PPI (regular CPI) prices is 0.43 (0.43) and statistically different from zero. In contrast, the correlation between macro estimates and final CPI prices, which include sales, is essentially zero. These results are not surprising since our model and data abstract from transitory sales. Moreover, these results are consistent with what we observe when we compare microbased estimates among themselves. The correlation between durations based on PPI and regular CPI prices is high (0.78) and statistically different from zero, but the correlation between either of them and durations based on final prices is low and not statistically different from zero. 4.2. Other parameter estimates Table 5 reports SMM estimates of the other structural parameters. The estimate of the capital adjustment cost parameter is 7.78 (3.23), where the term in parenthesis is the standard error. This estimate is statistically different from zero but quantitatively smaller than values reported in the previous literature that estimates χ using aggregate data alone (e.g., Kim, 2000). The reason is that in our model, input–output interactions induce strategic complementarity in pricing across sectors and greatly amplify the effects of monetary shocks, thereby reducing the quantitative importance of real rigidities, like capital adjustment costs. Labor supply shocks are relatively persistent with low volatility innovations, while money demand shocks are only mildly persistent but its innovations are very volatile. Regarding the estimated monetary policy rule, the autoregressive coefficient is 0.904 (0.428) and the inflation and output coefficients are, respectively, 0.75 (1.22) and 0.00 (0.15). The inflation the coefficient is quantitatively large but imprecisely estimated. These estimates imply that monetary policy shocks are persistent, that an increase in inflation induces the monetary authority to reduce money growth, but that the latter does not react to output during our sample period. The autoregressive coefficients of the productivity shocks range from 0.61 in services to 0.93 in manufacturing, while the standard deviations of innovations range from 0.05 in manufacturing to 0.89 in mining. In general, productivity innovations in primary sectors (agriculture and mining) are substantially more volatile than in other sectors. These results are similar to those in Horvath (2000), who also finds innovations to agriculture and mining to be the most volatile. The correlation between our estimates and Horvath's is high (0.64) and statistically different from zero. We will see below that the very large volatility in mining shocks, the flexibility of oil prices, and the input–output structure induce a channel through which oil helps explain a non-trivial proportion of the unconditional volatility of aggregate output and inflation in the U.S. Overall, results reported so far support the idea that our highly disaggregated DSGE model with heterogenous price rigidity captures reasonably well basic features of the micro data, and motivate the policy analysis carried out in Section 5. 5. Implications of heterogeneity in price rigidity We now examine the implications of heterogeneity in price rigidity for the responses of sectoral output and inflation rates to monetary policy shocks and for the relative contribution of the structural shocks to aggregate and sectoral fluctuations. To that end, we estimate a restricted version of our model in which price rigidity is constrained to be the same in all sectors. Although this restriction (that is, that ϕj ¼ ϕ for all j) is rejected by the data, this model is the appropriate benchmark to evaluate the contribution of modeling heterogeneity in price rigidity. The estimate of the price rigidity parameter is 5.46 (0.73), which implies a duration of 1.52 quarters for prices in all sectors (see Panel B in Table 4). Since the median price duration in the heterogeneous model is 2.4 quarters and numerically close to 1.52, it seems likely that the differences in the implications of both models arise primarily from the heterogeneity price rigidity in the latter model rather than from quantitative differences in the median price rigidity.18 5.1. Sectoral responses to monetary policy shocks We start by documenting differences in the sectoral responses to monetary policy shocks and investigating whether heterogeneity in price setting is important in explaining those differences. We proceed as follows: first, we derive the impulse responses of sectoral inflation and output to a 1% unexpected increase in the growth rate of money supply, which then gradually returns to its steady state. Then, we project the 30 initial responses (that is, the responses in Quarter 1) on the degree price rigidity (measured by the implied durations reported in Table 4) and other sectoral characteristics. (footnote continued) in Bils and Klenow's data, there are 79 ELIs corresponding to food products, but only 2 corresponding to fabricated metal. This means that not all sectoral mean durations are equally accurate. In order the limit the effect of estimates based on too few ELIs, we restricted the analysis to estimates constructed using at least five ELIs. The only exception is tobacco products where cigarettes and cigars account for most of the sectoral output. 18 Table 5 reports estimates of the other parameters of the restricted model. They are generally consistent with those obtained for the heterogenous model though, as one would expect, the parameters of the sectoral productivity shocks are more precisely estimated.

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Table 5 Other parameter estimates. Description

Heterogenous rigidity Estimate

Capital adjustment Productivity shock AR coefficient Agriculture All mining Construction All manufacturing All services All sectors SD of innovation Agriculture All mining Construction All manufacturing All services All sectors Labor supply shock AR coefficient SD of innovation Money demand shock AR coefficient SD of innovation Monetary policy Money growth Inflation Output SD of innovation n

Identical rigidity s.e

Estimate

s.e.

n

3.233

2.122

2.174

0.895n 0.679n 0.888 0.930n 0.610n

0.313 0.081 0.589 0.062 0.258

0.478n 0.999n 0.748n 0.998n 0.000

0.211 0.026 0.114 0.017 –

0.115n 0.890n 0.096 0.054n 0.075n

0.025 0.195 0.083 0.011 0.016

0.218n 0.030n 0.172 0.025n –

0.023 0.005 0.095 0.008 –

0.977n 0.011

0.090 0.016

0.607 0.002

26.522 0.037

0.557n 0.268n

0.117 0.032

0.538n 0.240n

0.212 0.057

0.904n  0.745  0.001 0.007n

0.428 1.223 0.145 0.003

0.999n  1.228  0.006 0.009

0.500 0.653 0.011 0.007

7.777

denotes significance at the 5% level.

The latter are labor and materials intensity,19 whether the sector produces a capital goods or not,20 the standard deviation of the productivity innovation, and the proportion of materials that are purchased from flexible-price producers.21 The responses of sectoral inflation rates in the model with heterogeneous price rigidity and an endogenous moneysupply rule are plotted as continuous lines in Fig. 1.22 The horizontal axes are quarters and the vertical axes are percentage deviations from the steady state. This figure shows that all inflation rates increase following the shock but that there is substantial heterogeneity in the size and dynamics of the sectoral responses. In some sectors, inflation reacts strongly to the shock but returns rapidly to steady state, while in other sectors, it responds weakly and returns slowly and monotonically to steady state. The figure also shows the responses of sectoral inflation rates generated by the identical-price-rigidity version of the model (in dotted lines). These responses are generally smaller and less variable than in the model with heterogenous rigidity: The initial effect ranges from 0.43 to 0.89 percentage points in the former and from 0.06 to 2.65 in the latter. The reason is that the model with identical rigidity tends to understate the response by flexible-price sectors and overstate the response by rigid-price sectors. On the other hand, the correlation between the two sets of responses is high. For example, the correlation between the initial responses in the two models is 0.68. These results suggest that other mechanisms common to both models (for example, materials inputs) work in the same direction in both specifications, but that the model with identical price rigidity misses a key source of sectoral heterogeneity, namely price rigidity. The initial inflation responses in each of the 30 sectors to the monetary policy shock are plotted in Panel A of Fig. 2. This plot underscores the heterogeneity in sectoral responses in the model where price rigidity is different across sectors. In order to better understand the causes of this heterogeneity, we project these initial responses on the sectoral characteristics enumerated above by means of an OLS regression. The results of this regression, reported in Column 1 of Table 6, reveal that the differences in sectoral inflation responses are primarily due to heterogeneity in price rigidity.

19 Since production functions exhibit constant returns to scale, intensities are linearly dependent. For this reason we dropped one of them (capital) from the analysis. 20 The capital-good producing sectors are construction, lumber and wood, furniture and fixtures, primary metal, fabricated metal, nonelectric machinery, electric machinery, transportation equipment, instruments, miscellaneous manufacturing, and stone, clay and glass. 21 For the computation of the latter variable, we classify as flexible-price producers all sectors for which the null hypothesis that ϕj ¼ 0 cannot be rejected (see Table 4). Then, for each sector in our sample, we add up the input shares (from the Use Table) of those flexible-price sectors. The average sector buys around 60% of its materials inputs from flexible-price sectors, but the proportion varies greatly across sectors, ranging from 18% in apparel to 88% in tobacco products. 22 We also performed this exercise replacing the estimated endogenous money-supply rule with the Taylor rule (18). Conclusions are similar to those described here and the graphs are not reported in order to save space.

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Fig. 1. Sectoral inflation responses to a monetary policy shock.

The price rigidity coefficient is statistically significant at the 5% level whereas the other coefficients are not. Note that we obtain very similar results in the version of the model with a Taylor rule (see Column 3 of Table 6). The negative coefficient of price rigidity means that, as one would expect, sectors with flexible prices (that is, shorter price durations) would tend to increase their prices by more than sectors with rigid prices following an expansionary monetary policy shock. Overall, our analysis suggests that heterogeneity in price rigidity is crucial understand the cross-sectional heterogeneity in sectoral inflation responses to monetary policy shocks. The coefficient of materials intensity is negative, meaning that sectors that require more materials as productive inputs would tend to increase their prices by less after a monetary shock. This result is consistent with the theoretical argument put forward by Basu (1995), who shows that intermediate inputs amplify price rigidity in a roundabout production economy. In particular, following a monetary policy shock, the marginal cost rises by less when intermediate goods are used in production. Hence, prices increase by less and output increases by more than in the case without materials. While the mechanism highlighted by Basu is present in our model, our findings suggest that it is not main factor explaining the heterogeneity in sectoral inflation responses to a monetary policy shock Column 5 of Table 6 reports the OLS results for the model with identical price rigidity. All the coefficients have the same sign as in the heterogenous-rigidity model, and are all statistically significant at the 5% level, with the exception of the coefficient attached to the standard deviation of the productivity shock. Recall that, by construction, the identical-rigidity model cannot account for the cross-sectional variation in sectoral responses on the basis of heterogeneity in price rigidity. Since the common price rigidity is subsumed in the constant term (which is now statistically significant), this model can only account for the cross-sectional variation relative to a sector with typical price rigidity. We now turn to the analysis of the sectoral output responses. The continuous lines in Fig. 3 represent the responses obtained from the model with heterogenous price rigidity. The monetary policy shock is expansionary in all sectors, except in tobacco products, where output initially falls by 0.05% but eventually expands after the third quarter. Thus, in general, there is positive output comovement following a monetary shock. Fig. 3 also shows considerable heterogeneity in sectoral output responses. Sectors that react the least are producers of primary goods (agriculture, metal mining, oil and gas extraction) or basic manufactured commodities (tobacco products and chemicals). The effects of a monetary policy shock on sectoral outputs in the economy with identical price rigidity are also plotted in Fig. 3 using dotted lines. It is interesting to note that for almost all sectors, these responses are smaller than those implied by the model with heterogenous price rigidity. Thus, the effects of monetary shocks at the sectoral level are larger in a setup that explicitly incorporates the crosssectional variation in price rigidity that is apparent in the micro data. The relation between sectoral output responses and sectoral characteristics implied by the heterogenous-rigidity model with an endogenous money supply rule is reported in Column 2 of Table 6. Recall that the dependent variable in this regression is the initial output responses, which are plotted in Panel B of Fig. 2. OLS results indicate that the coefficients attached to price rigidity and to whether the sector produces a capital good are statistically significant at the 5% level, while

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Fig. 2. Initial responses to a monetary policy shock. (a) Sectoral Inflation and (b) Sectoral Output.

Table 6 Relation between sectoral responses and sectoral characteristics. Sectoral characteristic

Intercept Price rigidity Capital-good producer Labor intensity Materials intensity Flexible-price inputs SD of productivity R-squared

Heterogeneous rigidity Endogenous money

Heterogeneous rigidity Taylor rule

Identical rigidity

Sectoral inflation

Sectoral inflation

Sectoral inflation

3.08 (1.66)  0.08n (0.03) 0.24 (0.21)  2.73 (1.79)  2.95 (1.68) 1.26 (0.65)  0.51 (0.44) 0.74

Sectoral output  1.11 (2.26) 0.07n (0.02) 0.80n (0.36) 4.11 (2.38) 2.61 (1.92)  0.51 (1.15) 0.21 (0.49) 0.64

1.90 (1.11)  0.04n (0.02) 0.16 (0.15)  1.93 (1.17)  2.01 (1.12) 0.86 (0.45)  0.34 (0.29) 0.69

Sectoral output  0.61 (1.46) 0.04n (0.01) 0.41 (0.24) 2.70 (1.53) 1.74 (1.24)  0.49 (0.76) 0.15 (0.32) 0.59

n

1.35 (0.22) – 0.10n (0.03)  0.66n (0.28)  1.06n (0.24) –  0.11 (0.06) 0.65

Sectoral output 0.79 (0.55) – 0.58n (0.12) 0.21 (0.75)  0.31 (0.62) –  0.22 (0.15) 0.61

Notes: White heteroskedasticity-consistent standard errors are reported in parenthesis. n denotes significance at the 5% level.

the other coefficients are not significant. The finding that the coefficient of capital-good production is positive means that sectors that produce capital goods tend to increase their output by more than non-capital good producers after an expansionary monetary policy shock. This result is due to the input–output structure of the economy and, in particular, to the fact that a general increase in output by all sectors requires an increase in the production of capital goods. Since the production of capital goods is concentrated in relatively small sectors, their output response is proportionally larger than that of other sectors. This feature is also present in the heterogenous-rigidity model with a Taylor rule (Column 4 of Table 6) and in the identical-rigidity model (Column 6 of Table 6), although it is only not statistically significant at the 5% level in the former case. The implication that capital-goods producers react strongly to monetary policy shocks is consistent with the VAR evidence reported by Barth and Ramey (2001) and Erceg and Levin (2006). Regardless of whether monetary policy is described by an endogenous money supply process or by a Taylor rule, the heterogeneous-rigidity model implies that sectors that require more materials inputs tend to increase their output by more

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Fig. 3. Sectoral output responses to a monetary policy shock. Table 7 Variance decomposition. Shock

All productivity (exc. oil) Oil productivity Labor supply Money demand Monetary policy

Heterogeneous rigidity Endogenous money

Heterogeneous rigidity Taylor rule

Identical rigidity

Aggregate inflation

Aggregate output

Aggregate inflation

Aggregate output

Aggregate Inflation

Aggregate output

30.55 19.07 0.36 13.39 36.64

17.48 10.88 47.63 4.59 19.42

24.96 13.59 45.59 – 15.86

15.72 9.95 53.52 – 20.81

15.39 0.01 0.14 33.05 51.42

94.66 2.95 0.06 1.45 0.88

after a monetary shock, consistently with Basu's model. However, as in the case of sectoral inflation above, this mechanism is not statistically significant at the 5% level. In sum, heterogeneity in price rigidity appears to be the main determinant of the cross-sectional variation in sectoral inflation and output responses to a monetary policy shock. In the case of output, whether the sector is a capital-goods producer appears to be an important explanatory variable as well.

5.2. Sources of aggregate and sectoral fluctuations 5.2.1. Aggregate fluctuations Next, we examine the question of whether heterogeneity in price rigidity affects the relative importance of the structural shocks in accounting for aggregate fluctuations. Table 7 reports the contribution of the different shocks to the unconditional variance of aggregate output and inflation. Four conclusions emerge from this table. First, the model with identical price rigidity implies that virtually all of the variance of aggregate output are explained by sectoral productivity shocks. In contrast, the model with heterogeneous price rigidity attributes roughly 50% of this variance to the labor supply shock and less than 30% to sector specific shocks. Interestingly, this result holds regardless of whether monetary policy is characterized by an endogenous money-supply rule or by a Taylor rule. The implications of the identical-rigidity model tend to corroborate the findings of earlier multi-sector RBC models, such as those by Long and Plosser (1987) and Horvath (2000), which predict that sector-specific shocks are an important source of aggregate volatility. This prediction, however, violates the empirical evidence reported by Long and Plosser (1987) and Foester et al. (2011), who instead find that aggregate shocks are the main drivers of aggregate fluctuations. Hence, our paper shows that allowing for heterogeneity in price rigidity

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Fig. 4. The relative importance of sectoral shocks heterogeneous price rigidity and endogenous money supply. (a) inflation and (b) Output.

across sectors (and not price rigidity per se) helps reconcile theory with evidence regarding the sources of aggregate fluctuations. Second, the model with identical price rigidity indicates that monetary policy shocks account for less than 1% of the variance of output. Once we allow for heterogenous price setting, however, this proportion rises to roughly 20%. (Again, this result is robust to the modeling monetary policy as an endogenous money-supply process or a Taylor rule.) The latter fraction is more in line with estimates reported by Shapiro and Watson (1988) and Bouakez et al. (2005), who respectively find that monetary shocks account for 28 and 27% of output variations. This result reflects the role of heterogeneity in price rigidity in amplifying the degree of aggregate money non-neutrality, a feature that is also discussed by Carvalho (2006) and Nakamura and Steinsson (2010) in the context of more restricted models. Third, more than 50% of the variability of aggregate inflation is attributed to monetary policy shocks in the model with identical price rigidity, but this fraction falls to roughly 36% in the heterogenous-rigidity model with an endogenous moneysupply rule and to less than 16% in the Taylor-rule version of that model. Finally, under the model with identical price rigidity, oil shocks (that is, productivity shocks to the oil and gas extraction sector) contribute very little to the unconditional variance of output and inflation. In contrast, in the model with heterogenous price rigidity the contribution of oil shocks reaches 10%, regardless of how monetary policy is modeled. This result is consistent with the recent evidence reported by Lippi and Nobili (2012), who also find that oil supply shocks explain roughly 10% of the variance of U.S. output. Intuitively, the reason for which the contribution of oil shocks is counterfactually small under identical price rigidity is that the prices of sectors that are large consumers of oil-based products (notably, construction, and transportation and utilities) are more flexible than in the actual data. Thus, faced with an increase in marginal costs after a positive oil shock, these sectors would increase prices rather than decrease output. In sum, these results suggest that ignoring the cross-sectional variation in price rigidity can lead to the mismeasurement of the contribution of different structural shocks to aggregate fluctuations. 5.2.2. Sectoral fluctuations The results in the previous section indicate that sectoral productivity shocks are less important than aggregate shocks in explaining the unconditional variance of aggregate output. However, this conclusion does not imply that sectoral shocks

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Fig. 5. Relative importance of sectoral shocks heterogeneous price rigidity and Taylor rule. (a) inflation and (b) Output.

play a small role in accounting for the variability of sectoral variables. In this section, we study the importance of sectoral shocks in explaining the micro data and, in particular, their contribution to the variance of sectoral output and inflation. In doing so, we contrast again the implications of the model with heterogenous price rigidity with those of the model with identical rigidity. First consider the results obtained under heterogenous price rigidity and an endogenous money supply rule. Fig. 4 reports the unconditional variance decomposition for sectoral inflation and sectoral output. In order to reduce cluttering, we group the structural shocks into the following three categories: the productivity shock to its own sector, the other sectoral productivity shocks, and the three aggregate shocks. Starting with sectoral inflation, the top panel of Fig. 4 shows that aggregate shocks explain the largest fraction of inflation variability only in 7 sectors out of 30, with a contribution that ranges between 50% in apparel and 70% in trade and primary metal. In contrast, the productivity shock to its own sector accounts for more than 50% of the inflation variance in 22 out of 30 sectors. In agriculture and most of the mining sectors, this fraction exceeds 90%. In a few other sectors, like food, oil refining, and FIRE, a non-negligible fraction of inflation variability is explained by shocks to the productivity in other sectors. This is particularly true for oil refining, where virtually all of the inflation variance are explained by the productivity shock to the oil and gas extraction sector. This observation underscores the importance of modeling sectoral interactions in order to understand the behavior of sectoral variables and the role of commodity shocks in inter-sectoral reallocations. Replacing the endogenous-money supply rule with a Taylor rule yields similar conclusions. The top panel of Fig. 5 reveals that sectoral productivity shocks explain most of inflation fluctuations in most sectors and play a fairly large role in the remaining sectors, whereas aggregate shocks are the main driver of sectoral inflation variability in only about one-third of sectors. These results indicate that sector-specific shocks play a significantly larger role in explaining sectoral inflation compared with aggregate inflation. Statistical factor models like those used by Boivin et al. (2007), and Mackowiak et al. (2009) also find that sector-specific conditions are important determinants of sectoral inflation rates. However, it is important to note that in factor models the idiosyncratic shock is basically a residual while in this model it is a structural disturbance. Moreover, the economic structure of this model means that idiosyncratic sectoral shocks, such as those to agriculture and oil and gas extraction, may have quantitatively important effects in other sectors as a result of input–output interactions. The variance decomposition of sectoral output is depicted in the bottom panel of Fig. 4. Although there is considerable heterogeneity across sectors, in most cases the productivity shock to a sector accounts for a significant fraction of the

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Fig. 6. The relative importance of sectoral shocks identical price rigidity. (a) inflation and (b) Output.

variance in its output, ranging from roughly 38% in leather to more than 95% in metal mining and in oil and gas extraction. Exceptions are trade, transport and utilities, primary metal, lumber, and food products, where aggregate shocks account for a substantial fraction of sectoral output variability. As is the case with sectoral inflation in oil and refining, roughly 95% of output fluctuations in this sector are due to the productivity shock to oil and gas extraction. In sum, sector-specific shocks appear to be a key source of output fluctuations at the sectoral level. Again, this conclusion is robust to the use of a Taylor rule as an alternative representation of monetary policy, as suggested by the bottom panel of Fig. 5. How would these results change if one were to abstract from heterogeneity in price rigidity? The variance decomposition implied by the model with identical rigidity is shown in Fig. 6. The top panel of this figure conveys a broadly similar message to that mirrored by the corresponding panel in Figs. 4 and 5 regarding the relative importance of aggregate versus sectorspecific shocks in accounting for sectoral inflation variability: sectoral productivity shocks account for the largest portion of inflation fluctuations in most sectors. Hence, allowing for sectoral heterogeneity in price rigidity does not alter in a substantive way the model's implications in this dimension. It is important to note, however, that the model with identical price rigidity generally attributes a smaller role to the productivity shock to its own sector and a larger role to productivity shocks in other sectors. However, there is an important exception: the contribution of shocks oil and gas extraction to the variability of inflation in oil refining is relatively low compared with models with heterogenous price rigidity. On the other hand, a comparison of the bottom panels in Figs. 4, 5 and 6 clearly shows that sector-specific shocks explain a significantly larger proportion of sectoral output variability under identical than under heterogenous price rigidity. In the vast majority of sectors, more than 85% of the variance of output is attributed to the sector's own productivity shock, and the rest is essentially explained by to the productivity shocks in the other sectors. In other words, aggregate shocks account for a negligible fraction of sectoral output fluctuations, which does not exceed 1 in most cases. Thus, as is the case with aggregate output, ignoring sectoral heterogeneity in price rigidity may lead to overstating the importance of sector-specific shocks in accounting for the variability of sectoral output. 5.2.3. Implications of other sources of heterogeneity In addition to the heterogeneity in price rigidity, our model features other realistic sources of sectoral heterogeneity, namely the persistence and volatility of sectoral productivity shocks, the production-function parameters, and the materials and investment inputs used by each sector. An important question is, therefore, the extent to which the results reported in

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Table 8 Variance decomposition under alternative assumptions. Shock

Identical processes for productivity shocks

Identical production function parameters

Symmetric I-O tables

Aggregate inflation

Aggregate output

Aggregate inflation

Aggregate output

Aggregate inflation Aggregate output

20.91 0.21 52.44 5.05 21.39

53.20 19.06 0.14 10.53 17.08

49.97 10.09 30.02 2.08 7.84

31.04 55.12 0.15 5.32 8.37

All productivity (exc. oil) 28.60 Oil productivity 0.31 Labor supply 0.51 Money demand 18.89 Monetary policy 51.69

25.41 33.86 32.56 1.75 6.42

Notes: For the model with identical process for the productivity shocks, the autoregressive coefficient is 0.76 and the standard deviation of the innovations is 0.10. For the model with identical production function parameters, ν ¼ 0:3399, α ¼ 0:1630, and γ ¼ 0:4971 in all sectors. For the model with symmetric I–O tables, ζ ij ¼ 1=30 and κ ij ¼ 1=30 for all i; j ¼ 1; 2; …; 30. The model with identical production function parameters and symmetric I–O tables also assume identical consumption weights.

Section 5.2 depend on these other types of heterogeneity. Focusing on the sources of aggregate fluctuations, we compute the variance decomposition of aggregate output and inflation under alternative assumptions about heterogeneity. The results are reported in Table 8. These results are based on versions of the model in which monetary policy is characterized by an endogenous money supply rule. Therefore, they will be compared to the results reported in the first two columns of Table 7. First, consider the case in which the process that generates productivity shocks is the same in all sectors. We computed the autoregressive coefficient and standard deviation of this process as the (weighted) average of estimates reported in Table 5, using as weights the consumption weights in Table 1. The results reported in the first two columns of Table 8 are similar to those reported in Table 7 for the model with heterogeneous price rigidity in that monetary policy shocks account for about 20% of the unconditional variance of output and for the largest fraction of the unconditional variance of inflation. In this sense, our results concerning the relative importance of monetary policy shocks in aggregate fluctuations are robust to abstracting from heterogeneity in the process of sectoral shocks. However, there is an important dimension along which results differ: the contribution of oil shocks to the unconditional variance of output and inflation is very small when one constrains the standard deviation of mining shocks to be that of a “typical” sectoral productivity shock in Table 8. Thus, one of the reasons oil plays an important role in accounting for unconditional variance of aggregates variables is the very large volatility of oil shocks. Second, consider the case where the production-function parameters and the consumption weights are constrained to be same in all sectors, while keeping the heterogeneity in price rigidity, productivity shocks and input–output tables. Although the contribution of monetary policy shocks to the unconditional variance of output is smaller, these results are generally similar to those reported in Table 7. This suggests that heterogeneity in production function parameters and consumption weights, even though realistic, are not crucial for the conclusions of this paper regarding the sources of aggregate fluctuations. Finally, consider the case where the input–output tables are assumed to be symmetric, while keeping the heterogeneity in price rigidity, productivity shocks, and production-function parameters. Comparing these results with the ones in Table 7 indicates that monetary policy shocks make a limited contribution to the unconditional variance of output and inflation, while oil shocks play a disproportionate role in explaining these variables. The reason is simply that symmetric input– output tables overstate the role of oil in production and generally make it a more important input than it actually is. As a result, its highly volatile shocks explain 55 and 34% of the variance of inflation and output, respectively.

6. Conclusions The purpose of this paper was to study the implications of heterogeneity in price rigidity for sectoral sensitivities to a monetary policy, and for the sources of aggregate and sectoral fluctuations. Using an estimated, highly disaggregated DSGE model with sticky prices, we show that heterogeneity in price rigidity is crucial to understand the heterogeneity in the responses of sectoral inflation and output to a monetary policy shock. We also show that ignoring sectoral heterogeneity in price rigidity leads one to understate the degree of monetary non-neutrality and to overstate the contribution of sectorspecific shocks to aggregate and sectoral fluctuations in output. As a by-product, this paper shows that estimating a DSGE model that takes an explicit account of sectoral heterogeneity— not only in price stickiness, but also in technology and the combination of materials and investment inputs employed in production—yields estimates of the frequencies or price changes that are consistent with those reported in micro-based studies. This is an important step forward as aggregate macroeconomic models, which typically abstract from heterogeneity, usually rely on implausibly long price spells in order to generate empirically plausible effects of nominal shocks. In this respect, our paper bridges two large strands of the literature in macroeconomics: the one based on DSGE models and the one that directly studies the statistical properties of the micro data. Our multi-sector setup allows us to get as close as one possibly can to the micro data, while preserving the theoretical advantages of a fully specified DSGE framework.

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Acknowledgments We thank the editor, the associate editor, anonymous referees, Niels Dam, Hubert Kempf, Emi Nakamura, and Jon Steinsson for helpful comments and suggestions. Financial support from the Social Sciences and Humanities Research Council of Canada is gratefully acknowledged. Appendix A. Aggregation Since net private bond holdings are zero, total share holdings in sector j add up to one, and firms in the same sector are j lj identical, meaning that pjt ¼ pljt , cjt ¼ cljt , njt ¼ nljt and dt ¼ dt . Then, the aggregate equivalent of the consumer's budget constraint is j

J wj nj J d pjt cjt mt  1 Υ t þ mt ¼ ∑ t t þ ∑ t þ þ : πt Pt j ¼ 1 Pt j ¼ 1 Pt j ¼ 1 Pt J

∑

ðA:1Þ

Substituting in the government budget constraint (15) and multiplying through by the price level yield J

J

J

j¼1

j¼1

j¼1

j

∑ pjt cjt ¼ ∑ wjt njt þ ∑ dt :

ðA:2Þ

Define the value of gross output produced by sector j ! J

J

i¼1

i¼1

i

V jt  pjt cjt þ ∑ xij;t þ ∑ hj;t ;

ðA:3Þ

and the sum of all adjustment costs in sector j ! J

J

i¼1

i¼1

j

i

Ajt ¼ Γ jt Q Xt þ Φjt pjt cjt þ ∑ xij;t þ ∑ hj;t :

ðA:4Þ

Then, aggregate nominal dividends are J

J

J

J

j¼1

j¼1

j¼1

j

j

J

J

j

j j ∑ dt ¼ ∑ V jt  ∑ wjt njt  ∑ Q Xt X jt  ∑ Q H t H t  ∑ At ;

j¼1

j¼1

j

ðA:5Þ

j¼1

j

j

j

j where we have used ∑Ji ¼ 1 pit xji;t ¼ Q Xt X jt and ∑Ji ¼ 1 pit hi;t ¼ Q H t H t . The nominal value added in sector j is denoted by Yt and is defined as the value of gross output produced by that sector minus the cost of materials inputs j

j Y jt ¼ V jt Q H t Ht :

ðA:6Þ

Substituting (A.5) and (A.6) into (A.2), using J

J

j¼1

j¼1

∑Jj ¼ 1 pjt cjt

¼ P t C t , and rearranging yield

J

j

Y t ¼ ∑ Y jt ¼ P t C t þ ∑ Q Xt X jt þ ∑ Ajt ; j¼1

ðA:7Þ

where Yt is nominal aggregate output. Appendix B. Estimation of production function parameters The production function parameters were estimated using the yearly data on nominal expenditures on capital, labor and materials inputs by each sector collected by Dale Jorgenson for the period 1958–1996. Jorgenson records separately expenditures on materials and energy inputs. In order to be consistent with the model, where energy is indistinguishable from other materials inputs, we add these two series into a single expenditure category. The nominal expenditures predicted by the model may be obtained from the first-order conditions of the firm's problem νj ðΨ jt P t yjt Þ ¼ wjt njt ; J

ðB:1Þ j

γ j ðΨ jt P t yjt Þ ¼ ∑ pit hi;t ;

ðB:2Þ

!     Λ t 1 j j j j j X j j ∂Γ t ; α Ψ t P t yt ¼ Ωt  1  ð1  δÞΩt P t kt þ Q t kt j βΛt ∂kt

ðB:3Þ

i¼1

j

j

j

where Ψt and Ωt are, respectively, the real marginal cost and the real shadow price of capital in sector j. Since, in equilibrium, firms in the same sector are identical, the firm superscripts are dropped. The right-hand sides of these are the wage bill, total expenditures on materials inputs, and the opportunity cost (net of capital gains) of the capital stock plus net adjustment costs. Jorgenson's data are empirical counterparts of these expressions, but the mapping for capital is imperfect because the

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data do not include adjustment costs and take into account distortionary taxes, from which our model abstracts (see j Jorgenson and Stiroh, 2000, Appendix B). In deriving Eq. (B.3) from the first-order condition for kt þ 1 , we used the assumption of rational expectations. Hence, this equation holds up to a mean-zero forecast error. This adds extra noise to the yearly estimates of all production function parameters. However, since the variance of this forecasts error is likely to be small compared with that of the other terms, and since we average over yearly estimates, it is reasonable to assume that the effect of this error on point estimates is small. Although the data set does not contain observations on Ψ jt P t yjt , it is possible to construct estimates of αj ; νj , and γj as follows. Use two of the three ratios: (19)/(19), (19)/(19) and (19)/(19), and the condition νj þ αj þ γ j ¼ 1 to obtain a system of three equations with three unknowns. The unique solution of this system delivers an observation of the production function j j j parameters for a given year. Our ffi estimates of ν ; α and γ are the sample averages of these yearly observations and their pffiffiffiffiffiffiffiffiffiffi standard deviations are s2 =T where s2 is the variance of the yearly observations and T¼ 39 is the sample size. Appendix C. Observational equivalence of the Rotemberg and Calvo models The log-linearized sectoral Phillips curve for a generic sector j in our model with quadratic adjustment costs is  1 θ1  j Et π^ jt þ 1 ¼ π^ jt  Ψ t  pjt ; j β βϕ where pjt ¼ pjt =P t is the real price and the circumflex denotes deviation from steady state. The log-linearized sectoral Phillips curve that would be obtained in a version of the model where firms follow Calvo pricing is  1 ð1 ϱj Þð1  βϱj Þ  j Et π^ jt þ 1 ¼ π^ jt  Ψ t  pjt ; j β βϱ where ϱj is the probability of not changing prices. Notice that the two curves are isomorphic and, given the elasticity of substitution (θ) and the discount rate (β), imply a correspondence between the rigidity parameter ϕj in the quadratic cost function and the Calvo probability, ϱj . In particular, given ϕj 4 0, the sectoral Calvo probability is the smaller root that solves θ1 ϕj

¼

ð1  ϱj Þð1  ϱj βÞ : ϱj

This is a quadratic equation with roots qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðθ  1Þ þϕj ð1 þ βÞ 7 ðð1  θÞ  ϕj ð1 þβÞÞ2  4βðϕj Þ2 2βϕj

:

Since ðð1  θÞ  ϕj ð1 þ βÞÞ2  4βðϕj Þ2 40 and ðθ 1Þ þ ϕj ð1 þβÞ 40, it follows that both roots are real and positive. It is easy to see that one root is larger than 1 and the other one is less than 1. References Altissimo, F., Mojon, B., Zaffaroni, P., 2009. Can aggregate inflation explain the persistance of inflation? J. Monet. Econ. 56, 231–241. Álvarez, L.J., Burriel, P., 2001. Is a Calvo price setting model consistent with individual price data? B.E. J. Macroecon. 10 (1), 1690–1935. Barth, M.J., Ramey, V.A., 2001. The cost channel of monetary transmission. NBER Macroecon. Annu. 16, 199–239. Basu, S., 1995. Intermediate goods and business cycles: implications for productivity and welfare. Am. Econ. Rev. 85, 512–531. Bils, M., Klenow, P.J., 2004. Some evidence on the importance of sticky prices. J. Political Econ. 112, 947–985. Boivin, J., Giannoni, M.P., Mihov, I., 2007. Sticky prices and monetary policy: evidence from disaggregated data. Am. Econ. Rev. 99, 350–384. Bouakez, H., Cardia, E., Ruge-Murcia, F., 2005. Habit formation and the persistence of monetary shocks. J. Monet. Econ. 52, 1073–1088. Bouakez, H., Cardia, E., Ruge-Murcia, F., 2009. The transmission of monetary policy in a multi-sector economy. Int. Econ. Rev. 50, 1243–1266. Bouakez, H., Cardia, E., Ruge-Murcia, F., 2011. Durable goods, inter-sectoral linkages and monetary policy. J. Econ. Dyn. Control 35, 730–745. Carlton, D.W., 1986. The rigidity of prices. Am. Econ. Rev. 76, 637–658. Carvalho, C., 2006. Heterogeneity in price stickiness and the real effects of monetary shocks. Front. Macroecon. 2, Article 1, http://dx.doi.org/10.2202/1534-6021.1320. Carvalho, C., Lee, J.W., 2011. Sectoral Price Facts in a Sticky-Price Model. Staff Report, Federal Reserve Bank of New York, No. 495. Carvalho, C., Nechio, F., 2011. Aggregation and the PPP puzzle in a sticky-price model. Am. Econ. Rev. 101, 2391–2424. Carvalho, C., Schwartzman, F.F., 2008. Heterogeneous Price-Setting Behavior and Aggregate Dynamics: Some General Results, Mimeo. Christiano, L.J., Eichenbaum, M., Evans, C.L., 2005. Nominal rigidities and the dynamic effects of a shock to monetary policy. J. Political Econ. 113, 1–45. Conley, T.G., Dupor, B., 2003. A spatial analysis of sectoral complementarity. J. Political Econ. 111, 311–352. Dixon, H., Kara, E., 2010. We explain inflation persistence in a way that is consistent with the microevidence on nominal rigidity. J. Money Credit Bank. 42, 151–170. Dixon, H., Kara, E., 2011. Contract length heterogeneity and the persistence of monetary shocks in a dynamic generalized Taylor economy. Eur. Econ. Rev. 55, 280–292. Dupor, W.D., 1999. Aggregation and irrelevance in multi-sector models. J. Monet. Econ. 43, 391–409. Eichenbaum, M., Jaimovich, N., Rebelo, S., 2011. Reference prices and nominal rigidities. Am. Econ. Rev. 101, 234–262. Erceg, C.J., Levin, A., 2006. Optimal monetary policy with durable consumption goods. J. Monet. Econ. 53, 1341–1359. Foester, A.T., Sarte, P.-D., Watson, M.W., 2011. Sectoral vs. aggregate shocks: a structural factor analysis of industrial production. J. Political Econ. 119, 1–38. Gagnon, E., 2009. Price setting during high and low inflation: evidence from Mexico. Q. J. Econ. 124, 1221–1263. Gali, J., Gertler, M., 1999. Inflation dynamics: a structural econometric analysis. J. Monet. Econ. 44, 195–222. Gertler, M., Leahy, J., 2008. A phillips curve with an SS foundation. J. Political Econ. 116, 533–572. Golosov, M., Lucas, R.E., 2007. Menu costs and phillips curves. J. Political Econ. 115, 171–199. Hogg, R., Craig, A., 1978. Introduction to Mathematical Statistics. Macmillan Publishing, New York.

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Horvath, M., 1998. Cyclicality and sectoral linkages: aggregate fluctuations from independent sectoral shocks. Rev. Econ. Dyn. 1, 781–808. Horvath, M., 2000. Sectoral shocks and aggregate fluctuations. J. Monet. Econ. 45, 69–106. Ireland, P., 2001. Sticky-price models of the business cycle: specification and stability. J. Monet. Econ. 47, 3–18. Ireland, P., 2003. Endogenous money or sticky prices? J. Monet. Econ. 50, 1623–1648. Jorgenson, D.W., Stiroh, K.J., 2000. Rising the speed limit: U.S. economic growth in the information age. Brook. Pap. Econ. Act., 125–235. Kehoe, P.J., Midrigan, V., 2010. Prices Are Sticky After All, NBER Working Paper No. 16364. Kim, J., 2000. Constructing and estimating a realistic optimizing model of monetary policy. J. Monet. Econ. 45, 329–359. Klenow, P.J., Kryvtson, A., 2008. State-dependent pricing or time-dependent pricing: does it matter for recent U.S. inflation?. Q. J. Econ. 123, 863–904. Lippi, F., Nobili, A., 2012. Oil and the macroeconomy: a quantitative structural analysis. J. Eur. Econ. Assoc. Eur. Econ. Assoc. 10, 1059–1083. Long, J.B., Plosser, C.I., 1983. Real business cycles. J. Political Econ. 91, 39–69. Long, J.B., Plosser, C.I., 1987. Sectoral vs. aggregate shocks in the business cycle. Am. Econ. Rev. 77, 333–336. Mackowiak, B., Moench, E., Wiederholt, M., 2009. Sectoral price data and models of price setting. J. Monet. Econ. 56 (S), 78–99. Midrigan, V., 2011. Menu costs, multi-product firms and aggregate fluctuations. Econometrica, 79, 1139–1180. Nakamura, E., Steinsson, J., 2008. Five facts about prices: a reevaluation of menu cost models. Q. J. Econ. 123, 1415–1464. Nakamura, E., Steinsson, J., 2010. Monetary non-neutrality in a multi-sector menu cost model. Q. J. Econ. 125, 961–1013. Rotemberg, J.J., 1982. Sticky prices in the United States. J. Political Econ. 90, 1187–1211. Ruge-Murcia, F., 2007. Methods to estimate dynamic stochastic general equilibrium models. J. Econ. Dyn. Control 31, 2599–2636. Shamloo, M., Silverman, C., 2010. Price Setting in a Model With Production Chains: Evidence From Sectoral Data. IMF Working paper, No. 10/8. Shapiro, M., Watson, M., 1988. Sources of business cycle fluctuations. In: Fished, S. (Ed.), NBER Macroeconomics Annual, MIT Press, Cambridge, pp. 111–148. Sheedy, K., 2007. Inflation Persistence When Price Stickiness Differs Between Industries, Mimeo. Smets, F., Wouters, R., 2003. An estimated dynamic stochastic general equilibrium model of the Euro area. J. Eur. Econ. Assoc. 1, 1123–1175. Taylor, J.B., 1993. Discretion versus policy rules in practice. Carnegie-Rochester Conference Series on Public Policy 39, 195–214. Vavra, J., 2010. The Empirical Price Duration Distribution And Monetary Non-Neutrality, Mimeo.