Sectoral Phillips Curves and the Aggregate Phillips1

Curve∗2

Jean Imbs† Eric Jondeau‡ Florian Pelgrin§3

May 11, 20114

Abstract5

Sector-level Phillips curves are estimated in French data. There is considerable het-6

erogeneity across sectors, with vastly different estimates of the backward looking7

component of inflation and the duration of nominal rigidities. A multi-sector model8

of inflation dynamics is calibrated on the basis of these sectoral estimates. Aggre-9

gate inflation, simulated on the basis of heterogeneous sectors, displays comparable10

dynamics to actual data. A comparison is drawn between the policy trade-offs im-11

plied by a Phillips curve based on macroeconomic estimates, vs. one based on a12

model with heterogeneous sectors. The difference is sizeable.13

JEL Classification Code: E31, E52, E6014

Keywords: New Keynesian Phillips Curve, Heterogeneity, Inflation Persistence,15

Marginal Costs.16

∗We are grateful to audiences at the ECB/CEPR conference on Wage and Labour Cost Dynamics(December 2006), ESSIM 2006, the 2006 meetings of the Society of Computational Economics, the2006 meetings of the Society for Economic Dynamics, the 2006 Dynare conference, the joint seminarof the National Bank of Belgium, Universite Catholique de Louvain, Universite Libre de Bruxelles andKatholieke Universiteit Leuven, and especially to Klaus Adams, Carlos Carvalho, Marco Del Negro,David Lopez-Salido and Rafael Wouters for insightful discussions. Thanks are also due to AlexanderWolman and an anonymous referee, who helped us sharpen considerably the paper’s point. StephaneGregoir was kind enough to give us access to French data. The paper was partly written while Imbs wasa Resident Scholar at the Research Department of the International Monetary Fund. Financial supportfrom the National Center of Competence in Research “Financial Valuation and Risk Management” isgratefully acknowledged. The National Centers of Competence in Research (NCCR) are a researchinstrument of the Swiss National Science Foundation. All errors are our own.

†(Corresponding author) Paris School of Economics and CEPR. Postal address: Paris School of Eco-nomics, 106 Boulevard de l’Hopital, 75013 Paris, France. Email: Jean.Imbs@parisschoolofeconomics.eu

‡Faculty of Business and Economics, University of Lausanne, and Swiss Finance Institute. Postaladdress: University of Lausanne, CH–1015 Lausanne, Switzerland. Email: Eric.Jondeau@unil.ch

§Faculty of Business and Economics, University of Lausanne and CIRANO. Postal address: Universityof Lausanne, CH–1015 Lausanne, Switzerland. Email: Florian.Pelgrin@unil.ch

1

1 Introduction17

The frequency of price adjustments varies across economic activities. This is one of18

the main conclusions of the European Inflation Persistence Network (IPN) that collects19

information on prices at a microeconomic level, for a cross-section of European countries.20

The duration of nominal rigidities varies across countries, but even more from one sector21

to the next. For instance, Altissimo et al. (2006) document the price of food changes22

on average every four months in Italy, but the price of capital goods remains on average23

unchanged for about 20 months. Similar heterogeneity appears to prevail in all countries24

covered by the IPN, as well as in the US, as documented by Bils and Klenow (2004) or25

Nakamura and Steinsson (2008a).26

We use French data to estimate sectoral Phillips curves, as implied by a disaggregated27

version of Galı and Gertler (1999). The implied sector specific estimates are documented28

across the 16 sectors with French data. The focus is on the dynamics of sectoral inflation,29

the significance of properly measured marginal costs, and the implied duration of nominal30

rigidities.31

Sector-level Phillips curves are well supported by French data. Prices respond to32

observed marginal costs, and are significantly forward looking. On average, the proportion33

of backward looking behavior is around 30%, as compared with 40% in the aggregate. The34

estimated reduced form coefficient on marginal costs is substantially larger at the sector35

level, and significant in most cases. The difference matters in an economic sense. Ceteris36

paribus, a larger role for marginal costs in driving prices corresponds to shorter nominal37

rigidities. Sectoral estimates imply nominal rigidities in the vicinity of two quarters, as38

opposed to a little less than one year in the aggregate.39

There is extensive sectoral heterogeneity. Across the 16 French sectors with data,40

the backward looking component of inflation ranges between 0 and 0.5, the reduced41

form coefficient on marginal costs takes values between 0 and 2, and the duration of42

nominal rigidities ranges between one quarter and almost two years. The frequency of43

price changes implied by our sectoral estimates maps well with existing studies on French44

2

data, both at the sector and the macroeconomic level. In particular, aggregate data imply45

conventional estimates of the aggregate Phillips curve. There is in fact nothing special46

about the data here.147

A multi-sector model of the macroeconomy is then calibrated on the basis of our48

sectoral estimates. The model is simulated to obtain a series for aggregate inflation. A49

conventional model of the Phillips curve is estimated on the thus generated synthetic se-50

ries. The measure of aggregate inflation simulated on the basis of our sectoral estimates51

shares most of the properties of directly observed inflation. Just like in conventional52

macroeconomic estimates of the Phillips curve, there is a sizeable backward looking com-53

ponent and relatively long lasting nominal rigidities. This happens even though aggregate54

inflation is simulated on the basis of sector-level parameters.55

Is such heterogeneity relevant for the conduct of monetary policy? Policy frontiers in56

the Taylor (2001) tradition are computed for two cases based on the multi-sector model.57

In the first case, a frontier is generated from the (incorrect) aggregate Phillips curve58

estimated on simulated data from the multi-sector model. It is compared with the true59

frontier based on the multi-sector model. In the former instance, aggregate inflation is60

given by an aggregate Phillips curve; in the latter, it is given by a GDP-weighted average61

of the heterogeneous inflation processes implied by the estimated sectoral Phillips curves.62

The conventional aggregate estimates of the Phillips curve imply a substantially less63

favorable policy frontier than the multi-sector model. For given volatilities of inflation64

and the nominal interest rate, a multi-sector economy with calibrated heterogeneous65

sectoral inflation dynamics implies a volatility of the output gap one-third to one-half66

of what conventional aggregate estimates suggest. This happens because, on average,67

sectoral inflation is less inherently persistent, prices are more responsive to cost shocks,68

and nominal rigidities less long lasting.69

The paper takes seriously the micro-foundations of the New Keynesian Phillips curve.70

The structural coefficients obtained in the estimation of sectoral Phillips curves are re-71

1For more details on sectoral estimates, see Imbs et al. (2008).

3

flective of firms’ pricing decisions. There is large heterogeneity across sectors, at least in72

French data. Such heterogeneity is liable to result in a mis-specified aggregate Phillips73

curve, with potentially large policy implications. Ignoring heterogeneity and using a74

Phillips curve model based on aggregate data leads to a markedly different policy frontier75

than the one implied by a multi-sector model calibrated to incorporate observed sectoral76

heterogeneity.77

Many others have taken interest in the aggregate consequences of heterogeneous pric-78

ing. Carvalho (2006) introduces heterogeneous price stickiness in an otherwise conven-79

tional purely forward-looking model. He shows the response of the economy to monetary80

shocks gains in persistence, as price changes are staggered according to their heteroge-81

neous frequencies. He also derives analytically a generalized Phillips curve accounting for82

heterogeneity. Interestingly, Sheedy (2007) contends heterogeneity may have the oppo-83

site effect on inflation persistence, as the first cohort of firms that change their prices in84

response to a monetary shock is likely to reverse its initial decision once the opportunity85

arises again and the shock has dissipated. Justiniano et al. (2006) construct a multi-86

sector model where sectoral prices adjust frequently, as suggested by the microeconomic87

evidence, but measured aggregate prices change more sluggishly because of input-output88

linkages.89

All these papers approach the question of pricing heterogeneity from a theoretical90

standpoint. In some cases, their results are complementary to ours as they add a theoret-91

ical backbone to our empirical conclusions. But they also differ in a number of important92

ways. Here, sectoral versions of conventional Phillips curves are estimated, and the im-93

plied aggregate inflation series is simulated. Aggregation is in fact of the simplest kind,94

since sectoral price indices are averaged up to the aggregate using observed GDP weights.95

Here therefore, it is the empirical consequences of heterogeneity that are explored. There96

is no analytical derivation of the true aggregate process implied by sectoral heterogeneity.97

Instead, a conventional Phillips curve is forced on the aggregate data, rather than the98

augmented version suggested by Carvalho (2006). The differences this omission implies99

4

are then examined.2 Since our aggregate framework is entirely standard, conventional100

policy analysis can be conducted. The policy trade-off between inflation and the output101

gap is in fact substantially altered by the existence of sectoral heterogeneity.3102

It is also possible to address the question of heterogeneity from an empirical stand-103

point, even when it is not directly observable. Zaffaroni (2004) and Altissimo et al.104

(2009) propose to do so. They derive aggregate inflation dynamics under assumptions on105

the specific (but unobserved) processes followed by sectoral prices. Both papers apply106

insights on the effects of cross-sectional aggregation of heterogeneous processes that were107

first introduced by Robinson (1978) and Granger (1980).108

The rest of the paper is organized as follows. Section 2 reviews the derivation of109

an expression for a sectoral Phillips Curve allowing for nominal rigidities and backward110

looking pricing that are sector specific. Our data and our estimator are then introduced.111

The estimation accounts for aggregate influences on sectoral prices in as general a manner112

as possible. Results follow, with a comparison of the sectoral estimates and those implied113

by the aggregated data. In Section 3, sector-specific results are used to calibrate a multi-114

sector model of the macroeconomy. The Section describes the model and the simulation115

method to obtain a synthetic series on aggregate inflation. The paper closes with the116

policy frontiers implied by the aggregate and sectoral dynamics of inflation.117

2Heterogeneity is but one example of a potential source of mis-specification. For instance, Dotsey(2002) shows a significant coefficient on lagged inflation obtains if the econometric specification imposesCalvo pricing, whereas the real underlying model is based on staggered contracts in the Taylor fashion.

3There are many other instances of monetary models with sectoral heterogeneity, but they are lessdirectly relevant to what is done here. Erceg and Levin (2002) allow for sectoral differences in demandcharacteristics, focusing on differences between durable and non-durables goods. Aoki (2001), Benigno(2004) and Huang and Liu (2004) analyze the implications of sectoral heterogeneity for the design ofmonetary policy. Dixon and Kara (2005) study the impact of heterogeneity in the context of Taylor-type staggered wage setting. Bouakez et al. (2009) construct and calibrate a model with heterogenousproduction sectors, and show substantial heterogeneity across sectors in the degree of sectoral sensitivityto monetary policy shocks. Nakamura and Steinsson (2008b) develop a similar argument with addedinput-output linkages. Alvarez et al. (2005) analyze the impact of heterogeneity under a variety ofdifferent assumptions on price-setting behavior.

5

2 Sectoral Phillips Curves118

An expression for a sectoral Phillips Curve is first derived, as implied by Galı and Gertler119

(1999). Price dynamics in each sector are assumed to respond only to the dynamics120

of marginal costs there. This is unlikely to happen in reality. Sectoral prices or costs121

can be related through input-output production linkages for instance, or because factor122

markets are integrated at the aggregate level. The empirics are careful to allow for sectoral123

disturbances that are potentially correlated across activities. They are general enough124

to incorporate the cross-sectoral interdependences that are absent from the model, but125

potentially present in the data.126

2.1 A Sectoral Phillips Curve127

For each sector j = 1, ..., J , a New Keynesian Phillips is derived, where the magnitude128

of backward looking behavior and price stickiness are sector specific. The Phillips curves129

are obtained combining ingredients from Sbordone (2001), Woodford (2003) and Galı and130

Gertler (1999). There is a continuum of firms on a unit interval, indexed by i in sector131

j, producing differentiated goods. With monopolistic competition, demand for product i132

in sector j takes the form133

Yij,t =

(Pij,t

Pj,t

)−η

Yj,t, (1)134

where Pij,t/Pj,t is the relative price of firm i’s production of good j, η > 1 denotes the135

elasticity of substitution across varieties and Yj,t is defined as136

Yj,t =

[∫ 1

0

Yη−1

η

ij,t di

] ηη−1

. (2)137

Each firm produces a differentiated good according to the production technology138

Yij,t = Zj,t H1−aj

ij,t , (3)139

6

where Zj,t denotes (sector specific) technology, Hij,t are hours worked and 1 − aj is the140

share of labor in industry j’s value added.141

Price setting decisions are governed by the Calvo (1983) mechanism. In each period,142

firms face a constant probability 1 − αj of being able to re-optimize their price. When143

they optimize, firms choose their price P ∗ij,t to solve144

maxP ∗ij,t

Et

∞∑k=0

(βαj)k [Yij,t,t+k P ∗

ij,t −Ψ(Yij,t,t+k)], (4)145

subject to the demand for good i. β is the subjective discount factor and Ψ(Yij,t,t+k)146

denotes total nominal costs. Yij,t,t+k is real output at date t + k for the firms that147

changed their price at t. Optimality implies148

∞∑k=0

(βαj)k Et

[Yij,t,t+k

(P ∗

ij,t −η

η − 1Sij,t,t+kPij,t+k

)]= 0, (5)149

where Sij,t,t+k = Ψ′(Yij,t,t+k)/Pij,t+k denotes real marginal costs.150

Define a steady state where Pij,t+k = Pij,t, Pt+k = Pt, P ∗ij,t = Pij,t+k = Pij, Yij,t,t+k =151

Yij and Sij,t,t+k = Sj = η−1η

.4 A Taylor expansion of equation (1) around that steady152

state gives153

p∗ij,t = (1− βαj)∞∑

k=0

(βαj)k Et [(sij,t,t+k + pij,t+k)] , (6)154

with sij,t,t+k = sij,t,t+k − sj and pij,t+k = pij,t+k − pij.155

2.1.1 Marginal costs156

There is a discrepancy between real marginal costs at the firm level Sij,t+k, and their157

sector average across firms, Savgj,t+k. We only observe the latter. Sbordone (2001) and Galı158

4Our (unfiltered) data is not consistent with a zero inflation steady state. This is a recurrent problemin the literature. An alternative to filtering the data is to construct a monetary model where trendinflation is allowed for, an avenue followed among others by Ascari (2004).

7

et al. (2001) establish the following relation159

Sij,t,t+k =Wj,t+k

Pj,t+k

∂Hij,t,t+k

∂Yij,t,t+k

= (Yij,t,t+k)aj

1−aj1

1− aj

Wj,t+k

Pt+k

Z− 1

1−aj

j,t+k ≡ (Yij,t,t+k)aj

1−aj Sj,t+k,

(7)160

where Wj,t are the nominal wages in sector j, and Sj,t+k is not firm specific. Moreover,161

sectoral average real marginal costs are given by162

Savgj,t+k = (Yj,t,t+k)

aj1−aj Sj,t+k, (8)163

and ultimately,164

Sij,t,t+k =

(Yij,t,t+k

Yj,t+k

) aj1−aj

Savgj,t+k =

(P ∗

ij,t

Pj,t+k

)− ηaj1−aj

Savgj,t+k. (9)165

This implies that real marginal costs vary across firms only if optimal pricing does. In the166

absence of any firm-specific shock, all firms that are allowed to re-optimize their price at167

date t select the same optimal price, which ensures a symmetric equilibrium across firms168

in each sector. As a result firm indices are omitted from now on. In deviations from the169

steady state, marginal costs follow170

sj,t,t+k = savgj,t+k −

ηaj

1− aj

(p∗j,t − pj,t+k

).. (10)171

2.1.2 Price indices172

Because of price rigidities, the sectoral (log) price level at time t is given by173

pj,t = αj pj,t−1 + (1− αj) p∗j,t. (11)174

Galı and Gertler (1999) introduce purely backward looking firms, assumed to obey a175

rule of thumb whereby the price in period t depends only on information dated t− 1 or176

earlier. A proportion ωj of the firms that are allowed to adjust their prices do so in a177

8

purely backward looking manner. By definition, newly set prices are given by178

p∗j,t = ωj pbj,t + (1− ωj) pf

j,t, (12)179

where pbjt (pf

jt) denote the price set by backward (forward) looking firms. Forward looking180

firms choose prices optimally according to equation (6). Backward looking firms merely181

adjust for inflation the prices they set the last time they could, i.e.182

pbj,t = p∗j,t−1 + πj,t−1. (13)183

As is well known, equations (6) and (10)-(13) combine to imply a (linearized) hybrid184

Phillips curve:185

πj,t =ωj

φj

πj,t−1 +βαj

φj

Etπj,t+1 +(1− ωj) (1− αj) (1− βαj)

φj

hj savgj,t . (14)186

With φj = αj + ωj [1− αj (1− β)] and hj = 1/(1 +

ηaj

1−aj

), equation (14) implements187

the correction derived in equation (10). Hatted variables denote deviations from the no188

inflation steady state. To economize on notation, define λbj =

ωj

φj, λf

j =βαj

φjand θj =189

(1−ωj)(1−αj)(1−βαj)

φj. A cost-push shock επ

j,t is introduced, which may embed measurement190

error. Following Woodford (2003), the shock is directly inserted in the reduced form191

expression.5 The Phillips Curve can be rewritten in its well known hybrid form192

πj,t = λbj πj,t−1 + λf

j Etπj,t+1 + θj hj savgj,t + επ

j,t. (15)193

The industry level Phillips curve does not include any reference to an aggregate variable,194

nor indeed to any relative prices. At face value, this may seem a contradiction relative195

to the findings in Aoki (2001), Benigno (2004) or Carlstrom et al. (2006). But all196

these authors use versions of the New Keynesian Phillips curve that refer to the output197

gap as a measure of economic activity. In contrast, here marginal costs enter directly.198

5See equation (4.38) page 451 and following.

9

Relative prices are effectively subsumed in our definition of savgj,t . This follows directly199

from Woodford (2003).6200

2.2 Data201

Data are constructed by INSEE, the French statistical institute. They are observed quar-202

terly from 1978:1 to 2005:3, with information on output, prices, wages and employment203

for sixteen sectors of the French economy, comprising all activities. Coverage includes204

agriculture, manufacturing (six sectors) and services (nine sectors).7 For each industry,205

the inflation rate is computed as the quarter-on-quarter growth rate of the value-added206

deflator.8 A sector-specific measure of marginal costs is computed following Sbordone207

(2001) or Galı et al. (2001). savgj,t is the (logarithm) deviation of the sector share of labor208

income in value added from its sample mean. We apply the sector specific correction im-209

plied by hj. From its definition, the correction is computed on the basis of the observed210

industry share of labor in production aj, and a value for η corresponding to a level of211

markups calibrated at ten percent.9212

These data are coarse. A partition of all economic activities in 16 sectors entails213

plenty of aggregation. Short of alternative data sources, however, there is simply nothing214

better available. In fact, these French data are already remarkable in that they provide215

quarterly information on prices, quantities, and labor market outcomes covering all French216

economic activities, and using the same sector definitions. It is quite difficult to obtain217

similar information of homogeneous quality for any country, including the United States.218

For instance, Leith and Malley (2007) estimate sectoral Phillips curves in US sectors,219

but on the basis of re-constructed data. The fact our data are still the result of some220

6This is developed in the Appendix B.7 to Chapter 3, and in particular in equation B.33 on page 668.7The sectors are ”Agriculture”, ”Food Manufacturing”, ”Consumption Goods”, ”Car Industry”,

”Equipment Goods”, ”Intermediary Goods”, ”Energy”, ”Construction”, ”Trade”, ”Transportation”,”Financial Activities”, ”Real Estate”, ”Business Services”, ”Personal Services”, ”Education and HealthServices”, and ”Government”.

8Firms’ pricing decisions presumably concern the price of gross output rather than value added. Thetwo are probably different in the data, even though they are not in our theory. Unfortunately, no dataon gross output prices are available for France at the level of disaggregation we focus on.

9This follows directly from Sbordone (2001) or Galı et al. (2001). The latter in particular arguethat different markup values do not alter any of their results (in footnote 24). We checked that using aunique, aggregate measure of aj does not change any of our results either.

10

aggregation is not necessarily crucial. The consequences of heterogeneity (in pricing221

behavior) are investigated across the 16 sectors with data. There may well be further222

heterogeneity within each one of these sectors. It is however likely to be of second order223

importance relative to the paper’s main point.224

Table 1 presents some summary statistics. The Table reports average inflation and225

average growth in real marginal costs, their serial correlations, and their contemporaneous226

cross-correlation, at both industry and aggregate levels. There is extensive heterogeneity227

across sectors in both average measures. Annual inflation ranges between 0.2% and 5.5%,228

and the average annual growth in real marginal costs ranges between −3.6% and 0.1%.229

There is also heterogeneity in the serial correlation in inflation, and the cross-correlation230

between sj,t and πj,t. In contrast marginal costs are consistently highly serially correlated.231

In all subsequent estimations, industry-specific means are subtracted from each series.232

Filtering the data instead implies virtually identical results.233

Table 1 also reveals that aggregate inflation and real marginal costs are highly se-234

rially correlated, and covary to a large extent. The covariance between aggregates is235

in fact larger than any of its sectoral equivalents. Such a discrepancy exemplifies the236

possibility that a Phillips curve estimated on aggregate data implies drastically different237

policy choices than an average of sectoral data would. Figure 1 confirms visually the two238

variables track each other closely over time, as they should given the existing empirical239

support for aggregate Phillips curves.240

2.3 Estimation Method241

The conventional estimators that have often been used on aggregate inflation series are242

implemented on equation (15). In the body of the text, a data generating process is243

assumed for marginal costs, following Fuhrer and Moore (1995), Sbordone (2001) or244

Kurmann (2007). With such assumption, future expected inflation can be solved out245

of the Phillips curve. And the obtained model can be brought to the data directly246

using a Maximum Likelihood (ML) approach. By assumption, marginal costs follow an247

11

autoregressive process of order two, which is validated in our sectoral data. The full248

model of sectoral inflation rests on the following system249

πj,t = λbj πj,t−1 + λf

j Etπj,t+1 + θj hj savgj,t + επ

j,t (16)250

savgj,t = ρ1j savg

j,t−1 + ρ2j savgj,t−2 + uj,t,251

where uj,t denotes an independent and identically distributed shock to real marginal costs252

in sector j, |ρ2j| < 1, ρ1j + ρ2j < 1, ρ2j − ρ1j < 1, σ2επj

= E(επ2j,t), and σ2

uj= E(u2

j,t). An253

appendix shows the dynamics of sectoral inflation can then be rewritten10254

πj,t = δ1jπj,t−1 + φ1jhj savgj,t + φ2jhj s

avgj,t−1 + επ

j,t, (17)255

where δ1j, φ1j, and φ2j are defined in the Appendix, and επj,t is an appropriate transfor-256

mation of επj,t.257

It is eminently likely that shocks to sectoral inflation or marginal costs can be cor-258

related across sectors. With factor markets that are integrated at the country level for259

instance, shocks to marginal costs are correlated across sectors, and E[ui,tuj,t] = σuiuj6= 0.260

The same would obtain in the presence of input-output linkages, which presumably exist261

in the data, but not in the model we estimate in equation (17). By the same token, in262

the presence of aggregate shocks, cost push shocks will correlate across sectors so that263

E[επi,tε

πj,t] = σεiεj

6= 0. Finally, the shocks to marginal costs uj,t have no unique structural264

interpretation. So it is possible they in fact correlate with επj,t. They would for instance in265

response to technological developments that affect both the marginal cost of production266

and firms’ market power. We therefore also assume E[επi,tuj,t] = σεiuj

6= 0.267

10All appendices are available directly from the Journal’s website as supplementary materials. Thisincludes codes and the data used in the paper.

12

A SURE correction is implemented to account for all three cross-sector interdepen-268

dencies. In the ML case, stacking all sectors implies sectoral dynamics given by269

Y1

Y2

...

YJ

=

X1 0 · · · 0

0 X2 · · · 0

.... . . . . .

...

0 · · · 0 XJ

Λ1

Λ2

...

ΛJ

+

v1

v2

...

vJ

, (18)270

where Yj =

πj

sj

, Xj =

πj,−1 hj sj hj sj,−1 0 0

0 0 0 hj sj,−1 hj sj,−2

, vj =

επj

uj

,271

πj = (πj,t), πj,−1 = (πj,t−1), sj = (sj,t), sj,−k = (sj,t−k), and Λj = (δ1j, φ1j, φ2j, ρ1j, ρ2j)′.272

The stacked disturbances vj have a covariance matrix Ω which standard maximum like-273

lihood techniques can account for.274

The SURE correction requires the estimation of a large-dimensional covariance ma-275

trix, which may affect the finite-sample properties of the estimators. For robustness,276

an alternative estimator proposed by Pesaran (2006) is implemented, that introduces a277

correction technique to account for unobserved common factors potentially correlated278

with sector-specific regressors. The sector-specific estimations are filtered by means of279

cross-section averages, which allow for unobserved common factors. The approach is280

particularly appealing because of its simplicity. It merely requires the addition of an281

auxiliary regressor, given by the cross-sectional average of the regressors, which suffices282

to filter the common correlated effect (CCE) out. An appendix describes the implemen-283

tation of the CCE estimator for our purposes. The results presented later correspond to284

the CCE estimator, and also to a conventional Generalized Method of Moments (GMM)285

estimator implemented on sectoral data.286

Neither SURE, nor CCE are quite the same as constructing a model of linkages287

between sectors, either via an explicit input-output structure, or with general equilibrium288

effects working for instance via integrated factor markets at country level. Recent papers289

by Carvalho (2006), Sheedy (2007) or Justiniano et al. (2006) have chosen to account290

13

for heterogeneity in theoretical models, and so have made progress down that route.291

However, their empirical implications are not always tractable. In contrast, the SURE292

approach is sufficiently general that our estimates of sectoral Phillips curves are in fact293

consistent with a broad range of theoretical reasons for cross-sector interdependencies.294

2.4 Results295

Sector-specific estimates are first presented, correcting or not for common factors across296

sectors. The results implied by aggregated data follow.297

2.4.1 Industry Estimates298

Industry-level estimates of the New Keynesian Phillips curve are obtained on the basis299

of a ML approach. Marginal costs are at the industry level are assumed to follow an300

autoregressive process of order two. The resulting reduced form equation is estimated.301

Several results stand out.302

First, the measured dynamics of sectoral marginal costs are well characterized by303

autoregressive processes of order two.11 The fit is tight in all cases, with R2 above 0.80 in304

thirteen of the sixteen sectors. The lowest value occurs in “Energy”, with a value of 0.43.305

Second, Table 2 suggests inflation dynamics at the industry level are consistent with the306

New Keynesian framework. The results correspond to simple ML implemented on each307

sector individually. Estimates of φ1 or φ2 are significant in ten of the sixteen sectors,308

so that marginal costs affect significantly the pricing decisions of firms. The estimates309

also display substantial heterogeneity across sectors. The coefficients corresponding to310

the reduced form Phillips curve given in equation (15) confirm large differences in the311

extent of backward looking behavior, with values of λb ranging from zero to around a half.312

The heterogeneity carries through to sector-level estimates of the structural parameters.313

We obtain values for αj between zero and virtually one, with vastly different implied314

11An Appendix reports our measure of real marginal costs, along with the fitted values implied by theestimated autoregressive process. The results are also available in Imbs et al. (2008).

14

durations. They range from less than one quarter in Food, to around one quarter in315

Agriculture, Energy or Transportation, to more than two years in Cars. On the whole,316

duration is found to take high values in virtually all service industries - although the317

point estimates are not always significant or well defined.318

Fisher tests were implemented to investigate coefficient equality across sectors. On319

the basis of the industry-level estimates in Table 2, there is overwhelming rejection of320

the homogeneity assumption across all parameters δ, φi, and ρi. Unreported results321

summarize the empirical plausibility of purely forward looking Phillips curves in our 16322

sectors. The fit worsens sizeably. Most regressors, especially marginal costs, become323

insignificant in virtually all cases. And the model’s ability to predict observed inflation324

rates becomes mediocre at best.325

Figure 2 plots observed inflation for each industry against the path predicted by326

the estimated Phillips curve in that sector. The fit is poor for “Food Manufacturing”,327

“Equipment Goods”, and “Business Services”, but tight for the other thirteen industries,328

with R2 above 0.25. In fact, both series are virtually identical for eight of our sectors. For329

instance, R2 are above 0.75 in “Trade”, “Education and Health Services”, “Real Estate”,330

and “ Government”.331

A technical appendix reports the results corresponding to a GMM estimation of equa-332

tion (15), using lagged inflation, lagged marginal costs and lagged wage inflation as in-333

struments for future expected inflation. Similar heterogeneity is uncovered: the backward334

looking coefficient ranges from zero in “Food” or “Energy” to 0.5 in “Finance” or “Real335

Estate”. The implied durations are around 1.3 quarters for “Agriculture” and “Food”,336

slightly higher in manufactures, with a point estimate of 4.6 quarters in “Car”, and337

even higher in services, with durations around 3 quarters in “Education and Health”,338

“Business” and “Real Estate”.339

The results in Table 2 correspond to sector-by-sector estimations of a Phillips curve.340

The approach ignores the possibility that sectoral prices may be related in the macroe-341

conomy. But there is no reason to expect the same from actual sectoral data. Tables342

15

3 presents results augmented with a SURE correction. The approach is general enough343

to account for common macroeconomic shocks, cross-sector linkages or indeed anything344

that would engender influences on sectoral prices or marginal costs that are contempo-345

raneously correlated across industries. Our conclusions are largely unchanged: marginal346

costs are significant in half of the industries, and they are persistent. The proportion of347

backward looking behavior ranges between zero and a half, with low values in “Food” or348

“Energy”, and high values in “Agriculture” or “Education and Health”. Relative to Table349

2, the Fisher test rejects homogeneity at even higher confidence levels. Like in Table 2,350

the implied durations are lowest for “Food” and “Agriculture”, higher in manufactures,351

and highest in services. The technical appendix reports the corresponding sectoral esti-352

mates implied by the CCE correction. Heterogeneity still prevails, with a similar ranking353

of sectors.12354

Table 4 offers a direct comparison of our sectoral estimates of the duration of nominal355

rigidities in France with the literature. The comparison draws on contributions by Gautier356

(2008), Vermeulen et al. (2007), Baudry et al. (2007, 2009) and Loupias and Ricart357

(2005). All these papers have made use of highly disaggregated French price data to358

identify the observed frequency of price changes, and infer the corresponding duration359

of nominal rigidities. Several caveats are in order. First, the mapping with our sectoral360

classification is far from perfect. In particular, there is little price information for services.361

For most service sectors, therefore, only the durations based on (our) Phillips curve362

estimates are available. Second, we use Producer Prices, whereas most of the papers363

using French data focus on Consumer Prices, with the exception of Gautier (2008) and364

Vermeulen et al. (2007). Third, the time periods are different. Our data go back to 1978365

and stop in 2005. Gautier (2008) uses data from 1994 to 2005, and Baudry et al. (2007)366

from 1994 to 2003. These limitations notwithstanding, Table 4 suggests a reasonably close367

mapping between our structural estimates and the micro-evidence gathered for France in368

12The CCE and SURE are only implemented on the ML version of the model. GMM requires an in-strument set, which is potentially different across sectors. This renders the SURE approach unpalatable.As for the CCE correction, nothing is known about its asymptotic properties when implemented on aGMM estimator.

16

the literature. For instance, in manufacturing longest durations are estimated for cars and369

equipment goods, as individual price data imply. Duration levels are virtually identical for370

food manufacturing, transportation, and education and health services. Given the vast371

differences involved in obtaining these estimates, such relative concordance is remarkable.372

Panel A of Table 5 reports the characteristics of a representative average sector as373

implied by our data. The reduced form estimates of δ, φi, and ρi from Tables 2 and 3374

are averaged to infer the corresponding structural parameters. A simple average of sector375

specific estimates is in fact exactly equivalent to what the Mean Group heterogeneous376

estimator introduced by Pesaran and Smith (1995) implies. Table 5 suggests the repre-377

sentative sector of our French data displays nominal rigidities that last around 2 quarters,378

consistent with most microeconomic studies in the literature. The average proportion of379

backward looking firms ranges between 25 and 30 percent.380

2.4.2 Aggregate Estimates381

Our data are aggregated using GDP weights to obtain series for aggregate inflation and382

marginal costs. We implement both a ML and a GMM estimator on the resulting data.383

The aggregate Phillips curve can be written as384

πt = λb πt−1 + λf Etπt+1 + θ hsavgt + επ

t , (19)385

where h is a corrective term accounting for staggered pricing decisions, given by an average386

of hj across sectors. Following the standard in this literature, equation (19) is estimated387

using a GMM estimator, with expected inflation instrumented by lagged inflation, lagged388

marginal costs, and lagged wage inflation.389

Assuming aggregate marginal costs continue to follow an autoregressive process of390

order two, with coefficients ρ1 and ρ2, equation (19) implies the reduced form391

πt = δ1πt−1 + φ1hsavgt + φ2hsavg

t−1 + επt , (20)392

17

where393

φ1 =θ

∆δ2λf, φ2 = φ1

ρ2

δ2

,394

∆ = 1− ρ1

δ2

− ρ2

δ22

,395

δ1 =1−

√1− 4λfλb

2λfand δ2 =

1 +√

1− 4λfλb

2λf.396

Equation (20) is estimated using ML techniques. Panel B of Table 5 reports our results.397

The proportion of backward looking firms, λb, is 0.35 with GMM, and 0.40 with ML.398

The coefficient θ on aggregate marginal costs, in turn, is weakly significant, 0.08 with399

GMM and 0.04 with ML. These values stand in stark contrast with the estimates obtained400

at the sectoral level. Panel A points to an average close to 0.30, four to eight times larger.401

The duration of nominal rigidities implied by aggregate French data is above three402

quarters, and not significantly different from one year. This is close to the estimates ob-403

tained by Benigno and Lopez-Salido (2006) who estimate a duration of nominal rigidities404

across European countries. In their Table 1 (page 596), they present estimates for France405

close to one year in two of three estimates - rising to 11 quarters when more instruments406

are included in the GMM estimation. For the Euro area as a whole, Galı et al. (2001)407

report a duration estimate of 4.7 quarters in their Table 2. Our estimate of the duration408

of nominal rigidities in aggregate French data is therefore slightly below conventional409

results in the literature.410

Nominal rigidities in the representative sector are close to two quarters, which is con-411

sistent with estimates based on disaggregated data. The very same data, when aggregated412

and constrained to fit a conventional New Keynesian Phillips curve, imply significantly413

longer nominal rigidities. This suggests heterogeneity in the pricing behavior of firms is414

a key driving force behind the interpretation of aggregate inflation dynamics.415

18

3 The Aggregate Phillips Curve416

This Section investigates the policy relevance of heterogeneity. A multi-sector general417

equilibrium model of the macroeconomy is calibrated and simulated using our (struc-418

tural) sectoral estimates. Conventional policy analysis is then performed on the resulting419

synthetic aggregate inflation measure. The Section closes with implications for stabiliza-420

tion policy.421

3.1 Simulation and Calibration422

Our purpose is to simulate a synthetic series for aggregate inflation, implied by a multi-423

sector model calibrated with our sectoral results. The sector-level Phillips curves are424

given by equations (2)-(6), which are calibrated directly using the structural estimates of425

αj and ωj from Section 2. Rather than imposing specific dynamics for sectoral marginal426

costs sj,t, and use the corresponding reduced form autoregressive coefficients obtained427

earlier, we go the structural route and introduce aggregate production, Yt. Preferences428

are given by429

U (Ct,Ht, Hij,t) =

[1

1− σ(Ct − γHt)

1−σ − 1

1 + ϕ

n∑j=1

∫ 1

0

(Hij,t)1+ϕ di

]exp (εy

t ) . (21)430

Preferences display external habit formation, with the habit stock Ht equal to the level431

of aggregate consumption in t − 1. σ > 0, ϕ > 0 and 0 ≤ γ < 1 have conventional432

interpretations. εyt is a demand shock, which follows an autoregressive process of order433

one434

εyt = ρyεy

t−1 + νyt , (22)435

with | ρy |< 1 and νyt is white noise with variance σ2

y . Following Carvalho (2006),436

consumers allocate their labor across all firms and sectors.437

19

With goods market clearing, the intratemporal labor-leisure choice implies438

Wij,t

Pt

= Hϕij,t (Ct − γCt−1)

σ , (23)439

where Pt denotes the aggregate price level. Using the definition of real wages and the440

sector production function, Woodford (2003) obtains an expression for (log-linearized)441

average real marginal costs savgj,t ,442

savgj,t =

(ϕ + aj

1− aj+

σ

1− γ

)y∗t −

γσ

1− γy∗t−1 −

1 + ϕ

1− ajzj,t, (24)443

where hatted variables are computed in deviation from the steady state, y∗t denotes444

yt + η (pt − pj,t), yt is the output gap defined in equation (27), and zj,t is a sectoral445

productivity shock, which follows an autoregressive process of order one given by446

zj,t = ρzj zj,t−1 + νz

j,t (25)447

with | ρzj |< 1 and νz

j,t is white noise with variance σ2j,z. Since our purpose is now448

a calibration, rather than an estimation, we put structure on the shocks that perturb449

the multi-sector model. In particular, under our assumptions on the production func-450

tion, sectoral productivity shocks are directly observable. Their persistence and variance451

properties can readily be calibrated from our sectoral data.452

On the basis of the system formed by equations (6), (10)-(13) and (24)-(25), sectoral453

inflation can be simulated as a function of relative sectoral prices and the aggregate454

output gap.13 The model is closed in the most conventional manner possible, following455

Woodford (2003). The intertemporal Euler equation is456

1

βEt

(1 + πt+1

1 + it

)= Et

((Ct+1 − γCt)

−σ exp(εy

t+1

)(Ct − γCt−1)

−σ exp (εyt )

). (26)457

13We also experimented with an aggregative model of sectoral inflation simulated on the basis of theAR(2) estimates for sj,t obtained in the empirical section of the paper. Even though this approach isnot structural, the end results were virtually identical.

20

In log-linearized form, and combined with goods market clearing, this can be rewritten458

into a standard hybrid IS curve459

yt =γ

1 + γyt−1 +

1

1 + γEtyt+1 −

1− γ

(1 + γ) σ(ıt − Etπt+1) + κεy

t , (27)460

with κ = (1−ρy)(1−γ)(1+γ)σ

, and it denotes the nominal interest rate. As usual, the demand side461

of the economy pins down the dynamics of the output gap.462

Finally, monetary policy follows an augmented Taylor rule with interest rate smooth-463

ing, given by464

ıt = ρıt−1 + (1− ρ) (ϕππt + ϕyyt) + εit, (28)465

where εit is a monetary policy shock, which follows an autoregressive process of order one466

εit = ρiεi

t−1 + νit , (29)467

with | ρi |< 1 and νit is white noise with variance σ2

i . Monetary policy pins down the468

dynamics of the nominal interest rate.469

Section 2 presented an aggregate Phillips curve estimated on the basis of GDP-470

weighted aggregates of sectoral inflation rates and marginal costs. This weighting scheme471

is reproduced in the model. Each sector is calibrated using the estimates for αj and ωj472

given in in Table 3, i.e. by the SURE approach. Aggregation in the model is similar to the473

treatment of the data: sectoral inflation rates are simply added up using GDP weights.474

We can do that because the model is calibrated on the basis of sectoral estimates arising475

from the SURE approach.476

The system formed by equations (6), (10)-(13), (22), (24)-(25) and (27)-(29) is sim-477

ulated. Sectoral Solow residuals are calibrated following Burnside et al. (1996). The478

correcting terms hj and aj, along with the GDP weights used in aggregation are identical479

to Section 2, as are the elasticity of substitution η (set at 11) and the subjective discount480

21

factor β = 0.99. The remaining parameters are aggregate and are chosen on the basis of481

existing estimations of an aggregate New Keynesian model for France.14482

The model is simulated 2, 000 times. Sector inflation and marginal costs are collected483

at each repetition. Each simulation gives rise to aggregate series for inflation and marginal484

costs, which can then be used to estimate an aggregate Phillips curve. Note this can be485

performed using either a ML approach or a GMM estimator. The mean reduced form486

estimates of the Phillips curve, averaged across 2, 000 repetitions, are then reported, along487

with the corresponding structural parameters. Using medians instead does not affect our488

conclusions.489

3.2 Results and Implications for Stabilization Policy490

Panel C of Table 5 reports Phillips curve estimates implied by simulated aggregate series.491

Results are presented corresponding to the usual estimations implemented on aggregate492

data. First, the ML approach, which rests on an assumed data generating process for493

marginal costs. We verify the dynamics of our synthetic series for marginal costs do494

indeed follow an autoregressive process of order two, as they do in the raw data. Second,495

GMM is implemented.496

The aggregate New Keynesian Phillips curves obtained in Table 5 are standard. The497

proportion of backward looking firms is estimated to range between 30 and 40 percent.498

The coefficients on marginal cost are relatively small in magnitude, and correspond to a499

duration for nominal rigidities between 3 and 4 quarters. In addition, the reduced form500

estimates of the process followed by aggregate marginal costs correspond to an AR(2).501

Most importantly, the estimates in the third panel of Table 5 are strikingly close to502

what is implied by aggregate data. Interestingly, both ML and GMM estimators imply503

similar coefficients whether they are implemented on the synthetic series or on actual504

data, with no significant differences in estimates across reduced form and quasi-reduced505

14In particular, following Jondeau and Sahuc (2008) the parameter values are: σ = 2, γ = 0.5, φ = 0.6,ρi = 0.603, σ2

i = 0.0052, ρy = 0.2, σ2y = 0.12, ρ = 0.90, ϕπ = 1.5, and ϕy = 0.5.

22

form coefficients. The estimate of λb equals 0.415 when a ML approach is imposed on506

simulated data, as against 0.402 when it is imposed on the raw data. The duration507

implied by ML on the simulated data is 3.29 quarters, while it is 3.43 quarters in the508

aggregate data. The durations implied by GMM are slightly smaller, 2.73 on simulated509

inflation, and 3.16 on the actual aggregate series.510

In other words, a simulated aggregation of sector-specific price dynamics reproduces511

the dynamics implied by the aggregated data. And this happens even though sector-512

specific dynamics are consistent with microeconomic evidence, whereas aggregate dynam-513

ics are not. These results indicate that the aggregation of heterogeneous sectors plays a514

large part in explaining the difficulty in rationalizing aggregate inflation dynamics. Ag-515

gregate inflation implies rather long nominal rigidities, difficult to map with observable516

data. But that should not be puzzling: it is merely an artefact of heterogeneity across517

sectors.518

This establishes the econometric importance of sector-level heterogeneity. A natural519

next question is to evaluate the policy relevance of the discrepancy. In particular, we520

can compare the policy trade-offs implied by observed aggregate inflation dynamics, with521

what would happen in a multi-sector model, characterized by the heterogeneous dynamics522

at sector level.523

Following Taylor (2001), a policy frontier is computed solving the following program524

Minρ,ϕπ ,ϕy

λV (πt) + (1− λ) V (yt) , (30)525

subject to the constraint that V (∆it) ≤ κ, ∆it = it − it−1. The operator V (.) denotes a526

variance, and λ ∈ [0, 1] captures the relative weight of inflation and output volatilities in527

the policymaker’s objective function.15 The program is solved using the general equilib-528

rium described by equations (19), (22) and (27)-(29), along with the aggregate analogue529

15Alternatively, the computation was performed with an objective function where V (∆it) entereddirectly. Our conclusions remained unchanged.

23

of equation (24), given by530

savgt =

(ϕ + a

1− a+

σ

1− γ

)yt −

γσ

1− γyt−1 −

1 + ϕ

1− azt531

where zt is an aggregate productivity shock, calibrated from aggregate data.532

The sole difference between the two models pertains to the modeling of aggregate533

inflation. In one case, it is given by a standard Phillips curve, calibrated to aggregate534

data as in Section 3.1. In the other, it is implied by the sectoral dynamics aggregated535

synthetically in our calibrated multi-sector model.16 Importantly, the New Keynesian536

Phillips curve functional form is not imposed on aggregate inflation; rather, its moments537

are collected from our multi-sector simulation.538

For each value of λ, the minimization identifies the optimal values for ρ, ϕπ and539

ϕy in the policy rule, and the implied volatilities of V (πt) and V (yt) given that the540

volatility in interest rates must stay below κ. Then letting λ vary traces a frontier in541

the [V (πt), V (yt)] space that captures optimal policy in the precise -yet limited- sense542

of the minimal volatility afforded by the considered type of Taylor rule. In other words,543

the approach pinpoints the lowest possible values for the volatilities of inflation and544

output that can be reached for all λ given an upper bound to the volatility of the policy545

instrument. In practice, the starting value is λ = 0, and it is changed it by increments of546

0.005. κ is set at 0.01.547

Within this setup, the following question is asked. Given the calibration choices in548

Section 3.1, how much do minimal volatilities change when we use estimates for λb, λf ,549

and θ that correspond to aggregate data, or when we feed simulated aggregate inflation as550

implied by our multi-sector model? The two policy frontiers are reported in Figure 3. The551

estimates corresponding to simulated inflation imply lower values for V (yt) at all values552

of inflation volatility. For all values of λ, the policy frontiers implied by heterogeneous553

16Each sectoral inflation process is subjected to an inflation shock measured as a residual. The residualbetween fitted sectoral inflation (as implied by our sectoral Phillips curves) and it observed counterpart iscomputed. The volatility of the residual is used to calibrate (the volatility of) sectoral inflation shocks,επj,t. The one sector model, in turn, is calibrated using the volatility in residual aggregate inflation,

defined as the difference between actual and predicted aggregate inflation.

24

sectors lie substantially below the one implied by aggregate estimates of the Phillips554

curve. For given values of the volatility in inflation and the nominal interest rate, policy555

can deliver a volatility of the output gap that is up to twice smaller than what is implied556

by aggregate estimates. These are substantial differences. Heterogeneity does matter in557

a policy sense.558

4 Conclusion559

Thanks to detailed French data observed at the sector level, it is possible to estimate560

sector-level Phillips curves. The estimates are obtained using conventional econometric561

approaches, and allowing for the possibility that prices and marginal costs are correlated562

across industries. On average at the sector level, prices respond significantly to marginal563

costs and are forward looking. The implied duration of nominal rigidities is around two564

quarters. There is considerable heterogeneity around these averages, which maps well565

with estimates obtained directly from microeconomic French price data.566

Once aggregated, our data imply inflation dynamics and New Keynesian Phillips567

curve estimates that are in agreement with the conventional macroeconomic literature.568

Heterogeneity does therefore explain the discrepancy between micro- and macro-studies of569

price setting behavior. The difficulty in rationalizing the dynamics of aggregate inflation570

can simply originate in the aggregation of heterogeneous sectoral dynamics.571

This establishes the econometric importance of heterogeneity in French data. Aggre-572

gation also matters in a policy sense. A standard calibration of a monetary economy is573

implemented. It shows sectoral estimates imply policies that can deliver volatilities in574

the output gap and in inflation that are half as big as what is implied by aggregate data.575

Our results are based on French data, and so it is difficult to ascertain their generality.576

To our knowledge, similar datasets do not exist elsewhere, that include quarterly measures577

of prices and real marginal costs using the same sectoral definition. Given the current578

interest in disaggregated price dynamics, it is our hope the present exercise provides but579

25

a first step on the way. Whether our quantitative results continue to be true elsewhere580

is an open question.581

26

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30

Table 1: Summary statistics

Industry Weights π s corr(πt−1, πt) corr(st−1, st) corr(πt, st)

Aggregate 100.00 3.996 −0.095 0.921 0.984 0.887Agriculture 2.92 1.255 −0.276 0.782 0.977 −0.247Food Mfg 2.33 3.477 −0.102 −0.075 0.778 −0.320Cons. Goods 3.02 2.639 −0.087 0.620 0.939 0.367Car 0.96 3.293 −3.616 0.291 0.981 0.198Equip. Goods 2.96 0.237 −0.128 0.041 0.915 −0.412Inter. Goods 5.72 2.788 −1.007 0.725 0.988 0.600Energy 2.18 5.393 −0.934 −0.281 0.683 −0.449Construction 6.67 4.889 −0.327 0.511 0.977 0.389Trade 10.57 4.241 −0.253 0.760 0.974 0.662Transportation 3.76 2.935 −0.112 0.027 0.777 0.034Finance 5.01 3.366 −0.410 0.600 0.971 0.143Real Estate 11.82 5.023 −0.272 0.864 0.983 −0.683Business Serv. 14.19 3.635 −0.021 −0.290 0.946 −0.362Personal Serv. 5.75 5.486 0.062 0.758 0.961 −0.707Educ. & Health 13.94 5.542 −0.261 0.933 0.986 0.848Govt. 8.21 4.419 −0.050 0.954 0.917 0.484

Note: Descriptive statistics (average inflation, average growth in real marginal costs,serial correlations, and contemporaneous cross-correlation) are reported at both industryand aggregate levels using quarterly French data from 1978:1 to 2005:3. Inflation rate iscomputed as quarter-on-quarter growth rate of the value-added deflator. Real marginalcost is defined as the (logarithm) deviation of the sector share of labor income in valueadded from its sample mean.

31

Table

2:

Sect

ora

lP

hillips

Curv

es

Indu

stri

esA

gr.

Food

Con

s.C

arE

quip

.In

term

.E

nerg

yC

onst

.Tra

deTra

nsp.

Fin

.R

.E

stat

eB

usin

essP

ers.

Serv

.E

duc.

&H

ealt

hG

ovt

Red

uced

Form

-E

quat

ion

(17)

δ 10.

776∗

∗∗(0

.061)

0.51

8∗∗∗

(0.0

84)

0.61

1∗∗∗

(0.0

73)

0.29

6∗∗∗

(0.0

77)

0.14

8∗(0

.079)

0.50

1∗∗∗

(0.0

65)

0.08

1(0

.114)

0.50

4∗∗∗

(0.0

70)

0.53

1∗∗∗

(0.0

65)

0.05

0(0

.084)

0.57

6∗∗∗

(0.0

66)

0.84

5∗∗∗

(0.0

57)

0.00

1(0

.076)

0.77

1∗∗∗

(0.0

59)

0.71

8∗∗∗

(0.0

61)

0.93

0∗∗∗

(0.0

28)

φ1

14.6

32(1

0.6

4)

13.1

31∗∗

∗(3

.947)

1.50

2∗∗∗

(0.5

50)

0.22

9∗∗∗

(0.0

74)

0.00

1(0

.003)

0.76

6∗∗∗

(0.1

74)

21.2

01∗

(11.8

1)

1.96

3∗∗∗

(0.6

28)

2.29

9∗∗∗

(0.4

65)

5.45

7∗∗∗

(1.5

46)

3.39

1∗∗∗

(1.0

35)

0.00

6(0

.269)

0.00

1(0

.004)

0.00

1(0

.001)

0.69

5∗∗∗

(0.2

16)

0.03

9(0

.062)

φ2

−10

.75

(7.8

99)

−3.

481∗

∗∗(1

.094)

0.03

8(0

.127)

−0.

063∗

∗(0

.029)

0.00

1(0

.001)

−0.

134∗

∗(0

.064)

−1.

686

(2.1

72)

−0.

421∗

(0.2

26)

−0.

587∗

∗(0

.238)

0.47

8(0

.390)−

1.91

2∗∗∗

(0.6

18)

−0.

004

(0.1

86)

0.00

1(0

.001)

−0.

001

(0.0

02)

0.13

6∗∗

(0.0

69)

0.00

8(0

.013)

ρ1

1.70

9∗∗∗

(0.0

59)

0.91

6∗∗∗

(0.0

86)

0.91

4∗∗∗

(0.0

88)

1.24

9∗∗∗

(0.0

78)

0.58

4∗∗∗

(0.0

84)

1.15

5∗∗∗

(0.0

78)

0.70

8∗∗∗

(0.0

80)

1.19

4∗∗∗

(0.0

83)

1.21

9∗∗∗

(0.0

81)

0.70

4∗∗∗

(0.0

83)

1.52

5∗∗∗

(0.0

60)

1.66

1∗∗∗

(0.0

69)

0.86

6∗∗∗

(0.0

78)

1.12

8∗∗∗

(0.0

94)

0.76

7∗∗∗

(0.1

01)

0.73

3∗∗∗

(0.0

96)

ρ2

−0.

758∗

∗∗(0

.057)

−0.

270∗

∗∗(0

.043)

0.02

6(0

.087)−

0.27

7∗∗∗

(0.0

77)

0.01

0(0

.078)−

0.17

7∗∗∗

(0.0

76)

−0.

080

(0.0

69)−

0.21

7∗∗∗

(0.0

82)

−0.

255∗

∗∗(0

.079)

0.08

9(0

.077)−

0.57

3∗∗∗

(0.0

55)

−0.

698∗

∗∗(0

.068)

0.02

1(0

.071)

−0.

201∗

∗(0

.093)

0.19

9∗∗

(0.0

99)

0.20

7∗∗

(0.0

96)

Red

uced

Form

-E

quat

ion

(15)

λb

0.44

2∗∗∗

(0.0

21)

0.34

3∗∗∗

(0.0

38)

0.38

2∗∗∗

(0.0

29)

0.22

9∗∗∗

(0.0

46)

0.12

9∗∗

(0.0

61)

0.33

5∗∗∗

(0.0

29)

0.07

5(0

.098)

0.33

6∗∗∗

(0.0

32)

0.34

9∗∗∗

(0.0

28)

0.04

8(0

.076)

0.36

8∗∗∗

(0.0

27)

0.46

1∗∗∗

(0.0

18)

0.00

1(0

.076)

0.43

7∗∗∗

(0.0

19)

0.42

1∗∗∗

(0.0

22)

0.48

8∗∗∗

(0.0

10)

λf

0.55

4∗∗∗

(0.0

21)

0.65

0∗∗∗

(0.0

38)

0.61

5∗∗∗

(0.0

29)

0.76

5∗∗∗

(0.0

46)

0.86

3∗∗∗

(0.0

61)

0.66

1∗∗∗

(0.0

29)

0.91

5∗∗∗

(0.0

98)

0.65

9∗∗∗

(0.0

32)

0.64

7∗∗∗

(0.0

28)

0.94

3∗∗∗

(0.0

76)

0.62

8∗∗∗

(0.0

28)

0.53

9∗∗∗

(0.0

18)

0.98

9(0

.076)

0.56

2∗∗∗

(0.0

19)

0.57

8∗∗∗

(0.0

22)

0.51

1∗∗∗

(0.0

10)

θ0.

469

(0.4

12)

3.14

5∗∗∗

(1.3

82)

0.07

1(0

.049)

0.00

6(0

.005)

0.00

1(0

.004)

0.01

7∗(0

.010)

7.41

7(5

.239)

0.04

3(0

.036)

0.06

9∗(0

.040)

1.12

4∗(0

.602)

0.11

6∗(0

.069)

0.00

1(0

.006)

0.00

1(0

.001)

0.00

1(0

.001)

0.02

1∗∗∗

(0.0

09)

0.00

2(0

.003)

Stru

ctur

alE

stim

ates

ω0.

281∗

∗∗(0

.094)

0.07

5∗∗∗

(0.0

22)

0.40

1∗∗∗

(0.0

70)

0.26

8∗∗∗

(0.0

46)

0.14

8∗(0

.089)

0.41

1∗∗∗

(0.0

60)

0.00

8(0

.009)

0.36

9∗∗∗

(0.0

67)

0.35

8∗∗∗

(0.0

57)

0.01

8(0

.029)

0.34

5∗∗∗

(0.0

51)

0.81

9(0

.678)

0.00

1(0

.001)

0.77

0∗∗∗

(0.1

59)

0.54

7∗∗∗

(0.0

58)

0.82

3∗∗∗

(0.0

82)

α0.

357∗

∗∗(0

.131)

0.14

2∗∗∗

(0.0

47)

0.65

2∗∗∗

(0.0

86)

0.90

4∗∗∗

(0.0

39)

0.99

9∗∗∗

(0.2

81)

0.82

0∗∗∗

(0.0

49)

0.10

0∗(0

.061)

0.73

0∗∗∗

(0.0

89)

0.67

2∗∗∗

(0.0

74)

0.35

2∗∗∗

(0.0

61)

0.59

6∗∗∗

(0.0

85)

0.96

8(0

.843)

0.99

9∗∗∗

(0.2

66)

0.99

9∗∗∗

(0.1

98)

0.75

7∗∗∗

(0.0

35)

0.87

2∗∗∗

(0.0

74)

Dur

atio

n1.

554∗

∗∗(0

.316)

0.16

6∗∗∗

(0.0

65)

2.87

1∗∗∗

(0.7

05)

10.4

29∗∗

(4.2

17)

-5.

557∗

∗∗(1

.523)

1.11

1∗∗∗

(0.0

78)

3.70

9∗∗∗

(1.2

30)

3.04

9∗∗∗

(0.6

83)

1.54

2∗∗∗

(0.2

17)

2.47

2∗∗∗

(0.5

19)

31.2

1(8

2.1

2)

−−

4.12

2∗∗∗

(0.5

90)

7.81

2∗(4

.503)

Not

e:St

anda

rdde

viat

ion

inpa

rent

hese

s.M

argi

nalc

osts

follo

wan

auto

regr

essi

vepr

oces

sof

orde

rtw

o.T

hees

tim

ates

are

obta

ined

usin

ga

Max

imum

Lik

elih

ood

proc

edur

e.T

hest

ruct

ural

esti

mat

esar

ein

ferr

edfr

omre

duce

dfo

rmco

effici

ents

usin

ga

Del

tam

etho

d.

32

Tab

le3:

Sec

tora

lP

hillips

Curv

esin

SU

RE

Indu

stri

esA

gr.

Food

Con

s.C

arE

quip

.In

term

.E

nerg

yC

onst

.Tra

deTra

nsp.

Fin

.R

.E

stat

eB

usin

essP

ers.

Serv

.E

duc.

&H

ealt

hG

ovt

Red

uced

Form

-E

quat

ion

(18)

δ 10.

693∗

∗∗(0

.063)

0.33

8∗∗∗

(0.0

91)

0.46

4∗∗∗

(0.0

40)

0.20

3∗∗∗

(0.0

74)

0.19

7∗∗∗

(0.0

72)

0.38

5∗∗∗

(0.0

61)

0.00

1(0

.068)

0.43

2∗∗∗

(0.0

69)

0.57

9∗∗∗

(0.0

67)

0.00

4(0

.079)

0.54

9∗∗∗

(0.0

62)

0.67

8∗∗∗

(0.0

65)

0.08

2(0

.073)

0.46

8∗∗∗

(0.0

79)

0.72

8∗∗∗

(0.0

51)

0.74

8∗∗∗

(0.0

52)

φ1

24.3

63(9

.639)

∗∗8.

406∗

∗∗(3

.087)

1.97

4∗∗

(0.7

60)

0.31

9∗∗

(0.1

26)

0.43

9(0

.347)

0.98

2∗∗

(0.3

62)

0.00

1(0

.072)

0.48

4(0

.726)

3.68

7∗∗∗

(0.8

10)

4.80

8∗(2

.673)

3.12

0∗∗

(1.2

79)

0.00

1(0

.056)

0.00

1(0

.021)

0.00

1(0

.011)

0.61

5(0

.367)

0.26

4∗∗

(0.1

04)

φ2

−15

.364

∗∗(6

.239)

−1.

618∗

(0.9

15)

−0.

200

(0.1

99)

−0.

074∗

(0.0

39)

0.03

0(0

.031)

−0.

085

(0.0

71)

−0.

001

(0.0

05)

−0.

129

(0.1

97)

−1.

236∗

∗∗(0

.388)

0.05

5(0

.289)

−1.

795∗

∗(0

.737)

−0.

001

(0.0

38)

−0.

001

(0.0

01)

−0.

001

(0.0

03)

−0.

227

(0.1

65)

-0.0

66(0

.045)

ρ1

1.57

0∗∗∗

(0.0

49)

0.91

1∗∗∗

(0.0

78)

0.96

9∗∗∗

(0.0

82)

1.11

5∗∗∗

(0.0

70)

0.82

7∗∗∗

(0.0

70)

1.00

5∗∗∗

(0.0

72)

0.97

9∗∗∗

(0.0

71)

1.23

4∗∗∗

(0.0

76)

1.20

6∗∗∗

(0.0

69)

0.62

9∗∗∗

(0.1

11)

1.51

8∗∗∗

(0.0

51)

1.62

2∗∗∗

(0.0

56)

0.98

4∗∗∗

(0.0

73)

1.10

6∗∗∗

(0.0

93)

1.30

7∗∗∗

(0.0

98)

1.22

7∗∗∗

(0.0

93)

ρ2

−0.

648∗

∗∗(0

.048)

−0.

195∗

∗∗(0

.059)

−0.

102

(0.0

82)−

0.23

3∗∗∗

(0.0

67)

0.06

9(0

.067)

−0.

088

(0.0

67)

−0.

065

(0.0

64)−

0.26

9∗∗∗

(0.0

73)

−0.

341∗

∗∗(0

.060)

0.01

2(0

.060)−

0.58

4∗∗∗

(0.0

43)

−0.

681∗

∗∗(0

.054)

−0.

045

(0.0

68)

−0.

240∗

∗(0

.091)

−0.

376∗

∗∗(0

.096)

−0.

255∗

∗(0

.101)

Red

uced

Form

-E

quat

ion

(15)

λb

0.41

4∗∗∗

(0.0

23)

0.25

4∗∗∗

(0.0

52)

0.31

8∗∗∗

(0.0

55)

0.16

9∗∗∗

(0.0

51)

0.16

5∗∗∗

(0.0

50)

0.27

9∗∗∗

(0.0

32)

0.00

1(0

.069)

0.30

3∗∗∗

(0.0

34)

0.36

9∗∗∗

(0.0

28)

0.00

3(0

.079)

0.35

6∗∗∗

(0.0

26)

0.40

6∗∗∗

(0.0

23)

0.07

6(0

.062)

0.32

0∗∗∗

(0.0

37)

0.42

4∗∗∗

(0.0

17)

0.43

0∗∗∗

(0.0

17)

λf

0.58

1∗∗∗

(0.0

23)

0.74

0∗∗∗

(0.0

51)

0.67

7∗∗∗

(0.0

39)

0.82

4∗∗∗

(0.0

50)

0.82

8∗∗∗

(0.0

49)

0.71

6∗∗∗

(0.0

31)

0.98

9∗∗∗

(0.0

67)

0.69

3∗∗∗

(0.0

33)

0.62

6∗∗∗

(0.0

27)

0.98

7∗∗∗

(0.0

78)

0.63

9∗∗∗

(0.0

26)

0.59

2∗∗∗

(0.0

24)

0.91

6∗∗∗

(0.0

61)

0.67

6∗∗∗

(0.0

36)

0.57

3∗∗∗

(0.0

17)

0.56

8∗∗∗

(0.0

17)

θ1.

249∗

∗(0

.620)

1.83

9∗(1

.013)

0.19

6∗(0

.058)

0.03

3∗(0

.018)

0.04

2(0

.045)

0.06

6∗(0

.038)

0.00

1(0

.007)

0.01

5(0

.029)

0.34

1∗∗

(0.1

32)

1.75

2(1

.410)

0.14

5(0

.082)∗

0.00

1(0

.002)

0.00

1(0

.001)

0.00

1(0

.001)

0.02

8(0

.022)

0.00

6(0

.006)

Stru

ctur

alE

stim

ates

ω0.

164∗

∗∗(0

.044)

0.07

6∗∗∗

(0.0

22)

0.25

4∗∗∗

(0.0

55)

0.16

4∗∗∗

(0.0

57)

0.15

5∗∗∗

(0.0

54)

0.27

2∗∗∗

(0.0

48)

0.00

1(0

.068)

0.36

2∗∗∗

(0.0

78)

0.25

6∗∗∗

(0.0

39)

0.00

1(0

.023)

0.31

5∗∗∗

(0.0

47)

0.67

7(0

.593)

0.08

2(0

.073)

0.46

8∗∗∗

(0.1

36)

0.53

4∗∗∗

(0.0

68)

0.63

9∗∗∗

(0.0

68)

α0.

232∗

∗∗(0

.067)

0.22

6∗∗∗

(0.0

83)

0.54

5∗∗∗

(0.0

89)

0.80

7∗∗∗

(0.0

50)

0.78

8∗∗∗

(0.1

04)

0.70

5∗∗∗

(0.0

65)

0.99

9∗(0

.567)

0.83

8∗∗∗

(0.1

42)

0.43

9∗∗∗

(0.0

62)

0.28

9∗∗

(0.1

22)

0.57

1∗∗∗

(0.0

94)

0.99

9(0

.887)

0.99

9∗∗∗

(0.1

71)

0.99

9∗∗∗

(0.2

40)

0.72

9∗∗∗

(0.0

80)

0.85

1∗∗∗

(0.0

68)

Dur

atio

n1.

302∗

∗∗(0

.113)

1.29

1∗∗∗

(0.1

39)

2.19

8∗∗∗

(0.4

33)

5.19

1∗∗

(1.3

56)

4.70

5∗∗

(2.2

93)

3.39

4∗∗∗

(0.7

52)

−6.

161

(5..373)

1.78

2∗∗∗

(0.1

96)

1.40

6∗∗∗

(0.2

41)

2.32

9∗∗∗

(0.5

10)

−−

−3.

689∗

∗∗(1

.094)

6.72

5∗∗

(3.0

93)

Not

e:St

anda

rdde

viat

ion

inpa

rent

hese

s.M

argi

nalc

osts

follo

wan

auto

regr

essi

vepr

oces

sof

orde

rtw

o.T

hees

tim

ates

are

obta

ined

usin

ga

Max

imum

Lik

elih

ood

proc

edur

eim

plem

ente

don

asy

stem

ofse

ctor

aleq

uati

ons

usin

gth

eSU

RE

proc

edur

e.T

hest

ruct

ural

esti

mat

esar

ein

ferr

edfr

omre

duce

dfo

rmco

effici

ents

usin

ga

Del

tam

etho

d.

33

Tab

le4:

Aco

mpar

ison

ofpri

cedura

tion

(in

quar

ters

)w

ith

other

Fre

nch

studie

s

Pro

duce

rpr

ices

∗C

onsu

mer

pric

es∗∗

Gau

tier

(200

8)Im

bset

al.

Bau

dry

etal

.(2

006,

2007

)A

gric

ultu

re-

1.30

1-

Man

ufac

turi

ngFo

odm

anuf

actu

ring

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Ric

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94-2

003.

34

Table 5: Single Equation Phillips Curves

Panel A Panel B Panel C

Representative Sector Aggregate Data Simulated AggregatesML ML / SURE ML GMM ML GMM

Reduced Formδ1 0.491 0.409 0.666*** 0.701***

(0.064) (0.024)φ1 4.076 3.091 1.514*** 1.561***

(0.424) (0.603)φ2 −1.148 −1.294 0.006 0.086

(0.146) (0.063)ρ1 1.082 1.138 0.969*** 0.917***

(0.098) (0.025)ρ2 −0.185 −0.253 0.004 0.056***

(0.099) (0.009)

Quasi Reduced Formλb 0.331 0.292 0.402*** 0.351*** 0.415 0.299***

(0.024) (0.064) (0.031)λf 0.664 0.703 0.595*** 0.645*** 0.582 0.697***

(0.024) (0.065) (0.038)θ 0.313 0.271 0.039* 0.080* 0.041 0.110***

(0.022) (0.042) (0.034)

Structural Estimatesω 0.231 0.209 0.475*** 0.368*** 0.491 0.270

(0.064) (0.037)α 0.469 0.508 0.708*** 0.684*** 0.695 0.635

(0.059) (0.097)Duration 1.882 2.031 3.430*** 3.165*** 3.289 2.732

(0.690) (0.094)

Note: ”Representative Sector” corresponds to the simple average of the re-duced form parameters δ1, φ1, φ2, ρ1 and ρ2 corresponding to Tables 2 and 3.The parameters from equation (15) and the structural estimates are inferredon the basis of these averages. ML-SURE uses the individual estimates fromTable 3. ”Aggregate Data” reports ML and GMM estimates of the PhillipsCurve on the basis of aggregated data. GMM makes use of lagged aggregateinflation, lagged marginal costs and lagged wage inflation as instruments forexpected inflation. ”Simulated Aggregates” reports Phillips curve estimatesobtained from the simulation of a multi-sector model. Mean absolute devia-tions are reported between brackets. GMM uses the individual estimates fromAppendix 4.

35

Figure 1: Aggregate Inflation and Marginal Costs (unfiltered)

1980 1985 1990 1995 2000 2005-6

-4

-2

0

2

4

6

8

10

12

Inflation a

nd r

eal m

arg

inal costs

Note: The plain line denotes inflation and the dotted line the observed marginal cost.

36

Figure 2: Industry Phillips Curves

1980 1985 1990 1995 2000 2005

-20

-10

0

10

20

Agriculture

Ob

se

rve

d a

nd

fitte

d in

fla

tio

n

1980 1985 1990 1995 2000 2005-30

-20

-10

0

10

20

Food manufacturing

Ob

se

rve

d a

nd

fitte

d in

fla

tio

n

1980 1985 1990 1995 2000 2005

-10

0

10

Consumption goods

Ob

se

rve

d a

nd

fitte

d in

fla

tio

n

1980 1985 1990 1995 2000 2005

-40

-20

0

20

Car industry

Ob

se

rve

d a

nd

fitte

d in

fla

tio

n

1980 1985 1990 1995 2000 2005

-40

-30

-20

-10

0

10

Equipment goods

Ob

se

rve

d a

nd

fitte

d in

fla

tio

n

1980 1985 1990 1995 2000 2005

-10

0

10

20

Intermediary goods

Ob

se

rve

d a

nd

fitte

d in

fla

tio

n

1980 1985 1990 1995 2000 2005

-100

-50

0

50

100

Energy

Ob

se

rve

d a

nd

fitte

d in

fla

tio

n

1980 1985 1990 1995 2000 2005

-10

-5

0

5

10

15

Construction

Ob

se

rve

d a

nd

fitte

d in

fla

tio

n

Note: The plain line denotes observed inflation and the dotted line is fitted inflation.

37

Figure 2 (continued): Industry Phillips Curves

1980 1985 1990 1995 2000 2005

-5

0

5

10

15

Trade

Ob

se

rve

d a

nd

fitte

d in

fla

tio

n

1980 1985 1990 1995 2000 2005

-10

0

10

20

Transportation

Ob

se

rve

d a

nd

fitte

d in

fla

tio

n

1980 1985 1990 1995 2000 2005

-20

-10

0

10

20

Financial activities

Ob

se

rve

d a

nd

fitte

d in

fla

tio

n

1980 1985 1990 1995 2000 2005

-5

0

5

10

Real estate

Ob

se

rve

d a

nd

fitte

d in

fla

tio

n

1980 1985 1990 1995 2000 2005

-20

-10

0

10

20

30

Business services

Ob

se

rve

d a

nd

fitte

d in

fla

tio

n

1980 1985 1990 1995 2000 2005

-5

0

5

10

Personal services

Ob

se

rve

d a

nd

fitte

d in

fla

tio

n

1980 1985 1990 1995 2000 2005

-5

0

5

10

Education and health services

Ob

se

rve

d a

nd

fitte

d in

fla

tio

n

1980 1985 1990 1995 2000 2005

-5

0

5

Government

Ob

se

rve

d a

nd

fitte

d in

fla

tio

n

Note: The plain line denotes observed inflation and the dotted line is fitted inflation.

38

Figure 3: Policy Frontiers

1 1.5 2 2.5 3 3.50

1

2

3

4

5

6

Inflation variability (σ %)

Outp

ut variability (

σ %

)

Note: The plain line denotes the policy frontier implied by the aggregate model. Thedotted line is the policy frontier implied by the multi-sector model.

39