Rational Bias in Inflation Expectations

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1 Rational Bias in Inflation Expetations Robert G. Murphy * Boston College Adam Rohde Charles River Assoiates August 2014 Revised Deember 2014 Abstrat This paper argues that individuals may rationally weight prie inreases for food and energy produts differently from their expenditure shares when forming expetations about prie inflation. We develop a simple dynami model of the eonomy with gradual prie adjustment in the manufaturing (or ore ) setor and flexible pries in the food and energy setors. Serial orrelation of supply shoks to the food and energy setors allows individuals to gain an understanding about future shoks, possibly making it optimal for individuals to plae more weight on the movement of pries in these setors, as past movements of these pries may help predit future inflation. In partiular, if food and energy prie inflation exhibits a suffiient degree of persistene and wage adjustment is not too sluggish, we show that it is rational to put more weight on inflation in these setors than their expenditure shares in the Consumer Prie Index would warrant. We test the predition of the model using data on expeted inflation from the Federal Reserve Bank of Philadelphia s Survey of Professional Foreasters. Our results show that the weights implied by the model for onstruting expetations of inflation differ from the expenditure shares of food and energy pries in the Consumer Prie Index for the United States. We find that food prie inflation is weighted more heavily and energy prie inflation is weighted less heavily. But importantly, we annot rejet the hypothesis that these weights reflet rational behavior in forming expetations about inflation. Our analysis validates onerns sometimes raised by poliymakers as to whether expetations might not be well anhored with respet to some ommodity prie shoks. As a onsequene, poliy may need to be alibrated arefully to prevent suh shoks from beoming embedded in expeted inflation. JEL Classifiation: E30, E31, E52, E58 Keywords: Inflation Expetations, Core Inflation, Food and Energy Pries, Anhored Expetations * Paper prepared for presentation at Amerian Eonomi Assoiation Meetings in Boston, MA January 3-5, Corresponding author: Robert G. Murphy, Department of Eonomis, Boston College, Chestnut Hill, MA 02467, murphyro@b.edu. The views expressed herein are the views and opinions of the authors and do not reflet or represent the views of Boston College, Charles River Assoiates, or any of the organizations with whih the authors are affiliated.

2 1. Introdution Expetations about prie inflation play a entral role in modern maroeonomi analysis. They are important for understanding how households and firms make saving, spending, and investing deisions, and are a key input into negotiations for labor ontrats and the priing of finanial instruments. Central banks trak them for omparison with internal foreasts and targets for inflation. The ability of monetary authorities to ahieve prie stability depends on an aurate understanding of inflation expetations. A onern sometimes raised by poliymakers is whether inflation in highly visible produts suh as food and energy might overly influene the publi s pereption of inflation. For example, disussion at the Federal Open Market Committee meeting in June 2008 learly illustrates this onern: Partiipants had beome more onerned about upside risks to the inflation outlook--inluding the possibility that persistent advanes in energy and food pries ould spur inreases in long-run inflation expetations. Some noted that the inrease was greatest for short-term survey measures of households' inflation expetations, whih may be influened disproportionately by onsumers' pereptions of hanges in the pries of food and gasoline 1 This onern is not a reent one, having featured prominently during poliy disussions about supply shoks during the 1970s. 2 1 Federal Open Market Committee, Minutes of the Meeting of June 24-25, 2008, pp See Van Duyne (1982) for several examples.

3 2 Our paper explores whether pries of items that individuals frequently purhase and that often are quite volatile, suh as food and energy produts, play a larger role in the formation of inflation expetations than their expenditure shares indiate. Similar to Van Duyne (1982), we show that it may be optimal for individuals to assign relative weights to prie inreases in the food and energy setors that are larger than those setors shares in onsumer expenditure. We develop a simple three-setor dynami aggregate demand-aggregate supply model of the eonomy with gradual prie adjustment in the manufaturing (or ore ) setor and flexible pries in the food and energy setors. Serial orrelation of shoks to food and energy pries allows individuals to gain an understanding about future shoks, possibly making it optimal for individuals to plae more weight on the movement of pries in these setors, as past movements of these pries may help predit future inflation. We solve the model for a relationship determining expeted inflation. Our framework extends Van Duyne (1982) by modeling aggregate demand as a funtion of the real interest rate and inorporating a Taylor-type poliy rule for the nominal interest rate. We also test whether any observed bias in expetations about inflation is optimal, whereas Van Duyne tests only whether suh bias is present but not whether it is optimal. We estimate the model using survey data on expeted inflation from the Federal Reserve Bank of Philadelphia. 3 Our results show that the weights implied by the model for onstruting expetations of inflation differ from the expenditure shares of food and energy pries in the Consumer Prie Index (CPI) for the United States. In partiular, we 3 As disussed in Setion 3, we use data on expeted CPI inflation from the Federal Reserve Bank of Philadelphia s Survey of Professional Foreasters (SPF) beause it provides measures of expeted inflation one-quarter and two-quarters ahead, whih our methodology requires. Fuhrer (2012) and Mishkin (2007), among other authors, also use the SPF to apture the publi s expetation of inflation at different horizons. See Croushore (1993) for an overview of the Survey of Professional Foreasters.

4 3 find that food prie inflation is weighted more heavily and energy prie inflation is weighted less heavily. But importantly, we annot rejet the hypothesis that these weights reflet rational behavior in forming expetations about inflation. Our analysis validates onerns sometimes raised by poliymakers as to whether expetations might not be well anhored with respet to some ommodity prie shoks. As a onsequene, poliy may need to be alibrated arefully to prevent suh shoks from beoming embedded in expeted inflation. Reent work by Trehan (2011) suggests that households are more sensitive to energy and food pries in forming inflation expetations than they are to ore measures of inflation that exlude those items. He uses orrelation analysis to show that survey measures of inflation expetations are more losely related to inflation in energy and food items than to ore inflation. Experimental evidene presented by Georganas, Healy, and Li (2014) finds that pereption of the eonomy-wide inflation rate is influened by the frequeny with whih goods pries are observed. A reent paper by Arora et al (2013) shows that expeted inflation responds strongly to (what they term) explosive deviations of overall inflation from ore inflation. All of these papers use non-strutural methods in their analyses and none expliitly test whether the observed response reflets rational behavior. 4 By ontrast, we develop a strutural model of the eonomy and use it to test diretly whether inflation expetations respond rationally to food and energy prie movements. 5 4 Other authors who have analyzed the relationship between expeted inflation and ommodity prie movements using non-strutural methods inlude Wong (2014) and Celasun et al (2012). 5 Whereas we study how expeted inflation responds to movements in ommodity pries, a separate but related literature has explored the question of whether survey measures of expeted inflation represent rational foreasts of future inflation. See, for example, the volume by Sinlair (2010) and artiles by

5 4 The paper proeeds as follows. Setion 2 develops a simple dynami model of the eonomy to show how individuals may optimally overweight or underweight food and energy pries in forming expetations about overall inflation. Setion 3 presents tests of the model s preditions using survey data on expeted prie inflation and provides support for rational bias in inflation expetations. Setion 4 summarizes our findings and offers suggestions for further researh. 2. The Model Our model assumes pries are flexible in the food and energy setors but adjust sluggishly in the ore (non-food and non-energy) setor, where firms with market power set prie as a markup over marginal ost. The model onsists of a standard wage-prie Phillips urve augmented to inlude supply shoks and a dynami aggregate demand relationship inorporating a Taylor-type rule for monetary poliy. Our approah builds on work by Van Duyne (1982), but differs from his by inluding a monetary poliy rule for the nominal interest rate and expressing aggregate demand as a funtion of the real interest rate Aggregate Supply 7 The omposite prie of goods and servies in the ore setor is given as a onstant markup (µ) over marginal ost, whih we proxy by unit labor osts: Capistran and Timmermann (2009), Mankiw et al (2004), Ehrbek and Waldmann (1996), Noble and Fields (1982), and Mullineaux (1978). 6 We also test in Setion 3 whether any observed bias in expetations of inflation is optimal. Van Duyne only tests for bias itself, not whether it is optimal. 7 See Whelan (1997) for a derivation of a wage-prie Phillips urve similar to the one we develop here.

6 5 P t = µ w tl t y t (1) where w is the wage, l is employment, and y is output. 8 For simpliity, we assume a onstant rate of labor produtivity growth in the ore setor so that equation (1) implies ore inflation (π t ) equals wage inflation (ω t ) minus produtivity growth (g): = ω t g. (2) The equilibrium wage is assumed to rise at the rate of expeted inflation plus produtivity growth, adjusted for the degree of slak in labor markets: ω t * = E t 1 + g a 1 u t (3) where E t 1 is the expetation in period t-1 of inflation for period t and u t is the gap between the atual rate of unemployment and its natural (full-employment) level. Atual wage inflation adjusts to its equilibrium rate gradually, either beause overlapping wage ontrats make nominal wages stiky or osts of aquiring information lead to lags in updating otherwise flexible wages. 9 We approximate this gradual adjustment of wage inflation with a simple relationship: ω t ω t 1 = a 2 (ω t * ω t 1 ) 0 < a 2 1 (4) 8 Profit-maximizing monopolistially ompetitive firms will set prie as a markup over marginal ost, where the markup may vary with demand onditions. For example, Mazumder (2014) finds that the markup in the U.S. manufaturing setor is ounterylial. For simpliity, and following Whelan (1997), we treat the markup as onstant. 9 The equilibrium wage an be interpreted as the wage that would prevail under full information. When information is ostly to aquire, firms and workers will update information with some lag, implying a gradual adjustment of wage inflation toward its equilibrium rate. See Mankiw and Reis (2002) for impliations of stiky information in a model of prie setting behavior.

7 6 where parameter a 2 determines the speed with whih wage inflation adjusts to its equilibrium value. We ignore differenes in setoral produtivity growth rates and assume that inflation rates in the food and energy setors relative to the inflation rate in the ore setor are driven by serially orrelated supply shoks (ν t and ε t ): f = π t +ν t π e t = π t + ε t (5) ν t = σ ν t 1 + ξ t ε t = δ ε t 1 + η t where σ, δ < 1, and ξ t, η t are mean-zero unorrelated random shoks. In priniple, the supply shoks ould be either positively or negatively serially orrelated and ould be represented by more ompliated time-series proesses. As disussed in Setion 3, we find that a first-order autoregressive proess fits the data well and provides for a parsimonious representation of these shoks. The overall rate of inflation for the eonomy is measured using a weighted average of prie inflation in the food, energy, and ore setors of the eonomy: = A f + B e + (1 A B) (6) where A and B are expenditure shares for food and energy items used to onstrut the prie index for onsumer expenditures Equation (6) holds for Laspeyres fixed-weight indexes. The offiial CPI for the United States uses a Laspeyres formulation at its upper level for aggregate items suh as food and energy. See Bureau of Labor Statistis (2007) for details.

8 7 Using equations (2), (3), (4), (5), and (6), we an solve for a Phillips urve relating overall inflation to expeted inflation and lagged values of inflation for the ore, food, and energy setors: f = a 2 E t 1 a 1 a 2 u t + (1 a 2 ) +σ A( e ) + δ B( ) (7) where the last two terms are written as deviations of food and energy inflation from ore inflation and an be interpreted as supply shoks. Equation (7) is similar to the expetations-augmented Phillips urve of Friedman (1968) as generalized by Gordon (1982) to inorporate supply shoks and inertia through lagged ore inflation Aggregate Demand To omplete the model, we speify an IS-type demand equation that relates the unemployment gap to the real interest rate: u t = a 3 (i t E t +1 ρ) υ t (8) where i t is the nominal interest rate, E t +1 is the expetation of overall inflation in period t+1 as of period t, ρ is the natural or long-run value of the real interest rate at whih the unemployment gap is zero, and υ t is a mean-zero unorrelated shok to 11 See also Gordon (1982, 1990), Fuhrer (1995), and Murphy (2000) who provide empirial support for standard Phillips urve models of inflation. Bernanke (2008) provides an overview of several important issues for Phillips urve analyses of inflation. Ball and Mazumder (2011) inorporate anhored expetations into an otherwise standard Phillips urve as a possible reason for why the United States did not experiene deflation during and immediately after the Great Reession. Murphy (2014) finds that a Phillips urve modified to aount for unertainty about regional eonomi onditions an explain the behavior of inflation following the Great Reession.

9 8 demand. 12 The monetary authority is assumed to target the nominal interest rate so as to raise (lower) the real interest rate when inflation exeeds (falls short of) its target or when unemployment is less than (greater than) its natural rate: 13 i t = + ρ +θ 1 ( π * ) θ 2 u t 0 < θ 1,θ 2. (9) Substituting this Taylor-type rule into equation (8) yields the following dynami aggregate demand relationship: u t = a 3(1+θ 1 ) a 3 E t +1 a 3θ 1 1 π * υ t. (10) 1+ a 3 θ 2 1+ a 3 θ 2 1+ a 3 θ 2 1+ a 3 θ 2 Equation (10) shows that when inflation inreases, the unemployment gap also inreases as the monetary authority raises the real interest rate to redue aggregate demand and ontain inflation. The unemployment gap will respond more to inflation when the monetary authority plaes a larger weight, θ 1, on deviations from the inflation target and it will respond less to inflation when the monetary authority plaes a larger weight, θ 2, on stabilizing unemployment at its natural rate. An inrease in expeted inflation, given urrent and target inflation, lowers the real interest rate, raises demand and lowers the unemployment gap. Note that when inflation is onstant and equal to its target level (and 12 Romer (2012), Chapter 6, derives a New Keynesian IS urve relationship similar to equation (8) from the maximizing behavior of households. 13 See Taylor (1993) and Bryant, Hooper, and Mann (1993) for a disussion of entral bank interest-rate poliy that appears to be well approximated by suh rules. We assume that θ 1 is greater than zero so that the entral bank responds to an inrease in inflation by raising the real interest rate a ondition ommonly known as the Taylor Priniple.

10 9 the demand shok is zero), equation (10) implies the unemployment gap is zero so that unemployment is equal to its natural rate. 2.3 Equilibrium We an solve for the equilibrium value of inflation by using equation (10) to substitute for the unemployment gap in equation (7) and rearrange to obtain: = (1+ a 3θ 2 )a 2 E t 1 + a 1a 2 a 3 X X E t+1 + a 1a 2 a 3 θ 1 π * + X (1+ a 3 θ 2 )(1 a 2 σ A δ B) + (1+ a 3θ 2 )σ A f + X X (1+ a 3 θ 2 )δ B e + a a 1 2 X X υ t (11) where X = 1+ a 3 θ 2 + a 1 a 2 a 3 (1+θ 1 ). Equation (11) shows how inflation in period t depends on inflation expeted for period t and inflation expeted for period t+1. An inrease in expeted inflation for period t as of period t-1 leads to higher wage inflation, whih in turn is partly passed through into higher ore inflation and, hene, overall inflation. An inrease in expeted inflation for period t+1 as of period t lowers the real interest rate and raises aggregate demand (i.e., redues the unemployment gap), thereby inreasing inflation. The equation exhibits a neutrality property: if expeted inflation rates, target inflation, and lagged setoral inflation rates all inrease by the same proportion (and the demand shok is zero), then overall inflation also will inrease by the same proportion, and from equation (10) the unemployment gap will be unaffeted. To obtain a relationship desribing equilibrium expeted inflation, we take expetations of both sides of equation (11) as of time t-1, and rearrange to yield:

11 10 E t 1 = a 1 a 2 a 3 Z E t a a a 1 2 3θ 1 π * +ζ [α * f + β * e Z + (1 α * β * ) ] (12) where: α * = σ A 1 a 2, β * = δ B 1 a 2 ζ = (1 a 2)(1+ a 3 θ 2 ) Z Z = (1 a 2 )(1+ a 3 θ 2 ) + [a 1 a 2 a 3 (1+θ 1 )]. Note that the relative weights on lagged food, energy, and ore inflation sum to one but in general are not equal to the expenditure shares used to ompute the overall rate of inflation. In partiular, the relative weights on food and energy inflation (α * and β * ) will exeed their respetive expenditure shares (A and B) when σ + a 2 > 1 and δ + a 2 > 1. These onditions are more likely to hold when the speed of wage adjustment is not too sluggish (so that a 2 is large) and the rate of inflation in the food and energy setors is persistent (supply shoks to these setors exhibit suffiient serial orrelation so that σ and δ are large). Conversely, the relative weights will fall short of their respetive expenditure shares when σ + a 2 < 1 and δ + a 2 < 1. Equation (12) imposes restritions on the relative weights individuals should optimally plae on inflation in the food and energy setors when forming expetations about overall inflation: α * = σ A 1 a 2 and β * = δ B 1 a 2. In the next setion, we desribe how these restritions an be tested using survey data on inflation expetations to estimate the parameters of our model.

12 11 3. Estimation Results We estimate relationships of the following form that math equation (12): t 1π E t = γ 0 + γ 1 t 1 π E t+1 f + γ 2 e + γ 3 + γ 4 (13) E where t 1 +i is a measure of expeted CPI inflation for period t+i as of period t-1 and π f, π e, and π are CPI inflation rates for food, energy and ore setors. Beause the monetary authority s target for inflation is assumed fixed, we inlude a onstant term in the equation. To estimate equation (13), we need data for inflation expeted one and two periods in the future. The Federal Reserve Bank of Philadelphia s Survey of Professional Foreasters (SPF) provides quarterly measures of CPI inflation in the United States expeted for multiple time periods in the future, allowing diret estimation of equation (13). 14 Although the University of Mihigan s Survey of Consumers is more representative of the population at large than the SPF, the Mihigan survey reports monthly measures of expeted inflation only over the next year and the next 5 to 10 years, not for one and two periods in the future. 15 In addition, the Mihigan survey asks only about generi inflation, whereas the SPF asks about speifi measures inluding the CPI. Beause the SPF mathes the timing of the expeted inflation variables in our model and asks speifially about the CPI, we use those data in our analysis The Survey of Professional Foreasters provides median inflation expeted one, two, three, and four quarters into the future, along with an estimate for the next ten years. See Federal Reserve Bank of Philadelphia (2014) for details. The Philadelphia Fed also oversees the Livingston survey of foreasters, but that survey is onduted only every six months and provides foreasts for inflation over the next 6 and 12 months. See Murphy (1986) for an analysis of the term struture of inflation foreasts using the Livingston expeted inflation data. 15 See Curtin (1996) for details about the Mihigan expeted inflation series. 16 See Fuhrer (2012) and Mishkin (2007) who also use the SPF median to measure the publi s inflation expetations at various horizons.

13 12 The parameters α * and β * in equation (12) are related to the estimated oeffiients of equation (13) by the following expressions: γ 2 α * γ 2 + γ 3 + γ 4 γ 3 β * γ 2 + γ 3 + γ 4 (14) and represent the relative weights plaed on food and energy pries in forming expetations about inflation. Under the null hypothesis that individuals form expetations about future inflation using our simple model, equations (12) and (14) imply the following restritions: γ 2 (1 a 2 ) (γ 2 + γ 3 + γ 4 )σ = A γ 3 (1 a 2 ) (γ 2 + γ 3 + γ 4 )δ = B (15) where we interpret A and B as the expenditure shares for food and energy used to ompute the CPI. To test these restritions, we need estimates of a 2,σ, and δ in addition to the parameters of equation (13). This requires estimation of equation (13) in ombination with the wage adjustment equation and the autoregressive relationships for the supply shoks. To reover the wage adjustment parameter, a 2, we estimate a Phillips urve for wage inflation derived by substituting equation (3) into equation (4) and rearranging: ω t = φ 0 φ 1 u t + φ 2 t 1 E + (1 φ 2 )ω t 1 (16)

14 13 where φ 2 a 2. We impose the onstraint that the sum of the oeffiients on expeted inflation and lagged wage inflation sum to one when estimating equation (16). To obtain estimates of the autoregressive parameters, σ and δ, we use equations (5) to derive the following relationships: f π f t = ϑ 1 ( ) π e t π e t = ϑ 2 ( ) (17) where ϑ 1 σ and ϑ 1 δ. Using equations (16) and (17), the restritions given by equation (15) an be written in terms of the estimated parameters: γ 2 (1 φ 2 ) (γ 2 + γ 3 + γ 4 )ϑ 1 = A γ 3 (1 φ 2 ) (γ 2 + γ 3 + γ 4 )ϑ 2 = B (18) where, again, A and B are the expenditure shares of food and energy in the CPI. We employ generalized method of moments (GMM) to jointly estimate equations (13), (16), and (17) using quarterly data for the United States. 17 For the inflation variables, we use the quarterly perent hange expressed at an annual rate for the food, energy, and ore omponents of the CPI for All Urban Consumers (CPI-U). We measure the unemployment gap using the differene between the quarterly ivilian unemployment rate and the quarterly value of the natural rate estimated by the Congressional Budget Offie (2014). For wage inflation, we use the quarterly perent hange in average hourly 17 The GMM estimation proedure allows for a generalized variane-ovariane struture of regression error terms for these equations, whih we use in our hypothesis tests. All data, exept as noted, are from the U.S. Bureau of Labor Statistis.

15 14 earnings expressed at an annual rate. And as disussed earlier, we measure expeted inflation using the SPF, whih provides data for median expeted inflation at an annual rate one and two quarters into the future. We start our sample period in 1982, the first full year that the SPF provides onsistent data for multi-horizon expetations of inflation. In our estimation, we use as instruments four lags eah of overall inflation, wage inflation, the unemployment gap, and inflation expeted two quarters ahead. 18 To test the hypotheses given by equation (18), we use the average relative importane for food and energy in the CPI-U as reported by the Bureau of Labor Statistis for our values of A and B. Figure 1 plots the relative importane of food and energy omponents over our sample period. Exept for an initial deline from 1982 through 1986, both shares are reasonably stable, flutuating in a band of only a ouple of perentage points around their average values. The food share gradually trends down after 1986 while the energy share moves up slightly during reent years. We report in Table 1 estimates for the oeffiients of equations (13), (16), and (17) along with their standard errors. 19 For the period 1982 to 2013, all oeffiients are of the orret positive sign and nearly all are statistially different from zero at very high levels of onfidene. Only the oeffiient on the unemployment gap in equation (16) is not signifiantly different from zero, possibly refleting downward nominal wage rigidity during the prolonged episode of high unemployment assoiated with the reent Great 18 Our instrument set uses lagged values of only two-quarter-ahead expeted inflation, sine the onequarter-ahead and two-quarter-ahead series are highly orrelated. Estimates when both series are inluded in the instrument set and when only the one-period ahead series is inluded give results similar to those reported in the text. 19 Estimates of the onstant terms in equations (13) and (16) (not reported) were small in magnitude and generally not statistially signifiant.

16 15 Reession. 20 Hansen s J-statisti shows that we annot rejet at standard levels of onfidene the set of overidentifying restritions on the instruments. Our point estimate of the persistene of inflation in the food setor (ϑ 1 ) is higher than for the energy setor (ϑ 2 ), onsistent the view that underlying shoks to raw energy pries feed through more rapidly into final-stage produts and thus dissipate more quikly than do shoks to raw food pries. 21 Wage inflation adjusts to its equilibrium value at a rate that eliminates roughly 14 perent of the gap in one quarter, as aptured by the point estimate of φ 2. Table 1 also presents test results for the hypothesis that individuals form expetations rationally so that the parameters jointly satisfy the two restritions given by equation (18). 22 The p-value of 0.53 indiates that we annot rejet the hypothesis that individuals form expetations rationally in aord with these restritions. We an, however, rejet the hypothesis that the estimated relative weights, as given by equation (14) and reported in Table 1 (also shown in Figure 1), are equal to the atual expenditure weights, as seen by the p-value of 0.00 for the test of relative weights. The estimated relative weight for food (0.249) is larger than its atual value (0.155) but the estimated relative weight for energy (0.041) is smaller than its atual value (0.083). This suggests rational overweighting for food but rational underweighting for energy in forming expetations about inflation. The underweighting of energy inflation is onsistent with evidene that monetary poliy was tightened sharply in response to energy-related supply 20 Gali (2011) also obtains an insignifiant oeffiient on unemployment in wage Phillips urves and argues that the estimate is overly influened by downward nominal wage rigidity during the period of prolonged high unemployment aompanying the Great Reession. 21 See Pedersen (2011) for analysis of the relative speed with whih food and energy prie shoks dissipate. 22 The reported test statisti is distributed as χ 2 and is omputed using the method desribed in Green (2012), p. 528, for both linear and nonlinear hypotheses. We use this method when alulating test statistis for all hypothesis tests reported in our paper.

17 16 shoks during the 1970s and early 1980s so as to dampen inflation, leading expetations to beome better anhored and less responsive to these shoks in subsequent deades. 23 As shown in Figure 1, the relative weights of food and energy in the CPI were higher in the early 1980s before falling sharply and beoming more stable after To assess whether our findings are robust to exluding the early 1980s, Table 1 also provides results for the period from 1986 to The estimates and test results are similar to those for the full sample period. One again, we annot rejet the hypothesis of rational bias in expetations formation. We also onsider a version of the model in whih food and energy setors are ombined. Here we use data on pries in the food and energy setors along with relative expenditure shares to ompute a prie index for the ombined setors. 24 We estimate a model of the same struture as before exept that now only one non-ore inflation rate enters the model: t 1π E t = γ 0 + γ 1 t 1 π E t+1 ef + γ 2 + γ 3 ω t = φ 0 φ 1 u t + φ 2 t 1 E + (1 φ 2 )ω t 1 (13a) (16a) ef π ef t = ϑ 1 ( ) (17a) where ef is the omposite rate of prie inflation in the food and energy setors. We use generalized method of moments to jointly estimate equations (13a), (16a), and (17a) and, 23 Hooker (2002) finds that monetary poliy has responded less forefully to energy prie shoks sine around 1980 beause expetations of inflation may have beome less sensitive to suh shoks. The underweighting of energy inflation in expetations formation is onsistent with evidene disussed in Bernanke (2007) that inflation expetations have beome better anhored with respet to energy prie shoks in reent deades. 24 See Bureau of Labor Statistis (2007), Chapter 17, pp , for details on how to onstrut omposite prie indexes using relative expenditure shares and prie indexes for setors.

18 17 as before, employ as instruments four lags eah of overall inflation, wage inflation, the unemployment gap, and inflation expeted two quarters ahead. The restrition in equation (18) now takes the form: γ 2 (1 φ 2 ) (γ 2 + γ 3 )ϑ 1 = C (18a) where C is the ombined expenditure share of food and energy in the CPI. Table 2 provides results for the omposite version of our model. All oeffiients are of the orret positive sign and all are statistially signifiant at the 10-perent or better level. For the period 1982 to 2013, we annot rejet the hypothesis that expetations are formed rationally aording to the struture of our model, as indiated by the probability value of 0.90 for the test of the restrition given in equation (18a). We an, however, rejet the hypothesis that the estimated relative weight for the food-energy omposite setor is equal to its atual value, as shown by the p-value of The estimated relative weight of is smaller than its atual value of 0.238, indiating rational underweighting of omposite food-energy inflation in the formation of expetations. Given the results of Table 1 showing underweighting of energy inflation and overweighting of food inflation, this underweighting of omposite food-energy inflation suggests that the influene of energy prie inflation dominates the influene of food prie inflation in forming expetations of overall inflation. As disussed above, this underweighting may reflet better anhoring of inflation expetations with respet to energy prie shoks sine the early 1980s. We again provide a robustness hek on our results by estimating the omposite model over the period 1986 to The seond

19 18 olumn of Table 2 shows that estimates over this shorter sample period are similar to those for the full sample. 4. Summary This paper has argued that individuals may rationally weight prie inreases in the food and energy setors differently from the expenditure shares of these setors in the CPI when forming expetations about overall prie inflation. We developed a simple dynami model of the eonomy to illustrate this finding. Serial orrelation of shoks to food and energy pries allows individuals to gain an understanding about future shoks, possibly making it optimal for individuals to plae more weight on the movement of pries in these setors, as past movements of these pries may help predit future inflation. In partiular, if the degree of persistene for shoks to food and energy inflation is high enough and the speed of wage adjustment is not too sluggish, the model predits individuals will overweight prie movements for food and energy ompared with their expenditure shares in the CPI. Using data on expeted inflation from the Federal Reserve Bank of Philadelphia s Survey of Professional Foreasters, we show that the weights implied by the model for onstruting expetations of inflation differ from the expenditure shares of food and energy in the CPI. Speifially, we find that food prie inflation is weighted more heavily and energy prie inflation is weighted less heavily. But we annot rejet the hypothesis that these weights reflet rational formation of expetations about inflation. These results indiate that expetations might not be well anhored with respet to some ommodity prie shoks. It follows that poliy makers may need to tailor responses to

20 19 suh shoks to aount for the disparity between expenditure shares and the weights individuals plae on setoral inflation in forming expetations. This may mean more foreful poliy is neessary in response to some shoks to prevent them from beoming embedded in expeted inflation. Our goal in this paper was to develop a simple dynami model of the maroeonomy to illustrate the possibility of rational bias in expetations formation and to provide some preliminary results using survey data on inflation expetations. The analysis showed how this bias depends on persistene in ommodity prie inflation and the degree of inertia in wage adjustment. Future researh should extend our work by exploring the links between rational bias and models of rational inattentiveness, where differenes in the ost of aquiring information aross setors (or differenes in willingness to pay attention to news aross setors) ould lead to over or underweighting of inflation aross setors. 25 Our approah ould also be applied to ountries other than the United States to asertain similarities and differenes in the response of inflation expetations to movements in food and energy pries. Finally, our simple model ould be modified to inorporate a greater degree of forward-looking behavior similar to New Keynesian stiky-prie models. 25 See, for example, Mankiw and Reis (2003) and Carroll (2003) for models where information is updated only periodially.

21 20 Referenes Arora, V., P. Gomis-Porqueras, and S. Shuping (2013): The Divergene Between Core and Headline Inflation: Impliations for Consumers Inflation Expetations, Journal of Maroeonomis, 38, Ball, L. and S. Mazumder (2011): Inflation Dynamis and the Great Reession, Brookings Papers on Eonomi Ativity, Spring 2011, Bernanke, B. (2007): Inflation Expetations and Inflation Foreasting, Speeh at the Monetary Eonomis Workshop of the National Bureau of Eonomi Researh Summer Institute, Cambridge, MA, July 10, Bernanke, B. (2008): Outstanding Issues in the Analysis of Inflation, in Understanding Inflation and the Impliations for Monetary Poliy, Fuhrer, J., Kodrzyki, Y., Little, J., and Olivei, G. (eds.), MIT Press, pp Bryant, R., Hooper P., and Mann, C., eds. (1993): Evaluating Poliy Regimes: New Researh in Empirial Maroeonomis, Washington, DC: Brookings Institution Press. Bureau of Labor Statistis (2007): Handbook of Methods, Chapter 17: The Consumer Prie Index, U.S. Department of Labor, Washington, DC. Capistran, C. and A. Timmermann (2009): Disagreement and Biases in Inflation Expetations, Journal of Money, Credit and Banking, 41, Carroll, C. (2003): Maroeonomi Expetations of Households and Professional Foreasters, Quarterly Journal of Eonomis, 118, Celasun, O., R. Mihet, and L. Ratnovski (2012): Commodity Pries and Inflation Expetations in the United States, IMF Working Paper 12/89, Marh Croushore, D. (1993): Introduing: The Survey of Professional Foreasters, Federal Reserve Bank of Philadelphia Business Review, November/Deember, Congressional Budget Offie (2014): The Budget and Eonomi Outlook: Fisal Years 2014 to 2024, February, Washington, DC. Curtin, R. (1996): Proedure to Estimate Prie Expetations, Manusript, University of Mihigan Survey Researh Center.

22 21 Ehrbek, T. and R. Waldmann (1996): Why are Professional Foreasters Biased? Ageny Versus Behavioral Explanations, Quarterly Journal of Eonomis, 111, Federal Open Market Committee (2008): Minutes of the Meeting of June 24-25, 2008, Board of Governors of the Federal Reserve System, Washington, DC. Federal Reserve Bank of Philadelphia (2014): Survey of Professional Foreasters Doumentation, February, Philadelphia, PA. Friedman, M. (1968): The Role of Monetary Poliy, Amerian Eonomi Review, 58, Fuhrer, J. (1995): The Phillips Curve is Alive and Well, New England Eonomi Review, Marh/April, Fuhrer, J. (2012): The Role of Expetations in Inflation Dynamis, International Journal of Central Banking, 8, Gali, J. (2011): The Return of the Wage Phillips Curve, Journal of the European Eonomi Assoiation, 9, Georganas, S., P Healy, and N. Li (2014): Frequeny Bias in Consumers Pereptions of Inflation: An Experimental Study, European Eonomi Review, 67, Gordon, R. (1982): Inflation, Flexible Exhange Rates, and the Natural Rate of Unemployment, in Workers, Jobs, and Inflation, ed. by M. Baily, The Brookings Institution, Gordon, R. (1990): U.S. Inflation, Labor s Share, and the Natural Rate of Unemployment, in Eonomis of Wage Determination, ed. by H. Koenig, Berlin: Springer-Verlag. Greene, W. H. (2012): Eonometri Analysis, 7th ed., Upper Saddle River, NJ: Prentie Hall. Hooker, M. (2002): Are Oil Shoks Inflationary? Journal of Money, Credit and Banking, 34,

23 22 Mankiw, N. and R. Reis (2002): Stiky Information Versus Stiky Prie: A Proposal to Replae the New Keynesian Phillips Curve, Quarterly Journal of Eonomis, 117, Mankiw, N., R. Reis, and J. Wolfers (2004): Disagreement about Inflation Expetations, NBER Maroeonomis Annual 2003, 18, Mazumder, S. (2014): The Prie-Marginal Cost Markup and its Determinants in U.S. Manufaturing, Maroeonomi Dynamis, 18, Mishkin, R. (2007): Inflation Dynamis, NBER Working Paper #13147, June Mullineaux, D. (1978): On Testing for Rationality: Another Look at the Livingston Prie Expetations Data, Journal of Politial Eonomy, 86, Murphy, R. (1986): The Expetations Theory of the Term Struture: Evidene from Inflation Foreasts, Journal of Maroeonomis, 8, Murphy, R. (2000): What s Behind the Deline in the NAIRU? in The Eonomi Outlook For 2000, ed. by S. Hymans, University of Mihigan, January Murphy, R. (2014): Explaining Inflation in the Aftermath of the Great Reession, Journal of Maroeonomis, 40, Noble, N., and T.W. Fields (1982): Testing the Rationality of Inflation Expetations Derived from Survey Data: A Struture-Based Approah, Southern Eonomi Journal, 49, Pedersen, M, (2011): Propagation of Shoks to Food and Energy Pries: An International Comparison, Seminarios de Maroeonomía y Finanzas del Bano Central año 2011, Central Bank of Chile. Romer, D. (2012): Advaned Maroeonomis 4 th Edition, MGraw-Hill Irvin: New York. Sinlair, P. (2010): Inflation Expetations, ed. by Sinlair, P., Routledge International Studies in Money and Banking, New York: Routledge. Taylor, J. (1993): Disretion versus Poliy Rules in Pratie, Carnegie-Rohester Conferene Series on Publi Poliy 39 (Deember):

24 23 Trehan, B. (2011): Household Inflation Expetations and the Prie of Oil: It s Déjà Vu All Over Again, FRBSF Eonomi Letter, , Federal Reserve Bank of San Franiso. Van Duyne, C. (1982): Food Pries, Expetations, and Inflation, Amerian Journal of Agriultural Eonomis, 64, Whelan, K. (1997): Wage Curve vs. Phillips Curve: Are There Maroeonomi Impliations? Finane and Eonomis Disussion Series, , Board of Governors of the Federal Reserve System. Wong, B. (2014): Inflation Expetations and How it Explains the Inflationary Impat of Oil Prie Shoks: Evidene from the Mihigan Survey, Centre for Applied Maroeonomi Analysis Working Paper 45/2014, June 2014.

25 24 Table 1: Estimation Results for Food and Energy Model t 1π E t = γ 0 + γ 1 t 1 π E t+1 f + γ 2 e + γ 3 ω t = φ 0 φ 1 u t + φ 2 t 1 E + (1 φ 2 )ω t 1 f π f t = ϑ 1 ( π e t π e t = ϑ 2 ( ) ) + γ 4 Sample Period 1982:1-2013:4 1986:1-2013:4 γ ** 0.847** (0.063) (0.094) γ ** 0.055** (0.011) (0.015) γ ** 0.010** (0.002) (0.002) γ ** (0.060) (0.086) φ (0.029) (0.028) φ ** 0.150** (0.042) (0.045) ϑ ** ** (0.073) (0.095) ϑ ** 0.361** (0.040) (0.043) Number of Observations J- Statisti: χ 2 (58) p- value (0.12) (0.21) Rationality: a χ 2 (2) p- value 1.28 (0.53) 0.94 (0.63) Relative Weights: b χ 2 (2) p- value (0.00) 6.90 (0.03) Relative Weights Food Energy Estimated Atual Estimated Atual E Note: t 1 +i is CPI inflation expeted for period t+i as of period t-1, π f, π e, and π are, respetively, CPI inflation in the food, energy, and ore (non-food, non-energy) setors, ω is wage inflation measured by average hourly earnings, and u is the unemployment gap omputed using the CBO s estimate of the natural rate. Data are quarterly and inflation rates are measured as quarterly perent hange at an annual rate. Estimation tehnique is GMM using as instruments a onstant term and 4 lags eah of overall CPI inflation, wage inflation, the unemployment gap, and inflation expeted two quarters ahead. Robust standard errors are presented in parentheses under the oeffiient estimates with * and ** indiating oeffiient is statistially different from zero at 10-perent and 1-perent levels, respetively. a Test of null hypothesis that estimated relative weights satisfy restritions given by equation (18). b Test of null hypothesis that estimated relative weights equal atual relative weights.

26 25 Table 2: Estimation Results for Food-Energy Composite Model t 1π E t = γ 0 + γ 1 t 1 π E t+1 ef + γ 2 + γ 3 ω t = φ 0 φ 1 u t + φ 2 t 1 E + (1 φ 2 )ω t 1 ef π ef t = ϑ 1 ( ) Sample Period 1982:1-2013:4 1986:1-2013:4 γ ** 0.671** (0.103) (0.111) γ ** 0.047** (0.008) (0.006) γ ** 0.283** (0.090) (0.097) φ * 0.075* (0.034) (0.030) φ ** 0.189** (0.046) (0.051) ϑ ** 0.345** (0.079) (0.082) Number of Observations J- Statisti: χ 2 (43) p- value (0.09) (0.27) Rationality: a χ 2 (1) p- value 0.02 (0.90) 0.76 (0.38) Relative Weights: b χ 2 (1) p- value (0.00) 3.95 (0.05) Relative Weights Food- Energy Estimated Atual Estimated Atual E Note: t 1 +i is CPI inflation expeted for period t+i as of period t-1, π ef is CPI inflation in the omposite food and energy setor, π is CPI inflation in the ore (non-food, non-energy) setor, ω is wage inflation measured by average hourly earnings, and u is the unemployment gap omputed using the CBO s estimate of the natural rate. Data are quarterly and inflation rates are measured as quarterly perent hange at an annual rate. Estimation tehnique is GMM using as instruments a onstant term and 4 lags eah of overall CPI inflation, wage inflation, the unemployment gap, and inflation expeted two quarters ahead. Robust standard errors are presented in parentheses under the oeffiient estimates with * and ** indiating oeffiient is statistially different from zero at 10-perent and 1-perent levels, respetively. a Test of null hypothesis that estimated relative weights satisfy restritions given by equation (18a). b Test of null hypothesis that estimated relative weights equal atual relative weights.

27 26 Figure 1: Relative Importane of CPI Components, 1982 to " Food"Es5mated" 20" Food" Food"Average" Perent" 15" 10" Energy" Energy"Average" 5" Energy"Es5mated" 0" 1982" 1984" 1986" 1988" 1990" 1992" 1994" 1996" 1998" 2000" 2002" 2004" 2006" 2008" 2010" 2012" Soure: Bureau of Labor Statistis and authors alulations.

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