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Lecture 3 :Current Applications
Prof. Michael WeberUniversity of Chicago Booth School of Business
September 17, 2015
1 )
Lecture Outline
I Overview of data sources
I Simple multi-sector New Keynsian Model
I Applications
2 )
Overview of Data Sources
3 )
Micro Pricing Data
I Micro data underlying US CPI and PPI
I Bureau of Labor StatisticsI Accessible in-house for researchersI Details under: On-site Visiting Researcher ProgramI Recent papers using data: Bils and Klenow (2004), Nakamura
and Steinsson (2008), Goldberg and Hellerstein (2011), Bergerand Vavra (2013), Kehoe and Midrigan (2014), Vavra (2014),Bhattarai and Schoenle (2014) Gorodnichenko and Weber(2015), Weber (2015), D'Acunto, Liu, P�ueger, and Weber(2015)
I Scanner price and quantity data from Symphony IRI
I Accessible for researchersI Details under: IRI Academic data setI Recent papers using data: Stroebel and Vavra (2015), Coibion
et al. (2015)
4 )
http://www.bls.gov/bls/blsresda.htmhttp://www.iriworldwide.com/en-US/solutions/Academic-Data-Set
Micro Pricing Data
I Consumer Panel and Retail Scanner Data from AC Nielsen
I Panel of 40,000 - 60,000 US households and purchases offast-moving consumer goods
I Weekly pricing and volume from more than 90 participatingretail chains
I Accessible to researcherI Details under: Kilts Center for Marketing Booth School of
BusinessI Recent paper using data: Beraja, Hurst, and Ospina (2015),
D'Acunto, Ospina, and Weber (2015)
I Micro data underlying UK CPI
I Accessible onlineI Details under: Tables with micro data; no establishment namesI Recent paper using data: Kryvtsov and Vincent (2014)
5 )
http://research.chicagobooth.edu/nielsen/http://research.chicagobooth.edu/nielsen/http://www.ons.gov.uk/ons/datasets-and-tables/index.html
Micro Pricing Data
I Online shopping platforms
I See for an overview: MIT Billion Price ProjectI See also Gorodnichenko and Talavera (2015)
I Other data sources include: shopping catalogues, nationalprice statistics, prices for speci�c goods, Dominick'ssupermarket price data, etc.
I See also Klenow and Malin (2010) and Nakamura andSteinsson (2013) for recent reviews
6 )
http://bpp.mit.edu/
Simple Multi-Sector New Keynesian Model
7 )
Simple Multi-Sector New Keynesian Model
I Carvalho (2006) multi-sector model
I Here: brief discussion of model
I See paper for more details
8 )
Households
I Representative household lives forever
I The instantaneous utility: positive in consumption; negative inlabor supply
I IES: σ
I Labor supply is �rm-speci�c
I For each �rm, the elasticity of labor supply is η
I Household's discount factor: β
I Households have a love for variety: CES Dixit-Stiglitzaggregator with the elasticity of substitution θ
9 )
Firms
I Firms set prices as in Calvo (1983)
I k sectors populated by a continuum of �rms
I Each sector is characterized by a �xed λk : probability toadjust price
I Share of �rms in industry k in the total number of �rms:density function f (k)
I Firms are monopolistic competitors
I Elasticity of substitution: θ; same within and across industries(relaxed later)
I Production function for output Y is linear in labor N
10 )
Firms' Problem
Problem of �rm j in industry k is to pick a reset price Xjkt :
maxEt∞∑s=0
Qt,t+s(1− λk)s [XjktYjkt+s −Wjkt+sNjkt+s ]
s.t. Yjkt+s = Njkt+s
Yjkt+s = Yt+s
(XjktPt+s
)−θQt,t+s = β
s
(Yt+s
Yt
)−σVariables without subscripts k and j : aggregate variablesW : wages (taken as given by �rms)Q: stochastic discount factor
11 )
Wage Rate
Household's optimization problem determines wages paid by �rms:
WjktPt
=N1/ηjkt
C−σt
12 )
Aggregate Prices and Output
The aggregate price level and output are given by:
Pt =
(∫ 10
f (k)P(1−θ)kt dk
)1/(1−θ)Pkt =
(∫ 10
P(1−θ)jkt dj
)1/(1−θ)Yt =
(∫ 10
f (k)1/θY(θ−1)/θkt dk
)θ/(θ−1)Ykt = f (k)
(∫ 10
Y(θ−1)/θjkt dj
)θ/(θ−1)
13 )
Taylor Rule
Central bank follows an interest rate rule:
exp(it) =
(Pt
Pt−1
)φπ( YtYt−1
)φyβ−1 exp(mpt)
mpt = ρmpmpt−1 + vt
exp(it): nominal interest rateφπ: response to in�ationφy : response to output growthvt : i.i.d. zero-mean policy innovation
14 )
Firm Value
Substitute in optimal reset prices, �rm-speci�c demand and wagesValue of the �rm V with price Pjkt is given by:
V (Pjkt) = Et{Y σt Pt
[∆
(1)kt
(PjktPt
)1−θ− ∆(2)kt
(PjktPt
)−θ(1+1/η)+ Υ
(1)kt − Υ
(2)kt
]}∆
(1)kt = Y
1−σt + β(1− λk)
(Pt+1Pt
)θ−1∆
(1)kt+1
∆(2)kt = Y
1+1/ηt + β(1− λk)
(Pt+1Pt
)θ(1+1/η)∆
(2)kt+1
Υ(1)kt = λkβ
(Xk,t+1Pt+1
)1−θ∆
(1)kt+1 + βΥ
(1)kt+1
Υ(2)kt = λkβ
(Xk,t+1Pt+1
)−θ(1+1/η)∆
(2)kt+1 + βΥ
(2)kt+1
15 )
Applications
16 )
Gorodnichenko and Weber (2015)
Research Question:
Does observed price stickiness at micro level imply costly stickyprices?
I New Keynesian model imply costly sticky prices
I New Monetary search model: stickiness equilibrium outcomeand costless for �rms
17 )
Framework
I Micro price data from the Bureau of Labor Statistics
I Stock returns for constituents of S&P500
I Monetary policy shock using federal funds futures
I Narrow event windows to rule out alternative explanations
18 )
Model Intuition: Pro�t as Function of Price (static model)
Price P
Profit π
P?
π∗
Old Profit Function
Student Version of MATLAB
19 )
Model Intuition: Pro�t as Function of Price (static model)
Price P
Profit π
P?
π∗
Band of InactionL
PL PL
φL
Old Profit Function
Student Version of MATLAB
20 )
Model Intuition: Pro�t as Function of Price (static model)
Price P
Profit π
P?
π∗
PL PL
φL
P?new
Band of InactionL
Old Profit FunctionNew Profit Function
Student Version of MATLAB
21 )
Model Intuition: Pro�t as Function of Price (static model)
Price P
Profit π
P?
π∗
PL PL
φL
P?new
Band of InactionL
Old Profit FunctionNew Profit Function
Student Version of MATLAB
22 )
Model Intuition: Pro�t as Function of Price (static model)
Price P
Profit π
P?
π∗
PL PL
φL
P?new
Band of InactionL
PH PH
φH
Old Profit FunctionNew Profit Function
Student Version of MATLAB
23 )
Theoretical Framework: Recap
I Returns can increase or decrease following shift in pro�tfunction
I After shocks, larger increase in volatility for high-menu cost�rms
I Empirical Speci�cation:
R2it = b0 + b1 × v2t + b2 × λi × v2t + b3 × λi + Controls + εit ,
where Rit is return of �rm i at time t, vt is a monetary policy surpriseand λi is frequency of price adjustment at �rm level
Prediction: Monetary policy shocks increase return variability
(b1 > 0).
This e�ect decreases in price �exibility (b2 < 0).
24 )
Data and Sample Period
I 137 event dates between February 1994 and December 2009
I 30 & 60 min event windows around the press releases of theFOMC
I Time stamps of press releases from FOMC
I Stock returns for constituents of S&P500 from NYSE taq
I Firm level controls such as size, book-to-market, price-costmargin, sales volatilities, sta� expenditures from CRSP andCompustat
I Micro data underlying PPI to measure price stickiness
25 )
Measuring Price Stickiness
I Frequency of price adjustment: mean fraction of months withprice change at good level
I Example:
I Observed price path of $4 for two months, then $5 for threemonths
I One price change during �ve months: frequency of 1/5
I Aggregation at establishment level: BLS identi�er
I Aggregation at �rm level: manual matching
I Equally and value of shipment-weighted frequencies
26 )
Monetary Policy Shocks
I High-frequency identi�cation of monetary policy shocks
I Tick-by-tick federal funds futures (FFF) data from CME
I FFF settles on average e�ective fed funds rate: use scaledchange
vt =D
D − t(ff 0t+∆t+ − ff
0t−∆t−) where D is # of days in month
03:00 09:00 15:00
5.25
5.27
5.29 Press release
August 8, 2006
03:00 09:00 15:00
4.85
4.95
5.05 Press release
September 18, 2007
03:00 09:00 15:00
2.55
2.60
2.65Press release
March 18, 2008
Student Version of MATLAB
I High trading activity with immediate market reaction
27 )
Event Returns
2.15pm
FOMC press release
2.05pm 2.25pm
Tight Event Window: -10 min -- +20 min
Pit-1 Pit+1
I Use tick-by-tick data from NYSE taq
I Last trade before (Pit−1) and �rst trade after (Pit+1) eventwindow
I Volume weighted returns as robustness
I Check all returns larger than 5% in absolute value
28 )
Baseline Analysis
I Study heterogeneity in reaction of volatility to monetary policyshock
I Empirical Speci�cation:
R2it = b0 + b1 × v2t + b2 × λi × v2t + b3 × λi + Controls + εit ,
where Rit is return of �rm i at time t, vt is a monetary policy surpriseand λi is frequency of price adjustment at �rm level
Prediction: Monetary policy shocks increase return variability
(b1 > 0).
This e�ect decreases in price �exibility (b2 < 0).
I Cluster standard errors at event level (similar if useDriscoll-Kraay)
29 )
Baseline Results
R2it = b0 + b1 × v2t + b2 × λi × v2t + b3 × λi + εit
Baseline Baseline
(Tight Window) (Wide Window)
All obs. No outliers All obs. No outliers
(1) (2) (3) (4)
v2t 128.50∗∗∗ 76.95∗∗∗ 119.60∗∗∗ 95.38∗∗∗(29.50) (15.95) (38.89) (24.82)
λi × v2t −169.80 ∗ ∗ −67.26∗∗∗ −130.40∗ −78.07∗∗∗(82.32) (5.02) (77.88) (27.10)
λi 0.41 0.09 0.55 0.08
(0.33) (0.16) (0.59) (0.21)
# Obs 57,541 57,441 57,541 55,002
R2 0.12 0.12 0.03 0.01
I 25 bps monetary policy surprise leads to increase in squared returns of8%2 for the most sticky �rms (0.252 × 128.50 = 8.03)
I Reduced by factor of 3 for �exible price �rms: (b1 − 0.5× b2)/b1 ≈ 1/330 )
Dynamic General Equilibrium Model
I Carvalho (BE Macro Advances, 2006) model:
I Mutliple sectors (5 in calibration)
I Continuum of �rms in each sector (100 in calibration)
I Sectors k di�er in Calvo rate of price adjustment λk
I Monopolistic Competions (CES aggregator)
I Linear production function in labor
I Taylor rule
I Monetary shocks are only source of variation
I Derive �rm valuations as function of �rm's price
I Calibrate and simulate model at quarterly frequency
31 )
Calibration
Parameter Value Source
Frisch η 2 Ashenfelter et al. (2010)
IES σ 0.5 standard
Demand Elasticity θ 7 standard
Discount Factor β 0.99 standard
In�ation Response φpi 1.5 Taylor (1993)
Output Gap Response φy 0.5/4 Taylor (1993)
Shock Persistence ρmp 0.9 Coibon and Gorodnichenko (2012)
Volatility of Shocks stdvt 0.0043 Coibon et al. (2012)
Sector k Share Frequency of Price Adjustment
1 0.2 0.094
2 0.2 0.164
3 0.2 0.277
4 0.2 0.638
5 0.2 0.985
32 )
Regressions on Simulated Data
R2it = b0 + b1 × v2t + b2 × λi × v2t + b3 × λi + εit
Baseline Alternative b1 b2 b3
Baseline 221.5 -256.0 -0.008
IES σ 1/2 1/3 161.2 -177.5 -0.006
Frisch η 2 1 433.5 -513.8 -0.014
Demand Elasticity θ 7 6 114.0 -120.7 -0.004
Taylor Rule Parameters
φπ 1.5 2 108.0 -127.5 -0.004
φy 0.5/4 0.75/4 245.7 -287.9 -0.009
ρmp 0.9 0.91 410.5 -494.7 -0.015
std(vt) 0.0043 0.004 197.7 -226.2 -0.006
I Simulate 100 �rms per sector for 2,000 periods
I Discard �rst 1,850 periods as burn-in (similar to empirical sample size)
I Report average values of regression coe�cients
33 )
Conclusion
I Fundamental questions:
I Does money matter?
I Are sticky prices costly?
I Alt. models w/ di�erent normative & positive implications
I NK Macroeconomics: �menu� cost of price adjustment
I Challenge: �menu� costs have di�erent varieties and shapes
I We present robust and model-free evidence that conditionalvolatility of stock returns is larger for sticky price �rmscompared to �rms with �exible prices � qualitatively andquantitatively consistent with New Keynesian interpretation atthe �rm level
34 )
Weber (2015)
I Nominal rigidities central in macro, unexplored in �nance
I Substantial variation in frequency across industries and �rms
Research Question:
I Same rigidities central for macro and asset pricing?
I Price stickiness determinant for cross section of stock returns?
35 )
Framework
I Micro-level price data from the Bureau of Labor Statistics
I Calculate frequency of product price adjustment at �rm level
I Merge with stock returns for constituents of S&P500
36 )
Portfolio Level
Average annual portfolio raw returns
Sticky S2 S3 S4 Flexible S1-S5
07/1963 - 06/2011 18.84 18.42 18.26 16.97 16.10 2.74∗(2.85) (2.02) (2.03) (2.19) (1.97) (1.46)
07/1982 - 06/2007 24.22 21.98 22.03 21.00 19.84 4.38 ∗ ∗(3.08) (2.66) (2.35) (2.46) (2.47) (1.91)
07/1982 - 06/1998 28.77 25.59 25.20 24.39 22.05 6.72∗∗∗(3.53) (2.93) (3.23) (2.64) (2.89) (1.61)
Newey-West standard errors in parentheses
∗p < 0.10, ∗ ∗ p < 0.05, ∗ ∗ ∗p < 0.01
I Sort all stocks into 5 portfolios
I Portfolio 1: stocks with low frequencies (sticky price �rms)
I Portfolio 5: stocks with high frequencies (�exible price �rms)
37 )
Panel Regressions
I Return di�erences potentially due to reasons ⊥ to frequency
I Di�erent cyclical properties of demand
I Di�erences in market power
I Di�erent characteristics
I Exploit XS variation in stock level panel regressions
I Add controls individually and jointly
I Cluster standard errors at �rm (and year) level
38 )
Panel Regressions
Ri,t = α+ βFreqi × Freqi +∑n
βn × Controlsin,t + YearFE + �i,t
Controls βFreqi βn Year FE # Obs.
(1) Baseline (no controls) −10.04∗∗∗ No 13,810(2.16)
(2) Baseline (no controls) −10.97∗∗∗ Yes 13,810(2.28)
(3) Size −8.04∗∗∗ −4.38∗∗∗ Yes 13,810(2.44) (0.29)
(4) Book to Market −12.94∗∗∗ 3.22∗∗∗ Yes 13,582(2.50) (0.84)
(5) CAPM Beta −8.54∗∗∗ 4.12∗∗∗ Yes 13,319(2.29) (0.75)
Baseline implies premium for sticky price �rms of 6.02% per year (10.04 × 0.6)
39 )
Panel Regressions
Ri,t = α+ βFreqi × Freqi +∑n
βn × Controlsin,t + YearFE + �i,t
Controls βFreqi βn Year FE # Obs.
(1) Baseline (no controls) −10.04∗∗∗ No 13,810(2.16)
(2) Baseline (no controls) −10.97∗∗∗ Yes 13,810(2.28)
(3) Size −8.04∗∗∗ −4.38∗∗∗ Yes 13,810(2.44) (0.29)
(4) Book to Market −12.94∗∗∗ 3.22∗∗∗ Yes 13,582(2.50) (0.84)
(5) CAPM Beta −8.54∗∗∗ 4.12∗∗∗ Yes 13,319(2.29) (0.75)
Baseline implies premium for sticky price �rms of 6.02% per year (10.04 × 0.6)
39 )
Panel Regressions
Ri,t = α+ βFreqi × Freqi +∑n
βn × Controlsin,t + YearFE + �i,t
Controls βFreqi βn Year FE # Obs.
(1) Baseline (no controls) −10.04∗∗∗ No 13,810(2.16)
(2) Baseline (no controls) −10.97∗∗∗ Yes 13,810(2.28)
(3) Size −8.04∗∗∗ −4.38∗∗∗ Yes 13,810(2.44) (0.29)
(4) Book to Market −12.94∗∗∗ 3.22∗∗∗ Yes 13,582(2.50) (0.84)
(5) CAPM Beta −8.54∗∗∗ 4.12∗∗∗ Yes 13,319(2.29) (0.75)
Baseline implies premium for sticky price �rms of 6.02% per year (10.04 × 0.6)
39 )
Panel Regressions cont.
Ri,t = α+ βFreqi × Freqi +∑n
βn × Controlsin,t + YearFE + �i,t
Controls βFreqi βn Year FE # Obs.
(6) Leverage −10.99∗∗∗ 1.06 Yes 13,735(2.32) (1.38)
(7) Cash Flow −10.98∗∗∗ −10.97 ∗ ∗ Yes 13,746(2.31) (5.55)
(8) Share Turnover −9.83∗∗∗ 52.39∗∗∗ Yes 13,810(2.27) (3.87)
(9) Bid-Ask Spread −10.16∗∗∗ −5.45∗∗∗ Yes 13,810(2.34) (0.54)
(10) Price to Cost Margin −9.52∗∗∗ 5.61∗∗∗ Yes 13,744(2.25) (1.66)
(11) Her�ndahl Index Sales −10.79∗∗∗ 0.23 Yes 13,210(2.36) (0.70)
40 )
Panel Regressions: All Controls
Ri,t = α+ βFreqi × Freqi +∑n
βn × Controlsin,t + YearFE + �i,t
Controls β Year FE # Obs.
Freq −7.07∗∗∗ Yes 13,029(2.73)
Size −4.97∗∗∗Book to Market 3.21∗∗∗CAPM Beta 0.10
Leverage 4.35 ∗ ∗Cash Flow 3.76
Share Turnover 37.00∗∗∗Bid-Ask Spread −7.37∗∗∗Price to Cost Margin 7.84∗∗∗Her�ndahl Index Sales 1.79∗
41 )
Conditional CAPM
Rolling time series regressions of portfolio excess return Rp on market excess return Rm
Rp,t = αp + βp × Rm,t + �i,t
Sticky S2 S3 S4 Flexible S1-S5
(1) (2) (3) (4) (5) (6)
mean αp 0.41∗∗∗ 0.35∗∗∗ 0.38∗∗∗ 0.37∗∗∗ 0.40∗∗∗ 0.00(0.19) (0.12) (0.14) (0.13) (0.14) (0.14)
mean βp 1.29∗∗∗ 1.21∗∗∗ 1.15∗∗∗ 1.08∗∗∗ 0.91∗∗∗ 0.37∗∗∗(0.05) (0.04) (0.05) (0.04) (0.06) (0.05)
Newey-West standard errors in parentheses
∗p < 0.10, ∗ ∗ p < 0.05, ∗ ∗ ∗p < 0.01
I CAPM cannot explain level of excess returns
I CAPM can explain spread in returns
I Spread in returns fully explained by di�erences in systematic risk
42 )
Monetary Policy Surprises
I Monetary policy important determinant of risk premia
I Empirically: Bernanke and Kuttner (2005), Savor and Wilson(2013a, 2013b), Lucca and Moench (2013), Campbell,P�ueger and Viceira (2013)
I In model: see later
I Heterogeneous response to monetary policy shocks?
I Regress monthly excess returns, Rp,t , on FFR surprises
43 )
Monetary Policy Surprises cont.
Excess returns, Rp , on negative of surprise component of change in FFR, −∆iutRp,t = αp + βp,FFR ×−∆iut + �p,t
Market Sticky S2 S3 S4 Flexible
(0) (1) (2) (3) (4) (5)
βactualp,FFR 9.35% 11.42% 10.19% 9.35% 8.85% 5.01%
[2.66]∗∗∗ [4.12]∗∗∗ [3.46]∗∗∗ [3.36]∗∗∗ [3.37]∗∗∗ [2.98]∗
βpredp,FFR
10.88% 10.65% 10.02% 9.38% 7.45%
Newey-West standard errors in parentheses
∗p < 0.10, ∗ ∗ p < 0.05, ∗ ∗ ∗p < 0.01
I Strong positive reaction to expansionary monetary policy shocks
I Stronger responsiveness of �rms with higher nominal rigidity
I Predicted sensitivity, βpredp,FFR , equals CAPM β times market sensitivity,
βactualmarket,FFR
44 )
Mutli-sector Calvo Model
I Households
I Utility from composite consumption and leisure
I External habit formation
I Provide di�erent labor types
I Have market power in setting wages
I Reset wage with certain probability each period: Calvo friction
I Production
I Production organized in k sectors
I Reset price with certain probability each period: Calvo friction
I Di�erent Calvo rates across sectors 1− θkI Monopolistic competition (CES aggregator)
I Taylor rule
I Monetary and technology shocks only source of variation
45 )
Mutli-sector Calvo Model
I Households
I Utility from composite consumption and leisure
I External habit formation
I Provide di�erent labor types
I Have market power in setting wages
I Reset wage with certain probability each period: Calvo friction
I Production
I Production organized in k sectors
I Reset price with certain probability each period: Calvo friction
I Di�erent Calvo rates across sectors 1− θkI Monopolistic competition (CES aggregator)
I Taylor rule
I Monetary and technology shocks only source of variation
45 )
Mutli-sector Calvo Model
I Households
I Utility from composite consumption and leisure
I External habit formation
I Provide di�erent labor types
I Have market power in setting wages
I Reset wage with certain probability each period: Calvo friction
I Production
I Production organized in k sectors
I Reset price with certain probability each period: Calvo friction
I Di�erent Calvo rates across sectors 1− θkI Monopolistic competition (CES aggregator)
I Taylor rule
I Monetary and technology shocks only source of variation
45 )
Mutli-sector Calvo Model
I Households
I Utility from composite consumption and leisure
I External habit formation
I Provide di�erent labor types
I Have market power in setting wages
I Reset wage with certain probability each period: Calvo friction
I Production
I Production organized in k sectors
I Reset price with certain probability each period: Calvo friction
I Di�erent Calvo rates across sectors 1− θkI Monopolistic competition (CES aggregator)
I Taylor rule
I Monetary and technology shocks only source of variation
45 )
Calibration
I Solve 5 sector version of model to second order using dynare
I Calibrate model at quarterly frequency
I Simulate for 500 quarters and 400 �rms / sector
I Discard �rst 250 periods as burn-in
Sectoral Distribution of Frequency of Price Adjustment
Sector k Share Frequency of Price Adjustment
1 0.2 0.105
2 0.2 0.164
3 0.2 0.277
4 0.2 0.638
5 0.2 0.985
46 )
Calibration Parameters
Parameter Value Source
Discount Factor β 0.99 standard
Habit Persistence b 0.76 Altig et al 2011
Risk Aversion γ 5 Jermann 1998
Frisch σ 2.5 Carvalho 2006
Consumption Elasticity across �c 8 Carvalho 2006
Consumption Elasticity within �ck 12 Carvalho 2006
Wage Calvo Rate θw 0.825 Heer et al 2012
Elasticity labor types �w 8 Altig et al 2011
In�ation Response φπ 1.24 Rudebusch 2002
Output Gap Response φy 0.33/4 Rudebusch 2002
Tech Shock Persistence ρa 0.95 Smets and Wouters 2007
MP Shock Persistence ρm 0.90 Coibion and Gorodnichenko 2012
47 )
Model Implied Annual Stock Returns
Sticky S2 S3 S4 Flexible S1-S5 ERP SR
(1) Baseline 7.91 6.84 6.56 5.96 5.51 2.39 6.56 0.39
(2) �ck = 13 8.70 6.81 6.41 5.68 5.15 3.55 6.55 0.36
(3) �ck = 11 7.40 6.89 6.70 6.21 5.85 1.55 6.61 0.41
(4) �c = 10 8.15 6.86 6.55 5.94 5.50 2.66 6.60 0.39
(5) �c = 6 7.71 6.82 6.57 5.98 5.53 2.18 6.52 0.39
(6) σε= 0.009 10.21 7.66 7.19 6.40 5.82 4.39 7.46 0.38
(7) φπ = 1.3 5.98 5.88 5.76 5.41 5.16 0.82 5.64 0.38
(8) φx = 0.5/4 7.90 6.84 6.56 5.96 5.51 2.39 6.55 0.39
(9) MP only 6.81 5.87 5.64 5.03 4.59 2.23 5.59 0.34
(10) Technol only 1.08 0.97 0.89 0.83 0.81 0.27 0.92 0.47
Larger Taylor Rule coe�cients on in�ation (φπ) and output growth (φx )
I Equity risk premium: ERPI Sharpe ratio: SRI Coe�cient of regressing annual returns on monthly frequency of price adjustment: βFreq
48 )
Conclusions
Does heterogeneity in price rigidity matter for XS of returns?
I Frequency of price adjustment associated w/ premium of 4%
I Premium strongly predictable in times series
I In XS, di�erences in systematic risk capture return premium
I Su�ciently high elasticity of substitution of within industryconsumption varieties crucial to obtain cross-sectional returnpremium
Price rigidities central in Macro and in Asset Pricing
49 )
Bibliography I
Beraja, M., E. Hurst, and J. Ospina (2015). The regional evolutionof prices and wages during the great recession. Unpublishedmanuscript, University of Chicago.
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