Post on 22-May-2018
The KinkedDemandCurve andPrice Rigidity
DosscheHeylen
Van den Poel
Introduction
Data
SignRestrictions
Model
Estimation
Conclusions
The Kinked Demand Curve and Price Rigidity:Evidence from Scanner Data1
Maarten Dosschea,b Freddy Heylenb Dirk Van den PoelbaNational Bank of Belgium, bGhent University
In�ation Dynamics in Japan, US and EUTokyo, June 28 2007
1The views expressed here are those of the authors and do notnecessarily re�ect the views of the institutions to which they are a¢ liated.
The KinkedDemandCurve andPrice Rigidity
DosscheHeylen
Van den Poel
IntroductionMotivationKinked DemandPreview Findings
Data
SignRestrictions
Model
Estimation
Conclusions
Macroeconomic MotivationBackground
Persistent e¤ects of monetary shocks on real output andin�ation (e.g. Christiano et al., 1999, 2005)=) frictions to price/wage adjustment:
Nominal price/wage rigidity (e.g. Calvo, 1983; Taylor,1980)
Strategic complementarities (e.g. Ball and Romer, 1990)
The KinkedDemandCurve andPrice Rigidity
DosscheHeylen
Van den Poel
IntroductionMotivationKinked DemandPreview Findings
Data
SignRestrictions
Model
Estimation
Conclusions
Macroeconomic MotivationRecent Contributions: Strategic Complementarity
Frequent and large price changes in micro data (e.g. Bils andKlenow, 2004; Dhyne et al., 2006 and Nakamura andSteinsson, 2007a)
Firm-speci�c production factors (e.g. Galí and Gertler,1999, Burstein and Hellwig, 2007)
Intermediate inputs (e.g. Bergin and Feenstra, 2000;Nakamura and Steinsson, 2007b)
Quasi-kinked demand (e.g. Kimball, 1995; Klenow andWillis, 2006)
The KinkedDemandCurve andPrice Rigidity
DosscheHeylen
Van den Poel
IntroductionMotivationKinked DemandPreview Findings
Data
SignRestrictions
Model
Estimation
Conclusions
The Kinked Demand CurveLoss Aversion
Kimball (1995) without discussion of microfoundation
Loss aversion as in Tversky and Kahneman (1991) orHeidhues and Köszegi (2005)
No deep habits as in Ravn, Schmitt-Grohé and Uribe(2006) (SR vs. LR elasticity)
Welfare implications are di¤erent (Levin, Lopez-Salido andYun, 2006)
This paper: identify shape of demand curve from microprice and quantity data
The KinkedDemandCurve andPrice Rigidity
DosscheHeylen
Van den Poel
IntroductionMotivationKinked DemandPreview Findings
Data
SignRestrictions
Model
Estimation
Conclusions
The Kinked Demand CurveElasticity and Curvature
qiQ =
� piP
��ε with ε the demand elasticity
ε =� piP
�ε with ε the curvature or "super elasticity" ofdemand
0.10
0.05
0.00
0.05
0.10
0.15
0.20
1 0.8 0.6 0.4 0.2 0 0.2 0.4 0.6
LN(qi/Q)
LN(p
i/P)
Curvature = 0
The KinkedDemandCurve andPrice Rigidity
DosscheHeylen
Van den Poel
IntroductionMotivationKinked DemandPreview Findings
Data
SignRestrictions
Model
Estimation
Conclusions
The Kinked Demand CurveElasticity and Curvature
qiQ =
� piP
��ε with ε the demand elasticity
ε =� piP
�ε with ε the curvature or "super elasticity" ofdemand
0.10
0.05
0.00
0.05
0.10
0.15
0.20
1 0.8 0.6 0.4 0.2 0 0.2 0.4 0.6
LN(qi/Q)
LN(p
i/P)
Curvature = 0
Curvature = 1
The KinkedDemandCurve andPrice Rigidity
DosscheHeylen
Van den Poel
IntroductionMotivationKinked DemandPreview Findings
Data
SignRestrictions
Model
Estimation
Conclusions
The Kinked Demand CurveElasticity and Curvature
qiQ =
� piP
��ε with ε the demand elasticity
ε =� piP
�ε with ε the curvature or "super elasticity" ofdemand
0.10
0.05
0.00
0.05
0.10
0.15
0.20
1 0.8 0.6 0.4 0.2 0 0.2 0.4 0.6
LN(qi/Q)
LN(p
i/P)
Curvature = 0
Curvature = 1
Curvature = 5
The KinkedDemandCurve andPrice Rigidity
DosscheHeylen
Van den Poel
IntroductionMotivationKinked DemandPreview Findings
Data
SignRestrictions
Model
Estimation
Conclusions
The Kinked Demand CurveElasticity and Curvature
qiQ =
� piP
��ε with ε the demand elasticity
ε =� piP
�ε with ε the curvature or "super elasticity" ofdemand
0.10
0.05
0.00
0.05
0.10
0.15
0.20
1 0.8 0.6 0.4 0.2 0 0.2 0.4 0.6
LN(qi/Q)
LN(p
i/P)
Curvature = 0
Curvature = 1
Curvature = 5
Curvature = 10
The KinkedDemandCurve andPrice Rigidity
DosscheHeylen
Van den Poel
IntroductionMotivationKinked DemandPreview Findings
Data
SignRestrictions
Model
Estimation
Conclusions
The Kinked Demand CurveElasticity and Curvature
qiQ =
� piP
��ε with ε the demand elasticity
ε =� piP
�ε with ε the curvature or "super elasticity" ofdemand
0.10
0.05
0.00
0.05
0.10
0.15
0.20
1 0.8 0.6 0.4 0.2 0 0.2 0.4 0.6
LN(qi/Q)
LN(p
i/P)
Curvature = 0
Curvature = 1
Curvature = 5
Curvature = 10
Curvature = 5
The KinkedDemandCurve andPrice Rigidity
DosscheHeylen
Van den Poel
IntroductionMotivationKinked DemandPreview Findings
Data
SignRestrictions
Model
Estimation
Conclusions
The Kinked Demand CurveElasticity and Curvature
qiQ =
� piP
��ε with ε the demand elasticity
ε =� piP
�ε with ε the curvature or "super elasticity" ofdemand
0.9
0.95
1
1.05
1.1
1.15
1.2
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6
qi/Q
pi/P
Curvature = 0
Curvature = 1
Curvature = 5
Curvature = 10
Curvature = 5
The KinkedDemandCurve andPrice Rigidity
DosscheHeylen
Van den Poel
IntroductionMotivationKinked DemandPreview Findings
Data
SignRestrictions
Model
Estimation
Conclusions
The Kinked Demand CurveParameter Values
Elasticity: Curvature:
� ∂ ln( qiQ )∂ ln( piP )
= ε ∂ ln ε∂ ln( piP )
= ε
Parameter Values
CurvatureKimball (1995) 471Chari, Kehoe and McGrattan (2000) 385de Walque, Smets and Wouters (2006) 20/60Eichenbaum and Fisher (2004) 10/33Coenen and Levin (2004) 10/33Klenow and Willis (2006) 10Woodford (2005) 6.67Bergin and Feenstra (2000) 1.33
The KinkedDemandCurve andPrice Rigidity
DosscheHeylen
Van den Poel
IntroductionMotivationKinked DemandPreview Findings
Data
SignRestrictions
Model
Estimation
Conclusions
Preview of Findings
Evidence supports the kinked (concave) demand curve
Sensible curvature value is 4
Signi�cant fraction of products negative curvature (convexdemand) =) multi-sector sticky price models
No correlation between price elasticity/curvature and thesize or frequency of price adjustment
The KinkedDemandCurve andPrice Rigidity
DosscheHeylen
Van den Poel
Introduction
DataScanner DataDescriptive Stats
SignRestrictions
Model
Estimation
Conclusions
DataScanner Data
Potatoes
0.00
0.20
0.40
0.60
0.80
1.00
1.20
1.40
1.60
1.80
1 6 11 16 21 26 31 36 41 46 51 56 61 66 71 76 81 86
Time period
LN(e
uro/
pack
age)
5
6
7
8
9
10
11
12
13
LN (#
of p
acka
ges
sold
in o
utle
t 5)
Quantities (r.h.)Price excl. markdownsPrice incl. markdowns
The KinkedDemandCurve andPrice Rigidity
DosscheHeylen
Van den Poel
Introduction
DataScanner DataDescriptive Stats
SignRestrictions
Model
Estimation
Conclusions
DataScanner Data
Lemonade
0.90
1.00
1.10
1.20
1.30
1.40
1.50
1.60
1.70
1.80
1 6 11 16 21 26 31 36 41 46 51 56 61 66 71 76 81 86
Time period
LN(e
uro/
pack
age)
3
4
5
6
7
8
9
10
11
12
LN (#
of p
acka
ges
sold
in o
utle
t 5)
Quantities (r.h.)Price excl. markdownsPrice incl. markdowns
The KinkedDemandCurve andPrice Rigidity
DosscheHeylen
Van den Poel
Introduction
DataScanner DataDescriptive Stats
SignRestrictions
Model
Estimation
Conclusions
DataScanner Data
Anonymous euro area supermarket
Sample of 6 outlets
In our sample: 2274 items from 58 product categoriesDetailed transaction records: prices and quantities
Bi-weekly observations, January 2002 - April 2005
Prices are predetermined and equal across outlets
The KinkedDemandCurve andPrice Rigidity
DosscheHeylen
Van den Poel
Introduction
DataScanner DataDescriptive Stats
SignRestrictions
Model
Estimation
Conclusions
DataScanner Data: 40% of consumption
19/58 Product Categories
Drinks: tea, coke, chocolate milk, lemonade ...Food: corn�akes, tuna, smoked salmon ...Equipment: airing cupboard, knife ...Clothes and related: jeans, jacket ...Cleaning products: dishwasher detergent ...Leisure and education: hometrainer, football ...Personal care: plaster, nail polish ...Other: potting soil, cement, bath mat ...
The KinkedDemandCurve andPrice Rigidity
DosscheHeylen
Van den Poel
Introduction
DataScanner DataDescriptive Stats
SignRestrictions
Model
Estimation
Conclusions
DataDescriptive Statistics: Nominal Price Adjustment
Nominal Price Adjustment
Incl. markdownsPercentile 25% 50% 75%Average Absolute Size 5% 9% 17%Implied Median Price Duration (quarters) 0.4 0.9 2.8
Excl. markdownsAverage Absolute Size 3% 5% 8%Implied Median Price Duration (quarters) 2.4 6.6 ∞
The KinkedDemandCurve andPrice Rigidity
DosscheHeylen
Van den Poel
Introduction
DataScanner DataDescriptive Stats
SignRestrictions
Model
Estimation
Conclusions
DataDescriptive Statistics: Real Price and Quantity Adjustment
Real Price and Quantity Adjustment
Including markdownsPercentile 25% 50% 75%Average absolute ∆ ln(pi/P�) 6% 9% 15%Average absolute ∆ ln(qi/Q) 39% 59% 80%Standard Deviation ∆ ln(pi/P�) 7% 12% 21%Standard Deviation ∆ ln(qi/Q) 52% 77% 102%
The KinkedDemandCurve andPrice Rigidity
DosscheHeylen
Van den Poel
Introduction
DataScanner DataDescriptive Stats
SignRestrictions
Model
Estimation
Conclusions
DataDescriptive Statistics: Real Price and Quantity Adjustment
Real Price and Quantity Adjustment
Including markdownsPercentile 25% 50% 75%Correlation (∆ ln(pi/P�);∆ ln(qi/Q)) -0.49 -0.23 0.02% Supply Shocks to ∆ ln(pi/P�) (a) 48% 68% 86%% Supply Shocks to ∆ ln(qi/Q) (a) 45% 64% 81%
% Supply shocks ∆ ln(pi/P�) =∑SS(∆ ln(pi/P�)� πi ) 2
∑ (∆ ln(pi/P�)� πi ) 2� 100
Boivin, Giannoni and Mihov (2007): "idiosyncratic componentsof prices and quantities move mostly in opposite directions,suggesting that idiosyncratic shocks are supply-driven shocks."
The KinkedDemandCurve andPrice Rigidity
DosscheHeylen
Van den Poel
Introduction
Data
SignRestrictions
Model
Estimation
Conclusions
DataSign Restrictions
0.10
0.05
0.00
0.05
0.10
0.15
0.20
1 0.8 0.6 0.4 0.2 0 0.2 0.4 0.6
LN(qi/Q)
LN(p
i/P)
Curvature = 10
I
III
II
IV
εH
εL
The KinkedDemandCurve andPrice Rigidity
DosscheHeylen
Van den Poel
Introduction
Data
SignRestrictions
Model
Estimation
Conclusions
DataSign Restrictions
85 time series observations of ∆ ln(pit/P�t ) and∆ ln(qit/Qt )Quadrant I, II, III and IV: Exclude movements in samedirection (demand)
Quadrant I and III: Exclude movements in oppositedirection (supply)
Quadrant II and IV: Keep movements in oppositedirection (supply)
Di¤erence εH and εL
Including markdownsPercentile 25% 50% 75%Median εH� εL -3.58 1.26 7.47
The KinkedDemandCurve andPrice Rigidity
DosscheHeylen
Van den Poel
Introduction
Data
SignRestrictions
Model
Estimation
Conclusions
Econometric Model: Almost Ideal Demand SystemDeaton and Muellbauer (1980)
AIDS suits our purpose well:
Flexible w.r.t. estimating price elasticities
Simple, transparent, easy to estimate for a large numberof product categories
Most appropriate in a setup (like ours) where consumersbuy di¤erent items of given product category
Not necessary to specify characteristics of all goods
$ other models, e.g. mixed logit model (Berry et al., 1995)Still, the AIDS is not �exible enough.
The KinkedDemandCurve andPrice Rigidity
DosscheHeylen
Van den Poel
Introduction
Data
SignRestrictions
Model
Estimation
Conclusions
Econometric Model: Almost Ideal Demand SystemDeaton and Muellbauer (1980)
AIDS is not �exible enough:
Curvature is only function of price elasticity
Negative curvature (convex demand) is nearly impossible
A behavioral extension of the AIDS model:
AIDS describes optimal behavior assuming indi¤erencesurface is given, only captures standard substitution andincome e¤ects of price changes
Extension: allow for changes in indi¤erence surface whenprice deviates from a reference price (Tversky andKahneman, 1991)
The KinkedDemandCurve andPrice Rigidity
DosscheHeylen
Van den Poel
Introduction
Data
SignRestrictions
Model
Estimation
Conclusions
Econometric Model: Almost Ideal Demand SystemDeaton and Muellbauer (1980)
Behavioral extension of the AIDS:
si = αi +N
∑j=1
γij ln pj + βi ln�XP
�+
N
∑j=1
δij
�ln(pjP)�2
for i = 1, ...,N (items)
si = expenditure share of item i
X = total nominal expenditure on the group of itemsanalysed
pj = nominal price of item j
P = price index for the group
The KinkedDemandCurve andPrice Rigidity
DosscheHeylen
Van den Poel
Introduction
Data
SignRestrictions
Model
Estimation
Conclusions
Econometric Model: Almost Ideal Demand SystemDeaton and Muellbauer (1980)
(Positive) own price elasticity of demand:
εi (LA/B�AIDS ) = 1�γiisi+ βi �
2δii ln(piP )
si+ 2
N
∑j=1
δij ln(pjP)
Elasticity is function of the relative priceIn steady state:
εi (LA/AIDS ) = 1�γiisi+ βi
The KinkedDemandCurve andPrice Rigidity
DosscheHeylen
Van den Poel
Introduction
Data
SignRestrictions
Model
Estimation
Conclusions
Econometric Model: Almost Ideal Demand SystemDeaton and Muellbauer (1980)
Curvature of demand function:
εi (LA/B�AIDS ) =1εi
0B@ (εi � 1) (εi � 1� βi )�2δii (1�si )
si
+2(δii � siN
∑j=1
δij )
1CAεi (LA/AIDS ) =
(εi � 1)(εi � 1� βi )
εi
Without our extension, the curvature is:
Only a function of the price elasticity
Almost unavoidably positive (β is very close to zero)
The KinkedDemandCurve andPrice Rigidity
DosscheHeylen
Van den Poel
Introduction
Data
SignRestrictions
Model
EstimationIdenti�cationResults
Conclusions
Identi�cation
simt = αim +5
∑j=1
γij ln pjt + βi ln�XmtPmt
�+
5
∑j=1
δij
�ln(
pjtP�mt
)
�2+
5
∑j=1
ϕijCjt + λit + εimt
i = 1, ..., 5 (items) m = 1, ..., 6 (outlets) t = 1, ..., 86(time periods)
Cjt = circular dummy λit = time dummy for publicholiday
Impose standard restrictions: Homogeneity in prices,symmetry, adding up
The KinkedDemandCurve andPrice Rigidity
DosscheHeylen
Van den Poel
Introduction
Data
SignRestrictions
Model
EstimationIdenti�cationResults
Conclusions
Identi�cation/Estimation
simt = αim +5
∑j=1
γij ln pjt + βi ln�XmtPmt
�+
5
∑j=1
δij
�ln(
pjtP�mt
)
�2+
5
∑j=1
ϕijCjt + λit + εimt
Estimation method: SURpit is uncorrelated with the error term εimt :
Prices are predetermined and equal across all outletsPredictable demand shocks and item speci�ccharacteristics that may a¤ect prices are captured by timedummies and �xed e¤ects (they do not show up in theerror term)Robustness tests later support our choice for SUR
The KinkedDemandCurve andPrice Rigidity
DosscheHeylen
Van den Poel
Introduction
Data
SignRestrictions
Model
EstimationIdenti�cationResults
Conclusions
Estimation Results
Elasticity
0%
5%
10%
15%
20%
25%
1 0.5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 7 8 9 10 + 10
Freq
uenc
y
The KinkedDemandCurve andPrice Rigidity
DosscheHeylen
Van den Poel
Introduction
Data
SignRestrictions
Model
EstimationIdenti�cationResults
Conclusions
Estimation Results
Curvature
0%
2%
4%
6%
8%
10%
12%
40 25 15 10 8 6 5 4 3 2 1 0 1 2 3 4 5 6 8 10 15 25 40 +40
Freq
uenc
y
The KinkedDemandCurve andPrice Rigidity
DosscheHeylen
Van den Poel
Introduction
Data
SignRestrictions
Model
EstimationIdenti�cationResults
Conclusions
Estimation Results
40
20
0
20
40
2 2 6 10 14 18 22 26
Elasticity
Cur
vatu
re
The KinkedDemandCurve andPrice Rigidity
DosscheHeylen
Van den Poel
Introduction
Data
SignRestrictions
Model
EstimationIdenti�cationResults
Conclusions
Estimation Results
Elasticity and Curvature
Unconditional Conditional on3 < ε � 6
Median Elasticity 1.4 3.7Median Curvature 0.8 3.5Correlation (ε, ε) 0.12 0.02Fraction ε < 0 42% 8%N.obs. 666 101Considering literature:
Studies on price elasticity (Bijmolt et al., 2005; Chevalieret al., 2003)
Industrial organization markups (Domowitz et al., 1998;Barsky et al., 2000; Nevo, 2001)
) Price elasticity between 3 and 6. Therefore we concludecurvature around 4.
The KinkedDemandCurve andPrice Rigidity
DosscheHeylen
Van den Poel
Introduction
Data
SignRestrictions
Model
EstimationIdenti�cationResults
Conclusions
Estimation Results
Correlation with Nominal Adj. Stats
Including Markdowns Excluding MarkdownsFrequency Size Frequency Size
Elasticity 0.04 -0.09 -0.10 -0.15Curvature 0.02 0.00 0.00 0.02
The KinkedDemandCurve andPrice Rigidity
DosscheHeylen
Van den Poel
Introduction
Data
SignRestrictions
Model
Estimation
Conclusions
Conclusions
Evidence supports the kinked (concave) demand curve
Sensible curvature value is 4
Signi�cant fraction of products negative curvature (convexdemand) =) multi-sector sticky price models
No correlation between price elasticity/curvature and thesize or frequency of price adjustment
The KinkedDemandCurve andPrice Rigidity
DosscheHeylen
Van den Poel
Introduction
Data
SignRestrictions
Model
Estimation
Conclusions
Robustness
Re-estimation of the model using IV-method (3SLS).Since cost data are lacking and prices are equal acrossoutlets, we use lagged prices as instruments fo pit .
Introduction of more time dummies (seasonal) to captureadditional possible demand shifts
Allow for gadual demand adjustment to price changes byadding a lagged dependent variable
) Highly similar results, conclusions una¤ected
The KinkedDemandCurve andPrice Rigidity
DosscheHeylen
Van den Poel
Introduction
Data
SignRestrictions
Model
Estimation
Conclusions
Variable Demand Elasticities
Kinked Demand (εH vs. εL) Customer Markets (εSR vs. εLR )
Okun (�81) Phelps, Winter (�70)Woglom (�82) Warner, Barsky (�95)*Ball, Romer (�90) Chevalier et al. (�03)*Kimball (�95) Ravn et al. (�04)Chari et al. (�00) Nakamura, Steinsson (�05)Bergin, Feenstra (�00)Eichenbaum, Fisher (�04)Coenen, Levin (�04)Dotsey, King (�05)Burstein et al. (�05)Corsetti, Bergin (�05)
Note: the starred contributions test the theory using micro data.
The KinkedDemandCurve andPrice Rigidity
DosscheHeylen
Van den Poel
Introduction
Data
SignRestrictions
Model
Estimation
Conclusions
Price Markdowns and Stockpiling(Hendel and Nevo, �02 & �05)
Median item 8% of time marked down
27% of output during markdown
Static demand models overestimate (downward) priceelasticity
Markdowns correlated with mention in circular
Controlling for circular, lagged dependent variablestatistically & economically insigni�cant