The Kinked Demand Curve and Price Rigidity: … Kinked Demand Curve and Price Rigidity Dossche Heylen Van den Poel Introduction Motivation Kinked Demand Preview …Published in: The

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.


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)


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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)


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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


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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


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qiQ =

� piP


ε =� piP


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


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qiQ =

� piP


ε =� piP


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


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qiQ =

� piP


ε =� piP


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


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qiQ =

� piP


ε =� piP


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


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qiQ =

� piP


ε =� piP


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


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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


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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


DosscheHeylen

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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


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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


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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


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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 ...


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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 ∞


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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%


DosscheHeylen

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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."


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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


DosscheHeylen

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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


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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.


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Conclusions


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)


DosscheHeylen

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Conclusions


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


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(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


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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)


DosscheHeylen

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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


DosscheHeylen

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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


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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


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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


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Estimation Results

40

20

0

20

40

2 2 6 10 14 18 22 26

Elasticity

Cur

vatu

re


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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.


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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


DosscheHeylen

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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


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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


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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.


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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

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The Kinked Demand Curve and Price Rigidity: … Kinked Demand Curve and Price Rigidity Dossche Heylen Van den Poel Introduction Motivation Kinked Demand Preview …Published in: The