The Kinked Demand Curve and Price Rigidity: Evidence from Scanner Data

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The Kinked Demand Curve and Price Rigidity
Evidence from Scanner Data

• Maarten Dossche
• (Ghent University National Bank of Belgium)
• Freddy Heylen
• (Ghent University, Sherppa)
• Dirk Van den Poel
• (Ghent University, Department of Marketing)
• Paper presented at the Conference on Price and
  Wage Rigidities in an Open Economy, National Bank
  of Belgium, October 2006

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Presentation Outline

• Broader context and motivation introducing the
  kinked demand curve
• Basic facts about our data
• Econometric model the Almost Ideal Demand
  System (Deaton-Muellbauer, 1980) and beyond
• Empirical analysis
• Econometric issues and specification
• Empirical results price elasticity and
  curvature
• Conclusions

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Broader context and motivation
Persistent effects of monetary shocks on real
output and inflation. (Christiano et al.,1999,
2005 Peersman, 2004.). The key role of price
rigidity

• Frictions to nominal price adjustment (Taylor,
  1980 Calvo, 1983
• Mankiw, 1985)

• Real price rigidity

• Real wage rigidity (Ball-Romer,1990
  Blanchard-Galí, 2006.).

• Firm specific factors of production and a high
  price elasticity
• of demand (Galí-Gertler, 1999 Woodford, 2003
  Altig et al., 2005)

• The kinked (concave) demand curve

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Introducing the kinked demand curve
Constant price elasticity of demand
(Dixit-Stiglitz, 1977)
? 3
price elasticity of demand
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Introducing the kinked demand curve
The kinked (concave) demand curve (Kimball, 1995)
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Introducing the kinked demand curve
The kinked (concave) demand curve (Kimball, 1995)
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Introducing the kinked demand curve
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Introducing the kinked demand curve

• Our contribution
• Does the kinked demand curve exist?
• Estimate the price elasticity of demand and
  especially
• its curvature

Allow for flexibility
? 3
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Presentation Outline

• Broader context and motivation introducing the
  kinked demand curve
• Basic facts about our data
• Econometric model the Almost Ideal Demand
  System (Deaton-Muellbauer, 1980) and beyond
• Empirical analysis
• Econometric issues and specification
• Empirical results price elasticity and
  curvature
• Conclusions

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Basic facts about the data

• Anonymous euro area supermarket, sample 6 outlets
• In our sample 2274 items from 58 product
  categories
• Detailed transaction records prices and
  quantities
• Bi-weekly observations, January 2002 April 2005
• Prices are predetermined and equal in each outlet

• Analysis of
• Size and frequency of price adjustment
• Importance of demand and supply shocks
• Asymmetry in demand sensitivity to price changes

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Basic facts nominal price adjustment

• Prices are predetermined
• High frequency of temporary price markdowns
• Price adjustment statistics

In between existing studies on US and Euro area
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Presentation Outline

• Broader context and motivation introducing the
  kinked demand curve
• Basic facts about our data
• Econometric model the Almost Ideal Demand
  System (Deaton-Muellbauer, 1980) and beyond
• Empirical analysis
• Econometric issues and specification
• Empirical results price elasticity and
  curvature
• Conclusions

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Econometric model The Almost Ideal Demand System
(Deaton and Muellbauer, 1980)

• Very good properties for our purpose
• Flexible with respect to estimating price
  elasticities
• Simple, transparent, easy to estimate for a large
  number of product categories
• Most appropriate in a setup (like ours) where
  consumers may buy different items of given
  product categories
• Not necessary to specify the characteristics of
  all goods

Other models, e.g. mixed logit model (Berry et
al., 1995)
Still, the AIDS is not flexible enough
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Econometric model The Almost Ideal Demand System
(Deaton and Muellbauer, 1980)
The AIDS model is not flexible enough (see below)

1. Curvature is a very restrictive function of price
   elasticity
2. Negative curvature (convex demand) is almost
   impossible

A behavioral extension of the AIDS model

1. AIDS describes optimal behavior assuming
   indifference surface to be given, only captures
   standard substitution and income effects of price
   changes.
2. Extension allow for changes in indifference
   surface when price deviates from a reference
   price (Tversky-Kahneman, Okun, Rotemberg,)

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Econometric model The Almost Ideal Demand System
(Deaton and Muellbauer, 1980)
Behavioral extension of the AIDS model
for i 1,.. N (goods) and t 1,. T (time
periods)
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Econometric model The Almost Ideal Demand System
(Deaton and Muellbauer, 1980)
?(Positive) own price elasticity of demand
In steady state
Elasticity can vary in relative price !
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Econometric model micro foundations
? Curvature of demand function

• Note ! Without our extension, the curvature
• is a direct function of the estimated price
  elasticity
• is almost unavoidably positive (for positive
  price elasticity)
• (beta is very close to zero)

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Presentation Outline

• Broader context and motivation introducing the
  kinked demand curve
• Basic facts about our data
• Econometric model the Almost Ideal Demand
  System (Deaton-Muellbauer, 1980) and beyond
• Empirical analysis
• Econometric issues and specification
• Empirical results price elasticity and
  curvature
• Conclusions

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Identification / Estimation
i 1,5 (goods) m 1,.6 (outlets)
t 1,.. 86 (time periods) Cjt circular
(folder) dummy ??it time dummy for public
holiday
Impose standard restrictions (homogeneity in
prices, symmetry, adding up)
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Identification / Estimation
Estimation method SUR Motivation pit is
uncorrelated to the error term ?imt

• Prices are predetermined and equal over all 6
  outlets
• Predictable demand shocks and item specific
  characteristics that
• may affect prices are captured by time dummies
  and fixed effects (they
• do not show in the error term)
• Robustness test later supports our choice for
  SUR.

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Estimation results (histogram)
N.Obs. 666
Median 1.4
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Estimation results (histogram)
N.Obs. 666
Median 0.8 / About 40 of estimated
curvatures are negative.
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Estimation results
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Estimation results

• Considering existing literature
• empirical studies on the price elasticity of
  demand (Bijmolt et al., 2005)
• Industrial organization studies of price-cost
  mark-ups (Domowitz et al., 1988 Konings et al.,
  2001 Dobbelaere, 2004)
• Price elasticity of demand is between 3 and 6.

Our conclusion curvature is around 4.
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Estimation results
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Conclusions

• Evidence supports the kinked (concave) demand
  curve in macro models

• Sensible curvature value is 4

• Significant fraction of products negative
  curvature (convex demand) ? two sector models?

• No correlation between price elasticity /
  curvature and the size or frequency of price
  adjustment

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Estimation results robustness

• Re-estimation of the model using an IV-method
  (3SLS). Since cost data are lacking and prices
  are equal across outlets, we use lagged prices as
  instruments for pit .

• Introduction of more time dummies (seasonal
  dummies) to capture additional possible demand
  shifts.

• Allow for gradual demand adjustment to price
  changes by adding a lagged dependent variable of
  the model.

Highly similar results, conclusions unaffected.