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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) = 3 : curvature or “super price elasticity of demand” : price elasticity of demand

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**Introducing the kinked demand curve…**

The kinked (concave) demand curve (Kimball, 1995) = 3 : curvature or “super price elasticity of demand” : price elasticity of demand

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**Introducing the kinked demand curve…**

The kinked demand curve in calibrated macro-models

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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) Curvature is a very restrictive function of price elasticity Negative curvature (convex demand) is almost impossible A “behavioral” extension of the AIDS model… AIDS describes optimal behavior assuming indifference surface to be given, only captures standard substitution and income effects of price changes. 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 : / 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.

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