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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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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

Presentation Outline

3

Broader context and motivation…

- Frictions to nominal price adjustment (Taylor, 1980; Calvo, 1983;

Mankiw, 1985)…

- Real price rigidity

- Firm specific factors of production and a high price elasticity

of demand (Galí-Gertler, 1999; Woodford, 2003; Altig et al., 2005)

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

Persistent effects of monetary shocks on real output and inflation…. (Christiano et al.,1999, 2005; Peersman, 2004;….).

The key role of price rigidity

- The kinked (concave) demand curve

4

Introducing the kinked demand curve…

Constant price elasticity of demand

(Dixit-Stiglitz, 1977)

PQq pii

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

-2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2

ln(qi/Q)

ln(P

i/P)

.

= 3

: price elasticity of demand

5

Introducing the kinked demand curve…

The kinked (concave) demand curve

(Kimball, 1995)

PQq pii

Ppi

: curvature or “super price elasticity of demand”

: price elasticity of demand

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

-2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2

ln(qi/Q)

ln(P

i/P)

.

= 3

02

6

Introducing the kinked demand curve…

The kinked (concave) demand curve

(Kimball, 1995)

PQq pii

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

-2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2

ln(qi/Q)

ln(P

i/P)

.

= 3

: curvature or “super price elasticity of demand”

: price elasticity of demand

Ppi

024

7

Introducing the kinked demand curve…

The kinked demand curve in calibrated macro-models

Price elasticity and curvature of demand in the literature

ε(1)

Kimball (1995) 11 471

Chari et al. (2000) 10 385

Bergin and Feenstra (2000) 3 1.33

Eichenbaum and Fisher (2004) 11 10, 33

Coenen and Levin (2004) 5-20 10, 33

de Walque, Smets and Wouters (2005) 3 20, 60

Woodford (2005) 7.67 6.67

Klenow and Willis (2006) 5 10

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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…

= 3

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

-2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2

ln(qi/Q)

ln(p

i/P

) .

Allow for flexibility…

0242

9

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

Presentation Outline

10

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 :

Nominal Price Adjustment Statistics, bi-weekly data, Jan. 2002-April 2005, 2274 items from 58 product categories

Incl. markdowns Excl. markdownsMedian Median

Average Absolute Size 9% 5%

Implied Median Price Duration 0.9 6.6(quarters)

In between existing studies on US and Euro area…

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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

Presentation Outline

13

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

Very good properties for our purpose :

(i) Flexible with respect to estimating price elasticities;

(ii) Simple, transparent, easy to estimate for a large number of product categories;

(iii) Most appropriate in a setup (like ours) where consumers may buy different items of given product categories;

(iv) 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)

(i) Curvature is a very restrictive function of price elasticity

(ii) Negative curvature (convex demand) is almost impossible

A “behavioral” extension of the AIDS model…

(i) AIDS describes optimal behavior assuming indifference surface to be given, only captures standard substitution and income effects of price changes.

(ii) 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)

N

1j

2N

1j*t

jtij*

t

tijtijiit

P

pln

P

Xlnplns

group for theindex price :P

j good of price nominal :p

analysed goods of group on the eexpenditur nominal total:X

i good of share eexpenditur : s

*t

jt

t

it

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

ii

iii s

1

*jN

1jij

i

*iii

ii

iii

P

pln2

s

)P/pln(2

s1

In steady state :

(Positive) own price elasticity of demand

Elasticity can vary in relative price !

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Curvature of demand function

Econometric model: micro foundations

N

jijiii

i

iiiiii

ii s

s

s

1

)(2)1(2

)1(11

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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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

Presentation Outline

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Identification / Estimation

imtit

5

1jjtij

5

1j

25

1j*mt

jtij*

mt

mtijtijimimt

C

P

pln

P

Xlnplns

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

imtit

5

1jjtij

5

1j

25

1j*mt

jtij*

mt

mtijtijimimt

C

P

pln

P

Xlnplns

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)

Elasticity

0%

5%

10%

15%

20%

25%

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Fre

qu

ency

-

-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

Median : 1.4

N.Obs. 666

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Estimation results (histogram)

Curvature

0%

2%

4%

6%

8%

10%

12%

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Fre

quen

cy -

-40 -15 -8 -5 -3 -1 0 1 3 5 8 15 40

Median : 0.8 / About 40% of estimated curvatures are negative.

N.Obs. 666

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Estimation results

R2 = 0.28N.Obs. 628

-40

-20

0

20

40

-2 2 6 10 14 18 22 26

Elasticity

Curv

ature

-

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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.

Unconditional Conditional on

ε > 1 ε > 3 1 < ε ≤ 3 3 < ε ≤ 6 6 < ε ≤ 10

Median Elasticity 1.4 2.4 4.2 1.8 3.7 7.8

Median Curvature 0.8 1.7 5.7 0.8 3.5 6.8

Correlation (ε, ) 0.12 0.45 0.4 0.33 0.02 0.53

Fraction <0 41% 26% 6% 15% 8% 0%

N.obs. 666 410 144 266 101 23

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Estimation results

Correlation with nominal price adjustment statistics

Including Markdowns Excluding MarkdownsFrequency Size Frequency Size

Elasticity 0.04 -0.09 -0.1 -0.15Curvature 0.02 0 0 0.02

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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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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 .

Estimation results : robustness

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.