Measuring and Testing Advertising-Induced Rotation in the Demand Curve



Table 1. Decomposition of Advertising’s Effects on the Own-Price Elasticities with Fixed Prices

Model Name
(Model version in parenthesis)

Own - Price Elasticity I

______η______

ln ηi / ln Ai

=Rotation effect - Shift effect

Rotation effect
ln i / ln Ai

Shift effect
αii

Without Interaction____________________________________________________________________________________________________________________________________________

Linear (A)

- cii( pi / qi )

___________________-αii___________________

0

αii

Semi-log (B)

_____________- cii / qi_____________

___________________-αii___________________

0

αii

Double-log (C)

______________- cii______________

0

_________α_________

αii

Rotterdam (D)

- cii / w

Σ^w7αy∙ - αii
____________________]______________________________________


________________________________]__________________________________________

αii

AIDS (E)

-(cii / wi-1)

ciiwα -αii)

i______________________

___________________cii - wi___________________

n

ciiwjα-jj -wiαii

i_________________________

_________________________cii - wi_________________________

V

With interaction________________________________________________________________________________

Interaction-related

Shift-related__________

Linear (F)

-( cii + γiAi)( pi / qi )

YiAi
--—--αii
_______________
cii + YiA_____________________

YiAi

( cii + YiAi)

0

αii

Semi-log (G)

-( cii + γiln Ai )/ qi

------Yi--αii
cii + γi ln Ai

Yi

cii + Yiln Ai

0

αii

Double-log (H)

-( cii+ γiln Ai)

Yi

________________( cii + Yiln Ai)________________

Yi

( cii + Yiln Ai)

αii

αii

Rotterdam (I)

-( cii+ γidln Ai)/ wi

n

------γ------+ wiαii - αii
( cii + γid ln Ai)                    ii

in it                i *           j

Yi

(cii + Yid lnAi )

Σ w,αi
j

αii

AIDS (J)

-((cii + γi lnA1 )/ wi -1)

n

γi + (cii + YilnAi)(wjαij ii)

_____________________________i___________________

n

Yi + Yi lnAi wjαy

___________________i__________

n

cii Σ wiαii - wiαιι

__i_________

αii

____________(cii + Yiln Ai - wi )____________

(cii + YilnAi -wi)

(cii + Yiln Ai - wi )

20



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