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 η_i / ∂ ln A_i =Rotation effect - Shift effect	Rotation effect ∂ ln ∆ _i / ∂ ln A_i		Shift effect ^αii
Without Interaction____________________________________________________________________________________________________________________________________________
Linear (A)	^-^cii⁽ pi / qi )	___________________^-^αii___________________	0		^αii
Semi-log (B)	_____________^-^cii / qi_____________	___________________^-^αii___________________	0		^αii
Double-log (C)	______________^{- c}ii______________	0	_________^α_________		^αii
Rotterdam (D)	^-^cii / ^w	Σ^^w7^α_y∙ - ^αii ____________________]______________________________________	∑ "Л ________________________________]__________________________________________		^αii
AIDS (E)	^-⁽^cii / wi^-¹⁾	cii∑w^{α -}αii) i______________________ ___________________^cii ^- wi___________________	n ^cii∑wj^α-jj ^-wi^αii i_________________________ _________________________^cii ^- wi_________________________		V
With interaction________________________________________________________________________________			Interaction-related	Shift-related__________
Linear (F)	^-⁽^cii + γiAi⁾⁽ pi / qi )	YiAi --—--α_ii_______________^cii ⁺ YiA_____________________	YiAi ⁽^cii ⁺ YiAi)	0	^αii
Semi-log (G)	^-⁽^cii ⁺ γi^ln Ai )/ qi	------Yi--αii cii + γi ln Ai	Yi ^cii ⁺ Yi^ln Ai	0	^αii
Double-log (H)	^-⁽^cii⁺ γi^ln Ai)	Yi ________________⁽^cii ⁺ Yi^ln Ai)________________	Yi ⁽^cii ⁺ Yiln Ai)	^αii	^αii
Rotterdam (I)	^-⁽^cii⁺ γi^d^ln Ai)/ wi	n ------^γ------+ ∑ w_iα_ii - α_ii( cii + γid ln Ai) ii in it i * j	Yi ⁽^cii ⁺ Yi^d^lnAi )	Σ w,α_ij	^αii
AIDS (J)	-((cii + γi lnA₁ )/ wi -1)	n γi ^{+ (}^cii ⁺ Yi^lnAi)(∑wj^αi_j ^-αii) _____________________________i___________________	n Yi ⁺ Yi ^lnAi ∑wj^αy ___________________i__________	n ^cii Σ w_i^αi_i ^- wi^αιι __i_________	^αii
AIDS (J)	-((cii + γi lnA₁ )/ wi -1)	____________⁽^cii ⁺ Yi^ln Ai ^- wi )____________	⁽^cii ⁺ Yi^lnAi ^-wi)	⁽^cii ⁺ Yi^ln Ai ^- wi )	^αii

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