2016 (8) Variety Expansion Effects by Feenstra (1994) 1 Variety Effects Dixit and Stiglitz (1977) CES n n? n t U t = ( nt i=1 σ > 1, a it > 0,

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1 Variety Expansion Effects by Feenstra Variety Effects Dix and Stiglz 1977 CES n n? n t U t σ > 1, a > 0, σ a q σ n a 1 σ a p q U t P t E U t, p t U t P t U t V p, I I t a σ p 1 σ a σ p 1 σ 1 σ 1 1

2 a a, p 1 V p, I I t a σ p 1 σ I t a σ I t n t a σ I t n 1 t a σ σ 1 n t 1 n t variety CES Love of Variety CES Love of Variety 1 Krugman Love of Variety Romer 3 CES CES? Red Bus, Blue Bus 1 Dix and Stiglz 1977 Love of Variety 2 Krugman, Paul Scale Economies, Product Differeiation, and the Pattern of Trade, American Economic Review, Vol. 70, No. 5, pp P.Romer 1987 Growth Based on Increasing Returns Due to Specialization, American Economic Review, 772, pp P. Romer 1990 Endogenous Techological Change, Journal of Polical Economy, 98, 5, pp S71-S012. 2

3 IIAIndependence of Irreleva Alternatives Love of Variety CES PC CES Love of Variety Poduct Differeiation Hotelling Dix and Stiglz 1977 CES Love of variety Love of Variety 4 Hotelling, Harold 1929 Stabily in Competion, The Economic Journal, 39,4157. Lancaster, K Variety, Equie and Efficiency, New York: Columbia Universy Press. Salop, Ste Monopolistic Competion wh Outside Goods, Bell Journal of Economics, 10,

4 Feenstra COLI 2 Feenstra 1994 CES E 1, p t P t a σ p 1 σ 1 σ t t 1 t I t I Ø a a a i P t a σ p 1 σ 1 σ t I t P t p t, I t a σ p 1 σ 1 σ COLI Feenstra 1994 P t p t, I t P t p t 1, I t 1 P I F S P t p t, I t P t p t 1, I t 1 λ r P I sv λt λ t 1 p i,rx i,r r p i,r x i,r P I sv : Sato-Vartia COLI for I P I sv Sato-Vartia COLI COLI Feenstra COLI Sato-Vatia COLI λ- Ratio λ t t σ > 1 λ t λ t 1 5 Feenstra, Robert C, 1994 New Product Varieties and the Measureme of Iernational Prices, American Economic Review, vol. 841, pages , March. 4

5 Feenstra COLI λ-ratio COLI i a a i a p w P t P t a 1 σ p 1 σ σ P t a σ p 1 σ P t a p w 1 P t p t, I t P t p t 1, I t 1 P t p t, I t P t p t 1, I t 1 1 σ 1 a p w a 1 p 1 w 1 1 p 1 w p 1 w 1 p p 1 1 w w 1 i w I w w I t w I t p i,r x i,t j I t p j,t x j,t p i,r x i,t j I p i,rx i,t j I t p j,t x j,t p i,r x i,t w I j I p j,tx j,t w I λ t j I p j,tx j,t j I p i,rx i,t j I t p j,t x j,t j I p j,tx j,t j I t p j,t x j,t P t p t, I t P t p t 1, I t 1 p w I λ t p 1 w 1 I λ t 1 5

6 s i P t p t, I t P t p t 1, I t 1 λt λ t 1 s i p p 1 si w I s i w 1 I w i1 w i0 / ln w i1 ln w i0 n w i1 w i0 / ln w i1 ln w i0 p si P I sv p 1 ln w I w 1 I si σ 1 σ 1 σ 1 s i w I s i w 1 I ln w I ln w 1 I w i1 w i0 / ln w i1 ln w i0 n w i1 w i0 / ln w i1 ln w i0 ln w I ln w 1 I w i1 w i0 n w i1 w i0 / ln w i1 ln w i0 w i1 w i0 w i1 w i w I s i 1 w 1 I P t p t, I t P t p t 1, I t 1 λt P I sv λ t 1 Feenstra 1994 COLI COLI 6

7 COLI Sato-Vartia COLI Weights Feenstra i a w a 1 σ p 1 σ Pt ln w 1 σ ln a + 1 σ ln p + σ 1 ln P t ln w Φ t σ 1 ln p + ε i,t Φ t σ 1 ln P t ε i,t 1 σ ln a ln p ln q + ξ > 0 q i ξ ε i,t w p q E t ln w ln p + ln q ln E t ln q ln w ln p + ln E t ln q ln w ln p + ln E 7

8 ln p ln w ln p + ln E + ξ 1 + ln p ln w + ln E + ξ ln w 1 + ln p ln E ξ σ σ ln w 1 + ln p ln E ξ Φ t σ 1 ln p + ε i,t ln p ln E + Φ t + ε i,t + ξ ln p ln E + Φ t + ε i,t + ξ ln p ln E + Φ t + ξ 1 + σ 1 + σ + ξ 1 + σ δ ln E + Φ t Ψ t 1 + σ ln p Ψ t + δ + ε i,t 1 + σ ε i,t 1 + σ ε i,t ln w Φ t + σ 1 ln p σ Φ t Ψ t Feenstra 1994 k k ε i,t ln w ln w kt + σ 1 ln p ln p kt δ ln p ln p kt ε i,t 1 + σ σ σ ln p ln p kt σ 1 + σ ln p ln p kt 1 + σ ln w ln w kt 1 + σ ln w ln w kt 8

9 σ mome ε i,t δ Feenstra 1994 ε i,t δ ln p ln p kt 2 1 σ σ σ σ 1 σ 1 ε i,t δ 1 + σ σ 1 + σ σ 1 ln w ln w kt 2 ln p ln p kt 2 + ln w ln w kt 2 Y ln p ln p kt 2 X 1i,t ln w ln w kt 2 X 2i,t ln w ln w kt ln p ln p kt ln p ln p kt ln w ln w kt σ ln p ln p kt ln w ln w kt 1 + σ Y θ 1 X 1i,t + θ 2 X 1i,t + u 1 + σ u ε i,t δ 1 σ 1 θ 1 1 σ 1 1 σ θ 2 1 σ 1 X 1i,t X 2i,t u ε i,t δ ε i,t δ u Y i θ 1 X 1i + θ 2 X 1i + u i 9

10 i.i.d. u i u i 6 7 X 1i X 1i u i θ 1 θ 2 Feenstra Broda and Weinstein 2010 Broda and Weinstein Feenstra 1994 COLI POSPoi of Sales CES Broda and Weinstein 2010 λ-ratio Broda and Weinstein COLI P I BW g G [ b g P I sv λbt λ bt 1 ] Φtw b σwb 1 λgt λ gt 1 σbg 1 Φ tb g λ st s g, b σw b σb g 6 Feenstra 1991 New Goods and Index Numbers: U.S. Import Prices, NBER Working Paper w Abe et al Broda, C. and Weinstein, D.E Product creation and destruction:evidence and price implications. American Economic Review, 100,

11 Φ tb s Φ tw s Sato-Vartia Φ tw s w b1 w b0 / ln w b1 ln w b0 b s w b1 w i0 / ln w b1 ln w b0 Weight Feenstra1994 Feenstra

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