2016 8 29 1 4 Variety Expansion Effects by Feenstra 1994 1 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
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 1980 2 Love of Variety Romer 3 CES CES? Red Bus, Blue Bus 1 Dix and Stiglz 1977 Love of Variety 2 Krugman, Paul. 1980. Scale Economies, Product Differeiation, and the Pattern of Trade, American Economic Review, Vol. 70, No. 5, pp. 950-959. 3 P.Romer 1987 Growth Based on Increasing Returns Due to Specialization, American Economic Review, 772, pp. 56-52. P. Romer 1990 Endogenous Techological Change, Journal of Polical Economy, 98, 5, pp S71-S012. 2
IIAIndependence of Irreleva Alternatives Love of Variety CES PC CES Love of Variety Poduct Differeiation Hotelling 1929 4 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. 1979 Variety, Equie and Efficiency, New York: Columbia Universy Press. Salop, Ste. 1979 Monopolistic Competion wh Outside Goods, Bell Journal of Economics, 10, 141-156. 3
Feenstra 1994 5 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 157-77, March. 4
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
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 i0 1 1 0 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
COLI Sato-Vartia COLI Weights Feenstra 1994 3 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
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 1 + + σ 1 1 + 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 + 1 + 1 + σ ln p ln p kt + 1 1 + σ 1 + σ ln p ln p kt 1 + σ ln w ln w kt 1 + σ ln w ln w kt 8
σ mome ε i,t δ Feenstra 1994 ε i,t δ ln p ln p kt 2 1 σ 1 1 + σ 1 + 1 + σ + 1 + σ 1 σ 1 ε i,t δ 1 + σ + 1 + 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
i.i.d. u i u i 6 7 X 1i X 1i u i θ 1 θ 2 Feenstra 1994 4 Broda and Weinstein 2010 Broda and Weinstein 2010 8 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 w3610. 7 Abe et al. 2016 8 Broda, C. and Weinstein, D.E. 2010. Product creation and destruction:evidence and price implications. American Economic Review, 100, 691 723. 10
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 1994 11