n 1 this gives n 1 equations but n 1 unknowns g

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Unformatted text preview: p p ¯ for each p ∈ [p , p ). EC 105. Industrial Organization. Fall 2011 (Matt Shum HSS, Lecture 12:Institute and price dispersion California Search of Technology) September 9, 2011 22 / 25 Sequential search model Estimation: sequential model Observe prices p1 , . . . , pn (order in increasing order, so p = pn ). ¯ Indifference conditions, evaluated at each price, are: (¯ − r ) ∗ (1 − G (¯)) = (pi − r ) ∗ (1 − G (pi )), p p i = 1, . . . , n − 1 This gives n − 1 equations, but n + 1 unknowns: G (pi ) for i = 1, . . . , n as well as r . Define α = 1 − G (¯): percentage of people who don’t search. p Assume that search distribution is Gamma distribution. (Eq. (13) in paper). Estimate model parameters (δ1 , δ2 , α, r ) by maximum likelihood (Eq. 9) EC 105. Industrial Organization. Fall 2011 (Matt Shum HSS, Lecture 12:Institute and price dispersion California Search of Technology) September 9, 2011 23 / 25 Sequential search model Results: sequential search model ss # Hong & Shum; art. # 2; RAND Journal of Economics vol. 37(2) 268 / THE RAND JOURNAL OF ECONOMICS TABLE 3 Estimates of Sequential-Search Model Mediana Selling δ1 δ2 Search Cost Cost r αb Fc−1 (1 − α ; θ ) Value Stokey-Lucas .46 (.02) 1.55 (.03) 29.40 (1.45) 22.90 (1.31) .58 19.19 31.13 Lazear .40 (.01) 1.15 (.01) 16.37 (1.00) 11.31 (.79) .69 4.56 34.35 Billingsley .25 (.01) 2.01 (.04) 9.22 (.94) 65.37 (.83) .51 8.43 23.73 Duffie .21 (.02) 4.57 (.29) 10.57 (2.01) 28.24 (1.63) .54 7.00 18.93 Product Log-L Note: Including shipping and handling charges. Standard errors in parentheses. δ1 and δ2 are parameters of the gamma distribution; see equation (13). a As implied by estimates of the parameters of the gamma search-cost distribution. b Proportion of consumers with reservation price equal to p , implied by estimate of r (see equation (11)). search cost for the Stokey-Lucas text consistent with the nonsequential-search model (as reported in the bottom panel of Table 2) is roughly $2.32, whereas the corresponding number for the sequential-search model (as reported in Table 3) is $29.40, over 10 times higher. Moreover, the estimates of r , the selling costs, are uniformly lower across the four books than the corresponding estimates in the nonsequential-search model.19 At first glance, the larger search-cost magnitudes for the sequential-search model might lead one to support the nonsequential-search model as a better descriptor of search behavior in the markets we consider. As pointed out by Morgan and Manning (1985), nonsequential- EC 105. Industrial Organization. Fall 2011 (Matt Shum HSS, Lecture 12:Institute and price dispersion California Search of Technology) September 9, 2011 24 / 25 Sequential search model Additional empirical evidence Online book markets (redux) Gasoline markets EC 105. Industrial Organization. Fall 2011 (Matt Shum HSS, Lecture 12:Institute and price dispersion California Search of Technology) September 9, 2011 25 / 25...
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