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Demand and Supply of Differentiated Products Demand and supply of differentiated products Paul Schrimpf Demand and supply of differentiated products Paul Schrimpf UBC Economics 567 January 28, 2021 Demand and supply of differentiated products 1 Introduction Paul Schrimpf Introduction 2 Demand in product space Demand in product space Demand in 3 Demand in characteristic space characteristic space Early work Early work Model Model Model Estimation and Model identification Aggregate product Estimation and identification data Estimation steps Aggregate product data Pricing equation Estimation steps Micro data Pricing equation References Micro data References 4 References Demand and supply of differentiated products References Paul Schrimpf Introduction Demand in product space Demand in • Reviews: characteristic space • Ackerberg et al. (2007) section 1 (these slides use their Early work notation) Model Model • Aguirregabiria (2019) chapter 2 Estimation and identification • Reiss and Wolak (2007) sections 1-7, especially 7 Aggregate product data • Classic papers: Estimation steps Pricing equation • Berry (1994) Micro data • References Berry, Levinsohn, and Pakes (1995) References Demand and supply of differentiated products Paul Schrimpf Introduction Demand in product space Demand in Section 1 characteristic space Early work Model Model Introduction Estimation and identification Aggregate product data Estimation steps Pricing equation Micro data References References Demand and supply of differentiated products Introduction Paul Schrimpf Introduction Demand in product space • Typical market for consumer goods has many Demand in characteristic differentiated, but similar products, e.g. space Early work • Cars Model • Model Cereal Estimation and identification • Differentiated products are a source of market power Aggregate product data Estimation steps • Having many products can result in many parameters Pricing equation Micro data creating estimation difficulties and requiring References departures from textbook demand and supply models References Demand and supply of differentiated products Motivation Paul Schrimpf Introduction Demand in product space • Counterfactuals that do not change production Demand in characteristic technology space Early work • Mergers Model • Model Tax changes Estimation and identification • Effects of new goods Aggregate product data Estimation steps • Cost-of-living indices Pricing equation Micro data • Product differentiation and market power References • Cross-price elasticities References Demand and supply of differentiated products Paul Schrimpf Introduction Demand in product space Demand in Section 2 characteristic space Early work Model Demand in product space Model Estimation and identification Aggregate product data Estimation steps Pricing equation Micro data References References Demand and supply of differentiated products Demand in product space 1 Paul Schrimpf • J products, each treated as separate good • Introduction Classical demand, Demand in product space q1 =D1(p1, ..., pJ, z1, η1; β1) Demand in . characteristic . = . space Early work Model qJ =DJ(p1, ..., pJ, zJ, ηJ; βJ), Model Estimation and identification Aggregate product data Estimation steps and supply (firms’ first-order conditions for prices): Pricing equation Micro data p =g (q , ..., q , w , ν ; θ ) References 1 1 1 J 1 1 1 . References . = . d pJ =gJ(q1, ..., qJ, wJ, νJ; θJ), where Demand and supply of differentiated products Demand in product space 2 Paul Schrimpf Introduction • Demand in pj = price product space • qj = quantity Demand in • z = observed demand shifter characteristic j space • ηj = unobserved demand shock Early work Model • βj = demand parameters Model • Estimation and wj = observed supply shifter identification • Aggregate product νj = unobserved supply shock data • Estimation steps θj = supply parameters Pricing equation Micro data • Dj typically parametrically specified, e.g. References References ln qj = βj0 + βj1p1 + ··· + βjJpJ + βjy ln y + Z1γ + νj Demand and supply of differentiated products Demand in product space Paul Schrimpf • Use reduced form to find instruments Introduction q q1 =Π1 (Z, W, ν, η; β, θ) Demand in . product space . =. Demand in q characteristic q =Π (Z, W, ν, η; β, θ) space J J Early work p Model p1 =Π1 (Z, W, ν, η; β, θ) Model Estimation and . identification . =. Aggregate product data p Estimation steps pJ =ΠJ (Z, W, ν, η; β, θ) Pricing equation Micro data References • Cost shifters of product j excluded from demand and References supply of product k, but in reduced form • Cost data often not available • If available, unlikely to be product specific • Attributes of other products • Hausman (1996) uses prices of other products • Hard to justify, especially with prices Demand and supply of differentiated products Demand in product space 1 Paul Schrimpf • Advantages of product space: Introduction • Demand in Flexible substitution patterns product space • Does not require detailed product attribute data Demand in characteristic • Problems with product space: space Early work 1 Representative agent and aggregation issues Model • With heterogeneous preferences, aggregate market Model Estimation and demand need not meet restrictions on individual identification Aggregate product demand derived from economic theory data Estimation steps • Cannot use restrictions easily to improve estimates Pricing equation • Can use simulation to aggregate (Pakes, 1986) Micro data 2 References 2 Too many parameters, O(J ) References • Can limit by restricting cross-price elasticities, e.g. Pinkse, Slade, and Brett (2002) 3 Too many instruments needed, J 4 Cannot analyze new goods Demand and supply of differentiated products Paul Schrimpf Introduction Demand in product space Demand in Section 3 characteristic space Early work Model Model Demand in characteristic space Estimation and identification Aggregate product data Estimation steps Pricing equation Micro data References References Demand and supply of differentiated products Demand in characteristic space Paul Schrimpf Introduction Demand in • Motivation: product space • Why do firms differentiate products? Demand in • characteristic Because consumers have heterogeneous tastes for space product characteristics Early work Model • E.g. cars: tastes for size, safety, fuel efficiency, etc Model Estimation and • identification Main idea: model consumer preferences for Aggregate product data characteristics and treat products as bundles of Estimation steps Pricing equation characteristics Micro data • Early work: Lancaster (1971), McFadden (1973) References References • Key extension to early work: Berry, Levinsohn, and Pakes (1995) Demand and supply of differentiated products Early work in characteristic Paul Schrimpf space • Introduction Consumer chooses one or none of J products Demand in • Utility of consumer i from product j product space Demand in uij = xjβ + εij characteristic space with εij iid across i and j (usually Type I extreme value) Early work Model • Implies aggregate demand (for logit) Model Estimation and identification exp(xjβ) Aggregate product qj = PJ data 1 + exp(x β) Estimation steps k=1 k Pricing equation Micro data • Problem: restrictive substitution “independence of References irrelevant alternatives” References • Two goods with the same shares have the same cross price elasticities with any third good (think about a luxury and bargain good with equal shares) • Goods with same shares should have same markups • Solution: add heterogeneity in β and/or allow correlation across j in εij Demand and supply of differentiated products Model 1 Paul Schrimpf Introduction Demand in product space • Consumers i, goods j, markets t Demand in • characteristic Utility: (include good 0 = buy nothing) space Early work unobserved Model z}|{ unobserved Model z}|{ Estimation and uijt = U( ˜xjt , ξjt , zit , νit , pjt ; θ) identification |{z} Aggregate product |{z} |{z} data observed observed observed Estimation steps Pricing equation Micro data RK RR RL References • xjt = (˜xjt, pjt)) ∈ , zit ∈ , νit ∈ References • Choose j if uijt > uikt ∀k ̸= j Demand and supply of differentiated products Model 1 Paul Schrimpf • Usually U(·) linear: Introduction 1×K K×1 1×1 Demand in z}|{ z }| { z}|{ product space u = x θ + ξ +ε ijt jt |{z}it jt ijt Demand in o u characteristic =θ¯+θ zit+θ νit space Early work Model Model Estimation and identification for j = 1...J and normalize ui0t = 0 Aggregate product data • ε Estimation steps Assume ijt i.i.d. double exponential Pricing equation Micro data • Assume νit ∼ fν(·; θ), e.g. independent normal References • Write as product specific + observed interactions + References unobserved interactions u = δ +x θo z + x θu ν + ε ijt |{z}j jt |{z} it jt |{z} it ijt K×R K×L =xjtθ¯+ξjt Demand and supply of differentiated products Endogeneity Paul Schrimpf Introduction Demand in product space • Demand in Usually assume E[νit|xjt, zit] = 0 and E[εijt|xjt, zit] = 0 characteristic • space Not interested in counterfactuals with respect to Early work changes in zit, so can treat as residual, i.e. Model Model Estimation and identification νit = θit − E[θit|zit] Aggregate product data Estimation steps • Market average νit or εijt plausibly correlated with pjt or Pricing equation Micro data other product characteristics, but this correlation References absorbed into ξjt and/or market fixed effects References Demand and supply of differentiated products Endogeneity Paul Schrimpf Introduction Demand in product space Demand in • Problem is ξjt characteristic space • Prices and
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