Demand and supply of differentiated. products. Paul Schrimpf. products. Paul Schrimpf. UBC Economics 565. September 22, 2015

Transcription

1 Demand and UBC Economics 565 September 22, 2015

2 1 Introduction Introduction product space characteristic space Early work Model Estimation and identification Aggregate product data Estimation steps Pricing equation Micro data Limitations 2 product space 3 characteristic space Early work Model Estimation and identification Aggregate product data Estimation steps Pricing equation Micro data Limitations

3 Introduction product space characteristic space Early work Model Estimation and identification Aggregate product data Estimation steps Pricing equation Micro data Limitations Reviews: Ackerberg et al. (2007) (these slides use their notation) Aguirregabiria (2012) Reiss and Wolak (2007) Key papers: Berry (1994) Berry, Levinsohn, and Pakes (1995)

4 Introduction product space characteristic space Early work Model Estimation and identification Section 1 Introduction Aggregate product data Estimation steps Pricing equation Micro data Limitations

5 Introduction Introduction product space characteristic space Early work Model Estimation and identification Aggregate product data Estimation steps Pricing equation Micro data Limitations Typical market for consumer goods has many, but similar, e.g. Cars Cereal Differentiated are a source of market power Having many can result in many parameters creating estimation difficulties and requiring departures from textbook demand and supply models

6 Motivation Introduction product space characteristic space Early work Model Estimation and identification Aggregate product data Estimation steps Pricing equation Micro data Limitations Counterfactuals that do not change production technology Mergers Tax changes Effects of new goods Cost-of-living indices Product differentiation and market power Cross-price elasticities

7 Introduction product space characteristic space Early work Model Estimation and identification Section 2 product space Aggregate product data Estimation steps Pricing equation Micro data Limitations

8 Introduction product space characteristic space Early work Model Estimation and identification product space I J, each treated as separate good Classical demand, q 1 =D 1 (p 1,..., p J, z 1, η 1 ; β 1 ). =. q J =D J (p 1,..., p J, z J, η J ; β J ), Aggregate product data Estimation steps Pricing equation Micro data Limitations and supply (firms first-order conditions for prices): p 1 =g 1 (q 1,..., q J, w 1, ν 1 ; θ 1 ). =. p d J =g J (q 1,..., q J, w J, ν J ; θ J ),

9 product space II Introduction product space characteristic space Early work Model Estimation and identification Aggregate product data Estimation steps Pricing equation Micro data Limitations where p j = price q j = quantity z j = observed demand shifter η j = unobserved demand shock β j = demand parameters w j = observed supply shifter ν j = unobserved supply shock θ j = supply parameters D j typically parametrically specified, e.g. ln q j = β j0 + β j1 p β jj p J + β jy ln y + Z 1 γ + ν j

10 product space III Use reduced form to find instruments Introduction product space characteristic space Early work Model Estimation and identification Aggregate product data Estimation steps Pricing equation Micro data Limitations q 1 =Π q 1 (Z, W, ν, η; β, θ). =. q J =Π q J (Z, W, ν, η; β, θ) p 1 =Π p 1 (Z, W, ν, η; β, θ). =. p J =Π p J (Z, W, ν, η; β, θ) Cost shifters of product j excluded from demand and product k, but in reduced form Cost data often not available If available, unlikely to be product specific Attributes of other

11 Introduction product space characteristic space Early work Model Estimation and identification Aggregate product data Estimation steps Pricing equation Micro data Limitations product space IV Hausman (1996) uses prices of other Hard to justify, especially with prices Advantages of product space: Flexible substitution patterns Does not require detailed product attribute data Problems with product space: 1 Representative agent and aggregation issues With heterogeneous preferences, aggregate market demand need not meet restrictions on individual demand derived from economic theory Cannot use restrictions easily to improve estimates Can use simulation to aggregate (Pakes, 1986) 2 Too many parameters, O(J 2 ) 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

12 Introduction product space characteristic space Early work Model Estimation and identification Section 3 characteristic space Aggregate product data Estimation steps Pricing equation Micro data Limitations

13 characteristic space Introduction product space characteristic space Early work Model Estimation and identification Aggregate product data Estimation steps Pricing equation Micro data Limitations Motivation: Why do firms differentiate? Because consumers have heterogeneous tastes for product characteristics E.g. cars: tastes for size, safety, fuel efficiency, etc Main idea: model consumer preferences for characteristics and treat as bundles of characteristics Early work: Lancaster (1971), McFadden (1973) Key extension to early work: Berry, Levinsohn, and Pakes (1995)

14 Introduction product space characteristic space Early work Model Estimation and identification Aggregate product data Estimation steps Pricing equation Micro data Limitations Early work in characteristic space Consumer chooses one or none of J Utility of consumer i from product j u ij = x j β + ε ij with ε ij iid across i and j (usually logit) Implies aggregate demand (for logit) q j = exp(x j β) 1 + J k=1 exp(x kβ) Problem: restrictive substitution independence of irrelevant alternatives 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, allow correlation

15 Model I Introduction product space characteristic space Early work Model Estimation and identification Aggregate product data Estimation steps Pricing equation Micro data Limitations Consumers i, goods j, markets t Utility: (include good 0 = buy nothing) unobserved {}}{ u ijt = U( x jt, ξ jt, z it, }{{}}{{} observed observed x jt R K, z it R R, ν it R L Choose j if u ijt > u ikt k j unobserved {}}{ ν it, y it p jt ; θ) }{{} observed

16 Usually U( ) linear: Model II Introduction product space characteristic space Early work Model Estimation and identification Aggregate product data Estimation steps Pricing equation Micro data Limitations u ijt = 1 K {}}{ x jt K 1 {}}{ θ }{{} it + = θ+θ o z it +θ u ν it for j = 1...J and normalize u i0t = 0 Assume ε ijt i.i.d. double exponential 1 1 {}}{ ξ jt +ε ijt Assume ν it f ν ( ; θ), e.g. independent normal Write as product specific + observed interactions + unobserved interactions u ijt = δ j +x jt }{{}}{{} θ K R =x jt θ+ξjt o z it + x jt θ u }{{} ν it + ε ijt K L

17 Introduction product space characteristic space Early work Model Estimation and identification Aggregate product data Estimation steps Pricing equation Micro data Limitations Endogeneity Usually assume E[ν it x jt, z it ] = 0 and E[ε ijt x jt, z it ] = 0 Not interested in counterfactuals with respect to changes in z it, so can treat as residual, i.e. ν it = θ it E[θ it z it ] Market average ν it or ε ijt plausibly correlated with p jt or other product characteristics, but this correlation absorbed into ξ jt and/or market fixed effects Problem is ξ jt Prices and other flexible product characteristics must be correlated with ξ jt If ξ jt serially correlated, then likely also correlated with inflexible product characteristics Need instrument, w jt such that E[ξ jt w jt ] = 0 Cost shifters Characteristics of other

18 Estimation and identification Introduction product space characteristic space Early work Model Estimation and identification Aggregate product data Estimation steps Pricing equation Micro data Limitations Depends on data: Aggregate product market shares and characteristics Individual characteristics and choices Additional assumptions: Use supply and equilibrium assumptions to get a pricing equation

19 Introduction product space characteristic space Early work Model Estimation and identification Aggregate product data Estimation steps Pricing equation Micro data Limitations Aggregate data I Often only have data on product characteristics and market shares Maybe also distribution of some individual characteristics for each market (e.g. income and education from CPS or census) Instrument w such that E[ξ j w] = 0 Distribution of ν f ν ( ; θ ν ) Combination of estimated market level distribution of observed individual characteristics and parametric distributions of unobserved individual characteristics e.g. ν it = (educ it, income it, e it ) ( ) e θ µ F ν,t (s, y, e; θ ν ) = ˆF t (s, y) Φ ν }{{} θν σ empirical distribution ˆF t (s, y) estimated from CPS or other similar data set

20 Aggregate data II Introduction product space characteristic space Early work Model Estimation and identification Aggregate product data Estimation steps Assume ε ijt double exponential (aka Gumbel or type I extreme value) as in logit Computationally convenient, but other distributions feasible too Pricing equation Micro data Limitations

21 Estimation outline Introduction product space characteristic space Early work Model Estimation and identification Aggregate product data Estimation steps Pricing equation Micro data Limitations 1 Estimate ˆξ jt = ξ( ; θ) 1 1 Compute shares given θ, σ( ; θ, δ) 2 Find δ( ; θ) such that observed shares, s jt = model shares, σ( ; θ, δ), then ξ( ; θ) = δ( ; θ) x jt θ 2 Estimate θ from moment condition E[ξ( ; θ) w] = 0 1 In this slide means the data. I will leave the out of the notation in subsequent slides. I will also leave out t subscripts.

22 Introduction product space characteristic space Early work Model Estimation and identification Aggregate product data Estimation steps Pricing equation Micro data Limitations Integrate over ν σ j (θ, δ) = Computing model shares exp(δ j + x j θ u ν) 1 + j k=1 exp(δ k + x k θ u ν) df ν(ν) Integral typically has no closed form, so compute numerically, usually by Monte Carlo integration σ j (θ, δ) = N s r=1 exp(δ j + x j θ u ν r ) 1 + j k=1 exp(δ k + x k θ u ν r ) where ν r are N s random draws from f ν Issues about how best to compute integral simulation vs quadrature, type of simulation (Skrainka and Judd, 2011) Simulation (more generally approximation) of integral affects distribution of estimator

23 Solving for δ and ξ Introduction product space characteristic space Early work Model Estimation and identification Aggregate product data Estimation steps Pricing equation Micro data Limitations Want δ s.t. σ j (θ, δ) = ŝ j Berry, Levinsohn, and Pakes (1995) show T(δ) = δ + log(ŝ j ) log(σ j (θ, δ)) is a contraction Unique fixed point δ such that δ = δ + log(ŝ j ) log(σ j (θ, δ)), i.e. ŝ j = σ j (θ, δ) Can compute δ(θ) by repeatedly applying contraction (in theory and practice often faster to use other method) ξ j (θ) = δ j (θ) x j θ Important identifying assumption: only θ s.t. ξ j (θ) = ξ 0 j is true θ 0

24 Introduction product space characteristic space Early work Model Estimation and identification Aggregate product data Estimation steps Pricing equation Micro data Limitations Estimating θ Conditional moment restriction E[ξ j (θ) w] = 0 Empirical unconditional moments: G J,T,N,Ns = 1 JT J j=1 T ξ jt (θ)f(w t ) where f(w) = vector of function of w J = number of T = number of markets N = number of observations in each market underlying ŝ j N s = number of simulations Asymptotic properties (consistency, distribution), depend on which of J, T, N, and N s are, see Berry, Linton, and Pakes (2004) Reynaert and Verboven : using optimal instruments greatly improves efficiency and stability t=1

25 Pricing equation I Introduction product space characteristic space Early work Model Estimation and identification Aggregate product data More moments give more precise estimates Assumption about form of equilibrium allows use of firm first order condition (pricing equation) as additional moment Nash equilibrium in prices Log linear marginal cost Estimation steps Pricing equation Micro data Limitations log mc j = r j θ k + ω j r j = observed product characteristics, input prices, maybe quantity, etc ω j = unobserved productivity, possibly endogenous

26 Introduction product space characteristic space Early work Model Estimation and identification Aggregate product data Estimation steps Pricing equation Micro data Limitations Pricing equation II Firm f producing set of product J f, First order condition: Collect as ( max pj C j ( ) ) Ms j (, p) p j :j J f j J f σ j ( ) + l J f (p l mc l ) σ l( ) p j = 0 s + (p mc) = 0 Rearrange and use log linear marginal cost log(p 1 σ) rθ c = ω(θ) Conditional moment restriction E[ω(θ) w] = 0 Add empirical moments to G, 1 JT jt ω jt(θ)f(w t )

27 Introduction product space characteristic space Early work Model Estimation and identification Aggregate product data Estimation steps Pricing equation Micro data Limitations Micro data Berry, Levinsohn, and Pakes (2004) Data on individual choices and characteristics u ijt = δ j +x jt }{{}}{{} θ K R =x jt θ+ξ jt o z it + x jt θ u }{{} K L ν it + ε ijt Random coefficients discrete choice model, so can identify and estimate δ, θ o, and θ u without assumptions about ξ and x Ichimura and Thompson (1998) give conditions for nonparametric identification of random coefficients binary choice models Estimate by MLE or (usually) GMM Still need θ for price elasticities, etc δ j = x jt θ + ξ jt Use IV Use IV with a pricing equation

28 Nevo Dubé, Fox, and Su (2012b) Part II Implementation

29 Computational issues Nevo Dubé, Fox, and Su (2012b) Non-convex optimization problems are almost always difficult to solve, this is no exception Nested iteration can be problematic Solve for δ(theta): while norm(t(delta) - delta) > tolerance1 { delta = T Minimize while norm(theta - thetaold) > toltheta && norm(f - f thetaold = theta fold = f // update theta by e.g. newton's method, set f = f(t } Error in δ can lead to error in minimization Error in δ is not a continuous with respect to θ (where changing θ changes number of iterations)

30 Nevo Nevo Dubé, Fox, and Su (2012b) Popular code provided by Nevo (2000) Requires: Matlab, optimization toolbox Nevo s code does not run in current version of Matlab, but Rasmusen (2006) update does Code runs in Octave after changing fminsearch to another optimization routine Worked on by three people Used by at least six other papers (see Knittel and Metaxoglou footnote 5 for list) Fast for data provided

31 Nevo - issues Nevo Dubé, Fox, and Su (2012b) Minimization difficult and not robust Starting value Algorithm Tolerance for finding δ (Dubé, Fox, and Su (2012b) show loose tolerance affects estimates) Knittel and Metaxoglou algorithms often stop at point where first and/or second order conditions fail Knittel and Metaxoglou differences among convergence points economically significant

32 Nevo Dubé, Fox, and Su (2012b) Dubé, Fox, and Su (2012b) I Fixed point iteration to compute δ messes up GMM minimization; also is not best method for finding δ Table 1: shows problem is too large a tolerance. NFP gives good estimates when tolerances are tight Can recast problem as constrained minimization min θ,δ l 1 JT subject to J j=1 ŝ = σ( ; θ, δ) T ξ jt (θ, δ)f l (w t ) t=1 2 Su and Judd (2012): mathematical programming with equilibrium constraints (MPEC) Use state of the art algorithm to solve constrained minimization

33 Dubé, Fox, and Su (2012b) II Nevo Dubé, Fox, and Su (2012b) Solvers work best with accurate (i.e. not finite difference) derivatives supplying 1st and 2nd order derivatives makes algorithm take approximately 1/3 as long as with just 1st order (Dubé, Fox, and Su, 2012a) Gains from exploiting sparsity of Jacobian of constraints and Hessian of objective function

34 Dubé, Fox, and Su (2012b) code Nevo Dubé, Fox, and Su (2012b) Code requires: Matlab, KNITRO KNITRO proprietary, free version limited to 300 variables & constraints KNITRO can be replaced with other optimization algorithm, but others do not seem to work as well: IPOPT uses similar algorithm, but I had trouble installing NLOPT has no interior point algorithm, its algorithms do not seem to deal with nonlinear constraints very well Skrainka (2012) uses SNOPT, which is similar algorithm to NLOPT s SLSQP Runs in Octave with KNITRO replaced by NLOPT

35 Nevo Dubé, Fox, and Su (2012b) Observations High quality commercial solver appears necessary; my attempts with NLOPT fail and take longer Skrainka (2012) uses SNOPT instead of KNITRO KNITRO and SNOPT not perfect Still sensitive to starting values MPEC replaces a contraction a problem we know we can solve with constraints that may make the optimization harder Reynaerts, Varadhan, and Nash (2012) give method to improve accuracy and speed of computing δ Dubé, Fox, and Su (2012a) using nested fixed point requires fewer solver iterations than MPEC, but takes as long or longer because of time spend solving for δ (can be much longer if contraction mapping is slow) Reynaert and Verboven : using optimal instruments makes optimization more robust

36 Nevo Dubé, Fox, and Su (2012b) about implementation Overviews Nevo (2000) Dubé, Fox, and Su (2012b), Dubé, Fox, and Su (2012a) Knittel and Metaxoglou Skrainka (2012) Particular issues Skrainka and Judd (2011): integration Reynaerts, Varadhan, and Nash (2012): solving for δ Course on discrete choice models with simulation by Kenneth Train http: //elsa.berkeley.edu/users/train/distant.html Bayesian: Jiang, Manchanda, and Rossi (2009), Brian Viard, Gron, and Polson, Sun and Ishihara (2013) Overview of optimization methods and software Leyffer and Mahajan (2010)

37 Part III Applications and extensions

38 Section 4

39 New review paper: (2015) summarizes Berry,, and Berry, Gandhi, and Haile (2013)

40 Micro data: (2009)

41 Consumer i, markets t, j J t Consumer observations z it = (z i1t,..., z ijt t) Model I Observed product characteristics x t = (x 1t,..., x Jt t) (includes prices, may include product dummies) Scalar product unobservable ξ jt (z it ) Random utility function u it : X R Formally, there s a probability space, (Ω, F, P) and v ijt = u it (x jt, ξ jt (z it ), z ijt ) = u(x jt, ξ jt (z it ), z ijt, ω it ) where ω it Ω and u is measurable in ω it with ω it (x jt, z it, ξ jt (z it )) E.g. random coefficients u(x jt, ξ jt (z it ), z ijt, ω it ) = x jt θ it + z ijt γ + ξ jt + ε ijt ω it = (θ it, ε i1t,..., ε ijt t)

42 Model II Allows distribution of θ and ε to depend on z, x, ξ Special regressor: z (1) ijt R s.t. Restrictions: ( v ijt = ϕ(ω it )z (1) ijt + µ x jt, ξ jt (z (2) it 1 invariance of ξ jt (z it ) to z (1) it 2 Additive separability ), z(2) ijt, ω it 3 µ monotonic in ξ jt Identifies mapping from choice probabilities to utilities Henceforth, all argument conditional on z (2) it, so leave out of notation Normalizations ξ jt U(0, 1) Location of utilities v i0t = 0 )

43 Model III Scale of utilities ϕ it = 1, v ijt = z (1) ijt + µ(x jt, ξ jt (z (2) it ), z(2) ijt, ω it) }{{} µ j (x jt,ξ jt,ω it )

44 Data: (t, y it, {x jt, w jt, z ijt } j Jt ) definition I Conditional choice probabilities p ijt = P ( y it = j t, {x kt, w kt, z ikt } k Jt ) Full identification of random utility model: means that for any given conditional choice probabilities there is a unique distribution of ξ jt (given z (2) ijt ) and a conditional distribution of utilities {v ijt } j Jt given {x jt, w jt, z ijt } j Jt that generates the given choice probabilities of demand: for any conditional choice probabilities there is a unique distribution of ξ jt (given z (2) ijt ) and unique structural choice probabilities ( ) ( ) ρ j {xjt, ξ jt, z ijt } j Jt = P yit = j {x kt, ξ kt, z ikt } k Jt that match the choice probabilities

45 Assumptions 1 Large support: supp{z ijt } j Jt {x jt } j Jt = R J t 1 2 Independence of instruments: ξ jt (w jt, z ijt ) j, t 3 Rank condition: the quantile version of bounded completeness from Chernozhukov and Hansen (2005) applies to D j (x jt, ξ jt )

46 proof I µ ijt = µ(x jt, ξ jt (z (2) it ), z(2) ijt, ω it) Large support: ( ) lim P yit = j t, {x kt, w kt, z ikt } k Jt = z (1) ikt k j z ijt + µ ijt z ikt + µ ikt k j = lim P z ijt + µ ijt 0 z (1) ikt k j t, {x kt, w kt, z ikt } k Jt =P ( ) z ijt + µ ijt 0 t, {x kt, w kt, z ikt } k Jt

47 Independence of z ijt and (ξ jt, ω it ) proof II P ( z ijt + µ ijt 0 t, {x kt, z ikt } k Jt ) =P ( zijt + µ ijt 0 t, x jt, z ijt ) =1 F µijt t( z ijt x jt, t) averaging over x jt identifies F µijt t, and so identifies conditional quantiles, e.g. Define δ jt median[µ j (x jt, ξ jt, ω it ) t] median[µ j (x jt, ξ jt, ω it ) x jt, ξ jt ] = D j (x jt, ξ jt ) Independence of w jt and ξ jt, and ξ jt U(0, 1) implies that P ( δ jt D j (x jt, τ) w jt ) = τ

48 proof III Nonparametric IV quantile regression of Chernozhukov and Hansen (2005) shows that with the bounded completeness condition D j is unique identified, and so is ξ jt = D 1 j (x jt, δ jt ) Joint distribution of µ from p i0t = P(z ijt + µ ijt 0 j 0 t, z it ) F µ t = F µ xt,z it,ξ t

49 Further remarks To summarize if (1)-(3) then the random utility model is identified If large support fails, then can still identify demand Identifying random utility model is not exactly the same as identifying random coefficients v ijt = x jt θ it + z ijt γ + ξ jt + ε ijt This paper identifies F v x,z,ξ, further conditions needed for distribution of θ, ε Given in this paper, we can treat v ijt as observed and use standard to identify distribution of coefficients (see conclusion of Berry for references) Most economic quantities that we might care about depend on the random utility model not the random coefficients

50 Berry and Haile

51 Model Mostly same as Berry Market characteristics χ t = (x t, p t, ξ t ), x t exogenous, p t endogenous Random utilities with distribution F v (v i1t,..., v ijt χ t ) Shares s jt = σ j (χ t ) = P(arg max v ikt = j χ t ) k

52 1 Index restriction: partition x jt = (x (1) then Normalize β j = 1 δ jt = x (1) jt β j + ξ jt Assumptions jt, x(2) jt F v ( χ t ) = F v ( δ t, x (2) t, p t ) ), define 2 Connected substitutes: 1 σ k (δ t, p t, x (2) t ) is nonincreasing in δ jt and p jt for k j 2 Among any subset K J, j, k K and j K s.t. σ k (δ t, p t, x (2) t ) is decreasing in δ jt and p jt 3 IV exogeneity E[ξ jt z t, x t ] = 0 4 Rank condition / completeness: B(s t, p t ) if E[B(s t, p t ) z t, x t ] = 0 a.s., then B(s t, p t ) = 0 a.s.

53 of demand I If 1-4, then ξ jt and σ j (χ t ) are identified [Theorem 1] Connected substitute (1) demand invertible IV & rank condition: δ jt = σ 1 (s t, p t ) E[x (1) t σ 1 (s t, p t ) z, x] = 0 If preferences are also quasilinear, v ijt = µ ijt p jt, then the distribution of µ ikt µ ijt on the support of p jt is identified [Theorem 2] If p jt has full support, random utility model fully identified

54 More assumptions: Marginal costs 1 σ j (δ t, p t ) continuously differentiable wrt p t 2 Known form of competition so know ψ j such that mc jt = ψ j (s t, M t, { σ p }, p t) Then mc jt is identified [Theorem 3] If want to do counterfactuals that change quantities, need to know marginal cost function, not just mc jt = marginal cost at observed quantity If mc jt = c j (Q jt, w jt ) + ω jt and have instruments y jt such that E[ω w, y] = 0, then c j and ω jt identified [Theorem 4] If ψ j is unknown, then with stronger assumptions about marginal cost function and cost instruments, can still identify ω jt [Theorem 5] Can then test for different forms of ψ j [Theorem 9] Require index restriction on c j, mc jt = c j (Q jt, w (1) jt γ j + ω jt, w (2) jt )

55 Simultaneous equations approach I Use demand and supply equations together and can replace completeness conditions with regularity conditions about demand and supply equations Will need no external instruments (but do need exclusions) Index assumptions imply x jt + ξ jt =σ 1 (s t, p t ) (1) }{{} =δ jt w jt + ω jt =π 1 (s t, p t ) (2) }{{} =κ jt Assume x, w ξ, ω and supp(x, w) = R 2J

56 Simultaneous equations approach II Assume conditions (including for each δ, κ there is unique s, p) such that can make change of variables so f s,p (s t, p t x t, w t ) = = f ξ,ω ( σ 1 (s t, p t ) x t, π 1 (s t, p t ) w t ) J (st, p t ) (3) where J (s, p) = Jacobian wrt s, p of (1) and (2) Then can identify ξ, σ, ω [Theorems 6 and 7] Integrating (3) wrt x, w identifies J (s, p), then dividing gives f ξ,ω Integrating f ξ,ω give F ξ Location normalization: assume σ 1 (s 0, p 0 ) x 0 ) = 0, then know F ξ (0)

57 Simultaneous equations approach III For other s, p, can find x such that F ξ (σ 1 (s, p) x ) = F ξ (0), i.e. σ 1 (s, p) = x, so σ 1 identified (1) identifies ξ jt Same argument for ω

58 references Berry, Gandhi, and Haile (2013) show connected substitutes is sufficient for invertibility of demand Fox and Gandhi (2011) identification of demand for any dimension ξ Chiappori and Komunjer (2009) identification through conditional independence instead of special regressor Fox et al. (2012) shows random coefficients logit (without endogeneity) is identified

59 Section 5

60 In U.S. in 1996 cable television deregulated Hope was that multiple cable operators would enter each area and compete Did not happen, but direct broadcast satellite (DBS) companies did enter Questions: How much did competition from DBS lower cable prices? How much did consumers gain from DBS?

61 Model Consumers n, j, markets m Utility: U nj =α 0 p mj + 5 α g p mj d gn +β x x mj + z n βj z + (ξ mj + ε nj ) g=2 }{{} income effects 5 = δ mj + α g p mj d gn + z n βj z + ε nj }{{} =α 0 p mj β x g=2 x mj +ξ mj ε n multivariate normal with unrestricted covariance across j (avoids IIA problem)

62 Similar to micro-blp Use micro data to estimate δ mj, β z Estimation Use estimated δ, instruments for price to estimate α 0, β x Uses local tax on cable revenues as instrument for price Effect of entry, need to know price as function of model primitives Could fully specify costs and form of competition Instead estimate reduced form pricing equation, p mj = f(observables) Use pricing equation to predict prices without DBS, calculate compensating variation as measure of consumer welfare

63 : demographics and demand

64 : demand elasticities

65 : welfare No DBS would increase cable prices by $4.17 per month Monthly consumer gains from DBS: $10.57 in consumer surplus for DBS subscribers $4.17 per month for cable subscribers from lower prices $1 per month for cable subscribers from increased quality

66 Section 6

67 Question: effect of mergers on product characteristics Merged firm will generally produce different product(s) than two separate firms Need to endogenize choice of product characteristics Setting: U.S. daily newspapers

68 Model I BLP style demand with endogenous price and other product characteristics, x jt = quality index, local news ratio (share of local news staff), news variety (HHI of staff shares across sections) Demand for advertising: log a jt = η + λ 0 log H jt + λ 1 log q jt + λ 2 log r j t +ι jt }{{}}{{}}{{} market size circulation advertising price Note: no cross price elasticities, i.e. no competition Variable profits: π II j where = (p j q j ac (q) j q j ) + (r j a j mc (a) j a j ) + (µ 1 q j + µ 2 /2q 2 j )

69 Model II ac (q) j is average cost of producing quantity q and has some parametric form mc (q) j is marginal cost of advertising sales and has some parametric form Definition of market: Newspapers compete in many overlapping local markets, so local paper in Portland, Maine potentially competes with local paper in Portland, Oregon Define market for newspaper j as the counties where 85% of circulation for newspaper j is contained Equilibrium: solving backward 3 Given Q jt, advertising rate chosen to equalize marginal cost and marginal revenue of advertising No competition in advertising rates 2 Given characteristics, prices chosen in simultaneous Nash equilibrium 1 Characteristics chosen simultaneous Nash equilibrium

70 Data I , market level data on newspaper quantity, price, and characteristics, and advertising quantity and price County demographics (education, age, income, urbanization) 5843 newspaper-year observations of newspaper characteristics and prices newspaper-county-year observations of quantity 422 newspaper-year also with advertising information

71 Estimation I Moment conditions Consumer demand: E[ξ jt w jt ] = 0 Advertiser demand: E[ι jt w jt ] = 0 Advertising first order condition: E[ζ jt w jt ] = 0 Price first order condition: E[ω jt w jt ] = 0 Characteristics first order condition: E[ν jt w jt ] = 0 Instruments from overlapping markets Suppose newspaper A is only in county 1, but newspaper B is in counties 1 and 2 Demographics in county 2 affect prices and characteristics of newspaper B, which in turns affects newspaper A s price and characteristics Use demographics in county 2 to instrument for newspaper A s price

72 I Parameter estimates Simulation of merger of Minneapolis Star Tribune and St. Paul Pioneer In reality: owner of Pioneer bought Star, DOJ filed antitrust complaint 3 months later, owner of Pioneer sold Star 2 months later Simulate with and without characteristic adjustment, compare

73

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78 Section 7

79 Motivation: Demand Estimation with Scanner Data: Revisiting the Loss-Leader Hypothesis gandhi2014 I Frequent price discounts (sales) in scanner data Chevalier, Kashyap, and Rossi (2003): loss-leader model implies prices can fall when demand increases because of promotional effect; evidence that prices fall during seasonal peak demand (e.g. tuna during Lent) Nevo and Hatzitaskos (2006): prices could also fall during high demand because elasticity of demand could increase (if buying more quantity, makes more sense to search for lower price) Methodology: estimate BLP demand model, see if demand elasticity is different during seasonal peak

80 Demand Estimation with Scanner Data: Revisiting the Loss-Leader Hypothesis gandhi2014 II Data: Dominick s scanner data (grocery store) Difficulty: many product categories have hundreds of, so many have 0 observed share in some markets Solution: optimally shift observed shares away from 0

81 Dominick s scanner data (grocery store) Data Estimate separately for each product category Market = store week (all stores in Chicago, , gives 400, 000 markets) Many in each category (Table 4) 283 cheese, 537 soft drinks, 820 shampoos, 118 canned tuna, etc Sales concentrated among top 20% of in each category (Table 4) approximately 80% High percent (20-80) of with 0 sales (Table 4) 35% for canned tuna Distribution of sales approximately follows Zipf s law kth most popular product has sales proportional to 1/k s for some s > 1

82 Model and zero share problem I BLP setup (but empirical are without random coefficients) Zero share problem, 0 = σ(δ) implies δ = Cannot just drop goods with 0 share because that creates selection (0 share implies low ξ) Laplace: when observe zero share, add 1 sale to each product s L jt S = n ts jt + 1 n t + J t + 1 Optimal Bayes estimator under uniform prior Could use Laplace transformation here, but what is optimal for estimating shares might not be optimal for estimating demand

83 Model and zero share problem II Choose transformation π (s t, n t ) that minimizes asymptotic (slowly growing n t ) MSE π (s t, n t ) = σ ( E [ σ 1 (π t ) s t, n t ]) F πt s t,n t unknown, show that if assume Zipf s law, can estimate it Use estimated F πt s t,n t to estimate optimal transformation Estimate rest of model using BLP with transformed shares

84 Section 8

85 Zero share correction reduces bias Table: Table 6: Average Bias for a Repeated Simulation Fraction of Zeros 16.48% 36.90% 49.19% 63.70% Using Empirical Share Using Laplace Rule Inverse Demand EB Note: T = 500, n = 10, 000, Number of Repetitions = 1, 000.

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