Berry et al. (2004), Differentiated products demand systems from a combination of micro and macro data: The new car market

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1 Empirical IO Berry et al. (2004), Differentiated products demand systems from a combination of micro and macro data: The new car market Sergey Alexeev University of Technology Sydney April 13, 2017 SA (University of Technology Sydney) BLP, 2004 April 13, / 39

2 Nevo (2000) A Random-Coefficients Logit Model ( αi β i u ijt = α i (y i p i ) + x jt β i + ξ jt + ε ijt ) ( ) α = + ΠD β i + Σv i, v i Pv (v), D i ˆP v (D) u ijt = α i y i + δ jt (x jt, p jt, ξ jt ; α, β) + µ ijt (x jt, p jt, v i, D i ; Π, Σ) + ε ijt s jt p kt p kt s jt = δ jt = x jt β αp jt + ξ jt, µ ijt = [ p jt, x jt ](ΠD i + Σv i ) s jt (x t, p t, δ t ; Π, Σ) = dpε (ε)dpv (v)d ˆP D(D) A jt { p jt s αi jt s ijt (1 s ijt )d ˆP D (D)dP v (v) if j = k, = p kt s αi jt s ijt s ikt (1 s ijt )d ˆP D (D)dP v (v) { αpjt (1 s jt ) if j = k, αp kt s kt otherwise. otherwise. Min s(x, p, δ(x, p, ξ; α, β); Π, Σ) S s(δ t ; Π, Σ) = S t θ SA (University of Technology Sydney) BLP, 2004 April 13, / 39

3 Introduction I BLP (Berry et al. 1995) requires only market-level price and quantity data, some information on distribution of consumer characteristics and product characteristics; Despite 20 year of data, they could not exctract precise estimates of the distribution of consumer utilities and, thus, substitution patterns suitable for out-of-sample exercises: The solution was to impose the equilibrium assumption that relates the price-setting process and demad parameters. Better solution is to add more data: 1 Characteristics of products; 2 Attributes of the U.S. population of households; 3 Match between the first and second vehicle choices of the households; 4 Match between household attributes and first choice vehicles. SA (University of Technology Sydney) BLP, 2004 April 13, / 39

4 The Model I u ij = k x jk βik + ξ j + ε ij (1) β ik = β k + r z ir β o kr + βu k ν ik (2) x jk and ξ j observed and unobserved product characteristics; β ik if the taste of consumer i for product characteristic k; ε ij is idiosyncratic individual preferences; z i and ν i vectors of observed and unobserved consumer attributes; Compare with a multinomial logit, the model s benchmark; Interaction gives intensity for given characteristics capturing substitution patterns; SA (University of Technology Sydney) BLP, 2004 April 13, / 39

5 The Model II u ij = k x jk βik + ξ j + ε ij (repeated 1) β ik = β k + r z ir β o kr + βu k ν ik (repeated 2) β allow consumers to differ in their tastes for different product characteristics: In BLT, substitution pattern unrealistically depend on only on market shares and not on characteristics of vehicle. Data allow to proxy for the most important sources of differentiation: ξ j is still neccesary because products with higher unmeasured quality likely sold at a higher price. Also note the product-specific constant term. SA (University of Technology Sydney) BLP, 2004 April 13, / 39

6 The Model III tom: charactarized by a, b, and ε coke: with attributes I, II, and ξ u tom,coke = β tom,i x coke,i + β tom,ii x coke,ii + ξ coke + ε tom,coke β tom,i = β I + β o I,a z tom,a + β o I,b z tom,b + β u I ν tom,i β tom,ii = β II + β o II,a z tom,a + β o II,b z tom,b + β u II ν tom,i SA (University of Technology Sydney) BLP, 2004 April 13, / 39

7 The Model IV The consumer-level choice model: u ij = δ j + kr x jk z ir β o kr + k x jk ν ik β u k + ε ij (3) where, for j = 0, 1,..., J δ j = k x jk βk + ξ j (4) The random coefficients allow the deviation from mean utility to depend both on product characteristics and on household attributes; Yet, economic predictions about the effect of changes in product characteristics will depend in part on the β that enter the definition δ, (note k) SA (University of Technology Sydney) BLP, 2004 April 13, / 39

8 The Model V u ij = δ j + kr x jk z ir β o kr + k x jk ν ik β u k + ε ij (repeated 3) where, for j = 0, 1,..., J δ j = k x jk βk + ξ j (repeated 4) Unlike in BLT, micro-data and (ν, ε) allow to identify θ = (δ, β o, β u ), i.e. no need for (ξ, x): Some question (e.g. ideal price index) can be unanswered straigh away SA (University of Technology Sydney) BLP, 2004 April 13, / 39

9 The Model VI δ j = k x jk βk + ξ j (repeated 4) Insufficient to identify own and cross-price (and characteristic) elasticities, δ j x kj, i.e. we need β: s j δ j Unless β 0, the choice specific constant δ is a function of product characteristics; For example, to calculate the impact of price on demand, we need to know the impact of price on δ, that is we need β. Number of δ is J, only product level data can estimate β: Need assumption on (ξ, x), e.g. ξ j are mean independent of the nonprice characteristics of all the products (Cf. BLP). E.g: HP and S, and assume there are two firms producing three products each. Then we have 6 instrumental variables: The values of HP and S for each product, the sum of HP and S for the firms other two products, and the sum of HP and S for the three products produced by the competition SA (University of Technology Sydney) BLP, 2004 April 13, / 39

10 The Model VII w i = (z i, ν i, ε i ) with distribution P w s j (δ, β o, β u ; x, P w ) = A j (δ, β o, β u ; x) = {w : A j (δ,β o,β u ;x) P w (dw) (5) max [u ir(w; δ, β o, β u, x)] = u ij } r=0,1,...j Household buys one unit of good (generate one point of data) that gives the highest utility; The fraction that choose j (aggregate demand) is integration over the set of attributes that imply a preference for j; A j is observed data and household is a vectro of demographic and product specific shocks; A given set of parameters predicts the market share of each product: Risking writing the obvious, z i, ν i, ε i are integrated out. SA (University of Technology Sydney) BLP, 2004 April 13, / 39

11 Notes on the interaction terms It ensure that households who substitute out of one car will substitute to another car with similar characteristics and that differently priced cars will be bought by consumers with different responsiveness to price; BLP, meanwhile generate reasonable own- or cross-price elasticities if the underlying micro framework allows for sufficient interactions between individual attributes and product characteristics; If β u = 0 unobserved attributes are not important and it is a standart logit model; If β o = 0 observed attributes are not important and it the original BLP, i.e. shares (first choices) are sufficient statistics to estimate of the whole distribution of consumer utilities. SA (University of Technology Sydney) BLP, 2004 April 13, / 39

12 Estimation: Outline of the Estimation Procedure I Micro data allow to estimate choice-specific constant term (δ j ) two ways with a familiar trade-off: 1 restrict (ξ, x) to get (β o, β u, β) or... 2 get robust θ = (β o, β u, δ) and only then restrictions (ξ, x) to get β from δ. CAMIP is large, so that precision is not a corncern; Two-step generalized method of moment estimator is constructed that match three sets of predicted moments to their data analogues: i.e. choose θ that minimizes the distance between the model s predictions and the data SA (University of Technology Sydney) BLP, 2004 April 13, / 39

13 Estimation: Outline of the Estimation Procedure II 1 The market shares of the J products: Given β = (β o, β u ) there is unique δ and matches the observed market share; With BLP algorithm, search over β, not (δ, β), i.e. guess β and use mapping to find δ that give the observed share, then δ(β) gives moments (1,2); 2 The first set of moments match observed consumer attributes, z, to the characteristics of the chosen vehicles, x: Particularly good for β o, the interaction of x and z; Moment conditions are E(x 1 z ) and E(z); 3 The second set of moments, between first- and second-choice product characteristics: If βk u = 0, βo k explaines both choices; subscript k says that substitution pattern specified for all characteristics. SA (University of Technology Sydney) BLP, 2004 April 13, / 39

14 Estimation: Outline of the Estimation Procedure III u ij = δ j + kr x jk z ir β o kr + k x jk ν ik β u k + ε ij (repeated 3) where, for j = 0, 1,..., J δ j = k x jk βk + ξ j (repeated 4) The sets of moment conditions again, we do have 40 minutes to kill anyway. SA (University of Technology Sydney) BLP, 2004 April 13, / 39

15 Estimation: The Fitted Moments I This is an optional section, the authors indicate that the reader can go directly to Data; How to compute the moments for GMM algorithm and what are the limiting distribution of the estimates; Little things Over 200 car models, so too many δ, so they concentrate out ;... SA (University of Technology Sydney) BLP, 2004 April 13, / 39

16 Estimation: The Fitted Moments II G 1 n,ns,n(β) j n j n x1 kj (n j) 1 n j i j =1 [( 1 n x kq q =j n i=1 z ij E[z yi 1 = j, β] G 2 n,ns,n (β) ) n j n x1 kj {yi 2 = q}{y1 i = j} j ] (12) Pr(y 2 = q y 1 = j, z, ν, β)p z (dz)p ν (dν) G 3 ns,n(θ) = s j N 1 ns z ν ns r=1 (8) Pr(y 1 = j z r, ν r, β, δ ns,m (β)) (7) SA (University of Technology Sydney) BLP, 2004 April 13, / 39

17 Data: CAMIP against CPS I CAMIP stand for... The results of a propriety survey made on behave of GM; A sample from the set of vehicle registrations in year 1993: Not GM only, across the US; The random sample conditional on purchased vehicle. CAMIP asks a limited number of household attributes. SA (University of Technology Sydney) BLP, 2004 April 13, / 39

18 Data: CAMIP against CPS II SA (University of Technology Sydney) BLP, 2004 April 13, / 39

19 Data: The choice set To define a choice set, vehicles need to be classified into models with associated characteristics and sold quantities: 203 vehicles (147 cars, 25 SUVs, 17 vans, 14 pickup trucks). The combination of options that was most commonly purchased within sample cell is used for x j ; Average price of the modal vehicle is used for p j : Unique data on the transacation prices (no need to define a base model and match with list prices) SA (University of Technology Sydney) BLP, 2004 April 13, / 39

20 Data: Cell Characteristics I SA (University of Technology Sydney) BLP, 2004 April 13, / 39

21 Data: Cell Characteristics II SA (University of Technology Sydney) BLP, 2004 April 13, / 39

22 Data: Groups Characteristics I SA (University of Technology Sydney) BLP, 2004 April 13, / 39

23 Data: Groups Characteristics II SA (University of Technology Sydney) BLP, 2004 April 13, / 39

24 The Estimates of β o, β u I For all characteristics except price, the β i s have a normal distribution whose mean is shiftet by the observed household attributes, i.e.: β ik = β k + r z ir β o kr + βu k ν ik (13) β s are subsumed for now in the product-specific constanst δ, while ν s are i.i.d (across consumer and characteristics) standart normal (cf. BLP): This gives one β u for every product characteristic; In other words, β u are standart deviations of the contribution of unmeasured consumer attributes to the variance in the marginal utility for characteristics k; Not all attributes, r, were interacted; SA (University of Technology Sydney) BLP, 2004 April 13, / 39

25 The Estimates of β o, β u II The coefficient on price is assumed to be minus a log-normal: Keeping it normally distributed coefficient guarantees that some consumers prefer to pay high prices, all else equal. Price coefficient is assumed to be a functin of effective wealth, say W i ( z ir β1r o + βu 1 ν i1), and then model it in terms of r household attributes: Price coefficient is e W so that its log is a decreasing function. i.e. the disutility of a price increase then declines in W : i.e. consumers who buy expensive cars are likely to have lower marginal utilities of income. SA (University of Technology Sydney) BLP, 2004 April 13, / 39

26 The Estimates of β o, β u III Finally, the utility from the outside good is also assumed to be a linear function of household attributes, a random normal disturbance, and the logit error; Effectively, the outside good is treated identically to all the other choices, except with a price of zero and with a constant as its only observed product characteristic: β ik = β k + r z ir β o kr + βu k ν ik (repeated 13) Again, recall that constant is includede in δ; If β o = 0 then we have BLP, i.e. there is no observed consumer attributes. SA (University of Technology Sydney) BLP, 2004 April 13, / 39

27 The Estimates of β o, β u IV ESTIMATES OF INTERACTION TERMS, fl LOG IT FULL First and VEHICLE CHARACTERISTIC AND MODEL First Second HOUSEHOLD ATTRIBUTE (1) (2) (3) Price: Constant (.142) (.0001) (.0003) Income x (income <75th percentile) (.044) (.002) (.001) Income x (income >75th percentile) (.083) (.091) (.007) Family size (.010) (.001) (.006) Minivan: Kids (kids have age :::;16) (.242) (.098) (.323) Pass: Adults (adults have age >16) (.095) (.0004) (.009) Family size (.052) (.003) (.0002) Age (of household head) (.003) (.00001) (.00001) HP: Age (.001 ) (.0004) (.0001 ) Ace: Age (.001) (.00001) (.0001 ) Age ( ) (.00001) (.00001) PUPayl: Age (.002) (.0001) (.00001) Rural dummy (.179) (.005) (.008) Safe: Age (.0006) (.001) (.0004) SUV: Age (.010) (.003) (.004) Rural dummy (.156) (.007) (.002) Allw: Rural dummy (.247) (.005) (.246) Outside good: Total income (.228) (.096) (.063) Family size (.002) (.057) (.004) Adults (.766) (.112) (.148) SA (University of Technology Sydney) BLP, 2004 April 13, / 39

28 The Estimates of β o, β u V SA (University of Technology Sydney) BLP, 2004 April 13, / 39

29 β and Substitution Pattern I Still need to get β, the effects of the characteristics on the mean utility from a choice (the {δ j }); K δ j = p j βp + x jk βk + ξ j (15) k =p In theory the observed market share point identifies {δ j }, yet ξ spoils everything; Original BLP had 20 year of data, one year suggest even more severe precision problems; There are a number of additional sources of information that can be used to increase the precision: SA (University of Technology Sydney) BLP, 2004 April 13, / 39

30 β and Substitution Pattern II 1 Assume (i) a functional form for marginal costs and (ii) that the equilibrium is Nash in prices: mc j = k x kj γ k + ω j (16) p j = x kj γ k + b(x, p, β p, β o, β u ) j + ω j (17) where ω j is an unobserved productivity term, which is mean independent of x, and γ k are to be estimated; Price is a sum of marginal costs and a mark up, which is implied by demand side parameters; The equilibrium markup term is determined by the (ξ, ω); Then equilibrium markus and price elasticities depend only on β o, β u, β p = δj p j, so (δ, {β}) gives price changes SA (University of Technology Sydney) BLP, 2004 April 13, / 39

31 β and Substitution Pattern III 2 Based on the GM experience, the aggregate (market) price elasticity in the market for new vehicles was near one: An alternative estimate of β p is then the value that sets the 1993 market elasticity equal to one. 3 The last is β p = 0, which corresponds to the effective assumption of those earlier authors who ignored the correlation of product-specific constants and prices. The substitution pattern was actually virtually independent of the estimates of β p so β p = 3.58 is used, an average. SA (University of Technology Sydney) BLP, 2004 April 13, / 39

32 β and Substitution Pattern IV SA (University of Technology Sydney) BLP, 2004 April 13, / 39

33 β and Substitution Pattern V SA (University of Technology Sydney) BLP, 2004 April 13, / 39

34 β and Substitution Pattern VI SA (University of Technology Sydney) BLP, 2004 April 13, / 39

35 Prediction Exercises The estimated demand for high-end SUVs in 1990s; The close down of Oldmobile in 2000; Note that the 1993 data is used; Other actors do not respond to the change: Upon shut down, no realignment of the price of other products in response is assumed; Once introduced, (i) prices of other vehicle do not respond (ii) and no other products are introduced; It is terrible complicated, yet has been done, and for the current prediction exercise the effect is known to be of second -order importance. SA (University of Technology Sydney) BLP, 2004 April 13, / 39

36 Prediction Exercises: New Model I A new Mercedes and Toyota SUVs were introduced in 1993; Ford Explorer was the biggest-selling SUV in 1993, so all characteristitc of the new cars were set equal to it, except ξ and p; ξ was set to the mean of all Toyota (or Mercedes) cars; p is obtained by regressing it onto a large set of characteristics and company dummies: A very good fit, so need for explicit cost and pricing assumptions. A precise comparison of predictions is confounded, but they are in line with what was happening: Introduction of other new products, important macroeconomic shocks. SA (University of Technology Sydney) BLP, 2004 April 13, / 39

37 Prediction Exercises: New Model II SA (University of Technology Sydney) BLP, 2004 April 13, / 39

38 Prediction Exercises: Discontinuing the Oldmobile Division I Oldmobile, with 2.44% market share, had been phased-out in 2000: While GM s total share was 2.44%. Dropping Oldmobile from the choice set redistribute to other family-sized GM cars: Chevy Lumina, Buick LeSabre, and Pontiac GrandAm. Still some of the Olds purchasers shift to high-selling family-sized cars produced by other companies: Notably the Honda Accord, Ford Taurus, and Toyota Camry. Overall, 43% purchasers substitute to a non-gm alternative, and GM s market share falls to 31.1%: Note a costs saved and the markup on on other GM cars people substituted with. SA (University of Technology Sydney) BLP, 2004 April 13, / 39

39 Prediction Exercises: Discontinuing the Oldmobile Division II SA (University of Technology Sydney) BLP, 2004 April 13, / 39

40 References Berry, S. et al. (1995). Automobile prices in market equilibrium. In: Econometrica: Journal of the Econometric Society, pp (2004). Differentiated products demand systems from a combination of micro and macro data: The new car market. In: Journal of political Economy 112.1, pp Nevo, A. (2000). A Practitioner s Guide to Estimation of Random-Coefficients Logit Models of Demand. In: Journal of economics & management strategy 9.4, pp