Structural Econometric Modeling in Industrial Organization Handout 4

Transcription

1 Structural Econometric Modeling in Industrial Organization Handout 4 Professor Matthijs Wildenbeest 19 May

2 Reading Kenneth Burdett and Kenneth L. Judd. Equilibrium price dispersion. Econometrica 51, , Han Hong and Matthew Shum. Using price distributions to estimate search costs. RAND Journal of Economics 37, , José Luis Moraga-González and Matthijs R. Wildenbeest. Maximum likelihood estimation of search costs. European Economic Review 52, , Ali Hortaçsu and Chad Syverson. Product differentiation, search costs, and competition in the mutual fund industry: A case study of S&P 500 index funds. Quarterly Journal of Economics 119, , Zsolt Sándor, José Luis Moraga-González, and Matthijs R. Wildenbeest. Consumer search and prices in the automobile market. Mimeo,

3 Consumer search Introduction to consumer search models Homogenous search models Burdett and Judd (1983): theory Hong and Shum (2006): MEL Moraga-González and Wildenbeest (2008): ML Heterogenous search models Hortaçsu and Syverson (q j econ, 2004): vertical differentiation Sándor, Moraga-González, and Wildenbeest (2011): horizontal differentiation 3

4 Introduction to consumer search models Bertrand (1883): in a world with perfect information and without transaction costs, price for a homogeneous good sold by firms with identical costs and no capacity constraint will converge to the Walrasian price. However, in real-world market price dispersion seems to be the rule, not the law of one price. Could be due to product differentiation (taste, quality). But also for seemingly identical goods price dispersion is observed. Possible explanation: consumers have imperfect information. 4

5 Introduction to consumer search models Due to search frictions some consumers do not search that much (high search cost). Others have lower search cost and search more. As a result even firms that set high prices (e.g., because of high marginal cost) sell their goods: they cater high cost consumers. But even if firms are the same search frictions can lead to price dispersion: mixed strategies. Literature studying price dispersion and search frictions started from the seminal article by Stigler (j polit econ, 1961). Since then lots of theory papers appeared, all trying to find a rationale for price dispersion as an equilibrium outcome. In the nineties a lot of empirical papers appeared. Now: shift from reduced form to structural. 5

6 Burdett and Judd (1983) Theory Burdett and Judd (econometrica, 1983) show that even if there is no heterogeneity at all price dispersion can emerge. Two models: nonsequential and noisy search. Focus here: nonsequential search. Consider first the supply side of the market. Continuum of (homogeneous) firms setting prices to maximize profits. Π(p) = (p r)µ q k k(1 F p (p)) k 1, k=1 where p is price, r is constant marginal cost, µ number of consumers per firm, q k is the share of consumers searching k times, and F p is the distribution of prices. 6

7 Burdett and Judd (1983) Theory Consumer side: given firm behavior, the number of prices i(c) a consumer with search cost c observes must be optimal, i.e., p i(c) = arg min c(i 1) + ip(1 F p (p)) i 1 f p (p)dp. i>1 p It can be shown that in an equilibrium consumers either search once (q 1 = 1) and firms set a price equal to the monopoly price, or q 1 > 0, q 1 + q 2 = 1 and firms draw there price from an atomless price distribution F p. 7

8 Burdett and Judd (1983) Theory Burdett and Judd define V as the difference in price paid by consumers searching once and twice, i.e., V = Ep 1:1 Ep 1:2 = p p p pf p (p)dp 2 p(1 F p (p))f p (p)dp. p A consumer will be indifferent between observing one and two prices only if V = c. If V > c the consumer will strictly prefer to observe two prices instead of one. 8

9 Burdett and Judd (1983) Theory 9

10 Burdett and Judd (1983) Estimation Both Hong and Shum (rand j econ, 2006) and Moraga-González and Wildenbeest (eur econ rev, 2008) try to estimate versions of Burdett and Judd (1983). Hong and Shum (2006) extend Burdett and Judd (1983) to allow for consumer heterogeneity. Moraga-González and Wildenbeest (2008) also allow for consumer heterogeneity, but in addition look at an N firm version of the model. 10

11 Burdett and Judd (1983) Consumer heterogeneity Now assume consumers draw their search cost c from some distribution F c (c) with density f c (c). Then i = Ep 1:i Ep 1:i+1, i = 1, 2,... is the search cost of the consumer indifferent between searching i and i + 1 prices. The fractions of consumers q i sampling i prices are then q 1 = 1 F c ( 1 ), q i = F c ( i 1 ) F c ( i ), i = 2, 3,... 11

12 Burdett and Judd (1983) Consumer heterogeneity 12

13 Burdett and Judd (1983) Consumer heterogeneity Given consumer behavior it is optimal for the firms to mix in prices: there have to be consumers comparing prices, which puts downward pressure on prices. However, since there are also consumers not comparing prices, p = r cannot be optimal, which puts an upward pressure on prices. Notice that with unit demand the upper bound of the price distribution p is equal to the valuation v. 13

14 Burdett and Judd (1983) Consumer heterogeneity Because of mixed strategies, firms should be indifferent between charging p = v and charging any other price in the support of the price distribution, so [ ] (p r) q i i(1 F p (p)) i 1 = q 1 (p r). i=1 Setting F (p) = 0 and solving for p gives the minimum price charged in the market: p = q 1(p r) i=1 iq i + r. Can be rewritten as r = p i=1 iq i q 1 p i=2 iq. i 14

15 Burdett and Judd (1983) Consumer heterogeneity The cutoff points i = Ep 1:i Ep 1:i+1 can be rewritten as a function of the price distribution: i = p p p[(i + 1)F p (p) 1](1 F p (p)) i 1 f p (p)dp, i = 1, 2,... Take the inverse of the equilibrium condition: p(z) = q 1 (p r) i=1 iq + r. i(1 z) i 1 A change of variable z = F (p) in the i equation yields i = 1 0 p(z)[(i + 1)z 1](1 z) i 1 dz, i = 1, 2,... 15

16 Hong and Shum (2006) Maximum Empirical Likelihood Hong and Shum (2006) estimate the model by using Maximum Empirical Likelihood (MEL). Suppose we observe n prices. Index these n prices in ascending order, i.e., p 1 p 2 p n 1 p n. Let K( n 1) denote the maximum number of firms from which a consumer obtains price quotes in the market. Then for each observed price p i the indifference condition is [ K (p i r) k=1 q k k(1 F p (p i )) k 1 ] = q 1 (p r), i = 1,..., n 1. 16

17 Hong and Shum (2006) Maximum Empirical Likelihood Consider the discrete price distribution ˆF p (p) = n i=1 π i1(p i p). Goal of the MEL procedure is to maximize n log π i, i=1 subject to the M sample moment conditions ( ) ] n (p r)q 1 π j [1 p j r + K k=1 kq k (1 s m ) k 1 s m = 0, j=1 the parameters θ, and the summing-up condition n i=1 π i = 1, where s m is the probability corresponding to the mth quantile. 17

18 Hong and Shum (2006) Maximum Empirical Likelihood It turns out that the MEL estimates of the parameters can be obtained from solving the saddle-point problem: [ ( ) ]) n max min log (1 + t (p r)q 1 1 p j r + θ t K k=1 kq k (1 s m ) k 1 s m, j=1 where t denotes the Lagrange multipliers associated with the sample moment restrictions. Need M K moment conditions, so if K is large, the dimension of the problem makes it computationally difficult. Moreover, because of the nature of the indicator function, changes in θ might not have any effect on the constraints, resulting in identification problems. 18

19 Moraga-González and Wildenbeest (2008) Maximum Likelihood Moraga-González and Wildenbeest (2008) estimate the model using Maximum Likelihood (ML). We are now looking at an N firm model, so replace in the equations by N. Applying the implicit function theorem to the equilibrium condition gives N i=1 f p (p) = iq i(1 F p (p)) i 1 (p r) N i=1 i(i 1)q i(1 F p (p)). i 2 19

20 Moraga-González and Wildenbeest (2008) Maximum Likelihood The upper and the lower bound of the price distribution can be estimated superconsistently using the highest and lowest observed price. The q i s have to sum up to 1, so q N = 1 N 1 i=1 q i. Finally, we can use the expression for r as a function of the parameters to replace r in the density function. Implies the following ML estimation problem: M 1 max {q i } N 1 i=1 l=2 log f p (p l ; q 1, q 2,..., q N ), where M is the number of prices and [ N ] iq i F p (p l ) solves (p l r) N (1 F p(p l )) i 1 for all l = 2, 3..., M 1. i=1 = q 1(p r), N 20

21 Moraga-González and Wildenbeest (2008) Comparison MEL and ML TRUE MEL ML T N M r (3.68) (7.27) p (0.27) (0.27) v (0.11) (0.11) q (0.142) (0.111) q (0.029) (0.018) q (0.042) (0.039) q (0.046) (0.045) q (0.048) (0.060) q (0.048) (0.088) q (0.050) (0.107) q (0.050) (0.114) q (0.050) (0.102) q (0.051) (0.221) Notes: Standard errors in parenthesis. Table: Estimation results comparison 21

22 Moraga-González and Wildenbeest (2008) Comparison MEL and ML: search costs MEL 22

23 Moraga-González and Wildenbeest (2008) Comparison MEL and ML: search costs ML 23

24 Moraga-González and Wildenbeest (2008) Comparison MEL and ML: fit MEL 24

25 Moraga-González and Wildenbeest (2008) Comparison MEL and ML: fit ML 25

26 Hortaçsu and Syverson (2004) Hortaçsu and Syverson (q j econ, 2004) study the role of nonportfolio fund differentiation and search frictions in the mutual fund industry. Focus is on about 85 retail S&P 500 index funds ($164 billion sector in 2000). Relatively homogeneous product since these funds all try to mimic the same underlying index. Still, price (fee) dispersion is huge: coefficient of variation (σ/µ) is and the seventy-fifth percentile price fund typically has investor costs more than three times those of the twenty-fifth percentile fund. 26

27 Hortaçsu and Syverson (2004) Puzzle: how can so many firms, charging such diffuse prices, operate in a sector where funds are financially homogeneous? No data on individuals decisions. Only aggregate price and quantity data available. Sources of price dispersion: Nonportfolio differentiation Switching costs Search cost/information frictions 27

28 Hortaçsu and Syverson (2004) The model Continuum of investors searching over funds with vertical characteristics. Investing in fund j gives indirect utility equal to u j = W j β p j + ξ j, where W j is a vector of fund attributes other than price p j and an unobservable component ξ j. Search (with replacement) is costly, heterogeneous investor population draws search cost from distribution G(c). First observation is for free. 28

29 Hortaçsu and Syverson (2004) The model Optimal search rule for investor with search cost c i is to search for another fund as long as c i ū u (u u )dh(u), where ū is the upper bound of the utility distribution H(u), and u is highest utility found so far. Assume investors observe the empirical utility distribution and label de N funds by ascending utility u 1 < < u N, so that H(u) = 1 N N I[u j u]. j=1 29

30 Hortaçsu and Syverson (2004) The model Optimal search rule yields critical cutoff points given by N c j = ρ k (u k u j ), k=j where ρ k is the sampling probability of fund k (known). Interpretation: as long as an investor s search cost is lower than c j keep searching until fund is found which offers higher utility than fund u j. 30

31 Hortaçsu and Syverson (2004) Market shares funds Lowest utility fund u 1 will only sell to investors with c > c 1 who happen to draw this fund in their first search, so market share of this fund is ( N )) q 1 = ρ 1 (1 G(c 1 )) = ρ 1 (1 G ρ k (u k u 1 ). Second-lowest utility fund u 2 will also sell to investors with c > c 2 but also consumer with c 1 < c < c 2 who find fund u 2 on their first search or after having first visiting fund u 1, i.e., k=1 q 2 = ρ 2 (1 G(c 1 ))+ ρ 2 1 ρ 1 [G(c 1 ) G(c 2 )] = ρ 2 [ 1 + ρ 1G(c 1 ) G(c ] 2) 1 ρ 1 1 ρ 1 31

32 Hortaçsu and Syverson (2004) Market shares funds Generalized market share equation is [ q j = ρ j 1 + ρ 1G(c 1 ) ρ 2 G(c 2 ) + 1 ρ 1 (1 ρ 1 )(1 ρ 1 ρ 2 ) j 1 ρ k G(c k ) + (1 ρ 1... ρ k 1 )(1 ρ 1... ρ k ) k=2 ] G(c j ). 1 ρ 1... ρ j 1 Maps observed market shares to the cdf of the search cost distribution evaluated at critical values. Is sampling probabilities unknown probabilities can be parameterized together with search cost distribution as ρ(ω 1 ) and G(c; ω 2 ). 32

33 Hortaçsu and Syverson (2004) Identification Market share information is only enough to trace out the search cost distribution in the special case of homogeneous funds: c j = N ρ k (u p k (u p j )) = k=j N ρ k (p j p k ), k=j where u is the common indirect utility of the funds. Otherwise calculate q j / p j (given knowledge of mc j ) by using q j (p) p j = q j(p) p j mc j. Use the elasticities in the derivative equation and solve for g(c j ) (see next slide). 33

34 Hortaçsu and Syverson (2004) Profit maximization Funds set prices to maximize profits Π k = Sq j (p, W )(p j mc j ), so where the derivatives are q j (p, W ) + (p j mc j ) q j(p, W ) p j = 0, q j = ρ 1ρ 2 j g(c 1) p j 1 ρ 1 j 1 ρ 2 ρ 2 j g(c 2) (1 ρ 1 )(1 ρ 1 ρ 2 ) ρ k ρ 2 j g(c k) (1 ρ 1... ρ k 1 )(1 ρ 1... ρ k ) k=3 ρ j( N k=j+1 ρ k)g(c j ) 1 ρ 1... ρ j 1. 34

35 Hortaçsu and Syverson (2004) Identification The difference between the cdf evaluated at c j 1 and c j can be approximated using the trapezoid method; i.e., Rewriting gives G(c j 1 ) G(c j ) = 0.5[g(c j 1 ) + g(c j )](c j 1 c j ). c j 1 c j = 2[G(c j 1) G(c j )]. g(c j 1 ) + g(c j ) Notice that we need a normalization at g(c N ), since this point is not identified. 35

36 Hortaçsu and Syverson (2004) Identification Since c j = N k=j ρ k(u k u j ), the calculated c k s can be used to calculate u j. The attribute loadings β can then be estimated with the following regression: u j + p j = X j β + β age ln(age j ) + η j, where X j are observed fund characteristics other than age, and η j is a fund-specific error term. Use IV, since η j (which contains unobserved fund attributes) is likely to be correlated with fund age (high quality funds are less likely to exit). 36

37 Hortaçsu and Syverson (2004) Estimation: basic model If ρ j = 1/N j, the market share equations simplify to q j = 1 j 1 N + k=1 1 (N k + 1)(N k) G(c k) so G(c j ) is nonparametrically identified. Because 1 N j + 1 G(c j), c j = 1 N N (p j p k ), k=j c j is also nonparametrically identified (exact identification). 37

38 Hortaçsu and Syverson (2004) Estimation: basic model 38

39 Hortaçsu and Syverson (2004) Estimation: unequal sampling probabilities Functional form specification for sampling probability ρ j : ρ j = Zj α N k=1 Z. k α Fund age is used for Z j. Search costs are parameterized as lognormal (with trend) with E[ln(c)] = µ and var[ln(c)] = σ 2. Mean marginal cost parameter also estimated. 39

40 Hortaçsu and Syverson (2004) Estimation: unequal sampling probabilities 40

41 Hortaçsu and Syverson (2004) Estimation: heterogeneous funds Assume again that the sampling probabilities are equal. Calculate G(c j ) using the market share equation. Calculate g(c j ) using the elasticity equation (marginal cost are assumed to be 10 and the same for each fund). Calculate c j using the trapezoid method. Search cost nonparametrically identified (exact identification). 41

42 Hortaçsu and Syverson (2004) Estimation: heterogeneous funds 42

43 Hortaçsu and Syverson (2004) Estimation: heterogeneous funds As explained above, the contribution of funds observable characteristics to utility can be estimated using u j + p j = X j β + β age ln(age j ) + η j Included attributes are a dummy indicating a load, number of family funds, manager tenure, fund age, etc. 43

44 Hortaçsu and Syverson (2004) Estimation: heterogeneous funds 44

45 Hortaçsu and Syverson (2004) Conclusions Fees retail S&P 500 index funds dispersed, even though homogenous. Search alone as explanation is rejected by the data, combination with nonfinancial fund differentiation (sampling probabilities or vertical characteristics) works best. Estimates show that average search cost decline over time, but distribution widens. Possibly due to inflow of inexperienced investors. 45

46 Sándor, Moraga-González, and Wildenbeest (2011) Setup of paper Paper develops a discrete choice model with optimal consumer search. Estimate the model using aggregate car data (sales, prices, characteristics) from the Netherlands. Consumer choice sets are endogenous (based on expected utility and search costs). Gives extra dimension to substitution patterns: not only because of car characteristics but also because of variation in cost of searching alternative brands. 46

47 Sándor, Moraga-González, and Wildenbeest (2011) Utility specification Starting point is the following utility function: u ij = αp j + x j β + ξ j + ε ij, where p j is price of alternative j and (x j, ξ j, ε ij ) are various attributes of j. Assumed x j is observed by econometrician, while ξ j is not. Interpret ε ij as a match parameter between product j and consumer i. Captures search-like attributes for which one has to visit a dealership. I.i.d. draw from type I extreme value distribution. 47

48 Sándor, Moraga-González, and Wildenbeest (2011) What is known and what is not Consumers much search to find the exact utility of options available. Consumers know: locations of car dealers and availability of makes and models price p j car characteristics x j and ξ j distribution of matching parameter ε ij Consumers do not know: matching parameter ε ij Follows Anderson and Renault (rand j econ, 1999) and Wolinsky (q j econ, 1986). 48

49 Sándor, Moraga-González, and Wildenbeest (2011) Non-sequential search Consumers use a non-sequential search strategy to determine which subset S of dealers to visit. By visiting a dealer f S consumers observe ε ij s for all cars sold by this dealer. Consumers differ in their search costs of visiting dealers f S: c is = f S c if + λ is, where λ is is stochastic shock across consumers and subsets of dealers. 49

50 Sándor, Moraga-González, and Wildenbeest (2011) Non-sequential search Important: we need to link search costs to something that only affects search cost heterogeneity and not preference heterogeneity. Is this consumer buying an Honda because it is the most preferred, or because it is the only one in her choice set? Distance from consumer to dealer seems suitable. Search costs are therefore: c is = f S d if γ + λ is, where d if is the distance from consumer i to dealer f. 50

51 Sándor, Moraga-González, and Wildenbeest (2011) Optimal non-sequential search search The expected gains to consumer i from searching the dealerships f in a subset S are [ E We can write m is as max j G f, f S {u ij} ] d if γ λ is, f S } {{ } mean expected gains m is ( m is = log 1 + exp[δ f ] d if γ, f S f S ( ) where δ f = log exp[δ j Gf j ] and δ j is consumer i s mean utility of alternative j: δ j = αp j + x j β + ξ j ) 51

52 Sándor, Moraga-González, and Wildenbeest (2011) Optimal non-sequential search search Consumer i will pick the subset S i that maximizes the expected gain m is λ is, i.e., S i = arg max [m is λ is ] S S [ ( = arg max S S log 1 + f S exp[δ f ] ) f S d if γ λ is ] We assume λ is to be i.i.d. type I extreme value distributed, so probability that i finds it optimal to sample the set of dealers S i is: P isi = exp[m is ] S S exp[m is ].. 52

53 Sándor, Moraga-González, and Wildenbeest (2011) Buying probability Given S i, the probability that consumer i buys j is equal to the probability that j is purchased out of the products of the firms in S i is: exp[δ j ] P ij S = 1 + r S exp[δ r ]. To get the unconditional probability we need to integrate out S i from this probability: s ij = S S f P is P ij S = exp[m is ] exp[δ j ] S S S S exp[m is ] 1 + r S exp[δ r ], f where S f is the set of all choice sets containing firm f. 53

54 Sándor, Moraga-González, and Wildenbeest (2011) Market share equation The probability that product j is purchased: s j = s ij df d (d ij ), where d if are the distances from consumers to dealers that need to be integrated out of s ij and F d (d ij ) is its cdf. Regard s j as the market share predicted by the model. Straightforward to extend to random coefficients α i, β i, (and γ i ) in the utility function (and search costs). 54

55 Sándor, Moraga-González, and Wildenbeest (2011) Data requirements Estimation procedure closely resembles BLP. Only market-level data is required to estimate the model: market shares prices brand characteristics Consumer choices are not directly observed but simulated. To identify search costs dealer locations are necessary as well as information on number of households on neighborhood level to calculate distances to dealers. 55

56 Sándor, Moraga-González, and Wildenbeest (2011) Essence of estimation method Predicted market shares should match observed market shares: s j (ξ, θ) s 0 j = 0 for all products j. This is a (nonlinear) system of equations in ξ. It is possible to solve for ξ through a contraction mapping (Berry, rand j econ, 1994; BLP); we obtain ξ as a function of all parameters and observed variables, ξ ( p, x, d, s 0, θ ). Identification assumption is a conditional moment restriction: E [ ξ j ( p, x, d, s 0, θ ) x, d ] = 0 implies θ = θ 0. This assumption allows for price endogeneity and makes estimation possible by GMM, in a way similar to BLP. 56

57 Sándor, Moraga-González, and Wildenbeest (2011) Simulation of market shares Predicted market shares s j (ξ, θ) cannot be computed analytically due to the integrals. Solution: simulation of market shares. We simulate ns consumers from empirical distribution of distances. For each consumer calculate purchase probability s ij. Simulated market share is s j = 1 ns ns i=1 s ij. 57

58 Sándor, Moraga-González, and Wildenbeest (2011) Simulation of market shares Note the difficulty in calculating individual i s purchase probabilities s ij = S S f P is P ij S due to the sum over S S f. This implies summing over all 2 F 1 choice sets that contain firm f. Moreover, to calculate the probability of being in a specific choice set exp[m is ] P is = S S exp[m is ], we need to sum over all choice sets. Problematic if there is a large number of firms: more than 137 billion choice sets with 38 firms (as in our case). Solution: importance sampling. We construct importance sampling probabilities that are close to the original probabilities and that are easy to sample from. 58

59 Sándor, Moraga-González, and Wildenbeest (2011) Importance sampling The probability s ij can be interpreted as an expected value of a discrete random variable. Replace probabilities P is by the importance sampling probabilities Q is to get s ij = ( ) PiS Q is P Q ij S, is S S f where, Q is = g S φ ig (1 φ ih ), h / S where φ ig is the probability that g is part of consumer i s choice set and (1 φ ih ) is the probability that h is not. Easier to draw from since it does not suffer from dimensionality problem. 59

60 Sándor, Moraga-González, and Wildenbeest (2011) Importance sampling For instance, use criterion that the two sets of probabilities are proportional at the singleton subset of firms {f }: which means: φ if 1 φ if g F\f and can be solved for 1 φ ig 1 φ ig = Q i{f } Q i = P i{f } P i, exp[m i{f } ] S S exp[m is ] φ if = exp[m i{f }] 1 + exp[m i{f } ]. S S exp[m is ], exp[0] Important detail: If Q is are computed at a value θ = θ 0 that stays fixed during the optimization algorithm, then the importance sampling simulator s j will be smooth in θ (Sovinsky Goeree, econometrica 2008). 60

61 Sándor, Moraga-González, and Wildenbeest (2011) Identification search costs Variation in market shares due to variation across choice sets allows us to identify the search cost parameter γ. Two cars with similar characteristics but different dealer locations. In the full information case the market shares should be the same. If not, differences must be due to variation in the cost of search. Put differently, after controlling for car characteristics and distances to closest dealer, small change in γ will lead to variation in choice sets that will ultimately be reflected in market shares. 61

62 Sándor, Moraga-González, and Wildenbeest (2011) Data Prices, sales, physical characteristics, and locations of dealers of all cars sold in the Netherlands between 2003 and Data is obtained from online database Autoweek Carbase. Additional data from Statistics Netherlands: number of households, CPI, gasoline prices, and distribution of household characteristics. We exclude all models which sold less than 50 cars in a given year. In total 39 brands, owned by 16 different companies. In a given year about 230 different models, 320 different models in total. 62

63 Sándor, Moraga-González, and Wildenbeest (2011) Prices, sales, and product characteristics No. of Cruise Year Models Sales Price European HP/Wt Size Control KPL KPe ,913 19, ,581 19, ,897 20, ,636 20, ,091 20, ,584 18, All 1, ,450 19, Notes: Prices are in 2006 euros. All variables are sales weighted means, except for number of models and sales. 63

64 Sándor, Moraga-González, and Wildenbeest (2011) Demographics and distances We want to link consumer locations to dealer locations. Demographic data is available on various levels of disaggregation: neighborhoods, districts, city councils, provinces. We focus on 11,122 neighborhoods (more disaggregated than zip-codes). We combine addresses of dealers with information on centroids of neighborhood to calculate Euclidian distance to nearest dealers using a geographical software package. We do this for all car brands and all neighborhoods, which means we get a matrix of 11,122 by 39 containing the minimum distances from the center of a neighborhood to a car dealer. There is a lot of variation in location. Example: Saab has only 20 dealers while Volvo has

65 Sándor, Moraga-González, and Wildenbeest (2011) Dealer locations (a) Saab dealerships (b) Volvo dealerships 65

66 Sándor, Moraga-González, and Wildenbeest (2011) Distances selected brands Weighted Weighted Percentage of Number of average std. dev. households Brand dealerships distance distance within 5 km Audi BMW Chevrolet Fiat Ford Honda Hyundai Jeep Lexus Mercedes-Benz Opel Porsche Renault Saab Subaru Toyota Volkswagen Volvo Notes: Average and standard deviation of distances are weighted by number of households. 66

67 Sándor, Moraga-González, and Wildenbeest (2011) Demand estimates No search Search OLS IV GMM/IV GMM/IV Logit Logit Logit Logit Demand Demand Demand Demand Variable (i) (ii) (iii) (iv) Constant (0.645) (0.898) (0.811) (0.775) HP/Weight (0.220) (0.699) (0.625) (0.754) Non-European (0.073) (0.129) (0.118) (0.134) Cruise control (0.087) (0.113) (0.104) (0.103) Fuel efficiency (0.024) (0.033) (0.029) (0.036) Size (0.057) (0.091) (0.083) (0.086) Price (0.004) (0.015) (0.014) (0.017) Search costs distance (0.018) (0.012) income (0.008) kids (0.619) senior (0.018) R n.a. n.a. n.a. Objective function n.a. n.a

68 Sándor, Moraga-González, and Wildenbeest (2011) Distribution number of searches Based on the parameter estimates, we estimated the distribution of the number of searches using 5,000 simulated households. (a) Estimated (b) Survey data 68

69 Sándor, Moraga-González, and Wildenbeest (2011) Substitution patterns In model without search elasticities are { s j p k αpj (1 s = j ), if j = k, p k s j αp k s k, otherwise. In search model elasticities are given by s j p k p k s j = { p j s j αsij (1 s ij )df d (d ij ) if j = k, p k s j αsij s ik df d (d ij ), otherwise. 69

70 Sándor, Moraga-González, and Wildenbeest (2011) Substitution patterns Ford VW Peugeot Citroën Honda Audi Mercedes BMW Fiesta Golf 308 C4 Picasso Accord A4/S4 C/CLC 7-series Search Fiesta Golf C4 Picasso Accord A4/S C/CLC series No search Fiesta Golf C4 Picasso Accord A4/S C/CLC series Notes: Percentage change in market share of brand i with a 1% change in the price of brand j, where i indexes rows and j columns. 70