Automobie Prices in Market Equiibrium Berry, Pakes and Levinsohn Empirica Anaysis of demand and suppy in a differentiated products market: equiibrium in the U.S. automobie market. Oigopoistic Differentiated Goods Market Price is determined from the oigopoistic market equiibrium. About 00 different automobie modes per year. Each mode has different observed characteristics: size, fue efficiency, etc. And aso each mode has unobserved characteristics such as brand image, reiabiity, etc. Data avaiabiity: some product characteristics of different modes (size, fue efficiency, etc.), aggregate saes share, aggregate consumer eve data (distribution of income, etc.) are avaiabe. No individua eve consumer data avaiabe. No cost information avaiabe. Hedonic approach: An automobie is a bunde of severa inherent hedonic characteristics that are observabe (size, mieage, etc) and unobserved (brand image, etc). Reduce 00 different modes into a bunde of severa characteristics.
Question that can be addressed: What is the own and cross price easticity of different modes? How much do consumers vaue each vehice characteristics. What is the impact of vountary export restraint (VET) on the U.S. automobie industry? What is the expected share of a new mode that has size fue efficiency y, etc? Mode Consumers Consumer i s utiity from purchasing a mode: U ς p, x, ξ, θ ( ) i, ς i: unobserved consumer characteristics. Distribution is known (income, famiy size, etc). p : price of a mode. x : observed characteristics of mode ξ : unobserved characteristics of mode θ : parameters of the utiity function.
Consumer i chooses mode if and ony if ( ς p, x, ξ, θ ) U ( ς, p, x, ξ, θ ) U for a i, i r r r r = 0,,..., J, r r = 0 means the consumer did not buy a car. A : set of consumer characteristics that buys mode : utiity of mode is higher than the utiity of any other modes incuding no purchase. (2.) A = ς : U ς, p, x, ξ, θ U ς, p, x, ξ, θ ; r = 0,.., J { ( ) ( ) } Consumers whose random unobserved characteristic ς is such that she gets the highest utiity by choosing mode. Let P 0 be the distribution of consumer s unobserved characteristics (or random utiity shock) ς. Then, Market share of mode : measure of consumers who buy mode (2.2) s ( p x, ; θ ), ξ = ς P0 ( dς ) A r r r
probabiity (or share) of the consumers for whom the utiity of purchasing mode is highest. Integrate over unobserved characteristics. Demand: Ms ( p, ξ;θ ) M :Number of consumers. Firms: F :modes for a singe firm. Profit of firm from a its modes ( ) π = p mc Ms p, ξ; (3.2) ( ) ( θ ) r F Fat margina cost (3.) n( mcr ) = w r γ + r r r ω w r:observabe cost characteristics ω :unobservabe cost characteristics r we assume that E[ ω w] = 0 i.e. the observabe demand and cost characteristics is exogenous. r r r
Bertrand Nash equiibrium under the differentiated goods economy. Given the prices of modes of other firms, pk : k Fr, take derivative of the profit function w.r.t. price and set it to zero. F.O.C. (3.3) ( p, ξ; θ ) sk s ( p, ξ, θ ) + ( pk mck ) = 0 p k F r
Moment conditions for estimation: What is in the data? Ony aggregate information: Market share of each brand Price and other mode characteristics, no cost info. Distribution of consumer characteristics (income, famiy size, etc). Demand Side: Suppose individua i s utiity for car mode has the foowing specification: u = u x, p, θ + ξ + ε (6.) i ( ) i x : mode specific observed characteristics (trunk space, mieage, horsepower, etc.) p : price of the mode ξ :mode specific unobserved characteristics (brand image, etc): assumed to be mean zero distributed conditiona on w (observed product characteristics or cost variabes). That is, [ w] = 0 E ξ i ε : individua specific unobserved taste component: assumed to be i.i.d. extreme vaue distributed.
The utiity of not buying a car is normaized to be 0. Then, the set of consumers who choose mode :Mode gives the consumer highest utiity. { ε i + ξ + εi (2.) A = : u( p, x ; θ ) ( p, x ; θ ) + ξ + ε, r = 0,.., J r } u, r r r Assume the error term ε is i.i.d. extremey vaue distributed. Share: the probabiity of consumers who coose mode : ir s p, ξ ; θ df( ε) (2.2) ( ) ε A [ u( p, x ; θ ) + ξ ] exp = J + exp + = [ u( p, x ; θ ) ξ ] The share of not buying a car: s ( p, ξ ; θ ) 0 df( ε ) ε A0 = + J [ u(, ; θ ) ξ ] exp p x + = for =,..., J
Then, [ s ( )] p, ξ ; θ n[ s ( p,, ξ; θ )] n 0 x ( p, x ) ξ = u ;θ + Now, we know that [ w] = 0 E ξ E. Hence, [ ξ ( w) ] = E{ E[ ξ w] ( w) } = 0 If we want our mode parameter to be cose to the true parameter vaue, then the parameter shoud satisfy the foowing sampe anaog to the above equation. J J = ( x, w ) ξ = 0 That is, the parameters shoud be chosen that the foowing equation is as cose to zero as possibe. J [ n s n s u( p, x ; θ )] ( x w ) J = 0,
Steps to construct demand side moments: Step : From the data, derive the share of mode s = No.of mode sod Tota sampe no. From the data, derive the no purchase share s = 0 No.of no purchase Tota sampe no. Step 2: Given p, x from the data, and given parameters θ, derive the sampe moment J [ n s n s u( p, x ; θ )] ( x w ) J = 0, Given the parameters, you can get back ξ by using ( p, x ) ξ = s n s u ;θ n 0
Suppy Side: margina cost equation n( mc ) = γ + ω (3.) w w :observabe cost characteristics: size, engine power, etc. ω :unobservabe cost characteristics: error term of the regression γ : parameters to be estimated. The probem about estimating the above regression equation is that there is no data on margina cost mc. If margina cost were observabe, estimating the above equation woud be simpe OLS or 2SLS. We recover the margina cost from the mode, i.e., from the First order condition of the firm s profit maximizing probem. (3.3) ( p, ξ; θ ) sk s + ( pk mck ) = 0 p k Fr s : market share of mode : can be cacuated from the data on automobie purchase. p k : price of mode k : get from the data. k
Aso, from the consumer s probem, given p,, and the parameter θ, we know that s ( p, ξ ; θ ) [ u( p, x ; θ ) + ξ ] exp = J + exp + = [ u( p, x ; θ ) ξ ] By taking derivative of the above equation with respect to Together, we get mc = p Δ p, we can derive s s k ( p, ξ; θ ) p x Δ k s = p k if mode k and Δ k = 0 otherwise. are produced by the same firm. Then, we get the foowing inear regression equation. [ ] ξ s = γ + ω (3.6) p Δ( p,, θ ) w We know that E[ ω w] = 0 k. Hence,
E [ ω ( w) ] = E{ E[ ω w] ( w) } = 0 If we want our mode parameter to be cose to the true parameter vaue, then the parameter shoud satisfy the foowing sampe anaog to the above equation. J J = ω ( x, w ) = 0 θ, γ shoud be chosen so That is, the parameters that the foowing equation is as cose to zero as possibe. J {[ ( ) ] p Δ p, ξ, θ s w γ } ( x, w ) J = In sum, parameters θ, γ shoud be chosen so that the foowing two sets of moments are made as cose to zero as possibe.
Generaized Method of Moments (GMM) estimation. Moments from consumer choice probem m ( p,,θ,γ ) w J [ n s n s u( p, x ; θ )] ( x w ) J = 0, Moments from firms profit maximization m ( p,,θ,γ ) = 2 w J {[ ( ) ] p Δ p, ξ, θ s w γ } ( x, w ) J = θ, γ to make those moments for We choose consumer choice probem and profit maximization probem as cose to zero as possibe.
Further Issues on Estimation. ) Notice that the price is not in the set of instruments. Instruments are ony ( x, w) : observed consumer and producer characteristics. The reason is that the prices are endogenous. ( p, ξ; θ ) sk s ( p, ξ, θ ) + ( pk mck ) = 0 p where mc = w + ω k Fr That is, modes that have high margina cost due to high ω is more ikey to set a higher price. Hence, the error term ω and the price p is ikey to be positivey correated. This is caed the simutaneity probem in estimating equiibrium modes. Other instruments that are used for product is : firm s average, competitor s, etc. w w 2) Some specification issues u = u x, p, θ + ξ + ε (6.) i ( ) i assume that u ( x, p, θ ) = x β p α Then, the cross price easticity is
s ( p, θ ) p s p = s p u ( x, p ; θ ) p = s p α That is, the cross price easticity of the price of mode to a mode ony depends on the mode price and mode s share. Yugo and Benz have the same market share. Increase in BMW price has the same effect on the market share of Yugo and Benz. Same increase in market share for Benz and Yugo, which is unreasonabe. Consumers who choose Benz have a preference over a arger car (because of arger famiy size, higher income, etc.). They woud be more interested in BMW. Fina utiity specification: (6.4a) u it = α n y p + x β + ξ σ x v + ε (6. ( it t ) t t + k kt ik it u 0 = α n y + ξ + σ v + ε 0 4b) it ( it ) 0t 0 i0 i t x t,,.., J Suppose = is the size of a mode. Then, for consumers who have high v i, size of a car is very important for her utiity. She is more k
ikey to purchase cars with arger size (such as Benz) than the others. For her, Benz and BMW are in a simiar group and more attractive than Yugo. For peope ike her, increase in BMW price wi increase Benz saes more than Yugo saes. Suppose that x 2 t is the mieage per gaon for mode. Consumers who buy Benz: ikey to have high v i (ove for size). Likey to buy more Benz when BMW price increases. Likey to not react to Fiat price increase. v i2 Consumers who buy Yugo. Likey to have high (care for fue efficiency). Likey to buy more Yugo when Fiat price increases. Likey to not react to BMW price increase. Cross easticities are high for simiar car modes and ow for different car modes, which is more reaistic.
Simuators for market share Given the parameters and the quaity ξ t the market share can be simuated in the foowing steps. Step. Draw from income distribution y mt Draw v mk, k = 0,..., K from standard norma distribution. Cacuate the utiity component without the error term ε u + σ x (6.4a) mt ( mt mt ) t t k k u kt = α n y p + x β + ξ v mk = α y + ξ + σ v (6.4b) mt0 n( mt ) 0t 0 m0 and the shares for simuation sampe m: s m ( p, ξ ; θ ) [ u + ξ ] exp mt = J + exp + = 0 [ u ξ ] mt
Step 2: Repeat step average. m =,..., M times and derive the s M ( p, ξ, θ, P) = s ( p, ξ, θ ) M m= If the simuation size M is arge enough, this simuated share shoud be very cose to the actua share. How do I get the quaity parameter ξ t for each mode? Choose them so that the computed share s ( p, ξ, θ, P) is equa (in practice, cose to) the actua share m s = No.of mode sod Tota sampe no. The probem is that now, it is not so easy to recover the quaity measure ξ from the observed og shares any more. This is because now, the shares are a compex noninear functions of ξ. But it turns out the agorithm of deriving the ξ s given the shares is a contraction mapping. So, given the observed shares and the parmeters, the
quaity measure for each firm is unique up to a constant, and can be obtained reativey easiy. Data: 97-990 Product characteristics: Automobie News Market Data Book: no. of cyinders, no. of doors, weight, engine dispacement, horsepower, ength, width, EPA MPG rating, front whee drive?, automatic transimission, power steering, air conditioning. Price: ist retai price for the base mode (983$) Additiona data: Gasoine price March Current Popuation Survey: income distribution of consumers. Consumer reports reiabiity ratings. Trends from 97 to 990 No. of modes: increases from 72 (974) to 50 (988). Saes per mode: decrease Price: fat unti 979, rises 50% during 80 s More fue efficient. Increase in Japanese cars market share, European shares constant.
Estimation Resuts Logit Estimation Dependent variabe: n( s ) n( s ) Variabe OLS Logit IV Logit Const -0.068 (0.253) -9.273 (0.493) HP/Weight -0.2 (0.277).965 (0.909) Air Cond. -0.035 (0.073).289 (0.248) MP$ 0.263 (0.043) 0.052 (0.086) Size 2.34 (0.25) 2.355 (0.247) Price -0.089 (0.004) -0.26 (0.23) No. Ineastic 494 22 Demands R sq. 0.387 n.a. Price easticity: ( s ) p 494 modes have easticity ess than. Not consistent with profit maximization. Possibe correation between price and unobserved product attributes. IV: size, No. of own and riva firm s products, etc. Ony 22 products that are ineastic. α 0
Singe easticity parameter is unreaistic because it impies that a modes have about the same markup. Aso, higher share modes have higher markup and ower share modes have ower markup, which is unreaistic.
Resuts from the fu mode Demand side parameters Mean β ' s Constant -7.06 0.94 HP/weight 2.883 2.09 Air.52 0.89 MP$ -0.22 0.320 Size 3.460 0.60 Std. dev. Constant 3.62.485 σ β Cost side parameters HP/Weight 4.628.885 Air.88.695 MP$.050 0.272 Size 2.056 0.585 n( y p) 43.50 6.427 Constant 0.952 0.94 Ln(HP/Weight) 0.477 0.056 Air 0.69 0.038 Ln(MPG) -0.45 0.055 Ln(size) -0.046 0.08 Trend 0.09 0.002 Negative MPG coefficient: popuar cars were the ones with ow fue efficiency.
The easticity of demand w.r.t. MP$ decines monotonicay with the car s MP$ rating. Individuas who purchase BMW, Lexus are not concerned with fue efficiency. Consumers who purchase the smaest cars vaue more on increased acceeration. A 227 modes in the sampe have easticity higher than. The most easticay demanded products are those that are in the most crowded market segments, the compact and subcompacts. Cross price easticities are arge for cars with simiar price characteristics. Markup: rises monotonicay with price. owest markup cars: Mazda, Sentra and Escort highest markup: Lexus and BMW