Estimating demand elasticities in a differentiated product industry: The personal computer market

NORTH-HOILAND

Estimating Demand Elasticities in a Differentiated Product Industry: The Personal Computer Market Joanna Stavins

Supply and demand functions are typically estimated using uniform prices and quantities across products, but where products are heterogeneous, quality differences should be considered explicitly. This study employs hedonic coefficients to estimate price elasticities for differentiated products in the market for personal computers. The methodology allows for the estimation of varying demand elasticities among models. Instead of restricting market competition to the two nearest models, as is typically done in the differentiated-product literature, cross-elasticities of substitution have been allowed to decline continuously with distance between models in quality space. Estimated demand elasticities are consistent with observed changes in market structure. Entrant firms and new models face more elastic demand. © 1997 Temple University

Keywords: Product differentiation; Demand elasticities; Personal computers JEL classification: L1; L63

I. Introduction Supply and demand functions are typically estimated using uniform prices and quantities across products, yielding a single industry-wide demand elasticity estimate. However, most industries are characterized by multiproduct firms producing differentiated rather than uniform goods. Each product is likely to face a different demand elasticity. It would be misleading, for example, to use a single estimate of demand elasticity for a Mercedes and a Ford Escort. Instead, individual products'

Federal Reserve Bank of Boston, Boston, MA, USA (JS). Address correspondence to: Dr. Joanna Stavins, Federal Reserve Bank of Boston, 60(1 Atlantic Avenue, Boston, MA 02106, USA.

Journal of Economics and Business 1997; 49:347-367 © 1997 Temple University

0148-6195/97/$17.00 PII S0148-6195(97)00010-6

348

J. Stavins attributes and their market position should be used in demand elasticity estimation. Beginning with Rosen (1974), economists have employed various means of estimating demand and supply for differentiated products or individual attributes. There is still no agreement as to the best way to estimate demand elasticities for products differentiated in several attributes. Recent studies include Bresnahan (1981), Levinsohn (1988), Trajtenberg (1990), Berry (1992), Feenstra and Levinsohn (1995), Berry et al. (1995). The large number of products has forced analysts to place strong restrictions on demand to avoid estimating thousands of elasticities. In most of the studies, models were assumed to compete only with their two nearest competitors, or cross-elasticities were estimated after the market was aggregated to two general types of products [see Bresnahan (1989) for review]. This study has applied hedonic coefficients in the estimation of price elasticities for differentiated products. In the context of the market for personal computers (PCs), differences among products have been modeled as distances in a linear quality space derived from a multi-dimensional attribute space using hedonic coefficients as weights. A supply and demand model allowed for variation in demand elasticities among differentiated products and over time. The relative positions of models in the quality space measured their market power. Instead of restricting market competition to the two nearest models, cross-elasticities of substitution declined continuously with distance in the quality spectrum. Two-stage least squares estimates of demand elasticities varied across models and over time, and were consistent with observed changes in market structure. Entrants were found to face more elastic demand than incumbents, although the difference is not statistically significant. Similarly, new models were found to face more elastic demand than models which had been on the market for one or two years. The paper proceeds as follows. Sections II and III describe the theoretical models of demand and supply, respectively, leading to two estimable equations. Section IV describes the data, while Section V provides estimation results. Section VI concludes.

II. Demand Personal computers are vertically differentiated products, where more of a given characteristic is considered better. 1 A computer model can be characterized by a set of its attributes and by its price. Each consumer, i, selects a computer model, m, to maximize his utility, U;m, which increases with the quantity of embodied characteristics, Zm, and decreases with model price, Pro" Consumers are distributed according to their valuation of quality, 8i. Utility functions vary subject to a random component, Ei,,, which includes consumers' brand preferences: Ui,,, = 8iz,,, -- °ePm + el,,,

E ~ iid

(1)

1The only horizontal aspect of PC models is IBM-compatibility.The feature was controlled for by the inclusion of firm dummies.

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349

Consumer i selects model m if Uim

> Uin

for all models n, or if: for all n .

~igm -- o t P m + IEim ~_~ ~iZn -- o t P . + f'i.

Assuming that the willingness to pay for quality equals /5i = ~ + ~i, so that E ( ~i ) = ~:2 ~Zrn -- Olern q- Eim d- ~ i Z m ~__ ~ Z n -- o l P n -~- ~in @ ~OiZn f o r all n ¢:0' Elm -- Ein "1" ~ i ( Z m

--Z.)

>_ ((~Z. -- o l e n ) -- ( ~Zrn -- o l P m ) f o r all n .

The probability of buying model rn by consumer i can be specified as: Pr(buy m) = Pr((eim - el, + ~oi(z m - z , ) ) > (~z,

-

aP,)

-

(~z m -

aPm))

for all n.

(2)

Market share of model m is determined by the proportion of consumers for whom the inequality in equation (2) is true. 3 Assuming that the residuals are distributed Weibull, the probability of selecting model m (i.e., model rn's market share, sin) will have a multinomial logit distribution. 4 e ~zm - ~ Pm Sm

=

EN=IeSZ.-ae,

•

(3)

Taking logs of both sides: N In s m = ( ~ z m -- o l P m ) -- I n ~ e ~ z . - " P . . n=l

As the model price is itself a function of attributes, including both prices and model attributes in the regression would create multicollinearity, making it difficult to interpret the results. Consumers care about prices and attributes simultaneously, and not independently. I can therefore constrain 3 = a. Market share is a function of quality-adjusted prices of PC models, 5 but firm effects have been included in the equation separately to control for brand reputation effects.

2 Although tastes vary, in the case of vertically-differentiated products, consumers care mainly about quality, and higher prices indicate higher costs. In the case of horizontally-differentiated goods, heterogeneity of tastes is much more important in demand determination (e.g., if a black refrigerator costs more than a white one, it is probably due to the distribution of taste rather than a cost difference). Therefore, ignoring the heterogeneity in taste and income in demand for PCs is not as important as in the case of other commodities. 3 I do not have any information on how many people did not buy a PC and, therefore, cannot predict absolute levels of demand, only market shares of each model. In particular, when all the prices drop, relative market shares are unchanged, while quantities change. 4 Because the variance of the residuals equals o'2 = o,2 + %2Z2m, it may yield heteroskedastic coefficient estimates. Therefore, I estimated robust standard errors. 5 Trajtenberg (1990) used hedonic residuals in his CT scanners analysis, a similar measure to quality-adjusted prices.

350

J. Stavins Market share of model m produced by firm i in year varying coefficients on all other models' prices, becomes:

t(Smit)

,

allowing for

N I n S m i t = ~ o -I- "Yi at- ~ l ( P m i t

-

qmit ) -- In

~

e y'zm~(P~t-qnt) q- 1,'mi ` .

(4)

n=l

Own demand (market share) changes with own quality-adjusted price (the coefficient is proportional to own price elasticity of demand) and with quality-adjusted prices of substitutes (the coefficients represent cross-elasticities of demand). 6 Unlike Feenstra and Levinsohn (1995), I have not assumed that two models with identical technical specifications are perfect substitutes. My model allows for brand effects, hence firm dummies in the demand equation.

A. Cross-Elasticities of Demand The above equation presents an estimation problem. Even in a 100 product market, there are 10,000 cross-elasticity coefficients to estimate, and the PC market has over 300 models in some years. Analysts have typically imposed stringent constraints on demand structure: either each product competes with its two nearest neighbors only [e.g., Bresnahan (1981)], or all the products are summarized by two general types [e.g., Gelfand and Spiller (1987)]. Even though I reduced the quality to a single dimension, I did not restrict market competition to the two nearest models--a sufficiently large price drop for a model located further away could make it a valid substitute. A cross-elasticity between a pair of products depends on the degree of substitution between them. It is therefore reasonable to expect that the more similar are two models' attributes (i.e., the closer to each other they are located in the product space), the more customers would consider them to be substitutes. The crosselasticity of demand between models m and n can therefore be assumed to be inversely proportional to the distance in quality space between them: "~t2m n -~~/2/dmn. The specification allows each model to have a non-zero cross-elasticity with each of the other products on the market.

B. Own Price Elasticities of Demand Own price and prices of substitutes are not the only factors which affect demand. Just as a monopolist faces more inelastic demand than does a competitive firm, a model with market power is likely to face more inelastic demand than a model with several substitutes. The market power can be measured by whether the model is located in a crowded or an empty area in the quality space. If a model is located in a crowded area, its price increase will have a bigger effect on its market share than if there were no models around it. The crowding is measured with the average distance from other models. Distance measures the degree of competition in the 6An alternative m e t h o d of market share estimation involves selecting one model as a base: s o = eSZo-"e°/lEn e ~zn-~en, and estimating relative market shares: l n ( s m / s o) = ( z m - Zo)~ - (Pro P o ) a . T h e specification does not allow for cross-elasticity estimation, however.

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351

market at the time. To account for each model's market power, own qualityadjusted prices are weighted by the average distance from each model's substitutes, d,... The demand equation becomes:

In s,.it

" mPit - - q m i t

= To + Yi + Y l

N

lnn=lEe Z ' i ( P " ' - q " ' ) / d " "

dmn

+ " f 3 d m n + Pmit"

(5)

A linear approximation to equation (5) is: 7 " raPit -- qrait

In s,,~t = To +

Yi "q- Y l

dm n

N +

Y2

In ~ e ~p.,-q.,)/am.

+ "Y3dmn + l:mi t

(6)

n=l

where din, = Y'Nn=ld m n / N = average distance from model m's substitutes, s and d,,n = distance between models m and n. The assumption that own demand elasticity and cross-elasticities depend on the distance from other models is motivated by the utility function in equation (1). Because a model's relative location (or quality) enters the consumers' utility function, each model's demand elasticity depends on its location in the quality space, not just on its quality-adjusted price. The assumption allows us to distinguish between a model with a low price and low quality, and a model with a high price and high quality. The two would face different demand elasticities, even if their quality-adjusted prices were identical. IlL Supply Firms engage in a two-stage game: in stage one, they enter or exit the market, and decide which models to produce, i.e., they compete in spatial location of models in the model quality space. The first stage was analyzed in Stavins (1995). Stage two is a Bertrand-Nash competition in prices: each firm chooses own models' prices to maximize its profit, taking other firms' prices and all the models' location as fixed. 9 Therefore, the attributes of models produced are predetermined in the second stage. Each firm, i, chooses prices of all its models, Pmit, to maximize its profit in year t, 1tit. The quantity sold of each model equals its market share, Smi ~ (a function of prices), times the quantity of all PCs sold, Qt. Model-specific fixed costs, such as retail agreements, advertising, and box design, give rise to economies of scale; the fixed cost is allowed to decrease with the number of models the firm has produced

7 The linear approximation facilitated the inclusion of all the competitors in cross-elasticity of demand estimation. The nonlinear equation (5) was estimated inclucing two nearest neighbors, then four, six, eight, and finally ten nearest neighboring models. In all the regressions, while the coefficient on the neighbors' prices was insignificant, the coefficient on own price remained identical. The linearization did not, therefore, bias the estimates, and was used when all the competing models were included in the regression. 8 Feenstra and Levinsohn (1995) used a harmonic mean of distances: H = ( ( 1 / N ) E N_ i ( l / d m n ) ) -1 . Using harmonic means generated higher standard errors and a lower explanatory power than arithmetic means. It also created a problem of division by 0. 9 Fixed costs of a new model can be assumed sufficiently large for the assumption to hold.

352

J. Stavins in the past, exhibiting economies of scope. Marginal cost does not change with the number of units produced, 1° although it does increase with the attributes embodied:

max Trit= ]~ emit

(emit-Cmit)Qtsmi

` -

Fro,

(7)

Mi,

m=|

where Mit is the number of models by firm i in year t; Cmit is the marginal cost of model m; Emi t is the fixed cost of model m, and E t-,=01Mi: is the cumulative number of models produced before t. Differentiating equation (7) with respect to the model's price gives the following first order condition: tgS m ( e m i t -- Cmit)Qt---U-A-' + QtSmit +

arm

Mi,

OSm,

E (Pm'it m'= 1 rn ' ~: m

Cm,it)Qt-~'-mm

= 0

(8)

or:

Smi t e m i t = Cmit

OSm/OPm

Mit C~Sm,// ogem E (era'it - Cm'i,) OSm/OPm m'= 1 m' 4~m

Substituting for all the partials from the market share equation (6):

e m i t = Cmit -- - - d m n

~'1

1 % - ~2

E

(era'it -

cm'it)

•

(9)

m~'~l

Equation (9) shows that price equals marginal cost (Cmit) plus price-cost margin (PCM). Cmit is a function of model attributes, while PCM increases with the model's market power, which is higher the larger is the model's distance from other firms' models [ - 1/Yl > 0 from equation (6)]. In other words, the closer the model is located to other firms' models, the closer its price is to its marginal cost: as dmn "'> 0 =:~ e m i t ----> Cmit . The model's market power is approximated by its relative position in the quality space. If the industry were perfectly competitive, distance from other models would have no effect on price. The model's PCM is also higher, the higher the markups on other models by the same firm are, reflecting firm effects (such as management and reputation advantages). As I do not have information about marginal costs of all other models, I solved for marginal costs to eliminate them from the equation. In equation (9), price is a

10 No individual producer is assumed to be large enough to create a monopsony effect on the marginal prices of PC components, largely manufactured by other firms.

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353

function of all other prices, marginal costs, and distances from other models. In a matrix form: p = MlC + M2P + D 1

yielding the marginal cost equation: c = M~l(I

- M 2 ) P + D 2.

(10)

Marginal cost can also be expressed as a function of model attributes: c = [3cZ + ~o.

(11)

Equating (10) and (11), and solving for P: P = ( I - M2)-IM1 ( tic z + o9) + D 3 or: p = B l z + n2D-'-mn + B3Dmm, + ~.

(12)

Price is therefore a function of model attributes (z) and of the average distance from models by other firms (Dmn), as well as the average distance from own models (D,,,,,). Both model attributes and model location in the product space are exogenous in the second stage of the market game.

IV. Data The data set includes annual prices and technical attributes for new personal computers sold in the United States from 1976 to 1988. n The period encompasses the beginning and rapid growth of the personal computer market. During the period, incumbents and potential entrants faced several major strategic decisions and the industry underwent standardization. The data set is an unbalanced panel. There are 1,480 model-level observations over the 13-year period. Due to some missing data, 1,436 were used in the hedonic estimation. For each observation, the sample included a set of technical specifications, price, as well as each model's name and its producer. The list of major attributes and descriptive statistics is in Table 1. A PC model is identified by its brand name. Although model names are fairly specific, the definition of a model changed over the span of the data. In the initial period, models did not carry discrete options for their memory, storage capacity, etc.; a model had a fixed specification. Towards the end of the sample period,

11The data were originally collected by Cohen (1988), and later updated by Kim (1989). Sources include technical model reviews in June issues of Byte, PC Magazine, and PC World for list prices and attributes, as well as ads in the business section of June issues of the Sunday New York Times for discount prices. Incompatibility of data sources for later data prevented the extension of the data beyond 1988.

354

J. Stavins Table 1. Summary Statistics for Major Variables, 1976-1988 Variable

Mean

Std. deviation

Min

Max

Real price RAM MHZ Hard disk # Floppy drives # Slots 16-bit processor 32-bit processor B & W monitor Color monitor Portable Additional hardware Discount price

1430.1 500.73 7.75 15.58 1.07 4.72 0.480 0.124 0.408 0.028 0.156 0.018 0.278

1102.2 496.43 4.808 34.482 0.614 3.721 0.500 0.329 0.492 0.166 0.363 0.134 0.448

22.7 0.5 0.5 0 0 0 0 0 0 0 0 0 0

7801.8 4096 25 314 3 22 1 1 1 1 1 1 1

however, most models could be custom-made with several configurations of RAM, M H Z , and hard disk capacity. T h e r e still remained, however, a strategic decision by the firms whether to introduce a new model or continue the old one with new specifications. Introduction of a new model carries a fixed cost of a new design, marketing, and dealer arrangements. I therefore used the same designation the producers did. Retail and discount sales channels are distinguished. The retail data include list prices of PC models based on their technical reviews, or models sold by their b r a n d - n a m e manufacturers (e.g., PC Limited models sold by PC Limited), while discount data include models sold by other sources (e.g., PCs sold through discount mail order, such as 47th Street Photo). Some models may appear with the same set of specifications in the retail and discount markets in the same year. Although the distinction between home, business, and education markets would be helpful, the data do not allow for such a distinction. The data encompass 330 distinct firm-years, and 472 distinct models. 12 The data set was merged with a data set containing PC shipment quantities per year, obtained from International D a t a Corporation (IDC). The I D C data did not contain all of the PC models in the initial sample. The overlap of the two data sets consists of 972 observations. In particular, there are no quantity data for the year 1976. Based on the total shipment quantities provided by I D C and Dataquest, the sample is almost complete for the initial years, but it embodies only about half of the total m a r k e t in the last few years. No evidence of sample selection was found for models for which quantity data exist. Some evidence of the changing market structure can be observed in Table 2. Both the Herfindahl index and C(3) 13 decreased over time. The average model's market share decreased continuously after 1978. Note the dominance of I B M in the PC market in the mid to late 1980s.

12 While the entire sample was used in hedonic estimation, only the retail (i.e., not discounted) sample was used in distance calculations. 13The Herfindahl index is the sum of each firm's market share squared, or En~v~1 $2t, while C(3) is the sum of market shares of the top three finns.

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355

Table 2. Market Share of Leading Firms, by Year Year

Herfmdahl index

1977

0.5177

1978

0.5819

1979

0.4328

1980

0.2137

1981

0.1614

1982

0.1219

1983

0.1071

1984

0.1278

1985

0.0872

1986

0.0393

1987

0.0338

1988

0.0210

Top 3 companies

C(3)

Commodore Radio Shack Apple Radio Shack Commodore Apple Radio Shack Apple Atari Radio Shack Apple Atari Radio Shack Apple Commodore Commodore Sinclair Radio Shack Commodore Radio Shack TI Commodore IBM Apple Commodore Apple IBM IBM Apple Commodore IBM Apple Radio Shack IBM Apple Commodore

0.9932

0.9784

0.9265

0.8791

0.8846

0.6798

0.6523

0.7835

0.7397

0.6106

0.5830

0.4802

V. Estimation I began with the supply equation estimation, as the supply equation is a reduced form regression of prices on exogenous variables. The estimated prices were then used to obtain two-stage least squares estimates of the demand equation.

A. Supply In scalar notation, equation (12) b e c o m e s : t4 N,

In Pmi, = )to + At + Ai + E AjZjmit + AI E j

n=l

dm n

--+;~2 Nt

14 Log-linear form was chosen based on the goodness of fit criteria.

Mit

am m ,

~] - - + ~ m i ,

m'=l m'~m

Mit

(13)

356

J. Stavins where: Pmit is the price of model m produced by firm i in year t; /~t a r e year dummies; h i are firm dummies; Zjmit is attribute j of model m by firm i in year t; dmn is the distance between model m and model n (produced by another firm); dmm, is the distance from model m' (produced by the same firm); n denotes other firms' models (n = 1. . . . . N~), and m' denotes other models by the same firm ( m ' --- 1 . . . . . Mit). The above equation allows for a separate effect of the distance to other firms' models (measures the model's and firm's market power; expect an unambiguously positive effect) and the distance to own models. Concentration of own models in a single market segment could lead to the firm's local market power, 15 but in Stavins (1995), I found that established firms disperse their models to preempt the market. The sign of the coefficient on own models' concentration is therefore ambiguous. To obtain distance measures between models differentiated in several attributes, each multidimensional model m was reduced to a unidimensional quality measure, qmt, 16 by using weights for each attribute. The quality measure was constructed as follows: qmt = Ej [3jZim t = [3 Zmt. The quality measure is a weighted sum of the technical attributes and firm dummies. The firm dummies serve as proxies for such firm attributes as service support, operating system, and availability of application software. The weights [3i should represent the marginal value which consumers and producers place on the jth attribute. Such values can be approximated by the estimated marginal implicit prices from the hedonic regression. Hedonic regression was used to estimate the relationship between product prices and their attributes. The estimated coefficients on attributes in the hedonic equation represent marginal implicit prices of each attribute. 17 For example, a hedonic coefficient on clock speed indicates the implicit price of an additional megahertz of speed, even if units of speed are not offered for sale. Hedonic coefficients represent the value attached to each attribute by the market, encompassing both demand for a particular characteristic and the additional cost a company has to incur to add an extra unit of that attribute. Hedonic coefficients were used as weights in the quality measure, q. As product attributes have vertical ordering, collapsing multidimensional products to one dimension does not destroy the analytical distinction among the goods. 18 A hedonic regression was performed of computer real prices (in 1982 dollars) on major technical attributes, producer and year dummies, and age of each model. For each model m, produced by firm i in year t, the pooled hedonic regression was specified as follows: A t

In Pmit = [30 + [3i + [3t + [31 l n ( R m M m i t )

+

" ' "

+ [ 3 j A G E + ... +emi t.

(14)

See Table 3 for the regression results. 19 Increasing storage capacity, clock speed or memory increased the price of a PC, holding the remaining attributes and firm

15The hypothesisis consistent with Feenstra and Levinsohn's(1995) finding. 16Inclucing all of the competing models' attributes would more than exhaust the degrees of freedom. 17See, for example, Griliches (1971, 1988) for a discussion of hedonic estimation. 18Although prices could be used as a measure of quality, prices are measured with error (the error constitutes a part of the hedonic residual) and contain other, non-quality-relatedfactors. 19A similar hedonic specificationwas used by Berndt and Griliches (1993) and by Stavins (1995).

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Table 3. Hedonic Regression D e p e n d e n t Variable: Log (Real Price) ~ Variable Log (hard disk) Log (RAM) Log (MHZ) Log ( # floppy drives) Log ( # slots)

Black & white monitor dummy Color monitor dummy Discount market dummy Extra equipment dummy Portable dummy 16-bit processor dummy 32-bit processor dummy

Age Apple dummy Atari dummy Commodore dummy Compaq dummy IBM dummy NEC dummy Radio shack dummy Zenith dummy Wyse technology Epson dummy Kaypro dummy NCR dummy Northgate dummy

Intercept R 2 = 0.757

Coefficient

t Statistic

0.164 0.339 0.213 0.367 0.085 0.068 0.134 - 0.274 0.224 0.218 0.252 0.587 0.055 0.157 - 0.574 - 0.413 0.339 0.032 0.137 - 0.023 0.242 0.040 -0.119 0.093 0.318 0.185 6.167 F = 117.6

19.64 18.10 5.82 7.98 4.38 2.53 1.93 - 9.86 2.68 5.66 7.24 9.59 3.95 2.67 - 7.66 - 6.23 6.51 0.75 2.25 - 0.45 3.78 0.54 - 1.53 1.18 4.04 1.94 66.78 N = 1436

aYear dummy coefficients omitted for clarity (see Table 5 for similar results).

effects constant. Similarly, holding the technical attributes constant, some brands commanded higher prices than others ("other" is the omitted brand category). In particular, Apple, Compaq, NEC, Zenith, and NCR were priced significantly higher than the other brands, while Atari and Commodore were priced below the other brands. The differences among brands may have been caused either by cost differences or by varying marketing strategies. The hedonic specification did not allow me to distinguish between the cost demand effects. The coefficients on all the year dummies were negative and significant (see Table 5 for similar results). As all those coefficients are relative to year 1977 (year 1977 was the omitted dummy), the results show that quality-adjusted real prices declined every year. As technology improved over time, the marginal costs of computer attributes dropped. A pooling of cross-section and time series data, with different intercepts for each year, but common coefficients for each attribute, was tested against the unrestricted model of annual regressions by means of the Chow test, and rejected at the 1% level. The restriction was rejected even when time interactions of major characteristics were included in the model, Because the market changed significantly in 1982, 20 separate pre-1982 and post-1982 regressions were estimated to 20 IBM joined the market in 1982, changing the nature of the competition.

358

J. Stavins

Q~

"t3

.5 .4

¢0

.2

a9'76

19130

19i~4

198~

YeaP

Figure 1. Mean distance from other models, by year.

test whether separating the two periods was sufficient and annual estimation could be avoided. The pre-1982 and post-1982 regressions were tested against annual estimation. Again, the restriction was rejected at the 1% level. 21 Instead, separate hedonic equations were estimated for each year, unlike in Berndt and Griliches (1993). Thus the weights, /3jr, vary across years. Table 3 shows the results of a pooled regression and therefore shows the marginal implicit prices averaged over the years, not the actual estimates used. The quality measure was then used in the computation of the distance between =

t

2

models: din, V/(/3'Zm-/3 z n) = V / ( q m - q,)2. Average distance from all other models, dr,,, is din, divided by the number of models. Its mean, by year, is shown in Figure 1. Descriptive statistics on the variables constructed above are listed in Table 4. The supply equation regresses price on model attributes and distances from other models. As model selection was done in stage one of the game, model location in the quality space could be treated as exogenous in stage two. 22 The price equation was estimated using OLS. Because of possible heteroskedasticity, robust standard errors were estimated. The results are reported in Table 5. Including firm dummies did not alter the distance coefficients--spatial location effects cannot be explained by brand effects. The average distance from other firms' models had a positive effect on model price. That is because models located in empty areas had a local monopoly power, which raised their price-cost margin, controlling for models' technical attributes and their makers. The coefficient on the average distance from own models is

21 One could assume that due to the market structure of a few dominating firms with several peripheral companies, individual firms could have varying marginal implicit prices of attributes. The restriction of common attribute slopes across firms was imposed, however, due to the presence of several single-model companies. 22 Potential estimation problems associated with that assumption are discussed in the Appendix.

359

The Personal Computer Market

Table 4.

D e s c r i p t i v e Statistics o n C o n s t r u c t e d V a r i a b l e s

Q u a l i t y is c o m p u t e d f r o m : In P = / 3 0 + / 3 t +/3i + / 3 ' z + u

In q =/30 +/3i +/3'z Variable Quality Average distance from all other models Price-quality Estimated price-quality (Price-quality)/average distance (Estimated price-quality)/ average distance

Table 5.

Mean

Std. deviation

767.70 0.2959

791.01 0.138

Min 45.5 0.068

Max 5048.0 1.271

662.35 581.57 2320.6

939.49 728.30 3115.8

- 1889.0 - 1620.1 - 6235.3

7517.2 4944.9 20558.5

2025.9

2337.5

- 4079.8

10793.2

Price E s t i m a t i o n , O L S D e p e n d e n t V a r i a b l e : L o g ( R e a l Price) a Variable

Coefficient

t Statistic b

Average distance from other firms' models Average distance from own models Single-model firm dummy Log (hard disk) Log (RAM) Log (MHZ) LOg ( # floppy drives) LOg ( # slots) Black & white monitor dun/my Color monitor dummy Discount market dummy Extra equipment dummy Portable dummy 16-bit processor dummy 32-bit processor dummy Age Year 1978 dummy Year 1979 dummy Year 1980 dummy Year 1981 dummy Year 1982 dummy Year 1983 dummy Year 1984 dummy Year 1985 dummy Year 1986 dummy Year 1987 dummy Year 1988 dummy Intercept R 2 = 0.758

0.152 - 0.048 -0.100 0.164 0.338 0.212 0.368 0.085 0.071 0.142 -0.277 0.228 0.219 0.260 0.586 0.053 - 0.449 - 0.575 - 0.635 -0.854 - 1.119 - 1.507 - 1.554 - 1.970 - 2.388 - 2.725 - 3.109 6.131 F = 109.05

1.92 - 0.93 - 1.75 18.21 7.38 4.22 6.09 4.02 2.52 2.36 - 10.48 3.38 5.52 7.34 9.19 3.28 - 2.90 - 4.21 - 4.71 -6.16 -6.93 - 9.23 - 10.25 - 11.57 - 13.11 - 14.57 - 15.73 42.22 N = 1436

aFirm dummy coefficients omitted for clarity (see Table 3 for similar results). bt statistics are based on robust standard errors.

360

J. Stavins negative, but insignificant. It is possible that the market penetration effect and the own market segment strengthening effect counteracted each other. 23 The results were c o m p a r e d to the hedonic regression results. The difference between the two models is the inclusion of the distance measures in the price regression. The hypothesis that the distance measures' coefficients are jointly equal to 0 was rejected at the 1% level, even though the hypothesis that coefficients remained unchanged between the two models could not be rejected. The above result has an important implication: as all the quality coefficients remained unchanged, the quality measure based on the hedonic regression is equal to the quality measure based on the price regression. Therefore the estimated price is the same whether quality is computed first and used in the distance computation (as above), or the estimation is done in a single step.

B. D e m a n d Quality-adjusted prices used in the market share equation (6) were computed using the unidimensional quality measure, i.e., applying hedonic marginal implicit prices as attribute weights. 24 Two-stage least squares (2SLS) estimation was used, with the predicted prices from the supply estimation used as instruments. Three-stage least squares (3SLS) estimation was also carried out to test for possible residual correlation between the two equations. The results of the two methods are in Table 6. 25

i. Own Price Elasticity of Demand. The coefficients on own quality-adjusted prices were negative and significant in both specifications. Deriving from equation (6), demand elasticity equals:

rl-

&s Pmit OP Smit

d In s &p Pmit =

Pmit "Y1

dm n

(15)

The specification allows for different demand elasticities for each model, depending on each model's relative market position in the quality space. The 2SLS price coefficient yielded an average estimated elasticity of demand of 6.3 (applying the formula above), ranging from 2.9 in 1977 to 7.2 in 1988. 26 The estimates are consistent with the imperfectly competitive market structure of the

23 In another specification, the number of models produced by the firm and the number of models produced by other firms in the same year were included instead of the distance measures. The results were qualitatively similar: the more models other firms marketed, the lower the model's price. The number of own models was insignificant, but models produced by single-model firms sold for less than models produced by multi-model firms, ceterisparibus. 24As I am interested mainly in demand effects, a better set of attribute weights would have been marginal utilities of the characteristics (instead of marginal costs), but they are not available. 25 I did not estimate the market share equation using logit, because of logit's independence of irrelevant alternatives property. In the case of choosing among the PC models, consumers' utility would most likely increase with a larger choice of PCs. Furthermore, I have no information about the consumers purchasing individual models. 26 The 3SLS estimates of price elasticities of demand averaged 10.8, ranging from 5.0 in 1977 to 12.4 in 1988.

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361

Table 6. Market Share Estimation, 2SLS and 3SLS Dependent Variable: Log (Market Share) 2SLS

Variable

3SLS t Stat

Coeff

t Star a

Coeff

(P-q)/average distance

- 0.00118

- 3.72

- 0.00295

- 4.67

Average distance from other m o d e l s

- 1.563 0.003

- 4.14 - 0.69

- 1.586 0.075

- 1.12 1.92

2.894

18.95

2.3117

6.79

1.199

6.62

0.461

1.18

2.602

10.47

2.270

5.62

ln(Y~ e (e - q)/distance)

- -

Apple d u m m y Atari d u m m y Commodore d u m m y Compaq

1.946

13.53

1.833

6.4 l

IBM d u m m y

dummy

2.021

13.00

1.946

10.14

NEC dummy

0.608

3.79

0.271)

0.89

Radio Shack d u m m y Zenith d u m m y

1.839

10.86

1.709

6.48

1.359

7.61

1.382

4.44

Wyse technology

0.964

6.74

1.019

2.59

Epson d u m m y

1.494

8.48

1.538

3.99

Kaypro dummy

0.869

3.18

0.885

2.36

NCR dummy

0.466

1.76

0.903

2.43

Northgate Year 1 9 7 8 Year 1 9 7 9 Year 1 9 8 0 Year 1981 Year 1992 Year 1983 Year 1 9 8 4 Year 1985 Year 1 9 8 6 Year 1987 Year 1988 Intercept

dummy

0.195

11.74

0.632

1.41

dummy

- 0.191

- 0.33

- 0.222

- 0.24

dummy

0.082

0.14

0.765

0.89

dummy

0.057

0.10

0.263

0.36

dummy

0.059

0.10

0.328

11.45

dummy

- 0.947

2.07

- 0.210

- 0.26

dummy

- 1.483

- 3.23

- 0.310

- 0.33

dummy

-2.030

-4.64

- 1.567

-2.11

dummy

- 2.066

- 4.73

- 1.187

1.38

dummy

- 2.241

- 5.15

- 1.763

- 2.30

dummy

- 2.830

- 6.67

- 2.950

- 4.28

dummy

- 2.631

- 5.83

- 3.076

- 4.53

- 3.448 - 7.15 R 2 = 0.511

resid correlation = N = 972

0.114

- 4.0211 - 3.119 R 2 = 11.324

resid correlation = 0 . 0 5 3 N = 972

at statistics are based on robust standard errors.

PC industry. As Figure 2 shows, the estimated average demand elasticity increased over time (in absolute value), as the industry became more competitive. There is a significant difference between the initial few years and the post-1982 period, when several IBM-compatible clones entered the market.

ii. Cross-Elasticity of Demand. The cross-elasticity coefficient on prices of substitutes was insignificant in all the specifications. 27 I tested whether a model competes only with its two nearest neighbors in a linear quality space [see Bresnahan (1981)]. Only the two nearest models were entered into the market share equation. The cross-price coefficient was still insignificant. The equation was re-estimated several times, by adding two more neighbors in each subsequent run. Each time the ~7 Other specifications included an average quality-adjusted price of substitutes, as well as residuals from the hedonic regression. The coefficient was always statistically insignificant.

362

J. Stavins

7 ,'4

~U3 .J ~3U7 E

6 5 4

3

19%

19bo

1964

198~

Year

Figure 2. Average demand elasticity by year: 2SLS.

cross-price coefficient remained insignificant, while the own quality-adjusted price coefficient did not change at all. The own price elasticity result is thus robust; regardless of how many neighbors the model is allowed to compete with, the effect of its own price on its market share does not change. The insignificant effect of other models' prices could be the result of simultaneous price changes of PC models due to the competitive structure of the industry. The average distance was included in the estimation to allow for a separate effect of spatial location on the model's market share.

iii. Firm Effects. Positive coefficients on major firm dummies indicate that those firms had a higher market share than predicted by the quality-adjusted prices of their models. The brand effect on model market share equals e 8. For example, the 2SLS coefficient on the IBM dummy of 2.021 indicates that, on average, IBM models' market share was over seven times higher than that of the omitted firms' models, controlling for quality-adjusted prices of models. Negative coefficients on year dummies indicate the decrease over time in market shares of individual models. It is worth noting that when firm and year dummies were omitted from the market share regression, price coefficients remained unchanged, which confirms the robustness of the estimated elasticities. As the market became more competitive, I expected the leading firms' advantage to diminish. To test whether the firm effects declined over time, firm-year interaction dummies were included for all major companies. Almost all of the interaction terms were negative, indicating a decline in firm effects over time. The estimated coefficients are in Table 7. The estimated brand effect decline ranged from 26% for IBM to 99% for Radio Shack over the 13-year period. it). Established Brands. Finally, I tested whether models produced by more established firms have an advantage over new entrants by comparing demand elasticities for incumbents' vs. entrants' models, as well as for new vs. older models. If established firms have an advantage over new entrants (due to their reputation and past marketing, for example), their models should have lower demand elastici-

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363

Table 7. B r a n d Effect D e c l i n e o n M a r k e t S h a r e ( 2 S L S ) D e p e n d e n t Variable: Log (Market

Share)

Variable

Coefficient

t Statistic

(Estimated p r i c e - q u a l i t y ) / average distance

- 0.00095

- 2.98

l n ( ~ e (l~-q)/dist . . . .

--

0.001

- 0.41

- 1.501 4.012 3.297

-3.57 7.62 4.40

Commodore dummy Compaq dummy

4.807 1.928

8.33 1.45

IBM dummy NEC dummy Radio Shack d u m m y Zenith d u m m y Wyse technology Epson dummy Kaypro dummy NCR dummy Northgate d u m m y Apple * year Atari * y e a r Commodore * year

2.058 - 0.769 6.278 3.968 - 6.824 2.574 7.142 3.696 4.964 -0.088 -0.178 - 0.217

2.40 - 0.61 13.04 1.67 - 1.39 0.59 3.03 0.89 4.51 -1.66 - 2.25 - 3.41

Compaq * year IBM * year NEC * year

- 0.013 0.013 0.131

- 0.11 0.17 1.20

Radio Shack * year

- 0.425 -0.209 0.649 - 0.104 - 0.557 - 0.299

- 8.51 -1.05 1.63 - 0.29 - 2.65 - 0.83

)

Average distance from other m o d e l s Apple dummy Atari d u m m y

Zenith * y e a r Wyse technology * year Epson * year Kaypro * year NCR * year

Northgate * y e a r Intercept R E = 0.492

- 0.622 - 5.997 F = 32.65

- 3.21 - 47.84 N = 972

ties. To test the hypothesis that entrants face higher demand elasticity for their models, both an entrant dummy and an interaction of the price terms with an entrant dummy were included in the second-stage market share regression. Similarly, model age and its interaction with price were included. Entrants' models had a significantly lower market share than incumbents' models (the entrant dummy coefficient was negative and significant). However, although the interaction of the own price term with an entrant dummy was negative, indicating more elastic demand for entrants' models, the coefficient was not statistically significant. 28 Although the difference in price elasticities between incumbents and entrants is small, the average elasticity decreased with a model's age (Table 8). Models' age

28 E n t r a n t s did, h o w e v e r , face significantly higher cross-elasticities o f d e m a n d than incumbents. Pooling of the two groups was tested using the Chow test. Joint regression was rejected at the 5% level, but c o u l d n o t b e rejected when the interaction terms were included.

364

J. Stavins Table 8. M e a n D e m a n d E l a s t i c i t y b y M o d e l A g e a n d F i n n ' s S t a t u s Finn's status Incumbents Entrants

6.202 6.578 Model's age

0 1 2 3 4 5

6.975 6.102 5.226 3.518 3.143 2.948

did not appear significant when treated continuously, but when the own price term was included in the market share regression separately for each age cohort, the price elasticity coefficients did decrease in absolute value for each of the initial few years (see Table 9). The results show that a model which has been on the market for one or two years faces more inelastic demand than a completely new brand just entering the market, because of reputation and marketing of individual models. The difference disappears after the initial couple of years on the market, when a model becomes obsolete. Incumbents faced more inelastic demand than entrants in most years, although the difference was not statistically significant.

VI. Summary and Conclusions The paper presents a model of market demand based on utility maximization, and market supply based on profit maximization, for goods differentiated in several attributes. Using data on personal computers, demand elasticities for individual models were estimated.' The elasticities varied across computer models according to their market power, as measured by distances between models in a quality space. The estimates were consistent with the increasingly competitive structure of the industry--the demand elasticities increased over time, while the brand effect on model market share declined. Incumbent firms and older models faced more inelastic demand. The paper builds on the relatively small set of empirical studies analyzing demand and supply for differentiated goods. The distance measure makes the model flexible by allowing for heterogeneous estimates of demand elasticities

Table 9. M a r k e t S h a r e R e g r e s s i o n , P r i c e T e r m f o r E a c h A g e C o h o r t Variable

(P-Q)/distance PRICE PRICE PRICE PRICE PRICE PRICE

if age if age if age if age if age if age

= = = = = >

[PRICE] 1 2 3 4 5 = 6

Coefficient

t Statistic

- 0.00143 0.00117 0.00205 0.00015 - 0.00027 - 0.00513 - 0.00655

- 4.09 2.72 2.99 0.12 - 0.21 - 2.95 - 3.16

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365

without limiting market competition to the two nearest neighbors. The study utilized hedonic regression methods in a new way. The results could help predict demand effects of price changes in various segments of a market, as well as effects of changes in an industry's market structure over time. In the case of industries with relatively low model turnover, effects on the change in market shares over time could be estimated, instead of levels. In the PC industry, however, few models survive beyond their first year. The accuracy of the estimation could be improved if better demand and supply instruments were available. Future empirical studies should focus on individual taste distribution, as endogeneity of taste in a market with continuously evolving technology could be incorporated. On the supply side, a firm-level cost measure could provide a good instrument.

Appendix Although I assumed that firms choose their models' location (and thus distance between models) in the first stage of the game, while prices are set in the second stage, one can suspect that in locating a new model, a firm will take into account previous period prices. Representing model price as a function of its distance from other models (omitting its attributes for simplicity): P, = / 3 d t + Et

(A1) Pt+l = / 3 d t + l + Et+l

but: dr+ 1 = YPt + r/t+ 1

(A2)

therefore:

Pt+l =/3")/Pt

q-

~T/t+l q- Et+l.

Even though lagged prices do not directly enter the equation, it is as if lagged dependent variables appeared on the right-hand side of the equation. It is well known that if there exists serial correlation, for example et+ 1 = pEt + ut+ l, the distance coefficient, /3, in (A1) is going to be biased as follows: coy ( d t + 1' ~t + 1 ) var( dt + 1)

=/3+

TP°'~ 2

var( dt + 1)

>/3.

As the stock of models changes every year, one has to consider two groups of models separately: models entering in period t + 1, and models surviving from t to t + 1. For the new models, the location is determined in t + 1, and can depend on past prices. But the new models have no past and, thus, for them p = 0 (i.e., there is no serial correlation). Therefore, I have to be concerned with the surviving models only. But the location of the surviving models is determined in period t, and is therefore exogenous in period t + 1 and, thus, ~- = 0 in equation (A2).

366

J. Stavins In order to test whether the distance coefficient was biased because of the presence of serial correlation for the surviving models in the sample, I ran separate price regressions for the new models (sample of 770) and for the models surviving from the previous period (sample of 666). The estimated coefficients for the new models are almost identical to the pooled coefficients. The average distance from the other firms' models' coefficient for the surviving sample is indeed biased upwards: 0.494 vs. 0.152 for the pooled sample, but the own models' distance coefficient is even lower than the pooled sample coefficient: -0.165 vs. -0.048. I tested whether the two groups could be pooled, and could not reject pooling at the 1% level. Therefore estimated prices were based on pooled estimates, even though the estimates might be inefficient.

The views in this paper do not necessarily reflect the views of the Federal Reserve Bank of Boston or the Federal Reserve System. Helpful comments were provided by Ernst Berndt, Richard Caves, Zvi Griliches, Adam Jaffe, Manuel Trajtenberg, and seminar participants at the Federal Reserve Banks of Boston and New York; Harvard, Northwestern, and George Mason Universities; and the National Bureau of Economic Research. Research for this paper was conducted while the author was working on her Ph.D. dissertation at Harvard University.

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