The effects of vertical integration between cable television systems and pay cable networks

JOIJRNAL OF

Econometrics ELSEVIER

Journal

of Econometrics

72 (1996) 357-395

The effects of vertical integration between cable television systems and pay cable networks David Waterman”, Andrew A. Weiss*%b

(Received

March

1993: final version

received January

1995)

Abstract Using data for 1646 cable systems, we find that vertical integration between pay cable programming networks and cable systems has substantial effects on final market outcomes. Cable systems owned by the two multiple system operators (MSOs) having majority ownership ties to four major pay networks tended to carry their affiliated networks more frequently and rival networks less frequently than did the average nonintegrated system. These systems also offered fewer pay networks in total than did the average nonintegrated system. We also find that when carriage differences are accounted for, integrated systems tended to ‘favor’ their affiliated networks with respect to pricing or other marketing behavior. The models we employ are obtained from a model selection technique involving backward elimination and the Schwarz criterion. Key war-ds: Model selection; Schwarz criterion JEL classjficurion: C2; L22; LK?

1. Introduction Vertical ownership ties between multiple cable television system operators (MSOs) and cable programming networks have recently attracted policy attention. A series of congressional hearings partly concerned with these ties

*Corresponding

author.

We are grateful to A.C. Nielson Co. for providing much of the data used in this paper and to the anonymous referees and various seminar participants for their helpful comments. We particularly thank Richard Blundell for his support. Any errors are our own.

0304-4076~96/$15.00 1’ 1996 Elsewer SSDI 030440769401726 T

Science S.A. All rights reserved

culminated in the Cable Television Consumer Protection and Competition Act of 1992. One provision of the Act required the Federal Communications Commission (FCC) to set limits on the number of channels a cable system can use to exhibit programming in which it (or its parent company) has a 5% or greater equity interest (FCC 1993). A principal concern leading to these developments has been that cable systems integrated with one or more networks might ‘favor’ their affiliated network(s) to the disadvantage of unaffiliated networks, either by the exclusion of rival networks from their program menus or, if the rivals are carried, by preferential pricing and promotion of their corporate relatives. Such possibilities are of particular interest because cable networks do not usually have viable means of distribution to consumers other than via cable systems; the lO,OOO-odd systems in the U.S. typically face little direct competition from other multi-channel delivery systems at the local level. As in other industries, the vertical integration in cable raises issues of economic efficiency. Policy-makers are also concerned, however, with preserving freedom of access by cable program suppliers to the public and with the achievement of ‘maximum diversity’ of cable programming (e.g., Brenner, 198X; Brennan, 1990). The recent debates about vertical integration in cable parallel long-standing controversies about ownership ties between the creators or packagers of other information products (e.g., broadcast television networks, electronic database suppliers) and downstream distributors of the products (e.g., broadcast television stations, local telephone companies). See, for example, Owen (1975) and U.S. VS. Western Electric Co. (1991). The main purpose of this paper is to quantify the effects of vertical integration between cable systems and one subset of cable program suppliers: monthly subscription pay cable networks specializing in recent theatrical feature films. Specially, we compare the availability, retail prices, and output (i.e., subscribership) of the four largest vertically integrated pay networks - HBO, Cinemax, Showtime, and The Movie Channel (TMC) -- on systems with and without vertical ties to them. We employ a sample of 1646 systems owned and operated in 1989 by the largest 25 MSOs, three of which had vertical ownership ties to the four subject pay networks.’ We first model the choices by systems of whether to carry each of the four subject pay networks and of the total numbers of networks carried, using probit and ordered probit models, respectively. We then model retail prices and subscriberships for each of the four networks. Because prices and subscriberships are only observed when the corresponding networks are carried on the system, tobit models are employed for these equations. We estimate the probit

I Preliminary econometric studies of the effects of vertical integration between cable TV systems and pay cable networks have been conducted by Salinger (1988) and Waterman, Weiss, and Valente (1989).

D. Waterman,

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and ordered probit models by maximum likelihood and apply Heckman’s two step procedure (e.g., Amemiya, 1985, Sec. 10.7) to the tobit equations. In these respects, the methods are straightforward. Several obstacles arise, however, in the application of these methods. First, whereas the estimation of probit and tobit models depends crucially on the assumption of normality of the errors, we cannot be certain that the errors in our models are normally distributed. We therefore test the normality in the probit equations, and include certain additional terms in the tobit equations to allow for potential nonnormality. Second, the retail price charged and the subscribership realized for any given pay network depend on which other networks are carried on the system. This implies that the overall effect of vertical integration on prices and subscribership is nonlinear and does not depend on any one parameter in each of the models. To estimate the overall effect of integration, we generate predictions of the net changes in prices and subscribership that can be attributed to vertical integration. We also obtain standard errors of these differences. We use a comparable method to generate predictions of the effects of integration on carriage decisions since nonlinearities in the probit model do not permit direct interpretations of its coefficients. Third, the various models employ potentially large numbers of explanatory variables. In the price and subscribership models, for example, interdependence between the networks means that the explanatory variables include exogenous variables, variables signifying which other networks are carried, variables representing the period of time each network has been carried, and variables representing the nonnormality. Among other problems. the large numbers of explanatory variables makes it difficult to identify the effects of the vertical integration. That is, the standard errors of the changes due to vertical integration are large. Our approach is to simplify the models using a model selection procedure based on backward elimination and the Schwarz model selection criterion (Schwarz, 1978). In the progress of our analysis we discuss the rationale for the use of model selection, outline the algorithm, suggest some methods for evaluating the output, and incorporate the tests for nonnormality into the algorithm. The paper continues in Section 2 with institutional information about the pay cable industry in 1989 and a brief description of our data set. In Section 3, we outline a theoretical model of cable system behavior and detail the model selection algorithm. In Section 4 we present the models and results for carriage, and similarly for prices and subscriberships in Section 5. Finally, a discussion and concluding comments are given in Section 6.

2. Background and data The channel menus offered by local cable television systems generally begin with a ‘basic’ package for a single monthly bundled price. This package typically

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includes local and distant broadcast stations and may include various ‘cableoriginated’ basic networks, such as CNN and MTV, which depend mainly on advertising. The ‘premium’ or ‘pay’ networks with which we are concerned carry no advertising and are offered to consumers a la cute, or optionally in packages of two or more, for extra monthly charges. Consumers cannot subscribe to pay networks without first buying the basic service. Table 1 gives basic statistics about nationally distributed pay networks and their ownership affiliations as of December, 1988. As columns 3 and 4 show, four of the five largest networks, accounting for approximately 80% of all pay subscriptions, were vertically affiliated with MSOs and hence local systems: HBO and Cinemax by means of Time Inc.‘s 82% ownership of American Television and Communications Corp. (ATC) and 50% share of Paragon; and Showtime and TMC by means of Viacom Inc.‘s sole ownership of Showtime Networks, Inc. As columns 5 and 6 indicate, these ownership relations began at or soon after the launch of the four integrated networks, except in the case of Paragon, whose affiliation with HBO and CMX resulted from a joint venture relationship with ATC begun in 1987. The four integrated networks are distinguished by their market importance and the apparent similarity of their programming menus. Some of the recent theatrical movies they exhibit can appear on all four networks. They differentiate among themselves, however, by offering theatrical films on an exclusive basis, as well as specials, sports events, and ‘made-for-pay’ feature films. The only other competitor with substantial market share, the Disney Channel, offers original programming, including made-for-pay movies, and various classic, family-oriented movies. Next, the statistics in columns 1 and 2 of Table 1 show the large variations in the carriage of the pay networks and suggest that these networks were more likely to be carried on systems serving larger numbers of basic subscribers. One evident reason for the variations is the channel capacity of cable systems. As Table 2 suggests, only the largest systems could accommodate all eleven of the nationally-distributed pay networks, in addition to the 70-odd basic cable networks and the numerous local broadcast, regional, and other channels available in 1989. In particular, the data of Table 3 show the wide variation in the number of different pay channels that systems chose to offer. An important concern of this study is thus whether cable networks are able to obtain ‘shelf space’, i.e., carriage, on local systems. Columns 1 and 3 of Table 1 further show that carriage and subscribership for Cinemax are less than for HBO, and similarly for TMC in comparison to Showtime. Apart from their launch dates and possible variations in product quality, these differences are also likely to reflect product bundling strategies of the Time Inc. and Viacom networks. Cinemax and TMC are usually marketed by systems to subscribers as ‘companion’ services, so that subscribers tend to accept them only in addition to one of the two market leaders, HBO and

1

64

31

Cmemax

The Disney Channel

The Movie Channel

5.9

Other

1.0

1.2

6.8

10.7

14.9

16.5

42.0

% market share

1.0

Movie Classics

23

56

95

85

86

99

% basic subscribers covered

Bravo

American

5

49

Showtime

Channel

50

HBO

The Playboy

83

Network

1988-89

% systems carrying network

Pay cable networks,

Table

(100%)

ma.

ma.

n.a.

None

Viacom

None (100%)

ATC (82%) Paragon (50%)

Viacom

ATC (82%) Paragon (50%)

MS0 affiliation

1980

1984

1982

1979

1983

1980

1976

1972

Launch date

1983

1980 1987

1976

1975 1987

Date of MS0 affiliation

362

D. Waterman, A.A. Weiss / Journal ~f‘Ecoconometrics 72 (1996) 357-395

Table 2 Channel capacity

of systems, 25 largest

MSOs

Channels

% of systems

Under 20 20-35 36-53 54 and over

2.4 41.6 39.4 16.6

Table 3 Distribution Number o-1 2 3 4 5 6 7 8 9 or more

of pay networks,

of pay networks

25 largest

MSOs % of systems 3.4 6.9 19.1 29.6 23.3 9.5 4.8 2.6 0.7

Showtime. In 1988, a little over half of basic cable subscribers, or about 29% of all TV households, accepted at least one pay network (Cablevision, March 14, 1988). Many households accepted more than one; the average number of pay networks sold per basic household in 1988 was 1.7 (The Kagan Media Index, December 24, 1991, p. 12). Except for one model, we confine our analysis to the four largest integrated networks, HBO, Cinemax, Showtime, and TMC. As noted earlier, we consider only systems in the largest 25 MSOs, which permits comparison of the behavior of the integrated systems with that of a large, presumably comparable group of nonintegrated systems. These MSOs accounted for approximately 59% of all U.S. basic cable subscribers in 1989. ATC was the second largest MSO, with 137 systems serving 7.1% of subscribers; Viacom was the 12th ranked MSO, with 23 systems serving 2.5% of subscribers; and Paragon was the 16th largest MSO, with 30 systems serving 1.6% of subscribers. Our primary data base is the A.C. Nielsen Cable On-Line Data Exchange, with supplementary data from the Paul Kagan Associates’ Cable TV Census. Details of these data are given in the Appendix.

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3. Models and model selection

3. I. Structural model The structural model to follow focuses on local cable systems and their carriage of the four movie-based pay networks. All systems offer a package of basic networks to consumers, and may also carry zero through four of the movie-based pay networks. The pay networks are then marketed to consumers, who must first accept the basic package. For a nonintegrated system, Profit = PBSB + i

NETjPjSj

- C(\VB,(wj: j = 1, . . . ,4f, M, T),

(1)

j=l

where PB and SB are the price and subscribership for basic service; the NETj are indicator functions for the carriage of the pay networks (NET, = 1 if network ,j is carried, = 0 if not); the Pi and Sj are the prices and subscriberships for the pay networks; C( .) is the cost function; wB and Wj are the input costs for the basic service and pay networks, respectively; the input costs are increasing functions of the relevant numbers of subscribers served (although we ignore any effects of joint network ownership on costs); M is a vector of marketing costs: and T represents other costs such as service and line maintenance and depends on various technological factors such as the size and density of the local service area. Given networks offered and prices, each consumer decides whether to accept basic cable, and which pay networks to accept. Aggregating over consumers gives the demand function for the basic service, Ss = Ss(Ps, and the demand

{NET,,

Sj, Pj: j = 1,

functions

Sj = Sj(PB, Sg, (NET,,

for pay networks

,4), M, DB),

(2)

that are carried,

Si, Pi: i = 1, . . . ,413 M, Dj),

(3)

where DB and Dj are vectors of demographic variables and other demand factors, such as prices and availability of competing entertainment services. Of course, these demands also depend on the attractiveness of the array of programming included in the basic package and of the programming on each pay network, but this is left implicit. Since the pay networks can only be obtained by first subscribing to basic, pay variables are included in the demand for basic, and vice versa. More importantly, the Pj and Sj are latent variables, since price and subscribership are only observed when a network is actually carried. The local cable systems maximize profits over PB, the NET, and Pi, and the components of the M vector. Focussing on the pay networks, we thus assume that the system picks the most profitable of the sixteen possible combinations of

364

D. Wuterman. A.A. Weiss 1 Journal of’Econometrics

the four networks, subject to its capacity constraint. function for the basic package is given by

PLJ= PB(SLI, (NET,, S/, Pj:,i = and the supply functions pj = Pj(P,,

With this choice, the supply

(4)

1, . . . ,4), M, Y,),

for the pay networks

SS, (NET,,

72 (1996) 357-395

Si, Pi: i = 1,

that are carried

are given by

,4), M, y,),

where the Y’s are vectors of programming and other costs in C( .). A vertical relationship between a pay network (say network 1) and a system can affect the carriage, pricing, or marketing decisions of the integrated system in two ways. First, transactions efficiencies may lower the implicit cost to the system of network 1, thus in effect shifting u’i downward. In a single-product monopoly, this would, under most assumptions, reduce the output price P, . But as Salinger (1991) shows, final outcomes in the general multi-product monopoly case depend on the shapes of demand curves and retaliation by rival networks; virtually any array of final prices can result. One plausible end result, however, is that the final price of the affiliated network falls, reducing demand for a rival network. The rival would be eliminated from the system’s menu if demand falls below the threshold level which makes its carriage profitable. A second possibility is that the combined firm could attempt to employ a cost raising strategy against a rival network (e.g., Salop and Scheffman, 1983). The combined firm, that is, considers the profits of the local systems it controls as well as the profits of its network branch from all local markets. In the presence of economies of scale in networking, excluding or disadvantaging a rival network in the MSO’s controlled systems would increase the average cost per subscriber of the rival. If the attractiveness of its programming subsequently suffers, the rival network would be disadvantaged in all local markets, and possible driven from the market altogether.2 Although a variety of outcomes could thus follow from network-system vertical integration, the structural model provides a rationale for the central concern of policymakers: that unaffiliated networks might be excluded from or otherwise disadvantaged by vertically integrated systems, and perhaps forced from the market altogether. For a detailed discussion of alternative theoretical models of vertical integration and their social welfare implications, see Waterman and Weiss (1996).

‘This foreclosure scenario has been the economic basis for numerous allegations in the legislative proceedings leading to the 1992 Cable Act and for several private antitrust suits in the cable industry, including one case involving the Time Inc. and Viacom pay networks: ‘Viacom International Inc. and Showtime Networks Inc. Plaintiffs. against Time Inc., Home Box Office Inc. American Television and Communications Corporation, and Manhattan Cable Television, Inc. Defendants’, Compliant, US District Court of New York, May 8, 1989 (settled in 1992). See also Roberts (1992).

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3.2. Use qf‘ reduced form models The structural model leads to a system with at least fourteen endogenous variables: carriage, price, and subscribership for the four pay networks, plus price and subscribership for the basic package. The exogenous variables include demographic variables and variables describing the size of the service area and the channel capacity of the system. The presence of vertical integration is also assumed to be exogenous, and is represented by dummy variables ATC, VIACOM, and PARAGON, which are equal to one if the system is in the relevant MSO, and zero otherwise. Problems with logical coherency, identification, and estimation, as well as data requirements, however, make it infeasible for us to estimate a simultaneous equations system. In any case, our primary objective of estimating the net effects of vertical integration can be achieved with reduced form equations for the twelve pay network variables.3 Our approach is to use simple specifications in which the four qualitative NET, variables are modelled by probit models and the eight pay network price and subscribership variables are modelled by tobit models.4 The coefficients on the MS0 dummies give the net effects of vertical integration on the endogenous carriage, price, and subscribership variables of interest. To consider whether the effects of the vertical integration are captured by the MS0 dummies, we also include interaction effects between the MS0 dummies and certain of the exogenous variables. In particular, we interact the MS0 dummies with variables representing the size and channel capacity of the systems. Larger capacity, for example, should make carriage of each network more likely; but for rival networks on integrated systems, transactions efficiencies or a cost-raising strategy may make the effects less pronounced. 3.3. Model selection The economic model suggests the type of variables to include in the structural and hence reduced form equations. With our data set, this yields more than twenty potential variables in the carriage probit models and more than thirty in

‘Some previous authors, e.g., Mayo and Otsuka (1991) and Rubinovitz (1993) have estimated models for cable television supply and demand using two-stage least squares methods in order to determine separate price elasticities of basic and pay cable services (where pay variables were simply averaged across networks rather than treated separately, as in the present study), or to measure the eficcts of basic service rate regulation. Cable rates were completely deregulated at the time of our study, so that regulatory variables are not relevant to our models. ‘Of course, other approximations are possible. The choice of networks, for example, could be viewed as a multinomial logit model. But the independence assumptions implicit in this model do not seem appropriate here and, since the explanatory variables do not vary over choices, the model would require different parameters for each of the sixteen possible combinations of networks.

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the price and subscribership tobit models. It seems likely that some of these variables are substantially irrelevant, leading to large standard errors on the estimates of the effects of vertical integration. Pragmatically, the alternative to simply reporting results for the ‘full’ models is to employ some type of general-to-specific modelling strategy to obtain more parsimoneous models. Within such a strategy, our options are to impose exclusion restrictions based on the economic model, to use hypothesis testing, or to use some model selection criterion. Since any exclusion restrictions would be to some extent arbitrary, and would apply to the structural equations rather than to the reduced form equations directly, we prefer not to use the first option. Our choice from the other two options is to use model selection rather than formal hypothesis testing. This choice is supported by general arguments recently given in Granger, King, and White (1995). These authors argue that hypothesis testing has several deficiencies when used as a means of deciding on model specification. First, hypothesis testing favors the null hypothesis. Second, it is typically based on an arbitrary choice of significance. Third, because model building typically involves a series of tests with little regard for controlling overall size, two investigators working on the same data can easily end up with different models purely because they performed the tests in different orders or used different levels of significance. These deficiencies are not shared by appropriately chosen model selection procedures. The model selection algorithm we employ gives consistent estimators of the parameters and asymptotically justified standard errors, and incorporates specification testing. The essential feature of the algorithm is that at each step, the variable with the lowest r-ratio is excluded from the model. One possible concern is therefore that variables whose ‘true’ coefficients are nonzero will be automatically dropped from the model.5 But this just means that a type II error has been made, and asymptotically, the algorithm ensures that the probability of a type II error is zero (as we shall see). More generally, it turns out that the likelihood ratio (LR) statistic comparing the full model to the ‘final’ model from the algorithm will be less than log n times the number of extra variables, where n is the sample size. In the linear regression model at least, this LR statistic bounds a measure of the sensitivity of the coefficients to the exclusion of the variables (e.g., McAleer, Pagan, and Volker, 1985). In cases when the LR statistic is numerically large (though ‘insignificant’), Pagan (1987) suggests the

’ Presumably, it is of less concern if variables are dropped at the discretion of the researcher ~ or not included in the first place. For example, if the consumer’s utility function is not separable with respect to the cable and other consumer goods, then we would need to include prices and quantities of the other goods.

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qf Econometrics

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calculation of the actual sensitivity. This also takes into account the collinearity between regressors6 The algorithm is based on backward elimination and the Schwarz model selection criterion. Let L(k) be the value of the likelihood function and k be the number of parameters in the model. Then in the Schwarz criterion, k is chosen to minimize: SC(k) = - 2 log L(k) + k log n.

(6)

In the standard regression model, log L(k) is replaced by - (42) log c2, where 6’ is the mean squared error. To compare two related models, note that SC(k + 1) - SC(k) = log y1- 2{logL(k

+ 1) - logL(k)].

(7)

Hence, - 2(log L(k) - log L(k + 1)) < log n * SC(k + 1) - SC(k) > 0.

(8)

In other words, the smaller model is chosen if the likelihood ratio (LR) statistic for the exclusion of variable k + 1 is smaller than log n. The algorithm begins with all possible variables on the right-hand side and reduces the size of the model according to the Schwarz criterion. At each step, the LR statistic from dropping each variable in the model is calculated, and the variable with the smallest statistic is dropped. The process continues until deleting any additional variables would lead to an increase in (6). The algorithm can therefore be thought of as a sequence of nested hypothesis tests. The use of the Schwarz criterion means that the sizes of the tests go to zero as the sample size increases; and since the critical value in the tests depends only on log n, the powers go to one as n -+ a. In other words, the procedure gives a consistent estimate of the model size (e.g., Geweke and Meese, 1981) and inference in the selected model is asymptotically valid (e.g., Potscher, 1991). This means that the asymptotic standard error obtained from the final model in the procedure can be used in the usual way.7 If the models are estimated by OLS, then the LR test statistics are functions of the ordinary t-ratios and it is not necessary to calculate the separate LR statistics. This is not the case, however, in nonlinear models such as probit and ordered probit models. To speed the computations in these models, we approximated the LR statistics using the squares of the asymptotic t-ratios. In many other cases, such as when the errors in a regression model are

“The sensitivity measure given in McAleer et al. (1985) is based on Learner’s extreme bounds analysis (e.g., Learner, 1978) and does not take into account the trade-off between changes in the value of the estimate and in its variance as variables are dropped. In our case, the decreases in vartances are large relative to the changes in the estimates. ’ As noted in Judge et al. (1985, p. 870), however, properties of such model selection procedures.

relatively

little is known

about

the finite-sample

368

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heteroskedastic or when the likelihood function is based on the normal distribution but the true distribution is not normal, the likelihood function itself is an approximation. Provided that the LR test based on the approximate likelihood function is consistent, however, the estimate of the model size will still be consistent. Granger et al. (1995) also comment on the role of diagnostic testing in model selection. Two possible approaches are, first, to conduct Lagrange multiplier or other conditional moment tests on the models and, second, to augment the models and perform selection in the larger class of models. Since it is not clear which approach is preferable, Granger et al. suggest using some combination of the two. It is clear, however, that the application of the second approach is quite difficult in probit models. This would require, for example, specifying that the errors come from some family of distributions containing the normal as a special case and doing maximum likelihood estimation within this expanded family (e.g., Gallant and Nychka, 1987; Gabler, Laisney, and Lechner, 1993). We therefore apply the first approach in the probit models and the second approach in the regression models. The particular tests we use are described below.

4. Carriage of pay networks 4.1. Carriage models To model the carriage decisions, it is convenient to introduce latent variables, NET:, i = 1, . . . ,1646,j = 1,2,3,4 (for HBO, Cinemax, Showtime, and TMC, respectively), which can be thought of as measuring the propensity of each system to carry each of the four different pay networks. The reduced from equations for NET,? are given by NETiS = Xr~j + (Uij,

(9)

where Xi is a vector of exogenous variables and the (Dij are independent over i and jointly normally distributed overj. We also define the observed dummy variables for carriage, NETij, such that NETij = 1 if network ,j is carried on system i and NET,, = 0 otherwise. The normalization rules for the intercepts in (9) imply that NETij = 1 if NET; > 0 and NETij = 0 if NET; < 0. Because the errors are assumed normally distributed, the carriage equations in (9) are estimated by probit maximum likelihood. The specific variables we employ in the carriage models are described in Table 4. Here we discuss the possible impacts of these variables, focussing on overall cable demand. In the individual carriage models, a factor encouraging a larger number of pay networks to be carried will, other things being equal, increase the probability that the individual network will be carried. Substitution effects working in the opposite direction, however, could also dominate.

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Table 4 Variable definitions Depvndw

u~riah1e.s

NET,,

dummy variables SHO. TMC)

LPEN,,

logarithm of the number of subscribers as a fraction of the total number of homes passed for network j on system i (LHBOPEN, LCMXPEN. LSHOPEN. LTMCPEN)

.NPAY4

total number the system

of the four movie-based

.NP,4 YALL

total number

of pay cable networks

Eupltrntrtor~

for carriage

of network

j on system i (HBO, CMX,

pay cable networks

offered by

offered by the system

rclricrbles

LMEDIANY

logarithm

of median

household

.AGE3554

percentage

of households

with head aged 35554, 1988

CHILDREN

percentage 1988

of households

with one or more children

RENTERS

percentage

of households

who are renters.

MC’LTIFAM

percentage

of households

who live in multi-family

TC

number

D/WA1

= 1 if system is in one of the largest 25 broadcast television markets, as measured by TV households in the viewing area, = 0 otherwise

of commercial

income.

broadcast

1988 ($10,000’s)

stations

living at home,

1988 units, 1988

in the market

(DMA)

DMA2

= 1 if system is in broadcast

markets

26-50,

DMA3

= I if system is in broadcast

markets

51- 100. = 0 otherwise

of homes passed

= 0 otherwise

LHPASS

logarithm

DENSITY

total miles of cable plant divided by the total numbers

CHANDISC

system channel capacity less the number stations in the market (DMA)

LFRANTIME

logarithm franchised

of the number

by the cable system (10,000’s)

of months

of commercial

of homes passed broadcast

since the system was originally

,4CT

= 1 if system is owned and operated

by ATC.

VIACOM

= I if system is owned and operated = 0 otherwise

by Viacom

P.4RAGON

= I if system is owned and operated = 0 otherwise

by Paragon

= 0 otherwise International

Communications

PRO& ,t

the probability that system i carries network j (HBOPROB, CMXPROB.

LTIME,,

logarithm of the number of months since system i first carried j (LHBOTIME, LCMXTIME, LSHOTIME, LTMCTIME)

MILLS

inverse

Mills’ ratio

Inc..

Inc.,

network k, given that it carries SHOPROB, TMCPROB) network

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The first five explanatory variables in Table 4 are franchise region-specific demographic variables. The first three - the logarithm of household income (LMEDIANY), the percentage of households with heads aged 35 to 54 (AGE3_5.54), and the presence of children (CHILDREN) ~ are usually associated with high cable demand. We have no prior expectations for the proportions of renters (RENTERS) and multi-family households (MULTZFAM). These two variables are likely to proxy for factors affecting cable demand, or they may represent cost factors. With respect to the number of competing broadcast stations in the market (TV), more competition should encourage operators to offer more services, but successful competition may limit the number that can profitably be oRered. The same applies for the DMA dummy variables; larger markets tend to offer a wider range of other entertainment alternatives, but the net effect on pay network carriage could be positive or negative. The natural logarithm of the number of homes passed by the system (LHPASS) indirectly represents a cost factor. If there are economies of scale in offering and marketing networks, then greater product differentiation is optimally offered with a larger subscriber base. LHPASS2 allows for further nonlinear effects, although we expect the overall effect from LHPASS to be positive. For DENSITY, we note that more dense population could cause lower marginal costs of operation, or like MULTIFAM or RENTERS, this variable might proxy for demand characteristics. The measure of channel capacity (CHANDISC) takes into account the system operator’s incentive (formerly legal obligation) to carry all ‘significantly-viewed’ broadcast channels in the area.* Ideally, the operator would construct a cable plant with capacity for an optimal menu of networks. We include CHANDISC as a predetermined variable, however, on the assumption that fixed plant decisions are relatively inflexible in the short term. LFRANTIME, the natural logarithm of the elapsed time since the system’s original franchise was awarded, has been found to be significant by several previous authors estimating demand functions for cable (e.g., Mayo and Otsuka, 1991, p. 402, Fn. 14). LFRANTZME may proxy for unknown characteristics, such as system management philosophy, that can influence carriage decisions. 4.2. Carriage model results The results from estimating the four carriage equations on the full sets of explanatory variables appear in columns 1 and 2 of Tables 558 and those from the final models in the model selection procedure appear in columns 3 and 4. We

‘The FCC’s ‘Must Carry’ rules were replaced in 1989 and partly reinstated by the 1992 Cable Act. Note that CHANDISC is a proxy measure only since most systems also offer dedicated services such as local access channels.

D. Wuterman.

A.A.

Weiss / Journal

of‘Econometrics

72 (19%)

357-395

371

see that the most important effects are from the homes passed and channel capacity variables - larger systems by either dimension are more likely to carry the pay networks. Competition from over-the-air broadcasters (TF) also appears to encourage pay network diversity. The demographic variables are less important. With respect to MS0 dummies and interaction effects, the results show that ownership by Viacom or ATC significantly influenced carriage decisions. ATC systems had higher probabilities than the average nonintegrated system of offering their affiliated network, Cinemax, and lower probabilities of offering the rivals, Showtime and TMC. Similarly, Viacom systems had higher probabilities for TMC carriage and lower probabilities for Cinemax. All 23 Viacom systems carried HBO, however, and there is no evidence that these systems had higher probabilities of carrying Showtime. All 29 Paragon systems offered HBO as well, but this MS0 did not have significantly different probabilities for the other networks. Further interpretations of these results, in terms of the numbers of systems involved, are given in the Section 4.3. A comparison of the full and final models shows that variables in the full models with t-ratios exceeding 2.72 - the critical value implicit in the LR tests in the model selection procedure (log 1646 = 2.722) - are generally retained. As insignificant variables are dropped, the standard errors on the remaining variables decrease and their r-ratios increase. It is also interesting to note that, except in the case of the ubiquitous HBO, the variables across the final models are basically the same. The diagnostic tests used in the probit models are RESET-type conditional moment tests of the normality of the errors (e.g., Pagan and Vella, 1989, p. S43) and more general chi-squared tests of the fit of the models (Andrews, 1988). The form of the RESET tests is that suggested by Newey (1985) and involves regressing a vector of ones on the vector of scores and the moment conditions. The resulting test statistics are asymptotically distributed as ~22.The chi-squared tests are those in which the partition is on NETij = O/l only (two cells, x:) and those in which the partition is on NET,, x each variable in Xi. In the latter, the ranges for the dummy and continuous variables in Xi are split at 0.5 and the variables’ medians, respectively. This gives four cells and test statistics that are asymptotically distributed as 1:. To ensure that the test statistics are well defined, we use the third estimate of the covariance matrix discussed in Andrews (1988) (see his equation 3.13) but with his Al,, instead of his AZ,, and the estimate of the information matrix in place of his Dzn. The RESET and two-cell x2 tests are given at the bottoms of Tables 5-8 and the variable-specific chi-squared tests in the final models are given in column 4 of the tables. At the size implicit in the model selection, the test statistics are generally not significant the critical values are 7.4 for the 1: and 10.1 for the xf. There is some evidence of nonnormality in the case of TMC, although CHILDREN, DMA3, and DENSITY were the last three variables dropped in the model selection.

372

D. Wcrbmmm, A.A. Weiss ! Journal of Economettics

72 (1996) 357-395

1646 - 142.7 7.92 2.56

1646 - 151.0 1.76 0.03

(1.6) (2.5) (1.1) (0.0) (0.0) (0.0) (0.1)

1.95 - 2.59 0.87 0.08 - 0.29 0.00 0.05

0.37Jl3.0

778

(6.0) (0.7) (4.9) (6.2)

0.25 ~ 0.01 - 0.06 ~ 0.10

0.34/40.2

778

(4.7) (5.5) (5.6)

(4.5) (6.3)

- 0.05 - 0.10 0.60 - 1.14 0.94

(5.6)

0.23

(i) n = Number of systems used in estimating the model. (ii) L = Log-likelihood function. (iii) Normal = Conditional moment test for normality, asymptotically distributed as zz with two degrees of freedom. (iv) Chi-sq, = Chi-squared test statistic, asymptotically distributed as zz with i degrees of freedom. (v) 111= Absolute value of t-ratio.

L Normal Chi-sq, R’/F

n

LHBOTIME x HBOPROB LCMXTIME x CMXPROB LSHOTIME x SHOPROB LTMCTIME x TMCPROB HBOPROB CMXPROB SHOPROB TMCPROB MILLS MILLS x (Xl/I) MILLS x(X:/,)’ MILLS x (X;/I)3

models

LMEDIAN Y AGE3554 CHILDREN RENTERS MULTIFAM TV DMAI DMAZ DMA3 LHPASS LHPASS’ DENSITY CHANDISC LFRANTIME ATC VVIACOM PARAGON ATC x CHANDISC VIACOM x CHANDISC PARAGON x CHANDISC ATC x LHPASS VIACOM x LHPASS PARAGON x LHPASS

c

Cinemax

Table 6

- 6.59 0.02 1.82 0.86 - 0.58 0.60 0.07 - 0.16 -0.17 - 0.04 0.95 - 0.04 - 1.95 0.04 - 0.00 - 0.54 13.8 - 4.22 - 0.01 0.01 0.03 0.16 1.10 0.41

probit

Full

(0.6) (8.0) (0.1) (0.4) (2.0) (1.5) (0.2) (0.2) (0.5) (1.2) (2.0) (1.4)

(2.9) (0.0) (1.2) (1.6) (1.1) (1.2) (3.0) (0.9) (1.4) (0.4) (3.8) (3.1)

IfI

(9.0)

(5.6)

(3.6)

- 2.10

0.08

(8.2)

0.23

0.04

(4.5)

(12.4)

1tI

0.06

- 2.94

Final probit

5.65 6.52 4.17 4.44 3.29 3.76 3.80 4.21 3.29 3.57 3.57 9.91 5.27 4.40 3.48 3.67 3.30

Chi-sq2

(0.4) (1.3) (1.3) (1.7) (0.4) (0.8) (0.1) (1.1) (0.8) (2.2) (2.3) (0.2) (0.4) (1.8) (1.5) (1.4) (4.3) (1.5) (0.1) (5.9) (1.0) (5.1)

- 0.56

(1.2)

ItI

25.1 0.06 1.37 0.40 0.61 ~ 0.14 0.03 - 0.02 0.10 0.07 1.64 - 0.09 0.45 0.01 - 0.23 - 3.88 4.35 3.74 - 0.02 - 0.01 0.05 0.19

Full PEN

1.38

- 0.23

0.82 - 0.05

39.62

PEN

Final

ltl

ii .g

S B

P

0.15 0.02

1646 - 773.8 3.80 3.29

1646 - 787.0

(1.9) (0.8) (1.5) (0.1) (1.1) (0.5)

- 3.80 - 1.34 - 3.14 0.07 0.72 ~ 0.40

0.2314.7

568

(3.6) (2.9) (4.1) (1.5)

(0.6)

0.04 0.21 - 0.06 - 0.12 - 31.5

(3.8)

(3.6) (2.4) (4.1) (1.9)

0.19114.2

568

- 0.78

0.22 - 0.05 - 0.10 ~ 45.0

(i) n = Number of systems used in estimating the model. (ii) L = Log-hkelihood function. (iii) Normal = Conditional moment test for normality, asymptotically distributed as x2 with two degrees of freedom. (iv) Chi-sq, = Chi-squared test statistic, asymptotically distributed as x2 with i degrees of freedom. (v) 1tI = Absolute value of t-ratio.

R'/F

Normal Chi-sq,

L

n

MILLS x (X,‘B) MILLS x (X:b)’ MILLS x(X:/J)”

LHBOTlMExHBOPROB LCMXTIMExCMXPROB LSHOTIMExSHOPROB LTMCTIME xTMCPROB HBOPROB CMXPROB SHOPROB TMCPROB MZLLS

models

LMEDIAN Y AGE3554 CHILDREN RENTERS MULTIFAM TV DMAl DMA2 DMA3 LHPASS LHPASS’ DENSITY CHANDISC LFRANTIME ATC VIACOM PARAGON ATC x CHANDISC VIACOM x CHANDISC PARAGON x CHANDISC ATC x LHPASS VIACOM x LHPASS PARAGON x LHPASS

c

Showtime

Table I

- 6.13 - 0.26 3.88 0.77 0.58 0.86 0.05 ~ 0.07 0.05 - 0.09 1.27 - 0.06 7.99 0.04 - 0.02 - 0.20 ~ 1.92 - 4.70 - 0.02 0.64 - 0.07 ~ 0.04 - 0.33 0.90

Full probit

(1.3) (0.9) (1.6) (2.1) (0.3) (0.4) (0.8) (4.5) (3.4) (1.9) (6.6) (0.2) (0.2) (0.1) (0.9) (1.8) (0.4) (1.6) (0.4) (0.1) (1.1)

(1.1) (2.6)

(2.5)

Itl

(3.9)

(4.6) (3.3) (7.7)

(9.9)

1.15 - 0.05 0.04

- 0.04

(6.5)

ItI

0.05

- 6.88

Final probit

1.24 0.9 1 4.42 5.46 2.22 3.08 0.82 1.20 2.18 3.64 3.64 0.93 0.98 5.19 4.13 5.76 2.07

Chi-sqz ~ 11.9 0.48 0.10 1.07 0.54 0.12 - 0.01 0.17 0.18 0.03 0.26 - 0.01 - 0.17 0.00 ~ 0.04 2.51 - 4.39 3.13 ~ 0.02 0.00 0.01 - 0.10 0.28 ~ 0.35

Full PEN

-

(0.4) (0.1) (0.5) (0.2) (0.7) Cl.41 (1.7) (1.0) (0.0) (0.4) (0.4) Cl.91 (1.2)

(3.4) (0.1) (3.3) (1.6) (0.4) (0.3) (1.5) (2.2) (0.4) (0.3)

(1.6)

If/

1.26

9.32 0.49

Final PEN

(4.1)

(9.4) (5.0)

ItI

3 5

A L

a .z

2

1646 - 656.2 5.88 0.43

1646 - 672.8 2.08 0.78

(0.7) (0.0) (0.6) (0.7) (0.5)

1.61 0.09 ~ 0.88 0.47 0.20

0.2816.6

588

(1.6) (6.1) (4.6) (4.1) (0.9) (0.5)

- 0.06 -0.13 0.28 - 0.09 2.20 _ 1.27

(3.3)

~ 0.60

0.24126.6

588

(4.7)

(6.1) (5.1) (3.8)

0.92

-0.11 0.28 - 0.08

(i) n = Number of systems used in estimating the model. (ii) L = Log-likelihood function. (ill) Normal = Conditional moment test for normality, asymptotically distributed as 1’ with two degrees of freedom. (iv) Chi-sq, = Chi-squared test statistic, asymptotically distributed as z* with i degrees of freedom. (v) 1t 1= Absolute value of t-ratio.

n L Normal Chi-sq, RZJF

LHBOTIME x HBOPROB LCMXTIME x CMXPROB LSHOTIME x SHOPROB LTMCTIME x TMCPROB HBOPROB CMXPROB SHOPROB TMCPROB MILLS MILLS x (X:p) MILLS x (X;/l)’ MILLS x (X;/l)’

models

LMEDIAN Y AGE3554 CHILDREN RENTERS MULTIFAM TV DMAI DMA2 DMA3 LHPASS LHPASS’ DENSITY CHANDISC LFRANTIME ATC VIACOM PARAGON ATC x CHANDISC VIACOM x CHANDISC PARAGON x CHANDISC ATC x LHPASS VIACOM x LHPASS PARAGON x LHPASS

c

The Movie Channel

Table 8

ItI (1.2) (0.6) (0.4) (2.3) (1.7) (2.1) (2.8) (0.2) (0.5) (1.9) (1.4) (0.6) (2.2) (8.4) (2.0) (0.5) (1.0) (0.6) (0.8) (0.7) (0.7) (0.4) (0.4) (0.9)

Full probit

~ 2.43 - 0.12 0.52 1.14 ~ 0.86 0.94 0.05 - 0.03 0.06 0.19 0.32 - 0.01 6.99 0.03 - 0.15 - 0.53 1.51 1.00 - 0.12 0.04 0.02 - 0.04 - 0.11 - 0.17 (4.4)

(6.8)

(8.9) (2.9) (8.0) (3.3)

0.18

0.03 - 0.20 - 1.37 1.27

(5.5)

ItI

0.05

2.00

Final probit

7.96 7.25 10.1 7.44 7.73 8.30 9.44 7.36 12.2 7.77 7.77 13.5 7.38 7.23 7.31 7.45 7.23

Chi-sq, - 5.52 0.07 1.05 0.55 0.49 0.16 - 0.01 0.13 - 0.04 - 0.21 - 0.18 0.01 0.58 0.01 - 0.23 - 1.63 2.97 4.27 0.05 0.01 0.04 0.31 - 0.10 - 0.59

Full PEN

(1.0)

- 0.25

- 0.27

_ 2.12

Itl

(0.4) (0.8) (1.4) (1.3) (0.4) (0.2) (0.8) (0.3) (2.2) (0.3) (0.4) (0.2) (0.2) (0.9) (1.2) (0.9) (3.0) (1.4) (0.5) (2.6) (0.8) (0.8) (3.3)

Final PEN

ITI

3 .g

f $

9.01 7.88

1646 - 941.4 7.06 7.23

1646 _ 952.8

(0.3) (0.1)

(0.5) (0.0)

0.23 2.19 2.41 - 2.23 1.16 0.10

0.48 0.02

0.27,'3.5

357

~ 0.11

(OS) (5.7) (4.2) (3.8) (1.2) (1.0) (0.9)

- 0.02 - 0.15 (3.7) (3.4)

- 0.08 0.21

0.24/26.6

357

-

(5.8)

-0.11

(i) n = Number of systems used in estimating the model. (ii) L = Log-likelihood function. (iii) Norma1 = Conditional moment test for normality, asymptotically distributed as zz wtth two degrees of freedom. (iv) Chi-sq, = Chi-squared test statistic, asymptotically distributed as x2 with i degrees of freedom. (v) 1fj = Absolute value of t-ratio.

R'IF

Normal Chi-sq,

L

n

MILLS x (X18)3

LHBOTIMExHBOPROB LCMXTIMExCMXPROB LSHOTIMExSHOPROB LTMCTlME xTMCPROB HBOPROB CMXPROB SHOPROB TMCPROB MILLS MlLL.Sx(X;/Q MILLSx(X,'/I)'

380

4.3.

D. Waterman, A.A. Weiss 1 Journal

Carriage

of Econometrics 72 (1996)

357-395

model predictions

While the probit models show that vertical integration has significant effects on carriage, we cannot directly interpret the magnitudes of these effects. In this section, we interpret the magnitudes in terms of numbers of systems. We compare predictions of the actual carriage patterns with predictions of the patterns that we would expect to observe if these MSOs behaved instead like the average nonintegrated system in the sample. The latter are obtained by setting the coefficients on the relevant MS0 dummies to zero. From Eq. (9) P(NETij = 1) = ~(Xl~j), where @ is the c.d.f. of the standard normal. Hence, the estimated number of systems is given by Cy= i @(X!flj), where Bj is the maximum likelihood estimate Of /Ij, nk is the number of systems in MS0 k, and i runs over these systems. Now, for the case when the interaction variables do not appear in the model, let Ir,, be flj with the coefficient on the kth MS0 dummy set to zero. Then the estimated number of systems that would carry the network if vertical integration had no effect is given by 1 YEr @(Xlfljk), and the number of systems corresponding to the estimated coefficient on the kth MS0 is given by ~ @(Xlfij) - ~ i= i=l

~(Xl~jk).

(10)

I

To assess the magnitude of this change, we also calculate the standard error of the change. Using a mean value expansion, for network j and MS0 k, CL, ~(Xl~j) - CY, ~(X!pjk) = CL, ~(Xlp*)Bjk, where iijk is the estimated coefficient on the kth MS0 dummy, /I* is the mean value, and 4 is the p.d.f. on the standard normal. Hence, the standard error is approximately

(11) i=l

where s.e.(bjk) is the estimate of the asymptotic standard error of ~jjk from the probit maximum likelihood estimation. A similar analysis applies when an interaction variable appears in the model. Part A of Table 9 shows the predictions of the network carriage patterns using the final models. Column 1 gives the predicted percentage of systems in ATC and Viacom that carry each of the four subject networks; column 2 gives the ‘normal’ predictions, derived by setting the relevant MS0 dummy in each model to zero; column 3 shows the differences between columns 1 and 2; and column 4 gives the absolute values of t-ratios for these differences. Since there was no evidence of carriage differences for Time Inc.‘s 50%-owned affiliate, Paragon, no predictions were generated for that MSO. As expected, the variations in Table 9 correspond closely to the relative magnitudes of the probit coefficients. Of note are the large variations for the ‘companion’ networks, TMC and Cinemax.

D. Waterman,

A.A. Weiss 1 Journal

ofEconometrics72

(1996)

381

357-395

Table 9 Predictions Predicted (A) Indiridual

carriage

Normal

models (X

Systems

- 13.4 36.9 39.7

(5.5) (7.6) (13.2)

109 109 109 109

60.1

(7.8)

- 35.2

(5.0)

20 20 20 20

of systems)

ATC HBO CMX SHO TMC

98.2 91.0 48.2 12.2

98.2 17.6 85.1 51.9

Viacom HBO CMX SHO TMC

98.4 14.6 80.2 85.1

98.4 14.1 80.2 49.9

(B) Acqyrrqare carriage

IfI

Change

models (number

of networks)

ATC NPAY4 NPAYALL

2.50 3.61

3.13 4.52

0.63 0.85

(12.0) (7.4)

109 109

Viacom NPAY4 NPAYALL

2.78 4.39

3.05 4.39

0.27

(3.4)

20 20

Paragon NPAY4 NPAYALL

3.25 4.41

3.25 4.86

0.39

(3.6)

29 29

(C) Suhcrihership

penetration

models (% of homes passed)

ATC HBO CMX SHO TMC

23.1 11.3 5.0 4.4

19.4 8.5 1.2 4.3

- 4.3 - 2.8 2.2 - 0.1

(2.7) (4.8) (7.9) (1.0)

50 45 18 4

Viacom HBO CMX SHO TMC

13.2 8.1 12.9 5.2

16.0 5.3 9.1 4.8

2.8 ~ 2.8 - 2.2 - 0.4

(13.7)

10 2 10 8

4.4. Aggregate

(0.6) (12.2) (7.4)

carriage results

The results on the individual carriage models indicate that vertically integrated systems tended to carry their affiliated networks at the expense of rival networks. Also important to concerns about the diversity of programming is

382

Table 10 NPAYALL

D. Waterman, A.A. Weiss /Journal

qjEconometrics

72 (1996) 357-395

models Full model

C

LMEDIANY AGE3554 CHILDREN RENTERS MULTIFAM TV DMAI DMA2 DMA3 LHPASS LHPASS= DENSITY CHANDISC LFRANTIME ATC VIACOM PARAGON ATC x CHANDISC VIACOM x CHANDISC PARAGON x CHANDISC ATC x LHPASS VIACOM x LHPASS PARAGON x LHPASS n

L (i) n = Numbers of systems used (iii) 1t 1= Absolute value of t-ratio.

ItI

~ 12.35 0.54 - 0.15 0.5 1 0.35 0.71 0.1 I - 0.31 - 0.26 - 0.06 1.78 - 0.08 5.44 0.05 - 0.11 0.48 0.46 2.07 - 0.03 - 0.03 - 0.03 - 0.06 0.01 - 0.13

(7.5) (3.3) (0.1) (1.3) (0.9) (2.0) (7.5) (2.4) (2.7) (0.8) (10.1) (8.0) (3.2) (21.7) (1.9) (0.6) (0.4) (1.3) (1.9) (0.8) (2.4) (0.8) (0.1) (0.7)

1646 ~ 2279.6 in estimating

Final model ~ 11.8 0.50

Itl

(8.6) (4.2)

0.9 1 0.09

(3.7) (9.9)

1.70 - 0.07 5.60 0.05

(10.5) (8.4) (3.4) (23.9)

~ 0.03

(7.7)

- 0.01

(3.7)

1646 - 2293.2 the

model.

(ii) L = Log-likelihood

function.

whether this behavior led to changes in the overall number or variety of pay networks offered to subscribers. We employ two measures of variety: NPAY4, which indicates the number of the four subject pay networks carried, and NPA YAM,, which measures the total number of pay networks carried. In both cases, we represent the effect of vertical integration by the change in the expected number of networks carried, averaged over all systems in the MSOs. The results for NPAY4 can be obtained by aggregating those for the four individual pay networks. In particular, the expected number of networks carried was estimated by simulation. In each of 50,000 replications, we generated NETij for the four networks and the systems in ATC and VIACOM, using the final versions of the four equations in (9) pseudo-random multivariate normal wii,

D. Waterman, A.A. Weiss / Journal of’Econometrics

72 (1996) 357-395

383

the maximum likelihood estimates of the pj, and maximum likelihood estimates of the elements of the covariance matrix of the Oij. Summing the generated NETij over i and j gave the average number of networks carried by systems in the MSO. This result was then averaged over the replications. The coefficients on the MS0 dummy variables were then set to zero and the procedure was repeated. The standard error of the change in the expected number of networks was obtained by a procedure analogous to that in the previous section.’ These results are shown in part B of Table 9. Both ATC and Viacom systems carried fewer networks in total than we would expect had they behaved like the nonintegrated systems in the sample. The elements in the covariance matrix in the multivariate normal were obtained from the six bivariate probit models resulting from pairing the final versions of the four equations in (9). The correlations, with their respective asymptotic t-ratios, are: HBO/Showtime ( - 0.61/8.1), HBO/Cinemax (0.68/l 1.5) HBO/TMC ( - 0.65/10.9), Showtime/Cinemax ( - 0.29/5.8), Showtime/TMC (0.20/4.0), and Cinemax/TMC ( - 0.34/8.0).” We can also interpret these values as correlations between heterogeneity components in the probit equations. This suggests that cable systems perceive networks of the two major rival firms to be substitutes for each other, while the ‘companion’ pairs offered by each firm are complements. Unfortunately, the results for NPAYALL cannot be obtained in the same way as those for NPAY4 because we do not have detailed data on all of the other pay networks then in business. Instead, we model NPAYALL directly

‘)In particular, the derivatives corresponding to the 4 terms in (11) were estimated numerically, while the variance-covariance matrix corresponding to the standard error term involves the coefficients on the MS0 dummies in the four probit carriage equations. Let Lj(flj) be the likelihood function from a generic model ,j with parameters b,. Then we can write

where nj contains the estimated parameters, the matrix of second derivatives is evaluated value, and the vector of first derivatives is evaluated at /Ij. Hence. asymptotically,

at a mean

This is estimated by replacing the expectations by the corresponding sample averages evaluated at the estimated parameters. Also, setting the number of replications to 50,000 means that the variance across replications can be ignored. The predicted number of networks for ATC, for example, is 2.50, and the standard error of this estimate across replications is O.O593/sqrt(50,000) = 0.000265.

I” Weiss (1993) for example, gives a detailed account of the bivariate ordered probit model. The results for the bivariate probit model follow as a special case. We do not use the other coefficients from the bivariate model because each network appears in three bivariate models.

384

D. Waterman, A.A. Weiss / Journal

of Econometrics 72 (1996) 357-395

(and approximately) using an ordered probit model. We hypothesize the existence of a latent variable, NPA YALL*, which represents the propensity to carry different numbers of the networks then in business. We define NPAYALLT

= X(7 + ii,

(12)

where ii is normally distributed. obtained from (12) according to NPAYALLi where

= k

=

-

7k

are

cc,

zK+

1 =

ok < NPAYALL:

values

< ~k+l,

for NPAYALL

are

k = 0, . . . ,K,

(13)

breakpoints, K is the maximum value of NPAYALL, and z1 is normalized to zero. NPAYALL takes on values zero through ten, although only two systems carried ten networks and these were aggregated with the systems that carried nine networks. Table 3 gives the distribution of NPAYALL and the estimated models for NPAYALL are given in Table 10. (We omit estimates of the zk.) The coefficient on ATC x CHANDISC indicates that the ATC systems again tended to carry fewer networks in total. The expected number of systems corresponding to this coefficient is obtained from a prediction methodology equivalent to that in the probit models. This result is given in part B of Table 9: ATC systems carried nearly one fewer pay network on average. z.

the

iff

The observed

cc,

5. Pay network pricing and subscribership 5. I. Pricing and subscribership

mode/s

Carriage data provide an incomplete, relatively crude picture of vertical integrations’ effects on cable system behavior. Most policy discussion, in fact, seems to focus on carriage differences as the only source of concern. As local monopolists, however, integrated cable systems have opportunities to price and market affiliated and nonaffiliated networks differently when both are offered on their menus. We have used two approaches to compare the behavior of integrated vs. nonintegrated systems, given their network carriage decisions. First, we estimated retail subscription price models for each of the four networks. Second, we estimated output, i.e., pay subscribership, models. It turned out, however, that in only one case was there any significant net effect of vertical integration on pay subscription prices (represented by the sum of the basic price and the a la carte price for the relevant network): the prices charged by ATC systems for TMC were significantly lower than would be expected had they behaved like the average nonintegrated system. For this reason, and also because the methodo-

D. Waterman, A.A. Weiss / Journal of Econometrics

72 (1996) 357-395

385

logy used in the price models is comparable to that for the subscribership models give below, we do not detail the analysis. Particulars are available upon request. One explanation for the basically neutral price results is that vertical integration simply has little effect on prices. Another possibility is that published a lu carte prices do not reflect true prices. Pay networks are often sold to consumers in bundles, for example, and even for a la carte sales, promotional discounts are commonly employed. Vertically integrated systems can employ these discounting strategies, as well as personal sales efforts and other marketing techniques, to favor affiliated over rival networks. Final output, i.e., subscribership, will reflect the net effects of both prices and other marketing behavior, and we now turn to the analysis of subscribership. To begin, we note that penetration (subscribership as a fraction of homes passed) is modelled rather than subscribership because of the widely differing sizes of cable systems. Still, the distribution of penetration is skewed to the right and as a result we also take natural logs. Next, we define PEN: as the (latent) penetration of networkI on system i and let PEN,, = PEN: =o

if

NET:

> 0,

otherwise,

(14)

corresponding observed variable. Similarly, let LPENG = and LPENij = log(PENij) when NET: > 0 and zero otherwise. The model for LPEN* is given by denote

the

log(PEN$),

LPEN,“j = Xfaj +

i

hjkNET;k + i

k=I:k#j

k=l

cj,LTIMEik

+
(15)

where the
” A shortcoming of these models is that we did not have available a variable to represent the presence of MDS or other competitive nonbroadcast delivery systems. However, such systems existed in relatively few markets in 1989, and had very low nationwide penetration. Some previous authors estimating demand functions for cable television have also included variables such as the degree of urbanization of the market and the type of broadcast stations also available. See in particular Comanor and Mitchell (1971), Park (1972), Webb (1983), Pacey (1985), Mayo and Otsuka (1991) and Rubinovitz (1993). Our models, however, include more detailed demographic data; and apparently unlike the work of these and some other previous authors, these are specifically defined for the exact zip code area of each cable franchise rather than for the county, ADI, or other general market area that contains the system.

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the average nonintegrated system simply because they carry rival networks less frequently. The endogeneity of the NET variables also means that the LPEN equations are not true reduced forms. But as we shall see, it is straightforward to allow for the endogeneity. The LTIME variables represent the natural logarithms of the number of months since the system began carrying the relevant network. These variables reflect the likelihood that consumer switching costs will advantage subscribership to a network that the system started carrying before others or that simply has had a longer time to develop subscriber loyalty. The logarithmic form again reflects an expectation of diminishing effects over time. It is not possible to estimate (15) directly because the LPEN z variables are only observed for systems that carry the network, i.e., where NETij = 1. Hence, following Heckman’s two-stage procedure, we take the expected value of LPEN: in (15), conditional on NETij = 1. This gives, for systems with NET,, = 1,

LPENij = Xl~j +

~

hj, PROBijk + i:

k=l:k#j

+ E[tij( NETij = l] +

cjkLTIMEik.

PROBijk

k=l

(16)

Vij,

where PROBijk = E[NETikI NETij = l] = P(NET,,

= 11NETij = 1)

(17)

G2 is the c.d.f. of the bivariate standard normal, is the correlation between Wij and mik, and vij is a heteroskedastic error term. Hence, for example, ifj 3 HBO, then the measure the effects on HBO penetration of changing the probabilities that the other networks are carried. Similarly, the time variables are only observed if the relevant network is carried. But since LTIMEik = LTIMEikNETik, it fOllOWSthat E[LTlMEikI NETij = l] = LTIMEikPROBijk. We expect the own-time variables to have a positive sign, while the other time variables should have negative signs. As noted in the Appendix, the LTIME data were only available for approximately 60% of cable systems in the sample, so the results are based on smaller samples than in the probit models. Now, if the errors in the penetration and probit equations, 5ij and Oij, respectively, are jointly normally distributed, then E[&loJ = ejW,j for some constants Hj. Hence, E[SijINETij = l] = ~jE[oijIOij > - XlBj] = @jA(XiBj), pjk

hjk

D. Waterman, A.A. Weiss 1 Journal @Econometrics

where i( .) is the inverse Mills’ ratio. Following to allow for nonnormality we approximate

k=l

for some constants E[4ijlNETij

Pagan

ejkW:j,

EC5ijIOijl = i

72 (1996) 357-395

381

and Vella (1989, p. S51),

(18)

Hence,

Hjk.

= l] = ~

(19)

ejkn(X!Bj)(X!aj)k~l.

k=l

Eq. (19) is then substituted into Eq. (16). The significance of terms from Eq. (19) other than that for k = 1 is an indication of nonnormality of the errors. Eq. (16) still contains unknown parameters in the Mills’ ratio and PROB terms - the flk and These parameters are replaced by their maximum likelihood estimates. The model selection algorithm is then applied, with estimation by OLS on the systems with NETij = 1. The covariance matrix of the OLS estimators is made up of two terms, the first reflecting the heteroskedasticity in the Uij and the second reflecting the correlation in the errors across observations resulting from the use of estimators of the ljk and Since the heteroskedasticity in the uij is of unknown form, we follow Ryu (1993) and estimate the first term using the heteroskedasticity-consistent form of the covariance matrix. The second term is estimated analytically. ’ 3 pjk.

pjk.12

5.2. Subscribership

results and predictions

The estimated models, before and after model selection, are shown in columns 669 of Tables 5-8. Several of the region-specific demographic variables are significant, while coefficients on the ‘carriage time’ variables suggest that consumer switching costs are indeed a demand factor. The three MS0 dummy variables are almost never significant, indicating that the most important effects of vertical integration on subscribership are through carriage, and that the marketing behavior noted above is not

” Amemiya (1985, Eq. 10.4.22) and Greene (1993. Sec. 22.4.3). for example. give the form of the covariance

matrix

in the special case of the tobit model.

” Let li/ be a vector containing /$ and Pjkr $j be the corresponding vector of estimates, Zi, be a vectoriontaining the variables with Mills’ ratio and PROB terms, and ZLj be Z,j evaluated at 6,. Then Eq. (16) becomes LPEN;, = X,‘a, + i;id, + vi, + qij, where dj contains b,t, cJL, and (Ilk, and ,I;, = d;(Z,j - i,j). In the covariance matrix, u,, contributes a diagonal matrix with ith diagonal element var(ri,). The contribution from gtj is obtained by applying a mean value expansion to Z,j in tl$,. and then using the argument described in Footnote 9 above. We thank a referee for pointing out the Ryu reference. Note also that the terms from vii would appear in the correlations between the errors for different j. This makes joint estimation of the penetration equations impractical.

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sufficiently similar across systems for its effect on penetration to be identified. It is difficult, however, to interpret the coefficients more fully because the net effect of MS0 ownership on penetration is derived from a combination of the direct effect through the relevant MS0 dummy and the indirect effects through the PROB and Mills’ ratio terms. A convenient way to estimate the overall effect of vertical integration, and hence to test the null hypothesis that vertical integration has no effect, is to predict the change is expected penetration when the coefficients on the MS0 dummy variables in the penetration and carriage equations are set to zero - that is, to assume that the vertically integrated MSOs act like the average nonintegrated MSO. The complication here is that we require predictions of actual penetration, whereas we have estimated the model on the natural logarithm of penetration. From Eq. (15) X!Uj +

i:

hjkNETik

k=l:k#j

+ i

CjkLTIMEik + tij}i NETij = I].

(20)

k=l

Unfortunately, the evaluation of the conditional expectation in (20) is quite complicated due to the endogeneity of NETik, and involves the joint distribution of NETi,, . . . , NETi and rij. Instead, we approximate (20) by the naive prediction exp(E[LPEN;jl = eXp X,‘Uj +

NET,,

= 11)

i

hjkPROB,jk + i k=

k=l:k#j

+ i

djkn(xlfij)(Xlpj)k-l

CjkLTIMEik. PROBijk 1

(21)

.

k=l

We argue heuristically that the bias from this approximation will lead to a conservative estimate of the effects of vertical integration. In the special case of no NET (or LTZME) variables and joint normality of the errors, Eq. (20) reduces to E[PENijI

NETij = I] = exp{Xiuj

+ af/2} ~(Xiaj + alzj)/@(XiUj)

= exp {XlUj} dij,

(22)

where ojZ is the variance of 1 unless criZj is strongly negative, the naive forecast will most likely be biased downward by a multiplicative dij =

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factor. Assuming that the same bias occurs in (20), we may expect that (21) and the similar expression when the coefficients on the MS0 dummies are set to zero, will also be biased downward. The estimate of the change in PEN due to vertical integration will therefore be biased downwards, as will the estimate of the standard error of this change; but the ratio of the change to its standard error will be less affected. Finally, since LTIMEik is observed only when NETik = 1, for systems with NETik = 0, the time variables are set equal to the average times on the systems with NETik = 1.14 The predicted penetration, averaged over systems in MS0 k, is given by

Izk

-’

zl eXp{X:dj + + i

gjki(x(fij)(xibj)kpl

i:

b;FROBijk + i:

k=l:k#j

k=l

9

EjkLTIMEik. ~ROBijk

(23)

k=l

where the tildas mean the corresponding terms are evaluated at the OLS estimates and the hats mean the terms are evaluated at the appropriate maximum likelihood estimates from the carriage equations. Evaluating this expression when the coefficients on the relevant MS0 dummies are set to zero gives the estimate of the average penetration had the systems in the MS0 behaved like the average nonintegrated system. The standard errors of the predictions are obtained using a similar argument to that leading to Eq. (11). No predictions are generated for Paragon since no significant direct or indirect effects appear in any of the prediction models. The predictions for ATC and Viacom systems, based on the final models, appear in part C of Table 9. In all four possible cases, predicted ‘normal’ subscribership rates are lower for the affiliated networks; that is, these MSOs appear to favor their affiliates with respect to overall marketing behavior. With

“Both referees suggested the evaluation of (20) via simulation. There are, however, several difficulties with this approach. First, in at least one of the models - that the Showtime the distribution of the tij is unknown. The marginal distribution of the tsj is not normal, as is indicated by the estimates of the parameters in Eq. (19) and hence the joint distribution of the NET; and <,, cannot be normal. Estimation of the joint distribution in this case seems quite difficult. Second, the tij may be heteroskedastic. The variance of the lij in the HBO equation, for example, may be smaller for the ATC systems. (The mean squares of the residuals in the ATC and non-ATC systems are 0.094 and 0.162, respectively.) Third, the simulations would use NETik rather than PROB,,. At the estimated coefficients, this could result in the exponential in (20) which is a forecast of penetration, being greater than one for some systems. Estimating the models by maximum likelihood. for example, would appear to avoid this difficulty; but this would involve estimating five-equation systems and would require knowledge of the distributions of the lij.

390

D. Waterman. A.A. Weiss i Journal qf

Econometrics 72 (1996) 357-395

respect to rivals, we see that ATC systems would have higher expected penetration for Showtime had they behaved like the average nonintegrated system and Viacom systems would have a higher expected penetration for HBO. The other two cases are based on very small numbers of systems (due to data limitations and the infrequency of carriage events). Finally, we give an example of how the model selection influences estimates of the overall effect of vertical integration. Fig. 1 shows, for the case of ATC in the Showtime penetration equation, how this estimate changes at each iteration in the model selection algorithm. The solid line gives the predicted penetration averaged over ATC systems at each iteration, the short-dashed line gives the predicted penetration when the relevant coefficients are set to zero, and the difference between these lines gives the estimate of the effect of vertical integration. The long-dashed lines give the first prediction plus and minus two standard errors of the difference in the predictions. Hence, if the short-dashed line falls within the two long-dashed lines, the effect of integration is not significant. As Fig. 1 illustrates, the model selection procedure is helpful in decreasing the standard error of the difference in the predictions. The ATC variables were dropped at iterations 11 (A TC x LHPASS), 15 (ATC x CHANDISC), 18 (A TC). The effects of the model selection in the probit equations were less dramatic, as might be expected from the patterns of t-ratios in those equations.

1 --\

\ \

-\

‘1 \ ----=--:---

/ / _---/

_‘-

v)

0

4

--=z-

---.-___

--+izEJg

I

I

8

12

I

16

20

24

Iteration

Fig. 1. Effects of model selection

in Showtime

penetration

model.

28

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391

6. Summary and discussion We find that cable systems operated by ATC and Viacom, the two MSOs having majority ownership ties to four major pay cable networks in 1989, tended to offer their affiliated networks more frequently and rival networks less frequently than did nonintegrated cable systems. Carriage differences were particularly large for the ‘companion’ networks, Cinemax and TMC. Both ATC and Viacom systems offered significantly fewer pay networks in total than did the average nonintegrated system, although this difference was insignificant in the case of Viacom for all pay networks combined. These carriage decisions were the most important identifiable factors in explaining pay network prices and subscribership. The net effects of vertical ties on prices were largely insignificant, but following the patterns for carriage, subscribership was in most cases relatively high for affiliated networks and low for unaffiliated networks. We find little evidence of Time Inc.‘s influence on Paragon systems with respect to either pay network carriage decisions or pricing and marketing behavior. These neutral results might reasonably be explained by Paragon’s relatively recent and minority ownership relationship with Time Inc. A variety of institutional and historical factors peculiar to these firms could influence our findings, such as the degree of autonomy offered by MSOs to local system managers and the dates when the subject MSOs acquired their systems. Also, some results, particularly with respect to the pricing and subscribership of rival ‘companion’ networks, involved few individual cable systems. Nevertheless, it seems clear that majority ownership relationships between pay networks and cable systems make a substantial difference in terms of final market outcomes. The weight of evidence thus supports the conclusion that majority ownership relationships do influence cable systems to ‘favor’ their affiliated pay networks, both with respect to carriage decisions and overall marketing behavior. research would be required Concerning social welfare issues, further to determine whether vertical integration between pay networks and cable systems has positive or negative consequences for consumers. As we discuss in Waterman and Weiss (1996), our results are generally consistent either with a vertical foreclosure model or a transactions efficiencies model. Note, however, that even if our results are due to transactions efficiencies, static economic welfare could rise or fall as a result of the particular price and subscribership effects we observe (Salinger, 1991) or as a result of any change in product variety (Spence, 1976; Dixit and Stiglitz, 1977). Our analysis does suggest, however, that vertical integration serves to resolve vertical contracting externalities of some kind in the cable industry. Our results also suggest consequences of vertical integration in cable television to First Amendment-related social objectives. It can be argued that, even apart from any lessening of program supplier ‘access’ to consumers that vertical

392

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integration may cause, any favoritism of even a very similar affiliated product by an information provider with local monopoly power is undesirable on freedomof-expression grounds. (Let us say, for example, that we are concerned with news, rather than movie, channels.) Such favoritism might be judged particularly harshly if unaffiliated products are not available in the integrated firm’s local market or perhaps are driven from the industry all together. In the cases of both ATC and Viacom, vertical integration is accompanied by the availability of relatively few pay networks. It may be, however, that integration with pay networks leads to greater carriage of basic or other networks. There is also a dynamic aspect to this market process. A history of integration into both pay and basic networking by MSOs (FCC, 1994) suggests that integration may promote innovation and, in that respect, may serve to increase product variety and economic efficiency. These conflicting considerations in measuring the benefits and costs of vertical integration also mirror important regulatory and other policy debates in the production of information by local telephone companies. In U.S. vs. Western Electric Co. (1991), a federal judge opened the way for the Regional Bell Operating Companies to produce as well as transmit data bases (such as 976 numbers and electronic fellow pages), and they may soon be permitted to both own and distribute cable programming. Evident similarities in the cable and telephone industries in their provision of information services - local monopoly power downstream with competing suppliers of differentiated products upstream - suggest that similar empirical events, with similar social implications, are likely to occur. Turning finally to the econometric techniques used, we note the importance of the model selection procedure to our analysis. Of particular note were the smaller standard errors resulting from the simpler models. The use of the Schwarz criterion meant that these standard errors were still asymptotically valid. More generally, many other models seem to share the central feature of those in this paper: large numbers of correlated right hand side variables. These correlations also complicate the behavior of the model selection procedure in small samples, but dealing with multicollinearity and the selection of variables is applied research is always difficult. Here, the procedure is explicit.

Appendix Our primary data base is the A.C. Nielsen Cable On-Line Data Exchange (CODE). The CODE data consist of several hundred items for each cable system in the U.S., which as of August 19, 1989, the date our tape was produced, included 10,544 cable systems, virtually all then operating. The CODE data consist primarily of institutional and demand side items, including demographic

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characteristics of each franchise area, projected to 1988 by Nielsen based on U.S. Bureau of the Census data. The CODE data are continuously updated by means of telephone survey. The dates on which key items are collected are recorded with the data. Our probit models and ordered probit models are based on systems meeting three criteria. First, we excluded all systems (approximately 8.9% of the 9150 total which had complete data reported) for which basic subscribership data had not been updated since January 1988. From the remaining systems we selected all those owned by the largest 25 MSOs in the U.S. (in terms of their national market shares of basic subscribers), after preJanuary 1988 data had been excluded. Overall, 420 systems of a total of 2210 in the top 25 MSOs were excluded due to pre-1988 data. No Viacom systems were excluded for this reason and three of ATC’s 137 systems were excluded. Finally, systems with missing data were dropped. For subscribership estimates, we merged into our sample data the dates on which each of the four pay networks were first carried by the cable system. These data were obtained from hardcopy reports of the 1988 Kagan Cable TV Census. These data were available only for about 60% of the Nielsen systems. partly because of different definitions of a cable ‘system’ in the two data bases. Nielsen generally defines a cable system as a single headend, or technical unit. while the Kagan Census sometimes includes several headends into a single system having common management. We attempted to eliminate ambiguous cases.

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Gabler, S., F. Laisney, and M. Lechner, 1993, Seminonparametric estimation of binary choice models with an application to labor-force participation, Journal of Business of Economic Statistics 11, 61-80. Gallant, A.R. and D.W. Nychka, 1987, Semi-nonparametric maximum likelihood estimation, Econometrica 55, 3633390. Geweke, J. and R. Meese. 1981, Estimating regression models of finite but unknown order, International Economic Review 22, 55570. Granger, C.W.J., M.L. King, and H. White, 1995, Comments on testing economic theories and the use of model selection criteria, Journal of Econometrics, 67, 1733187. Greene, W.H., 1993, Econometric analysis, 2nd ed. (Macmillan, New York, NY). Judge, G.G., W.E. Griffiths, R.C. Hill, H. Liitkepohl, and T.-C. Lee, 1985, The theory and practice of econometrics, 2nd ed. (Wiley, New York, NY). Learner, E.E., 1978, Specification searches: Ad hoc inference with nonexperimental data (Wiley, New York, NY). Mayo, J.W. and Y. Otsuka, 1991, Demand, pricing, and regulation: Evidence from the cable television industry, Rand Journal of Economics 22, 396-410. McAleer, M., A.R. Pagan, and P.A. Volker, 1985, What will take the con out of econometrics?, American Economic Review 75, 2933307. Newey, W.K., 1985, Maximum likelihood specification testing and conditional moment tests, Econometrica 34, 1047~1070. Owen, B., 1975, Economics and freedom of expression (Ballinger, Cambridge, MA). Pacey. P.L.. 1985, Cable television in a less regulated market. Journal of Industrial Economics 34, 81~91. Pagan, A.R., 1987, Three econometric methodologies: A critical appraisal, Journal of Economic Surveys I, 3-24. Pagan, A.R. and F. Vella, 1989, Diagnostic tests for models based on individual data: A survey, Journal of Applied Econometrics 4. S299S59. Park, R.E., 1972, Prospects for cable in the 100 largest television markets, Bell Journal of Economics 3, 130~150. Paul Kagan Associates, 1988, Kagan cable TV census (PKA, Carmel, CA). Paul Kagan Associates, Cable TV programming (PKA, Carmel, CA). Paul Kagan Associates, Pay TV newsletter (PKA, Carmel, CA). Potscher, B.M., 1991, Effects of model selection on inference, Econometric Theory 7, 163%185. Roberts. J., 1992, How TCI uses self-dealing, hardball to dominate market, Wall Street Journal, January 27. Rubinovitz, R., 1993, Market power and price increases for basic cable service since deregulation, Rand Journal of Economics 24. I- 18. Ryu, K.. 1993, A consistent, positive definite covariance matrix estimator of Heckman’s two-step estimators, Mimeo. (Department of Economics, University of California, Los Angeles, CA). Salinger, M.A.. 1988, A test of successive monopoly and foreclosure effects: Vertical integration between cable systems and pay services, Unpublished manuscript (Graduate School of Business, Columbia University, New York, NY). Salinger, M.A., 1991, Vertical mergers in multi-product industries and Edgeworth’s paradox of taxation, Journal of Industrial Economics 5, 5455556. Salop, S.C. and D.T. Scheffman, 1983, Raising rivals costs, American Economic Review 73,267-271. Savin. N.E., 1984, Multiple hypothesis testing, in: Z. Griliches and M.D. Intriligators, eds., Handbook of econometrics, Vol. II (North-Holland, Amsterdam). Schwarz, G., 1978, Estimating the dimension of a model, Annals of Statistics 6, 461464. Spence, A.M., 1976, Product selection, fixed costs, and monopolistic competition, Review of Economic Studies 43, 217-235. United States v. Western Electric Co.. Opinion 82-0192, D.D.C., July 25, 1991.

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Waterman, D., A.A. Weiss, and T. Valente, 1989, Vertical integration of cable television systems with pay cable networks: An empirical analysis, Paper presented to Telecommunications Policy Research Conference (Airlie, VA). Waterman, D. and A.A. Weiss, 1996, Vertical integration in cable television (MIT Press, Cambridge, MA; American Enterprise Institute, Washington, DC). Webb, G.K., 1983. The economics of cable television (Lexington Books, Lexington, MA). Weiss, A.A., 1993, A bivariate ordered probit model with truncation: Helmet use and motorcycle injuries. Applied Statistics 42, 487499.