FEDERAL COMMUNICATIONS COMMISSION

MEDIA BUREAU STAFF RESEARCH PAPER

 

A Survival Analysis 

of Cable Networks

By Keith S. Brown 

December 2004

2004-

1
1

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. 
2

A Survival Analysis of Cable Networks

KEITH S. BROWN*

FEDERAL COMMUNICATIONS COMMISSION

Abstract

This paper employs survival/duration analysis to determine how subscriber levels

affect cable networks’ survival probabilities. According to these survival/duration 

estimates, a cable network that grows at our calculated mean rate requires

approximately 42 million subscribers by its tenth year to obtain a 70% chance of survival 

over its first ten years. 

Media Bureau Staff Research Paper No. 2004-1

December, 2004

__________________

*Senior Economist, Media Bureau. The views expressed are those of the author and do not 

necessarily reflect the views of the Media Bureau, the Commission, or other members of the 

Commission’s staff.

The author thanks Jerry Duvall, Marcia Glauberman, Royce Sherlock, Tracy Waldon, and many 

others in the Media Bureau for many very helpful comments that greatly improved this paper.
3

Table of Contents

I. Introduction..............................................................................4

II. Data..........................................................................................7

III.Estimation Methods and Empirical Results........................................10

A. Overview........................................................................10

B. Estimation and Results of Parametric Models............................12

C. Estimation and Results of Semiparametric Models...................22

D. Discussion of Results.........................................................25

IV. Conclusion.................................................................................29

V. Appendices...............................................................................................33 

A. Appendix 1: Sampled Cable Networks ............................................33 

B. Appendix 2: The Average Number of Subscribers by Age 

 and the Implied Rate of Year-to-Year Growth...................................40
4

I. Introduction

The majority of Americans today receive their television programming from a 

multi-channel video programming distributor (MVPD). The most widely

available MVPDs are cable television and direct broadcast satellite (DBS)

systems.1 Over 88% of the 106,641,910 U.S. television households subscribe to an 

MVPD service, with 74.87% of the MVPD subscribers choosing cable service and 

21.63% choosing DBS service. In addition to delivering local broadcast stations, 

MVPDs carry “cable” networks.

2 Cable and satellite providers generally package 

these cable networks in bundles and/or tiers, and offer some additional

programming services on a per-channel or pay-per-view basis.3 Because so

many U.S. households choose MVPD service, such services play an important 

role in the quality of people’s lives.

The number of national cable networks and the variety of programming they 

offer have increased dramatically in recent years. In 2003, 339 satellite-delivered 

national cable networks were in operation, an increase of 233 networks since 

1994.4 Similarly, competition among cable networks and their diversity of source 

and content has increased. In 1992, there was only one non-broadcast national 

news network, CNN. Today, CNN competes with MSNBC, Fox News Channel, 

and CNBC for subscribers. In children's programming, consumers can now 

choose from Nickelodeon, several Disney networks, Cartoon Network, and 

Noggin. With respect to basic service movie channels, before 1992, there was 

only AMC; now there are TCM, Fox Movie Channel, Sundance, Independent 

Film Channel and the Lifetime Movie Network. Today, there is also a

tremendous variety of more specialized niche programming, such as Food

Network, Sci-Fi, Golf, HGTV, Outdoor Life, and the Speed Channel. Even in 

niches where an existing network enjoys a strong brand name, new networks are 

entering, as National Geographic has entered to challenge Discovery. 

 

1 Other technologies for distributing multi-channel video programming may be available in some areas 

and/or in planning stages in some areas. Cable and satellite currently make up the vast majority of MVPD 

subscriptions.

2 These non-broadcast networks are often referred to as cable networks, because they were initially 

developed for cable carriage. Today, MVPDs (e.g., cable, DBS, private cable, or Satellite Master Antenna TV 

operators) distribute these networks. 

3 Under the provisions of the Communications Act, a cable operator can require a subscriber to buy no 

more than the basic tier (i.e., the programming tier with broadcast and PEG channels) in order to subscribe to 

premium channels (e.g., HBO, Showtime) or other services, such as pay-per-view.

4 See 10th Annual Report on Video Competition, 19 FCC Rcd at 1690-91.
5

Over the years, a significant number of cable networks have been announced 

and planned.5 Some networks launched and succeeded, other networks have yet 

to initiate service, other networks have begun operation and failed, and still

others have begun operation and then merged with other services. For a variety 

of reasons, researchers, policymakers, and investors want to know the primary 

determinants of cable network survival. We therefore benefit the public if we 

reasonably answer the following questions: 

1. How many subscribers have cable networks needed in the past to 

continue operations?

2. What does this tell us about the revenue structure, cost structure, and exit 

decisions of cable networks?

When a cable network begins operations, it often attracts very few

households and suffers heavy losses during its start-up period, seeking future 

present-valued quasi-rents6 that will equal or outweigh the initial losses. Given 

the high losses that a cable network suffers during its start-up phase, that

network must expect many future households as subscribers in order to begin 

operations. 

A cable network’s decision to exit depends on its expected present value of 

future quasi-rents; if the expected present value of future quasi-rents drops

below zero, then the network exits. Because a cable network incurs sunk entry 

costs, the quasi-rents a cable network needs to stay in business are clearly far less 

than the expected profits that induce entry by a cable network. 7 Once a cable 

network incurs sunk entry costs, these sunk entry costs are not relevant to the 

cable network’s later exit decision. For example, suppose that a cable network 

incurs sunk entry costs of $10, expecting $11 in present-valued future quasirents. Subsequently, the cable network discovers that its present-valued future 

quasi-rents are only $5. Notwithstanding the negative difference between its 

sunk costs and quasi-rents, the cable network would still continue operations, 

since the sunk entry costs are not affected by continuing operations or shutting 

down and exiting the market. Some positive level of quasi-rents, although 

insufficient to recover total sunk costs, helps minimize losses.

 

5 See, e.g., 19 FCC Rcd at 1735-37, Table C-4; 17 FCC Rcd at 26901, 26992-94, Table C-4; 17 FCC Rcd at 

1244, 1357-58, Table D-4.

6 These revenue streams are quasi-rents and not profits, because they may not equal the sunk costs of 

entry, but still may be greater than the minimum revenue required to keep the cable network operating.

7 Dixit (1989) explores this gap between the prices that induce exit and the prices that induce entry and 

finds that even a small gap induces significant hysterisis.
6

Cable programming has a high fixed cost of production and a very low 

marginal cost of distribution. That is, producing programming can be very

expensive, but distributing that programming to an additional household is

virtually costless. It costs a cable network as much to produce programming that 

could reach one subscriber as it does to produce the same programming that 

could reach one million subscribers.

8 Programming costs therefore do not rise 

when the programming network reaches more subscribers, but revenues do

increase when the network reaches more subscribers. Hence, profits definitely 

increase with the number of subscribers, so that cable networks seek to maximize 

program distribution, conditional on price. 

Analyzing cable networks’ profit and revenue streams may seem ideal, but 

because revenue and cost data for many networks (particularly “deceased” 

networks) are unavailable, such analysis is not possible. In addition, Fisher and 

McGowan (1983) and others demonstrate the virtual impossibility and high

likelihood of error when researchers try to infer economic profits from observed 

accounting profits, so that using profit and revenue data may not be desirable. 

Survival/Duration analysis enables us to estimate the number of subscribers

that cable networks need to stay in business. Engineers and biologists first

applied Survival/duration methods to estimate how different ball bearings affect 

a machine’s longevity or how a new drug affects a patient’s longevity. 

Economists then discovered survival/duration analysis and applied it to a

variety of economic settings. For example, Lancaster (1979) uses survival

analysis to analyze unemployment duration, as does Meyer (1990). Chung, 

Schmidt and Witte (1991) employ survival analysis to determine causes of

criminal recidivism. Ham and Lalonde (1996) use survival analysis to study the 

effect of a job training program on unemployment duration. Lancaster (1990) 

provides a notable monograph on survival analysis. 

The economics/business/finance literatures are rich with survival/duration 

analyses of media products like movies (DeVany and Walls (1996), DeVany and 

Walls (1997), Walls (1998)), Broadway shows (Simonoff and Ma (2003)), and 

newspapers (Kranenburg, Palm, and Pfann (2002)). However, no published

research has applied survival analysis to cable networks. Moreover, there does 

not appear to be any data source that specifically deals with cable networks that 

have failed in the past. This is not surprising; non-existent cable networks do not 

attract interest from most consumers of cable industry data, and MVPD data 

producers therefore do not collect and keep such data. 

 

8 Of course, programmers may charge distributors on a per-subscriber basis, but that does not change 

the fact that the cost of making a program is fixed, and that the actual cost of making the program need not 

rise when the program reaches more subscribers.
7

II. Data

We collected data on cable networks from a variety of sources.9 The Television 

and Cable Factbooks10 from the years 1984-2001 report the number of subscribers 

for a cable network in a given year from 1984-2001. This study focuses on

national non-premium networks, and therefore includes neither regional cable 

networks nor premium networks like HBO and Showtime. If we do not observe 

a cable network in a given year’s Factbook after it appeared in previous Factbooks, 

then we assume that the cable network exited (unless we see it again in following 

Factbooks). 

The number of subscribers and network genre may determine a cable

network’s survival. Network genre may determine survival probabilities

because important underlying determinants of survival vary across network

genres. Production costs may vary across genre, because different types of 

programming have different costs of production. This variation would generate 

a different relationship between subscribership and survival probability. 

Different genres may also face different demands from subscribers. One

genre might attract intense interest from a handful of households and only the 

slightest interest from all other households. In this case, as Spence and Owen 

(1977) demonstrate, the cable operator would capture only a fraction of

subscribers’ total willingness to pay for the channel.11 A different genre,

however, might attract middling interest from all households. In this case, the 

cable operator can capture (almost) the entire sum of subscribers’ willingness to 

pay for a channel.12 Therefore, different programming genres may require

different numbers of subscribers for survival, even if these genres have identical 

programming costs.

Other factors, however, may also be important. A cable operator’s ownership 

interest in a programming network may lead that operator to favor the

 

9 Ms. Jane Frenette provided valuable assistance with this important task.

10 Warren Communications, Television and Cable Factbook, Warren Publishing, 1984-2001.

11 The intuition of this proposition is illustrated in the following example: Ten households are willing 

to pay $10 for an old classic movie channel, while 90 households are only willing to pay $1 for the same 

channel. The sum of households’ willingness-to-pay is $190. The most the single-price cable operator can 

obtain, however, is $100, by charging $10 and attracting only ten households. This case represents a more 

convex demand schedule.

12 Consider this example: All 100 households in a system may be willing to pay $1.90 for a channel 

featuring game show reruns. The cable operator charging a single price can obtain all $190 by charging $1.90 

and attracting all 100 households. This case represents a more concave demand schedule.
8

programming network in its carriage decisions13 (possibly because the operator 

receives some of the programming network’s advertising revenue). We therefore 

include the vertical ownership measure obtained from past FCC Video

Competition Reports (which rely heavily on the National Cable Television

Association’s Cable Developments) and Kagan’s Economics of Basic Television

Networks. So-called “spinoff” networks (cable networks spawned by other

programming networks) may also face a higher survival probability, possibly 

because they can forgo the costs of producing original programming by airing 

previously-aired programming from their parent cable network. We collected 

data on these spinoffs from past FCC Video Competition Reports and Kagan’s 

Economics of Basic Television Networks. Finally, a cable network’s start year may 

influence its probability of survival. Our sample begins in 1984. Therefore, 

among the cable networks starting before 1984, we observe only those that

survive at least until 1984. 

We do not observe every explanatory variable for every cable network. In 

addition, our ability or inability to observe a variable may reveal important 

information concerning a network’s survival probability. Table 1 lists the

explanatory variables, their data source, the number of networks with missing 

observations for each variable, the number of failures observed, and the

probability of failure. As we can observe more about a cable network (including 

the network’s subscriber count, vertical integration, and spinoff status) the cable 

network’s survival probability rises. More specifically, if we observe a cable 

network’s subscriber count, vertical integration, and spinoff status, that cable 

network has an estimated failure probability of 19.0%. All other networks have a 

43% chance of failure.14

 

13 To clarify, the operator would favor the programming network by carrying it under circumstances in 

which it would normally not carry a comparable network in which it lacks any ownership. 

14 The derivation of this estimated failure probability is as follows: (96 total failures – 28 “observe 

everything” failures) = 68 failures. (305 total networks – 147 “observe everything” networks) = 158. 

Dividing 68 by 158 yields 43%.
9

TABLE 1

EXPLANATORY VARIABLES AND DATA SOURCES

Explanatory Variable

Number of 

Observed 

Networks

Source Number of

Failures

Percentage 

Failures

Network Name, Genre, Start 

Year

305 Factbooks 96 31.5

Number of Subscribers 194 Factbooks 47 24.2

Vertical Integration 210 FCC Video Reports, 

Kagan

53 25.2

Spinoff 210 FCC Video Reports, 

Kagan

54 25.7

Subscribers, Vertical, and 

Spinoff Observed 147 Factbooks, FCC Video Reports, Kagan 28 19.0

We adjust for the bias induced by missing observations by creating two

dummy variables that take on a value of one when the number of subscribers 

(Missing Subs) and vertical integration (MissingVerticalorSpinoff) cannot be

observed.

15 We create two more new variables by multiplying the measures of 

subscribers and vertical integration status by one minus the value of Missing Subs

and Missing Vertical. This creates two new variables; namely, SubsMiss and 

VerticalMiss, which equal zero when observations are missing. 

The population sample begins in 1984. Many cable networks, however,

began (and possibly ended) before 1984. The data therefore suffer from stock

sampling, which occurs where the researcher samples from the population at a 

given point in time. The sampling period ends in 2001, notwithstanding that 

cable networks continued in business after 2001. We therefore face right 

censoring, which occurs where the researcher ends the sampling period at a given 

point in time. We do not observe network exits or entrances before 1984. 

Consequently, there are truncation problems stemming from the stock

sampling.16 In addition, we cannot observe cable network exits that occur after 

2001 (right censoring). We therefore employ analysis that takes this censoring 

 

15 Because we obtain data on vertical integration and spinoff status from the same sources, any 

observation that is missing for vertical integration is also missing for spinoff status (though one more 

observation is missing for spinoff status), so that it is unnecessary to create a missing dummy variable for 

both vertical integration and spinoff status.

16 However, because all networks’ start dates are observed, left censoring problems are avoided.
10

into account. Finally, there remains the issue of grouped duration data. Ideally, 

we could observe the exact date and time of each programming network’s exit. 

Instead, we only observe the year of exit. Consequently, cable networks can exit 

during only 17 intervals, one for each possible year of exit. Therefore, we

employ a methodology that addresses grouped duration data. Discrete time

survival/duration models provide this analysis. 

Survival models first estimate an underlying baseline hazard function, which 

simply means estimating the cable network’s underlying probability of exit in 

each period, given that the network did not exit in the past. The researcher then 

multiplies that baseline hazard by measures of different covariates. 17 Once the 

hazard is estimated, it can be used to calculate a network’s chance of survival for 

any given amount of time and to estimate a programming network’s chance of 

survival for any given future time period, given that the network has survived so 

far.

III. Estimation Methods and Empirical Results 

A. Overview

We estimate a model of survival for cable networks using two methods. One 

method is parametric, where we assume that the hazard survival probabilities 

follow a known statistical distribution. The parametric method has one distinct 

advantage; unlike some other methods to be discussed later, the researcher need 

not assume a condition called strict exogeneity to obtain statistically sound

estimates.18 In addition, parametric methods enable the researcher to model

easily unobserved heterogeneity. This means that the researcher can adjust for 

many differences between cable networks even where the researcher cannot 

observe such differences.19 One drawback to parametric methods is that they 

estimate a smooth curve on the survival probability, which may impose

unnecessary structure on the hazard and survival probabilities and can at times 

lead to some odd predictions based on the smooth curve itself.20 These odd 

 

17 Technically, this discussion applies to proportional hazards models only, and not to accelerated 

failure time models. Since this study employs a proportional hazards approach, we focus the discussion on 

these models.

18 Strict exogeneity (also called sequential exogeneity), unlike the usual definition of exogeneity, means that 

there is no correlation between unobserved characteristics and future values of a time-varying explanatory 

variable. 

19 However, the researcher must then assume strict exogeneity of the explanatory variables, conditioned 

on the unobserved heterogeneity. In addition, the unobserved heterogeneity must be distributed

independently of the explanatory variables. The expectation of the unobserved heterogeneity cannot be 

larger or smaller based on the size of any of the independent variables.

20 This would occur if extrapolating well beyond existing data points based on the smooth curve itself.
11

predictions may indicate misspecification introduced by imposing the wrong

statistical distribution.

A second method employs semi-parametric estimation, which uses the data 

itself to build an underlying baseline hazard function. Because semi-parametric 

estimation methods use the actual data to build the baseline hazard function, 

there is no curve-fitting for the baseline hazard, which avoids the imposition of 

structure on the data. This allows the researcher to avoid errors arising from 

misspecifying the underlying probability distribution. Unfortunately, because of 

data limitations, the researcher cannot easily employ this method to model

unobserved heterogeneity. In addition, according to Wooldridge (2002), “. . . 

with time-varying covariates, Cox’s method evidently requires the covariates to 

be strictly exogenous”.21 Meanwhile, another semi-parametric method,

piecewise-constant proportional hazard estimation,22 does not easily allow for 

stratification.

The assumption of strict exogeneity is problematic. Kalbfleisch and Prentice 

(1980), discussing time-varying covariates (i.e., those explanatory variables that 

vary over time), divide these covariates into external covariates and internal 

covariates. In this context, if a time-varying covariate moves independently of 

whether or not a cable network exits, then that covariate is external. If a timevarying covariate’s value depends on whether the programming network exits, 

then that covariate is internal. The number of subscribers is an internal covariate, 

because a cable network cannot attract any subscribers after it exits. Internal 

covariates clearly cannot be strictly exogenous, so that the assumptions

underlying the Cox semi-parametric method and the parametric method with 

unobserved heterogeneity do not hold. However, these methods still impose less 

structure or model possibly important unobserved heterogeneity. We estimate 

the parametric model without unobserved heterogeneity, thereby gaining

estimates that do not rely on the strict exogeneity assumption. We then check 

these estimates against the semi-parametric estimates and parametric methods 

with unobserved heterogeneity that require strict exogeneity. We can therefore 

discover whether the violation of strict exogeneity generates seriously inaccurate 

estimates. Table 2 lists the advantages and drawbacks of each estimation

method. None of our three estimation methods scores three for three on our list 

of three virtues, but each method has different virtues. Consequently, each

method can be compared to discover which method yields the greatest overall 

net advantage.

 

21 Wooldridge, Econometric Analysis of Cross Section and Panel Data, p. 714.

22 The piecewise-constant proportional hazard method is called “semi-parametric” only because it does 

not estimate an underlying hazard function as a smooth curve over time. The piecewise approach is 

parametric in that it employs an underlying statistical distribution.
12

TABLE 2

ADVANTAGES AND DRAWBACKS OF EACH ESTIMATION METHOD

B. Estimation and Results Of Parametric Models

For estimating the parametric model, we employ the Weibull distribution. 

The Weibull tends to be the more popular parametric distribution for survival 

estimation, because the Weibull is straightforward to estimate and has enough 

flexibility to allow the researcher to check for an increasing, constant, or

decreasing probability of survival over time. 

In survival models, negative duration dependence indicates increasing exit 

probability over time, because the probability of survival falls as the subject gets 

older. Adult humans exhibit negative duration dependence, because our

likelihood of dying increases as we age. Positive duration dependence indicates 

that the probability of survival increases as the subject gets older. 

Examination of the Weibull distribution illuminates its advantages. The

conditional Weibull probability density function tells us the probability of exiting 

at time t conditional on the explanatory variables xi. The Weibull probability 

density function is 1( | ; ) exp ( ) exp [ exp ( ) ] i i i f t x x t x t aq b a b a −= − . The 

parameters to be estimated are a and b. In this model, the value of a determines 

whether the process exhibits positive or negative duration dependence, and the 

values in the vector b determine the impact of the explanatory variables on the 

probability of survival. Several other functions can be derived from the Weibull 

probability density function. The survivor function,

( ; ) exp [ exp ( ) ] S t i i x x ta= − b (1)

Semi-Parametric

(Cox/Piecewise)

Parametric (no unobserved 

heterogeneity)

Parametric (with 

unobserved heterogeneity)

Impose structure? No/No Yes Yes

Model unobserved 

heterogeneity? No/No No Yes

Requires strict 

exogeneity? Yes/No No Yes
13

is the probability of a cable network surviving until at least time t. Dividing the 

Weibull probability density function by the survivor function generates the

hazard function

 

1

(t; x ) exp ( ) x tal b a −= . (2)

This hazard function provides the probability of the network exiting at time t, 

conditional on not having exited prior to time t. It is this function that we

estimate to recover a and b.

As noted previously, the data for this study begin in 1984, after some

programming networks had already launched; cable networks that both

launched and died before 1984 are not observed. Also noted previously, this 

creates a stock sampling issue, where the data suffer left-truncation, meaning 

cable networks that both entered and exited the market before 1984 are not seen. 

In addition, the data set ends at 2001, so cable networks that exit after 2001 are 

not observed. This means that the data are right-censored. Given these data 

restrictions, estimation requires maximization of the log-likelihood function 

1 0

{ log[(|; )] (1 )log[1 (|; )] log[ ( | ; )] log1[ ( | ; )] (|;)

N b

i i i i i i i i i i

i

d f t x q d F t x q k a x h F b mqm xkxd h m

=

∑ + − − + − − − ∫ , (3)

where F is the cumulative Weibull distribution; t is time; b is the point where the 

sampling period begins; di is a binary variable that equals zero if the network 

was still surviving in 2001 and one otherwise; and ai measures when each

observation enters the sample.23 In addition, ( | ; ) i

k x • h is the density of starting 

times given xi. The statistical estimation package Stata performs this estimation 

procedure when the researcher has identified the relevant values b and ai.

 

We now consider unobserved heterogeneity, which represents unobserved 

determinants of cable network duration. In order to model unobserved

heterogeneity, we must make the following three assumptions:

(1) The heterogeneity is independent of the observed covariates.

(2) The heterogeneity has a distribution known up to some finite number of 

parameters.

(3) The heterogeneity enters the hazard function multiplicatively.

 

23 h and q are both vectors of parameters to be estimated. 
14

We illustrate these assumptions by adding heterogeneity to the Weibull

distribution. The Weibull marginal hazard is

1

(; , ) exp( ) i i i i t x v v x ta l b a −= (4)

where vi is the unobserved heterogeneity, which enters the distribution

multiplicatively. Because this heterogeneity cannot vary across covariates, the 

primary value of including this unobserved heterogeneity is that it allows more 

flexible estimation of duration dependence. Lancaster (1990) notes that ignoring 

multiplicative heterogeneity in the Weibull model results in underestimating the 

value of a. 

Applying independence of xi and vi, the new cumulative distribution function

ti

* given xi is

0

( | ; , ) ( | ,;)(;) G i i t x q g Ftx v q g h v dv

∞

= ∫ , (5)

where F is the Weibull distribution function, and h is the probability density 

function of v with mean one and variance g. Of course, stock sampling and right 

censoring remain problems. We therefore substitute the new distribution and 

density functions, G(.) in equation (5) and its derivative g(.), that incorporate 

unobserved heterogeneity into the earlier likelihood function that is adjusted for 

right censoring and stock sampling. This yields 

1 0

{ log[ ( | )] (1 )log[1 ( | )] log[ ( | ; )] log1[ ( | )] ( | ; )

N b

i i i i i i i i i i

i

d g t x d G t x k a x h G b m x kxd m h m

=

∑ + − − + − − − ∫ (6) 

which we maximize in order to estimate survival following a Weibull

distribution with unobserved heterogeneity. We use the Gamma distribution to 

model the distribution of unobserved heterogeneity, as this is the only applicable 

distribution available in Stata 8 to estimate discrete-time duration models with 

heterogeneity. Under the Gamma distribution of unobserved heterogeneity,

1 1

1

( ) exp ( ) /() vh v v

g

g g d

g g

−

= − Γ , where Γ •( ) is the Gamma function. 

We estimate a discrete-time Weibull mode with and without unobserved

heterogeneity, and we stratify by the sports and shopping genres. Table 3 

displays the estimation results. Estimating the Weibull marginal hazard, i.e.,

1

exp( ) ix tal b a −= , (7)
15

generates an estimate of a, which yields the baseline marginal hazard probability 

together with the vector b, which yields the covariates’ effects on a network’s 

marginal hazard, i.e., its probability of exit in a given period, given that it did not 

exit before that period.24 

 

24 Using discrete-time models, the estimated marginal hazard is actually 

( ln )

1

X t e

e

b a+

−

− .
16

TABLE 3

PARAMETRIC WEIBULL SURVIVAL ESTIMATES

(Z-statistics in parentheses)

Weibull

(No Unobserved Heterogeneity)

Weibull

(Gamma-distributed Unobserved 

Heterogeneity)

Millions of Subs -0.07***

(3.92)

-0.13***

(3.95)

Missing Subs -0.65***

(2.61)

-1.07**

(2.31)

Vertical Integration 0.00

(0.07)

0.00

(0.02)

Spinoff -1.39***

(2.64)

-2.69***

(2.67)

Missing Vertical or

Spinoff

0.56**

(2.51)

1.74***

(3.22)

Born before 1984 -0.89*

(1.94)

-3.48***

(3.25)

Constant -2.87***

(9.23)

-4.46***

(6.58)

a 0.28*

(1.83)

2.39***

(3.95)

asports

0.79

(1.63)

3.36

(1.27)

ashop

0.68**

(2.52)

4.26***

(2.57)

g variance 6.30***

(3.24)

Observations 305 305

Failures 96 96

Log Likelihood -363.10*** -348.97***

*- significant at 10% level, ** - significant at 5% level, *** - significant at 1% level
17

In the estimation without unobserved heterogeneity, an additional one 

million subscribers reduce the marginal probability of exit by 7%. Ten million 

subscribers generate a hazard ratio of (10*( .07)) ( .7)

e e

− −

= = .50, so that 10 

million subscribers would reduce the probability of exit by 50%. If the

observation on the number of subscribers is missing, then the hazard ratio is 0.52, 

so the probability of exit is 48% lower than the probability of exit if we observe 

zero subscribers. Thus, observing over nine million subscribers confers the same 

probability of exit as not being able to observe the number of subscribers,

because (9*( .07)) ( .63) e e − −

= ≈ 0.52. Spinoff networks have a hazard ratio of 0.25, 

so a network’s probability of exit declines by 75% if that network is a spinoff 

network. If cable network’s vertical ownership or spinoff status cannot be

observed, then that cable network has a 75% greater chance of exit. If the

network began before 1984, then we do not observe other networks in its birth 

cohort that died before 1984. That network’s marginal probability of exit

therefore declines by 59%. In addition, both sports channels and shopping

channels have a greater probability of exit than non-sports and non-shopping 

channels. A sports channel is 67% more likely to exit and a shopping channel is 

49% more likely to exit in any given year than are other types of programming 

networks.

The addition of gamma-distributed heterogeneity significantly changes the 

coefficient estimates. The likelihood ratio test for these models rejects the null 

hypothesis that they yield the same coefficient estimates. An additional one

million subscribers multiplies the hazard ratio by 0.87, so that one million

subscribers reduce the marginal probability of exit by 13%. Ten million

subscribers would create a hazard ratio of (10* (.13)) ( 1.3)

e e

− −

= = .27, so that ten 

million subscribers would reduce the probability of exit by 73%. If the

observation on the number of subscribers is missing, then the hazard ratio is 0.34, 

so the probability of exit is 66% lower than the probability of exit if we observe 

zero subscribers. Thus, observing over 8 million subscribers confers the same 

marginal probability of exit as not being able to observe the number of

subscribers, because (8*( .13)) 1.04

e e

− −

= ≈ .34. Spinoff networks have a hazard ratio 

of 0.07, so a network’s probability of exit declines by 93% if that network is a 

spinoff network. If cable network’s vertical ownership or spinoff status is not 

observed, then that programming network has a 470% greater chance of exit. If 

the network began before 1984, so that other networks in its birth cohort that 

died before 1984 are not observed, then that network’s marginal probability of 

exit declines by 97%. In addition, shopping channels have a greater probability 

of exit than non-sports and non-shopping channels. A shopping channel is 649% 

more likely to exit in any given year.
18

To obtain marginal effects, we need the specific time period and all of the 

covariates’ values. Because the covariates and the time period affect the

marginal hazard through a nonlinear function, the marginal effects at specific 

values for time and all other covariates must be evaluated. For example, we 

calculate the marginal effect of increasing the number of subscribers from four 

million to five million for a cable network in year number five. That network 

began after 1984; is not vertically integrated; is not a spinoff; and has no missing 

values for the number of subscribers, the degree of vertical integration, or spinoff 

status. In addition, the network genre is neither sports nor shopping. Using the 

Weibull values with unobserved heterogeneity,25 a network with zero subscribers 

would face a marginal exit hazard of 40.5%; a network with four million

subscribers would face a marginal exit hazard of 26.6%; and a network with five 

million subscribers would face a marginal exit hazard of 23.7%. Therefore, the 

marginal effect of going from four million to five million subscribers in year five 

would reduce the marginal probability of exit by 2.9%.

The discrete-time survivor function at time t is 

1 2 (1 )*(1 )*. . . *(1 )t

− l − − l l , (8)

which is equivalent to 

1

ln(1 )

t

x

x e

l

=

∑ −

. (9)

Using this survivor function, which is the discrete-time counterpart of the

aforementioned continuous-time survivor function,

( ; ) exp [ exp ( ) ] S t i i x x ta= − b , we calculate subscriber profiles over a cable 

network’s first X years that generate a given probability of survival, which is one 

of many ways to examine the influence of subscribers on the success of a

network. 

Any number of years and any probability of survival may be chosen. For this 

discussion, we select the first five years and the first 10 years of a cable network’s 

life, and select a 70% survival probability.26 We assume that the network began 

after 1984; is not vertically integrated; is not a spinoff; and has no missing values 

for the number of subscribers, the degree of vertical integration, or spinoff status. 

In addition, the network genre is neither sports nor shopping. Finally, a realistic 

 

25 Recall that the heterogeneity term is independent of the covariates and has a mean equal to one, so 

that unobserved heterogeneity can be ignored when calculating expected values of the probabilities.

26 These values simply illustrate how to generate survival profiles and are not intended to suggest 

appropriate values for the calculation. 
19

growth path of subscribers over the time period must be chosen, because a

variety of subscriber profiles over five or ten years could generate a 70% chance 

of survival. For example, using the Weibull model with unobserved

heterogeneity, a cable network could achieve a 70% survival probability over its 

first five years by obtaining zero subscribers over its first three years and

obtaining almost 15 million subscribers in its fourth and fifth years. A cable

network could also achieve a 70% survival probability over five years by

obtaining 8.6 million subscribers in all five years. Our chosen subscriber growth 

path reflects the typical subscriber growth rate of cable networks. A good

approximation of this growth path is the percentage change in the average

number of subscribers for a cable network, conditional on that cable network’s 

age. For example, the average number of subscribers at the end of cable

networks’ first year is 2.51 million, and the average number of subscribers at the 

end of cable networks’ second year is 3.51 million, which yields a growth rate of 

48.26% between the two years.27 

This simple approach for estimating subscriber growth rates may have

problems. If a cable network fails because it grows more slowly, then the 

estimated growth rate using conditional means may overstate a cable network’s 

rate of subscriber growth as it ages, because we fail to observe those cable

networks that grew more slowly, since those networks exit and leave the sample. 

Thus, we check to determine whether a lower rate of growth increases the chance 

of failure over time. It may seem obvious that a lower rate of subscriber growth 

increases the probability of failure, but this is not necessarily so. A cable network 

may grow rapidly from a small base and still fail for a lack of subscribers. In 

short, having a low number of subscribers does not necessarily imply a lower 

past subscriber growth rate. 

We test the fitness of the conditional means by considering the procedure 

used to adjust for a sample selection problem.28 For the first stage, we employ a 

probit regression with failure as the dependent variable and the rate of

subscriber growth as the independent variable; this probit is calculated for each 

given cable network age. The next stage employs the inverse Mills Ratios

obtained from these regressions in a pooled OLS regression with the growth rate 

as the dependent variable. The results are not statistically significant, indicating 

that our conditional means method does not create a biased growth rate. In 

addition, to the extent there is sample selection bias, this bias does not

significantly change the final results of the analysis. Given the small baseline 

 

27 Appendix 2 lists the average subscriber growth rates by network age. 

28 Wooldridge (2002) discusses this procedure in detail at pages 581-585.
20

marginal hazard in each year, then the failure to account for failed networks 

would not significantly change the year-to-year growth estimates.

TABLE 4

SUBSCRIBER PROFILES FOR 50% SURVIVAL PROBABILITY 

OVER 5 AND 10 YEARS

Weibull

No Unobserved 

Heterogeneity

5 Years

Weibull

No Unobserved 

Heterogeneity

10 Years

Weibull Unobserved 

Heterogeneity

5 Years

Weibull

Unobserved 

Heterogeneity

10 Years

Year Subscribers

(in millions) Year Subscribers(in millions) Year Subscribers(in millions) Year Subscribers(in millions)

1 0 1 0.85 1 1.29 1 4.10

2 0 2 1.27 2 1.91 2 6.08

3 0 3 1.71 3 2.59 3 8.22

4 0 4 2.18 4 3.30 4 10.49

5 0 5 2.75 5 4.16 5 13.22

6 3.39 6 16.27

7 4.09 7 19.64

8 4.73 8 22.74

9 5.52 9 26.52

10 5.85 10 28.09
21

TABLE 5

SUBSCRIBER PROFILES FOR 70% SURVIVAL PROBABILITY 

OVER 5 AND 10 YEARS

TABLE 6

SUBSCRIBER PROFILES FOR 90% SURVIVAL PROBABILITY 

OVER 5 AND 10 YEARS

Weibull

No Unobserved 

Heterogeneity

5 Years

Weibull

No Unobserved 

Heterogeneity

10 Years

Weibull Unobserved 

Heterogeneity

5 Years

Weibull

Unobserved 

Heterogeneity

10 Years

Year Subscribers

(in millions) Year Subscribers(in millions) Year Subscribers(in millions) Year Subscribers(in millions)

1 0.33 1 3.51 1 3.24 1 5.36

2 0.49 2 5.21 2 4.80 2 7.94

3 0.67 3 7.04 3 6.48 3 10.74

4 0.86 4 8.99 4 8.28 4 13.71

5 1.08 5 11.33 5 10.43 5 17.27

6 13.95 6 21.27

7 16.84 7 25.67

8 19.50 8 29.72

9 22.74 9 34.66

10 24.08 10 36.72

Weibull

No Unobserved 

Heterogeneity

5 Years

Weibull

No Unobserved 

Heterogeneity

10 Years

Weibull Unobserved 

Heterogeneity

5 Years

Weibull

Unobserved 

Heterogeneity

10 Years

Year Subscribers

(in millions) Year Subscribers(in millions) Year Subscribers(in millions) Year Subscribers(in millions)

1 9.15 1 10.17 1 7.02 1 8.11

2 13.57 2 15.08 2 10.40 2 12.02

3 18.35 3 20.39 3 14.07 3 16.25

4 23.42 4 26.02 4 17.95 4 20.74

5 29.51 5 32.79 5 22.62 5 26.14

6 40.38 6 32.19

7 48.73 7 38.85

8 56.43 8 44.98

9 65.81 9 52.46

10 69.70 10 55.56
22

The gamma-distributed unobserved heterogeneity estimates are all

significantly farther away from zero than the estimates without unobserved

heterogeneity,29 and generate very different subscriber profiles for a 70%

probability of survival over both five and 10 years. However, these estimates 

still rest on the assumption of strict exogeneity, a questionable assumption. By 

using discrete-time data, the statistical estimation actually estimates a panel

model, where the dependent variable is whether the programming network 

exits. By assuming unobserved heterogeneity, we estimate a random-effects 

panel data complementary log-log model, where the random effect’s distribution 

is the unobserved heterogeneity. By including the log of the cable network’s age 

in the vector of independent variables, we create a Weibull baseline hazard. 

When we don’t assume unobserved heterogeneity, we estimate a complementary 

log-log population-averaged panel effects model (again including the log of the 

network’s age to create a Weibull baseline hazard), where every programming 

network is a population, and that population is made up of each yearly 

observation for that programming network. Thus, ESPN would be one

population, and each yearly observation of ESPN would be a member of that 

population. When we estimate population-averaged effects panel models, we 

assume that each population has its own within-group correlation structure. In 

other words, yearly observations of the Lifetime network are correlated with 

each other but are not necessarily correlated with ESPN’s yearly observations. 

Assuming an independent correlation structure, such that the unobserved

heterogeneity is network-specific but random, we obtain the same results as the 

standard non-panel Weibull regression. If we constrain the correlations to be 

equal within the network, we obtain very similar results.30 The correct

estimation method depends on the nature of unobserved heterogeneity. If the 

unobserved heterogeneity is network-specific, then the estimates without

unobserved heterogeneity are more accurate. If the unobserved heterogeneity is 

a separate function that multiplies across every network, then the estimates with 

unobserved heterogeneity are more accurate. 

C. Estimation and Results of Semiparametric Models

We employ two semi-parametric models which do not use statistical

distributions to estimate the baseline hazard. The Cox proportional hazards

model builds an empirical likelihood function based on networks that have

failed, while the piecewise-constant proportional hazards model estimates a

 

29 The likelihood ratio statistic between the two models, 28.24, is statistically significant.

30 Prentice and Gloeckler (1978) and Meyer (1990) provide the theoretical basis for the relationship 

between discrete-time survival models and conditional log-log panel estimation. Jenkins (1995)

demonstrates how to estimate discrete-time hazard models in a simple framework.
23

separate baseline hazard for each possible duration. Estimates from these

models can be compared to the estimates from the parametric models to examine 

the effects of the parametric restrictions. Furthermore, the Cox model relies on 

the assumption of strict exogeneity to generate consistent estimates, while the 

piecewise-constant model does not. Therefore, by comparing the results from 

the Cox and piecewise-constant models, we can obtain an indication of any bias 

introduced by assuming strict exogeneity. In this application, the flexibility of 

the semiparametric methods comes with a cost. No programming networks exit 

during their ninth, fourteenth through seventeenth, or after their nineteenth year. 

The methods do not allow estimation of baseline hazard rates for periods where 

no networks failed.

Table 7 displays the results of the semiparametric estimation methods. The 

semiparameteric coefficients bear some similarity to the parametric results

without unobserved heterogeneity. The piecewise-constant results are almost 

identical to the Weibull results with unobserved heterogeneity. This result

indicates that the Weibull distribution provides a good fit for the underlying 

baseline hazard, and the addition of unobserved heterogeneity may generate

more accurate results. 

The Cox results depend on the assumption of strict exogeneity; a questionable 

assumption. However, the coefficients may still reasonably approximate the true 

underlying relationship between a network’s survival probability and the

covariates. An increase in one million subscribers generates a hazard ratio of 

94%, so that one million subscribers decrease the probability of exit by 6%. Ten 

million subscribers generate a hazard probability of (10* .06) ( .6)

e e .55 − −= = , so

that ten million subscribers reduce the probability of exit by 45%. A spinoff

network has a 70% greater chance of surviving in any given year, because

1.21 e .30 −

= . 

The piecewise-constant results do not depend on the assumption of strict

exogeneity. Because we estimate a separate baseline hazard for each possible 

duration length, we estimate a completely flexible underlying baseline hazard. 

The results from the piecewise-constant model indicate that an increase in 

one million subscribers generates a hazard ratio of 83%, so that one million

subscribers decrease the probability of exit by 17%. Ten million subscribers

generate a hazard probability of (10* .17) ( 1.7)

e e 18% − −= = , so that ten million

subscribers reduce the probability of exit by 82%. A spinoff network has a 78% 

greater chance of surviving in any given year, because 1.5

e .22 −= . If a network 

began before 1984, then that network has 64% greater chance of surviving in any 

given year. 
24

TABLE 7

SEMI-PARAMETRIC SURVIVAL ESTIMATES

(Z-statistics in parentheses)

Cox Proportional Hazard

(With Stratification by Sports and 

Shopping Genres)

Piecewise-Constant Hazard

(No Stratification)

Millions of Subs -0.06***

(4.96)

-0.17***

(6.73)

Missing Subs -0.51**

(2.21)

-2.10**

(2.12)

Vertical Integration 0.00

(0.07)

-0.01

(1.15)

Spinoff -1.21**

(2.40)

-1.50***

(2.95)

Missing Vertical or 

Spinoff

0.26

(1.23)

-0.22

(1.22)

Born before 1984 -0.74

(1.62)

-1.08**

(2.01)

Duration 2 years -1.03***

(3.91)

Duration 3 years -0.93***

(3.36)

Duration 4 years -0.49*

(1.91)

Duration 5 years -0.82**

(2.43)

Duration 6 years -1.92***

(3.23)

Duration 7 years -0.44

(1.25)

Duration 8 years -0.60

(1.36)

Duration 10 years -0.47

(3.47)

Duration 12 years -0.35

(0.55)

Duration 13 years -1.03

(0.98)

Duration 19 years 1.52

(1.29)

Constant

Observations 305 305

Failures 96 96

Likelihood Ratio -364.60*** -324.91***

* - significant at 10% level, ** - significant at 5% level, *** - significant at 1% level
25

D. Discussion of Results

This study concludes that the piecewise-constant model generates the most 

reliable results. The piecewise-constant hazards model allows for a completely 

flexible hazard form and does not rely on the assumption of strict exogeneity. 

Therefore, the discussion of results uses the piecewise-constant estimates.

As mentioned before, an increase in one million subscribers generates a

hazard ratio of 83%, so that one million subscribers decrease the probability of 

exit by 17%, and ten million subscribers reduce the probability of exit by 82%. If 

the observation on the number of subscribers is missing, then the hazard ratio is 

0.12, so the probability of exit is 88% lower than the probability of exit if we 

observed zero subscribers. Therefore, observing 12.35 million subscribers

confers the same probability of exit as not being able to observe subscribers. 

As before, we use the estimates from the Cox model and the piecewiseconstant model to generate 70% survival probabilities over five and 10 years, as 

shown in Table 9, using typical subscriber growth rates.31 Again, we assume that 

the network began after 1984; is not vertically integrated; is not a spinoff; and has 

no missing values for the number of subscribers, the degree of vertical

integration, or spinoff status. In addition, the network genre is neither sports nor 

shopping. Table 10 reports the subscriber profile required to reach a 90%

survival probability. 

 

31 These values are simply used to illustrate how to generate survival profiles and are not intended to 

suggest appropriate values for the calculation.
26

TABLE 8

SUBSCRIBER PROFILES FOR 50% SURVIVAL PROBABILITY 

OVER 5 AND 10 YEARS

TABLE 9

SUBSCRIBER PROFILES FOR 70% SURVIVAL PROBABILITY 

OVER 5 AND 10 YEARS

Cox Proportional 

Hazards

5 Years

Cox Proportional 

Hazards

10 Years

Piecewise-Constant

Hazard

5 Years

Piecewise-Constant

Hazard

10 Years

Year Subscribers

(in millions) Year Subscribers(in millions) Year Subscribers(in millions)

Yea

r

Subscribers

(in millions)

1 0 1 1.43 1 3.63 1 3.99

2 0 2 2.05 2 5.39 2 5.92

3 0 3 2.77 3 7.28 3 8.00

4 0 4 3.53 4 9.29 4 10.21

5 0 5 4.45 5 11.71 5 12.87

6 5.48 6 15.85

7 6.62 7 19.12

8 7.66 8 22.14

9 8.94 9 25.82

10 9.47 10 27.35

Cox Proportional 

Hazards

5 Years

Cox Proportional 

Hazards

10 Years

Piecewise-Constant

Hazard

5 Years

Piecewise-Constant

Hazard

10 Years

Year Subscribers

(in millions) Year Subscribers(in millions) Year Subscribers(in millions)

Yea

r

Subscribers

(in millions)

1 5.87 1 6.52 1 5.90 1 6.06

2 8.38 2 9.31 2 8.75 2 8.99

3 11.33 3 12.59 3 11.83 3 12.15

4 14.46 4 16.06 4 15.10 4 15.50

5 18.23 5 20.24 5 19.03 5 19.54

6 24.93 6 24.06

7 30.08 7 29.04

8 34.83 8 33.62

9 40.62 9 39.21

10 43.03 10 41.53
27

TABLE 10

SUBSCRIBER PROFILES FOR 90% SURVIVAL PROBABILITY 

OVER 5 AND 10 YEARS

Generally, a reasonable observer expects a network to have a positive number 

of subscribers, but the number of subscribers is set equal to zero when we 

observe no subscribers. The coefficients on the missing subscriber dummy

variables therefore represent joint functions of both

(1) A possible set of completely unobservable network characteristics 

that determine both the observability of the characteristic in

question and the network’s probability of exit;

and 

(2) the expectation of the observations’ true values conditional on the 

observations being missing.

Absent prior assumptions about (1) and (2), the effects of each cannot be

explicitly estimated. However, the effects of (1) increase a network’s estimated 

marginal probability of exit, and the effects of (2) may increase or decrease a 

network’s estimated marginal probability of exit.

Earlier estimates show that not observing subscribers produces the same 

hazard as observing 12.35 million subscribers. This result raises several

possibilities. Unobservable characteristics that reduce the ability to observe the 

number of subscribers may not affect the network’s exit probability. The mean 

Cox Proportional 

Hazards

5 Years

Cox Proportional 

Hazards

10 Years

Piecewise-Constant

Hazard

5 Years

Piecewise-Constant

Hazard

10 Years

Year Subscribers

(in millions) Year Subscribers(in millions) Year Subscribers(in millions)

Yea

r

Subscribers

(in millions)

1 18.43 1 18.52 1 10.73 1 10.75

2 26.34 2 26.46 2 15.91 2 15.94

3 35.61 3 35.77 3 21.51 3 21.55

4 45.45 4 45.65 4 27.45 4 27.51

5 57.27 5 57.53 5 34.59 5 34.66

6 70.84 6 42.68

7 85.50 7 51.51

8 99.00 8 59.65

9 115.45 9 69.56

10 122.29 10 73.68
28

number of subscribers conditional on not observing the number of subscribers 

would then be nine million. Unobservable characteristics that reduce the ability 

to observe the number of subscribers may increase the likelihood of exit. This 

result would occur, for example, if a network’s failure to inform the Cable 

Factbook of their subscriber base correlated negatively with a network’s

managerial competence, so that managers who incur higher costs in reaching 

subscribers are also less likely to inform the Cable Factbook of their subscriber 

levels. The mean number of subscribers conditional on not observing the

number of subscribers would then be greater than 12.35 million. Finally,

unobservable characteristics that reduce the ability to observe the number of

subscribers may decrease a network’s exit probability. This outcome would

occur if, for example, following a niche strategy that makes a network less likely 

to report their subscribers to the Cable Factbook. Because regional networks are 

excluded from the sample, this niche strategy could involve targeting smaller 

populations that generate more advertising revenue per subscriber or targeting 

smaller populations that cost less to reach per subscriber.

A spinoff network has a 78% greater chance of surviving in any given year, 

because 1.5

e .22 −= . This result may indicate that spinoff networks have

significantly lower costs, because the spinoff network can recycle programming 

from the parent network. This may also indicate that a spinoff network increases 

the parent network’s subscribers, which leads the parent network to support the 

spinoff network. Finally, a spinoff network, when combined with channel

bundling, may enable the cable operator to exclude entry by the parent

network’s competitors and split the profits with the parent network. If a 

network began before 1984, then that network has a 64% greater chance of 

surviving in any given year. 

Like the coefficient on the missing subscribers dummy variable, two factors 

drive the coefficient on the missing vertical or spinoff dummy variable, namely, 

(1) A possible set of completely unobservable network characteristics 

that determine both the observability of the spinoff status and

vertical integration and the network’s probability of exit;

and 

(2) the expectation of the observations’ true values conditional on the 

observations being missing.

This coefficient is not significant in the piecewise-constant estimation.
29

IV.Conclusion

This study analyzes the survival of multi-channel video programming

networks using the tools of survival analysis. Using the estimates from a

piecewise-constant model, the study finds that a network growing at the average 

rate requires over 19 million subscribers at the end of five years to have a 70% 

probability of survival over its first five years, and over 41.5 million subscribers

to have a 70% probability of survival over its first ten years. Recall, however, 

that a network requires far fewer subscribers for survival if it acquires all of those 

subscribers from day one. According to the piecewise-constant estimates, a 

network requires only 10.18 million subscribers from day one to have a survival 

probability of 70% over its first five years, and 13.94 million subscribers from day 

one to have a survival probability of 70% over its first ten years. Thus, Comcast, 

which reaches over 21 million subscribers,

32 could confer a 70% chance of

survival on that cable network over the cable network’s first 10 years by agreeing 

to carry a cable network to half of its subscriber base from the network’s first 

day. Echostar, which reaches slightly less than 10 million subscribers, would be 

unable to confer a 70% chance of survival to a cable network over that cable 

network’s first 5 years.33

We advise caution when drawing inferences from survival analysis. By

definition, survival examines the exit decisions of firms that have already entered 

the market. Firms considering whether to exit the market have already incurred 

sunk entry costs, and therefore decide whether to exit based on expected quasirents. Firms considering whether to enter the market have not yet incurred sunk 

entry costs, and therefore decide whether to enter based on expected profits. The 

sunk entry costs are the gap between expected profits and expected quasi-rents. 

Dixit (1989) points out that even small sunk entry costs drive a significant wedge 

between entry and exit decisions, and cable entrants face at least some sunk entry 

costs in the form of launch fees and up-front marketing investments. In addition, 

the underlying model of cable network survival that drives survival analysis 

assumes an exogenous probability of exit given by nature. If firm survival does 

not follow this pattern, then other models of firm survival may be more

appropriate.

 

32 For this analysis, we assume that Comcast reaches 21 million subscribers, because NCTA reports that 

Comcast reached approximately 21 million subscribers through its owned and managed systems as of 

December, 2003. When we include all subscribers that could be attributed to Comcast under FCC attribution 

rules, Comcast has 26 million attributable subscribers. See Letter from Peter H. Feinberg, Associate General 

Counsel, Comcast Cable Communications, LLC, to Marlene H. Dortch, Secretary, FCC, MM Docket No. 

92-264 at 2 (Sept. 22, 2004). 

33 The best Echostar could offer is a 45% chance of survival over a cable network’s first ten years.
30

This study therefore raises an important question for future research. If we 

assume that different potential entrants have some range of beliefs about their 

potential networks’ profitability, with some potential entrants being overly

pessimistic and others overly optimistic about future profit streams, then we

expect the overly optimistic potential entrants to enter the market. If entrants 

face sunk entry costs, then some networks may continue operations because they 

are marginally profitable, i.e., make some positive quasi-rent, even though the 

entry decision turned out to be unprofitable. Overly optimistic beliefs amplify 

this phenomenon. Future research should focus on finding the marginal

networks, i.e., those who believed upon entry that they would make zero

economic profits,34 and discover the subscriber levels those cable networks

require to continue. In addition, future research should consider other

underlying models of cable network survival and should estimate these models.

 

34 Of course, zero economic profits simply means that the cable network’s accounting profits equal the 

average return on all other investments of similar risk, so non-economists should not interpret “zero 

economic profits” as meaning that the cable network makes zero dollars. 
31

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Wooldridge, Jeffrey M. 2002. Econometric analysis of cross section and panel data. 

Cambridge: MIT Press.
Channel Start year End year

Subscribers 

Missing

Vertical 

Integration 

Missing

Spinoff 

Status 

Missing

A&E 1984 - 0 0 0

ABN/Biznet 1982 1994 1 1 1

Access Entertainment 1998 1999 1 1 1

ACTS Satellite Network 1984 - 1 0 0

ActTV 1997 - 1 1 1

AETN 1984 1985 1 1 1

Agrisat 1987 1990 1 0 0

AIT 1984 1987 1 1 1

All News 1990 2001 1 0 0

Alternate View 1989 1995 0 0 0

AMC 1985 - 0 0 0

AMC's American Pop 1998 - 1 0 0

America One 1995 - 1 0 0

American Independent Network 1994 - 1 0 0

American Political Channel 1995 1998 1 1 1

American Sports Classics 1997 1999 1 0 0

Americana 1994 1995 0 0 0

America's Collectibles 1993 - 1 0 0

America's Shopping Channel 1984 1990 1 0 0

America's Store/Spree 1995 - 1 0 0

America's Talking/MSNBC 1994 - 0 0 0

America's Value Network 1987 1989 1 0 0

America's Voice/NET 1994 - 0 0 0

Animal Planet 1996 - 0 0 0

Arabic 1991 - 1 0 0

Arena 1997 1999 1 1 1

Art & Craft 1997 1999 1 1 1

Arts and Antiques 1994 1998 1 1 1

Asian American 1992 1998 1 1 1

AsiaNet 1993 - 1 0 0

ASN 1985 1987 1 0 0

ATN 1996 1998 0 0 0

AVN 1990 1993 1 0 0

Baby Bear 1995 1997 1 0 0

Baby TV 1999 - 1 0 0

BBC 1998 - 0 0 0

Behavior Communications 1999 - 1 1 1

BET 1980 - 0 1 0

BET on Jazz 1996 - 0 0 0

BET-HSN 1996 1999 1 0 0

Better Health 1996 2000 0 1 1

Biograpy Channel 1998 - 1 0 0

Black Shopping 1997 1998 1 1 1

Bloomberg 1994 - 1 0 0

B-Movie 2000 - 0 1 1

Boomerang 2000 - 1 1 1

Box 1986 - 1 0 0

APPENDIX 1

LIST OF SAMPLED CABLE NETWORKS

33
Channel Start year End year

Subscribers 

Missing

Vertical 

Integration 

Missing

Spinoff 

Status 

Missing

Box Country 1997 - 0 0 0

Box Edge 1999 - 1 0 0

Box Pulse 1999 - 1 0 0

Box Set 1999 - 1 0 0

Box Urban 1999 - 1 0 0

Boyz 2000 - 1 0 0

Bravo 1980 - 0 0 0

Business Vision 1996 - 1 0 0

C-3D 1999 - 1 1 1

Cable Newspaper 1984 1985 1 1 1

Cable Sports Net 1984 1985 1 1 1

Cable Value Network 1986 1992 1 0 0

Camnet/Nancys 2000 - 1 0 0

Canal de Noticias 1993 1997 1 1 0

Cancom 1987 - 1 0 0

Carribean Satellite 1993 1995 1 1 1

Cartoon 1993 - 0 0 0

Catalog Channel 1999 - 1 1 1

CBS Eye On People/Discovery People 1999 - 0 1 1

CBS Telenoticias 1995 1999 1 1 1

Channel America 1988 1998 1 0 0

Channel Black 1984 1985 1 0 0

Channel Earth 1997 1999 1 1 1

Channel Korea 2000 - 1 1 1

Children's 1995 - 1 1 1

Chinese Communication Channel 1989 1999 1 1 1

Classic Music 1996 1999 1 1 1

Classic Sports 1995 1999 1 0 0

CNBC 1989 - 0 0 0

CNN 1980 - 0 1 0

CNN en Espanol 1999 - 0 0 0

CNN International 1995 - 0 0 0

CNNfn 1996 - 0 0 0

CNNsi 1996 - 1 0 0

Collectible Showcase 1987 1988 0 0 0

Comedy Central 1989 - 1 0 0

Computer Television 1996 1999 1 0 0

Consumer Discount 1987 1989 1 1 1

Consumer Resource/FYI 1995 - 1 1 1

Country Music Television 1983 - 1 1 0

Courtroom 1991 - 0 0 0

Cowboy 1990 1992 0 1 1

Crazy Eddie 1987 1990 1 0 0

Crime 1993 - 1 0 0

C-SPAN 1979 - 0 1 1

C-SPAN II 1986 - 1 1 1

Cupid 1994 - 1 1 1

34
Channel Start year End year

Subscribers 

Missing

Vertical 

Integration 

Missing

Spinoff 

Status 

Missing

CVN 1996 - 1 0 0

Dating Channel 1995 2000 1 0 0

Deep Dish 1986 - 1 0 0

Deutsche Welle 1991 - 1 1 1

Discovery 1985 - 1 1 0

Discovery Civ 1997 - 1 0 0

Discovery Kids 1997 - 1 0 0

Discovery Living Channel 1999 - 1 1 1

Discovery Music 1985 1989 1 0 0

Discovery Science 1997 - 1 0 0

Discovery Showcase 1996 - 1 0 0

Disney 1983 - 0 0 0

Do-It-Yourself 1999 - 0 0 0

Dream 1995 - 0 1 1

E! 1987 - 1 1 1

Ecology Channel 1995 - 1 0 0

ESPN 1979 - 0 0 0

ESPN News 1996 - 0 0 0

ESPN2 1994 - 0 0 0

Eternal Word 1981 - 0 0 0

Eye on People 1997 1998 1 1 1

Family Channel 1977 - 0 1 0

FamilyNet 1980 1996 1 0 0

Fashion Channel 1988 1993 0 1 1

Fashion Network 1996 - 1 1 1

Fifth Avenue 1998 - 1 1 1

Fight Channel 1999 - 0 1 1

Filipino 1996 - 0 0 0

Financial 1981 1991 0 1 1

Fit TV/America's Health/Health Network 1994 - 1 0 0

Football Network 1998 - 1 0 0

Fox Kids 1998 1999 1 0 0

Fox Sports Americas 1995 - 1 0 0

Fox Sports Net 1997 - 0 0 0

Fox Sports World 1997 - 1 0 0

FoxNews 1996 - 0 0 0

Free Speech 1989 - 1 0 0

FX 1994 - 1 0 0

FXM 1995 1998 1 0 0

Game Show 1995 - 0 0 0

Gay 1993 - 1 0 0

Girlz 2000 - 1 1 1

Global Shopping 1997 1997 0 0 0

Golden American 1993 1998 1 1 1

Golf Channel 1997 - 1 0 0

Goodlife TV Network 1984 - 1 0 0

Gospel Music 1996 1998 1 0 0

35
Channel Start year End year

Subscribers 

Missing

Vertical 

Integration 

Missing

Spinoff 

Status 

Missing

Great American Country 1996 - 0 0 0

HA! 1990 1993 1 0 0

Headline news 1981 - 0 1 0

Health and Fitness 1993 1997 1 0 0

History 1995 - 0 0 0

History International 1999 - 1 1 1

Hit Video USA 1986 1995 1 0 0

Home and Garden 1995 - 0 0 0

Home Improvement 1994 - 1 0 0

Home Shopping Network 1985 - 1 0 0

Home Shopping Network II 1986 1997 1 0 0

HomeMed Channel 1996 - 1 0 0

HTV 1997 - 1 0 0

ICG Netcom. 1999 - 1 1 1

Idea Channel 1992 - 1 0 0

Infomerica TV 1996 - 1 1 1

International 1988 - 1 0 0

Intro 1994 - 1 1 1

IntroNet 1994 - 1 0 0

Jones Computer 1994 1997 0 0 0

Kaleidoscope 1990 - 1 0 0

Keystone 1988 1997 1 1 1

KIDZTIME TV 1996 1999 1 0 0

Korean 1986 - 1 0 0

Las Vegas 1996 - 1 0 0

Las Vegas Shopping 1995 1997 1 0 0

Learning 1979 - 0 0 0

Lifetime 1984 - 0 0 0

Lifetime Movie Network 1999 - 1 0 0

Lottery 1995 - 1 0 0

M2: Music Television 1999 - 0 1 1

Maranatha 1985 1987 1 1 1

MBC Gospel Network 1999 - 1 0 0

Merchandise 1994 1997 1 0 0

Military 1994 2000 1 0 0

Mind Extension University 1988 2000 0 0 0

Monitor Channel 1991 1992 0 0 0

MOR 1993 2000 1 0 0

Motivation 1985 1988 1 0 0

MSN Info 1984 1986 0 1 1

MTV 1981 - 0 1 0

MTV Latino 1994 - 1 0 0

MTV2 1996 - 1 0 0

Muchmusic 1994 - 1 0 0

My Pet 1997 - 0 0 0

NASA 1991 - 1 0 0

National & International Singles TV 1998 - 0 0 0

36
Channel Start year End year

Subscribers 

Missing

Vertical 

Integration 

Missing

Spinoff 

Status 

Missing

National Christian1 1980 1986 0 0 0

National Christian2 1987 1993 1 0 0

National College Television 1991 1992 0 1 1

National Jewish 1981 - 1 1 1

National Journal 1998 - 1 1 1

National Shopping Club 1988 1989 1 1 1

National Weather 1991 2000 1 0 0

Nationality Broadcasting 1985 - 0 1 1

NBA.com 2000 - 1 1 1

Network One 1989 - 1 0 0

NewSport 1994 1998 1 0 0

NewsTalk 1994 1998 1 0 0

NewsWorld 1998 - 0 1 1

Nickolodeon 1979 - 0 1 0

Noggin 1999 - 1 0 0

OASIS 1998 - 1 0 0

Odyssey 1985 1987 0 1 0

Odyssey 1988 - 0 0 0

ORB TV 1995 - 1 1 1

Outdoor1 1994 - 0 0 0

Outdoor Life 1995 - 0 0 0

Outdoor, Motorsports, Collectibles 1994 - 1 0 0

Outlet Mall Network 1997 2000 1 1 1

Ovation 1996 - 1 0 0

Oxygen 2000 - 1 0 0

Pacific 1984 1987 0 1 1

Pandamerica 1995 - 1 0 0

PBS Kids 1999 - 1 1 1

Peoples Network 1995 - 1 0 0

Performance Showcase 1998 - 1 1 1

Pet 1995 - 1 1 1

Praise Television 1996 - 1 0 0

Prime of Life 1984 1986 1 1 1

Product Information 1996 - 0 0 0

Promoter 1990 - 1 0 0

PTL 1979 - 0 1 1

Public Interest 1979 - 1 0 0

Q2 1994 - 1 0 0

QVC 1987 - 0 0 0

QVC Fashion 1994 1995 0 0 0

Radar Channel 1997 - 1 0 0

Radio Television Portugal 1992 - 1 0 0

RAI Italia 1987 - 1 1 1

RAP-TV 1999 - 1 1 1

Recovery 1994 - 1 0 0

RFD-TV 1989 1992 1 0 0

Romance Classics/We 1994 - 1 0 0

37
Channel Start year End year

Subscribers 

Missing

Vertical 

Integration 

Missing

Spinoff 

Status 

Missing

Russian Television 1991 - 1 0 0

Satellite Program 1979 1986 0 1 1

Sci-Fi 1991 - 1 0 0

SCOLA 1994 - 0 0 0

Shalom USA 1990 - 1 0 0

Shepherds Chapel 1987 - 1 0 0

Shop at Home 1986 - 1 1 1

Shop TV 1987 1990 1 1 1

Shopping Line 1987 - 1 1 1

Silent Network 1984 1995 0 0 0

Single Vision 1995 - 1 0 0

Sky Merchant 1999 2000 1 1 1

SoapNet 2000 - 1 1 1

Speedvision 1996 - 1 0 0

Sporting Channel 1994 - 1 0 0

Sportstime 1985 1985 0 1 1

Sportsvision 1985 1986 0 1 1

S-TV The Surfing Channel 1998 1999 1 1 1

Style 1999 - 0 0 0

Sur 1993 - 1 0 0

Talkline 1981 - 1 1 1

TCM 1994 - 1 0 0

Telemundo 1987 - 1 1 1

Telenoticias 1996 1997 1 1 1

Television Food Network 1994 - 0 0 0

Telshop 1986 1992 1 1 1

Tempo Galeria 1987 1988 1 1 1

Tempo Television 1979 1988 1 1 1

The Computer Network 1996 1999 1 1 1

The Nashville Network 1983 - 0 0 0

TNT 1989 - 0 0 0

Toon Disney 1998 - 0 0 0

Total Communication 1995 - 1 0 0

Travel Channel 1987 - 1 0 0

Trinity 1973 - 0 0 0

Trio 1998 - 0 1 1

Tropical Television Network 1996 2000 1 0 0

TV Bingo 1994 - 1 0 0

TV Land 1996 - 0 0 0

TV5 1998 - 0 1 1

TVG 1999 - 1 1 1

U-Network 1994 - 0 0 0

United Satellite 1985 1988 0 0 0

USA 1977 - 0 0 0

ValuVision 1991 - 1 1 1

Vector 1984 1991 0 1 1

VH-1 1985 - 1 0 0

38
Channel Start year End year

Subscribers 

Missing

Vertical 

Integration 

Missing

Spinoff 

Status 

Missing

VH1 Classic 1998 - 0 0 0

VH1 Music First 1998 - 0 0 0

VH-1 Soul 1998 - 0 0 0

Via 1994 2000 1 0 0

Video Catalog 1991 - 1 0 0

Video Concert Hall 1984 1993 1 1 1

Video Shopping Mall 1986 1993 1 1 1

VIVA 1993 1998 1 0 0

Weather Channel 1982 - 0 0 0

Weatherscan 1998 - 1 1 1

Weird TV 1994 1997 1 0 0

WGN 1978 - 0 0 0

Wingspan, Air and Space Channel 1998 - 1 1 1

Wisdom Network 1997 - 1 1 1

WOR 1979 1997 0 1 1

World Cinema 1999 - 1 1 1

World Fight Channel 1999 - 1 1 1

Worship 1992 - 1 1 1

WPIX 1984 - 0 1 1

WTBS 1976 - 0 0 0

Youth Sports Broadcasting Channel 1999 - 1 1 1

ZDTV 1998 - 1 1 1

ZTV 1993 2000 1 0 0

39
40

APPENDIX 2

THE AVERAGE NUMBER OF SUBSCRIBERS BY AGE AND THE 

IMPLIED RATE OF YEAR-TO-YEAR GROWTH

Subscribers

(in millions)

Age Implied 

Growth Rate

2.17 1 -

3.51 2 48.26%

4.99 3 35.18%

6.59 4 27.64%

8.54 5 26.01%

10.76 6 23.14%

13.24 7 20.69%

15.50 8 15.79%

18.31 9 16.62%

19.42 10 5.92%

22.14 11 13.09%

25.09 12 12.52%

28.36 13 12.24%

30.57 14 7.52%

32.88 15 7.27%

35.45 16 7.54%

37.43 17 5.44%

38.91 18 3.86%

42.69 19 9.28%