*Pages 1--41 from  DOC-241968A1.doc*
 FEDERAL  COMMUNICATIONS  COMMISSION 
 MEDIA  BUREAU  STAFF  RESEARCH  PAPER 


 A  Survival  Analysis  of  Cable  Networks 
 By  Keith  S.  Brown 
 December  2004 


 2004-  1 
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 The  Media  Bureau  Staff  Research  Paper  Series  consists  of  reports  and  papers  prepared  by  the  professional  staff  of  the  Media  Bureau, 
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 . 
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 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 
 Commissions  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. 
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 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 
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 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  peoples  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  10  th  Annual  Report  on  Video  Competition,  19  FCC  Rcd  at  1690-  91. 
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 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-  rents  6  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  networks  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  networks  later  exit  decision.  For  example,  suppose  that  a  cable  network  incurs  sunk  entry  costs  of  $10,  expecting  $11  in  present-  valued  future  quasi-rents. 
 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. 
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 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  machines  longevity  or  how  a  new  drug  affects  a  patients  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. 
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 II.  Data 
 We  collected  data  on  cable  networks  from  a  variety  of  sources.  9  The  Television  and  Cable  Factbooks  10  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  years  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  networks  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  operators  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. 
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 programming  network  in  its  carriage  decisions  13  (possibly  because  the  operator  receives  some  of  the  programming  networks  advertising  revenue).  We  therefore 
 include  the  vertical  ownership  measure  obtained  from  past  FCC  Video  Competition  Reports  (which  rely  heavily  on  the  National  Cable  Television 
 Associations  Cable  Developments)  and  Kagans  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  Kagans 
 Economics  of  Basic  Television  Networks.  Finally,  a  cable  networks  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  imp  ortant 
 information  concerning  a  networks  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  networks  subscriber  count,  vertical  integration,  and  spinoff  status)  the  cable  networks  survival  probability  rises.  More  specifically,  if  we  observe  a  cable 
 networks  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%. 
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 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. 
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 into  account.  Finally,  there  remains  the  issue  of  grouped  duration  data.  Ideally,  we  could  observe  the  exact  date  and  time  of  each  programming  networks  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  networks  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  networks  chance  of  survival  for  any  given  amount  of  time  and  to  estimate  a  programming  networks  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. 
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 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,  Coxs  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  time-varying  covariates  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. 
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 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  (|;)  e  x  p()  e  x  p[  e  x  p()]  ii  i  f  txxtx  t  a  qbab  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, 
 (;)  e  x  p[  e  x  p()]  i  i  S  txx  t  a  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 
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 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 
 (;)  e  x  p()  txx  t  a  lb  a  -1  =  .  (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 


 0 
 {log[(|;)](  1)  log[  1(|;)]  log[(|;)]  log  1  [(|;)](|;) 
 b  N 


 iii  iiiiii  i  dftxdFtxkaxFbx  k  x  d  qqhm  q  mh  m  i=1  +--+--  -      ,  (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  xh    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. 
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 We  illustrate  these  assumptions  by  adding  heterogeneity  to  the  Weibull  distribution.  The  Weibull  marginal  hazard  is 
 (;  ,  )exp()  iii  i  txvvx  lb  at  a-1  =  (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 
 (|;  ,  )(|,;)(;)  i  i  GtxF  t  xvhvdv  qgq  g 
  
 =    ,  (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 


 0 
 {log[(|)](  1)  log[  1(|)]  log[(|;  )]  log  1  [(|)]  (|; 
 b  N 


 iiiiiiiii  i  dgtx  dGtxkaxGbxk  x  hmmh  )dm  i=1  +-  -+--  -      (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  ()  exp()/()  v  hv  v  g  g  g  d 
 g  g 


 1- 
 =-  G  ,  where  ()  G    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., 
 exp()  i  x  a  lb  at  -1  =  ,  (7) 
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 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  networks  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  +  -  -  . 
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 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) 


 sports  a  0.79  (1.63)  3.36  (1.27) 
 shop  a  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 
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 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  networks  probability  of  exit  declines  by  75%  if  that  network  is  a  spinoff  network.  If  cable  networks  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  networks  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  networks  probability  of  exit  declines  by  93%  if  that  network  is  a 
 spinoff  network.  If  cable  networks  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  networks  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. 
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 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  ll  --  -l  ,  (8) 
 which  is  equivalent  to 


 ln(1  )  t  x  x 
 e 
 l  =1  -   


 .  (9) 


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


 (;)  e  x  p[  e  x  p()]  i  i  S  txx  t  a  b  =  -  ,  we  calculate  subscriber  profiles  over  a  cable 
 networks  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  networks 


 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. 
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 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  networks  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  networks  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
 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
 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
 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  effects  distribution  is  the  unobserved  heterogeneity.  By  including  the  log  of  the  cable  networks  age 
 in  the  vector  of  independent  variables,  we  create  a  Weibull  baseline  hazard.  When  we  dont  assume  unobserved  heterogeneity,  we  estimate  a  complementary 
 log-  log  population-  averaged  panel  effects  model  (again  including  the  log  of  the  networks  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  ESPNs  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
 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  networks  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)  .55  e  e  -  -  =  =  ,  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 
 .30  e  -  =  . 


 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)  18%  e  e  -  -  =  =  ,  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  .22  e  -  =  .  If  a  network  began  before  1984,  then  that  network  has  64%  greater  chance  of  surviving  in  any 
 given  year. 
24
 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
 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  piecewise-constant  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
 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
 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  networks  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  networks  estimated 
 marginal  probability  of  exit,  and  the  effects  of  (2)  may  increase  or  decrease  a  networks  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  networks  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
 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  networks  failure  to  inform  the  Cable 
 Factbook  of  their  subscriber  base  correlated  negatively  with  a  networks  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  networks  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  .22  e  -  =  .  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  networks  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 
 networks  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  networks  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
 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  networks  first  10  years  by  agreeing  to  carry  a  cable  network  to  half  of  its  subscriber  base  from  the  networks  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 
 networks  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  quasi-rents. 
 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  networks  first  ten  years. 
30
 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  networks  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
 31 
 References 
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 Cox,  D.  R.  1972.  Regression  models  and  life  tables.  Journal  of  the  Royal  Statistical  Society.  Series  B  34:  187-  220. 
 DeVany,  A.,  and  W.  D.  Walls.  1996.  Bose-  Einstein  dynamics  and  adaptive  contracting  in  the  motion  picture  industry.  Economic  Journal  106:  1493-  1514. 
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 Dixit,  Avinash.  1989.  Entry  and  exit  decisions  under  uncertainty.  Journal  of  Political  Economy  97:  620-  638. 
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 Ham,  J.  C.,  and  R.  J.  Lalonde.  1996.  The  effect  of  sample  selection  and  initial  conditions  in  duration  models:  evidence  form  experimental  data  on  training.  Econometrica 
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 Kalbfleisch,  J.  D.,  and  R.  L.  Prentice.  1980.  The  statistical  analysis  or  failure  time  data.  New  York:  Wiley. 
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 Kranenburg,  H.  L.  Van,  F.  C.  Palm  and  G.  A.  Pfann.  2002.  Exit  and  survival  in  a  concentrating  industry:  the  case  of  daily  newspapers  in  the  netherlands.  Review  of 
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 _____.  1990.  The  econometric  analysis  of  transition  data.  Cambridge:  Cambridge  University  Press. 
 Meyer,  B.  D.  1990.  Unemployment  insurance  and  unemployment  spells.  Econometrica  58:  757-  782. 
 NCTA.  Cable  Developments.  Various  years. 
32
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 Prentice,  R.,  and  L.  Gloeckler.  1978.  Regression  analysis  of  grouped  survival  data  with  application  to  breast  cancer  data.  Biometrics  34:  57-  67. 
 Simonoff,  J.,  and  L.  Ma.  2003.  An  empirical  study  of  factors  relating  to  the  success  of  broadway  shows.  Journal  of  Business  76:  135-  150. 
 Spence  and  Owen.  1977.  Television  programming,  monopolistic  competition,  and  welfare.  The  Quarterly  Journal  of  Economics  91:  103-  126. 
 Warren,  Albert.  Various  years.  The  television  and  cable  factbooks.  Washington,  D.  C.:  Warren  Communications. 
 Wooldridge,  Jeffrey  M.  2002.  Econometric  analysis  of  cross  section  and  panel  data.  Cambridge:  MIT  Press. 
33
 Channel  Start  year  End  year 
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 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 
34
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 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 
35
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 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 
36
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 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 
37
 Channel  Start  year  End  year 
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 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 
38
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 Vertical 
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 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 
39
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 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
 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% 
41