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in markets such as New York, Chicago, and San Francisco. These three markets alone account for almost a quarter of the potential subscribers in the top 50 markets.
His regression equation is similar to that utilized by ComanorMitchell with one important difference: each off-the-air signal is weighted by its distance from the B contour, expressed as a fraction of the radius of the B contour. Thus, distance is taken as an invariant measure of signal reception by households. This assumption is quite dubious on its face for two reasons. First, a station's signal strength is allowed to vary considerably by the FCC and the procedure for estimating the location of the B contour is known to be imprecise. Second, the quality of the local signal is in large part a reflection of the household's investment in antennas. In older areas with older television stations, these antennas are likely to be larger and more sophisticated. In future years, normal attrition of these antennas will make cable more attractive, but examination of any of these markets at present will underestimate future cable penetration.
In estimating his demand function, Park attempts to estimate an exponential maturity factor similar to that attempted by ComanorMitchell. He finds that the "best" estimate of this growth factor is
-3.3/t equal to e where t is system age in months. Comanor-Mitchell,
-450/t on the other hand, discovered that e
was the best fitting maturity factor. These two estimates--neither of which is utilized by Mitchell in his simulations are quite different and give rise to very different paths to eventual system maturity. Surprisingly, Park then proceeds to estimate his equation under the assumption that a system approaches maturity at a linear rate of t/18 for the first eighteen months, reaching maturity at a mere eighteen months. He argues that this gives him his best fit in the penetration equation, and all of his estimates are dependent upon imposing this maturity path upon the penetration expression.
Mitchell uses the parameter estimates of Park's ultimate penetration equation, but imposes his own maturity path, which he neither defends nor supports with statistical evidence. The differences between the Comanor-Mitchell, Park exponential, Park linear, and Mitchell maturity paths are given in Table C-1.
Note that Mitchell's assumption of maturation is more conservative than either of Park's, but Mitchell continues to use Park's mature penetration parameter estimates, imposing his own slower maturation path--a totally indefensible procedure. If Park's mature penetration results are to be accepted, they can only be accepted in conjunction with his linear maturation path.
There are numerous other problems in applying the Park equation to Mitchell's universe of CATV systems. First, the sample Park utilizes is supposed to represent the environment in the top 100
markets. Mitchell uses results for the purposes of projecting penetration in all markets and outside the defined markets. Second, Park finds that the impact of educational stations exceeds the impact of independent stations--a dubious result given all statistics on relative viewing of the two types of outlets. The elasticity of penetration with respect to the educational station variable is 0. 204--meaning that an increase in the number of educational stations from 0 to 1 will increase penetration by 20.4 percent (of its ex ante value). A similar increase in independent signals will increase penetration by only 14.5 percent. Finally, Park makes no allowance for local origination even though in a subsequent publication he has argued that ambitious local originations will lead to
18 a substantial increase in penetration in the Dayton-Miami Valley area.
Because the form of the penetration equation (and its maturation factor) is important in predicting cable system profitability, we shall examine each published demand equation's ability to predict actual penetration for a randomly drawn sample of cable systems from the Factbook.
Our sample of CATV systems was obtained by selecting a system at random from the 1972-1973 Factbook and choosing every twentieth system sequentially thereafter. In this manner, we collected data on 153 systems, but the data required for fitting the Park and Comanor-Mitchell demand equations were incomplete for 66 of these (usually because the number of homes passed by plant was unavailable). Of the remaining 87, six were found to have erroneous data on homes passed; therefore, we were left with a sample of 81 systems--of which 20 were located in the top 100 markets.
None of the three demand equations predicted demand any better than one could by a random process. All three were rather strongly biased downward, and all three had root mean square errors
18L. L. Johnson, et al., op. cit., Addendum 2A.
in excess of the standard deviation of the distribution of actual penetration rates. The performance of each demand equation is summarized in Table C-2.
Mitchell's adaptation of Park's equation performs the worst of all, providing the largest values for root mean square error. For the settings which Mitchell posits in his recent paper, Comanor-Mitchell provides much higher estimates of major penetration than the Park equation, but even these estimates are considerably below those derived by a group of Major System Operators (MSO's) themselves. These predictions appear with each demand function's estimates in Table C-3.
lThese estimates are taken from Andersson, op. cit.; 1987 projections for
Given the poor performance of all three demand equations, we do not feel that use of any of them is justified in predicting future penetration for the purpose of calculating rates of return on cable investment. The considerable downward bias in each would create a similar downward bias in profitability calculations. Therefore, we are forced to rely upon the cable system operators' own projections of demand even though these estimates are derived from cable systems which provide little significant origination and only a minor amount of special services such as motion pictures or sports events by leased channels. When ese services reach fruition, we can expect the attractiveness of cable to be enhanced considerably and penetration to rise accordingly.