Option value, telecommunications demand, and policy

Information

Economics and Policy 5 (1993) 125-144. North-Holland

125

Option value, telecommunications demand, and policy Donald J. Kridel Un~~~~r.~~t~ of Missouri, St. Louis, MO, USA

Dale E. Lehman Fort Lewis College, Duranga, CO, USA

Demand estimation and welfare analysis for telecommunications services have often been plagued by apparent inconsistencies between actual consumer behavior and standard economic theory. The latter posits that consumers will subscribe to services when their consumer’s surplus exceeds the subscription price. This paper presents an alternative model of subscription behavior under uncertainty. Drawing on the option value Iiterature, we show that expected consumer’s surplus is generally not an adequate basis for subscription decisions. We present an empirical example in which option value significantly improves demand estimation. We discuss policy implications, including possible ‘market failures’ in which socially beneficial new technology is not deployed. Keywurd.~: Option value: Telecommunications

demand; Policy

JEL CI~~si~cQf~o~: L9 Public titilities

1. introduction New t~~~eommuni~ations services increasingly comprise options to use network facifities. These services can be based on new network teeh~oIogies and/or existing network technofogy accessed under new pricing structures. An example of the former is ISDN access while the latter may be repreCorrespondence ro; Dale E. Lehman, Department of Econnmics, Fort Lewis College, Durango, CO 81302, USA. Tel: 3133-247-7204or 303-259-6238; Fax 303-259-1774; E-mail: Lehman_D~FL~.Colorado.~.du. The authors wish to thank P. Srinagesh and K. Train for helpful comments while absolving them of responsibility for any errors.

0167-6245/93/$~.00

Q 1493--Elsevier

Science Publishers E3.V (forth-Holland)

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sented by pricing plans that permit an expanded flat rate local calling area for a fixed monthly premium. Understanding consumer reaction to such services has proven difficult and demand estimation has been troublesome for regulatory oversight or for telephone company planning. The standard theoretical approach to consumer decision making for such services has proven inaccurate. This paper provides insight into one source of inaccuracy - that deriving from the uncertain demand for such services which can generate option values that are not related to the actual use of these services. Option values require modification of the existing framework for analyzing customer subscription decisions. Option values also have pricing implications which differ from traditional regulatory wisdom. This paper demonstrates that option value is not only theoretically valid, but is an important empirical consideration for demand estimation. Failure to recognize and appropriately consider option values can result in reduced consumer welfare, foregone company profits, and/or ‘market failure’ where socially beneficial services are not offered. This paper proceeds by examining, in Sections 2 and 3, two practical examples in which existing telecommunications demand modelling may be deficient: demand for new technology in the public network; and optional calling plan subscription. The inadequacy of the existing theory is demonstrated, and the potential role of option value is explored. Section 2 is based on the theory of option value, as developed in the environmental economics literature, here applied to the demand for new telecommunications services. Section 3 contains an empirical analysis for a specific optional calling plan - extended area service (EAS). Section 4 presents our conclusions regarding the role of option value in modelling telecommunications demand and welfare analysis.

2. New technology

deployment

Regulators repeatedly must determine who should pay for the deployment of new technology in the public network. Little theoretical guidance is available beyond the apparent common sense conclusion that those who benefit from the technology should pay for it. For example, a recent Aspen Institute conference addressed the costs and benefits of modernizing the public network as well as who should bear the burden of these costs.’ The common sense solution often expressed is ‘that government should offer access to services without making them mandatory. People who do not want single party service should not have to pay for it, and those who do ’ Entman

(1989)

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innocuous solution is correct in a should bear the cost.” This seemingly world of certainty, and it is supported by the traditional analysis of consumer subscription decisions. 2.1.

The two stage decision model

The standard model of the subscription decision is the two stage model. Consumers first must decide whether or not to subscribe, and, second, how much to use a service upon subscription.3 If the consumers’ surplus associated with the optimal level of usage in the second stage exceeds (falls short is to (not to) of) the subscription price, then the first stage decision subscribe. More formally, consider a representative consumer with utility function u(z, x) where x is consumption of the telecommunications service and z represents all other goods. The decision stages are solved in reverse order: the consumer, given access to the service, will maximize

u(z, X) subject

to px + z = Y ,

where Y is income and p is the usage price of service (the price of the composite good has been second stage decision problem for a consumer who network. The first order conditions (assuming the are satisfied) yield the demand curve x( p, Y). problem can then be stated as

subscribe

if

I

the telecommunications normalized). This is the already has access to the second order conditions The first stage decision

X(I, Y) dr 3 K

P

do not subscribe

if

I

X(T, Y) dr < K ,

where K is the subscription price. This two stage decision process forms the backbone for most applied telecommunications demand analysis. New network technology can be thought of in the same manner. Users with sufficient consumers’ surplus from usage will ‘subscribe’ for its use. The efficient pricing of new technology (i.e., into usage sensitive and non-usage

’ Entman (1989, p. 9), quoted from Stanford Levin, former Illinois Commerce missioner. ’ The two stage decision process, pioneered by Squire (1973) and Littlechild (1975), formulated in Taylor (1980) or Train (1991).

Comis well

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sensitive components) presumably depends on the cost structure for provision of new services.4 Notwithstanding this apportionment into subscription and usage fees, the efficient burden for these costs falls on those who benefit ex post, i.e., use, the new technology. Uncertainty about future demand may appear to offer only a practical complication - but appearances are deceptive. The obvious modification would be to replace the usage demand with expected usage and then compare the subscription price with expected consumers’ surplus. Risk aversion would lead to a certainty equivalent demand somewhat smaller than this expected demand. In any case, the expected consumers’ surplus would be compared with the subscription price to determine the optimal subscription decision. However, the two stage decision approach will be shown, in many cases, to be inappropriate once such uncertain demand is introduced, and such uncertainty is endemic to new telecommunications technology. The same Aspen Institute study cites ‘the enormous difficulty of knowing in advance what services large or small customers will want. The same uncertainty remains a major stumbling block to the Regional Bell Operating Companies and other private firms seeking to expand intelligent capabilities in the public network.‘5 Pricing of new technology based on the two stage decision analysis will fulfill the common sense principles described above, but run the risk of inefficiently preventing the deployment of new technology.6 The possibility of such ‘market failure’ is not obvious and requires more explicit consideration of the nature of the uncertainty of future demand and its relevance for consumer subscription decisions. Fortunately, an extensive literature has been developed which accomplishes this. The option value literature was prompted by the question ‘is expected consumers’ surplus an appropriate measure of the consumer benefits derived from preservation of unique natural resources?’ Our motivation appears to be different, but the analysis is identical.

’ We are ignoring potential network externalities which may call for below cost subscription pricing and demand heterogeneity which could call for nonlinear pricing beyond two part tariffs. Neither of these factors are germane to our discussion ’ Entman (1989, p. 9). ‘More precisely, if pricing of new services is based on a two part tariff with a cost based usage component and the fixed component set to generate zero profits, then there is no assurance that socially beneficial new technology will be deployed. If expected consumers’ surplus were equal to the social value of new technology, then this two part tariff structure would be efficient since technology would be deployed if and only if the social value exceeded the fixed costs of deployment. This is the standard result for the pricing of Dupuit’s (1844) bridge. The non-equivalence of expected consumers’ surplus and social value is responsible for the inefficiency cited herein.

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Option value

Weisbrod (1964) initiated the concept of option value as an explanation for how markets may fail to provide some socially desirable services, such as wilderness parks: “It is certainly true that a profit-maximizing

entrepreneur

would cease operating

if all costs could not be covered - that is, if the present value of future costs exceeded the present value of future revenue. But it may be unsound socially for him to do so. To see why, the reader need recognize the existence of people who anticipate purchasing the commodity (visiting the park) at some time in the future, but who, in fact, never will purchase (visit) it. Nevertheless, if these consumers behave as ‘economic men’ they will be willing to pay something for the option to consume the commodity in the future. This ‘option value’ should influence the decision of whether or not to close the park and turn it to an alternative use. But it probably will not exert any influence if the private market is allocating resources, because there may be no practical mechanism by which the entrepreneur can charge nonusers for this option.“’

The market ‘fails’ due to usage uncertainty combined with the failure to collect the value of reducing uncertainty about the availability of supply. This is parallel to Kahn’s (1966) example of the discontinuance of railroad service between New York City and Ithaca, due to the inability of usage sensitive pricing to recover the predominantly non-usage sensitive costs of providing the service. Since the railroad was only used during inclement weather, usage sensitive prices failed to generate sufficient revenue to maintain the line. Kahn speculated that prospective train travelers, like himself, would have been willing to pay for the option to use the train, independent of their actual use of the train. If such willingness to pay had been sufficient to cover the costs of maintaining the line, then the closure of the line constituted a ‘market failure.‘x Kahn further raised this possibility in the context of reliance of MCI on the Bell System for overflow or backup capabilities. The value of this option to use was not likely to be collected through the usage sensitive charges which are based on actual, not potential, usage.” The theoretical literature on option value provides a more general formulation of the problem-it proceeds by examining the value of an option to use a resource (or service) in an uncertain world, where the ’ Weisbrod (1964. p. 472). ’ In a similar vein, the change in government defense procurement practices may necessitate that the defense industrial base be subsidized so that there is an ensured source of supply in the future. Without such subsidies, there is concern that the government will not have the option to purchase materials in the future, should the need arise. See also Kovacic (1991). ‘An application of this idea to bypass is provided in Weisman (1989).

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hide1

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uncertainty can involve preferences, income, prices, and/or supply. Specifically, let uI(Yj, 8) be the indirect utility function in state of the world i (i=l,..., n), where Y is income and 6 (=0 or 1) is an index reflecting whether or not the resource (or service) in question is available. Define option price, OP, to be the (state independent) maximum willingness to pay for access to this resource, and let CS, be the (state dependent) compensating variation measure of consumers’ surplus in state i. Let rr, represent the probability that state i will occur. Then, CS, is defined by

U;(Y, - CS,, 1) and OP is defined

,t

= ui(Y,,

0)

i = 1, . . . , n

by

m;u;(Y; - op,

1) = ,$

7r;U;(Y;, 0) .

Option value, OV, is defined as the difference expected consumers’ surplus (ECS), i.e.,

ov=

OP - i

between

option

price

and

7-r;cs;.

i=l

It is well documented elsewhere that OV S 0 depending on attitudes towards risk, the sources of uncertainty, and the opportunities available to protect against risk.“’ Some intuitive motivation for the nonequivalence of OP and ECS is useful. OP is a state independent measure of welfare change, while ECS is the weighted sum of state contingent measures. The sign of OV will depend on how dollars are valued in different states of nature, which, in turn, depends on both the sources of uncertainty facing the individual and the individual’s attitude towards risk. Risk averse individuals will prefer to make payments in states of nature with lower rather than higher marginal utilities of income. OP represents a certain payment, independent of the state of nature, while CS, is a benefit measure derived in a particular state of nature. Risk averse individuals will generally be willing to pay a state independent premium beyond their expected consumers’ surplus in order to resolve or reduce the source of uncertainty. Indeed, this is the principle behind the demand for insurance.” ” See Bishop (1982), Freeman (1984, 1986), Schmalensee (1972), and Smith (1981). ” As Weisbrod (1964, p. 473) notes, ‘The analogy with insurance may be drawn. Loss (purchase) is infrequent, and a person may, as in the case of property insurance, never have a loss though he pays annual premiums for the protection for many years. The insurance was providing a service, protection against a large financial loss, though the protection was only of a stand-by nature and was, in fact, never “used”.’

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The possible sources of uncertainty are myriad, including, but not limited to: tastes, income, prices, supply; and the opportunities to insure against such risks are similarly varied, including risk sharing or risk trading arrangements such as contingent or insurance markets. Consequently, the sign of option value is not unambiguously positive, even for risk averse individuals. For instance, if I am uncertain as to my future demand because my future income is uncertain, then I may prefer state contingent payments to the state independent option price as the vehicle for expressing my valuation of a future option. Such contingent payments would provide the opportunity to minimize payments in states of nature where my income turns out to be relatively low. The existing literature is readily adapted to our problem at hand, given the reinterpretation of S as indicating whether or not a new telecommunications service is made available in the public network. The common sense principle that only ex post users of a service should bear its cost can lead to ‘market failures’ in circumstances where OV > 0.” Here, even a perfectly discriminating monopolist using two-part tariffs if individuals are identical, and fully non-linear tariffs if they are not (where the fixed component captures ex ante ECS and the variable component covers only usage sensitive costs) may fail to collect the full value of the service (OP). If the total sum collected is less than the fixed costs of provision, such services will not be offered and a ‘market failure’ can be said to occur. Since OV is generally indeterminate in sign, it is important to distinguish those conditions under which it can be expected to be positive. These can lead to inefficient deployment of new capabilities in the event that only ex post users are required to pay for such costs. The following is a less than exhaustive list of properties for option value {see Freeman, 1986): Case I: OV < 0: Risk averse individuals facing demand uncertainty derived from income uncertainty. Case II: OV > 0: Risk preferring individuals facing demand uncertainty derived from income uncertainty. Case ZZZ: OV > 0: Risk preferring (or risk neutral) individuals facing demand uncertainty derived from uncertainty about the price of a complementary good. Case IV: OV > 0: Demand certainty, risk aversion, and supply uncertainty of the form that the option guarantees the supply while lack of exercising the option leaves some non-zero probability of supply. Case V: OV > 0: Risk aversion, supply certainty, demand uncertainty arising ‘* Indeed, the Tennessee Public Service Commission recently decided to use $100 million of overearnings by South Central Bell to finance infrastructure development rather than refunding it to ratepayers. This controversial decision was apparently predicated on the belief that a ‘market failure’ might result if infrastructure development were left to normal market forces.

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from exogenous factors which do not affect the marginal utility of income across states of nature (strong separability of the indirect utility function). Case VI:OV= 0: Demand certainty and supply certainty of the form that supply is guaranteed if the option is purchased but supply probability = 0 without the option. Other cases are indeterminate in sign. As Freeman (1986, p. 162) concludes: “The question of the relationship between option price and expected surplus when both demand and supply uncertainty are present is difficult. It clearly depends on the pattern of supply uncertainty. the degree of demand uncertainty. . . and the determinants of demand uncertainty as well as the properties of the indirect utility function. It appears that in the general case the relationship between option price and the increase in expected surplus can only be determined through a quantitative analysis based on knowledge of the relevant probabilities and the specific properties of the utility function.”

For example, consider the case of Mr. Technophobe who is uncertain about his demand for ISDN. Suppose his uncertainty is such that he is unsure whether a particular ISDN based service will become available; if it does (with probability OS), his consumer’s surplus will be $175; if it is not available (with probability 0.5), his consumer’s surplus will be zero. He would be willing to sign a contingent contract for $175 or $0, contingent on whether or not the service becomes available. In the absence of such a contract, he would be willing to pay more than $87.50 now (his expected value of consumer’s surplus) to preserve his option to subscribe to ISDN, since the only uncertainty is about the supply of the service in question - his option value is positive (Case IV). Alternatively, suppose the service availability is certain, but Mr. Technophobe’s income is not. High income would cause him to subscribe, low income would not. In this case, he would be willing to pay less than $87.50 now for the service, since these dollars would be more valuable in the low income state of nature than in the high income state - option value is negative (Case I). It is beyond the scope of the present paper to investigate the sign of option value for new network technology deployment, and this sign is likely to be positive for some consumers and negative for others. More research is needed into the sign and magnitude of option value for particular technologies and their associated demand andlor supply uncertainties. We hope this paper stimulates such research. Our more modest goal is to dispel the common sense wisdom that burdening only ex post users with the costs of new technology is an efficient approach to deployment decisions. The benefits derived from ex post usage may or may not understate the social value of new technology. However, with uncertain demand, there is no

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assurance that expected consumers’ surplus should be a good measure of these social benefits. In the end, the importance of option value is an empirical matter, at least until further theoretical results are available. The next section provides evidence of the potential significance of option value for one particular optional calling plan.

3. Optional calling plans Another class of new telecommunications services offers new pricing structures to individual consumers, usually on a voluntary subscription basis. Generally, these involve some reduction in the marginal usage price in exchange for a non-usage sensitive fee. Examples include local measured service (LMS) versus flat-rate pricing, optional calling plans (OCPs), and extended area service (EAS). Demand analysts have consistently had difficulty explaining subscription choices for such plans. Indeed, the almost universal penetration of plain old telephone service (POTS) is hard to explain on the basis of usage benefits alone. As of July 1989, 93.3% of all U.S. households were subscribers to the public telephone network. However, a nontrivial proportion of these generate modest or no usage. As many as one-third of LMS customers in Missouri and Arkansas do not generate enough monthly usage to ‘justify’ telephone access based on their consumers’ surplus from usage.‘” While flat rate customers generate significantly more monthly usage, approximately lo-15% of these should not purchase access on the basis of their consumers’ surplus from usage. In fact, 3% of the flat rate customers and 15% of LMS customers generate no originating usage at all. This may suggest that incoming calls are highly valued. More troublesome is the fact that the elderly have among the highest penetration rates but the lowest usage levels of all the groups tracked by the FCC. The elderly are only about half as likely as the general population to have LMS, despite having low originating usage.‘” Many explanations have been offered, and it has long been recognized that non-usage sensitive benefits may be present, but empirical studies have either ignored these non-usage benefits, or included such benefits without any theoretical foundation. Customers also exhibit an unexplained preference for flat rate pricing over a variety of optional calling plans despite apparent bill savings and consumers’ surplus benefits which would derive from subscription to such plans. Only 7% of customers self select into LMS, and approximately 10% ” All local usage data is from Missouri and Arkansas for the period January-April 1985, the last period for which reliable SWBT Subscriber Line Usage Study (SLUS) data are available. ” These data are based on Missouri and Arkansas usage and tariffs as of 1985.

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of these are on the “wrong” plan. That is, they could have a lower bill on flat rate service. On the other hand, of the 93% who self select flat rate service, nearly 65% couId save money by purchasing LMS. Of course, bill savings is not the proper subscription criterion, according to the two stage decision rule. If consumers’ surplus gain is used as a decision rule, then 50-55% of current flat rate local customers would benefit by switching to LMS. 3.1, Flat rate preference Explanations for these phenomena traditionally involve consumer lack of information, irrationality, poor telephone company marketing, aversion to being metered and/or an unexplained aversion to bili uncertainty. For example, Train et al. (1989) suggest that a substantial fraction of consumers do not correctly anticipate their own demands, yielding ex post choices which do not minimize their expenditures for the quantities purchased. Train (1991) further states that ‘There are reasons to believe, however, that consumers do not behave in accordance with these assumptions. _ . the empirical analysis indicates that consumers strongly prefer the flat-rate service, even though the two cost the same. This phenomenon is called the ‘flat-rate bias,’ and has been found in many studies of local phone service. The existence of this bias is problematical. Standard theory of consumer behavior does not incorporate it.“’ Kling and Van der Pioeg (1990) ambitiously estimate the entire local usage distribution and calculate expected consumer surplus for flat-rate and measured service. Their choice of service equation includes a term ‘Bias: constant introduced to capture household preference for flat rate service relative to measured service not related to usage or pricing.’ Mitchell and Vogelsang (1991, pp. 179, 191-192) offer ‘that consumers simply over- or under-estimate their own demand for the good, for example, due to producer advertising.’ They report that ‘AT&T’s forecast using this model underestimated the relative attractiveness of Plan B, which added a 15% discount on evening-period calls.’ For another OCP, they state that ‘it is likely that many of the 45 percent of OCP subscribers who use fewer than 40 minutes a month during night/weekend period have in this sense chosen the “wrong” tariff.’ Some of these analyses are based on a bill savings IsTrain (1991, pp. 7-25, 26, 27). Train incorporates this ‘flat-rate bias’ into his empirical work: ‘If the bias that is observed in consumers’ choices is considered to constitute a real component of consumers surplus, then a move from flat-rate to measured service would be inadvisable, because the evidence indicates that it will decrease consumer surplus, perhaps considerably.’ As we have shown, consumers’ surplus, by itself, may be the wrong welfare measure -use of OP (which includes OV) lends theoretical support to Train’s empirical incorporation of the ‘flat-rate bias.’

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model, but even usage stimulation fails to account for much of the actual subscription behavior. Mitchell and Vogelsang also ask ‘Do consumers use optional prices as insurance against certain states of the world?’ but answer in the negative. It is this question we wish to reexamine in the context of option values. While we do not reject any of the above explanations for failures of the two stage subscription model, we offer an alternative mode1 in which subscription decisions may be perfectly rational but not in accordance with expected consumers’ surplus gains. 3.2.

Extended

area service

Extended area service (EAS) is a route specific calling plan, introduced by Southwestern Bell Telephone in Rockwall, Texas (a Dallas suburb) in December 1988. EAS offers unlimited calling (at a 0 marginal usage price) into (or from) the Dallas local calling area for a fixed fee of $19.85/month. Non-EAS subscribers face a marginal usage price of approximately $0.111 originating minute.” As of late 1989, approximately two-thirds of the 6600 Rockwall residential subscribers were actually purchasing EAS. As we will see, based on a sample of 2786 Rockwall customers for which we have usage and demographic data, neither the bill savings mode1 nor the consumer surplus mode1 do a good job of predicting these subscription levels.” Explicit consideration of option value, however, substantially improves the estimation. Consider a representative customer contemplating subscription to EAS, with indirect utility function u,(Y, p) where Y is income, p is the non-EAS usage price, and i is the uncertain state of the world (i = 1, . . . , n). EAS subscription involves a fixed cost, K, and a marginal usage price of 0 (within the extended calling area). Consumers’ surplus for EAS in state i is defined bY u,(Y;-K-CS;,O)=u,(Y,,p) OP is given

,%

i=l,...,

n.

by

r;u;(Y, - K - OP, 0) =

,$ntui(Y;, P)

“This is a weighted average; the usual time-of-day discounts apply. “For each respondent we had 8 months of usage data prior to introduction (MayDecember 1988). For each EAS respondent we also had 14 months of usage data (May 1989-June 1990). Our survey data included income, household size, reasons for liking EAS, ratings of features, perceived usage, etc.

136

and,

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as before,

ov=

OP - i

Triccs, .

i=l

We can normalize prices so that p = 1, and since the index 6 = 0,l has no cardinal importance, the theoretical framework for EAS value is identical to the option value framework posited above. This means that when OV > 0,a customer may self-select EAS even when ECS < K. As before, the sign of OV will depend on the particular sources of uncertainty and individual attitudes towards risk. For risk averse individuals, income uncertainty will cause OV < 0, and there are sufficient conditions under which uncertain preferences will cause OV > 0.Freeman (1986) assumes strong separability of the indirect utility function in order to prevent exogenous factors from affecting the marginal utility of income across states of nature. In that case, demand uncertainty arising from such exogenous demand factors will give rise to positive OV. This may be the most reasonable case for EAS, since most of the variation in local calling may be due to such exogenous factors (e.g., weather) and not affect the marginal utility of income.” We now turn to the empirical evidence. There are two difficulties involved with calculation of ECS. First, not all states of the world are observable. We can only rely on the 8 months for which we have data. Consequently, we consider these 8 months as the relevant states of the world for the consumer. Second, we only observe monthly usage rather than the underlying uncertainties from which usage is derived. The simplest assumption is that the sources of uncertainty are exogenous and do not affect the marginal utility of income across states of nature. Then, we can replace ECS with CS, defined as the consumers’ surplus change based on the average demand (2) over the 8 month period.‘” If the source(s) of uncertainty does influence the marginal utilities of income across states of nature, then matters are more complicated. We would not know how to compare consumers’ surplus changes in different I’ A curious exception might be individuals whose local calling is tied to their income, as with home offices. In such cases, the strong separability assumption commonly made in the option value literature would be violated. If high local calling is associated with high income states (as would be the case when local calling is tied to the individual’s source of income, e.g., a therapist), then OV < 0, since the individual would prefer state dependent payments over the state independent OP. “The use of the ordinary demand curve to estimate ACs is inaccurate as we want the compensating variation (CV) measure of consumers’ surplus. Using Willig’s (1976) approximations, it is easily shown that the error of using C.S in place of CV is less than 2%. Furthermore, the error here is to overstate the consumers’ surplus change associated with EAS. We ignore this approximation, realizing that our estimates of option value will be slightly understated.

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states of nature without knowing how to weight these dollar measures in different states. This remains a problem for future empirical and theoretical work. As our results indicate potentially large sizes for option values, we believe such work is important. Ultimately, it is the relationships between sources of uncertainty, attitudes towards risk, and marginal utilities across states of nature which will determine the option value characteristics of a new service or pricing plan. For the purposes of this paper, we use the simplifying assumption that the sources of uncertainty do not influence the marginal utility of income in different states. 3.3.

Market

observations

Of the 2200 Rockwall EAS subscribers in our sample, 24% had average toll bills (within the Dallas local calling area) greater than $19.85 over the last eight months of 1988. Clearly, bill savings can not be used to explain the actual subscription levels. Since we observe plan usage for subscribers, however, we can estimate consumer surplus using a linear approximation.*” Only 60% of EAS subscribers had average usage benefits exceeding $19.85/ month. Since we are not able to observe the entire ex ante usage distribution, we also calculated the maximum consumer surplus based on the available data. This is derived by using the largest pre- and post-introduction usage levels and then calculating the consumer surplus gain (using the linear approximation). This is equivalent to ignoring all months with usage levels which yield smaller consumer surplus gains. Even in this extreme case, over 17% of the subscribers had consumer surplus lower than $19.85. Of the 40% of EAS customers with usage benefits less than $19.851 month, their average consumers’ surplus gain is approximately $12.401 month, leaving $7.50/month in unexplained benefits from EAS. Some of these benefits derive from the fact that EAS is a two way service - incoming as well as outgoing calls are covered by the $19.85/month charge. If we assume that incoming calls are equally valuable on the average as outgoing calls (a conservative assumption, since the customer does not control incoming calls to the extent that they can control originating usage), then approximately $4.60 of this $7.50 can be attributed to increased incoming benefits. However, even after these adjustments, more than 27% of the EAS customers still had total expected usage benefits less than the subscription price. For these, average usage benefits were $13.25/month or $6.00

X’ We use the same eight months contamination due to seasonality. analyzed as well; very little change for the analysis.

after introduction for this analysis to mitigate any possible An additional six months of post-introduction data was was noted, suggesting that eight months may be sufficient

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less than the subscription price, leaving 25-30% of the total EAS benefits unexplained. On the other hand, only 3% of those who did not purchase EAS had an average bill exceeding $19.85/month. Based on stimulation rates from EAS subscribers, it is estimated that only 9% of non-subscribers would have usage benefits exceeding $19.85. Thus, expected consumers’ surplus cannot explain at least 30% of the customers’ decisions (40% of the 2/3 subscribing to EAS + 9% of the l/3 non-EAS subscribers). Several explanations are possible. Users could be choosing incorrectly or choosing on the basis of imperfect information. We cannot rule this out categorically, but the steady increase in EAS subscription over time and the low drop rate suggest that error is not a viable explanation. Users could be attempting to reduce transactions costs by obviating the need to keep track of a segment of their calls (although they must incur the costs associated with deciding to change from their current service). Alternatively, the eight months of data may not be sufficient to accurately reflect expected usage benefits. It is unclear why a longer time period would systematically work to increase predicted subscription rates. Still, the model may be misspecified in a way which systematically underpredicts subscription. However, viewing EAS subscription as rational decision making under uncertainty, and explicitly modelling this uncertainty through option value, significantly improves the estimation. 3.4.

A discrete choice model

Utilizing observed purchasing and usage data from a sample of households, a discrete/continuous demand model can be posited and estimated. The discrete portion of the probabilistic choice model is employed to predict the likelihood that an individual household will subscribe to EAS. The market penetration prediction is then derived by sample enumeration, e.g., a weighted sum of the individual probabilities where the weights are based on the underlying sample and population proportions of each household type. EAS usage may be predicted using the continuous portion of the model. To develop the model we proceed as follows. Suppose the demand function for usage is semi-log, e.g., x = Ae-aPyP, where x is usage, p is price, and Y is income. The subscriber can calculate usage benefits from the purchase of EAS by integrating the demand function over the price range to, PI: ACS = (AY’la where

- Ae-“PYP/a)

xN is the customer’s

expected

= (x,-x,)/a usage

under

, EAS

and x,, is the usage

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under toll.‘l We wish to consider ACS,, where i is the uncertain state of the world, and then calculate ECS = C 7rjCSj. If ECS > K, the two stage decision procedure would predict EAS subscription, otherwise not. Total benefits, which are unobservable, can be written as TB=OV+ACS+&, where OV is option value, error term. The probability Prob(EAS)

= Prob(e

ACS is defined above, and E is a well-behaved that a customer will purchase EAS is given by > K - OV-

Since E is assumed to have zero mean may be rewritten as Prob(EAS)

= Prob(E*

ACS) . and unknown

> y(K - OV-

scale,

this probability

ACS) ,

where E* = EIU and y is a choice parameter = l/v.22 Deriving estimates for the parameters (Y, y, and OV would yield estimates of EAS penetration and usage stimulation (since xN = exp( - “p)x”). Since we observe actual usage for EAS subscribers, however, we can utilize this information to further refine our parameter estimates, e.g., by comparing expected usage and actual usage under EAS. The modified Tobit model is estimated using maximum likelihood methods, as shown below.23 The estimated equations are for the parameters (Y, y, and OV. The specific forms are: a =

CQ

exp(a,

(Y - p,,) + a,(HH.SZZE

- pHH) + cx,(INT - p,)

+ ‘yd(CR - /4x) where Y is the log of income ( pr household size ( pHH is its mean), ‘interest’ in Dallas (p, is its mean), *’ Ideally, x, and x,, should becomes numerically intractable

is its mean), HHSZZE is the log of ZNT is a survey variable indicating and CR is the log of the perceived

be treated as random, in this case.

as well.

Unfortunately,

the problem

22 Parametrically, ignoring the option component but assuming the error term has nonzero mean yields the same model. The interpretation, however, is changed. 23 Amemiya (1985) employs the term Type II Tobit model to describe this general class of models. The discrete choice equation is given above. The continuous usage equation simply sets the actual EAS usage equal to ‘expected’ usage plus an error term, e.g., xN = iN + Y, where v is an error term and i, = x0 exp(-ap). The correlation coefficient, p, measures the correlation between the unobservable variables in the two equations. The estimated standard deviation of v was 1.445 (O.OZ), and of p was 0.823 (O.Ol), with the standard errors in parentheses.

D. J. Kridel et al. I Option value,

140

number

where

of calls received

demand,

and policy

(with its mean);

ED is an education

OV= 4. +

telecommunications

index

with its mean;

and

$,ln(ci> ,

where ct is the variance of household usage over the 8 month period prior to EAS introduction. Of particular interest is the sign and significance of #+, which will depend on the source(s) of uncertainty which give rise to the varying usage level. As previously discussed, if uncertain income is causing x to vary, then 4, < 0, as well as OV < 0. Under more plausible circumstances that exogenous factors cause x to vary but not the marginal utility of income, 4, and OV would be expected to be positive. 3.5.

Model

results

The likelihood function is maximized using a Newton optimization routine.24 Coefficient estimates given in Table 1. All coefficient estimates are statistically significant signs. This model predicts penetration of 64.7% subscription is 65.8%. Predicted average usage is compared with actual usage of 376 minutes/month. option value was $9.49 (28% of total benefits).

Table

hybrid BHHHIQuasiand standard errors are and have the expected for EAS, while actual 347.3 minutes/month, The average value for

I

Variable

Estimate

Standard

constant (a,) Y(ff,) HHSIZE (CT,) INT (a,) CR (a,)

2.005 -0.282 0.472 0.077 0.769

0.25 0.12 0.16 0.04 0.07

constant ( yO) ED (Y,)

0.041 -0.051

0.002 0.03

constant ut (@I)

-6.49 2.39

1.05 0.13

(4,)

24 The estimation was performed developed by Richard Spady.

using

PERM.

The optimization

algorithm

error

was originally

D.J.

Kridel et al. I Option value, telecommunications

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It appears that non-usage sensitive benefits (as measured by the variation in usage) are significant and improve the estimation of EAS subscription rates considerably. The significance of usage variation means that we can reject the hypothesis that transactions costs are negligible, since the consumer could otherwise switch to whichever plan is cheaper in each given month. We take this evidence as supportive of the significance of option value for EAS demand.25 EAS only offers access to a zero marginal usage price, i.e., bill certainty. EAS is not required for access to calling in the Dallas area. EAS offers an opportunity to resolve a particular form of uncertainty facing particular types of subscribers. Apparently, this opportunity is highly valued by Rockwall residential subscribers. While all of this value is clearly not option value, equally clearly some of it is. This part of the benefits of EAS is unrelated to actual usage levels - it is related to the sources of usage uncertainty.

4. Conclusions Our principal conclusion is methodological: the two stage subscription decision process, so widely used in telecommunications demand modelling, is not adequate for decisions made under uncertainty. Calculation of consumers’ surplus based on ex post usage will fail to capture ex ante option value, if it is present. Under conditions where OV > 0 (CO),the two stage decision rule will under- (over-)estimate subscription. Demand analysts will need to devote attention to the sources of individual risk, individual attitudes towards risk, and the means available for reducing risks. The design of OCPs, as well as assessment of their revenue neutrality, will need to consider option values in predicting take rates. Many telecommunications services are potential candidates for significant option values. Second lines, call waiting, call forwarding, cellular services, and other premium services all have monthly costs which our casual empiricism suggests cannot be justified for a significant portion of their subscribers on the basis of their usage benefits alone. Data are not readily available on individual usage for these services, but this appears to be a promising area for future research. Both theoretical and empirical work is needed to categorize types of services and/or types of customers for which OV can be expected to be significant (whether positive or negative). The implications for pricing and welfare can be important. I5 We are indebted to K. Train for this observation. We also point out the relevance of the ‘Dansby Plan’, (attributed to Robert Dansby of Bellcore) wherein the customer would receive whichever plan yields the lowest bill in each month. The transparency of plan choice poses some unresolved problems for modelling customer choice (price cannot be known at time of consumption), but would render option value equal to zero.

142

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and policy

Research into telecommunications demand modelling under uncertainty needs to consider incomplete consumer information, telephone company marketing practices, transactions costs, consumer irrationality, as well as option values. We propose that the list include the latter, as consumers may derive benefits which are not associated with their actual use of these services. Such benefits may derive from the value of the option to use a service whether or not it is actually exercised. Our initial estimates suggest that these benefits are potentially large and significant. Indeed, our estimates of 30% of total benefits may be too large to attribute solely to option value. Our contribution is to bring some of the currently unexplained biases in subscription behavior back into the fold of the existing theory of consumer behavior under uncertainty.26 To this end, about half of the estimated OV has been significantly associated with usage variability.*’ The existence of option values has important policy implications aside from their relevance for demand, revenue, and cost estimation. The apparent ethically responsible attitude that only users of new network technology should bear its costs may be economically irresponsible policy. Ex post non-users may also derive value from the option to use new services in a world where there is uncertainty about their value, price, and/or availability. Ex post users may derive values beyond those associated with their actual use. Ex post welfare measures may be inadequate guides for ex ante benefits.28 Failure to charge for option value can lead to ‘market failures’ in which usage revenue forecasts do not cover the costs of new technology. In such cases, telephone companies may fail to adopt new technology even when it is socially beneficial. This puts the regulator in a difficult position. Option value cannot be a ‘blank check’ in which any new service is paid for by all subscribers, regardless of the actual beneficiaries. At the same time, errors of omission can be equally egregious in which subscribers are prevented from the opportunity (option) to use new services which they may or may not eventually use. Ex post analyses are dangerous in a world where significant ex ante benefits exist-the seemingly rational regulatory policy that ‘only users should pay’ may fail to serve the public interest. Innovative x It is useful to recall Freeman’s (1986) conclusions regarding option value: ‘it is at best misleading to speak of option value as a separate category of benefits. Option value is defined as the algebraic difference between two different concepts of welfare change, the ex ante concept. . , and the ex post concept’. ” In the OV equation, about half of the estimated option value was in the constant term, @,,, with the other half, on the average, accounted for by the variance of usage, 2XGraham (1981) explores this point, including the possibility that even OP is not the correct measure of welfare change. He shows the importance of public policies which permit better risk bearing and sharing across individuals facing different risks and with different attitudes towards those risks.

af

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pricing structures, which permit subscribers to self select those options of value to them, may help avoid such potential inefficiencies.2y However, regulators will need to make some difficult decisions regarding who is to pay for new technology in the public network. Researchers will need to conduct further theoretical and empirical research into the sign and size of option values for telecommunications services.

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demand

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ex post

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Train, K.E., 1991, Optimal regulation: the economic theory of natural monopoly (MIT Press). Train, K.E., M. Ben-Akiva and T. Atherton, 1989, Consumption patterns and self-selecting tariffs, The Review of Economics and Statistics 62-73. Weisbrod, B.A., 1964, Collective consumption services of individual consumption goods, Quarterly Journal of Economics 78, 471-477. Weisman, D.L., 1989, Optimal Re-contracting, market risk and the regulated firm in competitive transition, Research in Law and Economics 12, 153-172. Willig, R., 1976, Consumer’s surplus without apology, American Economic Review, 66, 589-597.