The Welfare Impacts of Competitive Telecommunications Supply: A Household-Level Analysis
by
Frank A. Wolak Department of Economics Stanford University and NBER Stanford, CA 94305-6072 Internet:
[email protected] January 1997
*Greg Crawford and Matt Shum provided excellent research assistance. Partial financial support for this research was provided by the Markle Foundation and National Science Foundation grant SBR-9057511. I would like to thank Gerald Faulhaber and Ariel Pakes for their insightful discussant comments. Peter Reiss and Roger Noll deserve special mention for their thoughtful comments on several previous drafts. Finally, I would like to thank the participants at the BPEA meeting for their stimulating discussion of this research.
Abstract Expanding competition in all aspects of telecommunications supply makes it increasingly difficult to maintain cross-subsidies in the supply of local telecommunications services. A large cross-subsidy flows from long-distance telephone service to local exchange service. Approximately 45 cents of every dollar spent on a long-distance call is paid to the local exchange providers at both ends of the call. A substantial fraction of these payments are in excess of costs of providing local access. The purpose of this paper is to assess the household level consumption and welfare impacts of eliminating this cross-subsidy by increasing the price of local exchange service with and without an accompanying decrease in the price of long-distance service. Using household-level data from the Bureau of Labor Statistics' Consumer Expenditure Survey, this paper estimates two types of complete systems of consumer demand functions for local telephone service, long-distance service, food, clothing and other nondurable goods. Both models account for zeros in the consumption of any of these five goods in manner that can be rationalized as consistent with household-level utility-maximizing behavior. The first system—the interior solution model—treats all observed expenditure shares, including zeros, as the interior solution to the household’s budget-constrained utility-maximization problem. The second system—the boundary solution model—explicitly recognizes that observed zero expenditure shares may be the result of nonnegativity constraints on the consumption of all goods when the household makes its utility-maximizing choices. With each of these demand systems, we compute the welfare impacts of various local and longdistance telephone service price changes using household-level compensating variation. For both demand systems, increasing the price of local service is found to be increasingly burdensome to the lower total expenditure households, even when it is coupled with an equal percentage decrease in the price of long-distance service. On the other hand, high-expenditure households find that increases in the price of local service coupled with decreases in the price of long-distance are net welfare improving, and increasingly so as total household expenditures on non-durable goods increases. Because the Consumer Expenditure Survey is a random sample from the US population of households, we can compute an estimate of the average US household-level welfare loss or gain associated with each price change scenario. We find that for the model that explicitly accounts for the non-negativity constraints on the consumption of all goods, the boundary solution model, the mean welfare change associated with all of the price change scenarios is substantially more negative, particularly for households in the lower tail of the total expenditures distribution. For the single price increase for local service scenarios, the boundary solution model also predicts greater welfare losses. For those scenarios balancing local price increases with long-distance price decreases, the boundary solution model yields significantly larger welfare losses for households experiencing welfare losses and significantly smaller welfare gains for households experiencing welfare gains. These results point out the importance of properly modeling the impact of zeros in consumption when making welfare assessments concerning the pricing of telephone services to households. The tremendous amount of heterogeneity in magnitude of the welfare impacts of these price changes, particularly at the low end of total expenditure distribution, points out the necessity of a household-level analysis for obtaining a complete description of welfare impacts of telephone services price changes.
1. Introduction The Telecommunications Act of 1996 defines a regulatory framework for increasing the intensity of competition in all aspects of telecommunications services supply. The Act mandates that all Regional Bell Operating Companies (RBOCs) provide interconnection, unbundled access to their basic network elements, and resale of any retail services that they offer to potential competitive local exchange carriers. Once the RBOC meets a competitive checklist of standards for the provision of access and interconnection services, the Act allows it to file with Federal Communications Commission (FCC) for permission to provide interLocal Access and Transport Area (LATA) long-distance service. The entry of competitive local exchange carriers and the eventual RBOC entry into the interLATA long-distance market should exert significant pressure on the cross-subsidies that currently exist in the pricing of telecommunications services. One cross-subsidy currently under intense scrutiny flows from long-distance to local exchange telephone service in the form of the charges paid by long-distance providers to the local exchange carriers at the originating and terminating points of a long-distance call. The rationale for this pricing policy for inter-exchange carrier access to the local telephone network is to maintain a low price for local residential service in order to achieve the goals of universal service. Because of this cross-subsidy, even during the past five years leading up to the passage of the Telecommunication Act of 1996, competition in the inter-LATA long-distance market and the growing number of competitive providers of long-distance access, particularly for large business customers, led to increasing RBOC revenue losses. Consequently, during this period, many RBOCs proposed and several were granted increased prices for basic residential service as a way to recover these lost revenues.1 The combination of the increasing amount of competition in all telecommunications service markets envisioned by the provisions of the Telecommunications Act of 1996 and the increasing penetration of CAPs
1 For example, effective January 1, 1995, the California Public Utilities Commission raised Pacific Bell’s price of local residential service by approximately 35 percent (California Public Utilities Commission, 1994). Recently, US West made an unsuccessful request to the Arizona Corporation Commission to approve a revenue-neutral rate re-balancing plan that would shift some $20 million in revenue away from intraLATA toll and onto local exchange service.
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will place further pressure on the prices of all telecommunications services to reflect their full cost of provision. The incumbent local exchange companies are aware of this logic, and in their recent filings with the FCC made various proposals to increase the price of local service by at least $10 per month over the next several years, in order raise the price of this service to reflect its cost of provision. Proponents of increasing the price of local service state that raising this price will enable reductions in the prices of long-distance access and other services to reflect their costs so that the typical household’s telephone bill may not rise by this full $10, and may in fact fall, if the prices of these other services decline enough. When considering whether to increase the price of local residential telephone service two questions should be addressed. The first concerns the magnitude of the welfare loss that a household would experience as a result of an higher price for local residential service. The second is whether increasing the price of local residential service together with reducing the price of long-distance access can achieve the household-level welfare benefits envisioned by its proponents. The purpose of this paper is to answer both of these questions at the individual household-level. Our analysis focuses on the individual household because the regulatory debate over increasing the price of local residential service often revolves around the likely impacts of this price change on specific demographic groups, such as low-income or elderly households. Even though the average household-level welfare loss from a proposed price change may be small, attempts to gain regulatory approval for this price increase are often foiled by concern over the potentially large the welfare losses to these households. This concern also arises when considering proposals to balance increases in the price of local service with the reductions in long-distance access prices. Critics argue that such policies increase the price of a good these households, particularly the elderly (for health and safety reasons), consider a necessity—local telephone service—and decrease the price of a good that they consider a luxury—long-distance service. By this logic, these households only experience the welfare loss of higher local phone service prices and little of the welfare gain of the decreased price of long-distance access, because they normally consume little, if any, long-distance service. 2
To perform the welfare and consumption change calculations for our proposed price change scenarios requires an estimate of the household-level indirect utility function for all observations in our sample. To obtain these household-level indirect utility functions, we specify and estimate a complete system of household-level demand functions that are derived from the assumption of static utility maximization. Our analysis is complicated by the fact that a significant fraction of households choose to consume none of one or two of the goods in our demand system. These zero consumption levels are much more prevalent among low-income and elderly households, precisely those households receiving a large weight in the regulatory debate over increasing the price local residential service. The decision of whether to consume zero local phone service is equivalent to whether to connect to the telecommunications network. The decision to consume a positive amount of long-distance service at current prices is crucial to determining whether the household will receive any benefit from a decline in the price of long-distance service that is accompanied by an increase in the price of local service. Therefore, properly modeling both of these binary decisions—whether to consumer zero or positive amounts of local service and long-distance service—is necessary to recover valid welfare impacts for our price change scenarios, particularly for low-income households. We also investigate of an often-maintained assumption about the structure of household-level preferences for both local and long-distance telephone service which can have a significant impact on our welfare calculations. Separability of local and long-distance telephone service from all other goods in the household's utility function implies that it substitutes between local service and such goods as food or clothing in the same manner as it substitutes between long-distance service and either of these two goods. For the reasons given above, particularly for low-income or elderly households, this assumption is not likely to be true. Therefore, imposing it on the utility function of these households will to lead to misleading welfare and consumption predictions for our price change scenarios. Our econometric modeling framework
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and household-level database provides an opportunity to test this often maintained assumption and we find substantial evidence against its validity. Our primary data source is the Bureau of Labor Statistics' (BLS) Survey of Consumer Expenditures, which we henceforth abbreviate CES. For this survey, the BLS collects information on household consumption, broken down by many classes of goods, income and various demographic characteristics on a quarterly basis. The survey also collects information on the consumption of several categories of nondurable expenditures which we include in our demand system. In addition to local and long-distance phone service, food, clothing, and other non-durable expenditures are included in our five-good demand system. To account for across-household heterogeneity in preferences, we also include demographic variables interacted with prices in the indirect utility functions. From the first quarter of 1988 to the first quarter of 1991, this survey collected data on household-level telephone consumption broken down by local and longdistance service, so that our sample is confined to this time period. We then estimate two models for the household-level indirect utility function which differ in terms of how each accounts for zeros in the household’s purchase decisions. For both of our models of the household-level indirect utility function, we consider three classes of price-change scenarios: (1) those with an increase in the price of local residential service only, (2) those with an increase in price of local residential service accompanied by an equal percentage decrease in the price of long-distance service, and (3) those with an increase in the price of local residential service combined with an long-distance service price decrease that is twice the percentage increase in the price of local phone service. The second and third set of scenarios are designed to cover the range price changes in local and long-distance services necessary to eliminate the current cross-subsidy in the pricing of local residential phone service. According to the estimated US population aggregate household-level own-price and crossprice demand elasticities from our preferred model estimates, approximately equal and opposite percentage changes in the prices of local and long-distance service are necessary to keep aggregate revenues from the aggregate US household sector to all local exchange carriers (LECs) unchanged as a result of eliminating the 4
cross-subsidy to local residential service. Because there are reasonable demand elasticity estimates that would imply long-distance price decreases that are twice large as the local service price increase in order to keep aggregate household revenues to the LECs unchanged, we also analyze the welfare implications of these price changes scenarios. For price changes scenarios that balance the percent increase in local service with a corresponding reduction in long-distance service—for instance, a twenty percent increase in the price of local service coupled with a twenty percent reduction in the price of long-distance service—the average household-level compensating variation is positive for our preferred model of the household’s indirect utility function, implying a net welfare loss to society from this price-change scenario. To emphasize the importance of properly accounting for zeros in household-level consumption patterns, we find that our model for the indirect utility function which ignores the corner-solution aspect of zeros in the household’s expenditure on all goods yields the opposite conclusion: the mean household-level compensating variation is negative, implying a net welfare gain to the average household as a result of these price changes. For the price changes scenarios that combine a local service price increase with a twice as large percentage decrease in longdistance prices, both models yield a negative average compensating variation, indicating an average net welfare gain. However, the model which accounts for zeros in a more realistic manner predicts substantially smaller household-level welfare gains for each of these scenarios. This difference in welfare implications across the two models can be attributed to the fact that the model which accounts for zeros in a more realistic manner results in very different estimates of the price and expenditure elasticities of clothing and longdistance service (two goods with a significant number of zeros) and overwhelmingly rejects separability of the underlying household-level utility function. These results illustrate the importance of properly accounting for zero consumption and the non-separability of local and long-distance service from other goods in the analysis of the consumption and welfare effects of these price changes scenarios. For local price increases unaccompanied by decreases in the price of long-distance service, both models of the household-level indirect utility function yield an average compensating variation that is small 5
relative to the household's total non-durable goods expenditure for all households in the sample. For example, a forty percent increase in the price of local service only results in a sample average householdlevel quarterly compensating variation of $17.86 in January 1988 dollars for our preferred model for the household’s indirect utility function. This figure is approximately 0.6 percent of the sample mean of household total nondurable expenditure, which is $3017.52 in January 1988 dollars. The sample 5th percentile to 95th percentile range of compensating variations for this price change for our preferred model is $13.06 to $23.12, so that even for these extremes of the sample, the welfare losses associated with these price changes seem relatively minor. Even for a price increase of this magnitude (40%), for both model estimates we do not find any households in the population consuming a positive amount of local service before the price change having a predicted reduction in their consumption of local telephone service to zero, which can be thought of as disconnecting from the local exchange network. Because of our empirical analysis recovers an estimate of each household’s indirect utility function, we can compute an estimate of the utility-constant or true cost-of-living increase associated with each of our price change scenarios for each household in the sample. For the 40% increase in the price of local service, the mean household-level true cost-of-living increase is 1.08 percent for our preferred model estimates. The 5th to 95th percentile range of true cost-of-living increases for this 40% local service price increase is 0.65 percent to 1.87 percent, respectively. Even the household at the 100th percentile, the 40% increase in the price local phone service translates into only a 3.01% increase in that household’s cost of living. These results point to the conclusion that there appears to be little loss of household-level welfare to all but a small fraction of households, and little, if any, reduction in the fraction of households connected to the local telephone network, due to this increase in the price of local service. Because the CES associates with each household a weight estimating the number of households in the United States with the same demographic composition as that household, we can compute the weighted sum of household level compensating variations which gives the total aggregate net benefit or loss to society from each price changes scenario. Dividing this magnitude by the sum of the weights—an estimate of the 6
total number of households—yields the US population average per-household compensating variation. A final exercise we undertake with these weights is to estimate the median compensating variation for the US population of households. We find that these estimated US population calculations agree with the analogous sample calculations in both sign and magnitude. We also attempt to determine how the burden associated with each of these price change scenarios is shared across the various types of households in our sample. Measuring this burden by the percent true cost-of-living increase as a result of the price changes, we find that the burden is much more than proportionately borne by the lowest total expenditure (income) segment of the population of US households. In addition, this burden is also borne to a greater extent by the older-headed households, those with a working head and working spouse, those in urban areas and those with more children in the age range from 2 through 15 years old. The remainder of the paper proceeds as follows. The next section provides more detail on the form and magnitude of the cross-subsidies described above. Section 3 then contrasts our analysis with other work relating to the issue of increasing the price local residential service, with or without an accompanying reduction in the price of long-distance service. Section 4 describes our data set and presents some descriptive statistics on the distribution of total phone expenditures, local-service expenditures and long-distance expenditures across our sample of households. These summary statistics help to motivate the results from our demand system estimations. Section 5 presents an indirect utility function model which treats the observed zeros in the household’s demands the same way it treats positive consumption levels and derives the resulting demand system. This section also motivates the stochastic specifications chosen for this demand system. Section 6 describes an indirect utility and demand system model which explicitly treats zero consumption as a corner solution in the household’s utility maximization problem and derives the resulting estimation procedure. Section 7 gives the results from estimating our two models and several specification tests, including our test for separability of local and long-distance phone service from all other goods. Section 8 first describes the price change scenarios that we consider for our welfare analyses. This 7
section then characterizes how these welfare impacts vary across households in sample. In light of the welfare calculations and telephone consumption changes presented in Section 8, the paper concludes with a discussion of the implications of these results for household welfare in an increasingly competitive telecommunications environment. 2. Increasing Competition and Cross-Subsidies in Telecommunications Markets The years leading up to the passage of the Telecommunication Act of 1996 have seen a increasing number of competitive providers of access to long-distance services for large business customers, traditionally the major source of revenues for local exchange carriers. The geographic concentration of local exchange business revenues makes relatively small-scale entry by competitive access providers (CAPs) extremely profitable. For example, in the state of Washington, US West, the RBOC serving that state, estimates that 30% of its business calling revenues come from customers in 0.1% of the land area of the state. CAPs focus on providing long-distance access services to customers in this 0.1% of the state, usually in the central business district of the largest city. Other states have similar geographic concentrations of business revenues in their large urban business centers. Significant revenue losses in the long-distance access market have forced the RBOCs to look elsewhere for increased revenues. Consequently, as a result of entry by CAPs, several state regulatory commissions have already implemented significant increases in the price of local residential phone service. United States Telephone Association (USTA) figures illustrate the outcome of this recent trend. Nationwide all LECs (including RBOCs and independent telephone companies) received 45.6% of their revenues from providing local phone service in 1994 versus 41.7% in 1988 (USTA, 1989 and 1995). Over this same time period, a growing number of states decided to allow competition in intraLATA toll service, historically a significant revenue source for LECs. At the present time, all states allow some form of intraLATA long-distance competition from facilities-based long carriers. Many states have implemented or are in the process of implementing plans for intraLATA long-distance dialing parity, where customers can pre-subscribe to the intraLATA toll carrier of their choice and all “1+” intraLATA long8
distance calls will automatically be handled by that carrier. These changes in the intraLATA market have resulted in substantial toll revenue losses to the LECs. According to the USTA, in 1988, 16.8 percent of all LEC revenues (RBOCs and independents) came from toll service (USTA, 1989). By 1994, the revenue share of toll service had declined to 13.4 percent (USTA, 1995). Over this same time period, there has been increased competition in the inter-LATA long-distance market in the sense that AT&T’s market share (in minutes) has declined from more than 85% in 1985 to less than 60% at the present time (Crandall and Waverman (1995, p. 157). However, a more important aspect of this market for our purposes is the extent to which reductions in the price access to the local exchange network by long-distance carriers are passed through to consumers in the form of lower prices for longdistance service. There is considerable debate over the extent to which this pass-through occurs. After an exhaustive survey of the literature and some analysis of their own, Crandall and Waverman (1995) conclude that there is approximately complete pass-through—a one cent reduction in access prices translates into an eventual one cent reduction in long-distance prices—for daytime interstate rates for the longer mileage distances in US inter-state long-distance market. Consequently, it seems reasonable to assume that a regulatory policy which increases the price of local service and reduces the price of access for long-distance providers will eventually result in the desired reduction in the price of long-distance service through the competitive interactions of the various inter-exchange long-distance providers. Between 40 and 45 percent of the total cost of a inter-LATA long-distance call is paid to the local exchange carriers at the originating and terminating points of the call. Although there seems to be general agreement that long-distance access is priced above its costs, there is some disagreement over the magnitude by which these prices are in excess of costs. According to Sievers (1994), approximately half of these payments to local exchange carriers are in excess of the costs of local access. In a recent decision involving US West, the Washington Utilities and Transportation Commission (WUTC) concluded that “it is not a matter of dispute that access charges greatly exceed the incremental cost of access” (WUTC, Docket No. UT950200). It should be noted that this same WUTC decision ruled that local residential service is not priced 9
below its average incremental cost, and that the price for local residential service given in the decision provides a substantial contribution to shared and common costs. However, the question still remains whether the contributions from local residential service are sufficient to allow the US West to cover all of the costs remaining after it has subtracted out all other revenue sources. In their recent Universal Service filings with the FCC, all of the RBOCs except NYNEX (the RBOC serving the New England and New York area), favored substantial increases in the price of local residential service in line with what they argue is the cost of providing this service (Mills, 1996). Mary McDermott, Vice President of Regulatory Policy for the (USTA) stated, “Right now the average local rate is about $18. Over the next four or five years it’s reasonable to think of a $28 basic rate (Mills, 1996).” She goes on to state that because the prices of long-distance access and other services will fall to reflect their costs, the typical consumer’s telephone bill may not rise by this full $10, and may in fact fall, if the prices of these other services decline enough. The provisions of the Telecommunications Act of 1996 which allow interconnection and access to basic network elements by the competitive local exchange carriers will exert further pressure on the prices of all services to reflect their costs. The Act explicitly states that the rates charged to competitive local exchange carriers will be "based on the cost (determined without reference to a rate-of-return or other ratebased proceeding) of providing the interconnection or network element" [Section 252(d)(1)(A)(i)]. In addition, the eventual RBOC entry into the interLATA long-distance market will make the rapid pass-through of access charge reductions even more likely to occur in the future. Although we cannot guarantee that substantial increases in the price of local residential service are inevitable, it is difficult to believe that, given the coming competitive entry into all markets served by the RBOCs, without a significant increase in the price of local residential service the RBOCs will experience substantial revenue losses, particularly if state and federal regulators continue to reduce the price of longdistance access and entry by CAPs continues to occur.
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Consequently, it seems reasonable to believe that whether or not one of the price change scenarios we analyze should be implemented will be the subject of serious debate in all of the coming state regulatory proceedings associated with implementing the Telecommunications Act of 1996 and in subsequent pricesetting proceedings in the years following its implementation. The recent WUTC decision is a case in point: US West proposed more than doubling of local residential service rate over the next four years. They received a small increase in basic residential rate for some customers and a significant reduction in longdistance access charges. 3. Research Question within the Context of the Existing Literature There have been many studies assessing the impact of increasing the price of local residential service on telephone subscribership rates. In addition, several studies have attempted quantify whether the combination of a local residential service price increase and a long-distance service price decrease will generate net welfare benefits to society.
Finally, there have been many studies of the structure
telecommunications demand. Taylor (1994) provides a book-length survey of these studies. Two recent studies attempt to quantify the welfare gains associated with an increase in the price of local service coupled with a decrease in the price of long-distance service. Crandall and Waverman (1995) consider the overall gains to society, to both telecommunications services producers and consumers, from making these two price changes in a manner consistent with Ramsey pricing. Using aggregate demand elasticities obtained from the studies surveyed in Taylor (1994) and estimates of the marginal cost of supplying local and long-distance service, they compute the aggregate welfare under Ramsey pricing and compare this to aggregate welfare at the current prices and find significant gains from to society from this rate re-balancing process. Gabel and Kennet (1993) also consider this same question and argue that because of the impact of varying technical standards on the cost-of-service, the marginal cost of local exchange service has been overstated. In addition, they argue that the elasticity of demand for long-distance service has been overstated in absolute value. They claim that the combination of these two circumstances leads to
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no clear welfare gains associated with reductions in the price of long-distance service accompanied by increases in the price of local service. A characteristic of these two studies is their focus on the aggregate demand for local and longdistance service. For the many studies of the impact of local and long-distance prices on subscribership, the analysis typically focuses on subscribership rates within a census block group or other geographic region. For long-distance consumption, the analysis typically focuses on aggregate demand for a state or for the US as a whole. See Crandall and Waverman (1995) for specific examples of these studies. Consequently, any estimate of the change in aggregate household welfare must be derived from the aggregate Marshallian demand curve, which could yield aggregate welfare change estimates wildly different from the sum of the individual household-level compensating variations associated with the price changes scenario under consideration. Consequently, this study focuses on characterizing the structure of household-level demand and on measuring household-level welfare in a manner consistent with economic theory.
We chose the
compensating variation relative to the actual prices faced by a household as our measure of the welfare change associated with a given price-change scenario.
We then compute the household-level utility-
constant cost-of-living increase associated with the price-change scenario for each household in our sample. In addition, because we have the CES sampling weights, we can also compute estimates of the US population household-level mean or median compensating variation or true cost-of-living increase.
As discussed
earlier, because the regulatory debate on the impact of the price changes we consider usually concentrates on certain kinds of households, typically low-income elderly or those from disadvantaged ethnic groups, it is especially important to measure these welfare changes at the household level to gain a clear understanding of the viability to state regulatory commissions of implementing these local residential service price increases. As discussed earlier, many of the households in this demographic group of particular concern to state regulators consume no local and/or long-distance service within quarter. Consequently, properly accounting 12
for the presence of zero consumption in the household-level demand is crucial to correctly recovering the household’s indirect utility function. We take two approaches to accounting for zeros. The tradeoff between the two is theoretical consistency of the demand system against the stringency of the statistical assumptions and ease of estimating resulting demand system. The first approach treats zero consumption as an interior solution to the household's budget-constrained utility-maximization problem. These zero consumption choices are treated no different from non-zero consumption choices in the household's system of demand functions, which is why we call it the interior solution approach. The second approach acknowledges that zero consumption is due to the imposition of the Kuhn-Tucker conditions for non-negativity of the utilitymaximizing vector of expenditure shares. Here, our econometric model of household-level demand explicitly accounts for these Kuhn-Tucker conditions for observations with zero consumption of one or more goods. We call this the boundary solution approach. Although this approach dominates the first approach on theoretical grounds, the explicit accounting for the non-negativity constraints on household demands requires explicit specification of distributional assumptions and considerably complicates the estimation of the resulting demand system. Besides its consistency with the household’s non-negativity constrained utility maximization problem, there is reason to expect that the boundary model will more accurately capture the types of welfare effects we would like to measure for those portions of the population of households of particular concern to state and federal regulators. The point we have in mind is the often-quoted argument against the existence of welfare gains as a result of cutting the price of long-distance service while increasing the price of local service (see for example, Mills (1996)). Consider Figure 1, which illustrates the household’s non-negativity constrained choice of long-distance service and all other goods at the prevailing prices p1 (the price of all other goods) and p2 (the price of long-distance service). As the chart is drawn the household is at a corner solution with zero consumption of long-distance service. Consequently, for price reductions up to the level of p2*, the household will still be at a corner solution and optimally choose only to consume the composite good. Consequently, any price decrease for long-distance from p2 to a price greater than or equal to p2* will 13
result in no change in welfare to the household because the utility maximizing consumption choice will not change. In contrast, the interior solution model assumes that the observed zeros in the household’s consumption choice are unconstrained utility-maximizing choices, so that any reduction in the price of longdistance service for this model will result in welfare improvements to the consumer. Whether or not separability of local and long-distance service from all other goods is imposed on the household’s utility function can have large effects on household-level welfare calculations. For both models, we find substantial evidence against the null hypothesis of separability of local and long-distance service from all other goods. This result implies that, at least for our dataset, to estimate consistently the parameters of the household-level demand for local and long-distance service, a two-stage budgeting approach with specifies the demand for local and long-distance service independent of the prices and expenditure on all other goods cannot be utilized. 4. Local and Long-Distance Household-Level Telephone Expenditure Distribution In this section we describe the dataset used in our analysis. We then examine the distribution of quarterly total telephone expenditure, local telephone expenditure and long-distance telephone expenditure for each of the four quartiles of the total quarterly non-durable expenditure distribution for our sample of households. These graphs provide an understanding of how telephone expenditures vary across the population of households in the United States. Our dataset consists of quarterly observations on consumption expenditures of local telephone service, long-distance service, food, clothing and other non-durable good consumption. We focus our demand analysis on total non-durable consumption to avoid the issues associated with the distinction between price of the current period’s service flow from a good versus the purchase price of the good. This distinction arises whenever the good purchased provides services for a longer time than the period in which the purchase is observed (in our case a quarter). By definition, this type of good is a durable good, hence our focus on total nondurable consumption, which we henceforth refer to as total expenditure. We now describe each of the goods classes in more detail. 14
Local telephone service, as defined in the CES, is all expenditures for local telephone service for that household. It includes the cost of local phone service for all phones in all dwellings the household owns and the installation charges associated with these phones, if an installation charge occurs within one of the quarters during our sample period. Long-distance telephone service consumption is defined by the CES as the total of all long-distance calling charges where the cost of a single call is broken out in detail on the phone bill. Food consumption is defined as all expenditures on food consumed both within the household and outside of the household (in, for example, restaurants). Clothing consumption is the total of all clothing purchases made by the household during that quarter. Other non-durable consumption includes spending on commodities such as fuel for automobiles and household heating, electricity, transportation services, and other non-durable consumption services. For the purposes of our analysis we convert all nominal magnitudes to January 1988 dollars using the BLS Consumer Price Index Detailed Report total nondurable goods price index normalized to have January 1988 as the base period. Consequently, all dollar magnitudes discussed in the paper are real January 1988 dollars deflated in this manner. To provide intuition for the demand system estimation results in Section 5, we decompose the distributions of local, long-distance, and total telephone expenditures across our sample of households according the quartiles of the total expenditure distribution. We perform this decomposition with respect to the total expenditure distribution rather than the distribution of household income, because for a large fraction of households, income in a given time period is a very poor predictor of the household's total consumption expenditures during that period. For the usual life-cycle, permanent-income considerations, we would expect total expenditure in any period to be more highly correlated with permanent income than it would be with actual income for that period. This point is discussed in Blundell, Pashardes, and Weber (1993) for the Family Expenditure Survey (the United Kingdom's analogue to the CES) and by Lusardi (1993) for the CES. We now turn to a description of the distributions of local, long-distance, and total telephone expenditures broken down by the quartiles of the distribution of quarterly total expenditure (QTE) for our 15
sample of N=11,467 households. These quartiles in January 1988 dollars are: 1st--(QTE < 1688.00), 2nd-(1688.00 QTE 2594.37), 3rd--(2594.37 QTE 3,787.27), 4th--(QTE > 3,787.27). The mean level of total expenditure in January 1988 dollars for the four quartiles are: 1,192.43, 2,126.83, 3,127.46, and 5,624.48, respectively. For each of these total expenditure quartile subsamples, we compute a kernel estimate of the density of expenditure on local telephone service, long-distance service, and the total telephone service.2 Before describing the density estimates we note one minor small-sample irregularity. Because of the local smoothing property of the kernel estimation process, these densities can take on positive values for negative values of telephone expenditure despite the fact that the actual data contains no negative values. In the limit, as the number observations tends to infinity, this estimated probability mass on negative values would tend to zero. Figure 2 plots estimates of the density of total quarterly local telephone expenditure for all of the quartiles of the total expenditure distribution. The striking aspect of this figure is the invariance of the distribution of local telephone expenditures across the quartiles of the total expenditure distribution. Even comparing the first to the fourth quartile, there is very little difference between the two local telephone expenditure density estimates. Figure 3 plots kernel estimates of the density of total quarterly long-distance phone service expenditures. A very different story emerges from these densities. We find that each density is generally a rightward shift and more positively skewed version of the density for the quartile below it. This pattern is indicative of a relatively expenditure-elastic demand for long-distance service. Figure 4 investigates which of the above two patterns of changes in distributional shapes dominates in characterizing the change in the shape of the distribution of total quarterly telephone service expenditures. The pattern of density shifts across expenditure quartiles is similar to the pattern for long-distance service, although the increase in the positive skewness associated with moving to a higher total expenditure quartiles is much less pronounced. The sample correlation between household-level local service expenditures and
2
Silverman (1986) provides a comprehensive discussion of kernel density estimation. We use a Gaussian kernel and the automatic bandwidth selection procedure Silverman recommends for all of the density estimates presented in this paper.
16
long-distance expenditures yields a value of 0.17, which implies a surprisingly small degree of positive linear dependence between these two components of the total telephone bill. This small correlation explains why the pattern of density shifts across the four total expenditure quartiles for total phone expenditures is less pronounced than for long-distance expenditures. We close this section with a discussion of the price data used in our econometric analysis. A major problem faced by all demand system studies using either US or UK household-level data is the fact that there is no cross-section dataset of commodity prices which can be linked to the sample of households, so that all price series used in these analyses vary only over time. Even if there were commodity-specific price data available at some degree of cross-sectional disaggregation, say at the state level, our analysis (and other analyses using household-level data such as the CES) are complicated by the fact that confidentiality considerations preclude the BLS from releasing any state identifiers for a substantial fraction, approximately a quarter, of our household-level observations. Until very recently, the BLS did not release information on state identifiers for any households. The degree of geographic detail available for all observations is whether or not that household lives in one of the four Census regions of the U.S. Although the BLS does compute price indexes for food, clothing and other non-durable goods on a monthly basis for each of these four Census regions, it only computes price-indexes for local and long-distance service on a monthly basis at the national level. It is plausible to assume that all households face the same price for long-distance service given the nature of the good being purchased. However, because of the state-level regulatory price-setting process, this assumption is less tenable for local phone service. Nevertheless, an argument in favor of local prices moving together is that there is a considerable amount of implicit and explicit across-state communication between regulatory bodies in setting these prices. An additional problem with assigning local service prices to specific households is that there are many, often more than ten or twenty different prices for basic residential service depending on where in the LEC’s network a household is located. This occurs because many state regulators set the price of local service at the wire center level for each LEC, depending on the supposed cost characteristics of that wire center. Consequently, even knowing the state or even the 17
town in which a household lives, we would still need information on the wire center that serves the household to accurately assign a price for local service for many of the households in our sample. Even given these wire-center level prices, it would still require substantial guesswork to assign prices to households even for those households whose state of residence we know. Despite these arguments in favor of our assumption, we must acknowledge that for data availability reasons and confidentiality considerations we are forced into making this unsatisfying assumption. To mitigate the impact of these data limitations, we introduce the possibility of unobservable household-level prices for both local and long-distance service into our boundary solution model of household level demand. In this way we account for the concern that different households can face different prices for local and long-distance service and this may be one reason why two very similar households—in terms of the observable characteristics—consume very different amounts of local and long-distance service. We introduce the maximum amount of meaningful price variation into our analysis by using all available cross-sectional and time series variation in the BLS price indexes. The BLS computes price indexes for food, clothing and other non-durable goods, the other three goods in our demand system, at the census region-level. For these three goods, we use the BLS price indexes for the census region in which that household resides. For confidentiality reasons, the BLS does not report a census region of residence for rural households, so we use the national price indexes for these three goods in this case. To account for the fact that the initial level of relative prices across the four census regions is unknown, because, by construction, all four regional indexes are normalized to equal 1 in the same base period, we include four census region dummies in each of the expenditure share equations.
(The excluded region is the rural region.) It is
straightforward to show that by including these regional dummies in each demand equation, we account the unknown beginning of sample differences in relative prices across regions. As mentioned above, for local and long-distance service, only a national price index is available. However, because of the rolling panel nature of the CES data collection process we are able introduce some across-household variation for the prices of these two goods and additional across-household variation for 18
the prices of food, clothing and other non-durable goods within a given quarter. Data for the CES is collected on a monthly basis for a each household for the consumption amounts in the previous quarter. This means that during any month a different set of households is being retrospectively interviewed for their consumption patterns in the previous quarter. Households usually remain in the survey for 3 quarters and then exit. Because of the retrospective nature of the questionnaire and the fact that all of the BLS price index series are collected on a monthly basis, we use the price index for local and long-distance phone service for the most recent month of three months covered by the retrospective survey. For the three price indexes available at the census region level, we use the value for the most recent month for the census region in which that household resides. We deflate all five of the nominal monthly commodity price indexes by the total nondurable consumption price index described above in order to obtain real price indexes relative to a January 1988 base period, so that our expenditure and price figures are in terms of comparable real magnitudes. Figure 5 plots the monthly nominal and real (deflated by the total non-durable goods price deflator) BLS price indexes for local and inter-state long-distance phone service from January 1988 to January 1993.3 Recall that the real and nominal series for both local and long-distance phone service are normalized to one in January 1988. The figure shows that although the nominal price of local phone service increased over this time period, the real price (deflated by the total nondurable goods price deflator) remains almost constant throughout this four-year period. The long-distance price index showed modest nominal declines and substantial real declines over this sample period. These price trends have continued up through the present for local service. Since the widespread availability of discount residential long-distance calling plans in 1992, the accuracy of the long-distance price index has been questioned by the inter-exchange long-distance carriers. Fortunately, our sample period ends in the first quarter of 1991, so these problems should not effect the accuracy of the long-distance price index for time period covered by our sample.
3 The times series pattern of the BLS intrastate long-distance price index closely tracks the BLS inter-state long-distance price index over our sample period. We use the inter-state long-distance price index in our analysis because the vast majority of long-distance calls are inter-state calls. Experimenting with alternate composite indexes of these two long-distance price indexes did not significantly change any of our estimation results.
19
5. Econometric Modeling Framework for Interior Solution Model Our econometric modeling framework must be sufficiently flexible to encompass several empirical and theoretical considerations. The first empirical consideration is the long-history of work indicating nonhomothetic preferences. The most well-known result along these lines is Engel's Law, which states that a household’s budget share devoted to food is declining in total expenditure. Deaton and Muellbauer (1980) survey the evidence against homothetic preferences. Along these same lines, recently there has been research providing evidence against traditional Engel curve representations with budget shares as linear in the log of total expenditure as first specified by Working (1943) and Leser (1963). Bierens and Pott-Buter (1990) and Hausman, Newey and Powell (1991) are representative of this line of research. Given the strong empirical evidence against homotheticity, we must select an underlying household-level utility function which is nonhomothetic and allows for budget shares that are nonlinear functions of the log of total expenditure. From the theoretical perspective, there are several requirements for our underlying utility function. The first is the ability to impose the restrictions implied by utility maximizing behavior on the demand functions estimated in a data-independent fashion. Our second requirement is second-order flexibility of the underlying utility function, which essentially means that for any point in the data space, the functional form can exactly reproduce any theoretically possible value of the function, its gradient, and matrix of secondpartial derivatives through appropriate choice of the parameters of the functional form. The final theoretical requirement is the ability to impose the restrictions implied by separability of local and long-distance phone service from all other commodities in a data-independent manner using restrictions on the parameters of the demand system. In this way, the null hypothesis of separability can be tested using conventional parametric hypothesis testing techniques. The translog is one functional form which satisfies these theoretical and empirical considerations. We utilize duality theory to recover the parameters of the indirect utility function from the Marshallian demand functions because we have observations on price indexes associated with the five goods consumed rather than quantity indexes, which are required to recover estimates of the parameters of the direct utility 20
function for the cases in which the underlying utility functions are not self-dual in the sense discussed by Houthakker (1965). Jorgenson and Lau (1975) provide a detailed discussion of this point. We now describe the translog indirect utility function and discuss how to impose the restrictions implied by optimizing behavior on the demand functions estimated. These restrictions are: (1) homogeneity of degree zero of the demand functions in prices and total expenditure, (2) symmetry of the Slutsky matrix (the matrix of compensated own- and cross-price effects) and (3) quasi-convexity of the indirect utility function in the prices, which is equivalent to negative semi-definiteness of the Slutsky matrix. Define the following notation. Let pi denote the price of good i, xi the quantity of good i consumed, and M the total expenditure. In terms of this notation we have M
N M
i 1
p ix i
pix i and wi
M
where wi is the share of total expenditure spent on the ith good and N is the total number of goods consumed. In terms of this notation, the translog indirect utility function is (1)
ln[V(P,M)] 0
N M
i 1
p i ln( i ) 1 M
N
N
2 i 1 j 1 M
M
p
p
M
M
ij ln( i )ln( j )
where P = (p1,p2,...,pN) is the vector of prices for the N goods. Applying the logarithmic version of Roy's Identity to this indirect utility function yields share equations
(2)
wi(P,M)
i N M
k 1
k
N M
j 1
p
ijln( j ) M
N
N
M
M
k 1 j 1
pj
.
(i=1,...,L)
kjln( ) M
Roy's Identity implies that if V(P,M) is a proper indirect utility function, then the right-hand side of (2) is the value of wi(P,M) that maximizes utility subject to the household's budget constraint. Unfortunately, Roy's Identity does not imply the constraint that this maximizing value of wi(P,M) is non-negative. We will explicitly account for this possibility in our boundary solution model, but for the purposes of the interior solution model we must assume that the application of Roy's Identity to the indirect utility function at the prevailing prices and total expenditure level always yields non-negative shares.
21
Because the share equation (2) is homogeneous of degree zero in the parameters i and ij, a single normalization restriction must be imposed to identify the remaining parameters. The usual restriction is to N
impose
M
i 1
i 1.
By inspection, the share equation is homogeneous of degree zero in the vector of
prices P and total expenditure M, so that homogeneity imposes no restrictions on the parameters of the model. As discussed in Jorgenson, Lau, and Stoker (1982), the Slutsky matrix is: (3)
S $ 1(
1 (I w ) pp(I w ) ww W)$ 1, D(P,M)
where $ is the (NxN) diagonal matrix with (pi/M) as the ith diagonal element, w = (w1,w2,...,wN), pp is an (NxN) matrix with ij as the (i,j)th element, W is the (NxN) diagonal matrix with wi as the ith diagonal element and is an N-dimensional vector of 1's. The function D(P,M) is the denominator of the fraction on the right-hand side of equation (2). This expression implies that symmetry of S is equivalent to symmetry of pp, which holds if ij = ji for all i and j. Equation (3) also shows that quasi-convexity of the indirect utility function in prices, which implies S is negative semi-definite, is a data dependent restriction. The S explicitly depends on the observed prices, shares and total expenditure. Consequently, our strategy is to estimate the model without imposing this restriction. Given the parameter estimates obtained, we check to see whether this constraint holds for each of the points in our dataset before performing our welfare calculations for that observation, because it makes little economic sense to perform these welfare calculations for observations failing the conditions for integrability. Because we are using across-household differences in consumption patterns to identify the parameters of the demand systems, we would like to distinguish between consumption differences due to differences in prices and total expenditure and those that are due to differences in household characteristics. For this reason we include household demographic characteristics in the translog indirect utility function. In order for these differences to be econometrically identified, they must enter interacted with functions of prices and total expenditure. Defining Ak as the kth demographic characteristic and A as the K-dimensional vector of these characteristics, the translog indirect utility function with demographic characteristics becomes
22
(4)
ln[V(P,M,A)] 0
N M
i 1
N
p i ln( i ) 1 M
N
2 i 1 j 1 M
M
p
p
M
M
ij ln( i )ln( j )
N
K
M
M
i 1 k 1
p
ikln( i )Ak. M
Applying the logarithmic version of Roy's identity, the translog share equations become
(5)
wi(P,M,A)
i N M
k 1
k
N
p
M
j 1
ijln( j )
N
N
M
M
k 1 j 1
M
K M
k 1
ikAk
pj
N
K
M
M
M
kjln( )
i 1 k 1
.
ikAk
The assumption of utility maximizing behavior does not impose any restrictions on the ik. To compute the Slutsky matrix for this demand system, the variable D(P,M) in equation (3) now becomes D(P,M,A) and is given by the denominator of equation (5). To estimate our interior solution demand system, we must specify a stochastic structure which accounts for differences between the observed expenditure shares and those predicted by our share equations in (5). To allow for these differences, we append to the share equation an additive mean zero error i, which can be correlated with the errors from the other share equations for a given household, yet are independently distributed across households. This implies that the observed expenditure shares, wi (i=1,...,N), satisfy the equation wi = wi(P,M,A) + i, where wi (P,M,A) is defined in equation (5). If = (1 ,2 ,...,N ) is the vector of share disturbances for a given household, our assumption is that E()=0 and E(1)=6(P,M,A), where
6(P,M,A) is some matrix which depends on the prices, total expenditure and household characteristics associated with that observation. We interpret as the unobservable (to the econometrician) portion of the household's indirect utility function, so that the general form for the household-level indirect utility function is V(P,M,A,). Brown and Walker (1989) show that under this interpretation for the stochastic structure of a demand system and associated indirect utility function, the vector of additive share equation disturbances,
, should be heteroscedastic conditional on prices and total expenditure. For this interior solution version of our demand system, we must assume that the application of the logarithmic version of Roy's Identity to ln[V(P,M,A,)] yields observed optimizing shares that are non-negative. To be more precise, the interior solution model assumes that the household’s observed vector of demands, x*, is the solution to max U(x,A,) subject to x
23
N M
i 1
p ixi M,
where U(x,A,) is the household’s direct utility function. The interior solution model only imposes the household’s budget constraint on the set of feasible demands. Choosing a specific functional form for the way in which enters the indirect utility function would imply a specific functional form for the dependence of 6 on P and M. This dependence could be exploited to yield more efficient estimates of the parameters of the model. However, this approach has the drawback that if our functional form for the matrix 6(P,M,A) is incorrect, this would adversely effect the consistency of the estimates of the parameters of the indirect utility function. Consequently, our strategy is to assume that there is an unobservable portion of the household's indirect utility function so that it takes the form V(P,M,A,) and to acknowledge the results of Brown and Walker (1989) in our estimation process. However, we do not explicitly model how enters the indirect utility function. Instead, we only require that it enters in a way that yields additive disturbances to the share equations which satisfy the moment restrictions for given above. To investigate the empirical importance of these considerations, we will test for the existence of heteroscedasticity (which depends on P and M) in disturbances to the share equations. If there is evidence of the dependence of 6 on these variables, rather than selecting a parametric model for this dependence and re-estimating the model, our strategy is instead to construct standard error estimates which are consistent in the presence of this form of heteroscedasticity. As a result, although our parameter estimates will be less efficient, all of our inferences will be based on asymptotically valid standard error estimates. Because the parameters of the interior solution version of the demand system can be consistently estimated by only imposing the assumed orthogonality restrictions between and the log-prices, log-total expenditure and the demographic characteristics, this seems to be the best research strategy to balance our competing goals of parametric flexibility and precise estimation of the parameters of the model given our relatively large sample. The final issue in making our stochastic structure consistent with utility maximization is that summability of the observed budget shares implies that the sum of the i over all goods is identically zero. In terms of our earlier notation, this restriction is 1 = 0, which implies 16(P,M,A) = 0. This restriction 24
turns 6(P,M,A) into a matrix of rank N-1. To estimate this model we simply drop one of the share equations of our model and estimate parameters of the demand system using the remaining N-1 system of share equations. So long as we utilize a quasi-likelihood function approach to estimate the model, our parameter estimates will be invariant to the share equation that we drop from our model. We utilize the multivariate normal density to construct the quasi-likelihood function used to estimate the parameters of the model. Gourieroux, Monfort, and Trognon (1984) prove the consistency of these quasi(or pseudo) maximum likelihood estimators for the parameters of our demand system and White (1982) provides consistent standard error estimates under the moment conditions we specify for . Using these results, we have a general estimation strategy which is consistent with utility-maximizing behavior yet does not require a specific distributional assumption for or a parametric form for the dependence of 6 on P, M and A to obtain consistent estimates of the parameters of the demand system and to make asymptotically valid inferences about the parameters of the demand system. Defining the multivariate normal quasi-likelihood function requires the following notation. Define yj to be the (N-1)-dimensional vector of expenditure shares for the jth household and fj(Pj,Mj,Aj,) to be the (N-1) dimensional vector of fitted expenditure shares which are functions of prices, expenditure, and household characteristics for the jth household. Let J denote the total number of households in our sample. In this notation denotes the vector parameters of the demand system to be estimated. To compute the quasi-maximum likelihood (QML) estimate of we maximize J
J 1 lndet(6) (yj f j(P j,M j,A j,)) 6 1(yj f j(P j,M j,A j,)). 2 j 1 2 with respect to and the parameters of the matrix 6. L(,6) J(N 1)ln(2%)
M
To test the null hypothesis of homoscedastic disturbances to the share equations, we perform the kurtosis-consistent version of the Bruesch and Pagan (1979) Lagrange Multiplier test for homoscedasticity against the alternative that the variance of the disturbances to each share equation depends on prices and total expenditure as is implied by the results of Brown and Walker (1989) discussed earlier. This test is implemented by taking the residuals from the QML estimation of each of the share equations and regressing 25
these residuals squared on a constant and the log prices and log total expenditure and all of the unique cross products of these log prices and log total expenditure. Taking J times the R2 from this regression yields the LM statistic, which is asymptotically distributed as 32 with degrees of freedom equal to ½((N+1)2 - (N+1)) + 2(N+1), where N is the number of goods in our model. For our N=5 good model, this number is 27. 6. Econometric Modeling Framework for Boundary Solution Model The major difference between the interior solution model and the boundary solution model is that the latter explicitly accounts for the fact that at the prevailing prices a household may have a notional demand for some good—that obtained from maximizing utility subject to only the household’s total expenditure constraint—which is negative. For those households, the requirement that demands must be non-negative implies that the household’s observed vector of demands, x*, is the solution to max U(x,A,) subject to
(6)
x
0
N M
i 1
p ixi M.
The boundary solution model explicitly imposes non-negativity constraints, in addition to household’s budget constraint, on the set of feasible demands. This explicit imposition of the non-negativity constraints on the household's feasible consumption bundle accounts for the possibility of the case given in Figure 1 where zero consumption of one or more goods occurs because the actual prices of non-consumed goods are greater than the virtual prices for these goods—those prices that yield unrestricted demands for non-consumed goods exactly equal to zero. A rigorous definition of virtual prices follows. Writing the objective function for (6) yields Z U(x,A,) (M
(7)
N M
i 1
p ix i)
N M
i 1
5ixi,
where is the Lagrange multiplier associated with household’s budget constraint and the 5i (i=1,...,N) are Kuhn-Tucker multipliers associated with the non-negativity constraints on the demands xi (i=1,...,N). Assuming that the household does not consume the first L goods (xi* = 0 for i=1,...,L), the first-order conditions for (7) are:
0U(x,A,) p 5 0, i i 0xi 0U(x,A,) p 0, j L1,...,M j 0xj 26
5i 0, i 1,..,L N M
j L 1
p ixi M,
> 0.
Neary and Roberts (1980) show that if U(x,A,) is continuous and strictly monotonic, then the virtual prices for the first L goods are: (8)
p i (p) p i v
5i 0U(x,A,)
pN 0U(x,A,) 0U(x,A,) . 0xi 0xi 0xN
(i=1,...,L)
Under these conditions on U(x,A,), the demand for good i is zero if and only if the virtual price for the good, piv(p), is less than or equal to the actual price of the good, pi , because > 0 (by strict monotonicity of the utility function) and 5i 0 if and only if the constraint xi 0 holds as the equality xi = 0. Note that the household’s utility function depends on , the unobserved portion of the household’s utility function, so that in order to determine whether a virtual price for a good is less than or equal to its actual price—whether the household consumes a nonzero quantity of this good—requires explicit specification the dependence of utility function on the vector . Values for these disturbances that imply virtual prices less than actual prices yield zero realized demands. Determining the likelihood function value for households with zero consumption of one or more goods requires integrating over the set of values giving rise to virtual prices less than or equal to actual prices for those goods not consumed by that household. Therefore both the dependence of the indirect utility function on the disturbances and a specific distributional assumption for these disturbances is required to compute the likelihood function necessary to estimate the parameters of the household's indirect utility function for the boundary solution approach. In contrast to the interior solution model of the previous section, the boundary solution model of this section has a firm foundation in economic theory with the cost being more stringent assumptions on the stochastic structure of the model. The development of the likelihood function follows the general approach given in Pitt and Lee (1986), who present a theoretical framework for estimating demand systems with binding non-negativity constraints. We utilize the dual approach and specify an indirect utility function where the dependence of ln[V(P,M,A, )] on , the N-dimensional vector of disturbances, takes the following form (9)
ln[V(P,M,A, )] 0
N M
i 1
p i ln( i ) 1 M
27
N
N
2 i 1 j 1 M
M
p
p
M
M
ij ln( i )ln( j )
N
K
M
M
N
p
i 1 k 1
ikln( i )Ak M
M
i 1
p
iln( i ). M
Applying the logarithmic version of Roy's Identity to this indirect utility function yields the household's potentially negative virtual demands
i
wi (P,M,A, i)
(10)
N M
k 1
k
N
p
M
j 1
ijln( j ) M
N
N
M
M
k 1 j 1
K M
k 1
ikAk i
pj
N
K
M
M
M
kjln( )
i 1 k 1
.
ikAk
Relating these share equations back to those given in (5), we see that the additive disturbance from Section 5, i, equals i/D(P,M,A), where D(P,M,A) is the denominator for the right-hand side of (10). This is consistent with the results of Brown and Walker (1989) that an additive disturbance to the share equation—in Section 5 this is i—must be heteroscedastic conditional on prices and/or total expenditure, in order to be consistent with the utility maximization hypothesis. We impose the same normalizations on the i (their sum over i equals -1) and on the i (their sum over i equals 0) as in Section 5. The restriction on the i implies that the covariance matrix of this N-dimensional vector has rank N-1. Let ( denote the covariance matrix of the N-1 dimensional vector = ( 1, 2,..., M-1). Because the translog indirect utility function satisfies the Neary and Roberts (1980) regularity conditions given above, the decision rule determining zero consumption of a good by household is that its virtual price is less than or equal to actual price of the good. In this case, the demands for the remaining goods are derived from the budget-constrained utility maximization problem subject to the constraint of zero demands for those goods whose virtual price is less than the actual price. Equivalently, as equation (8) illustrates, the remaining demands can be determined from substituting in the virtual prices for the goods not consumed and the actual prices of goods consumed into the demand functions for the goods that are consumed. If all virtual prices are greater than their respective actual prices then all observed demands are positive. The use of virtual prices is nothing more than a simplified mathematical technique for solving for the non-negativity-constrained utility-maximizing level of demand for a specific value of , given the 28
household’s stochastic indirect utility function. Because we observe which of the goods the household does not consume, we know that the virtual price for each of these goods is less than the actual price. However, this inequality constraint on the virtual demands only gives us a set of inequalities on the errors to the share equations with zero expenditures. The remaining equations of the demand system also contain these same share equation errors because the virtual prices, which depend on these errors, enter each of these equations. Consequently, to compute the likelihood function value for households with zero observed demands for some goods, we must integrate with respect to the unobserved share equation errors, i, over the set of values which generate virtual prices less than or equal to actual prices for those goods with zero observed demands. Appendix 1 describes the computation of the likelihood function for three classes of observations: (1) no zeros, (2) one zero, and (3) two zeros. There are no observations in the sample with more two zeros. The case of no zeros is very similar to likelihood function given in Section 5, with the exception of a Jacobian term because the boundary solution model requires an explicit specification of the dependence of additive share equations on P, M and A. Computing the likelihood function for the case a single zero requires a univariate integration with respect to i, the disturbance to the expenditure share equation with zero demand. The case of two zeros requires a bivariate integration with respect to i and j, the disturbances to the two expenditure share equations with zero demands. The likelihood function for the complete sample is the product of likelihoods associated with all of the households in our sample. To complete the specification of our likelihood function we discuss our distributional assumptions concerning household-level prices for local and long-distance phone service. We assume that there is a joint distribution of the prices of local and long-distance service for our sample of households. The observed price indexes for local service and long-distance service are assumed to be the means of these distributions for each household. Let pl denote the observed price of local service and pd the observed price of long-distance service to the household. Specifically, our assumption is that the actual prices faced by the household satisfy the relations p(act)l = pl and p(act)d = pd , where E() = 1 and E( ) = 1 and the random vector (, ) is independent and identically distributed across households. We further assume that (, ) possesses a discrete 29
distribution { i,i, i} (i=1,...,L). Because there is good reason to believe that the distribution of prices differs across households in urban versus rural areas, we utilize two different discrete joint distributions for household-level local and long-distance price heterogeneity depending on whether the household is located in a rural or urban area.4 To compute the likelihood function for a single observation under this assumption, for 0, 1, or 2 zeros, we compute the summation
mrz(w| ,(, )
(11)
H M
k 1
rkLz(p lrk, p d rk, p f, p c, p o,M,A, ,(),
where the price vector faced by the household is P = (plr,pd r,pf,pc,po), Lz(w|P,M,A) is one of the three likelihood function values given in Appendix 1 for z = 0,1, or 2, and is a 2×3H-dimensional vector of the
ir, ir, and ir . The superscript r accounts for our assumption of different distributions of price heterogeneity in urban versus rural areas. Because of the difference in the telephone services price heterogeneity across urban and rural areas, the likelihood function differs across these two geographic areas. We assume the value H=2 in the estimation for both the urban and rural price heterogeneity distributions. The log-likelihood function for all observations is the logarithm of the sum of these terms, where Lz is replaced by the value relevant for the number on zeros in each observation (z=0,1,2). We then maximize the log-likelihood function with respect to the parameters (of the indirect utility function), ( (covariance matrix of ), and
the parameters of the joint distributions of (r, r), r = urban and rural, subject to the constraints H M
k 1
rk 1,
H M
k 1
krk 1, and
H M
k 1
k rk 1,
which correspond to the constraints that probabilities sum to one, E(r) = 1 and E( r) = 1, for both rural and urban households. Consequently, our estimation procedure also accounts for the potential that different households face different prices and that the across-household distribution of these prices differs between urban and rural households.
4
Telephone companies serving sparsely populated rural areas face a serve a different set of constituencies than telephone companies serving large urban metropolitan areas. Companies in rural areas primarily serve residential customers, whereas those in the urban metropolitan areas obtain a significant fraction of their revenues of from business customers and network services not demanded in rural areas. These differences in pricing incentives and product offerings should result in different distributions of acrosshousehold price heterogeneity for local service and long-distance service for these two geographic areas.
30
Having completed the description of our log-likelihood function, we note that the estimation is substantially more computationally intensive because computing the likelihood function contribution for households with zero consumption in one or two goods requires the computation of a univariate or bivariate integral, respectively, and these observations comprise more than 10 percent of the observations in sample. Table 1 gives the breakdown of zeros for our sample. The diagonal elements give the number of single zero observations for each good and the off-diagonal elements, the number of two zeros observations for each combination of row and column label. The vast majority of zeros are associated with long-distance expenditures, with clothing a close second and with local service a distance, but still significant second. There are a few two-zero observations, with the most common pair of zeros long-distance service and clothing purchases. Because of this fact, the boundary solution and interior solution models recover very different preference structures for these two goods, which has important implications for the subsequent welfare calculations for the multiple price changes scenarios. The significant number of households consuming zero of at least one good points out the potential importance of properly accounting for these boundary solutions in our empirical work. We now turn to a discussion of our empirical results for both models. 7. Estimation Results This section describes the estimation of both the interior and boundary solution models. We first describe the specific household characteristics entering into our model. We then proceed with a discussion of our estimation procedures and their output. We then perform our separability tests for both models. In our choice of household characteristics to include in the vector A = (A1,A2,...,AK) we attempt to control for across-household differences in the preferences for goods that do not depend on the prices faced by the household or its total expenditure. We include the age and age-squared of the head of household, because we anticipate cohort differences in the demand for telephone service. Dummies for whether the household contains a working head and a working spouse are included, because there is strong evidence (which we confirm), for example Browning and Meghir (1991), that employment status and hours of work 31
affect consumption patterns. For this same reason, we also include variables measuring the number of hours worked annually by the head and by the spouse. To account for differences in the geographic location of the household to the extent possible given confidentiality constraints and to account for the unobservable base period across-region relative prices for food, clothing and other non-durable goods discussed in Section 4, we include a dummy for each of the four census regions, with the excluded group those households living in rural areas. Because we believe that a household's demographic composition will influence its preferences, we include variables measuring the total number of persons in the household, the number of persons 65 years old and over, the number of males between 2 and 15 years old, and the number of females 2 to 15 years old. Finally, we include dummy variables that quantify race and educational status. Specifically, we include a dummy variables for whether the head of household is white, is a high school graduate, and is a college graduate. Finally, we include indicator variables for whether the household head is a female, the head is single, and the head works in a professional occupation as defined by the CES. While there are other household characteristics we could include in our model, based on our preliminary model estimations, the variables we selected appeared sufficient, relative models with more household characteristics included, to explain much of the acrosshousehold differences in consumption not due to differences in prices and total expenditure. Table 2 presents the QML estimates of the parameters of interior solution demand system in terms of the notation for the translog indirect utility function given in equations (4) and (5). Table 3 contains the ML parameters estimates for the boundary solution model in terms of the notation given in equations (9) and (10). Both models are estimated with the summability, homogeneity and symmetry restrictions imposed so that the resulting demand systems can be used to perform welfare calculations. Formal statistical tests of these restrictions yield little evidence against their validity for both the interior and boundary solution estimates. Despite the price data used, both models yield fairly precisely estimated own-price effect coefficients and some precisely estimated cross-price effects. The very small standard errors relative to coefficient estimates for the vast majority demographic variables implies that these variables substantially 32
improve the explanatory power of both demand systems. A Wald test of the null hypothesis that all demographic variables do not enter any of the share equations is overwhelmingly rejected for both models. Table 4 reports the LM statistics against heteroscedasticity of the elements of conditional on the log of prices and log total expenditure for all five share equations for the interior solution model. For all share equations, the test statistic is substantially larger than the critical value for any conventional size hypothesis test, providing strong evidence against homoscedastic error variances relative to the alternative hypothesis of heteroscedasticity conditional on log prices and log total expenditure as is implied by our approach to including as an unobservable vector of household-level variables in the indirect utility function in manner consistent with utility maximizing behavior. For this reason, the standard errors given in Table 2 are computed from the heteroscedasticity-consistent QML covariance matrix estimates given in White (1982). Because of the presence of heteroscedasticity, comparing values of the QML objective function cannot be used to compute valid test statistics, so that all hypotheses about the interior solution model will be examined using Wald statistics based on this covariance matrix estimate. We use the inverse of the matrix of outer products of the gradients of the individual terms of the log-likelihood function to compute standard error estimates and as the covariance matrix used to construct all Wald tests for the boundary solution estimates. We now discuss our test for homothetic separability of local and long-distance phone service from food, clothing, and all other nondurable goods in the household-level direct utility function for the translog model. This test asks whether or not the household-level direct utility function, U(x1,x2,...,xN), can be written as U(g(x1,x2),x3,...,xN), where xi is the quantity consumed of good i and g(.,.) is a homothetic aggregator function. Assuming x1 and x2 are the amounts of local and long-distance service consumed, g(x1,x2) then represents the telephone service aggregate good. If this restriction on the household-level direct utility function holds then the household's demand problem can be thought of in the two-stage budgeting context, where the household first determines its demands for the telephone aggregate and the other three goods using a price index for this telephone aggregate and the prices of the other goods; then conditional of the total amount of telephone expenditures determined from this first-stage problem, the household solves for the 33
optimal local versus long-distance split by maximizing g(x1,x2) subject to p1x1 + p2 x2 = MT , where MT is total telephone expenditures determined from the first-stage optimization problem. Homothetic separability of the household-level direct utility function is implicit in any analysis of the demand for local and longdistance service which ignores the household's expenditures on, or the prices for, all other goods consumed. Without this restriction on its utility function, a household cannot solve for the optimal local versus longdistance split without regard to its optimal demand for all other goods. Most all existing analyses of telecommunications demand make this two-stage budgeting assumption. Our many goods household-level dataset provides an ideal opportunity to investigate its empirical validity. See Taylor (1994) for more evidence in favor of the importance of examining the validity of this restriction on household preferences. Although the restriction of homothetic separability given above is specified in terms of the household's direct utility function, Theorem 4.4 of Blackorby, Primont, and Russell (1978) shows that homothetic separability of the direct utility function is equivalent to homothetic separability of the indirect utility function. In terms of the parameters of the translog function, global imposition (for all values of prices and total expenditure) of this restriction for a household with attribute vector A implies (12)
1 (A)
1i for i 1,2,...N, 2i
2 (A) where i*(A) is defined in equation (A-1) in Appendix 1, the subscripts 1 and 2 denote local and longdistance service, and N=5 for our case. This test involves 5 nonlinear restrictions on the parameters of the translog demand system. Because this test depends on specific attributes of each household through the ratio
1*(A)/ 2*(A), ideally we should investigate its validity for each household. For each observation, we compute the Wald test statistic for the 5 nonlinear restrictions given in (12) for both sets of parameter estimates. For the interior solution estimates, the smallest value of the Wald statistic over all observations in the sample is 72.36 and the largest is 76.99. For the boundary solution model, the smallest value of the Wald statistic is 51.86 and the largest value is 218.65. These results provide substantial evidence against the validity of (12) for both model estimates. An alternative way to investigate the validity of (12) that does not involve computing test statistics for all observations in the sample is to examine the validity of the four 34
nonlinear restrictions in (12) that do not depend on A. For the interior solution model, the Wald test for these four nonlinear restrictions is 72.35. For boundary solution, the Wald test is 45.57. These test results provide significant evidence against the last four nonlinear constraints given in (12). Finally, we investigate whether this restriction holds when the first ratio in (12) is evaluated at the sample mean of A. In this case the interior solution Wald statistic is 72.52 and the boundary solution Wald statistic 255.41, which provides more evidence against the validity of the nonlinear restrictions given in (12). Taken together all of these results provide strong evidence against the validity of homothetic separability of the household’s utility function in local and long-distance service. We should caution that this rejection of homothetic separability, and therefore the validity of the two-stage budgeting assumption, is conditional on our maintained hypothesis of a translog indirect utility function. In addition, as discussed in Blackorby, Primont, and Russell (1977) imposing homothetic separability on the translog function destroys the second-order flexibility property of this function. Unfortunately, the property that global imposition of separability destroys second-order flexibility is shared by all other existing flexible functional forms that have been used to test for this restriction on utility functions. Although we can reject homothetic separability conditional on the assumed translog indirect utility function, we do not know if this due to a mis-specification of the true underlying utility function or because the homothetic separability null hypothesis is false. Tests for additive separability of the household’s indirect utility function for the interior and boundary solution models are also overwhelmingly rejected for both models. Additive separability implies the following six restrictions on the second-order parameters of the translog indirect utility function:
lf 0, lc 0, lo 0 df 0, dc 0, do 0, where l = local, d = long-distance, f = food, c = clothing and o = other nondurable goods. For the interior model the Wald statistic is 10,777.0. For the boundary model the Wald statistic is 143.7. Given these separability results, for both models we use the demand system estimates which do not impose any separability restrictions to perform the welfare calculations and consumption simulations given in the next section. 35
8. Assessing the Welfare Impacts of Price Increases for Local Telephone Service In this section, we utilize the two integrable demand systems to assess the impact of various price change scenarios for local and long-distance service on household-level welfare. We consider six price change scenarios. The first two involve increases in the price of local service alone. The second two involve price increases in local service accompanied by equivalent decreases in the price of long-distance service. The final two involve price increases in local service accompanied by twice as large percent decreases in the price of long-distance service. The first two scenarios attempt to capture the range of likely impacts increased prices of local service. The last four attempt to assess the likely impacts of balancing a local service price increase with a corresponding decrease in the price of long-distance service as might be expected if long-distance access charges are reduced in response to local price increases in a manner that leaves nationwide LEC revenues collected from the household sector unchanged. Our framework also allows us to assess the regressivity of these proposed price increases as well as determine which types of households, as measured by their observable characteristics, bear a greater portion of the burden of these price changes. Finally, we can use the CES weights to extrapolate our household-level welfare change results to the US population at large and determine (conditional on the validity of our modeling assumptions) whether these price change scenarios result in a net welfare gain or loss for the population of U.S. households. Before presenting the results of these simulations, we discuss the sample average own-price and total expenditure elasticity estimates given in Table 5 for the interior and boundary solution models. With some important exceptions, the mean elasticity estimates are similar across the two indirect utility functions. Consistent with Figure 2, the household-level total expenditure elasticities for local service, are very small. The boundary solution model recovers substantially smaller in absolute value own-price elasticities for local service than the interior solution model, and slightly smaller in absolute value own-price elasticities of demand for long-distance service as well.
The range from the 5th to 95th percentile of the own-price
elasticity of local service for the boundary model is below the 5th to 95th percentile range of this same 36
elasticity for the interior model. For both models, the mean expenditure elasticity of local service is slightly positive, with the boundary model value slightly larger. For in the interior model, the 5th to 95th percentile range includes both positive and negative values. For long-distance service we find, at the mean values for our sample, a price-elastic demand for long-distance service (with the boundary model less elastic) and an expenditure elasticity that is greater than the one for local service (with this statement less true for the boundary solution model). Both mean expenditure elasticities indicate that long-distance service is a normal, but not luxury good. A major difference across the two models is the own-price elasticity for clothing. For the boundary model, clothing is much more price elastic than for the interior model. Recall that there are many zeros for clothing and long-distance phone service jointly, so that it is no surprise that the models recover different estimates of the price effects involving these goods. The 5th percentile to 95th percentile range for the own-price elasticity of clothing for both models is indicative of the potential for substantial differences in the welfare and consumption impacts of price changes across households. These differences in price effects across the two models combine to result in the opposite aggregate welfare conclusions for our two equal price changes scenarios. The six price changes scenarios are: (1) a 20 percent increase in the price of local service alone, (2) a 40 percent increase in the price of local service alone, (3) a 20 percent increase in the price of local service accompanied by a 20 percent decrease in the price of long-distance service, (4) a 40 percent increase in the price of local service accompanied by a 40 percent decrease in the price long-distance service, a 10 percent increase in the price of local service combined with a 20 percent decrease in the price of local distance service and (6) a 20 percent increase in the price of local service combined with 40 percent decrease in the price of long-distance service. Appendix 2 sets out a framework for determining revenue neutral price change combinations using estimates of the revenue shares of the LEC’s three major products—local service, network access service, and long-distance service—and estimates of the US population own- and cross-price demand elasticities for local and long-distance telephone service from the household sector. The aggregate own- and cross-price elasticity estimates implied by both our boundary and interior solution models, 37
combined with the most recent values for the US average LEC revenue shares by product, imply that the price changes which leave aggregate US revenues to the LECs from the household sector unchanged should balance the percent increase in the price of local service with a equal percent decrease in the price of longdistance service. We consider price changes scenarios where the long-distance price decrease is twice in absolute value the local service price increase because there are plausible values for the aggregate household sector elasticities which indicate these price changes would leave aggregate revenues from the household sector unchanged. For our welfare analysis we compute the compensating variation associated with each of these price changes. Assuming P0 is the initial vector of prices, M0 is initial total expenditure, P1 is the proposed vector of prices, V(P,M,A) is the indirect utility for a household facing prices P, and having total expenditure M and characteristics A, the compensating variation is the value of CV which solves the nonlinear equation V(P 1,M 0CV,A) V(P 0,M 0,A). In words, CV is the amount of additional total expenditure that must be paid to a household with characteristics A in order for it to be indifferent between total expenditure M0 + CV and prices P1 and total expenditure M0 and price P0. A negative value of CV implies that the new prices P1 are welfare enhancing. Both the boundary and interior solution models assume that the disturbances to the demand system are unobservable household characteristics in the indirect utility function V(P,M,A, ), where is the vector of disturbances to the demand system. As emphasized in the discussion surrounding equations 4 and 5, I do not assume a specific functional form for how these disturbances enter the indirect utility function for the interior model. For the case of the boundary model, in order to compute the likelihood function, a specific functional form must be assumed for the dependence of V(P,M,A, ) on . Computing the compensating variation under this interpretation of the disturbances to the demand system implies that CV is a function of
, because it is the solution to the equation V(P1,M0+CV,A, ) = V(P0 ,M0 ,A, ). For each household we can compute E(CV( )), the expected value of its compensating variation with respect to the distribution of unobserved household characteristics, and Var(CV( )), the variance of its compensating variation. For the 38
boundary solution model, computing CV(v) is straightforward for any value of , because the dependence of V(P,M,A, ) on is specified in equation 9, so that taking a large number of draws from the estimated distribution of for each household and computing the sample moments of CV( ) for these draws yields simulation estimates of E(CV( )) and Var(CV( )). For the interior solution model, the dependence of indirect utility function on the vector of unobserved household characteristics is left unspecified, so that the expected value and variance of CV for each household cannot be computed without further assumptions. Because it is unclear how the unobserved household characteristics should enter the indirect utility function for the interior solution model, I decided instead to compute the compensating variation for each household for both the boundary and interior model estimates at the expected value of the disturbances to the demand system, so that vector of unobserved household characteristics is set equal to zero for all compensating variation calculations. Therefore, any differences in the welfare calculations across the interior and boundary solution models is attributable to the differences in the parameter estimates of the indirect utility function across the two models rather than differences in the estimated distribution of unobservable household characteristics. As a check of the difference between CV( =0) and E(CV( )), I computed both magnitudes for the boundary solution model. For all of the price change scenarios considered, the difference between CV( =0) and E(CV( )) is minor because of the very small estimated variances of the elements of . At most these two magnitudes differ only in the second significant digit. Although Var(CV( )) reveals significant uncertainty in CV( ) for any specific household, computing either the mean of CV( ) over all households in our sample or the estimated U.S. population mean of CV( ) using the CES weights yields standard errors that are less than one-percent of these estimated means. These standard errors are computed using the estimated values of Var(CV( )) for each household and the assumption that the ’s are independent and identically distributed across households.
Consequently, there is no difference in the quantitative
conclusions that I am able to draw from the welfare analysis of the boundary solution model from setting the
39
value of the vector of unobserved household characteristics equal to its mean value in computing the distribution of the welfare impacts of the price changes scenarios we consider. Utilizing duality theory, we know that associated with V(P,M,A) is the expenditure function E(P,U,A) which gives the minimum expenditure level necessary to achieve utility level U. Define U0 = V(P0 , M0,A) as the utility at existing prices and total expenditure. By definition of the expenditure function M0 = E( P0,U0,A), and by the definition of compensating variation M0 + CV = E( P1,U0 ,A). We can then define the utility-constant or true percent cost-living increase as a result of increasing prices from P0 (existing prices) to P1 (the new prices under the price changes scenario) as PTCLI Percent True Cost of Living Increase 100×
E(P 1,U 0,A)
1 100×( CV0 ).
E(P 0,U 0,A) M We can compute this true cost-of-living increase for all observations in our sample. Examining how this ratio changes with M0, allows us to determine the extent of the regressivity or progressivity of these price change scenarios. Finally, in order to assess how that true cost-of-living increase relates to the characteristics of the household, we estimate best linear predictor functions for PTCLI as a function of our household characteristics and total expenditure. For all of these price change scenarios to yield theoretically valid household-level consumption changes and compensating variations, the estimated demand system must satisfy all the restrictions implied by utility maximizing behavior at the prices, total expenditures, and household characteristics for that observation. Because we estimate both models with summability, homogeneity, and symmetry imposed, we only need to check that negative semi-definiteness of the Slutsky matrix holds at each observation. This process involves computing the Slutsky matrix given in equation (3), with D(P,M,A) in place of D(P,M), for each observation and then computing the five eigenvalues of this matrix and verifying whether or not they are all non-positive. As discussed earlier, because there are no necessary and sufficient conditions (there are sufficient conditions) on the parameters of the translog indirect utility function which guarantees the Slutsky matrix is negative semi-definite for all prices and expenditures, we must follow this procedure to select those observations that can be used to compute the telephone consumption changes and household-level welfare 40
changes as a result of our price-change scenarios. For the interior solution model we lose only a small percentage of observations due to failure of the negative semi-definiteness of the Slutsky matrix. Even for those observations that fail the restriction there is only one positive eigenvalue and this eigenvalue is a small fraction, less than 1/5, of the value of the smallest, in absolute value, negative eigenvalue. There are 11,344 observations out of the full sample of 11,467 observations which satisfy the necessary curvature restrictions. All of the calculations for the interior solution model are based on this regular sample. For the boundary solution model we lose more observations due to the failure these curvature restrictions. In this case, 8,492 of the observations satisfy the negative semi-definiteness of the Slutsky matrix.5 For this case as well, those observations that fail the restriction have just a single marginally positive eigenvalue that is a small fraction of the smallest, in absolute value, negative eigenvalue. All calculations for the boundary solution model are for this restricted sample of regular observations. Figure 6 plots the sample density of household-level compensating variation in January 1988 dollars for the four two-price changes scenarios for the interior solution estimates. Figure 7 plots these same magnitudes for the boundary solution estimates. The interior solution household-level compensating variations show considerably more variability than the boundary solution estimates and tend to be more negative than the boundary solution values, indicating that the interior solution estimates find all of the twoprice changes scenarios substantially more welfare enhancing than the boundary solution estimates. The summary statistics associated with these densities presented in Table 6A bear out this point. At the 5th and 95th percentiles and at the sample mean, comparing the two model estimates for the same two-price change scenario, the relevant characteristic of the household-level compensating variation distribution from the boundary model is substantially more positive, indicating that this model finds greater welfare losses or smaller welfare gains associated with these price changes scenarios that the interior solution estimates.
5
Linear probability models predicting whether individual observations satisfied these curvative restrictions as a function of observable household-level characteristics, including total expenditures, did not uncover any readily discernable reasons why observations failed to satisfy these curvature restrictions.
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There is a divergence between the welfare implications across the two models for the two-price changes scenarios that set the local price increase equal to the long-distance price decrease. As shown in Appendix 2, these two-price changes scenarios are consistent with keeping the LECs revenue neutral with respect to the US household sector given the aggregate demand elasticity estimates implied by our two models. The interior solution estimates a negative sample mean compensating variations for both equal price changes scenarios, -$3.48 for PL +20% and PD -20% and -$7.95 for the PL +40% and PD -40%, indicating average household-level welfare gains associated with these price changes. On the other hand, the boundary solution finds mean compensating variations for these two scenarios of $2.66 and $6.14, respectively. These positive sample average compensating variations imply sample average household-level welfare losses associated with these equal yet opposite in sign price changes scenarios. For the price change scenarios that have a long-distance price decrease that is twice, in percentage terms, the local service increase, both models find mean welfare gains (negative sample mean household-level compensating variations), although the 95th percentile values for the boundary model implies that some households experience welfare losses associated with these price changes. This more pessimistic view of the combination price changes emerging from the boundary results is driven by the fact that we estimate a significantly higher expenditure and price elasticity for clothing under the boundary solution model relative to the interior solution model. In addition, we also estimate a substantially higher cross-price elasticity between clothing and long-distance service under the boundary solution model. These elasticity estimates imply that for many households, as the result of the lower price of long-distance service, they substitute into clothing purchases, rather than substantially into long-distance service as is predicted by the interior solution estimates. Consequently, the net effect of these price changes for these households is still a welfare loss. This effect is particularly true for the low total expenditure households consuming very small amounts of long-distance service initially. Because it explicitly accounts for the existence of corner solutions in the household's choice problem, the boundary solution model is
42
ideally suited for modeling the responses of these low total consumption and low long-distance service consuming households. Table 6B uses the CES weights to compute estimates of US population mean and median household-level compensating variations associated with these price changes scenarios. For all scenarios and both models, there is close agreement between the sample mean and the estimated US population mean. Multiplying these mean per-household figures by the number of households in US yields an estimate of net amount of money that could be raised (negative values) or must be given to households (positive values), assuming all households are paid their CV, in order for all households to be indifferent between the existing price and the proposed prices. Both models rationalize the single price changes as aggregate welfare losers, and the unequal price change scenarios as net aggregate welfare gainers. However, the interior solution model finds the equal price change scenarios to be net gainers, whereas the interior solution finds them to be net losers for the US population of households. Figures 8 and 9 plot the densities of the household-level true cost-of-living increases that result from the four two-price changes scenarios. These densities show that for the same price changes scenario, the boundary model densities in Figure 9 tends to be a rightward shift and more concentrated version of the comparable interior solution density in Figure 8. This result implies that the boundary solution model finds, on average, a higher cost-of-living increase associated with each of the two-price changes scenarios than the interior solution model. Table 7A presents summary statistics on the household-level true cost-of-living increases for all of the welfare scenarios. The divergent welfare implications for the equal price changes scenarios between the interior and boundary models continues for the true cost-of-living indexes. The boundary model finds a mean household-level true cost-of-living increase and the interior model finds a mean true cost-of-living decrease for both equal price changes scenarios. Both models agree for the unequal price changes scenarios. They find an household-level average true cost-of-living decrease associated with each of these scenarios.
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The mean household-level percent true cost-of-living increase associated with a 40 percent increase in the price of local service only is 1.08, with a 5th to 95th percentile range of 0.65 to 1.87. The interior solution estimates find slightly smaller values for the mean, and 5th and 95th percentiles of the true cost-ofliving increases. The largest value for the percent cost-of-living increase over all households in our sample is 3.0 for the boundary solution estimates and 3.8 for the interior solution estimates. On basis of these true cost-of-living increases, neither model finds that this 40 percent increase in the price of local service results in a significant increase in the true cost-of-living of any of the households in our sample. Table 7B applies the CES weights to the sample values of the true cost-of-living increases associated with the six scenarios. These estimated US population means are very similar to the sample means given in Table 7A. Estimated household-level mean US population percent cost-of-living increase associated with a 40 percent increase in the price local service is 1.07 for the boundary model and 0.81 for interior model. Neither of these mean true cost-of-living increases seem very significant. The equal price changes scenarios for the boundary model implies US population household-level mean and median true cost-of-living increases. The interior model implies US population mean and median true cost-of-living decreases. Both models find the unequal price changes scenarios to lead to US population mean and median cost-of-living decreases. An argument often raised against increasing the price of local phone service is the fact that households will disconnect from the telephone network. The interior solution model is poorly suited to addressing the problem of zero consumption because the underlying demand system implicitly assumes satisfaction of the first-order conditions for utility maximization without the imposition of the Kuhn-Tucker conditions for non-negative consumption. On the other hand, the boundary solution model is designed with this aspect of household choice in mind. Conditional on a predicted positive expenditure for local service, we compute the number of negative predicted local or long-distance demand shares that result from each price change scenario for both models. We interpret a negative predicted share for local service as a disconnection from the telephone network. All six of our price change scenarios yield no negative shares 44
for either local or long-distance service for either model; indicating that, at least for our sample of households, disconnection from the network appears to be a very unlikely response to increases in the price of local service of the magnitudes we consider. In order to assess how the burden of these price changes are shared across households we compute best linear predictor functions for the percent true cost-of-living increases as a function of the household characteristics and the log of total expenditure. The coefficients from these regressions provide an estimate of how the best linear predictor of PTCLI changes as a result of changes in any of the household characteristics or log of total expenditure. Tables 8 and 9 present these best linear predictor functions and White (1980) heteroscedasticity-consistent standard error estimates for the interior and boundary solution models for the local +20% and long-distance -40% price changes scenario. The best linear predictor functions are very similar across the two tables. The negative coefficient on the log of total expenditure indicates that households with higher total expenditures are predicted to have lower values of PTCLI, which implies that the burden is more heavily borne by the lower total expenditure portion of the population. We estimate a steep regressivity to the burden of these price changes as measured by PTCLI. The boundary solution results in Table 9 imply that the best linear predictor of PTCLI increases by approximately 1.4 units for a for 10 percent decrease in total expenditures. A plot of PTCLI versus ln(M) reveals that this estimated relation is determined by the very regressive nature of these price changes at very low values of ln(M). At higher values of ln(M) these price changes are much less regressive. Several other conclusions emerge from these regressions. The best linear prediction of the true costof-living increase is increasing the age of the head of household, indicating that older households bear an increasing relative burden of these price changes. Urban households are predicted to bear higher true cost-ofliving increases. Households with males ages 2 through 15 and females 2 through 15 are both predicted to bear a greater burden. Households with working heads and spouse and households with heads and spouses with more annual hours of work are found to experience higher true cost-of-living increases. Repeating these
45
best linear predictor calculations for other price changes scenarios yields similar conclusions about the relationships between PTCLI and household characteristics, including total expenditure. These differences in true cost-of-living increases are driven by the fact that we allow household characteristics to shift the household-level indirect utility function and expenditure share equations, so that the price and expenditure elasticities differ across households according to these characteristics. Within in the context of our modeling framework, why these true cost-of-living increases vary in the manner that they do can only be explained by this difference in price and expenditure elasticities by household characteristics. Because our model takes the household as the unit of analysis, we are unable to distinguish between the many within-the-household explanations for these differences in price and expenditure responsiveness using our data and modeling framework. 9. The Viability of Rate Re-Balancing in Competitive Telecommunications Markets Assuming our estimated demand systems are valid descriptions of the observed pattern of householdlevel consumption patterns, the calculations of the previous section allow several conclusions to be drawn. All of the evidence seems consistent with the view that the substantial increases in the price of local service proposed as a result of increasing competition in telecommunications markets will result in very small losses in household-level welfare to vast majority of households. Balancing these local service price increases with reductions in long-distance access charges as would result if the hypothesized cross-subsidies from longdistance service to local service were eliminated, appears to result in net household welfare gains to the many of households in our sample. According to our household-level demand function estimates, price changes scenarios that combine local prices increases with equal long-distance price decreases are the type most likely to leave US aggregate LEC revenues from the household sector unchanged. For these price changes scenarios, whether or not the sum of all compensating variations over the populations of U.S. households is positive or negative depends on how zeros are accounted for in the household's consumption choices. Accounting for zeros in a manner which acknowledges the existence of non-negativity constraints in the household's utility maximization 46
problem yields the result that sample and estimated US population average of these household-level compensating variations is slightly positive, implying an average household-level welfare loss. Neither model overturns the conventional belief that local price increases more than proportionately burden lowincome (or in our case low total-expenditure households), head-employed, spouse-employed, older-headed households, or urban households. However, the boundary solution model which solves the Kuhn-Tucker solution to the household's choice problem finds relatively larger welfare losses among low total expenditure households associated with these local service price increases balanced with a long-distance price decreases. This occurs because the according to the boundary solution model estimates when the price of long-distance falls this has little benefit to low total expenditure households because long-distance is not a good they purchase very much of, or at all, at both the original and new prices. Recall the discussion of Figure 1 given at the end Section 3. Despite these differences in aggregate welfare results, neither set of estimation results suggest that for the price changes we consider this burden is not sufficiently large to merit disconnection from the local telecommunications network. Our separability test results signal the importance of modeling telephone demand jointly with the demand for all other goods in order to accurately measure price and expenditure elasticities and to perform theoretically valid welfare calculations, particularly for those households at the lower-end of the non-durable expenditure (or income) distribution, which are more likely to have zero expenditures in one of the five goods at prevailing prices. The comparison of the interior solution results to the boundary solution results points out importance of properly accounting for the presence of zeros in the household's choice problem for the resulting average individual-level and aggregate net welfare calculations. Particularly, for phone service, which comprises a very small fraction of the household's budget, properly allowing for these outcomes results in very different estimates of the household's underlying preference function which implies different estimates of the household level welfare impacts of the price-change scenarios we consider.
47
Appendix 1 This appendix derives the likelihood function for boundary solution model for three classes of observations depending on the number of zero expenditure shares: (1) no zeros, (2) one zero, and (3) two zeros. Although the model can allow for up to N-1 zeros, where N is the number of goods the household can potentially buy, we stop at the two-zero case because that is the maximum number of zeros in our sample. To simplify notation, let (A-1)
i (A) (i
K M
k 1
DEN(P,M,A)
ikAk),
N M
i 1
i (A)
N
N
M
M
p
ijln( j ). M
i 1 j 1
First consider the case of all nonzero expenditure shares. In terms of this notation wi
i (A)
N M
k 1
ikln(pk/M) i , so that
DEN(P,M,A)
i (DEN(P,M,A))wi ( i (A)
(A-2)
N M
j 1
ijln(pj/M)),
where wi is the observed share of the ith good because all observed demands are positive. The likelihood function for observations with no zeros is (A-3)
L0(w|(, ,P,M,A) (2%) (N 1)/2|D(P,M,A)|N 1|(| 1/2exp( 1/2( ( 1 ))
where is the vector composed of all of the parameters of the indirect utility function and the elements of
are defined in (A-2). The likelihood function for the no-zero case is very similar to the quasi-likelihood function given Section 5 except that the change of variables from i to the wi yields a Jacobian of the transformation that is not equal to the identity matrix, because i is normalized by D(P,M,A) in the share equation given in (10). Consider the case that the virtual price is less than or equal to the actual price ( piv(p) pi) for one i (1,2,...,N). This event occurs if (A-4)
((i (A)
N M
k 1
ikln(pk/M)) i)/ii 0,
because D(P,M,A) < 0, so this event is equivalent to the event i/ii (i (A)
N M
k 1
ikln(pk/M))/ii. The
remaining demands for the other goods can be computed by solving the household's budget-constrained 48
utility maximization problem conditional on wi = 0 with virtual prices in place of the actual prices for the goods not consumed, and the resulting demands are the same as those which result from the explicit solution to Kuhn-Tucker conditions for budget-constrained utility maximization problem subject to the constraints that the household must consume non-negative amounts of all goods. For good i, the zero consumption good, this virtual price, piv(p), is computed by solving (A-4) for the value of pi which satisfies the inequality with equality. Under our functional form assumptions the logarithm of the total expenditure normalized virtual price for the ith good is N
ln(%i(P,M,A, i) (i (A)
M
j 1, jgi
ijln(pj/M) i)/ii.
This is the virtual price which supports wi = 0 and the other non-zero observed shares as the non-negativity constrained utility-maximizing choices. The remaining shares are given by wj
where
NUMj(P,M,A, i) j DEN(P,M,A, i)
NUMj(P,M,A, i) j (A)
M
k
DEN(P,M,A, i)
and
N M
j 1
j (A)
1, k g i N M
j 1
jkln(pk/M) jiln(%i(P,M,A, i))
N
[
M
,
k 1, kgi
jkln(vk) jiln(%i(P,M,A, i))].
This implies
j = DEN(P,M,A, i)wj - NUMj(P,M,A, i).
(A-5)
Consequently, the likelihood function for this observation is
L1(w| ,(,P,M,A)
1 |DEN(P,M,A, i)|N 2(2%)((N 1)/2)|(| 1/2exp( ( 1 ))d i 2
P
( i (A)
M ln(p /M)) N
k 1
ik
k
where the remaining elements of the (N-1)-dimensional vector besides i are given in (A-5). Because of this dependence of each of these j on i, this integral cannot be written as a multivariate normal probability. Consequently, general univariate numerical integration techniques must be employed to compute this likelihood function value. We use an algorithm suggested by Gill and Miller (1972).
49
The computing the likelihood function for the case of two zeros follows this same process. Suppose that piv(p) pi and pjv (p) pj for two i,j (1,2,...,N). This event occurs if i and j satisfy the inequalities ln(%i(P,M,A, i, j)) ln(p i/M)
(A-6)
ln(%j(P,M,A, i, j)) ln(pj/M),
where the right hand sides of the inequalities in (A-6), the expenditure normalized virtual prices for nonconsumed goods i and j, are given by
(A-7)
ln(%i(P,M,A, i, j) ln(%j(P,M,A, i, j)
ii ij
i (A)
1
ji jj
N M
m 1, mgi,j N
j (A)
M
m 1, m
gi,j
imln(pm/M) i .
jmln(pm/M) j
These are the virtual prices that support wi = 0 and wj = 0 and the remaining vector of positive shares as the solution to a budget-constrained utility maximization problem. The remaining positive shares are given by wk
(A-8)
NUMk(P,M,A, i, j) k DEN(P,M,A, i, j)
where
NUMk(P,M,A, i, j) k kiln(%i(P,M,A, i, j kjln(%j(P,M,A, i, j) N
kmln(pm/M)
M
m
1, m g i,j
DEN(P,M,A, i, j)
(A-9)
N M
k 1
N M
k 1
k (A)
[kiln(%i(P,M,A, i, j)) kjln(%j(P,M,A, i, j))
N M
m 1, mgi,j
kmln(pm/M)].
In this notation k = DEN(P,M,A, i, j)wk - NUMk (P,M,A, i , j ), so that the likelihood function for two zeros is the double integral L2(w| ,(,P,M,A)
|DEN(P,M,A,-i,-j)|N 3
P
P
0
0
ii ij ji jj
(2%)(N 1)/2|(| 1/2exp( 1/2 ( 1 ))d-id-j
where
-i -j
ln(p i/M) ln(p j/M)
ii ij ji jj
1
i (A)
j (A)
50
N M
m 1, mgi,j N M
m 1, m
gi,j
imln(pm/M) i .
jmln(pm/M) j
In terms of -i and -j, the elements of are defined as follows. The share equation disturbances for the goods with zero demands are:
i j
ii ij -i ji jj -j
i (A)
j (A)
N M
m 1 N M
m 1
imln(pm/M) .
jmln(pm/M)
The remaining N-3 k necessary to compute the likelihood function value depend on i and j through the relations given in (A-8) and (A-9). The calculation of this likelihood function requires numerical computation of a general bivariate integral because all of the elements depend on -i and -j.
51
Appendix 2 This appendix sets out a framework for determining the percentage change in long-distance service that should accompany a given percentage change in the price of local service so as to keep unchanged the total revenue collected from the population of US households by all LECs (RBOCs and independents). Using elasticity estimates from our household-level demand modeling effort and from other sources, we use it to determine the range of plausible revenue-neutral two-price changes scenarios analyzed in the paper. LEC revenues are usually classified into four categories: (1) local network services, (2) network access service, (3) long-distance network services and (4) other services. Let LR = local network revenues, AR = access revenues, TR = toll revenues and OR = other revenues, so that TOT = total revenues, satisfies the equation: TOT = LR + AR + TR + OR. We assume that LR, AR and TR are functions of the prices of local service and long-distance service, and that OR does not depend on either price. By definition of rate re-balancing, the percentage change in TOT brought about by a given percentage change in pl, the price of local service, plus the percentage change in TOT brought about by a given percentage change in pd, the price of long-distance service, should equal zero. Taking the derivative of TOT with respect to pl, yields (B-1)
0TOT 0LR 0AR 0TR 0OR . 0pl 0pl 0pl 0pl 0pl
Assuming that OR does not depend on pl, we can re-write (B-1) as: (B-2)
0TOT pl 0LR pl LR 0AR pl AR 0TR pl TR . 0pl TOT 0pl LR TOT 0pl AR TOT 0pl TR TOT
Let SJ = (J)R/TOT, where J = L, A or T, denote the share of total revenue from product J, and p TOT,pl 0TOT l 0pl TOT
and
p (J)R,p l 0(J)R l , 0pl (J)R
denote, respectively, the elasticities of TOT with respect to pl and the elasticity of revenue from product J with respect to pl. Using these definitions, we can re-write (B-2) as (B-3) Define
TOT,pl SLRLR,p l SARAR,pl STRTR,p l. p J,pl 0J l as the elasticity of the quantity demanded of good J with respect to pl. The 0pl J
following relationships hold between the revenue elasticities and quantity elasticities: 52
LR,pl (1 L,p l),
(B-4)
AR,p l A,pl and TR,p l T,pl.
Using the household-level elasticities computed from the model estimates and the CES sampling weights, our models of household-level demand provide one source of estimates of these demand elasticities for the population of US households. Substituting the relations in (B-4) into (B-3) yields:
TOT,pl SLR(1 L,p l) SARA,pl STRT,p l.
(B-5)
Repeating (B-1) through (B-3) for pd yields:
TOT,pd SLRLR,p d SARAR,pd STRTR,p d.
(B-6)
Analogous expressions to those in (B-4) are:
LR,pd L,p d,
(B-7)
AR,p d (
pd pA
A,p l) and TR,pl (1 T,p l),
where pA is the price of long-distance access. The elasticity of access revenues with respect to pd embodies the results discussed in Section 2 of the paper, that there is complete pass-through of access price changes into long-distance price changes. Assuming pd = pA + pIXC, where pIXC is the price received by the IXC for a long-distance call. Assuming that all long-distance price reductions come from reductions in the price of access, implies (B-8)
0pA 0pIXC
1 and
0. 0pd 0pd
Given that AR = A×pA, computing the elasticity of AR with respect to pd using the expressions given in (B-8) yields the second equation in (B-7). Substituting (B-7) into (B-6) yields (B-9)
TOT,pd SLRL,p d SAR(
pd pA
A,pd) STR(1 T,p d).
Combining (B-5) and (B-9) yields the following expression for the rate re-balancing percentage change in the price of long-distance service that results from a given percentage change in the price of local service:
(B-10)
% pd Z(% p l), where Z
SLR(1 L,p ) SARA,p STRT,p l
SLRL,p SAR( d
pd pA
l
l
.
A,p d) STR(1 T,pd
According to the most recent USTA Annual Report (USTA, 1995), the 1994 revenue shares over all LECs (RBOCs and independents) are: SLR = 0.456, SAR = 0.318 and STR = 0.134. As discussed in Section 53
2, pA = 0.4pd, meaning that approximately 40% of the price of a long-distance call is paid in access charges, so pd/pA = 2.5. For the simple case of zero cross-price elasticities and a zero own-price elasticity for local service and -1 as the own-price elasticity of long-distance service along with the above revenue shares yields a value of Z = -0.96. This value of Z implies that the revenue neutral percent decrease in the price of longdistance service should be a little less in absolute value than the percentage increase in the price of local service considered. Using the interior solution model estimates and the CES weights for each households, we can construct estimates of the required aggregate household-level price elasticities. These aggregate elasticities are:
L,pl 0.9, L,pd 0.05, T,pd 2.0 and T,p l 0.06.
(B-11)
Assuming the price elasticity of demand for long-distance is the same whether it is provided by the LEC or the IXC implies:
A,pd T,p d and A,pl T,p l.
(B-12)
Using the elasticities given in (B-11), the ratio of pd to pA of 2.5 and the equalities in (B-12) yields Z = -1.3, which implies that the revenue neutral long-distance price decrease is 1.3 times the percentage increase in the price of local service. The boundary solution model estimates can be used to construct the following aggregate demand elasticity estimates: (B-13)
L,pl 0.4, L,pd 0.7, T,pd 1.75 and T,p l 0.4.
Substituting these elasticities into (B-10), under the same assumptions as for the interior solution estimates, gives a value for Z of -0.96, which implies that the revenue neutral price decrease in long-distance service is a little less in absolute value than the local service percentage increase. These calculations provide the basis for our combination two-price changes scenarios. All three calculations favor the equal and opposite in sign local and long-distance percentage price changes. However, because there are plausible values for the elasticities that will yield values of Z on the order of -2, we also 54
consider two-price changes scenarios with long-distance percentage price decreases that are twice the local service price increases. For example, an own-price elasticity of local service of -0.4 and an own-price elasticity of long-distance service of -1.75 combined with zero cross-price elasticities yields Z = -2.
55
References Bierens, H.J. and Pott-Butter H.A. (1990), "Specification of Household Engel Curves by Nonparametric Regression," Econometric Reviews, 9, 123-184. Blackorby, C., Primont, D., and Russell, R.R. (1977), "On Testing Separability Restrictions With Flexible Functional Forms," Journal of Econometrics, 5, 195-209. Blackorby, C., Primont, D., and Russell, R.R. (1978), Duality, Separability, and Functional Structure, New York: Elsevier/North-Holland. Blundell, R.W., Pashardes, P. and Weber, G. (1993), "What Do We Learn About Consumer Demand Patterns from Micro-data?," American Economic Review, Vol. 83, No. 3, 570-597. Breusch, T. and Pagan A. (1979), "Simple Test for Heteroscedasticity and Random Coefficient Variation," Econometrica, 47, 1287-1294. Brown, B.W. and Walker, M.B. (1989) "The Random Utility Hypothesis and Inference in Demand Systems," Econometrica, 57(4), 815-829. Browning, M.J. and Meghir, C. (1991), "The Effects of Male and Female Labour Supply on Commodity Demands," Econometrica, 59, 925-951. California Public Utilities Commission, (1994), “In the Matter of Alternative Regulatory Frameworks for Local Exchange Carriers, Decision 94-09-065, September 15, 1994. Crandall, R.W. and Waverman, L. (1995), Talk is Cheap: The Promise of Regulatory Reform in North American Telecommunications. Washington, D.C.: The Brookings Institution. Deaton, A.S. and J. Muellbauer (1980), Economics and Consumer Behavior. Cambridge: Cambridge University Press. Gabel, D. and Kennet, M.D. (1993), “Pricing of Telecommunications Services,” Review of Industrial Organization, 8, 1-14. Gill, P.E., and G.F. Miller (1972) "An Algorithm for the Integration of Unequally Spaced Data," The Computer Journal, 15, 80-83. Gourieroux, C., Monfort A. and Trognon, A. (1984), "Pseudo Maximum Likelihood Methods: Theory," Econometrica, 52(3), 681-700. Hausman, J.A., E.K. Newey, and J. Powell (1988), "Nonlinear Errors in Variables: Estimation of Some Engel Curves," 1988 Jacob Marschak Lecture of the Econometric Society, Australian Economics Congress. Houthakker, H.S. (1965), "A Note on Self-dual Preferences," Econometrica, 33: 797-801. Jorgenson, D., and L. Lau (1975), "The Structure of Consumer Preferences," Annals of Economic and Social Measurement, 4, 49-102. 56
Jorgenson, D.W., L.J. Lau, and T.M. Stoker (1982), "The Transcendental Logarithmic Model of Aggregate Consumer Behavior," in Advances in Econometrics, Vol. 1, ed. by R. Basmann and G. Rhodes, Greenwich, Connecticut: JAI Press, pp. 97-238. Lee, L.-F., and M.M. Pitt (1986), "Microeconomic Demand Systems with Binding Non-negativity Constraints: The Dual Approach," Econometrica, 54(5), 1237-1242. Leser, C.E.V. (1963), "Forms of Engel Functions," Econometrica, 31, 694-703. Lusardi, A. (1993), "Euler Equations in Micro Data: Merging Data from Two Samples," CentER Discussion Paper 9304, Tilburg University, The Netherlands. Kellogg, M.K., Thorne, J. and Huber, P.W., (1992) Federal Telecommunications Law. Boston: Little, Brown and Company. Mills, M. (1996), “Phone rates face new hike,” San Jose Mercury News, May 7, 1996, p. A1. Neary, J.P., and K.W.S. Roberts (1980), "The Theory of Household Behavior Under Rationing," European Economic Review, 13, 25-42. Sievers, M. (1994), "Should the InterLATA Restrictions Be Lifted? Analysis of the Significant Issues," Paper Presented at Rutgers University Advanced Workshop inn Regulation and Public Utility Economics, July 6-8, 1994. Silverman, B.W. (1986), Density Estimation for Statistics and Data Analysis. London: Chapman and Hall. Taylor, L.D. (1994), Telecommunications Demand in Theory and Practice. Boston: Kluwer Academic Publishers. Telecommunications Act of 1996, 104th Congress, 2nd Session, Conference Report. Washington Utilities and Transportation Commission, Docket Number UT-950200, April 11, 1996. White, H. (1980), "A Heteroscedasticity-Consistent Covariance Matrix Estimator and Direct Test for Heteroscedasticity," Econometrica, 48, 817-838. White, H. (1982), "Maximum Likelihood Estimation of Misspecified Models," Econometrica, 50(1), 1-25. Working, H. (1943), "Statistical Laws of Family Expenditure," Journal of the American Statistical Association, 38, 43-56. United States Telephone Associate, (1989), Statistics of the Local Exchange Carriers For the Year 1988, Washington, D.C. United States Telephone Associate, (1995), Statistics of the Local Exchange Carriers For the Year 1994, Washington, D.C.
57
Table 1 - Joint Empirical Distribution of Zero Expenditures
Local Long-Distance Food Clothing Other Total
11,467 Total Observations; 9,389 All-Positive Observations Local Long-Distance Food Clothing 146 4 999 0 0 0 8 209 0 712 0 0 0 0 158 1208 0 712
58
Other
0 0
Table 2 - Coefficient Estimates for Interior Model (L=local, D=long-distance, F=Food, C=clothing, O=other, and M=total expenditure)
Mi
Coefficient
L D F C LL LD LF LC DD DF DC FF FC CC ML MD MF MC MO
N M
j 1
ij, assuming ij ji. Estimate -1.86e-02 -3.49e-02 -2.77e-01 -1.52e-01 -2.07e-03 -1.02e-03 -6.46e-03 -5.27e-03 1.90e-02 -3.48e-02 -1.26e-02 1.22e-01 -6.71e-02 1.07e-01 -9.92e-03 4.07e-04 3.42e-02 4.94e-02 1.59e-01
59
Standard Error 1.54e-03 3.91e-03 1.88e-02 1.20e-02 1.12e-02 4.71e-03 1.01e-02 5.38e-03 5.92e-03 1.41e-02 8.49e-03 6.43e-02 3.13e-02 2.77e-02 1.54e-03 7.62e-04 8.62e-03 7.14e-03 2.31e-02
(Table 2 Continued) Estimate Standard Error Lk, k=1,2,...,K (Demographics for Local Share Equation) -2 Age of Head × 10 -8.11e-04 1.02e-02 (Age of Head)2 × 10-4 -6.61e-04 1.04e-02 Number of Family Members -1.12e-03 3.02e-04 Members 65 years old -3.48e-04 7.26e-04 Head White (Dummy) 7.32e-04 6.96e-04 Head Female (Dummy) 4.42e-06 7.80e-04 Head College Graduate (Dummy) 1.32e-03 1.11e-03 Head HS Graduate (Dummy) 3.77e-04 7.24e-04 Head Single (Dummy) 7.91e-05 1.25e-03 Head Professional (Dummy) 8.59e-05 7.79e-04 Head Hours Worked per Year -4.19e-03 4.81e-03 Spouse Hours Worked per Year -1.13e-04 4.78e-03 Head Non-Worker (Dummy) 1.98e-03 1.10e-03 Spouse Non-Worker (Dummy) 1.99e-04 1.15e-03 Males Age 2 through 15 1.16e-03 4.23e-04 Females Age 2 through 15 6.17e-04 3.74e-04 North East (Dummy) 3.20e-03 1.46e-03 North Central (Dummy) 1.85e-03 1.07e-03 South (Dummy) 2.22e-03 1.10e-03 West (Dummy) 3.18e-03 1.06e-03 Dk, k=1,2,...,K (Demographics for Long-Distance Share Equation) Age of Head × 10-2 3.85e-02 1.25e-02 2 -4 (Age of Head) × 10 -1.57e-02 1.23e-02 Number of Household Members -3.11e-03 7.19e-04 Members 65 years old -3.13e-04 8.39e-04 Head White (Dummy) -1.93e-04 1.09e-03 Head Female (Dummy) -2.92e-03 1.20e-03 Head College Graduate (Dummy) -3.29e-03 1.74e-03 Head HS Graduate (Dummy) -3.93e-04 8.93e-04 Head Single (Dummy) -1.41e-03 2.00e-03 Head Professional (Dummy) 6.57e-04 1.16e-03 Head Hours Worked per Year 9.62e-03 7.08e-03 Spouse Hours Worked per Year 9.92e-03 7.18e-03 Head Non-Worker (Dummy) 5.55e-03 1.82e-03 Spouse Non-Worker (Dummy) 6.57e-05 1.71e-03 Males Age 2 through 15 4.94e-03 1.04e-03 Females Age 2 through 15 3.88e-03 8.84e-04 North East (Dummy) 1.06e-02 2.16e-03 North Central (Dummy) 9.38e-03 1.71e-03 South (Dummy) 7.68e-03 1.69e-03 West (Dummy) 2.96e-03 1.79e-03 Coefficient
60
(Table 2 Continued) Estimate Standard Error Fk, 1,2,...,K (Demographics for Food Share Equation) -2 Age of Head × 10 -1.21e-03 1.49e-01 (Age of Head)2 × 10-4 -8.22e-03 1.44e-01 Number of Household Members -1.94e-02 5.40e-03 Members 65 years old -1.35e-02 1.22e-02 Head White (Dummy) -3.88e-02 1.18e-02 Head Female (Dummy) 3.56e-02 1.31e-02 Head College Graduate (Dummy) 3.56e-02 1.79e-02 Head HS Graduate (Dummy) 1.47e-02 1.07e-02 Head Single (Dummy) -5.43e-03 2.45e-02 Head Professional (Dummy) 6.18e-03 1.36e-02 Head Hours Worked per Year 7.60e-03 7.79e-02 Spouse Hours Worked per Year -1.13e-02 9.74e-02 Head Non-Worker (Dummy) 3.07e-02 1.73e-02 Spouse Non-Worker (Dummy) -1.34e-02 2.40e-02 Males Age 2 through 15 1.04e-02 8.60e-03 Females Age 2 through 15 7.64e-04 6.32e-03 North East (Dummy) -1.81e-02 2.93e-02 North Central (Dummy) 1.58e-02 1.82e-02 South (Dummy) 2.95e-02 1.77e-02 West (Dummy) -2.46e-02 2.20e-02 Ck, k=1,2,...,K (Demographics for Clothing Share Equation) Age of Head × 10-2 2.16e-01 3.44e-02 2 -4 (Age of Head) × 10 -1.64e-01 3.16e-02 Number of Household Members 1.94e-03 1.25e-03 Members 65 years old -6.07e-04 2.63e-03 Head White (Dummy) 5.46e-03 2.78e-03 Head Female (Dummy) -2.05e-02 4.40e-03 Head College Graduate (Dummy) -4.65e-03 5.27e-03 Head HS Graduate (Dummy) 4.72e-05 2.52e-03 Head Single (Dummy) 1.48e-02 6.39e-03 Head Professional (Dummy) -1.37e-02 4.33e-03 Head Hours Worked per Year -2.74e-02 2.45e-02 Spouse Hours Worked per Year 3.42e-02 2.80e-02 Head Non-Worker (Dummy) 2.64e-03 4.80e-03 Spouse Non-Worker (Dummy) 9.10e-03 6.26e-03 Males Age 2 through 15 4.68e-03 2.35e-03 Females Age 2 through 15 -1.80e-03 2.11e-03 North East (Dummy) -9.77e-03 7.15e-03 North Central (Dummy) -7.19e-03 4.71e-03 South (Dummy) 3.60e-04 4.74e-03 West (Dummy) 3.60e-04 4.74e-03 Coefficient
61
(Table 2 Continued) Estimate Standard Error Ok, k=1,2,...,K (Demographics for Other Share Equation) -2 Age of Head × 10 1.16e-01 1.73e-01 (Age of Head)2 × 10-4 -2.12e-01 1.65e-01 Number of Household Members 3.23e-03 4.85e-03 Members 65 years old -1.89e-02 1.59e-02 Head White (Dummy) -5.26e-02 1.47e-02 Head Female (Dummy) -2.98e-03 1.58e-02 Head College Graduate (Dummy) 1.38e-02 2.43e-02 Head HS Graduate (Dummy) -9.38e-03 1.33e-02 Head Single (Dummy) 4.45e-02 3.04e-02 Head Professional (Dummy) 7.79e-03 1.78e-02 Head Hours Worked per Year 4.22e-02 1.01e-01 Spouse Hours Worked per Year 6.30e-02 1.33e-01 Head Non-Worker (Dummy) 7.12e-02 2.23e-02 Spouse Non-Worker (Dummy) 2.53e-02 3.01e-02 Males Age 2 through 15 2.19e-02 9.68e-03 Females Age 2 through 15 5.90e-03 7.61e-03 North East (Dummy) 3.81e-02 3.68e-02 North Central (Dummy) 5.77e-02 2.44e-02 South (Dummy) 8.40e-02 2.46e-02 West (Dummy) 5.11e-02 2.60e-02 Coefficient
62
Table 3 - Coefficient Estimates for Boundary Model (L=local, D=long-distance, F=Food, C=clothing, O=other, and M=total expenditure)
Mi
L D F C LL LD LF LC DD DF DC FF FC CC ML MD MF MC MO
N M
j 1
ij, assuming ij ji.
Estimate
Standard Error
-2.10e-02 -1.64e-02 -3.18e-01 -1.17e-01 -6.86e-03 5.05e-03 -5.49e-03 -7.14e-05 6.12e-03 -1.20e-03 -4.05e-03 -2.75e-02 -8.78e-03 3.65e-02 -3.94e-03 -4.36e-05 2.31e-02 2.84e-02 8.70e-02
5.21e-04 1.07e-03 5.83e-03 4.52e-03 9.79e-04 4.31e-04 1.88e-03 9.35e-04 5.27e-04 1.50e-03 6.38e-04 2.33e-02 1.08e-02 9.00e-03 1.20e-04 2.01e-04 1.05e-03 7.97e-04 1.19e-03
63
(Table 3: Boundary model estimates, cont'd) Coefficient
Estimate
Std Error
2.77e-02 -2.90e-02 3.26e-05 8.12e-03 2.83e-04 7.11e-04 1.32e-03 1.06e-04 -2.14e-04 -1.66e-04 1.02e-03 5.41e-04 4.37e-03 -6.75e-07 -1.63e-04 1.99e-03 3.18e-03 1.47e-03 1.68e-03 2.56e-03
1.91e-03 2.07e-03 7.94e-04 1.06e-03 6.99e-05 1.55e-04 1.53e-04 1.48e-04 1.24e-04 1.25e-04 1.84e-04 1.44e-04 2.38e-04 1.32e-04 2.28e-04 2.26e-04 2.33e-04 1.85e-04 1.91e-04 2.01e-04
Lk, k=1,2,...,K (Demographics for Local Share Equation)
Age of Head × 10-2 (Age of Head)2 × 10-4 Head hours worked per year Spouse hours worked per year Number of Household Members Members > 65 years old Head White (Dummy) Head Female (Dummy) Males aged 2 to 15 Females aged 2 to 15 Head College Grad (Dummy) Head HS Grad (Dummy) Head Single (Dummy) Head Professional (Dummy) Head Non-worker (Dummy) Spouse Non-worker (Dummy) Northeast (Dummy) North Central (Dummy) South (Dummy) West (Dummy)
Dk, k=1,2,...,K (Demographics for Long Distance Share Equation) Age of Head × 10-2 (Age of Head)2 × 10-4 Head hours worked per year Spouse hours worked per year Number of Household Members Members > 65 years old Head White (Dummy) Head Female (Dummy) Males aged 2 to 15 Females aged 2 to 15 Head College Grad (Dummy) Head HS Grad (Dummy) Head Single (Dummy) Head Professional (Dummy) Head Non-worker (Dummy) Spouse Non-worker (Dummy) Northeast (Dummy) North Central (Dummy) South (Dummy) West (Dummy)
1.15e-02 -5.55e-03 3.29e-04 1.02e-02 -1.80e-04 4.39e-04 7.65e-04 -8.47e-04 5.15e-04 8.91e-04 -1.25e-03 -8.32e-06 3.25e-03 4.82e-05 -3.13e-05 1.64e-03 4.42e-03 4.18e-03 2.84e-03 2.12e-03
64
3.91e-03 4.29e-03 1.46e-03 1.83e-03 1.25e-04 2.87e-04 2.89e-04 2.65e-04 2.08e-04 2.15e-04 3.40e-04 2.75e-04 4.28e-04 2.47e-04 4.29e-04 3.96e-04 4.13e-04 3.15e-04 3.15e-04 3.21e-04
(Table 3: Boundary model estimates, cont'd) Coefficient
Estimate
Std Error
3.48e-01 -3.47e-01 4.39e-02 1.29e-01 4.27e-03 5.19e-03 -4.87e-03 1.37e-02 -9.57e-03 -6.96e-03 2.20e-02 1.02e-02 6.82e-02 3.94e-03 7.31e-03 2.50e-02 2.46e-02 1.90e-02 2.72e-02 8.36e-03
2.07e-02 2.21e-02 7.94e-03 9.82e-03 7.10e-04 1.60e-03 1.73e-03 1.55e-03 1.19e-03 1.27e-03 1.92e-03 1.52e-03 2.28e-03 1.35e-03 1.79e-03 2.07e-03 2.26e-03 1.82e-03 1.85e-03 1.94e-03
Fk, k=1,2,...,K (Demographics for Food Share Equation)
Age of Head × 10-2 (Age of Head)2 × 10-4 Head hours worked per year Spouse hours worked per year Number of Household Members Members > 65 years old Head White (Dummy) Head Female (Dummy) Males aged 2 to 15 Females aged 2 to 15 Head College Grad (Dummy) Head HS Grad (Dummy) Head Single (Dummy) Head Professional (Dummy) Head Non-worker (Dummy) Spouse Non-worker (Dummy) Northeast (Dummy) North Central (Dummy) South (Dummy) West (Dummy)
Ck, k=1,2,...,K (Demographics for Clothing Share Equation) Age of Head × 10-2 (Age of Head)2 × 10-4 Head hours worked per year Spouse hours worked per year Number of Household Members Members > 65 years old Head White (Dummy) Head Female (Dummy) Males aged 2 to 15 Females aged 2 to 15 Head College Grad (Dummy) Head HS Grad (Dummy) Head Single (Dummy) Head Professional (Dummy) Head Non-worker (Dummy) Spouse Non-worker (Dummy) Northeast (Dummy) North Central (Dummy) South (Dummy) West (Dummy)
1.74e-01 -1.38e-01 -1.71e-02 6.41e-02 4.59e-03 1.07e-04 7.14e-03 -9.53e-03 -1.44e-03 -3.06e-03 -4.84e-04 3.87e-04 2.84e-02 -6.93e-03 -4.70e-03 1.75e-02 6.89e-05 -2.88e-03 2.94e-03 2.71e-03
65
1.61e-02 1.76e-02 5.66e-03 7.03e-03 5.17e-04 1.12e-03 1.17e-03 1.06e-03 8.63e-04 8.34e-04 1.33e-03 1.13e-03 1.68e-03 9.90e-04 1.76e-03 1.58e-03 1.63e-03 1.32e-03 1.33e-03 1.43e-03
(Table 3: Boundary model estimates, cont'd) Coefficient
Estimate
Std Error
6.30e-01 -6.61e-01 2.94e-02 2.77e-01 1.92e-02 6.42e-03 -4.84e-03 -1.69e-03 -8.30e-03 -8.12e-03 2.00e-02 2.73e-03 1.30e-01 2.72e-03 -2.36e-03 6.84e-02 5.21e-02 4.09e-02 5.27e-02 4.45e-02
2.33e-02 2.49e-02 9.14e-03 1.18e-02 8.09e-04 1.78e-03 1.88e-03 1.68e-03 1.39e-03 1.39e-03 2.12e-03 1.70e-03 2.73e-03 1.53e-03 2.51e-03 2.71e-03 2.50e-03 2.03e-03 2.08e-03 2.15e-03
Ok, k=1,2,...,K (Demographics for Other Share Equation)
Age of Head × 10-2 (Age of Head)2 × 10-4 Head hours worked per year Spouse hours worked per year Number of Household Members Members > 65 years old Head White (Dummy) Head Female (Dummy) Males aged 2 to 15 Females aged 2 to 15 Head College Grad (Dummy) Head HS Grad (Dummy) Head Single (Dummy) Head Professional (Dummy) Head Non-worker (Dummy) Spouse Non-worker (Dummy) Northeast (Dummy) North Central (Dummy) South (Dummy) West (Dummy)
Price Heterogeneity Probability and Support Points Estimates
%2,Urban %2,Rural 1,Urban 1,Rural 2,Urban 2,Rural 1,Urban 1,Rural 2,Urban 2,Rural
4.66e-02 4.52e-02 1.05e+00 1.05e+00 6.33e-02 4.21e-02 1.05e+00 1.05e+00 1.96e-02 1.50e-02
66
2.52e-03 5.30e-03 2.71e-03 5.60e-03 1.81e-02 1.39e-02 2.75e-03 5.74e-03 8.75e-03 7.36e-03
Table 4 -- Share Disturbance Heteroscedasticity Test LM Test Statistics - Interior Model Share Equation
Interior Model
Local Expenditure
268.38
Long-Distance Expenditure
101.94
Food Expenditure
288.16
Clothing Expenditure
164.80
Other Expenditure
288.08
3227,=0.05 = 40.11, 3227,=0.01 = 46.96
Table 5 -- Own-Price and Expenditure Elasticity Estimates (L=local, D=long-distance, F=food, C=clothing, O=other, M=expenditure) Mean, 5th percentile, and 95th percentile values Interior Model
Boundary Model
Elasticity
Mean
5th%
95th%
Mean
5th%
95th%
eL,L
-0.88
-0.96
-0.79
-0.39
-0.54
-0.26
eD,D
-2.07
-3.02
-1.62
-1.80
-2.38
-1.50
eF,F
-1.35
-1.49
-1.27
-0.76
-0.83
-0.63
eC,C
-2.85
-4.99
-1.70
-3.53
-7.76
-1.51
eO,O
-1.00
-1.03
-0.98
-0.88
-0.91
-0.82
eM,L
0.11
-0.28
0.33
0.30
0.11
0.45
eM,D
0.75
0.63
0.82
0.65
0.45
0.77
eM,F
0.84
0.74
0.89
0.81
0.68
0.89
eM,C
1.61
1.12
2.51
2.68
1.18
5.86
eM,O
1.11
1.06
1.22
1.12
1.05
1.29
67
Table 6A - Sample Distribution of Household-Level Compensating Variations For Price Change Scenarios January 1988 dollars (Interior and Boundary Models) Interior Model
Boundary Model
Scenario 5th%
Mean
95th%
5th%
Mean
95th%
PL +20% PD +0%
6.98
9.45
12.12
6.82
9.26
11.91
PL +40% PD +0%
13.01
17.59
22.61
13.06
17.86
23.12
PL +20% PD -20%
-15.94
-3.48
4.04
-0.8
2.66
5.6
PL +40% PD -40%
-32.12
-7.95
6.52
0.09
6.14
11.46
PL +10% PD -20%
-20.78
-7.96
0.19
-6.52
-2.23
1.28
PL +20% -40.56 -15.91 -0.29 -11.37 PD -40% Note: PL = Price of local service, PD = price of long-distance service.
-3.60
2.78
Table 6B - Estimated US Population Distribution of Compensating Variations For Price Change Scenarios January 1988 dollars - Using CES Weights (Interior and Boundary Models) Interior Model
Boundary Model
Scenario
Mean
Median
Mean
Median
PL +20% PD +0%
9.43
9.39
9.24
9.17
PL +40% PD +0%
17.55
17.49
17.83
17.68
PL +20% PD -20%
-2.95
-1.99
2.61
2.81
PL +40% PD -40%
-6.91
-5.06
6.03
6.34
PL +10% PD -20%
-7.41
-6.56
-2.27
-1.97
-3.68
-3.13
PL +20% -14.85 -13.18 PD -40% Note: PL = Price of local service, PD = price of long-distance service. 68
Table 7A - Sample Distribution of Household-Level Percent True Cost-of-Living Increases For Price Change Scenarios (Interior and Boundary Models) Interior Model
Boundary Model
Scenario 5th%
Mean
95th%
5th%
Mean
95th%
PL +20% PD +0%
0.16
0.42
0.84
0.33
0.56
0.98
PL +40% PD +0%
0.29
0.78
1.56
0.65
1.08
1.87
PL +20% PD -20%
-0.30
-0.04
0.35
-0.03
0.20
0.56
PL +40% PD -40%
-0.60
-0.14
0.56
0.00
0.44
1.13
PL +10% PD -20%
-0.45
-0.24
0.01
-0.26
-0.10
0.12
PL +20% -0.87 -0.49 -0.02 -0.44 PD -40% Note: PL = Price of local service, PD = price of long-distance service.
-0.15
0.25
Table 7B - Estimated US Population Distribution of Percent True Cost-ofLiving reases For Price Change Scenarios (Interior and Boundary Models) Interior Model
Boundary Model
Scenario
Mean
Median
Mean
Median
PL +20% PD +0%
0.43
0.38
0.56
0.51
PL +40% PD +0%
0.81
0.70
1.07
0.98
PL +20% PD -20%
-0.03
-0.08
0.19
0.16
PL +40% PD -40%
-0.12
-0.20
0.43
0.36
PL +10% PD -20%
-0.24
-0.26
-0.10
-0.11
PL +20% -0.48 -0.52 -0.15 PD -40% Note: PL = Price of local service, PD = price of long-distance service.
-0.18
69
Table 8 -- Best Linear Predictor of Percent True Cost-of-Living Increase for Interior Model Estimates (PL +20% and PD -40 % Scenario) Estimated Variable
Coefficient
Constant
Std. error
-2.97e-01
1.54e-02
1.04
3.92e-02
4.81e-02
4.39e-02
Number of Family Members
-7.69e-02
9.49e-04
Members 65 years old
-1.77e-02
2.17e-03
Head White (Dummy)
2.91e-02
2.84e-03
Head Female (Dummy)
-1.14e-01
1.85e-03
Head College Graduate (Dummy)
-1.88e-01
2.44e-03
Head HS Graduate (Dummy)
-4.11e-02
2.00e-03
Head Single (Dummy)
-8.49e-02
2.65e-03
Head Professional (Dummy)
2.32e-02
1.40e-03
Head Hours Worked per Year
5.08e-01
9.84e-03
Spouse Hours Worked per Year
3.29e-01
1.00e-02
Head Non-Worker (Dummy)
1.38e-01
3.21e-03
-2.45e-02
2.27e-03
Males Age 2 through 15
1.32e-01
1.37e-03
Females Age 2 through 15
1.25e-01
1.37e-03
North East (Dummy)
3.04e-01
2.63e-03
North Central (Dummy)
2.87e-01
2.01e-03
South (Dummy)
1.52e-01
2.05e-03
West (Dummy)
5.75e-02
2.06e-03
Log of Non-Durable Expenditure
-9.70e-02
1.87e-03
Age of Head x 10-2 (Age of Head)2 x 10-4
Spouse Non-Worker (Dummy)
Note: White (1980) heteroscedasticity-consistent standard error estimates
70
Table 9 -- Best Linear Predictor of Percent True Cost-of-Living Increase for Boundary Model Estimates (PL +20% and PD -40% Scenario) Estimated Variable
Coefficient
Std. error
Constant
9.21e-01
3.35e-02
Age of Head x 10-2
-8.62-01
4.76e-02
1.49
5.03e-02
Number of Family Members
-3.93e-02
2.01e-03
Members 65 years old
-2.24e-02
2.96e-03
Head White (Dummy)
4.05e-03
3.66e-03
Head Female (Dummy)
-5.76e-02
3.85e-03
Head College Graduate (Dummy)
-1.76e-01
4.34e-03
Head HS Graduate (Dummy)
-3.54e-02
2.66e-03
Head Single (Dummy)
-6.98e-02
6.38e-03
Head Professional (Dummy)
4.38e-03
2.62e-03
Head Hours Worked per Year
5.23e-02
1.71e-02
Spouse Hours Worked per Year
1.58e-01
1.84e-02
Head Non-Worker (Dummy)
2.19e-02
5.10e-03
Spouse Non-Worker (Dummy)
-4.50e-02
4.13e-03
Males Age 2 through 15
6.16e-02
2.64e-03
Females Age 2 through 15
8.76e-02
2.74e-03
North East (Dummy)
1.86e-01
8.14e-03
North Central (Dummy)
2.40e-01
3.07e-03
South (Dummy)
9.68e-02
3.09e-03
West (Dummy)
1.15e-02
3.90e-03
Log of Non-Durable Expenditure
-1.40e-01
3.90e-03
(Age of Head)2 x 10-4
Note: White (1980) heteroscedasticity-consistent standard error estimates.
71
Figure 1: Corner Solution in Actual Price (P2) and Interior Solution in Virtual Price (P2*)
72
Figure 2: Densities of Household-Level Local Telephone Expenditure in January 1988 Dollars by Quartiles of Total Non-Durable Expenditure Distribution
Figure 3: Densities of Household-Level Long-Distance Telephone Expenditure in January 1988 Dollars by Quartiles of Total Non-Durable Expenditure Distribution
73
Figure 4: Densities of Household-Level Total Telephone Expenditure in January 1988 Dollars by Quartiles of Total Non-Durable Expenditure Distribution
Figure 5: Monthly Price Indexes for Nominal and Real Local and Long-Distance Telephone Service
74
Figure 6: Densities of Sample Household-Level Compensating Variations in January 1988 Dollars for Price Change Scenarios for Interior Model Estimates
Figure 7: Densities of Sample Household-Level Compensating Variations in January 1988 Dollars for Price Change Scenarios for Boundary Model Estimates
75
Figure 8: Densities of Sample Household-Level True Cost-of-Living Increases for Price Change Scenarios for Interior Model Estimates
Figure 9: Densities of Sample Household-Level True Cost-of-Living Increases for Price Change Scenarios for Boundary Model Estimates
76
