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Finance and Economics Discussion Series: 2008-12 Screen Reader version ^♣

The Effect of Satellite Entry on Product Quality for Cable Television*

Chenghuan Sean Chu

January 2008

Keywords: Entry, endogenous quality, vertical differentiation, bundling

Abstract:

In vertically differentiated markets, the effects of firm entry are contingent upon whether incumbent firms can respond to entry by adjusting product quality in addition to simply lowering prices. Using market-level data, I estimate a structural model of supply and demand for subscription television that takes into account the endogeneity of quality choice. Using counterfactual analysis, I decompose the effect of satellite entry on existing cable into two components: the conventional price response and the effect of endogenous quality adjustments (measured by changes in programming content). Consistent with the empirical observation that cable prices rose during the 1990s and early 2000s "in spite of" increasing competition, I find that raising both price and quality for the most comprehensive subscription package--i.e., competing "head-to-head"--is the rational response to entry by cable systems in markets with relatively homogeneous consumer types. Elsewhere, incumbents respond less aggressively and relegate themselves to being the low-end provider. When an entrant credibly commits to serving consumers with the highest preferences for quality, competition over both price and quality lowers the welfare gains due to entry, relative to pure price competition. In particular, head-to-head competition results in "crowding" of quality choices toward the high end of the market and inefficiently low product differentiation. In such cases, consumers with weak quality preferences may actually become worse off following entry. The evidence also suggests that the observed degradation of the lowest-quality cable tier in many markets during this time period--while commonly seen as an attempt to evade price regulation--may actually have been welfare-enhancing.

1 Introduction

A number of models imply that when firms have fixed costs, excess entry can result in social inefficiencies (Berry and Waldfogel, 1999; Anderson, de Palma and Nesterov, 1995). However, when markets are vertically differentiated, entry can also lead to inefficiencies through its effect on firms' choice of product characteristics, even with zero fixed costs. In the common case in which a "new and improved" good enters the market, the efficiency gains due to price competition may be mitigated by the endogenous quality response. In particular, the tendency for firms to crowd into the high end of the market implies that private incentives lead to insufficient product differentiation.

Because firms are competing over both price and quality, the welfare impact depends on the relative effect of entry on each dimension. Just as a monopolist decides on how "downmarket" to go by choosing the proportion of consumers with low quality preferences to exclude, ¹ an incumbent faced with a higher-quality entrant must also choose the proportion of high-end consumers to cede to the new firm. The optimal incumbent response may involve lowering both quality and price (differentiating downward), raising quality and price (competing "head-to-head"), or some combination of lowering price and raising quality ("fighting"). The choice of response depends on cost and demand factors, as well as on whether the entrant can commit to high quality.

I study these issues empirically in the subscription television industry. Until the entry of Direct Broadcast Satellite (DBS) in 1994, most cable firms were local monopolies. The entry of satellite brought a higher-quality substitute with more channels and a clearer picture. In the years before and after entry, the average cable firm also expanded channel offerings in its most comprehensive package. Previous authors attribute this effect to increased competition. ² However, average trends mask a considerable degree of heterogeneity in the supply response, and one of my contributions is to explain the relationship between the incumbent response and local market conditions.

I begin by estimating a structural model of supply and demand, in which consumers have heterogeneous preferences over content quality (measured by the amount of television programming), the satellite firm commits to offering a high-end good, and cable firms endogenously choose prices and quality levels. In the estimation, I exploit optimality conditions on consumer choice and on price-setting by the cable firms, and account for the endogeneity of cable quality through the use of instrumental variables. Because I do not impose optimality of quality choices in the estimation, the relationship between my parameter estimates and a firm's actual quality choices is not predetermined. However, actual cable menus are generally similar to the profit-maximizing outcomes.

The structural estimates make possible the key methodological contribution of this paper, which is a decomposition of the effects of entry into separate components corresponding to competition over price and competition over quality. First, I determine the overall effect of entry by computing the optimal choice of price and quality, in response to satellite as well as for the counterfactual scenario in which entry does not occur, and taking the difference. This comparison indicates that entry induces head-to-head competition in the majority of markets, dampening the oft heard complaint ³ that satellite entry has been ineffective in constraining growth in cable prices: while non-quality-adjusted prices have indeed risen in most cities, raising both price and quality is the incumbent firm's competitive response to entry. At the same time, head-to-head is by no means the universal response, for in other markets, entry induces the cable firm either to "fight" or to differentiate downward. Controlling for firm costs, for differences in satellite quality across locations, and for other "brand effects," the latter response is most likely to occur in markets in which consumers are relatively heterogeneous in their willingness to pay for quality.

The second step of the decomposition involves computing the profit-maximizing prices under actual entry conditions, but conditional on product qualities being held fixed at the optimal monopoly levels. In other words, I determine the optimal price response if incumbent firms were prevented from adjusting programming contents following entry. The contribution of the pure price response to the overall effect of entry is indicated by the difference in outcomes between this counterfactual ("no quality adjustment") and the previous counterfactual ("no entry"). Similarly, we can determine the contribution of endogenous quality adjustments by differencing between the no-quality-adjustment counterfactual and outcomes under the jointly optimal price and quality response.

While entry is unambiguously welfare-enhancing for consumers when firms only compete over price, taking into account endogenous quality adjustments implies that the overall effect of entry may actually make some consumers worse off. In many cases, the incumbent response actually creates "too much" quality, especially in markets where the cable system competes head-to-head. Because the entry-induced changes in cable offerings are determined by the preferences of consumer types that are marginal between consuming cable and satellite, and because such consumers have higher preferences for quality than the typical cable consumer, consumers as a whole would be better off if firms had a lower propensity to compete for the high-end market. Aggregate consumer surplus would be 4.3% higher ($118M for the entire economy, over the course of the representative year 1997) if the firms competed only over price. This aggregate loss of welfare reflects a combination of small changes in welfare for consumers with high preferences for content quality, together with large welfare losses for consumers with low preferences for content quality. Moreover, under conservative assumptions about satellite profit margins, total surplus would be $389M higher economywide (for the representative year 1997) if firms competed only over price.

Although the empirical model maintains that cable firms optimize prices jointly for all goods, my discussion focuses on the price and quality of the top cable package. This emphasis is motivated by the far greater empirical significance of the top package. While the average number of packages offered by each firm has increased over time, only 24% of all cable systems offer two or more packages in the average year. Even among firms offering multiple goods, the top good accounts for 86% of the total market share. Moreover, because satellite is a higher-quality substitute for cable, the first-order impact of competition is manifested at the top of the cable menu.

Nonetheless, my findings also give a new angle to recent controversies over quality degradation at the bottom of the cable menu. Consumer groups have alleged that cable systems remove channels from the bottom good in order to evade regulation of basic cable prices. ⁴ I cannot directly address the validity of this claim. However, I do find evidence that among cable markets offering two or more packages, all consumers (including those with low willingness to pay for quality) tend to benefit more from entry in exactly those markets in which the incumbent firm either degrades or leaves unchanged the quality of the lower good. With cable firms crowding toward the high-end market with their top product tier, keeping quality low at the bottom of the cable menu helps to preserve a greater degree of product heterogeneity. Having greater product heterogeneity is welfare-enhancing, because it gives consumers with low willingness to pay more alternatives besides purchasing nothing at all or purchasing a high-quality but expensive good.

The rest of this paper is organized as follows. The following section reviews prior research. Section 3 describes the data and surveys the observed heterogeneity in cable menu changes from 1994 to 2002. In Section 4, I present a model showing how demand conditions affect the nature of the incumbent's response to entry. This model also guides the empirical estimation. Section 5 presents the estimation results, counterfactual exercises, and welfare analysis. Section 6 concludes.

2 Prior Literature

Other than government reports (GAO, 2000; FCC, 2006), the primary existing study of the effect of DBS entry on cable is by Goolsbee and Petrin (2004). Goolsbee and Petrin estimate household demand for cable and satellite, quantify the aggregate consumer surplus gains due to entry, and find that higher satellite quality--as captured by an estimated fixed effect in each market--is negatively correlated with cable prices and positively correlated with cable quality. My study builds on theirs by investigating how firms jointly choose optimal prices and qualities in response to entry. In contrast to their focus on average effects, I am able to explain why different firms make different tradeoffs between quality and price changes, and explore the welfare implications of these decisions.

Another key difference in approach is that while Goolsbee and Petrin treat all cable subscriptions as a single good, ⁵ I account for the fact that cable menus often offer several vertically differentiated tiers. In this regard, my research draws from the work of Crawford and Shum (2005), who study quality- and price-setting using a screening model of price discrimination, but without taking into account the effect of competition. Crawford and Shum find that under monopoly, significant quality degradation occurs at the bottom of the cable menu, relative to socially optimal levels. In other work, Crawford and Shum (2006) establish that regulation of minimum cable quality tends to reduce the amount of degradation. My analysis of the entry of a high-end entrant serves as a counterpoint to Crawford and Shum's investigation of regulation at the bottom of the menu.

3 The Subscription Television Industry

This section provides background information on the subscription television industry and describes the data used in my analysis. Subscription television is an ideal industry in which to study the effect of a high-quality entrant on the behavior of a price- and quality-setting monopolist. Except for a handful of systems facing competition from "overbuilds," cable systems generally hold local monopolies, on terms negotiated with the city franchising authority. Moreover, except for certain rudimentary standards imposed by regulators (discussed below), firms exercise almost complete discretion over quality levels. As a result, quality is largely dictated by strategic considerations.

Individual cable networks are bundled together and sold as tiered services, with the lowest tier typically sold as "Basic Cable" and ones above it as "Expanded Basic," "Expanded Basic 2," and so on. ⁶ Tiers are "nested"--with all channels in a given tier also included in the ones above it--making cable television a textbook example of a vertically differentiated good. An exception to this rule are the pay-per-view and premium movie channels, which are sold on an a-la-carte basis. The arrival of DirecTV's DBS service in 1994 brought the first true substitute for cable. Similar to cable, the DBS firms offer nested service tiers, and also deliver many of the same networks. In 1997, Echostar's Dish Network entered the market with a slightly less expensive (and somewhat lower quality) DBS service. DirecTV and Dish Network have grown to claim 12.3M and 9.4M households in 2002, respectively, compared to 64.5M subscribers for cable.

From the start, the satellite subscriptions offered higher quality than most cable tiers. For example, within a year of their respective launch dates, DirecTV's flagship Total Choice package delivered 39 channels, and Dish Network's standard America's Top 40 delivered 42 channels, in addition to optional sports subscriptions and other programming unavailable to cable consumers. By comparison, in 1995 the high cable good had only 14.1 channels on average, and 34 channels at the 99th percentile of the distribution of bundle sizes. DirecTV also offered a degraded "budget" package, but this lower-quality alternative was unpopular and, moreover, still offered more channels than the highest cable tier in most markets. ⁷ The high quality of satellite is also reflected in its price. In 1997, Total Choice cost $29.95 per month, compared to a mean of $20.25 for the highest cable tier. America's Top 40 cost less than Total Choice, at $19.99, but as in the case of DirecTV, involved much higher installation fees than is typical for cable.

While each satellite firm offers a single nationwide menu, cable menus are set individually for each market. In part because of technological constraints, ⁸ satellite subscriptions offer virtually identical products across markets, apart from slight differences in regional sports networks. By contrast, even cable Multiple System Operators (MSOs) such as Time Warner Cable, Cox Cable, and Comcast typically offer different products across locations.

An open question is why satellite firms do not price discriminate across markets. ⁹ One possibility is that precommitting to a single nationwide menu complements committing to being the high-end competitor in each market (which presumably earns larger profits than the low-end competitor). Suppose satellite can somehow make its commitment to nationwide pricing credible (for example, by establishing a reputation via public announcements or advertising). Because no individual cable system can induce the satellite firm to differentiate downward through unilateral action, nationwide pricing reduces the incentive for cable firms to compete for the high end of the market.

Regulation: Subscription television is a partially regulated industry. Following deregulation in the 1980s, the 1992 Cable Act reinstated the following controls: (1) a minimum quality standard for the lowest tier, requiring systems to carry a certain number of local broadcast, public, educational, and government channels, (2) "must-carry" rules allowing local broadcasters to demand carriage by cable companies, (3) authorization for local authorities to regulate Basic prices, after "certifying" with the FCC, (4) empowerment of the FCC to regulate prices for non-Basic tiers, on a complaint basis, and (5) exemption from price regulation for systems facing "effective competition." ¹⁰

Due to the proximity in timing of the Cable Act, we may worry about the confounding effects of regulation on the analysis of satellite entry. One obvious concern is whether the minimum quality constraint binds. Under the standard monopoly screening model, regulating the bottom good leaves quality unchanged at the top of the menu, while either raising or lowering the high good's price, depending on how regulation affects the downward incentive-compatibility constraints (Besanko, Donnenfield, and White 1988; Corts 1995). Empirically, Crawford and Shum (2005) find that local regulatory oversight is in fact correlated with higher quality for the bottom cable good and slightly lower prices for the high good, while leaving high-good quality unaffected.

In practice, the price controls were seldom binding constraints. Most importantly, enforcement was weak to begin with, and the FCC further relaxed the price caps soon after their enactment by means of a number of "going-forward" rules. ¹¹ The Telecommunications Act of 1996 went even further and rolled back all regulation of non-Basic rates, starting March 1999. In addition, in cases in which the price controls were actually relevant, cable systems often engaged in "evasive rebundling," removing costly channels from Basic and, in some cases, marketing them as unregulated a-la-carte services. ¹² This tactic facilitated higher quality-adjusted prices without actually violating the price caps. ¹³

Because of the potential for evasive rebundling, slack price constraints do not necessarily imply that regulation had no effect. My empirical specification does not explicitly incorporate the regulatory constraints, but nor does it presume the optimality of firms' quality-setting decisions. On the other hand, I exploit the non-binding nature of the price caps: conditional on chosen quality levels, observed prices should match the prices that maximize profits in the absence of regulation.

One final observation: whether through price caps on Basic or through the minimum quality standard, regulation primarily affects the bottom cable tier. By contrast, satellite entry directly affects margins at the top of the cable menu. Therefore, existing regulations do not change the principal effects of satellite entry on cable menus.

3.1 Data

The data for cable firms come from annual editions of Warren Publishing's Cable and Television Factbook for the years 1992-2002. Covering all cable systems in the United States, the Factbook lists information on prices, channel contents, the number of subscribers for each product tier, and cable system characteristics, including the total number of homes passed, channel capacity, and franchise fees. Data on prices and demand for a-la-carte premium services (primarily movie channels such as HBO) are available, but not used in my study. After eliminating observations with missing data, 78,165 observations remain, each corresponding to a cable system in a single year. 59,069 of these have just one programming tier, 17,089 have two, 2,006 have three, and just one has 4. Due to inconsistencies across firms in naming practices, I simply refer to the best (and usually only) cable tier as the "high good" and the second best (whenever available) as the "low good." In my discussion and tables, though not in my estimation, I ignore the even lower tiers for systems with three or more tiers, and refer to all systems with two or more tiers as "two-good" systems. ¹⁴

Data on Dish Network's prices and product offerings for each month of the firm's existence came to me from company executives. I also constructed an analogous history of prices and program offerings for DirecTV, by synthesizing archived versions of the DirecTV company website, press releases, and paper copies of old brochures. ¹⁵ To facilitate cross-year comparisons, I deflate all cable and satellite prices by the Consumer Price Index.

Satellite company officials declined to supply detailed demand data. However, I have counts of the total number of DBS subscribers in each of 210 Designated Market Areas (DMAs), aggregated across firms, for each year between 1997 and 2004. ¹⁶ Even though I have cable subscriber data for all years, satellite entered in 1994, so I do not have a complete picture of demand for the years 1994-1996. Therefore, in my estimation, I only use data for the years 1992, 1993 and 1997-2002.

Data on affiliation fees--the per-subscriber programming costs paid by cable and satellite firms to content providers--are available for various years for 81 out of the 166 cable networks represented in the cable data, including all of the empirically relevant channels. Certain networks, such as the shopping channels, are provided to carriers free of charge. A shortcoming of the cost data is that the figures are not actual amounts paid by the cable and satellite firms, which differ slightly across firms: for 1989-1998, the figures are the per-subscriber list prices; reported fees for 1999-2003 are the average amounts paid by all cable firms. ¹⁷

3.2 Heterogeneity in the Response to Entry

My goal is to explain not only the overall time trends in cable prices and qualities, before and after entry, but also the wide variety of responses to entry seen in different markets. In this section, I document the basic intertemporal and cross-sectional trends in the raw data. Table 1 summarizes prices as well as four alternative proxy measures for the content quality of various cable tiers. The measures are weighted sums of the number of channels, using the following weights:

Uniform weights (i.e., counting the simple total number of channels).
Average Nielsen ratings for each channel over the period July 1993 through December 2002. Channels that appear on Nielsen's weekly Top-15 list during this period receive a weight proportional to total viewership; all other channels receive a weight of zero. ¹⁸
Per-subscriber channel costs, averaged over the period 1993-2003. ¹⁹ Each channel receives a weight equal to the mean affiliation fee of that network over all markets and time periods. For example, ESPN receives a weight of 1.39, and USA receives a weight of .374.
Uniform weights counting only the top five channels with the highest Nielsen Ratings (i.e., counting the number of channels from among ESPN, TNT, USA, CNN and Nickelodeon).

Overall trends are robust to the specific choice of weights. Table 1 shows an increase in the average channel content for one-good cable systems, from 11.4 to 18.0 channels over the period 1994-2002, while inflation-adjusted prices rise by $2.15. Similarly, the high good offered by two-good systems increases from an average of 19.5 channels to 27.1, while prices rise by $1.51. The quality of the low good, where available, falls from 10.5 to 9.0 (perhaps reflecting the effects of evasive rebundling), while its price falls from $17.52 to $11.25. In effect, the quality range widens, with the ratio of low-good quality to high-good quality declining by 38-40% (depending on the choice of weights).

Much variance in the behavior of individual systems underlies the industrywide means. Table 2 reports the number of markets experiencing improvement, degradation, or no change in the quality of each good. In most cases, the high good improves over time, but no change is also common, and declines in quality occur in 1-6% of all cases, depending on the measure used.

To see how changes in bundle quality vary conditionally with market characteristics, I regress the change from 1994 to 2002 on market observables, including region dummies, the number of over-the-air channels, and initial channel quality in 1994 (tables available on request). Including the initial quality is a way to control for unobserved factors that affect optimal quality levels under both monopoly and duopoly. Among the trends illustrated by the regressions, I find that in general, larger markets and more urbanized markets tend to experience greater content improvements in the high good. During this time period, an increase in cable system size (as measured by the number of homes passed by the network) by a factor of predicts the addition of 2.0 more channels. Moreover, after controlling for other observables, large MSOs add 2.7 fewer channels to the high good, on average, and 2.4 fewer channels to the low good. ²⁰ The qualitative trends are robust to the choice of weighting scheme.

Capacity constraints: My model does not take into account the bandwidth constraints of cable technology. The two alternative modes of transmission--coaxial and fiber optic cable--both place upper limits on the number of channels that can be delivered. If binding, this constraint would make it harder to improve the quality of the high good. However, two pieces of evidence suggest that heterogeneity in the supply response is not merely driven by variation in firms' channel capacities.

First, firms with greater excess capacity in the initial year actually tend to add fewer channels over time. The Factbook includes data on the number of unused channel slots for each cable system. When I regress the 1994-2002 change in the number of channels on the number of excess slots in 1994, along with controls for market characteristics and the initial channel count, I find that each additional unused slot in the initial year predicts 0.10 fewer channel additions from 1994 to 2002. Second, the channel capacities appear to be a "soft" constraint: from 1993 to 2002, the average total capacity increased from 34.6 to 44.3, and the number of excess slots remained roughly constant, at 9.2 in 1993 and 9.8 in 2002. During this time period, new technologies for data compression and multiplexing became available, making it relatively easy for firms to add capacity.

4 Model

In this section, I present a model of demand and supply for subscription television. The range of incumbent responses to entry can be understood in terms of variation in the model's underlying primitives. Following a discussion of the theoretical implications, I describe the estimation strategy.

4.1 Demand

I consider a model of vertical differentiation. In each market and time period, households choose either one subscription television package or the outside good. Prior to entry, the choice set comprises the set of all cable goods; following entry, the satellite good is added to the choice set.

Consumer types are drawn from a distribution $G(\cdot)$ over support $[0, \bar{t}]$ , where $\bar{t}$ may equal $\infty$ . A consumer's type describes his taste for television programming relative to all other goods. In particular, for a consumer with taste for quality , consuming good from firm at time yields a utility that is quasilinear in price and has the form

$\displaystyle u_{ijkt} = t_i q(x_{1,jkt}) - p_{jkt} + \xi_{jkt}$

(1)

$x_{1,jkt}$ is a vector of indicators for included channels. The function $q(\cdot)$ translates $x_{1,jkt}$ into units of utility, is strictly increasing in each component of $x_{1,jkt}$ , and is diminishing in returns to channel content (). $\xi_{jkt}$ measures the quality of product characteristics other than programming content, relative to the outside good. ²¹ This term varies across individual products as well as across firms , because it includes noise from factors such as unobserved channels and product-specific discounts and promotions. However, for brevity I still refer to $\xi_{jkt}$ as the "brand effect," because non-content-related quality characteristics tend to be specific to firms rather than individual bundles. Of course, "brands" and "products" are clearly synonymous when a firm offers only a single tier.

A consequence of placing $\xi_{jkt}$ outside of multiplication by the vertical type in the utility function is that consumers differ from each other in their tastes for channel content $x_{1,jkt}$ , but not for the brand effect $\xi_{jkt}$ . The implication is that when consumers form preferences, their valuation of unobserved things such as reception quality and Digital Video Recorders (DVRs) is uncorrelated with their valuation of actual channel content. ²²

Defining $\delta_{jkt}\equiv - p_{jkt} + \xi_{jkt}$ and $q_{jkt}\equiv q(x_{1,jkt})$ , we can reexpress (1) as

$\displaystyle u_{ijkt} = t_i q_{jkt} + \delta_{jkt}$

(2)

Letting $q_{0mt}$ denote the quality of the free outside good in market at time , which can be thought of as over-the-air broadcast television, the reservation utility is

$\displaystyle u_{i0t} = t_i q_{0mt}$

(3)

In each period, consumers purchase their most preferred package from among the cable offerings or--following entry--the satellite good. With one dimension of consumer heterogeneity, the product qualities are strictly ordered, with each good competing only against its two nearest neighbors in quality. Thus, demand is characterized by cutoff types. To illustrate, suppose a market has three goods: a low-quality cable good (L), a high-quality cable good (H), and an even higher-quality satellite good (S). Omitting the subscripts for time and firm, the cutoff types are

$\displaystyle v_L = -\frac{\delta_L}{q_L-q_0},\; v_H = \frac{\delta_L-\delta_H}{q_H-q_L},\;$ and $\displaystyle \; v_S = \frac{\delta_H-\delta_S}{q_S-q_H}$

(4)

where types buy nothing, types buy the low cable good, types buy the high cable good, and types buy the satellite good.

Following the example of Mortimer (2005), I specify that follows a Weibull distribution with market-specific parameters $(\lambda_m,\rho_m)>0$ . The CDF and density of a Weibull distribution with parameters $(\lambda,\rho)>0$ are, respectively:

$\begin{displaymath}\begin{array}{c} F(t) = 1 - exp\left[-\left(\lambda t\right)^{\rho}\right], \;\;\;\;\;t\in[0,\infty)\\ f(t) = \lambda\rho\left(\lambda t\right)^{\left(\rho-1\right)} exp\left[-\left(\lambda t\right)^{\rho}\right], \;\;\;\;\;t\in[0,\infty) \end{array}\end{displaymath}$

(5)

The Weibull family is flexible, and can approximate a wide variety of single-peaked empirical distributions. ²³ $\lambda$ is inversely proportional to the scale of the distribution. When the "shape" parameter $\rho<1$ , the density function decreases monotonically, with a thinner right-hand tail as $\rho$ approaches zero. When $\rho>1$ , the density function has a positive-valued mode and resembles a normal distribution truncated at zero. Holding $\lambda$ fixed, as $\rho$ increases over the range $[1,\infty)$ , the mean of the distribution changes very little, while the variance decreases and consumer types become more densely concentrated around the mode. ²⁴ Therefore, over this range, higher $\rho$ corresponds to greater homogeneity in tastes. Freedom to adjust $\rho$ and $\lambda$ independently of each other allows for a distribution with an arbitrary mean and variance.

By combining the cutoff types with the Weibull distribution assumption, we can obtain explicit expressions for the market shares. Suppose that at time , market has $J_{mt}$ inside goods. Without loss of generality, we can number the goods in increasing order of quality $1,\dots, J_{mt}$ . Omitting subscripts and for economy of notation, the following expressions give the market shares:

$\displaystyle s_0$	$\displaystyle =$	$\displaystyle 1 - exp\left[-\left(exp\left(\lambda\right)\cdot\frac{-\delta_1}{q_1-q_0}\right)^{\rho}\right]$	(6)
$\displaystyle s_j$	$\displaystyle =$	$\displaystyle exp\left[-\left(exp\left(\lambda\right)\cdot\frac{\delta_{j-1}-\delta_j}{q_j-q_{j-1}}\right)^{\rho}\right] - exp\left[-\left(exp\left(\lambda\right)\cdot\frac{\delta_{j}-\delta_{j+1}}{q_{j+1}-q_j}\right)^{\rho}\right],\;$
		$\displaystyle j = 1,\dots,J-1$	(7)
$\displaystyle s_{J}$	$\displaystyle =$	$\displaystyle exp\left[-\left(exp\left(\lambda\right)\cdot\frac{\delta_{J-1}-\delta_J}{q_J-q_{J-1}}\right)^{\rho}\right]$	(8)

4.2 Supply

I treat the number of cable products in a given market and time period as exogenous. While this is a standard assumption in the literature on multiproduct firms, it is a limitation of the analysis. Nevertheless, this feature of the model reflects the empirical reality that firms adjust bundle prices and qualities far more frequently than they adjust the number of bundles. The data also indicate that larger cable systems tend to offer more tiers. These facts suggest that fixed costs are involved in offering more complicated menus, even if doing so allows for more complete price discrimination. Hence, we see more bundles in large markets, where we would expect lower per-consumer menu costs. Section 5.5 discusses the impact of changing the number of goods on profits, but fully endogenizing the number of goods is beyond the scope of this paper.

Firm costs display constant returns to scale and are independent across goods. Specifically, firm 's marginal cost of selling good to an additional consumer is $\tilde{mc}(x_{1,jk};\zeta_{jk})$ . $\tilde{mc}(\cdot)$ is rising in each of its arguments, which include channel dummies $x_{1,jk}$ and a product-specific cost shock $\zeta_{jk}$ . Because quality $q(x_{1,jk})$ is also monotone in each element of $x_{1,jk}$ , we can redefine the cost function in terms of instead of : $mc(q,\zeta)\::=\: \displaystyle\min_x\{\tilde{mc}(x,\zeta)\;\vert\;q(x) = q$ }. Also, $\frac{\partial \tilde{mc}}{\partial x}>0$ and imply that $\frac{\partial mc}{\partial q}>0$ .

In each period, the cable firm sets a menu of prices and quality levels, taking the number of cable goods as given. In pre-entry periods, the incumbent chooses prices and qualities that maximize profits as a multiproduct monopolist. At an exogenous time, satellite enters all markets simultaneously with a single higher-quality good, offered at the same price and quality in all markets. I treat satellite price and quality as exogenous to the cable firm's decision, because the satellite firms' nationwide menu-setting policy implies that they do not best-respond to cable systems at the level of individual markets. A particular cable system's menu choice therefore has a minimal effect on overall satellite profits, and we can think of satellite as a being a "big" player and each cable system as being a "small" player.

On the other hand, the cable firm chooses prices and quality levels as a best response to the satellite offering. Behavior is non-strategic, and the incumbent chooses statically profit-maximizing prices and qualities as a monopolist over the residual demand. Denoting the set of goods offered by firm at time by $\mathcal F_{kt}$ , the market size by , the fixed cost by $C_{kt}$ , and the model parameters by $\theta$ , the cable firm's () profit function in period is:

$\displaystyle \pi_{kt} = \sum_{j\in {\mathcal F_{kt}}}(p_{jkt} - mc(q_{jkt},\zeta_{jkt}))Ms_{jkt}(p_{t},q_{t},xi_{t},\theta) - C_{kt}$

(9)

4.3 Theoretical Implications

In each market, different values of the underlying parameters imply different profit-maximizing choices of cable prices and qualities, both under monopoly as well as under competition from satellite. The effect of entry can be understood as the difference between the two settings. While there are no closed form expressions for the profit-maximizing solution, we can place bounds on the outcome for the polar cases in which satellite entry is either very "aggressive"--with extremely high quality and prices that are low in comparison to quality--or very "weak." ²⁵ In particular, for any continually differentiable consumer type distribution, if there are either two incumbent goods (i.e., a high good and a low good ) or just a single high good (), the following are true:

If satellite quality is below a certain threshold, the incumbent's best response is to raise the quality of the high good. Intuitively, if satellite has only slightly better quality than the high good, the incumbent can earn near-monopoly-level profits by mimicking the entrant's quality and undercutting it on price.
If marginal costs $mc(q;\zeta)$ are sufficiently convex with respect to and consumer types are sufficiently homogeneous, then satellite qualities above a certain threshold induce the incumbent to lower the quality of the high-good. This threshold depends on the price premium for satellite over the high good. Additionally, if there is only one incumbent good, the price of that good moves in the same direction as its quality, following entry.
As the proportion of consumers willing to pay the premium for satellite goes to zero, no level of satellite quality is sufficient to induce the incumbent to lower high-good quality.

Thus the incumbent's decision rule for the limit cases is as follows: compete for the high-end market if satellite is only slightly better quality or is sold at a high price premium; differentiate downward if satellite has much better quality and is sold at not too high a price premium. All formal statements of results and proofs are in Appendix A, which also discusses numerical simulations dealing with the mapping from parameters into market outcomes for the intermediate cases.

4.4 Model Covariates

This subsection details the observable covariates upon which the model components depend.

Utility from content: In the specification of consumer utility (1), the function $q(\cdot)$ maps from programming content into units of utility. Rather than attempt to estimate the effect of each individual channel, I treat consumer utility as a function of a univariate aggregate measure of cable programming. The alternative--computing a separate coefficient for each channel--would introduce high-dimensional combinatorics into the counterfactual exercises, making them less tractable. ²⁶ Thus, I redefine to be the cost-weighted proxy measure, as defined in Subsection 3.2. ²⁷ The cost weights are preferable to the alternatives for various theoretical reasons, though in practice, the specific choice of weights does not dramatically affect the results. ²⁸

Without loss of generality, we can normalize the utility for the outside good, $q_{0mt}$ , to zero. The content quality of all inside goods depends on the number of over-the-air (OTA) local channels as well as on whether the format is cable ( ) or satellite ( ), because subscribing to cable or satellite does not preclude viewers from watching local broadcast but changes the effective quality of those channels. I assume that utility from content for good has the form:

$\displaystyle q(x_{1,jkt}) =$ (# OTA channels) $\displaystyle _t\cdot(\beta_0+\beta_1\cdot satellite + \beta_2 satellite\_local) + \beta_3 log(x_{1,jkt})^2$

(10)

The dummy $satellite\_local$ is an indicator for satellite in market-years in which DirecTV retransmitted OTA channels, following the 1999 act rescinding the ban on DBS rebroadcasting of local channels. ²⁹ The $log(\cdot)^2$ transformation makes utility convex in , necessary for the existence of interior solutions. ³⁰ To check for robustness, I also try a few alternative concave transformations, none of which significantly alters the estimates of the parameters outside of (4.4).

Brand effects: The brand effect $\xi_{jkt}$ is a function of observable firm characteristics and market covariates, $x_{2,kt}$ , as well as an unobserved component $\Delta\xi_{jkt}$ :

$\displaystyle \xi_{jkt} = \xi'x_{2,kt} + \Delta\xi_{jkt}$

(11)

$\Delta\xi_{jkt}$ is observed by the market participants, and is the structural error upon which my estimation strategy will depend. The observed characteristics $x_{2,kt}$ include the format (dummies for cable and for satellite) as well as dummies for specific MSOs. MSO ownership affects demand through differences in matters such as customer service, marketing, and the availability of technologies like DVRs. Format affects demand if consumers have preferences between the two technologies that are independent of regular subscription contents. For example, during the sample period, the satellite firms introduced an array of a la carte options for out-of-market professional sports (such as DirecTV's NFL Sunday Ticket), unavailable to cable customers. Similarly, toward the end of the sample period, cable firms began bundling television with broadband internet. Section 5.2 discusses the consequences of having random coefficients for horizontal format preferences, but for now I assume fixed effects for each format, interacted with year dummies.

As controls, I also include dummies that interact satellite format with region dummies and with the percentage of the consumers in each market living in multiunit dwellings (defined by the 2000 Census as buildings with two or more housing units). The region dummies control for differences in reception quality caused by the positioning of the DBS satellites, which transmit from fixed points above the equator. Similarly, multiunit housing residents may not be able to get a proper signal if they cannot find a well-situated attachment point for their receivers.

Consumer type distribution: The parameters of the consumer type distribution $(\lambda,\rho)$ depend on a vector of market demographics , taken from the 2000 Census, which includes a constant, summary measures of household income distribution, and the total population and population density (including households not passed by cable) of the town in which the franchise is located. I restrict these parameters to plausible ranges by specifying $\lambda_m = exp(z_m'\gamma_1)$ and $\rho_m = n_1 + n_2 exp(z_m'\gamma_2)/(1 + exp(z_m'\gamma_2))$ , for constant terms and . ³¹

Marginal costs: The marginal cost of serving an additional consumer has two components: the cost of content and all other costs. Contracts between content providers and cable firms are signed on a per-subscriber-per-month basis, resulting in content costs that scale linearly with the number of consumers.³² The remaining component includes all non-content-related costs of providing service that scale with the number of customers but are invariant in the actual programming selection. I specify the marginal cost function as:

$\displaystyle mc(x_{1,jkt},x_{2,kt},z_{m},\zeta_{jkt}) = \psi_1'(x_{1,jkt},(x_{1,jkt}\cdot MSO_{kt})) + \psi_2'(x_{2,kt}, z_{m}) + \zeta_{jkt}$

(12)

The $\psi_1'(\;\cdot\;)$ term is the cost of content and depends on $x_{1,jkt}$ , the same proxy measure of programming content that enters into consumers' utility function. $MSO_{kt}$ is a dummy indicating ownership by any MSO. I allow for MSOs and non-MSOs to have different content costs, reflecting differences in bargaining power for horizontally integrated firms. The non-content-related costs $\psi_2'(\;\cdot\;)$ depend on the time-and-firm-varying covariates $x_{2,kt}$ (which include fixed effects for each MSO and for each year) as well as market demographics .

The error $\zeta_{jkt}$ is observed by firms but not by the econometrician. In addition to capturing the unobserved component of non-content costs, $\zeta_{jkt}$ also absorbs violations of the assumption that channel costs are purely additive. For example, in some cases, upstream owners of horizontally integrated content networks ³³ pressure cable firms to package the commonly owned networks in certain ways. Therefore, the effective cost of each channel may depend on interactions with other channels as well as the product tier in which it is offered.

4.5 Estimation

The initial estimation step involves recovering the structural errors $\Delta\xi$ (unobserved quality) and $\zeta$ (the unobserved cost shock).

The key dependent variable that enables us to recover the unobserved qualities $\Delta\xi$ is the product market shares. Given the parameters of the type distribution $(\lambda,\rho)$ and the channel coefficients ( $\beta$ ), we begin by inverting (6) to obtain an expression for $\delta_1$ in terms of the empirical share of the outside good $s_{0}$ . We can then determine $\delta_2,\dots,\delta_j\dots\delta_J$ as functions of the empirical market shares by recursively solving (7) and (8). One complication is that while the number of subscribers is observed for individual cable products, the demand data for satellite are aggregated over all products offered by DirecTV and Dish Network. I deal with this problem by treating satellite as an aggregate good, a solution detailed in Appendix B alongside several other measurement issues. Finally, the unobserved quality $\Delta\xi$ can be recovered as the residual of the brand effect:

$\displaystyle \Delta\xi_{jkt} = \delta_{jkt} + p_{jkt} - \xi'x_{2,kt}$

(13)

The constant term for the scale parameter ( $\lambda$ ) of the type distribution is not separately identified from the scale of the coefficients for content quality, $\beta$ : in (6)-(8), scaling up content quality and $\lambda$ by the same factor would leave the market shares unchanged. Therefore I normalize the demand coefficient for in (4.4) at $\beta_{3}=1$ .

The cost shock $\zeta$ is implied by optimality conditions on cable menus. In particular, the statically optimal $J_{kt} \times 1$ price vector solves the following system of first-order conditions:

$\displaystyle \frac{\partial\pi_{kt}}{\partial p_{kt}}\;=\; s(p_t,q_t,\xi_t,\theta) - \frac{\partial s_{kt}(p_t,q_t,\xi_t,\theta)}{\partial p_{kt}} \cdot(p_{kt}-mc(q_{kt},\zeta_{kt}))\;=\;\mathbf{0}$

(14)

where $\frac{\partial s_{kt}(p_t,q_t,\xi_t,\theta)}{\partial p_{kt}}$ is the $J_{kt} \times J_{kt}$ matrix of cross-price elasticities, which we can obtain analytically under the Weibull distributional assumption. Because quality is vertically differentiated, the cross-elasticities are non-zero only for goods that are adjacent in the quality space. After inverting (14) to solve for the imputed marginal costs $\hat{mc}$ , the cost shock for good can be recovered as the residual in (12):

$\displaystyle \zeta_{jkt} = \hat{mc}_{jkt} - \psi_1'x_{1,jkt} - \psi_2'(x_{2,kt}, z_{m})$

(15)

By recovering the cost shocks from the price- rather than quality first-order conditions, the estimation procedure implicitly assumes that cable prices are fully profit-maximizing, given quality levels. On the other hand, I do not incorporate optimality assumptions about quality-setting, although the model implies that quality is endogenous and must therefore be instrumented for. It would also be possible to impute the marginal costs from the first-order conditions on quality, instead of imposing the optimality of prices. ³⁴ However, this alternative would make the estimation routine more difficult, because the econometric errors would no longer be linear in the parameters for content costs. ³⁵ Moreover, recall that the 1992 Cable Act may have given two-good cable firms incentives to alter the quality of the low good, whereas the price caps were generally non-binding. If regulation is a factor, estimates based on quality moments could be biased.

Parameter estimates are estimated using the generalized method of moments. The key moment assumptions are that the residual brand effect ( $\Delta\xi$ ) and the residual cost shock ( $\zeta$ ) are orthogonal to the brand-quality covariates (, denoted in matrix notation by ), the type-distribution covariates (, denoted in matrix notation by ), and the number of over-the-air channels ( # OTA channels). A standard concern is that price is correlated with unobserved quality ( $\Delta\xi$ ), and that channel quality is correlated with both structural errors ( $\Delta\xi$ and $\zeta$ ), invalidating their use as instruments. As such, one more moment restriction is necessary for identification of the demand equation, and two more for identification of the cost function. ³⁶

Additional demand instruments come from assuming that the following components of are cost shifters that can be excluded from the demand equation: (1) mean per-worker wages for firms in the "Information" sector, (2) mean per-worker wages for firms in the "Broadcasting, except Internet" subsector of "Information", ³⁷ (3) log of cable system size, measured by the total number of homes passed. Local wages proxy for the cost of non-content-related inputs (Appendix B details the assumptions underlying these variables), and cable system size captures economies of scale, which I assume to be uncorrelated with demand after controlling for total population.

For identification of the supply side, I assume that ( # OTA channels) does not enter into the cost function. I also assume that interactions between MSO-ownership and the above cost shifters can be excluded from both the supply and demand functions. ³⁸

As an alternative to the above base specification, we can also exploit additional overidentifying restrictions for the demand equation by constructing "quality" instruments, just as the cost shifters instrument for price. Specifically, I consider measures of vertical integration between cable systems and content providers. To a greater extent than would be expected based on cost incentives alone, MSOs tend to favor carrying channels with which they are vertically integrated, while excluding rival firms' channels. This effect may arise from either efficiency considerations (lower transaction costs) or from incentives to engage in vertical foreclosure. ³⁹ Therefore, additional demand instruments are dummies for each of the networks owned by Turner Broadcasting (equal to 1 if included in a bundle) interacted with an indicator for vertical integration between the owning MSO and Turner. Turner is vertically integrated with the MSOs Time Warner, ATC and TCI, which together own 38.3% percent of all the systems in the estimation dataset. ⁴⁰ To the extent that each of the Turner channels (CNN, TNT, Headline News, TBS, Cartoon Network and Turner Classic Movies) contributes more or less to the content quality of a bundle than substitute channels owned by rival firms, the instruments will be correlated with quality. By assumption, vertical integration status has no direct effect on consumer utility and can be excluded from the demand equation. However, because vertically integrated firms may receive additional discounts on contents, the vertical integration proxies cannot be used as instruments for the supply equation.

The joint estimator minimizes the GMM objective function, $Q = \omega(\theta)'\hat{Z}V\hat{Z}'\omega(\theta)$ , where $\omega(\theta) = [\Delta\xi'\;\;\zeta']'$ is the stacked vector of errors. Each element of $\Delta\xi$ corresponds to a system, year, and a cable or satellite product. $\zeta$ only has elements corresponding to cable goods, because we are only modeling the supply decision of the cable firms. $\hat{Z}$ is a conformably defined block-diagonal matrix with a block of demand instruments and a block of supply instruments . Specifically, $Z_D = [X_2\;\;Z\;\;W_D]$ , with being the excluded cost shifters (as well as the vertical integration instruments, in the alternative specification). is similar to , but excludes the satellite observations as well as any variable that interacts with the dummy for satellite products. is the weighting matrix. ⁴¹

I find the minimum of the objective function using a combination of gradient-based and simplex methods, starting from various initial estimates. Because the demand parameters $\xi$ and the cost parameters $\psi$ enter linearly into the expression for the econometric errors, they can be "concentrated out" and expressed as functions of the nonlinear parameters $\beta$ (the programming-content-related coefficients) $\gamma_1$ (covariates for the scale parameter of the vertical-type distribution) and $\gamma_2$ (covariates for the shape parameter of the vertical-type distribution), thereby reducing the number of parameters over which nonlinear search must be performed.

4.6 Identification

How do observed market shares and bundle characteristics identify the parameters of the consumer type distribution? The demand moment conditions suffice on their own, but the supply moments also aid in identification. First, note that because the brand effects $\xi$ are unrestricted in the values they can take in a given market-year, the type distribution for a given market would not be identified if it were allowed to vary completely freely: given any choice of $\lambda$ and $\rho$ , we can find brand effects that would exactly explain the observed market shares. However, we can restore identification by "pooling" information across markets through the assumption that $\rho$ and $\lambda$ are either perfectly determined by observable market covariates or (to make a weaker assumption) are observed up to an error term that is independent of the covariates in the demand equation. ⁴²

The scale parameter $\lambda$ determines the importance of programming content to consumers' utility, relative to price and brand effects: doubling the value of $1/\lambda$ in a given market, say, implies a doubling in each consumer's valuation of channel content relative to all other goods. If $1/\lambda$ is positively correlated with an observable market characteristic, then in markets with that characteristic, demand is greater for high-quality goods (as well as for subscription television as a whole).

The shape parameter $\rho$ is identified by the degree of similarity in consumers' purchases. Controlling for $\lambda$ , higher values of $\rho$ imply that consumer types are more densely concentrated. At one extreme, certain goods offer a great deal of quality at a high price, and appeal to consumers with high preferences for quality; other goods offer little quality at a low price, with the outside good at the extreme. When $\rho\to\infty$ , only one good in each market (possibly the outside good) has positive market share; when $\rho\to 0$ , the variance of the type distribution increases without bound, leading to higher demand for the "extremal" goods.

It is tempting to try to fit the data by allowing both $\lambda$ and $\rho$ to covary with as many demographic characteristics as possible. However in practice, separate identification of all the covariate parameters is weak unless we restrict certain demographic characteristics to affect only one of $\lambda$ or $\rho$ . For example, intuition suggests that median income is a more important predictor for mean tastes (and thus $\lambda$ ), while income dispersion is a more important predictor for the heterogeneity of tastes (and thus $\rho$ ). Given the finite amount of data, if we imposed no restrictions, the effect of each covariate on $\lambda$ would be poorly identified separately from its effect on $\rho$ . To understand why, recall from (6-8) that a low $\rho$ , holding $\lambda$ fixed, would imply large market shares for goods appealing to consumers with extreme tastes. However, the data place most of the observed cutoff types within one or two standard deviations--usually to right--of the mode; the lowest-type consumers are priced out of the market and are thus unobserved. Within the range of the type distribution in which we observe actual cutoff types, lower $\rho$ (holding $\lambda$ fixed) and lower $\lambda$ (holding $\rho$ fixed) have similar implications, with both implying a fatter right-hand tail and larger shares for high-end goods.

The contribution of the supply moments to identification of the type distribution parameters is subtle. The imputed markups (net of the unobserved cost shock $\zeta$ ) are a function of prices and cost covariates. This function is defined by the first-order conditions on price, which imply that the markup on good must be higher when its market share is more elastic with respect to price or quality. In turn, the elasticity at a given cutoff point depends on the type distribution parameters: higher $\rho$ implies higher (lower) elasticity for goods whose cutoffs are close to (far away from) the mode of the distribution; higher $\lambda$ implies higher (lower) elasticity for goods with low (high) cutoffs. Thus, so long as there are cross-equation restrictions on the supply and demand covariates, the link between markups and the type-distribution parameters provides an additional source of identification. However, the above logic is somewhat imprecise because the cutoff types are endogenous. Moreover, determining the impact of $\rho$ and $\lambda$ on markups is hard when there is more than one good, because markups also depend on the cross elasticities between adjacent goods.

Identification of the remaining parameters is straightforward. On the supply side, the cost coefficients $\psi_1$ and $\psi_2$ are identified by variation in the imputed marginal costs with respect to the instruments. On the demand side, the coefficients for over-the-air channels ( $\beta_0,\beta_1,\beta_2$ ) are identified by variation in the market share of all inside goods with respect to the number of over-the-air channels and its interaction with cable or satellite format. The parameters $\xi$ for the observed components of the brand effect are identified by variation in market share with respect to non-content-related observable product characteristics.

5 Results

5.1 Parameter Estimates

The estimation sample contains observations for 10,405 market-years, 4,937 of which are for two-good markets (a higher proportion than in the full dataset). These are the observations that remain after excluding observations with missing data as well as those for markets with overbuilds (to rule out the effects of unobserved competition). I also exclude observations for cities with populations outside the range of 5,000-200,000. The upper cutoff limits the confounding effects of partially overlapping markets, which tend to be in the largest cities. The lower cutoff is motivated by the fact that the Factbook is not updated every year for certain markets, and is least likely to be current for the smallest markets.

Tables 3 and 4 report the second-stage demand and supply estimates. In addition to the estimates from the base case (Column 1), I also report specifications that make use of the vertical-integration instruments for quality (Column 2) and that replace simple year fixed effects for costs with year-specific channel content costs (Column 3). The estimates are similar across specifications, so unless otherwise noted, the remainder of the discussion focuses on the base case.

The tables report the estimates from a parsimonious specification in which the scale of tastes $\lambda$ depends on the median household income ( $MED.\;INC$ ) and the log of population density ( $POP.\;DENSITY$ ), the latter of which proxies for differences between urban and rural areas (e.g, tastes for television might be stronger in rural areas due to the absence of alternative entertainment options). The shape parameter $\rho$ is assumed to depend on the total population of the town in which the franchise is located and on income dispersion, as measured by the difference between the 90th quantile and the median ( ). ⁴³

The cross-market averages of the estimated distributional mean and standard deviation for consumer types are 1.56 and .51, respectively. The former implies that the mean-of-mean consumer derives $12.84 in utility from the programming content of a typical package (excluding the valuation of the non-content-related brand effect). For comparison, the typical package (averaged over all years, firms and products) is priced at $22.06. Estimates for the $\lambda$ covariates indicate that tastes for quality are higher in high-income and low-population-density markets. Estimates for the $\rho$ covariates indicate that consumer types are more homogeneous in larger markets and in markets with less income dispersion. This negative correlation between total population and heterogeneity in tastes is driven in the data by the fact that cable menus tend to be somewhat similar across all large markets, relative to the amount of cross-market variation in market shares. As a check for robustness, I also try a specification allowing $\lambda$ and $\rho$ each to depend on all of the demographic covariates, as well as a specification allowing only $\rho$ to depend on demographics. However, estimates of the remaining parameters do not vary much across specifications.

Demand is lower for MSOs, with MSO ownership associated with a disutility of $2.57 per month. The year dummies indicate no strong time trends. Positive fixed effects for cable systems offering two or more service tiers indicate that such systems have higher quality than one-tier systems, for reasons not captured by my content quality proxy. The satellite-region interaction effects (not reported) are small and positive. The satellite-year interactions are negative, perhaps a reflection of learning or switching costs that prevent consumers from moving freely into the new good. The interaction effect between multiunit housing ( $PCT.\;MULTIUNIT$ ) and satellite format is positive--which is somewhat surprising--but small.

The supply-side estimates point to higher non-content-related costs in high-wage, low-density, large-population, and higher-income markets. The base-specification estimates indicate that for non-MSOs, ten units of programming content cost $6.08, implying a content cost of $10.72 for the average-sized package, which has 17.62 units of programming content. MSOs have only slightly lower content costs ($0.11 less per ten units of programming content) as well as lower non-content-related costs ($2.73 less per month).

5.2 Random Horizontal Preferences

In the model, differentiation between satellite and cable based on non-content-related product characteristics is captured by fixed effects in the demand equation (for format and its interaction with year dummies, regions, and $PCT.\;MULTIUNIT$ ). The model abstracts away randomness in horizontal preferences between the two formats, both in order to focus on the effects of entry on vertical quality, as well as to preserve closed-form expressions for the market shares.

However, if true horizontal preferences are randomly distributed (e.g., along a Hotelling interval with cable and satellite on either end), then the imputed marginal costs for the post-entry years are biased upward, assuming independence between horizontal and vertical tastes. The bias arises because ignoring horizontal differentiation results in overestimation of the cross-price elasticity between the high cable good and satellite. ⁴⁴

It therefore comes as no surprise that the estimated cost of content rises over time when the model provides such flexibility (specification 3), or that the year fixed effects trend upward in the base specification. In effect, the model uses a rising time trend in marginal costs in order to explain why prices do not fall by as much as would otherwise would be predicted in the absence of horizontal random effects. That the cost of content is indeed rising over time is corroborated by the independent Kagan cost data, but the especially large jump from 1993 to 1997 may suggest the influence of unobserved randomness in horizontal preferences between cable and satellite.

5.3 The Impact of Entry

Using the parameter estimates, I calculate the expected profit-maximizing cable qualities and prices under various market regimes. While my estimation approach does not impose optimality of quality, as a post-estimation exercise we can calculate the jointly optimal prices and qualities both for the pre-entry period (hereafter "M") as well as for the duopoly regime during the post-entry period ("D"). When we use the parameter estimates from specification 3 (time-varying content costs) rather than from the base specification, the optimal choices of price and quality tend to be higher and lower, respectively. However, the differences across specifications do not affect the analysis in any qualitative way, and I only report the results based on the base specification.

I also compute the profit-maximizing cable qualities and prices for two counterfactual scenarios. The first addresses how cable firms would set prices and content quality over the period 1994-2002 if there were no satellite entry ("NSE") and cable firms remained monopolies. The second scenario, which I call "no quality adjustment" ("NQ"), addresses how cable firms would respond to entry if they could only adjust prices but not content quality. Under NQ, I assume that the satellite good is present and offered at the prices and quality levels actually observed in the data, but that cable qualities are constrained to equal the optimal qualities under NSE.

The counterfactual findings for the post-entry period allow us to assess the overall entry effect, as well as to decompose it into two constituent parts: the endogenous quality response and the pure price response. The entry effect is determined by comparing outcomes under NSE either against outcomes under D, or against actual outcomes. The two comparisons have slightly different interpretations: comparing NSE to D asks how profit-maximizing cable behavior differs with and without entry; comparing NSE to actual values asks what the actual effect of entry is, assuming that behavior sans entry would be optimal. Of course, the comparisons are identical if actual cable firm behavior is optimal. The endogenous quality response compares fully profit-maximizing behavior under duopoly (D) against profit-maximizing duopoly behavior if cable firms cannot adjust content quality (NQ). This effect captures the component of the supply response to entry that can be attributed to quality adjustments. Finally, the pure price response is the difference between NQ and NSE, and indicates the changes that would occur if firms only competed over price.

For each counterfactual, I constrain the number of cable goods to be less than or equal to the actual number, and fix the unobserved cost shocks $\zeta$ and brand effects $\xi$ at levels implied by the parameter estimates. ⁴⁵ When there are multiple goods in the market, computing the profit-maximizing prices and qualities is made difficult by the existence of corner solutions or, in some cases, multiple roots to the price- and quality first-order conditions. To find the globally optimal menu, I do the following for each market-year: (1) gridsearch to obtain initial values for qualities, including test cases for all possible quality orderings, ⁴⁶ (2) compute initial values for prices that ensure positive demand for each good, taking as given the quality levels chosen in step 1, and finally, (3) perform joint maximization over prices and qualities starting from the initial values given by steps 1 and 2.

Table 5 counts the number of market-years in which entry induces increases or decreases in the price and quality of the high good, respectively. When the comparison is between actual outcomes and the NSE counterfactual, more than half (60.3%) of all market-years respond to entry by raising quality, accompanied by price increases ("head-to-head"). However, in 22.5% of market-years, the incumbent lowers price as well as raises quality ("fighting"). Finally, in 17.2% of cases the incumbent differntiates downward. Comparisons between D and NSE also show heterogeneity in response, but with a larger proportion of firms competing head-to-head.

Table 6 summarizes prices, quality levels, market shares, and cable profits under each scenario. To conserve space, I only report outcomes for multiproduct firms, because there are no qualitative differences (on average) between one-good firms' offerings and the high good offered by two-good firms, with regard to either the impact of entry or the endogenous quality response. ⁴⁷ For 9.5% of the observations for two-good firms, the profit-maximizing solution under M or NSE involves offering only a single, high, good. Likewise, 2.8% of these markets offer only one good under D. ⁴⁸ Actual prices do not exactly match the optimal prices (M for years before 1994, and D for 1994-2002) because the estimation only imposes conditional optimality of prices given qualities, while and compute the jointly optimal prices and qualities. The main findings from Table 6 are as follows:

Over the period 1992-1993, quality and prices for the high good are close to optimal (M), suggesting that the NSE counterfactual is a reasonable benchmark for assessing the effect of entry in later years. The optimal quality choice underpredicts actual levels during the pre-entry period by only 12%, on average. Optimal prices are on average only 2.4% below actual prices ($21.67 versus $22.20). However, the degree of underprediction is greater for the low good's price (by $3.82) and quality (by 62%).
Reflecting the prevalence of head-to-head competition, entry raises average high-good quality and price, as indicated by comparing levels under NSE (quality of 14.7 and price of $23.93) against the corresponding levels under D (quality of 21.6 and price $25.75) for the period 1994-2002. The mean entry effect is somewhat smaller in magnitude when the comparison is between NSE and actual values (quality of 17.9 and price of $23.19), because D slightly overpredicts the actual post-entry quality and price. ⁴⁹ The correlation between these two measures of the effect of entry on the high good (i.e., actual minus NSE, versus D minus NSE) is .665. The model does poorly at predicting the actual entry effect on the low good (with a correlation of -.052), perhaps reflecting the effects of regulation.
Endogenous quality choice results in higher post-entry cable prices than would be the case under pure price competition. If cable firms could not adjust content quality in response to entry (NQ), satellite entry would result in lower cable prices relative to no-entry (NSE). The average NQ price of the high good is $21.45, versus $23.93 under NSE and $25.75 under D.
Cable profits under NSE exceed profits under D by 49%, and exceed profits under NQ by 74%. (At $2.01 per consumer-month, actual post-entry cable profits are somewhat lower than the profits of $2.39 under D). Note that profits under D must weakly exceed NQ profits, because the optimal menu under NQ is also feasible under D. The numbers suggest the degree to which content changes enable higher profits: quality adjustments allow firms to recoup 22.5% of the profit losses due to entry.⁵⁰

The model implies that the form of the optimal incumbent response depends on the distribution of consumer types and therefore on the observable market covariates. The most salient empirical relationship is between larger market population and the tendency to compete head-to-head, which the parameter estimates rationalize by making large population the strongest predictor for a concentrated consumer-type distribution (high $\rho$ ). Table 7 demonstrates this point by reporting the mean entry effect on the high good for various groupings of observations, as classified by total population and by high-good quality or price under NSE. ⁵¹ (Grouping observations by NSE quality and price is a control for unobserved product characteristics and cost shocks, which affect optimal cable menus both with and without entry.) The numbers indicate that after controlling for NSE quality, the amount of quality improvement tends to be greater in larger markets.

5.4 Consumer Welfare

Table 6 reports the actual and counterfactual consumer surplus (which is analytically computable under the Weibull assumption) for the post-entry period, both in the aggregate and for specific subsets of consumers. For the same reason as in the previous section, I focus on two-good firms, except when discussing economywide totals. ⁵² Not surprisingly, competition generally benefits consumers, with actual total consumer surplus ($3.16 per consumer per month) and surplus under D ($2.94) exceeding the total consumer surplus under NSE ($1.32) during the post-entry period.

However, differences in consumer surplus at different quantiles of the type distribution indicate that entry has large distributional effects, with the greatest absolute consumer surplus gains going to consumers with stronger preferences for quality. ⁵³ Table 6 reports average consumer welfare for various subsets of consumers, as grouped according to their purchasing decisions. Generally, consumers purchasing higher-quality goods experience greater surplus gains. For example, gains due to entry average $4.61 for the typical consumer who actually consumes satellite post-entry but would consume the high cable good under NSE (in the table, "H to sat"). The gain is less, at $2.48, for purchasers of the high good under both NSE and in reality ("H to H"). At the lower end of the market, consumers who would switch from the low good to the high good ("L to H") gain $0.97 in surplus, while switchers from the outside good to the low good ("O to H") gain $0.19. In fact, in some cases, entry actually reduces surplus for consumers with weak preferences for quality. In 10.1% of markets, consumers at the 10th percentile of the distribution have lower surplus under D than under NSE. The same holds for consumers at the 25th percentile in 11.5% of markets. Comparing the welfare of such consumers under NSE against their actual outcomes yields qualitatively similar findings.

We can also quantify the impact that is specifically due to the endogenous quality component of the entry response. Over all markets (including the set of one-cable-good markets), aggregate consumer surplus is 4.3% higher under pure price competition (NQ) than under competition over both price and quality (D). The percentage difference implies an absolute difference of $118M over the course of a typical year (1997) for the entire United States, assuming the estimation sample is representative. For comparison, the total consumer welfare gain due to entry in 1997 (D minus NSE) is $1.509B. Table 6 also breaks down the effect of endogenous quality choice by consumer type. The reduction in welfare from NQ to D is greatest for types that purchase lower-end goods, while consumers with high preferences are almost equally well off under the two regimes. ⁵⁴ For example, quality adjustments result in a 56% and 34% welfare reduction for types that switch from the outside good to the low cable good or to the high cable good, respectively ("O to L" and "O to H"), but only by 1.2% for types that switch from the high good to satellite ("H to sat"). Likewise, the quantile figures indicate that consumer types other than those with the highest preferences for quality (for example, at the 90th quantile) prefer not to have quality adjustments.

Because we lack information on the satellite firms' costs, the exact size of the total social surplus is indeterminate. However, as long as the satellite markup is not much lower than that of cable, total social surplus is also higher under pure price competition (NQ) than with quality adjustments (D). Although cable firm profits are lower under NQ than under D ($2.05 against $2.39 for two-good firms, shown in Table 6; $1.97 against $2.51 for one-good systems, not shown), this difference is offset by higher profits for satellite. A very conservative assumption is that, as a large competitor, satellite firms have the same costs per unit of content as MSOs and the same non-content-related cost shock ( $\zeta$ ) as the average high cable good. This assumption is similar in spirit to existing models of vertically differentiated oligopoly that find higher markups and profits for the highest-quality good. ⁵⁵ Under this assumption, the total surplus averaged across all (one-good and two-good) markets is $6.444 per consumer per month under NQ, compared to $5.958 under D. For a representative year (1997), the aggregate total surplus loss is $183M for the estimation sample and $389M economywide. ⁵⁶

To summarize, head-to-head competition in response to entry results in inefficiently little differentiation in the available range of product qualities, relative to pure price competition. Intuitively, the incumbent chooses the "least costly" mix of price reduction and quality increase in order prevent marginal consumers from switching to the new good. Under D, the firm has a larger set of instruments for accomplishing this objective than under NQ. Therefore, if there were only one consumer type (i.e., $\rho\to\infty$ ), that consumer must have weakly higher utility under D than under NQ. But with any nondegenerate distribution of consumers, most consumers are not marginal between cable and satellite, and have weaker preferences for quality than the potential switchers to satellite. Therefore, from the perspective of maximizing consumer surplus, the chosen mix of price reductions and quality increases too heavily favors quality increases. While high types benefit from the higher-quality goods, low types would prefer that the incumbent respond to entry with greater price reductions and fewer quality increases.

5.5 Discussion

The result of "too little differentiation" rests on the assumption that satellite is exogenously committed to offering the highest-quality good, which precludes it from responding to rising cable quality by offering a lower-quality good, undercutting cable on price, and taking the bottom of the market. This is a reasonable assumption in the case of subscription television, due to the nationwide menu-setting by satellite. On the other hand, if the two competitors were identical and both best-responding to each other, there may be more product differentiation following entry than implied by my model. ⁵⁷ However, the result of excessive quality could be restored if firms are sufficiently asymmetrical. For example, if satellite has lower unit costs for quality, or if satellite has a much higher brand effect than cable because people intrinsically prefer the newer technology, then even in equilibrium, the cable incumbent will seldom find it profitable to set quality so high that the satellite firm's best response is to differentiate downward.

Furthermore, my analysis focuses on the high cable good. It turns out that offering a second (low) good may mitigate some of the welfare losses due to the quality response. If cable offers only one good and competes with satellite for the high-end market, consumers with low willingness to pay for quality face a stark choice between consuming the outside good or purchasing an expensive good, neither of which gives them much net utility. On the other hand, with a second cable good, the price and quality of the lower-quality good are no longer directly determined by the preferences of the potential switchers to satellite. Indeed, the counterfactuals indicate that conditional on entry causing high-good quality to go up, the average increase in consumer surplus (from NSE to D) at each quantile of the type distribution is higher among markets in which low-good quality goes in the opposite direction or stays unchanged rather than also increasing, leading to an aggregate consumer surplus gain o