The Effect of Links and Excerpts on Internet News Consumption

Notation, Timing, and Period Utility

We present the model from the perspective of a single consumer, bearing in mind that different consumers have different preferences for news. Every day, the consumer engages in a browsing session, which is indexed d. By a “browsing session,” we refer to the process of sequentially visiting zero or more sites within a day (visiting zero sites means not browsing that day). Figure 1 depicts the sequence of events within each browsing session (Figure 1 includes notation that we explain subsequently).

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Figure 1.

Schematic representation of steps in browsing sessions.

At each step of the browsing session, t = 1,…, T_d, the consumer decides which site to visit next, if any (Figure 1, °3). Visiting a site and viewing its content does two things: (1) it provides utility to the consumer and (2) it changes the consumer’s information set (Figure 1, °4). Consumers are indexed with i and the sites with j. When discussing linking, we sometimes refer to the linking site by the index j = L, and the site receiving the link by the index j = R. The option j = 0 denotes the option to end the browsing session. The set J i d 1 contains the J sites under consideration, plus the option to end the session.

We follow the literature on sequential browsing online and assume that the consumer sees all available content at each site visited, and therefore visits each at most once per session (Kim, Albuquerque, and Bronnenberg 2010). This assumption matches both the empirical context of celebrity news sites (whose home pages display all content posted each day), and choices observed in the estimation data (which we describe subsequently). Thus, the consumer’s choice set, which is initially J i d t , is reduced to J i d t + 1 = J i d t \ j after visiting site j (Figure 1, °5). At each step t, the consumer must choose which previously unvisited site to visit next, or whether to end the session (Figure 1, °6). We denote by a_idt the index of the option j chosen by consumer i at step t of browsing session d.

The utility from visiting site j at step t of browsing session d comprises three parts.

U ijdt =μ ijd − γ id + ∊ ijdt .

1

The first is μ i j d , denoting the horizontal match utility consumer i gains from reading site j’s content on day d. This component of utility is unknown to the consumer before visiting site j, as we discuss next. The second component, γ i d > 0 , reflects the opportunity cost of forgoing the outside alternative (not browsing) in favor of reading celebrity news sites. We assume that γ i d is known to the consumer, and constant throughout the browsing session. In our empirical setting, we expect the incentive to browse for celebrity news might differ between weekdays and weekends or U.S. federal holidays (Columbus Day, Veterans Day, Thanksgiving, and Christmas). Thus, if day d falls on a weekend or holiday, γ i d = γ i exp ( γ w ) , and otherwise γ i d = γ i . The third component of utility is ∊ i j d t , which is idiosyncratic to each consumer, site, and step of each browsing session. This utility shock is private information learned just prior to the decision at step t of the browsing session and is unobserved by the researcher (Figure 1, °2). Ending the session (or not starting a session in the first place) is an endogenous choice, yielding net utility of U i 0 d t = ∊ i 0 d t .

Apart from γ i d , which affects the overall value of browsing relative to the outside option, the model does not include a day-level component of utility that is a priori known to all consumers. Common knowledge of such a component of utility, when the good consumed is news, is difficult to justify, as the day-level fixed effect would imply some foreknowledge of the day’s news prior to visiting a news site to learn the day’s news.

Horizontal Match Utility from Content

The horizontal component of utility, μ i j d , arises from the match between the site’s content on day d and the consumer’s preferences. Because news sites post new content every day, the match utility provided to each consumer varies from session to session. A site that typically posts news about film actors, for example, might occasionally report on reality television. On these occasions, a consumer who prefers film over reality TV might experience lower utility from reading the site’s content. Accordingly, the news events that take place each day, and which of those events site j chooses to report, influence the daily value of μ i j d .

In these examples, as well as in our model, we make an important distinction between a site’s long-run average match with the consumer, and daily deviations from that average. The consumer’s long-run average match with a site depends on the type of content the site publishes on average. This long-run average is therefore the same for every browsing session. On the basis of a potentially long history of browsing, an experienced consumer knows their own long-run average match with each site. By contrast, daily deviations from that average arise due to news events and the sites’ choices about what to publish. These daily deviations are therefore unknown at the start of each session (Figure 1, °1 and °7). We model the horizontal match utility consumer i receives from site j’s content on day d as a function of (1) site j’s long-run average position in a horizontal attribute space, z_j; (2) site j’s deviation from this average position on day d, ν_jd; and (3) the consumer’s preferences, v_i.

μ ijd = ( z j + ν jd ) v i .

2

This formulation implies that consumers, on average, prefer sites for which sign ( z j ) = sign ( v i ) . ³ We model the ν_jds as coming from the following distribution.

ν jd ∼N ( 0,τ ν -1 )

3

Like the z_js, we assume that consumers know the value of τ ν − 1 on the basis of their prior browsing.

Signals of Horizontal Match Utility from Links

If the consumer visits site L during session d, and if site L has linked to site R that day, then the consumer will learn something about their horizontal match with site R that day. Site R, for example, might rarely report on rap artists. Site L’s link to R’s coverage of Kanye West thus signals that R’s coverage leans more in the direction of rap artists that day. If site L links to site R on day d, we say ℓ L → R d = 1 (and ℓ L → R d = 0 otherwise). We denote the signal contained in this link as s L → R d , and model these signals as noisy but unbiased reflections of sites’ true horizontal positions each day.

s L → R d | ℓ L → R d = 1 , ν R d ∼ N ( z R + ν R d , τ s − 1 ) .

4

Although horizontal position z R + ν R d is a characteristic particular to site R on each day d, two links to R from two sites L and L′ can signal two different aspects of R’s horizontal position. Thus, signals are indexed by both the receiving site R and the linking site L. The extent to which links accurately signal sites’ daily horizontal match positions is known to consumers and denoted τ s .

This setup highlights the informative role of linking among news sites. Links help consumers ascertain whether a site’s content is more or less congruent with their preferences that day. Importantly, because different values of ν _jd imply higher or lower levels of match utility (relative to the site’s long-run average), links can signal lower-than-average match (in which case they make the consumer less likely to visit the linked site). Furthermore, because consumers have different horizontal preferences, v_i, the same link from L to R might make some of L’s readers more likely to visit R, and others less likely.

Updated Beliefs About Horizontal Match Utility

Let n_ijd t–1 denote the number of links to site j that consumer i has seen prior to choosing what to do at step t of session d, and s ¯ i j d t − 1 denote these links’ average signal value.

n i j d t − 1 = ∑ a ∈ { a i d 1 ,... , a i d t − 1 } ℓ a → j d ,

5

s ¯ i j d t − 1 = { 1 n i j d t − 1 ∑ a ∈ { a i d 1 , … , a i d t − 1 } s a → j d if n i j d t − 1 > 0 0 if n i j d t − 1 = 0

6

Before the consumer sees any links ( n i j d t − 1 = 0 ), expected horizontal match utility is simply equal to its long-run average, E ( μ i j d | n i j d t − 1 = 0 ) = z j v i . But if the consumer has seen one or more links ( n i j d t − 1 > 0 ), their beliefs about j ’s horizontal match utility change. Standard Bayesian updating for conjugate normal distributions yields an expression for expected horizontal match utility, after seeing n_ijd t–1 links to site j (West and Harrison 1999).

E ( μ i j d | n i j d t − 1 , s ¯ i j d t − 1 ) = z j v i + ( τ s n i j d t − 1 τ s n i j d t − 1 + τ ν ) ( s ¯ i j d t − 1 − z j ) v i

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Expected match utility at site j is thus a weighted average of the consumer’s long-run average match, z_jv_i, and the match signaled by previously seen links to j, s ¯ i j d t − 1 v i . The weight given to each of these depends on (1) the variability of sites’ daily horizontal positions, τ ν − 1 ; (2) how informative links are about those horizontal positions, τ s ; and (3) the number of links the consumer has seen, n i j d t − 1 . Equation 7 therefore illustrates the value of links to the consumer: on average, they can shift expectations about horizontal match utility away from their typical long-run values and toward their true day-specific values. The left side of Table 1 summarizes the variables involved in this within-session, Bayesian updating of expected horizontal match.

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Table 1.

Summary of Bayesian Updating for μ i j d and β i j d t .

Horizontal Utility, μ i j d		Vertical Utility, β i j d t
Received		Received
( z j + ν j d ) v i	Horizontal utility from site j on day d	( K i d t + j − K i d t − 1 ) λ i	Vertical utility from site j at step t on day d
vi	Horizontal preference	λ i	Vertical preference
zj	Long-run average horizontal position	K i d t − 1	Bits seen prior to choice at step t of day d
ν jd	Deviation in horizontal position on day d, unknown to consumers	K i d t + j	Bits seen after visiting site j at step t of day d, unknown to consumers
Expected		Expected
zjvi	Expected match utility prior to seeing links	( α j 1 + α j ) N λ i	Expected vertical utility before seeing bits
z j v i + ( τ s n i j d t − 1 τ s n i j d t − 1 + τ ν ) ( s ¯ i j d t − 1 − z j ) v i	Expected match utility after seeing links	( α j 1 + A ( h i d t − 1 ) + α j ) ( N − K i d t − 1 ) λ i	Expected vertical utility after seeing bits
τ ν − 1	Variance of unknown horizontal position	N	Maximum total bits each day
τ s	Precision of link signals	α j	Long-run average daily bits
n i j d t − 1	Number of links seen prior to step t choice	h i d t − 1	Sites visited prior to step t choice
s ¯ i j d t − 1	Average signal value of links seen	A ( h i d t − 1 )	Sum of α j s for sites already visited

Value Function for Present and Future Browsing

When consumers visit a site, they not only gain utility but also may update their beliefs about match utility at other sites if they see outbound links (Figure 1, °4). As we show subsequently, forward-looking consumers anticipate this updating and thus face the standard exploitation–exploration trade-off when choosing which site to visit next. A consumer, for example, might decide to visit a site that frequently links to many others, expecting any links encountered to increase (decrease) their chance of visiting (avoiding) sites with higher (lower) daily match. For such consumers, sites that provide many outbound links provide value, in part, by raising the expected utility of the remainder of the browsing session.

The following value function corresponds with consumer i’s utility function and beliefs about match utility at step t of session d.

V ( I i d t − 1 , ∊ i d t ) = max { ∊ i 0 d t , max 0 < j ∈ J i d t [ E ( U i j d t | I i d t − 1 ) + δ ∫ I ' , ∊ ' V ( I ' , ∊ ' ) f ( I ' | I i d t − 1 , j ) g ( ∊ ' ) ] }

8

Equation 8 introduces the following notation:

δ determines how much the consumer discounts the future expected utility from browsing,

We describe the latter two bulleted terms next.

Consumer Information Set

The consumer’s information set, I_idt, includes three variables. ⁴ The first two, the number of links to each site encountered, { n i 1 d t , n i 2 d t , … , n i J d t } , and the average signal value of those links, { s ¯ i 1 d t , s ¯ i 2 d t , … , s ¯ i J d t } , determine the level of expected match (per Equation 7). The third variable, the set of sites that have been visited, is represented as a binary vector, h i d t ∈ { 0 , 1 } J , and determines the consumer’s choice set. The transition function, f ( I ' | I i d t − 1 , j ) , reflects the consumer’s beliefs about how each of these three variables, I i d t ≡ { n i d t , s ¯ i d t , h i d t } , will evolve if site j is visited at step t.

First, and most simply, given the choice to visit site j, the set of sites visited, h_idt, will evolve deterministically to reflect this choice. Second, if site j has not linked to any other sites, then neither n_idt nor s ¯ i d t change. ⁵ However, if site j has linked to another site k (i.e., ℓ j → k d = 1 ), then n i k d t = n i k t t − 1 + 1 , and the consumer anticipates a new value of s ¯ i k d t from the following posterior predictive distribution (West and Harrison 1999):

s ¯ i k d t | ℓ j → k d = 1 , n i k d t − 1 , s ¯ i k d t − 1 ∼ N [ z k + τ s n i k d t − 1 ( s ¯ i k d t − 1 − z k ) τ s n i k d t − 1 + τ ν , τ s − 1 + ( τ s n i k d t − 1 + τ ν ) − 1 ] .

9

Prior to visiting site j, however, the consumer does not know if site j has linked to any other sites. Because links are a priori unobserved by consumers, the transition function also reflects consumer i’s uncertainty about whether they will see links to other sites. We assume these probabilistic beliefs are rational, to the extent that experienced consumers know the average frequency with which each site j links to every other site k. We denote this long-run average linking frequency ω j → k . From the perspective of each consumer i, given their knowledge of ω j → k , encountering a link to site k after arriving at site j is a random event with the following i.i.d. probability:

Pr i ( ℓ j → k d = 1 | ω j → k ) = ω j → k .

10

This link probability does not imply that site j links to site k at random. Importantly, why site j chose to link to site k on day d does not matter as long as the consumer’s expectations about links are based on their knowledge of ω j → k . We elaborate on this point when discussing model identification.

Effects of Linking on Choice

The value function in Equation 8 encapsulates two routes through which linking can affect choice. The first is the within-session effect described in Equations 2 –7. This effect operates through Bayesian updating of expected horizontal match utility as consumers are exposed to the set of available links, ℓ j → k d , over the course of each session. Upon encountering a link, the consumer may become more or less likely to visit the linked site, depending on the information in the link. This change in the likelihood of a visit, however, only affects choices within the current session.

The second route through which linking can affect choice is the across-session effect. This effect is a consequence of consumers’ forward-looking behavior (Equations 8 –10), and in particular, consumers’ rational expectations about the sites’ long-run average link frequencies, ω j → k . The consumer knows that encountering links improves the precision of predicted match utilities. Seeing a link thus increases the overall expected value of subsequent browsing. Consequently, sites that typically provide many outbound links may be especially attractive to visit in any session, in particular when visited in the early steps. Importantly, this higher valuation due to linking exists in expectation. A site visit therefore does not depend on whether the site has actually made any links that day. If consumers are myopic—that is, if δ = 0 —then they do not attend to the benefit of seeing links and a priori do not assign extra value to sites that (on average) provide many outbound links. In this model, the across-session effect of linking only makes the linking site more attractive if consumers are forward looking.

To illustrate these implications, we use our model to simulate browsing in a stylized setting with two news sites and one consumer. Site L sometimes links to site R, but R never links to L (thus, ω L → R > 0 , whereas ω R → ​ L = 0 ). Because links to R provide unbiased signals of R’s horizontal match utility each day, half of L’s links signal higher-than-average match with R, and half signal lower-than-average match. To simplify the illustration, we assume that both sites provide the same average match utility to the consumer (i.e., their z_js are the same) and set the consumer’s opportunity cost of browsing high enough that each site has less than 50% chance of being visited each day. The simulations illustrate how linking affects browsing decisions in ways that can be either beneficial or detrimental to the linked site. We report further details and full results in the Web Appendix. Next, we summarize three main insights.

Utility from Vertically Differentiated News Sites

To account for vertical differentiation in the volume of news facts sites publish, we update the consumer’s utility function (Equation 1) to the following:

U ijdt =μ ijd + β ijdt − γ id + ∊ ijdt

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The term β i j d t represents a vertical component of utility. As a vertical component of utility, all consumers value it in absolute terms, albeit to varying degrees. Because the value of gaining factual information serves as the canonical example of such a vertical dimension, we normalize the utility from no news (i.e., being uninformed about the day’s events) to 0 and assume that β i j d t ≥ 0 .

We follow Allen (1983, 1986, 1990) by representing news facts as a collection of unique and indivisible “bits” that are observed by consumers, but not by the researcher. These bits correspond with the smallest units of news content that can generate a vertical component of utility (e.g., “Actor X will star in movie Y”). A new set of no more than N bits is available each day. Some of these bits are distributed heterogeneously across sites. A bit might appear at more than one site, or the bit might appear at none of the sites. If some bit b appears at site j on day d, we write ι b j d = 1 (and ι b j d = 0 otherwise). We assume only the first encounter with a bit generates utility, and that thereafter the bit becomes part of the consumer’s state of knowledge. The utility from seeing a news bit for the first time is heterogeneous across consumers and is denoted by the parameter λ i > 0 . ⁶

The number of distinct bits that have been seen, prior to choosing what to do at step t, is denoted K i d t − 1 . We use the notation K i d t + j to indicate the number of distinct bits that will have been seen if site j is visited next. Thus, K i d t + j − K i d t − 1 is the number of remaining (i.e., unseen) bits that will generate utility if j is visited next. ⁷ We express the vertical utility consumer i gains in terms of this quantity.

β i j d t = ( K i d t + j − K i d t − 1 ) λ i

12

The consumer knows K i d t − 1 before visiting site j at step t. However, due to the nature of news, K i d t + j , which indicates a future state of knowledge, is not known ahead of time.

Distribution of Bits and Consumer Learning

The number of bits at each site is obtained from a stylized model of information availability. On each day, there are at most N bits that can be published. The probability that bit b is available at site j is

Pr [ ι b j d = 1 | α j , π b ] = 1 − ( 1 − π b ) α j ,

13

π b ∼ U ( 0 , 1 ) .

14

The parameter α j ∈ ( 0 , 1 ) determines the extent of site j’s news coverage, with higher values of α j indicating more extensive coverage. Bits with higher values of π b are more likely to be published at all sites. Sites with higher values of α j are more likely to publish all bits (some may be unique to site j, and others available at many sites). In this way, the α j s also determine the extent to which sites tend to publish the same bits. Bits are distributed jointly across sites with correlations determined by the α j s.

Given their past browsing, experienced consumers know sites’ long-run, average daily number of bits—that is, they know the sites’ α j s. On any given day, however, consumers are uncertain about which bits are in the news ecosystem. Thus, consumers’ choices are only affected by their expectations about the number of bits they have not already seen. Accordingly, we augment the consumer’s information set, I_idt, so it includes K i d t − 1 and extend its transition function, f ( I ' | I i d t − 1 , j ) , to reflect the consumer’s beliefs about likely values of K i d t + j − K i d t − 1 .

We assume consumers’ prior beliefs about the availability of bits at each site are consistent with Equations 13 and 14). An application of Bayes’ rule then leads to the following (binomial) posterior distribution for K i d t + j − K i d t − 1 (see the Appendix for the derivation).

K idt +j − K id t − 1 |K id t − 1 ,h id t − 1 ∼ B [ N − K id t − 1 , α j 1+A ( h id t − 1 ) + α j ] ,

15

A ( h ) = ∑ k=1 J h k α k .

16

Recall that the state variable h i d t − 1 is a binary vector indicating which sites have already been visited in the session. Thus, A(h) is the sum of the α k s for all previously visited sites k. The term N − K i d t − 1 represents the maximum number of unseen bits that might yet be seen at one of the remaining news sites that day. The term α j / [ 1 + A ( h i d t − 1 ) + α j ] is the consumer’s expected probability of finding any of those unseen bits if site j is visited next.

It follows from Equation 15 that the expected vertical utility from the next site j is

E ( β i j d t | K i d t − 1 , h i d t − 1 ) = { [ α j 1 + A ( h i d t − 1 ) + α j ] ( N − K i d t − 1 ) } λ i .

17

The expected level of vertical utility in Equation 17 is the expected number of new bits found at site j from Equation 15, multiplied by the consumer’s preference for them, λ i . Before visiting any sites, A ( h i d 0 ) = 0 and K i d 0 = 0 . Thus, E ( β i d 1 | K i d 0 , h i d 0 ) = [ N α j / ( 1 + α j ) ] λ i at the start of the session. The right side of Table 1 summarizes the within-session, Bayesian updating process for the expected vertical component of utility.

Implications for Browsing

Here we briefly comment on the implications of this part of the model for browsing. Equation 17 reflects how the expected vertical utility is (1) higher at sites that publish more news facts on average, α j ; (2) higher for consumers who receive the most utility from news facts, λ i ; but (3) lower if a large amount of news information has already been obtained, K i d t − 1 . Moreover, due to the term A(h) in Equation 17, expected vertical utility is lower if many sites have already been visited—and lower still if the sites that were visited had large values of α j . The intuition is that any bits that were not already found at a high-α site are unlikely to be available from a low-α site—whereas the reverse is not true (bits not found at a low-α site might yet be available from a high-α site). All else equal, a consumer will, on average, prefer to visit sites with higher αs earlier in the browsing session, and sites with lower αs later.

Because each bit can potentially be published by more than one site, the volume of news published each day is correlated across sites. This correlation in news volume affects the consumers’ browsing choices at steps t > 1 of each browsing session—that is, after the consumer has visited one or more sites and learned something about the day’s news coverage. The number of bits at one site thus provides the basis for learning about the number of bits at other sites. We assume that the presence or absence of links is not directly informative about the number of bits at the linked site. The presence of links, however, can be indirectly informative about bits. This is because links can affect the order of visits, and the ordering of site visits determines which bits are encountered. In this way, links can affect the consumer’s beliefs about the bits available at the remaining sites. ⁸

This stylized specification of the vertical component of utility achieves two main objectives. First, the specification captures a long-run average component of utility that all consumers value in absolute terms, and thus, it cannot be reflected in the model of horizontal match utility. Second, and relatedly, the specification accounts for the impact of daily variation in news volumes and redundant coverage on traffic to news sites.

Consumer Data

The browsing data were provided by comScore as part of a larger data set describing visits by a rolling panel of U.S. consumers to more than 3,000 sites (all of which are members of the same blog-oriented advertising network). We focus on celebrity news sites in this study because (1) these sites cover a limited range of news items each day, (2) they frequently excerpt from each other, and (3) they format their home pages like blogs (i.e., as scrolling lists of news stories). We limit our attention to the five most visited celebrity news sites among the panel: Celebuzz, Dlisted, Egotastic!, Perez Hilton, and The Superficial. ⁹

Browsing data

A consumer’s browsing session includes all of their site visits occurring on the same day (as celebrity news sites operate under the same 24-hour news cycle as other media; Leskovec, Backstrom, and Kleinberg 2009). Thus, for each panelist, we compile the order in which any of the five sites were visited each day (the step t choices, a_idt, in the model). During Q4 2009, the 127 panelists in our estimation sample made 19,130 such choices over the course of 5,757 browsing sessions (where a session might comprise the choice not to browse that day).

Recall that visiting the same site more than once within the same browsing session is not feasible in our model framework. For the median consumer in our sample, 96.9% of sessions generated data consistent with this no-revisit assumption (for a graphical depiction of this distribution, see the Web Appendix). Furthermore, 96.9% might be a lower bound, because internet panel data contain false positives for site/page visits due to web browsers refreshing pages in open tabs (without any action taken by the consumer). Modeling revisits would add significant computational burden in exchange for limited insights. Thus, consistent with the online browsing literature (e.g., Kim, Albuquerque, and Bronnenberg 2010), we do not model revisits. The a_idts thus reflect the daily rank order of the earliest page request for each of the five sites.

Panelists differ in the subset of sites they visited most, as well as in the typical order of those visits within the session. Table 2 shows that Perez Hilton was the most popular site among both male and female consumers and was visited earliest in the session on average. Although panelists vary in the order of site visits across sessions, their typical ordering is stable over time (i.e., they are not learning which site is their favorite on average). The audiences of the other four sites differ noticeably by gender: male panelists visited Egotastic! and The Superficial relatively more, and female panelists visited Dlisted and Celebuzz relatively more.

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Table 2.

Summary of Browsing Behavior by Site and Gender.

	Visitors per Day			Step in Session
Site	Male	Female	All	Male	Female	All
Celebuzz	2.5	7.9	10.3	1.37	1.46	1.44
	(2.2, 2.7)	(7.3, 8.4)	(9.7, 11)	(1.29, 1.46)	(1.41, 1.51)	(1.4, 1.49)
Dlisted	3.4	9.0	12.4	1.42	1.28	1.32
	(3.1, 3.7)	(8.5, 9.6)	(11.8, 13)	(1.35, 1.5)	(1.25, 1.32)	(1.29, 1.35)
Egotastic!	6.8	2.9	9.5	1.23	1.57	1.33
	(6.3, 7.2)	(2.6, 3.2)	(8.8, 10.1)	(1.18, 1.27)	(1.44, 1.7)	(1.27, 1.37)
Perez Hilton	12.3	28.5	40.8	1.19	1.14	1.15
	(11.8, 12.8)	(27.4, 29.5)	(39.6, 41.9)	(1.17, 1.21)	(1.12, 1.16)	(1.14, 1.17)
The Superficial	4.6	3.6	8.0	1.38	1.94	1.62
	(4.3, 4.8)	(3.3, 3.9)	(7.5, 8.5)	(1.32, 1.46)	(1.86, 2.01)	(1.57, 1.67)

Notes: Means and bootstrapped 95% CIs based on 19,130 observed choices over the course of 5,757 browsing sessions. There are 127 consumers in the estimation panel (45 male and 82 female). “Visitors per Day” indicates the average number of male or female panelists visiting each site per day. “Step in Session” indicates the average time index t across visits; thus, lower values indicate visits that occurred earlier in the browsing session.

Men make up 35% of the panel but browsed more often than women. The median man browsed on 46 (out of 92) days, averaging 1.12 site visits per session, and the median woman browsed on 44.5 days, averaging 1.05 site visits per session. Variation within each group exceeds these cross-group differences.

Website Data

We created an automated web crawler to collect the full text from all news posts published at each of the five sites in Q4 2009. We use the text scraped from each site to determine, for each day, which other sites the linking site linked to and how many words each site published. We describe each of these next.

Link data

Links that appear within the text of posts are typically accompanied by an excerpt from the linked site or a brief description of the linked content (Dellarocas, Katona, and Rand 2013). Thus, even though we use the shorter term “link” to refer to both the link and excerpt, the excerpted content, and not the link per se, signals consumers’ match with the linked site. We therefore ignore static sidebar links that may be part of a site’s navigation but are never accompanied by an excerpt. After determining which (if any) of the other sites were linked each day (the ℓ L → R d s), we use the browsing data to infer the number of links to each site consumers would have already seen at each step of the browsing session ( n i j d t − 1 in Equation 7). ¹⁰

We derive the ω L → R s —the average frequencies with which each site linked to every other site—by averaging over observed links during the 92 days in Q4 2009, and treat them as data during estimation. These frequencies appear in Table 3. As many sites never linked to each other, half of the entries in Table 3 contain zeros (and thus half of the ω L → R s are zero). By contrast, Dlisted and Egotastic! linked to each other about 67% of the time during Q4 2009.

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Table 3.

Empirical Link Frequencies (%).

	Link Target
Linking Site	Celebuzz	Dlisted	Egotastic!	Perez Hilton	The Superficial
Celebuzz	—	6.5	0	1.1	9.8
Dlisted	69.6	—	68.5	2.2	2.2
Egotastic!	0	65.2	—	0	0
Perez Hilton	7.6	0	0	—	0
The Superficial	63	0	0	0	—

Notes: Links were embedded in news articles. We ignore static or sidebar links, as well as links to a site’s own content.

The model assumes consumers know these average link frequencies, ω L → R , but not on which days those links will appear, ℓ L → R d . One implication of this assumption is that the choice to visit a site at the start of a session should not be related to the site’s inbound or outbound links that day. To determine whether the data contradict this assumption, we conducted an analysis of the first site consumers visited on days with different numbers of in- and outbound links. Results, which are reported in the Web Appendix, show that browsing sessions are equally likely to start at sites, regardless of how many in- or outbound links they have that day. This result is consistent with the assumption that the decision to browse on day d is independent of the set of links appearing that day, ℓ L → R d (conditional on the consumer’s knowledge of the average linking frequencies among sites, ω L → R ). The distinction between consumers’ knowledge of average link frequencies, ω L → R , and their uncertainty about daily link realizations, ℓ L → R d , is central to our strategy for identifying link effects on browsing. We elaborate on this point when discussing model identification.

Word counts

Recall that the vertical component of utility is motivated in part by potentially large differences in the amount of news facts the sites publish each day. We use the number of words that sites have published each day as a measure for the unobserved quantity of news facts. As discussed in the model section, a consumer who has just visited a site with a large amount of news facts that are potentially redundant with content at the remaining sites might be more likely to end the session (and vice versa after visiting a site with very little news information). By using word counts as proxies for sites’ unobserved daily quantities of news information, we can measure more precisely the extent of this state dependence due to redundancy. For each site, we calculate the number of words in all posts published that day (including the text of hyperlinks to other sites, if any). Sites’ word counts are summarized in Table 4. We transform the daily word counts to define w j d ∝ log ( 1 + w o r d s j d ) and consider w_jd to be an indirect measure of the total news volume at site j on day d.

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Table 4.

Summary of Daily Word Counts by Site.

Site	Min	25%	Median	Mean	75%	Max
Celebuzz	0	1,140	1,923	1,912	2,873	4,076
Dlisted	1,746	6,627	11,013	11,072	14,137	33,461
Egotastic!	0	0	463	604	727	2,872
Perez Hilton	0	2,113	4,906	4,482	6,336	9,002
The Superficial	0	280	928	755	1,068	1,769

Notes: Counts include all words in the headline and body text of all posts published on a given day.

Recall that the vertical component of utility described in the previous section is defined in terms of the amount of news facts (bits) available at each site, but not the number of words. We relate the two as follows. First, after visiting the first site in any session, the consumer will have seen all of the bits published at that site. Thus, the state variable for the number of bits seen after visiting the first site, K i d 1 , is equal to the number of bits that site published on day d. The estimation strategy is thus to functionally equate the values of w_jd with daily realizations of the state variables K i d 1 , so K i d 1 ∼ B [ N , q ( w j d ) ] . We provide the derivation of q ( ⋅ ) in the Appendix. ¹¹

Preliminary Analysis

Recall that an excerpt in our model can signal either higher or lower horizontal match utility, thereby increasing or decreasing the likelihood of visiting the linked site. To understand whether variation in the data is consistent with the model, we conduct a preliminary analysis at the level of individual consumers. We first define two empirical choice probabilities for each consumer i at each site j. The first is the probability that consumer i visits site j after seeing one or more links to j at a previous site:

Pr ^ i ( a = j | n i j > 0 ) = ∑ d ∑ t 1 ( a i d t = j and n i j d t − 1 > 0 ) ∑ d ∑ t 1 ( n i j d t − 1 > 0 ) .

18

The second is the probability that consumer i visits j without previously seeing a link to site j:

Pr ^ i ( a = j | n i j = 0 ) = ∑ d ∑ t 1 ( a i d t = j and n i j d t − 1 = 0 ) ∑ d ∑ t 1 ( n i j d t − 1 = 0 ) .

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We next calculate, for each consumer i, the frequency-weighted average of each of these probabilities (i.e., averaging across all five sites). Thus, Pr ^ i ( a > 0 | n a > 0 ) and Pr ^ i ( a > 0 | n a = 0 ) denote the probability that consumer i visits any site a , given prior exposure to either n a > 0 or n a = 0 links to that particular site. Finally, we calculate the difference between these two probabilities: Δ i = Pr ^ i ( a > 0 | n a > 0 ) − Pr ^ i ( a > 0 | n a = 0 ) . If links tend to encourage consumer i to visit (avoid) linked sites, then we expect Δ i > 0 ( Δ i < 0 ); if links have no average effect on browsing, then we expect Δ i ≈ 0 .

Because observed links only affect choices at steps t = 2 and later (they are seen only after visiting a site), we compute these statistics using a subset of the full sample that excludes choices at step t = 1. We also repeat the analysis using only the subset of choices made at step t = 2. Figure 2 plots the empirical cumulative distribution of the difference in visit probabilities with and without links, Δ i , for both subsets. Individuals with negative values of Δ i are most prevalent. The left tail in Figure 2 corresponds with the majority of consumers who were less likely to visit a linked site after seeing the link. The right tail corresponds with the remaining minority who were more likely to visit a linked site. ¹²

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Figure 2.

Average effect of exposure to links on consumers’ probability of visiting the linked site.

This analysis provides preliminary support for our modeling approach, whereby individual links encountered during a browsing session can either increase or decrease the chance of visiting the linked site. The relative prevalence of negative values of Δ i in the estimation sample shows that links can potentially discourage individuals from visiting the linked site, and that this discouragement might occur to a meaningful extent.

Although this result indicates that for many individuals encountering links might be detrimental to the linked site, recall that the average effect (over all consumers) on site traffic might still be positive, because there is a floor on the probability of visiting the excerpted site. We see evidence for this positive outcome in Figure 2, as the magnitudes of increases in choice probability (the right tail) are greater than the magnitudes of decreases (the left tail). To understand if the overall effect is positive, we also calculate frequency-weighted averages of the probabilities in Equations 18 and 19 for each site—meaning we average across choice occasions to derive Pr ^ ( a = j | n j > 0 ) and Pr ^ ( a = j | n j = 0 ) for each site j. We then again calculate the difference in site-level visit probabilities with and without inbound links. The average effects are positive for four of the sites (ranging, in the t > 1 subset, from a .3% increase at The Superficial to a 3.6% increase at Egotastic!), and negative for Perez Hilton (−3.7%).

The preliminary analysis exploits variation in consumer choices on days when sites linked or did not link to one other. However, this data is not enough to determine what would be the result of a policy that bans links completely, because the choices recorded in the data occurred in a world in which linking, as a practice, was allowed. Consumers did not know which links would appear at any given site, but they knew the appearance of a link was possible (and might occur with a known average frequency, ω j → k ). Thus, to assess how linking, as a practice, affects browsing, we fit our structural model to the data, and use the estimates to simulate a counterfactual policy of banning links. We next present details relevant to estimation, and then present the model estimates and results of the counterfactual simulations.

Model Specification

Consumer parameters

Consumers are heterogeneous with respect to horizontal match preferences, v_i, their vertical utility from bits of news information, λ i , and their opportunity costs from browsing, γ i . We model this heterogeneity using consumers’ observed demographic variables, D_i, via the following prior distributions:

ν i ∼ N ( η v + D i ϕ v , ζ v 2 ) , log λ i ∼ N ( η λ + D i ϕ λ , ζ λ 2 ) , log γ i ∼ N ( η γ + D i ϕ γ , ζ γ 2 ) .

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Although this prior distribution assumes conditional independence among these parameters, they may be dependent in the joint posterior distribution.

Model likelihood

Following the literature on single agent, dynamic discrete choice models, we assume that the unobserved utility shocks, ∊ i d j t , follow an i.i.d. EV(0, 1) distribution (Aguirregabiria and Mira 2010). Conditional on the state variables I_idt–1, the value of visiting site j is V j ( I i d t − 1 ) + ∊ i d j t , where V j ( I i d t − 1 ) denotes the choice-specific value function:

V j ( I i d t − 1 ) = E ( μ i j d | I i d t − 1 ) + E ( β i j d t | I i d t − 1 ) − γ i d + δ ​ ​ ∫ ​ ​ log ∑ k ∈ J i d t \ j exp [ V k ( I ' ) ] f ( I ' | I i d t − 1 , k ) d I ' .

21

The choice-specific value function comprises two parts: (1) the expected period utility from visiting site j at step t and (2) the expected maximum utility from the remainder of the session, after visiting site j. The latter is an expectation taken with respect to the consumer’s information set, I ≡ { n , s ¯ , K , h } , which evolves differently depending on which site (if any) is visited after j. Dropping subscripts, the transition function for consumer i’s information set is

f ( I′|I,j ) =p ( s ¯ ′ |n ′ , n , s ¯ , j ) p ( n′|n,j ) p ( K′|K,h,j ) p ( h′ |h,j ) ,

22

where (1) p ( h ' | h , j ) denotes the deterministic update of the set of visited sites to include the visit to j; (2) p ( K ' | K , h , j ) is given by Equation 15; (3) p ( n ' | n , j ) is such that, per Equation 10, for every site k ≠ j , n k ' = n k + 1 with probability ω j → k , and n k ' = n k otherwise; and p ( s ¯ ' | n ' , n , s ¯ , j ) is given by Equation 9.

Integrating over the unobserved utility shocks, ∊ i d j t , leads to the likelihood of the model parameters, θ , conditional on (1) observed browsing choices, a i d t ; (2) state variables, I i d t ; (3) average site linking frequencies, ω L → R ; and (4) word counts, w j d :

L ( θ|a,I,ω,w ) ∝ ∏ i ∏ d ∏ t T id ∏ j ∈ J i d t { exp [ V j ( I id t − 1 |θ ) ] 1+ ∑ k ∈ J i d t exp [ V k ( I id t − 1 |θ ) ] } 1 ( a idt =j ) .

23

Parameter normalizations

Several parameter normalizations are necessary for estimation. First, recall the term N in Equation 17 represents an upper limit on values of K i d t (the number of bits seen). Model fit is insensitive to this value, as the λ i s can scale up or down at different values of N. We set N = 30 during estimation. Second, we set τ ν = 1 because the link data can only identify the ratio τ s / τ ν . Third, average horizontal match locations, z_j, are latent; thus, we normalize them with respect to consumer’s horizontal match preferences, v_i, by setting the mean of the z_js to be zero. Finally, to avoid a degenerate posterior density for the v_is, we set the prior intercept and scale of the v_is to η v = 0 and ζ v = 1 , respectively (Roos and Shachar 2014). The parameters to be estimated are summarized in Table 5.

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Table 5.

Summary of Estimated Parameters.

Parameter	Dimension	Description
( z j , α j )	5 × 2	Sites’ long-run average (horizontal) match locations and (vertical) bit quantities
( ϕ v , ϕ λ , ϕ γ )	7 × 3	Demographic coefficients for horizontal match preferences ( v i ), vertical utility ( λ i ), and the opportunity cost of browsing ( γ i )
( η λ , η γ )	1 × 2	Intercepts for vertical utility and the opportunity cost of browsing
( ζ λ , ζ γ )	1 × 2	Prior scales for vertical utility and the opportunity cost of browsing
γ w	1 × 1	Incremental (multiplicative) opportunity cost of browsing on weekends and holidays
τ s	1 × 1	Precision of link signals
δ	1 × 1	Discount rate for future browsing

Notes: Parameters that are integrated out of the posterior distribution through data augmentation are not listed.

Bayesian posterior distribution

We assume the following prior distributions for the model parameters:

logit α j ∼ N ( 0 , 1 ) , z j ∼ N ( 0 , 1 ) , τ s − 1 / 2 ∼ G a ( .4 , 5 ) ⇒ E ( τ s − 1 / 2 ) = 2 , η λ ∼ N ( 1 , .5 ) , η γ ∼ N ( − 1 , .5 ) , ϕ | ζ ∼ N ( 0 , ζ 2 ) , ϕ v ∼ N ( 0 , 1 ) , ζ 2 ∼ Sc - Inv - χ 2 ( 10 , .4 ) , γ w ∼ N ( 0 , 1 ) , δ ∼ U ( 0 , 1 ) .

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The likelihood function in Equation 23 depends on the state variables, I_idt. The state variables n (number of observed links) and h (sites previously visited) are observed by the researcher, whereas K (number of bits seen) and s ¯ (average signal value of observed links) are not observed. To obtain the marginal likelihood L ( θ | a , n , h , ω , w ) , we integrate over the posterior distribution of the unobserved state variables K and s ¯ using the standard Bayesian approach of data augmentation (Rossi, Allenby, and McCulloch 2005; Tanner and Wong 1987). To improve the efficiency of our sampling procedure, we transform the s ¯ . First, we define s L → R d * ≡ ( s L → R d − z R − ν R d ) τ s − 1 / 2 , so that s L → R d * follows a standard normal distribution independent of z_R and ν_Rd. Second, we enforce the identifying restrictions E ( s L → R d * ) = 0 and V ( s L → R d * ) = 1 through pairwise sampling of the s * s, using the method of Musalem, Bradlow, and Raju (2009). We use a parallel strategy to sample the data-augmented ν_jds.

Identification

Estimation

We use the IJC method to sample from the data-augmented posterior distribution of the model parameters. This method is based on the random walk Metropolis–Hastings (MH) algorithm, but augmented with a method for approximating the forward-looking component of the choice-specific value function (Equation 21). The computational gains from IJC are substantial, but may still produce sample chains with high autocorrelation. We alleviate some of this autocorrelation by using Girolami and Calderhead’s (2011) MMALA procedure to construct high-quality MH proposal distributions. These proposal distributions have two important features. First, they are centered over points lying in the direction of higher density regions of the parameter space (relative to the current parameter vector). Second, the covariance of the proposal distribution approximates the local curvature of the target distribution.

These features greatly improve the rate of convergence and reduce autocorrelation. Figure 3 illustrates this improved efficiency. The figure plots the first 1,000 draws from the full model estimated with random walk and MMALA proposal distributions. The MMALA chain reaches the maximum log density attained by the random walk chain with less than a third as many iterations. The benefits of MMALA proposal distributions are not limited to models estimated using IJC. When we estimate the myopic model using MMALA, lag-1, -5, and -50 autocorrelations are 19%, 36%, and 56% lower, respectively, compared with random walk, and effective sample sizes are 13 times higher.

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Figure 3.

Illustration of IJC’s faster rate of convergence with MMALA proposal distributions.

Constructing the MMALA proposal distribution requires the first, second, and third partial derivatives of the target log-density function with respect to the parameters. For single-agent dynamic discrete choice models, these derivatives are not available in closed form. Thus, we obtain their values through automatic differentiation (AD). ¹⁵ The MH proposal distributions we construct are based on derivatives of the model posterior distribution while ignoring the IJC approximation to the forward-looking component of the value function. Performing AD on the IJC approximation reduces the numerical stability of the derivative calculations and increases the computational expense. Estimation code is written in MATLAB and C++ using the CppAD library for automatic differentiation (Bell 2007) and is tested using the method of posterior quantiles (Cook, Gelman, and Rubin 2006). The Web Appendix provides additional details about the sampling algorithm.

Model Fit

We compare model specifications using two measures of fit. First is the median absolute percentage error (MAPE) of the posterior predictive distribution of the total visits to each site across all consumers and days in the sample, which provides a broad measure of fit with the sample data. Second is the expected deviance, which provides a measure of predictive accuracy (Gelman et al. 2004). Table 6 shows the full specification performs best for both measures, and the differences in fit are substantial. Because models with more parameters may have lower expected deviance due to overfitting, Table 6 also presents the Akaike and Bayesian information criteria. These penalize expected deviance by 2p and ln ( O ) p , respectively, (for p equal to the number of unrestricted parameters, and O equal to the number of observations).

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Table 6.

Model Fit Statistics.

Model	Parameter Restrictions	MAPE of Site Visits	Expected Deviance	Unrestricted Parameters	Observations	AIC	BIC
Full	—	22.8	51,205.7	38	19,130	51,271.7	51,580.3
Myopic	δ = 0	26.2	51,277.8	37	19,130	51,351.8	51,642.5
No signals	δ = 0 , τ s = 0	32.4	51,329.4	36	19,130	51,401.4	51,684.3

Notes: MAPE = the median absolute percentage error of posterior predicted browsing at each of the five sites; AIC = Akaike information criterion; BIC = Bayesian information criterion.

The model comparisons suggest not only that links provide useful information that enables consumers to find better matching content but also that consumers anticipate these benefits and use them in the way suggested by the full model. First, accounting for exposure to links to other sites in the model helps rationalize consumers’ choices within the current session. Second, accounting for the anticipated value of links to other sites helps to rationalize consumers’ choices across all sessions.

Table 7 reports the MAPE of total traffic across all consumers and days in the sample for each site. All specifications fit total traffic at Perez Hilton and Egotastic! better than at the other three sites. The full model performs relatively worse at Perez Hilton in terms of prediction error (perhaps because Perez Hilton does not provide or receive as many outbound and inbound links as the other four sites). In terms of overall fit, the full model has the lowest prediction error, and we present results from this specification next.

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Table 7.

MAPE of Posterior Predictive Distribution of Total Site Visits.

Model	Parameter Restrictions	Celebuzz	Dlisted	Egotastic!	Perez Hilton	The Superficial
Full	—	24.5	26.1	2.3	5.2	36.8
Myopic	δ = 0	26.4	31.8	2.6	4.1	35.2
No signals	δ = 0 , τ s = 0	35.5	35.0	9.5	2.3	36.1

Parameter Estimates

Horizontal match utility

Recall that average horizontal match utility is factored into a site-specific location, z_j, and consumer-specific preference, v_i. Posterior means and standard deviations for sites’ average match locations (z_j) are shown in Table 8, and posterior densities are depicted along the x-axis in Figure 4. Drawing on an informal sampling of site content, our post hoc, qualitative interpretation is that sites are horizontally differentiated depending on whether they emphasize content that is more or less sexual (e.g., pictorials of attractive female entertainers and models). Two sites have negative values of z_j, Egotastic! (−2.72) and Dlisted (−.89); the other three sites are positive: The Superficial (.45), Celebuzz (.95) and Perez Hilton (2.20). This ordering is consistent with what we see as a relatively greater amount of salacious content at Egotastic!, Dlisted, and The Superficial. Although Celebuzz and Perez Hilton also publish sexually oriented content, they do so less frequently and feature attractive male celebrities more than the other three sites. Moreover, reporting at Celebuzz and Perez Hilton aligns more closely with traditional tabloid celebrity gossip compared with the other three sites.

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Figure 4.

Joint posterior distribution of sites’ average vertical quality ( α j ) and horizontal match location (z_j).

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Table 8.

Horizontal ( z ) and Vertical ( α ) Quality Parameter Estimates by Site.

Parameter	Celebuzz	Dlisted	Egotastic!	Perez Hilton	The Superficial
z j	.95	−.89	−2.72	2.20	.45
	(.04)	(.07)	(.06)	(.02)	(.07)
α j	.030	.222	.010	.082	.014
	(.003)	(.007)	(.002)	(.003)	(.002)

Notes: Estimates are posterior means with standard deviations in parentheses.

Consumers’ horizontal match preferences (v_i) are highly heterogeneous, as shown in column 1 of Table 9. This heterogeneity is partly explained by two demographic variables. The most important of these is gender. The match preference coefficient for gender is positive, with a 95% Bayesian credible interval (CI) that excludes zero. This implies a higher preference among men (on average) for sites with z_j < 0 (i.e., the more salacious content of Egotastic! and Dlisted) and higher preference among women for sites with z_j > 0 (i.e., the more gossipy content of Celebuzz and Perez Hilton). The other demographic match preference coefficient with a 95% CI excluding zero is African American: these consumers receive higher match utility at Egotastic! and Dlisted, although we note that this estimate reflects the preferences of just five panelists. In total, demographic variables account for 12.7% of the heterogeneity in horizontal match preferences.

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Table 9.

Consumer Heterogeneity Parameter Estimates.

	Horizontal Match Location ( v )	Vertical Quality Preference ( log λ )	Opportunity Cost of Browsing ( log γ )
Observed Factors
Female	.92*	.79*	.21*
	(.18)	(.26)	(.10)
Age <25 years	.03	−.56*	.03
	(.19)	(.25)	(.10)
Age >55 years	.08	−1.03*	−.25
	(.32)	(.50)	(.17)
Income	.37	.41	.17
	(.24)	(.37)	(.14)
Children	.10	.02	−.13
	(.24)	(.34)	(.12)
Household size	.09	−.21	.08
	(.24)	(.33)	(.12)
African American	−1.38*	.86	.09
	(.36)	(.52)	(.20)
Intercept ( η )	.00	−1.94*	1.29*
	—	(.36)	(.14)
Unobserved Factors
Prior variance ( ζ 2 )	1.00	1.30	.51
	—	(.10)	(.04)
Posterior variance	2.21	1.34	.22
Total Heterogeneity
Posterior variance	2.55	1.66	.24
Explained by observed factors	12.7%	16.0%	6.0%

* For observed heterogeneity parameters, indicates that the estimates with 95% CIs exclude zero.

Notes: Estimates are posterior means with standard deviations in parentheses.

Link informativeness

Horizontal match utility from each site varies each day, and links signal these deviations to consumers. The informativeness of links, relative to daily variation in horizontal match, is reflected in the parameter τ s in Equation 7. The marginal posterior distribution of τ s has a 95% CI of (.01, .22) with a mean of .06. The inverse root of this parameter, τ s − 1 / 2 , is the ratio of the standard deviations of signals and daily match deviations. Its posterior mean is 5.2 with a 95% CI of (2.1, 10.3). Figure 5 illustrates the informativeness of links by showing the reduction in uncertainty about a site’s match utility after observing increasingly more links. The first link reduces uncertainty about match utility by approximately 6%, and the second link by another 4%.

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Figure 5.

Links reduce uncertainty about match utility.

Overall, we find compelling evidence that links provide informative signals about content at other sites, inasmuch as after seeing a link, consumers are less uncertain about match utility at the linked site. The counterfactual simulations further demonstrate that the information provided by links can have a meaningful impact on browsing.

Average Linking Frequency and Site Differentiation

Next, we comment briefly on how the frequency of links between competing sites affects how sites are differentiated in the eyes of consumers. Sites are differentiated by their average horizontal match locations, z_j, average news volumes, α j , and linking frequencies, ω j → k . Figure 6 depicts these characteristics spatially. Sites are indicated as points according to their horizontal match location along the x-axis and vertical quality along the y-axis. Link frequencies are overlaid as arcs of varying widths.

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Figure 6.

Summary of link frequencies and site heterogeneity.

Figure 6 shows that sites tend to link to competitors with similar values of z_j (i.e., their closest neighbors along the x-axis). ¹⁶ Because links provide signals about daily match locations, sites that frequently link to their closest competitors provide value by informing their audiences about sites with similar levels of match utility. If instead, links tended to point to sites with very different match locations—if Egotastic! were to link to Perez Hilton, for example—then consumers would find links to be less useful, because the links would be telling consumers about sites they are highly unlikely to visit anyway. As we demonstrate next through counterfactual simulation, a meaningful portion of some sites’ value to consumers stems from their tendency to link to other sites.

Procedure

We measure the impact of linking in terms of the amount of browsing, the flow of traffic between sites, and total traffic at each site, by comparing demand simulated under two scenarios. In the baseline scenario, we simulate demand using all links that are observed in the data (see Table 3 and Figure 6). In the counterfactual scenario, we remove these links and update consumers’ expectations about linking frequencies. In other words, we set all of the ℓ j → k d s and ω j → k s to zero before simulating demand. This counterfactual scenario assumes there has been an external intervention prohibiting linking (e.g., an extreme version of a “link tax”), and that sites continue to produce the same type of content as before. Banning links might also induce sites to change their typical content, but because we do not model these decisions, we cannot consider such an outcome. These results should therefore be interpreted as conditional effects in light of the existing content strategies.

We simulate the full 92-day sequence of browsing S times for every consumer under the baseline and counterfactual scenarios. Each of the S simulations corresponds with a sample from the data-augmented posterior distribution of the model parameters. For each simulation, we calculate a quantity of interest (e.g., the change in a site’s traffic particular site), then take the average over all S simulations (i.e., we integrate over the posterior distribution). Because consumers’ expectations about the links they will encounter depend on the ω j → k s, we reestimate the value function for each of the S parameter draws. This reestimation is computationally expensive, and thus we set S = 500. To account for simulation error, we calculate bootstrap confidence intervals for all estimates and focus attention on measured effects that are reliably different from zero. To facilitate intuition, we frame the results as changes from the counterfactual with no linking to the baseline with linking. Thus, when speaking of a quantity y as the expected percentage change from links, we mean E θ [ ( y b a s e l i n e − y c o u n t e r ) / y c o u n t e r ] .

We present the results in two stages. First, we discuss the total effect of links on consumers and sites at the aggregate level. Second, we decompose this total effect into two theoretically distinct effects of linking on choice: (1) the within-session effect due to observing a particular link on a given day (as a result of the ℓ j → k d s) and (2) the across-session effect due to the anticipation of outbound links (as a result of the ω j → k s).

Total Effect of Links

Among these sites, links positively affect browsing, as shown in Table 10. When we compare the baseline with linking to a counterfactual without, the total number of browsing sessions increases .11%. For the median consumer, the number of browsing sessions increases by .59%, the number of sites visited per session by .14%, and the total number of site visits increases by .54%. The impact of linking on the median consumer is more positive than the average effect across all consumers. This is because the increases in browsing and site visits due to linking are greatest among consumers who browse relatively less. Put another way, links provide less of an incentive to browse for those who would browse anyway, and more of an incentive for the marginal consumer. Turning to the site-specific browsing results, Table 10 shows that links also increase sites’ traffic to varying degrees. The greatest gains in total visits are found at Dlisted (.18%) and Egotastic! (.14%), sites that give and receive relatively greater numbers of links.

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Table 10.

Total Effects of Linking on Consumers and Sites.

		Relative Change (%)
		Median Consumer	All Consumers
Number of browsing sessions		.59*	.11*
Sites visited per browsing session		.14*	−.05
Total sites visited		.54*	.06
Visits to:
Celebuzz			.10
Dlisted			.18
Egotastic!			.14
Perez Hilton			.09
The Superficial			.01

* Indicates that the 95% bootstrap CI around the estimate excludes 0.

Notes: Percentage changes are expressed relative to the counterfactual with no linking.

The total effects reported in Table 10 reflect both the within- and across-session effects and are averaged across conditions in which links affect browsing decisions to different degrees. At the start of a browsing session, for instance, only forward-looking consumers’ expectations about links influence choice. Later in the session, choices are also affected by the actual links they might encounter. Because sites do not always provide outbound links, and because consumers do not visit every site, we interpret the results in Table 10 as the total effect of a broader policy of allowing links, with the understanding that some consumers may see few or even none of those links. To understand how exposure to any particular link affects consumers’ choices, we decompose the total effect into its constituent parts.

Decomposition of the Total Effect of Links

The across-session effect due to changes in beliefs about linking frequencies

Linking has a different effect on decisions at step t = 1 of a session, compared with later steps. At step t = 1 (prior to observing any links), only the across-session effect (due to ω j → k ) matters. Choices are affected by forward-looking consumers’ anticipation of links they might encounter but unaffected by specific realizations of links between sites (none have been encountered yet). The columns labeled “All Consumers” in Table 11 show how linking changes aggregate site traffic differently at the first step of consumers’ browsing sessions (when only expectations of links contribute to choice), compared with later steps (when both expectations and prior exposure to links matter). The columns labeled “Core Audience” and “Noncore Audience” provide insight into the heterogeneity of linking effects, as the statistics in those columns are calculated using a different subset of consumers for each site. Specifically, consumers are defined to be part of a site’s core audience if they are among the top 30 most frequent visitors to that site in the raw data. Otherwise, they are noncore.

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Table 11.

Relative Change in Total Visitors by Step of Browsing Session (%).

	Arriving at Step t = 1			Arriving at Steps t > 1
	Core Audience	Noncore Audience	All Consumers	Core Audience	Noncore Audience	All Consumers
Celebuzz	.42	.72	.21	.73	.68	.45
Dlisted	.13	1.18*	.21	−.20	2.76*	.42
Egotastic!	.07	1.66	.03	1.31*	5.50*	1.32*
Perez Hilton	.22*	.23	.21*	.01	−.47	−.55
The Superficial	.89	1.83*	.76	−.05	.82	−.14
All sites			.11*			−.07

* Indicates that the 95% bootstrap CI around the estimate excludes 0.

Notes: Percentage changes are expressed relative to the counterfactual with no linking. Consumers are included in either the core audience or noncore audience segments based on how many times they visited each site in the raw data. The top 30 consumers comprise the core audience and the remainder the noncore audience.

The difference between the within-session and across-session effects for Egotastic! provide a useful illustration. Egotastic! gains little traffic at step t = 1 (.03% in total) due to the cross-session effect. This suggests that Egotastic!’s outbound links do not make it more attractive. But Egotastic! does gain substantially more traffic at later steps t > 1 (1.32% in total) due mostly to the within-session effect. This result shows how the across-session effect depends on both sites’ horizontal positions and the other sites to which they link. Specifically, Egotastic! creates and receives a large number of links, but only in exchange with Dlisted. Dlisted, in contrast, links to all other sites. Because a substantial portion of Egotastic!’s audience frequently visits Dlisted as well (even in the absence of links), the information value of Egotastic!’s links is lower than Dlisted’s in expectation. Accordingly, when linking is allowed, Egotastic! actually loses a portion of its audience to Dlisted at step t = 1 (and Dlisted gains 1.18% in traffic from its noncore audience). The loss in some of Egotastic!’s traffic to Dlisted at step t = 1 thus offsets any gains that might have accrued to Egotastic! from its own outbound links. Accordingly, the increase in traffic at step t = 1 (due to the across-session effect) is greater for Dlisted (.21%) than for Egotastic! (.03%). At the same time, the within-session effect for Egotastic! is substantial. When linking is allowed, the number of visitors to Egotastic! at later browsing steps is 1.32 % higher. Moreover, among Egotastic!’s noncore audience, the gain in total traffic is 5.5%.

The within-session effect due to exposure to a link

Although the increase in traffic at later stages is relatively large for Egotastic!, this increase is defined as an average over cases in which some consumers encounter a link and others do not. We are also interested in comparing consumers’ choices when they have been exposed to a link against counterfactual choices in which the link has been removed. The challenge with making this comparison is that, as Figure 6 shows, sites often link to their closest neighbors in terms of match location. Thus, the propensity to visit a linked site, conditional on having already visited the linking site, is a priori high.

To deal with this challenge, we introduce the concept of a “removed link,” meaning a link that a consumer would have seen, had we not removed that link under the counterfactual of no linking. ¹⁷ We compare baseline choices, in which a link was observed, against counterfactual choices, in which a removed link would have been observed had the link not been deleted. Thus, the measured effect is almost entirely due to the exogenous presence or absence of the link itself. These differences in consumers’ propensities to visit a linked site are somewhat analogous to click-through rates for (untargeted) internet ads, in the sense that their measurement is predicated on exposure to a particular link (or ad).

Table 12 summarizes the results of this analysis. The third column of Table 12 compares consumers’ baseline choices after exposure to links with their counterfactual choices after “exposure” to removed links. For example, the probability of visiting Dlisted after exposure to a link is .26% higher than the visitation probability would be without the link. This result represents a 3.8% increase in the amount of Dlisted’s traffic originating from linking sites. The changes in visit probabilities differ in magnitude among sites’ core and noncore audiences. Links to Dlisted from other sites have a greater impact on visits to Dlisted among its noncore audience than among its core audience. Links to Dlisted thus increase its traffic relatively more on the extensive margin. By contrast, links to Egotastic! (all of which come from Dlisted) have a greater impact on visits to Egotastic! among its core audience than among its noncore audience. Links to Egotastic! thus increase its traffic relatively more on the intensive margin.

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Table 12.

Difference in Choice Probability by Prior Exposure to Link (%).

	After Exposure to Actual or Removed Links			With No Prior Exposure to Links
	Core Audience	Noncore Audience	All Consumers	Core Audience	Noncore Audience	All Consumers
Celebuzz	.27	−.04	.04	−.01	.01	.01
Dlisted	.02	.42*	.26*	−.04	.00	−.02
Egotastic!	.27*	−.01	.08*	−.02	.01*	.00
Perez Hilton	.72	.25	.47	−.17	−.11*	−.14*
The Superficial	.26	.21	.27*	−.07	−.07	−.03
All sites			.14*			−.02*

* Indicates that the 95% bootstrap CI around the estimate excludes 0.

Notes: Differences are expressed relative to the counterfactual with no linking. Consumers are included in either the core audience or noncore audience segments based on how many times they visited each site in the raw data. The top 30 consumers comprise the core audience and the remainder the noncore audience.

The difference in how links affect traffic among Dlisted and Egotastic!’s core and noncore audiences is related to the order in which these sites are typically visited when linking is allowed or banned. When linking is allowed, a substantial portion of Egotastic!’s core audience is made up of individuals who prefer to visit Dlisted first because of its outbound links. This result thus demonstrates another way in which the across-session effect moderates the within-session effect—it determines in part which consumers are (or are not) exposed to links.

The overall frequency-weighted average increase in the probability of visiting a linked site due to prior exposure to a link is .14%, a 2.3% increase. A relevant baseline for comparison is paid forms of links, such as display advertising. These typically have click-through rates less than .05% (Chaffey 2017; Lambrecht and Tucker 2013; Lewis, Rao, and Reiley 2011), and the effect we measure is large by comparison. ¹⁸