INTRODUCTION

This paper examines the welfare effects of different libel law standards as applied to the publication of news stories about public figures. Because of public (social) externalities, not all benefits or costs stemming from publication accrue to, or are borne by, the newspaper. As a result of these distortions, the socially optimal solution is unlikely to obtain.

The paper models the application of libel law by assuming that the newspaper's decision to publish is determined by the expected liability (costs) arising from publication of false stories, where its ability to mitigate some of the costs depends on the applicable liability standard. We show that compared with strict liability, the current standard governing libel law — termed "negligence" — leads to greater publication costs for stories that are likely to be true and potentially increased publication of stories that are likely to be false. This result is due to additional liability protection provided by negligence, enabling a newspaper to "insure" against liability.

We also show that an implicit agency problem exists between the newspaper and society under both standards, and determine conditions for which the social optimum can be consistently attained under strict liability, when using conventional policy tools. We demonstrate that the negligence standard cannot be adjusted in a similar manner. Finally, we provide other applications for this modeling approach.

Prior to 1964, the legal rule governing libel in the United States was a "strict liability" standard, under which a newspaper would be liable for all damages caused to someone's reputation by any story that was not provably true.¹ In its decision of New York Times v. Sullivan,² the Supreme Court ruled that "a public official cannot recover damages for a defamatory falsehood unless he proves that the statement was made with "actual malice," — that is "with knowledge that it was false or with reckless disregard of whether it was false or not."³ It thereby reduced the range of stories for which a newspaper could be found liable. In 1967, the Supreme Court extended this protection to stories about public figures.⁴ Thus, a negligence-style standard now governs libel suits brought by public officials or public figures.⁵

The motivation for this paper is to analyze implications for public welfare of these different liability standards in the presence of public externalities. Libel is an example of a "single activity accident" [Brown 1973; Diamond 1974], such that the actions of a newspaper damage an individual.⁶ For single activity accidents, a strict liability standard in the absence of other externalities is generally efficient [Shavell 1980; 1987]. Such models examine cases in which the only externality from an activity is the harm done to a third party.⁷ However, publishing news about public issues is deemed to entail a positive externality.⁸ The concern with a strict liability standard for libel is a potential chilling of publication and concomitant reduction of this externality.⁹ If publishers internalized all benefits from their activities and the only distortion was the negative externality from libel, this would not be of any concern. Since conventional tort models typically assume the party will internalize all benefits and costs other than third-party damages, it is important to consider some deviation from those assumptions in order to assess whether the New York Times v. Sullivan standard is appropriate.

The model in this paper will allow for the possibility that, absent any libel, the social value of publishing differs from the private incentive.¹⁰ We do this by assuming that the newspaper pursues policies that maximize expected value, and that the costs and benefits from publication differ from those of society. Such an assumption implies that a strict liability standard, by itself, does not result in the social optimum. However, we show that in theory we can adjust the strict liability standard using policy tools so that the problem solved by the publisher is proportional to that needed to maximize public welfare. In contrast, the negligence standard will fail to attain the social optimum even with the use of policy tools.

We extend the existing liability literature and study the distortions caused by liability rules in a two-stage decision model where the newspaper has the option to obtain further information regarding the truthfulness of a story, and we allow abandonment of the activity.¹¹ The former permits a revision of the expected value of a story; the latter allows a story to be pursued that would otherwise not be sufficiently plausible to publish under a strict liability standard. Permitting investigation also allows us to examine the qualitative differences between the two liability standards, namely that under negligence, investigation permits a publisher to inure itself against liability. Using the two-stage model we are able to define regions governing the actions of the publisher based on the ex ante (or perceived) probability that a story is true.

The remainder of the paper is organized as follows. The next section discusses the details of the model and derives the probability boundaries that are central to the model and govern the publishing decisions of the newspaper. The subsequent section derives the welfare equation and examines the deviation from the social optimum created by the agency problem. This section also develops the conditions under which policy tools can be used to correct for agency, and discusses policy implications. The penultimate section provides applicable extensions. The final section presents the conclusions.

THE MODEL

General setup and assumptions

General setup

Assume that a newspaper has access to a number of newsworthy stories, and that each has a perceived probability of being true.¹² The newspaper has three potential actions with regard to each story: publish without investigation, investigate, or kill. If the newspaper chooses to investigate, then it will publish or kill the story based on the results of the investigation. The decision tree of the newspaper is given in Figure 1. The newspaper is assumed to face one of two liability standards: strict liability or negligence. To determine the chosen action, we compute the expected value of the actions given the liability standard, and then determine the range of probabilities over which each action is optimal for the newspaper. We then compare standards by comparing the range of probabilities over which the actions are taken.

Figure 1.

Actions of the newspaper. Our model implies the following decision structure for the newspaper. The newspaper can publish, kill, or investigate a story. If it investigates, the newspaper updates its probability, and then decides whether to publish or kill. The payoffs depend on the liability regime that confronts the newspaper.

Full figure and legend (5K)

Assumptions and notation

Each story is assumed to have a probability p of being true, where f(p) is the corresponding distribution of p for stories being considered by the newspaper.¹³ If the newspaper publishes a true story, it obtains benefit v>0. If it publishes a false story, it suffers a loss d>0, which is independent of any liability. We can think of the benefits and losses as stemming from increases/decreases in circulation or advertising revenue that can be attributed to the publication of a story. If the newspaper publishes a false story, it may also be liable for damages to the individual, D_I, depending on the liability standard.

The newspaper has the option of investigating a story for a cost C. The investigation will signal that a story is "true" or "false," and based on that signal, the newspaper chooses to "publish" or "kill" the story.

Investigation is assumed to be imperfect, and can yield an incorrect signal about the truth of a story. Let be the probability that the investigation will signal that a true story is "false," and be the probability that the investigation will signal that a false story is "true." Assume that <0.5 and that <0.5.

The first standard we consider is termed "strict liability," where the newspaper incurs liability damages if it publishes a false story. The second standard is termed "negligence."¹⁴ The Supreme Court's definition of negligence is "with knowledge that [the story] ... was false, or with reckless disregard of whether it was false or not." To reflect this in our model, the newspaper incurs liability damages under negligence only when it publishes a false story when the investigation has signaled that it is false, or publishes a false story that has not been investigated.¹⁵ The newspaper does not incur a liability if it publishes a false story that it has investigated when the investigation has signaled that the story is true.

Newspaper actions

Since the newspaper receives benefits from publishing a true story and incurs damages when publishing a false story, the expected value of each story is a function of the liability standard, the story's probability, and the action taken. Thus, given a liability standard and a probability, the newspaper must decide whether to publish without investigation, investigate, or kill a story, in order to maximize the story's expected value:

The intuition is straightforward. At date 0, the newspaper takes the action yielding the maximum expected payoff for a story with a probability p of being true. For example, a decision to publish without investigating means that the expected payoff from that action is greater than the expected payoff from killing or investigating (less the cost of investigation).

To determine the range of p over which each action is optimal, we compute two boundary equations (probability bounds): a lower bound for p along which the newspaper is indifferent between investigating and killing a story, and an upper bound along which the newspaper is indifferent between investigating and publishing a story. These boundaries are determined by equating the expected values for the alternative actions, and solving for the corresponding p. The newspaper thus kills all stories with p below the lower bound, and publishes all stories with p above the upper bound. It investigates all stories with p between the two bounds.

Regardless of the liability standard, if the newspaper kills a story, then there are no expected benefits, damages, or investigation costs: the expected value is 0. Likewise, regardless of standard, if it publishes without investigation, there are no investigation costs, so the expected value is the expected benefits of publishing a true story less the expected damages from publishing a false story:

However, because the negligence standard provides liability protection when stories are investigated, and strict liability does not, the expected value of investigating a story (and corresponding probability bounds) must be determined contingent on a standard. The next two sections develop respectively the expected value of investigation subject to strict liability and negligence, and compute the corresponding probability bounds determining the newspaper's actions.

Strict liability

Under a strict liability standard, a story will only be published after investigation when the investigation signals that the story is true.¹⁶ Thus, the expected value from investigation is the expected benefit from publishing a true story, less the expected damages from publishing a false story, less the cost of investigation (for proof, see appendix; payoffs for the decision tree are illustrated in Figure 2):¹⁷

Figure 2.

Actions of the newspaper. There are three potential actions for the newspaper under strict liability. The actions are kill the story without investigation, publish without an investigation, or investigate and publish if the investigation signals that the story is true. The payoffs to the newspaper for these actions are illustrated by the following diagram.

Full figure and legend (10K)

To establish the lower bound for which an investigation is undertaken (p_s'), we equate (3) with the expected value of "killing" the story (zero), and solve for the probability:

Likewise, to obtain the upper bound on p for which investigation is optimal (p_s"), we equate (2) with (3) and solve for the corresponding probability:

When a story's probability lies below p_s', it is not sufficiently plausible to investigate given the expected costs and benefits, and is immediately "killed" by the newspaper. Above p_s", the story is so credible that the newspaper publishes the story without investigation. The reason is that the cost of investigation exceeds the expected damages from publishing a false story; thus, it is economically inefficient to investigate. Finally, in the region between p_s' and p_s", an investigation is conducted. The story is "killed" if the signal is false, and it is published if the signal is true.¹⁸ Figure 3 summarizes the actions of the newspaper under strict liability.

Figure 3.

Actions of the newspaper under strict liability. The figure summarizes the optimal actions of the newspaper regarding a story with a probability (p) of being true under a strict liability standard. The newspaper's action is determined by the relationship of p to the probability bounds p_s' and p_s". No investigation occurs for C>C_s".

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Note that p_s' slopes upward in C — as investigation costs increase, so does the minimum p for which EV(Investigation)>0. Likewise, p_s" slopes downward in C because the maximum p for which EV_s(Investigation)>EV(Publish W/O) declines. Because these bounds converge, there is an upper bound on the cost of investigation (C_s"), beyond which it is economically sub-optimal to investigate any story. C_s" is determined by equating p_s' with p_s", and solving for C.

The optimal action under strict liability is summarized in the following proposition:¹⁹

Proposition 1

Assume that the newspaper is subject to a strict liability standard; then there is a lower bound, p_s' (that is positively sloped in C), and an upper bound, p_s" (that is negatively sloped in C), such that the newspaper will: kill a story when p<p_s', publish the story without investigation when p>p_s", and investigate the story and publish only if the investigation signals the story is true, when p_s'<p<p_s". Defining C_s" as the value of C at which p_s' and p_s" converge to a single boundary p_CC"S, when CC_s", the newspaper will publish all stories for p>p_CC"_S and kill all stories for pp_CC"_S.

Proof

See appendix. 

Negligence

The qualitative results under a negligence standard are similar: there is, however, a significant difference. Because the newspaper is absolved of liability when it investigates and receives a signal that the story is true, two more probability boundaries exist (defining a fourth range of p) for which the newspaper has economic incentives to investigate, merely to insure against potential liability. This region only exists when investigation costs are low.

Under negligence the expected value from investigating and publishing after an investigation signals the story is true is given by²⁰

Thus like strict liability standard, there is a lower bound (p_n') and an upper bound (p_n"), under negligence, that determine whether a story is killed, investigated, or published. The lower bound is obtained by equating equation (6) with the expected value of killing the story. The upper bound is found by equating equations (6) and (2).

As shown in Figure 4, all stories with a probability less than p_n' are killed without investigation. When investigation costs exceed a threshold value C', stories with probabilities between p_n' and p_n" are investigated and published if the investigation signals that the story is true, and stories with probabilities greater than p_n" are published without investigation. The bounds derived under negligence differ from those of strict liability (and, in fact, are wider), but the paper's actions are qualitatively the same.

Figure 4.

Actions of the newspaper under negligence. The figure summarizes the optimal actions of the newspaper regarding a story with a probability (p) of being true. The newspaper's action is determined by the relationship of p to the four probability bounds p_n', p_n-lb, p", and p, and the cost of the investigation (C) relative to the threshold value C'. No investigation occurs for C>C_n".

Full figure and legend (10K)

However, unlike strict liability, when the cost of investigation is below C', there is an additional region where the newspaper investigates and publishes regardless of the investigation signal. This region is defined by the bounds p_n and p_n-lb shown in Figure 5.

Figure 5.

The "Insurance Effect." If investigation costs exceed C' the newspaper only investigates stories that require a true signal to be published. Thus, the newspaper only publishes stories without investigation, or that have been signaled to be true. The boundary p_n" separates those actions. However, if the cost is below C', it will investigate stories that it is certain to publish, between p_n-lb and p_n. Since stories with probabilities above p_n" are published without investigation, the newspaper investigates in the region between p_n" and p_n only to gain liability protection.

Full figure and legend (12K)

Since stories with probabilities greater than p_n" are published without investigation, the newspaper investigates a story in the region between p_n" and p_n because the cost of investigation is less than the expected liability damages for publishing a false story,²¹ and because it can eliminate that liability by investigating and receiving a true signal. This sole benefit causes the newspaper to investigate stories in this region to "purchase" the liability protection, or to gain the "insurance" value. The intuition is that the newspaper "buys" insurance when insurance is "cheap."²²

In the region above p_n-lb and below p_n", the newspaper publishes regardless of investigation results for a different reason. It publishes a story with a false signal because the marginal expected benefits from publishing on a false signal exceed the marginal expected damages.²³

The expected value of investigating and publishing regardless of the investigation signal is given by

The expression for p_n-lb is found by equating equations (6) and (7),²⁴ and then solving for p. The expression for p_n is similarly found by equating equations (7) to (2), and solving.

Derivation of these critical values is presented in the appendix; the results are summarized in the following proposition:

Proposition 2

Assume that the newspaper is subject to a negligence standard. There is an upper bound on the cost of investigation (C_n"), beyond which it is sub-optimal to investigate. There is also a lower bound (C'<C_n"), below which the newspaper will investigate stories that it will subsequently publish regardless of the investigation's outcome. Assume C<C_n"; there are four probability boundaries p_n'<p_n"p_n-lb<p_n, such that:

1. The boundaries p_n-lb and p_n converge at C', which is where p_n-lb ends and p_n begins. Likewise, p_n' and p_n" converge at C_n".
2. The newspaper will kill all stories when p<p_n'.
3. If C<C', the newspaper will: publish a story without investigation, for p>p_n, investigate and publish regardless of investigation results, for p_n-lb<p<p, investigate and publish (only) when the investigation indicates the story is true, for p_n'<p<p_n-lb.
4. If C'<C<C_n", the newspaper will: publish a story without investigation, for p>p_n"; investigate and publish (only) when the investigation indicates the story is true, for p_n'<p<p_n".

Proof

See the appendix. 

Comparison of standards

Figure 6 compares the actions of the newspaper under the two standards. The investigation region for negligence completely contains the investigation region for strict liability. This is because investigation is more valuable under negligence: investigation is imperfect, and the newspaper is able to eliminate the liability from publishing a false story by investigating and obtaining a true signal. As a result, relative to strict liability, the lower bound shifts down because the increased value of investigation makes it economically feasible to investigate stories with lower probabilities.²⁵ Consequently, there is increased publication of lower probability stories. (Note: As will be shown, this does not necessarily lead to lower societal welfare, which is also sensitive to parameter values and distributional assumptions about p.)

Figure 6.

Comparison of liability standards. The investigation region for strict liability (the dashed line) is a subset of the region under negligence where stories are investigated and published if true. Under negligence, p_n-lb and p_n are an upper bound to the region where stories are investigated and published if true, and p_n' is the corresponding lower bound. The upper and lower boundaries under the strict liability standard are p_s" and p_s', respectively. C' and C_s" are always strictly less than C_n", but C_s" may be greater, or less than, C'.

Full figure and legend (10K)

Likewise, the upper bound shifts up under negligence, because investigation provides liability protection beyond merely discriminating between true and false stories, which is the sole function of investigation under strict liability. Thus, the newspaper investigates higher probability stories to gain this added liability protection. Indeed, when investigation costs are less than C', there is a region under negligence in which stories are investigated solely to obtain insurance, since these stories will be published regardless of the investigation results. Thus, for any set of stories, more low probability stories will be investigated and published, and more high probability stories will be investigated, under negligence.²⁶ Proposition 3 summarizes these results:

Proposition 3

For any given set of parameters pertaining to a story (v, d, D_I, , , and C), C_n">C_s". Likewise, the relationship between the probability bounds for strict liability and negligence can be expressed:

For C<C': then p_n'<p_s'<p_s"p_n-lb<p_n, with p_n converging to p_n-lb at C'.

For C'<C<C_n": then p_n'<p_s'<p_s"<p_n", with p_s' and p_s" converging at C_s", and p_n' and p_n" converging at C_n".

Proof

See the appendix. 

WELFARE ANALYSIS

The welfare optimum

Welfare is the net benefit (or loss) to society from publication of a story. If a story is true, society receives a benefit (V>v). If a story is false, society receives no benefit; the cost to society is the sum of the damage to society (D_S) and the damage to the individual (D_I).²⁷ If an investigation is conducted, the society incurs a cost (C), whether or not the story is published.²⁸ The expected welfare is the expected value to society of a true story less the expected cost to society from publication of a false story, and any investigation costs.

If society internalizes all the costs and benefits from publishing a story, strict liability is efficient [Shavell 1980; 1987]. Thus, it is under strict liability that society computes the lower and upper boundaries (p' and p") to solve for the social optimum. These boundaries are derived in the same manner as those of the newspaper under strict liability, except that d=D_S and v=V, and they determine whether society kills, researches, or publishes a story without research. This is summarized by the following proposition:

Proposition 4

To maximize expected welfare, society computes lower and upper probability bounds p' and p", respectively. Society would kill all stories when p<p', publish a story without investigation when p>p", and investigate and publish only when the investigation indicates that the story is true, for p'>p>p".

Proof

See appendix. 

The expected welfare is

The first integral is the expected utility from a story that is investigated and published. p is the probability that the story is true, and 1- is the probability that the investigation has correctly signaled that the story is true. 1-p is the probability that the story is false, and is the probability that the investigation has incorrectly signaled that the story is true. The distribution of p is f(p).²⁹ Investigation costs are incurred over the region p(p', p") regardless of whether a story is published.

The second integral is the expected utility from stories that are published without investigation. If the story is true, society receives benefit V with a probability p. If a story is false, society incurs collective damages of D_S+D_I with a probability 1-p. Since no investigation has been conducted, no costs are incurred.

The expected welfare equation differs from the expected value of a story to a newspaper under strict liability,³⁰ and under negligence. Crucially, the bounds of integration (p' and p") — which are the probability bounds — differ from those of the newspaper under either liability standard. Since it is the bounds chosen by the newspaper (not society) that determine which stories are killed, investigated, or published without investigation, there will be a departure from publication policies that maximize expected welfare.³¹

Inherent inefficiencies of agency

Society faces an agency problem because the newspaper computes probability boundaries that are different from those of society (with the exception of footnote 30). Under strict liability, society's expected welfare is computed by substituting the newspaper's upper and lower boundaries for its welfare maximizing boundaries. Sub-optimality results and gives rise to the agency problem if the newspaper's bounds do not equal p' and p".

Under negligence, the problem is more complex; because the probability bounds used by the newspaper are dependent on C', it is divided into two regions: CC' and C<C'. If CC', (then like strict liability) p_n' and p_n" are substituted for society's lower and upper bounds, and a loss of welfare results if the bounds are not equal in value to those computed by society.³²

However, if C<C', the newspaper carries out an additional action that society would not — investigate and publish regardless of the result. It will do so between the boundaries p_n-lb and p_n. This action is sub-optimal because society internalizes all costs and does not benefit from the additional liability protection received by the newspaper. Hence, investigation when publication is certain provides no additional benefit to society, but creates additional costs.

The resulting welfare equation is

The third term of this equation reflects the additional cost to society of investigating a story that will be published with certainty, and because of it, (9) is always less than the social optimum. The reason is, to maximize welfare, the bounds of integration for the first two terms of (9) must equal the bounds that maximize the expected welfare equation, for example p_n'=p' and p_n-lb=p". Thus under negligence, when C<C', we have (8) less the third term — a deadweight loss — expected welfare is always sub-optimal. A derivation of (9) is provided in the appendix.

Welfare comparison

The social optimum does not obtain when boundaries on the welfare equation (under strict liability or negligence) do not equal p' and p". Thus, specific parameter values and distributional assumptions (about p) are necessary to determine which standard provides the greatest expected welfare for a given story. Comparison of Figures 7a to 6d, and 8a–c, illustrates the conditions for which each standard is best suited; the figures map the difference in welfare (between standards) as a function of the indicated axis variables. To avoid introducing additional non-linearities, we assume that p is uniformly distributed. In general, parameter values are permitted to range over the unit interval, so as to represent a fraction of the value to society of a true story (V=1), as a benchmark.³³ Figures 7b and 8b/c contrast these benchmarks with that for a high-value story (V=2).

Figure 7.

(a–c): Welfare comparison in - space. The difference in welfare between the strict liability and negligence standards, for p uniformly distributed between zero and one. The parameters (V, D_I, C, v, d) for each graph are (1, 0.5, 0.01, 0.3, 0.3), (2, 0.2, 0.01, 0.4, 0.4), (2, 0.2, 0.01, 0.2, 0.4), and (2, 0.2, 0.1, 0.4, 0.4), respectively. D_S is computed as 1-D_I; thus, total damages to society equal unity. Light gray indicates that welfare from strict liability equals or exceeds that under negligence; dark gray indicates that it is less.

Full figure and legend (197K)

Figure 8.

(a–c): Welfare comparison in v-d space. The difference in welfare between the strict liability and negligence standards, for p uniformly distributed between zero and one. The parameters (V, D_I, C, , ) for each graph are (1, 0.5, 0.01, 0.2, 0.05), (2, 0.2, 0.01, 0.2, 0.05), and (2, 0.2, 0.2, 0.2, 0.05), respectively. D_S is computed as 1-D_I; thus, total damages to society equal unity. The light gray region indicates that welfare from strict liability exceeds that under negligence; the dark gray indicates that it is less.

Full figure and legend (153K)

Light gray indicates that society's welfare from strict liability equals or exceeds that of negligence, and dark gray indicates that it is less. Contrasting Figures 7a and b reveals that higher values of V, D_S (relative to D_I), and proportional increases in v and d, lead to a greater range of error rates over which strict liability provides higher welfare. Figure 7c shows that when v is low relative to d, negligence is generally superior. Likewise, higher investigation costs tend to favor the negligence standard (see Figure 7d). Note that in the presence of high investigation costs, high type 1 and type 2 error rates (high and ) result in no investigation being conducted under either standard. The ravine (in Figure 7d), where negligence is clearly superior, is bounded in by C_s" to the right and C_n" to the left. Negligence is distinctly superior in the ravine, because to the left of C_s" no investigation occurs under strict liability, and reflects the greater value of investigation to the newspaper under negligence.

Comparison of Figures 8a–c reinforces these conclusions. Figure 8b shows the effect of an increase in V; Figure 8c illustrates the impact of higher investigation costs — for either small values of v or d, no investigation is conducted under either standard.³⁴ In summary, the region over which strict liability is welfare superior to negligence increases with V and the ratio of D_S to D_I. The region declines as investigation costs increase.

Use of policy tools and the advantage of strict liability

Without the use of policy tools, the social optimum cannot be assured for either standard. However, under strict liability there exists an investigation subsidy and scaling of damage award for which social optimality is consistently achieved, based solely on V, D_S, D_I, v, and d, and does not require knowledge of the investigation error rates, and .³⁵ This solution is not available for negligence and is independent of distributional assumptions.

Proposition 5a

Under strict liability, the socially optimal subsidy and liability scaling is (1-v/V)C and [v/V(D_s+D_I)-d]1/D_I, respectively.

Proof

See the appendix.³⁶ 

Under the negligence standard, such a correction is impossible: (1) for C<C', the social optimum can never be obtained due to the deadweight loss indicated in (9), (2) for CC', the value of and must be known to determine the socially optimal subsidy and liability scaling. These values place increased informational burden on policymakers. The latter problem is summarized by the following proposition:

Proposition 5b

Assume a negligence standard, with CC'; the subsidy and damage scaling that are required for socially optimal publication are sensitive to values of á and â.

Proof

See the appendix. 

CONCLUSIONS

This paper studies the decision-making process of a newspaper in publishing a story about public officials under two liability regimes. It has been established by previous research that if private and social benefits and costs are equal, then strict liability is the socially optimal standard. However, we find that because the newspaper does not internalize all public externalities, neither liability standard will reliably attain the social optimum, except under special conditions. This deviation in benefits also leads to an implicit agency problem between the newspaper and society.

We show that under negligence, the newspaper will investigate more low and high probability stories because of the liability protection that standard provides. This leads to two inefficiencies: (1) the newspaper may have incentives to investigate and publish very low probability stories, merely because of its ability to protect itself from liability; (2) when investigation costs are below a threshold, the newspaper has incentives to investigate stories that it is certain to publish, merely to gain the additional insurance value. The latter inefficiency results in a deadweight loss to society. We also show that by partly subsidizing investigation costs and by scaling the liability damages, the social optimum can be reliably obtained under strict liability, without knowledge of investigation error rates. In contrast, we show that the negligence standard requires knowledge of all parameters, thereby creating increased informational burden for policymakers.

Finally, one possible extension of the model is to allow investigation accuracy to vary in terms of its cost. Likewise, the model does not permit investigation accuracy to vary with likelihood that a story is true. Both extensions would require additional parameterization. The model also ignores issues of risk aversion; risk aversion will alter the probability bounds computed by the newspaper. Finally, the model abstracts from issues of competition. Competition among newspapers for market share is likely to alter publishing policies, by introducing strategic considerations requiring a game-theoretic approach. This would be an interesting direction to meaningfully extend the model.

Notes

¹ Simply for expositional convenience, we will refer to the potential tortfeasor as a newspaper. None of the arguments are specific to that medium, however.

² 376 US 254 (1964).

³ 376 US 254, 279–280 (1964).

⁴ Associated Press v. Walker, 388 US 130 (1967).

⁵ While "negligence," "gross negligence," and "actual malice" have different legal meanings, liability standards based on them have the same basic structure. All three allow for a defense for publishing a defamatory false statement. It is easier for a newspaper to avoid liability under a gross negligence standard than under a negligence standard and still easier to do so under an actual malice standard, but we view these differences as matters of degree.

⁶ Opportunities provided the individual to avoid the appearance of impropriety are (presumably) not a serious consideration in formulating libel law.

⁷ Other examples of models that use the care-activity framework to study the incentives of the injurer and the victim to reduce losses are: Green [1976]; Diamond [1974]; in the context of medical malpractice — Shavell [1978]; Simon [1982]; and Danzon [1990]; product liability — Oi [1973]; Eppel and Raviv [1978]; and obtain information about risk [Shavell, 1992].

⁸ In New York Times v. Sullivan, the Supreme Court said that a major consideration was the "profound national commitment to the principle that debate on public issues should be uninhibited, robust, and wide-open." 376 US 254, 270 (1964).

⁹ Hylton [1996], Posner [1998], and Cooter [2000] argue that when the newspaper publishes a story it is a public good and are unable to capture the full value of the story it has published. Since they are unable to capture the full social benefit of their publication, holding them strictly liable will result in a chilling effect on speech.
Renas et al. [1983] develop a model of a profit maximizing newspaper and analyze how the newspaper reacts to changes in the liability rules imposed on it. They argue that the newspaper will not behave in a manner to optimize social welfare and analyze the second-best solutions that will prevail. Garoupa [1999a, 1999b] address the implications of the tort of libel on political corruption where the media is powerful enough to influence the electorate.

¹⁰ Shavell [1997] studies the divergence between private and social motives to settle lawsuits. He argues that the distortion arises because of litigation costs that are incurred by both parties, and suggests a number of remedies to align the private and the social, including litigation subsidies, and fee shifting. Spier [1997] examines the role of litigation subsidies, punitive damages, and allocation legal costs. Our paper extends this area of research by exploring how liability standards give rise to distortions, and by examining the use of policy tools to correct inefficiencies. Also see Calabresi and Klevorick [1985] and Schwartz [1985].

¹¹ In an effort subsequent to earlier versions of this paper, Oren Bar-Gill and Assaf Hamdani [2003] use a Baysian approach to analyze optimal levels of verification under libel. Their approach is similar to that used in an earlier version of this paper. They depart from us by studying optimal levels of verification and by studying only strict liability. Their findings reinforce ours: policy tools are necessary to ensure optimal investigation and publishing policies.

¹² Hereon, we define this as a story's "probability."

¹³ The potential stories available to a paper in this model are assumed to be random and exogenous. A natural extension of the model would be to allow the newspaper to make the population of potential stories a function of the newspaper's expenditures.

¹⁴ We make the simplifying assumption that the courts enforce both standards perfectly. For an analysis of tort law in which enforcement is imperfect, see Calfee and Craswell [1984]. Extending the analysis here to allow for imperfect enforcement would be particularly desirable because the ambiguity of "actual malice" is the basis of one of the major criticisms of the current doctrine. See, for example, Epstein [1986].

¹⁵ We interpret "actual knowledge" that a story is false to mean that the paper investigates the story and obtains information that it is false. We interpret "reckless disregard" for whether the story is true or false to mean a failure to investigate.

¹⁶ Under strict liability, a newspaper is fully libel for D_I if a story is false, regardless of investigation signal. Thus, it will not investigate a story that will be published regardless of the investigation result, because the expected value resolves to equation (2), less the cost of investigation.

¹⁷ The first term is the expected benefit from publishing a true story: (1-p)v, multiplied by the probability the investigation correctly signals that the story is true, 1-. The second term is the expected damages from publishing a false story: (1-p)(d+D_I), multiplied by the probability the investigation will incorrectly signal that the story is true, .

¹⁸ This result arises in all "value of information" problems. The paper only incurs the cost of investigation if the outcome of the investigation affects its actions.

¹⁹ If investigation is too expensive, then there are no probabilities under which investigation is optimal. The critical value for C is the investigation cost above which investigation does not occur. If C is above that level, then there is a single critical probability that divides stories that are published without investigation from those that are killed without investigation.

²⁰ Because the newspaper is absolved of liability, equation (6) is equation (3) less the liability damages, D_I.

²¹ For example, C<(1-p)(D_s).

²² The intuition for the "insurance effect" can be observed by adding (1-p)D_I-C, the expected liability from publishing a false story after receiving a true signal less the cost of investigation (a net add-back), to equation (2). This yields the expected value of investigating and publishing regardless — equation (7).

²³ Add pv-(1-p)(1-)(d+D_I), the expected value for publishing despite a false signal, to the expected value from publishing only on a true signal. Therefore, the newspaper publishes on a false signal so long as pv-(1-p)(1-)(d+D_I).

²⁴ The first two terms of this action are the expected value from investigating and publishing when the investigation signals that the story is true. The third and fourth terms comprise the expected value from investigating and publishing when the investigation signals that the story is false.

²⁵ A newspaper, with a sufficiently low d, may have the perverse incentive to investigate stories that it believes are false (have a low probability of being true), merely to obtain a signal exempting it from liability. This may explain the behavior of some tabloids, whose circulation appears insensitive to reputational damage.

²⁶ The reason we differ with conclusions of the standard tort models (which find that negligence and strict liability are equally efficient) is the imperfection of investigation, and that under negligence, the newspaper is able to eliminate liability by investigating and receiving a signal that the story is true.

²⁷ V includes the benefits to the newspaper, v, and D_S includes the damages to the newspaper, d, but excludesD_I.

²⁸ This is the same cost incurred by the newspaper.

²⁹ Since the firm receives a number of stories, it has a prior probability about the truth of each story. We assume that these prior probabilities are distributed over the interval [0, 1].

³⁰ Unless (strict liability only) the newspaper internalizes all costs and benefits to society, for example v=V and d=D_S.

³¹ There are respective solution hyper-planes for strict liability and negligence (when CC') that equate the newspaper's boundaries with those of society. However, any departure from the required parameter combinations defining that hyper-plane will result in a sub-optimal level of welfare. Under negligence, if 0<C<C', optimality is never attained.

³² Structurally, the objective function in the welfare equation differs from that of the expected value to the newspaper under negligence because society computes its expected welfare by internalizing all costs — it must include individual damages D_I if a false story is published. In contrast, the newspaper eliminates this cost when it investigates and receives a true signal.

³³  and (representing the probability of type 1 and type 2 errors) are assumed to range from 0 to 0.5. D_S=1-D_I, so that total damages to society always sum to one.

³⁴ Because of perspective, C_n" is on the left and C_s" is on the right.

³⁵ The intuition behind this subsidy and damage scaling is that the newspaper should bear costs and damages in the same proportion to benefits as is borne by society.

³⁶ If we can make the assumption that all stories have benefits and damages to the newspaper and society in the same proportion, then the socially optimal subsidy and damage scaling are dependent only on investigation cost: (1-K)C and K (respectively), where v/V=d/D=K.

References

1. Bar-Gill, Oren., and Assaf Hamdani. 2003. Optimal Liability for Libel. The Berkeley Electronic Press, http://www.bepress.com/bejeap, in Contributions to Economic Analysis & Policy 2, Issue. 1, Article 6.
2. Brown, John P. 1973. Toward an Economic Theory of Liability. Journal of Legal Studies, 2: 323–349.
3. Calabresi, Guido., and Alvin K. Klevorick. 1985. Four Tests of Liability in Torts. Journal of Legal Studies, 14: 585–627.
4. Cooter, Robert D. 2000. The Strategic Constitution. Princeton: Princeton University Press.
5. Calfee, John E., and Richard Craswell. 1984. Some Effects of Uncertainty on Compliance with Legal Standards. Virginia Law Review, 70: 965–1003.
6. Danzon, Patricia M. 1990. Alternative Liability Regimes for Medical Injuries. The Geneva Papers on Risk and Insurance, 15(54): 3–21.
7. Diamond, Peter A. 1974. Single Activity Accidents. Journal of Legal Studies, 3: 107–164.
8. Eppel, Dennis, and Artur Raviv. 1978. Product Safety: Liability Rules, Market Structure, and Imperfect Information. American Economic Review, 68: 80–95.
9. Epstein, Richard A. 1986. Was New York Times v. Sullivan Wrong? University of Chicago Law Review, 53: 782–818.
10. Garoupa, Nuno. 1999a. Dishonesty and Libel Law: The Economics of the "Chilling" Effect. Journal of Institutional and Theoretical Economics, 15: 284–300.
11. Garoupa, Nuno. 1999b. The Economics of Political Dishonesty and Defamation. International Review of Law & Economics, 19: 167–180.
12. Green, Jerry. 1976. On the Optimal Structure of Liability Laws. Bell Journal of Economics, 7: 553–574.
13. Hylton, Keith N. 1996. A Missing Markets Theory of Tort Law. North Western University Law Review, 90: 977–1004.
14. Oi, Walter Y. 1973. Economics of Product Safety. Bell Journal of Economics, 4: 3–28.
15. Posner, Richard A. 1998. Economic Analysis of Law, 5th ed. Gaithersburg, Maryland: Aspen Law & Business.
16. Renas, M.Stephen, Rishi Kumar, Charles J. Hartmann, and Donn G. Shankland. 1983. Toward an Economic Theory of Defamation, Liability, and the Press. Southern Economic Journal, 50: 451–460.
17. Schwartz, Alan. 1985. Products Liability, Corporate Structure and Bankruptcy: Toxic Substance and the Remote Risk Relationship. Journal of Legal Studies, 14: 689–736.
18. Shavell, Steven. 1987. Economic Analysis of Accident Law. Cambridge: Harvard University Press.
19. Shavell, Steven. 1992. Liability and the Incentive to Obtain Information about Risk. Journal of Legal Studies, 21: 259–270.
20. Shavell, Steven. 1980. Strict Liability vs Negligence. Journal of Legal Studies, 9: 1–25.
21. Shavell, Steven. 1997. The Fundamental Divergence Between the Private and the Social Motive to Use the Legal System. Journal of Legal Studies, 26: 575–612.
22. Shavell, Steven. 1978. Theoretical Issues in Medical Malpractice, in The Economics of Medical Malpractice, edited by S. Rottenberg, Vol. 178. Washington, DC: American Enterprise Institute, 35–64.
23. Simon, Marilyn J. 1982. Diagnoses and Medical Malpractice: A Comparison of Negligence and Strict Liability Systems. Rand Journal of Economics, 13: 170–180.
24. Spier, Kathryn E. 1997. A Note on the Divergence Between the private and the Social Motive to Settle Under a Negligence Rule. Journal of Legal Studies, 26: 613–622.

Appendices

Appendix

DERIVATION OF EQUATION (3)

Let I denote the investigation signal and let S denote whether the story is true (T) or false (F). If the newspaper investigates, the probability that it receives a true investigation signal is

If a story is published, and S=T, it receives a payoff v, if S=F, it receives a payoff -(d+D_I). If a story is killed, its payoff is 0 regardless of S. Also, if a story is investigated, the newspaper incurs an investigation cost, C, independent of the signal. Thus, the expected value from publishing on a true signal (and killing on a false signal) yields (3). Figure 2 shows the expected value of these actions. The probability of receiving a false signal and corresponding expected value are

Thus, the expected value of publishing regardless of signal is E(False)+E(True), or equation (2) — C. Since (2) is the expected value from publishing without investigation, it is inefficient under strict liability to investigate and publish regardless of signal.

Proof of Proposition 1

Under strict liability, a newspaper can choose one of three distinct actions: kill the story without investigation,₁, investigate and publish if the investigation signals that the story is true, ₂, and publish without an investigation, ₄. We first solve for the probability boundaries separating these actions. Then, to determine optimal actions of the newspaper, compare the expected values for each action relative to the regions defined (in the p-C plane) by the boundaries. E denotes expected value.

Setting (3) equal to 0 and solving for p yields the lower probability bound:

Thus, for p>p_s', E(₂)>E(₁); for p<p_s', E(₁)>E(₂).

Equating (2) and (3) yields the upper probability bound:

Likewise, for p>p_s", E(₄)>E(₂); for p>p_s", E(₂)>E(₄).

Since p_s' and p_s" intersect, solving p_s'=p_s" for C defines an upper bound on C, beyond which investigation (action ₂) no longer occurs:

Finally, equating (2) to zero determines the boundary governing the actions of the newspaper for CC_s":

Comparing the above inequalities yields ₁ for p<p_s', ₂ for p_s'<p<p_s", and ₄ for p>p_s", when C<C_s". For CC_s", ₁ for p<p_CC"S and ₄ for p>p_CC"_S are obtained. The optimal actions for the newspaper are described in Figure 3. 

Proof of Proposition 2

Under negligence, a newspaper can choose from actions ₁, ₂, ₄, and the additional action unique to negligence: investigate and publish regardless of the signal, ₃. In an approach similar to that used for Proposition 1, we first solve for the probability boundaries, and then identify the optimal actions of the newspaper for the regions defined by the probability bounds.

Setting (6) equal to 0 yields the lower probability bound:

For p>p_n', E(₂)>E(₁); for p<p_n', E(₁)>E(₂).

Equating (6) and (2) yields the bound separating ₂ and ₄:

For p>p_n", E(₄)>E(₂); for p<p_n", E(₂)>E(₄).

Equating (6) and (7) yields the bound separating ₂ and ₃:

For p>p_n-lb, E(₃)>E(₂); for p<p_n, E(₂)>E(₃).

Equating (6) and (2) yields the bound separating ₃ and ₄:

For p>p_n, E(₄)>E(₃); for p<p_n, E(₃)>E(₄).

Since p_n-lb and p_n intersect, solving p_n-lb=p_n for C defines an upper bound on C, beyond which action ₃ no longer occurs:

For C<C', p_n>p_n">p_n-lb, where p_n" intersects with p_n-lb and p_n at C'. Comparing the inequalities corresponding to (A6), (A7), and (A8), yields ₃ as the dominant action when p(p_n-lb, p_n).

For C>C', we have p_n<p_n"<p_n-lb. Comparing the same inequalities reveals that the actions of the newspaper are completely described by p_n" (and p_n'). Likewise, solving p_n'=p_n" for C defines a second upper bound, beyond which the optimal action is ₁ for p<p_CC"_S, or ₄ for p>p_CC"_S:

Since C_n"-C'>0 , C_n">C'. Likewise, since solving p_n-lb=p_n" also yields C', this is where the boundaries intersect. The newspaper's actions are characterized by Figure 4. 

Proof of Proposition 3

By Propositions 1 and 2, p_s'<p_s", p_n'<p_n", and, for C<C', p_n'<p_n-lb<p_n. Thus, to show that the combined inequalities hold, we establish the following bilateral relationships:

1. C_n">C_s". Proof: C_n"-C_s">0.
2. p_s' and p_s" intersect to the left of p_n' and p_n". Proof: C_n">C_s".Let C<C_n", for (b), (c), and (d):
3. p_n">p_s". Proof: p_n"-p_s">0.
4. p_s'>p_n'. Proof: Since (1-)v-C_n">0, (1-)v>C. Therefore, p_s'-p_n'>0.
5. p_n-lb>p_s", when 0C<C'. Proof: p_n-lb-p_s"0. 

Proof of Proposition 4

Substituting V for v and D for d into (A1) and (A2) yield the following optimal boundaries for society:

DERIVATION OF EQUATION (9)

When C<C', the expected welfare equation is composed of three terms: the first is the expected welfare from action ₂, the second is the expected welfare from ₃, and the third is the expected welfare from ₄:

Because society internalizes all costs regardless of liability standard, the objective function of the second term is that of the first term less the cost of investigation. The equation simplifies to (9).

Proof of Proposition 5a

Under strict liability, the newspaper chooses p_s' and p_s" to subject to the subsidy S_S and attenuation of damages . Define X=C-S_S, the net cost of the investigation after receiving the subsidy. Equations (A1) and (A2) become

Let: S_S=(1-v/V)C and =[v/V(D_S+D_I)-d]1/D_I.

Substituting S_S and into (A13) and (A14) yields the socially optimal bounds (A11) and (A12). 

Proof of Proposition 5b

Define X=C-S_N. Under negligence the newspaper chooses the lower critical probability p_n' subject to X; thus, (A5) becomes

Equating (A15) to (A10) and solving for S_N yields the socially optimal subsidy

This reduces to

To derive the corresponding socially optimal damage scaling, note that (A6) likewise becomes

Equating to (A11), and solving for _N,

Therefore, S_N and _N are sensitive to the values of and .

Note: Even under the assumption v/V=d/D_S=K,

Acknowledgements

The authors would like to thank Gilbert Skillman and two anonymous referees for substantially improving the quality of this paper. The first author acknowledges his debt of gratitude to John Donaldson and Michael Salinger for their encouragement and guidance. We would also like to thank Chris Stefanadis for his comments on the paper. We accept responsibility for all the errors contained herein.