Related Literature

Research on underreporting bias in conflict data focuses on nonstrategic sources: inconsistent media coverage (Hendrix and Salehyan Reference Hendrix and Salehyan2015; Weidmann Reference Weidmann2015), aggregation bias from combining sources (Cook and Weidmann Reference Cook and Weidmann2019), or geographic biases associated with cellphone coverage (Weidmann Reference Weidmann2016). In contrast, we explore the interdependent strategic forces that determine underreporting bias in government- and NGO-provided data, considering the motivations of each actor when reporting unpopular violence. Thus, our paper relates to Drakos and Gofas (Reference Drakos and Gofas2006), who study how terrorists anticipate media coverage, creating underreporting bias. Whereas their work is largely empirical and focuses on the decision of terrorist groups to attack, this paper is largely theoretical and focuses on the decision of governments to acknowledge illegitimate violence. Our analysis demonstrates how incentives to report and investigate illegitimate violence affect underreporting bias even when the underlying frequency of illegitimate violence is exogenous.

To do this, we construct a formal model similar to those in the literature on auditing and risk disclosure (Avenhaus, Von Stengel, and Zamir Reference Avenhaus, Von Stengel and Zamir2002; Dobler Reference Dobler2008). Auditing games appear in the study of arms control (Arena and Wolford Reference Arena and Wolford2012; Baliga and Sjöström Reference Baliga and Sjöström2008), covert affairs (Spaniel and Poznansky Reference Spaniel and Poznansky2018), and cyberwarfare with attribution problems (Baliga, Bueno de Mesquita, and Wolitzky Reference Baliga, de Mesquita and Wolitzky2020). Besides our focus on the production and analysis of conflict data, the model below departs from this literature in two noticeable ways. First, whereas previous theoretical work has one uninformed audience, in our model the government (our inspectee) sends a report to two different uninformed audiences with different preferences over outcomes, the NGO (our inspector) and a third-party observer. Ex post, both types of governments benefit from third-party support, but only those perpetrating legitimate violence benefit from NGO investigations. Nonetheless, we show that governments benefit ex ante from stronger NGOs if the resulting investigations are thorough enough to commit governments to the truth.

Second, in our model the government’s actions are reports or disclosures. As such, they only affect government payoffs indirectly through endogenous third-party support instead of having a direct effect or altering the structure of strategic interaction. Thus, lying costs are fully endogenous in our model and arise via the observer’s distaste for cover-ups and equilibrium beliefs. In contrast, previous work treats lying costs as a black box by appealing to long-term reputational costs (e.g., Crescenzi et al. Reference Crescenzi, Kadera, Mitchell and Thyne2011; Smith Reference Smith2021). This distinction is important because we show that when lying costs are endogenous, it becomes more difficult to observe them in data generated from the model’s equilibrium. The difficulty arises because uninformed third-parties internalize the possibility of cover-ups when the government conceals illegitimate violence on the equilibrium path—even truthful governments are affected by lying costs.

More broadly, our analysis contributes to the literature examining how media shapes regime accountability—see Graber (Reference Graber2003) and Baum and Potter (Reference Baum and Potter2008) for reviews. Briefly, a robust civil society provides information to citizens that allows them to hold leaders accountable for unpopular decisions. Even autocrats may adopt partial press freedoms to incentivize local or bureaucratic officials (Egorov, Guriev, and Sonin Reference Egorov, Guriev and Sonin2009; Lorentzen Reference Lorentzen2014) or balance coup threats (Boleslavsky, Shadmehr, and Sonin Reference Boleslavsky, Shadmehr and Sonin2021; Hollyer, Rosendorff, and Vreeland Reference Hollyer, Rosendorff and Vreeland2019). In the domain of national security, Colaresi (Reference Colaresi2012) and Bell and Martinez Machain (Reference Bell and Machain2018) argue that increasing transparency institutions is a win-win for democratic governments: strong transparency institutions simultaneously satisfy temporary secrecy demands and long-term accountability demands through retrospective oversight by the media.Footnote ² Implicit in these accounts is an assumption that “the media serve primarily as a linkage mechanism rather than as an independent, strategic actor in the policymaking process” (Baum and Potter Reference Baum and Potter2008, 50). In contrast, we treat NGOs as strategic actors who allocate investigative effort according to budgetary pressures and expectations about government behavior. Doing so helps to elucidates the relationship between transparency institutions and actual information disclosed by governments and also accounts for why governments adopt these institutions.

Theoretical Approach and Illustrative Cases

Three premises constitute the foundation of our formal model. First, warring parties rely on the support of third-party noncombatants. In civil war, localized support can produce resources or information about the tactical strategies of the opponent (Condra and Shapiro Reference Condra and Shapiro2012; Kalyvas Reference Kalyvas2006; Shaver and Shapiro Reference Shaver and Shapiro2021). In international conflict, support from locals in theater provides similar benefits, but leaders in both autocracies and democracies need the support of their selectorate at home to ensure political survival (Bueno de Mesquita et al. Reference de Mesquita, Bruce, Siverson and Smith1999; Prorok Reference Prorok2016; Weeks Reference Weeks2012). Over the course of a conflict, a government may, intentionally or otherwise, perpetrate violence that they expect their potential supporters to find abhorrent, should they learn of it. Because violent conflict is messy, potential supporters do not have complete information about the nature of violence. Consequently, governments may attempt to conceal illegitimate violence to ensure continued support in the immediate term.

Second, although governments would like to conceal their use of illegitimate violence, they also wish to avoid getting caught in a cover-up, which could further undermine support. Societies with a minimally free press present the potential that watchdog NGOs or newspapers may also investigate the conflict and, in doing so, they may uncover evidence that contradicts the government’s official narrative about its wartime behavior. Watchdog, transparency, or human rights organizations view their primary purpose as gathering and disseminating information, and they derive monetary benefit via donors from doing so. For example, Human Rights Watch and Global Witness rely on donations from the public to continue fact finding and publishing reports on human rights violations both in and outside the context of violent conflict. These benefits might be even larger when their reports contradict information provided by the government. Therefore, when the government has concealed illegitimate violence, it cannot ensure that the violence will not be exposed by this kind of watchdog NGO. Such exposure may cause the government to lose supporters who care about the government’s honesty.

Third, NGOs and governments provide different types of information to observers. Governments have more information on the state of violence, given their participation in the event and the chain of command that regularly allows for the transfer of information through the ranks. However, even if the government would like to release verifiable information about the nature of a conflict event, constraints on military intelligence may prevent them from doing so. Nongovernmental organizations do not know the nature of violence at the outset but need to exert costly effort to investigate, providing verifiable information.Footnote ³ This creates an incentive for governments to conceal illegitimate violence that affects their support in the short term, so long as the potential cost of lying is not perceived to be too great in the long run. Of course, NGO investigations may not always be successful. Their likelihood of success depends on the amount of devoted resources, which is strategically allocated according to expectations about what an investigation could find. Although NGOs may be more or less driven by this expectation, they are unlikely to fabricate illegitimate violence because their survival and funding is contingent on their reputation as credible actors.

This theoretical framework captures primary empirical features of cases as disparate as the Naxalite conflict in India and civilian deaths from US drone strikes abroad. These cases motivate our main assumptions and illustrate how the model works on the ground. We do not use the cases to test the model or in a process-tracing exercise. Instead, we rely on them to identify prominent contextual features that we believe a model of strategic reporting should include. Our model is, in that sense, motivated by the cases. The model further provides a precise and internally consistent account of how reporting incentives of governments and NGOs interact, producing a set of intuitive as well as counterintuitive implications for conflict scholars.

Formal Framework

The model consists of three actors: a government, a watchdog NGO, and a third-party observer who is a potential supporter of the government, labeled G, N, and O, respectively. The government is involved in an ongoing violent conflict. At the beginning of the interaction, the current state or type of violence is $ v\hskip0.35em \in \hskip0.35em \left\{0,1\right\}. $ The state $ v=1 $ denotes an occurrence of illegitimate violence—for example, violations of human rights, violence against noncombatants, or destruction of critical infrastructure. In contrast, the state $ v=0 $ means no illegitimate violence occurred. Initially, the state of violence is known only to the government, and the probability that violence is illegitimate is $ \mathrm{\Pr}\left(v=1\right)=q $ . The parameter q captures at least three sources of illegitimate violence including how often the government chooses to violate laws or norms of war, agency problems between leaders and on-the-ground troops, and mere bad luck. These last two sources are outside the government’s purview, so $ q>0 $ .

After observing state $ v, $ the government chooses whether to acknowledge that illegitimate violence occurred (denoted $ m=1) $ or not (denoted $ m=0). $ The message $ m=1 $ corresponds to the government disclosing its use of illegitimate violence to reflect the deaths of civilians, for instance. We interpret $ m=0 $ as the business-as-usual message where the government does not update its list of government-perpetrated noncombatant killings or its list of drone strikes with civilian casualties. The government’s disclosure decision may not occur immediately after the state of violence is revealed, but this disclosure phase occurs before NGOs can investigate.

Both the third-party and the NGO observe the government’s message m. Subsequently, the observer chooses an initial level of support for the government $ {s}_1\hskip0.35em \in \hskip0.35em \unicode{x211D} $ . The NGO then chooses a level of effort $ e\hskip0.35em \in \hskip0.35em \left[0,1\right] $ for investigating the state of violence. With probability e, enough information is uncovered to publish a report revealing the type of violence ( $ r=1 $ ). With probability $ 1-e $ , the investigation fails to uncover enough information to publish ( $ r=0 $ ). If a report is published ( $ r=1 $ ), then the type of violence $ v $ is revealed to the observer. If the report is not released ( $ r=0 $ ), then the type of violence remains unknown.Footnote ⁶ In other words, NGOs find and disseminate evidence that verifies either type of violence $ v\hskip0.35em \in \hskip0.35em \left\{0,1\right\} $ .Footnote ⁷ The likelihood that they find such evidence depends on their chosen effort e. The observer then chooses a second level of support $ {s}_2\hskip0.35em \in \hskip0.35em \unicode{x211D} $ .

Consider how this setup captures the cases. In the Naxalite conflict, government troops regularly encounter rebels when patrolling villages. During these encounters, noncombatants may be targeted or killed by government forces. The third-party observer is the local, noncombatant population that determines the degree to which to support government forces—for example, by providing tactical information that could be used to defeat the rebels. If noncombatants are killed in an encounter, either accidentally or because they were incorrectly labeled as Naxalites, then the locals may consider the violence to be illegitimate. Initially, only the Indian government knows whether its forces engaged in illegitimate violence. Because war is messy and information is incomplete, locals outside of those immediately affected by the violence do not know its legitimacy. The government decides whether to report noncombatant causalities (i.e., disclose the legitimacy of violence) when updating its list of rebel encounters. The local population then decides whether to lend support to the government—for example, by providing more or less useful tips to the government about the insurgents’ tactical operations. At this point, NGOs may decide to investigate whether the government is being truthful in its description of the conflict. After their reports are published, potential supporters may change their level of support based on the findings.

In the US’s targeted-killing program, drone strikes may or may not entail noncombatant causalities or the destruction of critical civilian infrastructure. In contrast to the Naxalite case, the observer represents a constituency that decides the degree to which to support the Obama administration at the voting booth or in the court of public opinion. If the administration’s goal is to create broad support, then the observer could be a representative US citizen. In contrast, if the goal is to motivate the progressive base, then it could be a representative member of the Democratic Party. The model accommodates either interpretation, although the preferences of the specific observer—which we describe below—would change across interpretations. Strikes that only destroy munitions stockpiles or terrorist cells are likely to be considered legitimate violence, but those that kill noncombatants or destroy hospitals, for example, are less likely to be viewed as legitimate. When these events occur, US citizens have limited information about them. The government, in contrast, has explicitly stated that it knows the civilian cost of each of its targeted attacks (Director of National Intelligence 2016). If citizens gain information about the degree of noncombatant casualties associated with drone strikes through NGO reports, such as those published by the BIJ, then public opinion of the administration or Obama’s legacy within the Democratic Party may change.

For payoffs, the government wants to maximize support from the observer—support offered before the NGO publishes and support offered after any potential dishonesty is revealed. Its payoff is

$$ {u}_G\left({s}_{\mathsf{1}},{s}_{\mathsf{2}}\right)=g\left({s}_{\mathsf{1}}\right)+\delta g\left({s}_{\mathsf{2}}\right). $$

Above, the function $ g:\unicode{x211D}\to \unicode{x211D} $ maps support into some benefit. The function $ g $ is strictly increasing and continuously differentiable with a nonvanishing derivative ( $ {g}^{\prime }(s)>0 $ for all s). These benefits naturally depend on the nature of the conflict and the interpretation of the third-party. In the Naxalite conflict, support comes in the form of tactical information reported to the government as tips from the locals that can be used to defeat the insurgency (Kalyvas Reference Kalyvas2006; Lyall, Shiraito, and Imai Reference Lyall, Shiraito and Imai2015; Shaver and Shapiro Reference Shaver and Shapiro2021). In the drone-strike case, support refers to Obama’s poll numbers that can be used as political capital required for reelection or his progressive legacy upon leaving office. The parameter $ \delta >0 $ captures the relative importance of timing. If $ \delta <1 $ , then the government prioritizes immediate support. If $ \delta >1 $ , then the government prioritizes final support.

The observer has an ideal level of support $ \hat{s} $ that depends on the state of violence, the government’s message, and a baseline popularity level:

$$ \hat{s}=\underset{\mathrm{baseline}}{\underbrace{\beta}}\hskip1em -\hskip0.5em \underset{\mathrm{dislike}\ \mathrm{of}\ \mathrm{illegitimate}\ \mathrm{violence}}{\underbrace{\gamma v}}\hskip0.1em -\hskip2em \underset{\mathrm{dislike}\ \mathrm{of}\ \mathrm{cover}\;\mathrm{ups}}{\underbrace{\kappa \boldsymbol{I}\left[m=0,v=1\right]}} $$

Above, $ \beta \hskip0.35em \in \hskip0.35em \unicode{x211D} $ is the baseline support for the government. The parameter $ \gamma >0 $ denotes the observer’s distaste for the government using illegitimate violence, and $ \kappa >0 $ is the observer’s distaste for the government after it hides illegitimate violence.Footnote ⁸ With ideal support level $ \hat{s} $ , the observer’s payoffs are

$$ {u}_O\left({s}_1,{s}_2\right)=-{\left({s}_1-\hat{s}\right)}^2-{\left({s}_2-\hat{s}\right)}^2, $$

which is the quadratic loss between the chosen support and ideal support.Footnote ⁹

Finally, the watchdog NGO wants to discover enough information to publish a report subject to some cost of investigating. Its payoff is

$$ {u}_N\left(e,r;m,v\right)=\underset{\mathrm{benefit}\ \mathrm{of}\ \mathrm{revealing}\ \mathrm{the}\ \mathrm{state}\;\mathrm{v}}{\underbrace{\left(\lambda +\left(1-\lambda \right)\boldsymbol{I}\Big[m=0,v=1\Big]\right)}}r\hskip1em -\underset{\mathrm{effort}\ \mathrm{cost}}{\underbrace{\frac{\rho }{2}{e}^2}}. $$

Above, we normalize the NGO’s benefit of revealing the state of violence to one but divide this benefit into two components. The first term $ \lambda \hskip0.35em \in \hskip0.35em \left(0,1\right] $ captures the proportion of benefit from releasing reports regardless of whether there is a cover-up. The second term $ 1-\lambda $ captures the proportion of benefit that arises from catching the government in a cover-up. If $ \lambda $ is close to zero, then a substantial proportion of NGO publication benefits depend on exposing government cover-ups. If $ \lambda $ is close to 1, then NGO benefits depend on releasing reports regardless of their salaciousness.

The term $ \frac{\rho }{2}{e}^2 $ is the cost of exerting effort, and the parameter $ \rho $ captures NGO efficiency. For a fixed probability of success, less efficient NGOs (larger $ \rho $ ) pay higher investigative costs than do more efficient ones. Efficiency likely varies across NGOs, depending on funding and transparency institutions. Better funded NGOs will be more efficient, as they are not likely to face binding budget constraints and thus large opportunity costs, so $ \rho $ should be smaller. Likewise, NGOs operating in countries with transparency institutions such as FOI laws and press protections will face lower investigative costs because it is easier to gather information (Colaresi Reference Colaresi2012).

Our two cases help to motivate these payoffs. Many watchdog NGOs rely on charitable donations for funding. The size and frequency of these donations relate to their ability to publish visible reports and to their provision of information that differs from the prevailing state narrative. Some NGOs benefit from a surprise dividend—that is, additional resources following their revelation of government cover-ups. Not all NGOs are similarly reliant on this surprise dividend and thus may have different preferences, representing cases where λ is closer to one. We expect λ to be small when there is competition among NGOs for attention and donations, as in India, which has one of the largest numbers of NGOs per capita. At least one of the NGOs investigating the Naxalite conflict was particularly resource scarce and relied heavily on a surprise dividend, attempting to be the first to reveal dramatic information contradicting the government’s narrative.Footnote ¹⁰

Notice that the government potentially trades off initial and final support, where $ \delta $ captures the relative importance of final support to initial support. In the Naxalite conflict, local support in the Chhattissgarh region might be instrumental for the government’s military success. Thus, we might suspect that δ is close to or smaller than one as the government might want to end the conflict as fast as possible. In the US case, δ might be correlated with the time until the next election. If the presidential election is far off, δ would be greater than $ 1 $ , but if an election is immediate, $ \delta $ is close zero. In addition, δ could capture the degree to which Obama prioritizes his postpresidential legacy. If this is sufficiently valued, δ would be greater than one.

Strategies and beliefs are straightforward. For the government, a strategy is a function $ {\sigma}_G:\left\{0,1\right\}\to \left[0,1\right] $ , where $ {\sigma}_G(v) $ is the probability that the government admits that it used illegitimate violence after violence state $ v $ . For the observer, a strategy is a function $ {\sigma}_O:\left\{0,1\right\}\times \left\{0,1,\varnothing \right\}\to \unicode{x211D} $ , where $ {\sigma}_O\left(m,v\right) $ is the support O gives the government after message m when the state of violence is unknown ( $ v=\varnothing $ ), revealed to be legitimate ( $ r=1 $ and $ v=0 $ ), or revealed to be illegitimate ( $ r=1 $ and $ v=1 $ ). Finally, a strategy for the NGO is a function $ {\sigma}_N:\left\{0,1\right\}\to \left[0,1\right], $ where $ {\sigma}_N(m) $ is the amount of effort N chooses after message m. In addition, $ {\mu}_m $ is the belief that conflict involved illegitimate violence after message m—that is, $ {\mu}_m=\mathit{\Pr}\left(v=1|m\right) $ .

We focus on perfect Bayesian equilibria where beliefs satisfy a version of the D1 criterion, referred to as equilibrium hereafter. Specifically, an equilibrium is an assessment $ \left(\sigma, \mu \right) $ where (a) $ \sigma =\left({\sigma}_G,{\sigma}_O,{\sigma}_N\right) $ is a sequentially rational strategy profile given beliefs $ \mu =\left({\mu}_0,{\mu}_1\right) $ and (b) beliefs $ \mu $ are consistent with the strategies and updated via Bayes rule whenever possible. In addition, for any message m not sent with positive probability in equilibrium, the belief $ {\mu}_m $ satisfies a version of D1 modified to account for endogenous verification of the sender’s type.Footnote ¹¹ In the analysis, the refinement removes an equilibrium in which the government always admits to illegitimate violence regardless of v. Given the rarity of governments admitting fault in military combat, this is a substantively appealing criteria.

Before proceeding, it is important to remember that when illegitimate violence occurs, the business-as-usual message represents the government concealing the true state of violence. This concealment may take two forms, however. The government may omit the presence of illegitimate violence or may explicitly claim violence was legitimate. If the interpretation is the former, then we expect the lying costs κ to be comparatively smaller in magnitude than if the interpretation is the latter. This approach is justified for three reasons. First, our substantive implications focus on the frequency with which the government admits illegitimate violence, so the exact nature of the concealment is not a first-order concern. This is similar to empirical work that uses counts or indicators of illegitimate violence. Second, the type of concealment is difficult to classify in our cases. For example, in the Naxalite case, when the government does not report a clash with the rebels that resulted in noncombatant fatalities, this could be interpreted as concealment via omission. Another interpretation would be that, because the government reports no clashes, there could not have been illegitimate violence, which represents concealment via a lie. Third, in a version of the model with three messages—representing acknowledge illegitimate violence, omit discussing violence, and say explicitly no illegitimate violence occurred—the government has peculiar incentives after legitimate violence in nonseperating equilibria. Specifically, it might want to send unexpected messages suggesting that it concealed illegitimate violence, in which case the NGO would have greater incentives to investigate (as it expects a cover-up), which increases the probability that legitimate violence will be exposed and then increases final support for the government. This incentive seems disconnected from our cases where we do not observe governments, after claiming legitimate violence, trying to convince NGOs that there was indeed illegitimate violence to encourage investigations.

Analysis

NGO’s effort. To see how NGOs investigate, note that after the government sends message $ m=0 $ , the probability of a cover-up is $ {\mu}_0 $ . Then the NGO selects an effort level after message m such that

$$ \underset{e\hskip0.15em \in \hskip0.15em \left[0,1\right]}{\max}\;\left(\lambda +\left(1-\lambda \right)\mathbf{I}\left[m=0\right]{\mu}_0\right)e-\frac{\rho }{2}{e}^2 $$

and its equilibrium effort therefore takes the form

(1) $$ {\sigma}_N(m)=\frac{\lambda +\left(1-\lambda \right)\mathbf{I}\left[m=0\right]{\mu}_0}{\rho }. $$

If $ \lambda <1 $ , then a proportion of NGO publication benefits depends on exposing government cover-ups. In this case, Equation 1 says that as the NGO expects the government to more frequently conceal illegitimate violence (i.e., $ {\mu}_0 $ increases), it allocates more investigative effort because it is more likely to expose a cover-up, which entails $ 1-\lambda $ of additional benefit. Likewise, because countries with press protections and FOI laws will have smaller investigative costs $ \rho $ , Equation 1 says that NGOs in these countries will exert more effort than those in countries without such transparency institutions, all else equal.

Observer’s support. When the observer chooses support (either initial $ {s}_1 $ or final $ {s}_2) $ it may not know whether the government concealed illegitimate violence. Also, note that the observer does not have private information and its actions do not influence the NGO’s equilibrium incentives in Equation 1. Thus, when the observer does not know the value of $ v $ but sees message $ m $ , its equilibrium support satisfies

$$ \underset{s_t\hskip0.15em \in \hskip0.15em \mathrm{\mathbb{R}}}{\max }-{\mu}_m{\left({s}_t-\beta -\gamma -\kappa \left(1-m\right)\right)}^2-\left(1-{\mu}_m\right){\left({s}_t-\beta \right)}^2, $$

for $ t=1,2 $ . In contrast, when the observer knows $ v $ —for example, when the NGO successfully investigated the government—then the observer can choose its level of support to match $ \hat{s} $ . Overall, this discussion implies that in equilibrium, third-party support takes the form:

(2) $$ {\sigma}_O\left(m,v\right)=\left\{\begin{array}{c}\beta -{\gamma \mu}_m-\kappa \left(1-m\right){\mu}_m\\ {}\beta \\ {}\beta -\gamma -\kappa \left(1-m\right)\end{array}\right.\hskip0.6em {\displaystyle \begin{array}{c}\mathrm{if}\hskip0.24em v=\varnothing \\ {}\mathrm{if}\hskip0.24em v=0\\ {}\mathrm{if}\hskip0.24em v=1\end{array}}. $$

Equation 2 illustrates why it is difficult to use variation in observed support over time to identify the distaste of cover-ups and illegitimate violence. Suppose violence is illegitimate and the government conceals it by sending message $ m=0. $ In equilibrium, initial support is $ {s}_1=\beta -\left(\gamma +\kappa \right){\mu}_0 $ . If the NGO does not release a report, then final support is also uninformed, $ {s}_2={s}_1 $ , but if the NGO releases a report, then $ {s}_2=\beta -\gamma -\kappa $ . After an investigation reveals a cover-up, the change in support is therefore $ {s}_2-{s}_1=\left(\gamma +\kappa \right)\left({\mu}_0-1\right) $ , which is muted by equilibrium beliefs $ {\mu}_0 $ . When the observer anticipates cover-ups and illegitimate violence, $ {\mu}_0 $ is large, so a smaller shift in support occurs than suggested by $ \gamma $ and $ \kappa $ .

Government’s message. The government sends message m to maximize its expected benefits given the type of violence v and assessment $ \left(\sigma, \mu \right) $ . The first result says that the government is truthful in equilibrium after legitimate violence ( $ v=0 $ ).

Lemma 1. If violence was legitimate, then the government sends the business-as-usual message—that is, $ {\sigma}_G(0)=0 $ in every equilibrium $ \left(\sigma, \mu \right) $ . After the business-as-usual message, equilibrium beliefs are

$$ {\mu}_{\mathsf{0}}=\frac{\left(\mathsf{1}-{\sigma}_G\left(\mathsf{1}\right)\right)q}{\left(\mathsf{1}-{\sigma}_G\left(\mathsf{1}\right)\right)q+\left(\mathsf{1}-q\right)}, $$

which is strictly decreasing in $ {\sigma}_G(1) $ and weakly increasing in the prior q.

Only after illegitimate violence ( $ v=1) $ does the government have incentives to lie. On the one hand, the government can send a truthful message ( $ m=1), $ thereby avoiding a lie but decreasing support. On the other hand, the government can lie ( $ m=0 $ ) to increase initial support in hopes that the NGO does not reveal the lie, in which case it enjoys uninformed support in both the immediate and long term.

The expected benefits of lying are thus endogenous to equilibrium behavior. After illegitimate violence, if the government lies by sending the business-as-usual message $ m=0 $ , then its payoff is

(3) $$ {U}_G^{\sigma, \mu}\left(m=0;v=1\right)={\displaystyle \begin{array}{l}\left(1+\delta \left(1-{\sigma}_N(0)\right)\right)\underset{\mathrm{uninformed}\ \mathrm{support}}{\underbrace{g\left({\sigma}_O\left(0,\varnothing \right)\right)}}\\ {}+\hskip2px {\delta \sigma}_N(0)\underset{\mathrm{informed}\ \mathrm{support}}{\underbrace{g\left({\sigma}_O\left(0,1\right)\right)}}.\end{array}} $$

In Equation 3, the government potentially receives two different levels of support if it sends the business-as-usual message after illegitimate violence. The observer’s first level of support (made before the NGO report) will be uninformed, $ {\sigma}_O\left(0,\varnothing \right)=\beta -\left(\gamma +\kappa \right){\mu}_0 $ . The second will be informed $ {\sigma}_O\left(0,1\right)=\beta -\gamma -\kappa $ with probability $ {\sigma}_N(0)=\frac{\lambda +\left(1-\lambda \right){\mu}_0}{\rho } $ and will be uninformed with complimentary probability.

In Equation 3 both the NGO’s effort and the observer’s uninformed support depend on equilibrium beliefs $ {\mu}_0. $ By Lemma 1, $ {\mu}_0\hskip0.35em \in \hskip0.35em \left[0,q\right] $ is strictly decreasing in $ {\sigma}_G(1) $ —that is, the truthfulness of the government. If the government is expected to lie— $ {\sigma}_G(1) $ close to zero—then the NGO exerts more effort to investigate and the observer reduces uninformed support. These forces decrease the government’s benefit from lying. If the government is expected to tell the truth— $ {\sigma}_G(1) $ close to one—then the NGO exerts less effort to investigate and the observer increases uninformed support. These forces increase the government’s benefit from lying. The following result details how the government balances these trade-offs in equilibrium.

Figure 1 illustrates the inequalities in Proposition 1 as functions of the cost of lying and the importance of future support. The main implication for conflict scholars is that as the observer’s distaste of lying increases or the government prioritizes long-term rather than immediate support, then the government becomes more truthful in equilibrium. In Appendix H, we illustrate how the equilibrium characterization changes when only illegitimate violence is verifiable rather than both types of violence being verifiable as in the baseline model. The substantive features of the equilibrium characterization do not change, but the government is weakly less truthful in equilibrium.

Figure 1. Government’s Equilibrium Behavior from Proposition 1

Note: Example generated assuming g(s) = s, γ = 1, λ = 0.5, ρ = 1, and q = 0.2.

Implications

Underreporting bias

Scholars often rely on government data because of its temporal span and ease of access. Yet domestic and international NGOs may criticize this data as incomplete or biased in favor of the government. For example, Human Rights Watch provides alternative accounts of the government’s use of violence in the Naxalite conflict (Human Rights Watch 2008). In the drone-strike case as well, there are multiple lists recording the extent of illegitimate violence in the conflict. How can researchers or policy makers know which ones to prioritize and when?

To answer these questions, define the probability that actor $ i=N,G $ reports illegitimate violence given strategy profile $ \sigma $ :

$$ {PIV}_i\left(\sigma \right)=\left\{\begin{array}{cc}\hskip-2.5em q{\sigma}_G(1)+\left(1-q\right){\sigma}_G(0)\hskip2.28em & \mathrm{if}\;i=G\\ {}q\left[{\sigma}_G(1){\sigma}_N(1)+\left(1-{\sigma}_G(1)\right){\sigma}_N(0)\right]& \mathrm{if}\;i=N\end{array}\right.. $$

Then i’s underreporting bias is $ {B}_i\left(\sigma \right)=q- PI{V}_i\left(\sigma \right) $ . In words, underreporting bias is the difference between the baseline frequency of illegitimate violence, q, and i’s frequency of reporting illegitimate violence $ PI{V}_i $ . In equilibrium, both actors have a tendency to underreport.Footnote ¹² The government’s source of underreporting bias is its incentive to conceal illegitimate violence. The NGO’s source of underreporting bias is that it needs to exert costly effort to uncover the truth. Which source does the most damage? To answer this question, we first introduce the following assumption.

Assumption 1. The benefits of support are sufficiently responsive: there exists $ s\hskip0.35em \in \hskip0.35em \unicode{x211D} $ such that $ g(s)<g\left(\beta \right)-\rho \frac{\left(1+\delta \right)\left[g\left(\beta \right)-g\left(\beta -\gamma \right)\right]}{\delta \lambda}. $

Comparing Assumption 1 to Equation 4, the assumption says that we can find a distaste of cover-ups, κ, that is large enough to ensure that the government is truthful in equilibrium. The assumption holds if g is concave, for example. The next result describes two cutpoints on the distaste of lying that demarcate the three equilibria.

Lemma 2. Under Assumption 1, there exist cutpoints $ \bar{\kappa},\hskip0.35em \underset{\_}{\kappa}\hskip0.35em \in \hskip0.35em \left(0,\infty \right) $ such that $ \underset{\_}{\kappa }<\bar{\kappa} $ and the following hold in every equilibrium $ \left(\sigma, \mu \right) $ :

1. 1. if $ \kappa \hskip0.35em \ge \hskip0.35em \bar{\kappa} $ , then the government is always truthful and has underreporting bias $ {B}_G\left(\sigma \right)=0 $ ;

2. 2. if $ \kappa \hskip0.35em \le \hskip0.35em \underset{\_}{\kappa } $ , then the government never admits fault and has underreporting bias $ {B}_G\left(\sigma \right)=q $ ; and

3. 3. if $ \kappa \hskip0.35em \in \hskip0.35em \left(\underset{\_}{\kappa },\bar{\kappa}\right) $ , then the government admits its use of illegitimate violence with probability strictly between zero and one and has underreporting bias $ {B}_G\left(\sigma \right)\in \left(0,q\right) $ .

In the left panel of Figure 2, we graph the underreporting bias for each actor as a function of κ. If the distaste of lying is large enough ( $ \kappa \hskip0.35em \ge \hskip0.35em \bar{\kappa} $ ), then the government is always truthful. This corresponds to the government having a bias of zero and the NGO having a bias of $ q\left(1-\frac{\lambda }{\rho}\right)>0 $ . In contrast, if the government’s cost of lying is small ( $ \kappa \hskip0.35em \le \hskip0.35em \underset{\_}{\kappa } $ ), then the government never admits fault. In this case, its bias is $ q $ and the NGO’s bias is $ q\left(1-\frac{\lambda +\left(1-\lambda \right)q}{\rho}\right)<q $ . In the intermediate range $ \kappa \in \left(\underset{\_}{\kappa },\bar{\kappa}\right) $ , the government admits fault after illegitimate violence with probability strictly between zero and one. This probability is strictly increasing in $ \kappa $ , so the government’s bias decreases to zero as $ \kappa $ gets larger. As the government becomes more truthful, however, the NGO is less likely to catch the government in a cover-up, so it invests less effort, thereby increasing its bias. As the distaste of cover-ups $ \kappa $ moves from $ \underset{\_}{\kappa } $ to $ \bar{\kappa} $ , the government’s bias becomes smaller than the NGO’s bias at the point $ {\kappa}^{\ast } $ .

Implication 1. Under Assumption 1, there exists cutpoint $ {\kappa}^{\ast }>0 $ such that the NGO’s underreporting bias is smaller than the government’s if and only if $ \kappa <{\kappa}^{\ast } $ . Furthermore, $ \frac{\partial {\kappa}^{\ast }}{\partial \rho }>0 $ if $ g $ is concave and $ \frac{\rho \left(1-q\right)\delta \lambda}{q\left(\rho +\delta \left(\rho +1-2\lambda \right)\right)}\ge 1 $ .

Figure 2. Comparison of Government and NGO Underreporting Bias

Note: Left panel graphs the actors’ equilibrium level of underreporting bias $ {B}_i $ as a function of κ. Right panel graphs $ {\kappa}^{\ast } $ as a function of $ \rho $ and λ. Graphs generated assuming $ g(s)=s $ , $ \gamma =1 $ , and $ q=0.2 $ . In the left panel, we fix $ \rho =1.5 $ and $ \lambda =0.5 $ , implying that $ {\kappa}^{\ast}\approx 1.83 $ .

Notice that the cutpoint $ {\kappa}^{\ast } $ can increase as the NGO’s cost of effort, $ \rho, $ increases, which is illustrated in Figure 2’s right panel. In words, the NGO’s underreporting bias is more likely to be smaller than the government’s (in the set inclusion sense) as the NGO becomes less effective at investigating conflict events.Footnote ¹³ Implication 1 states a sufficient condition for this relationship, which is more likely to hold when q is small and δ is sufficiently large. This captures situations where the government’s use of illegitimate violence is not rampant and the government cares about its long-term prospects.

One could imagine the opposite result: greater investigative costs disincentivize NGO effort, thereby making NGO data less reliable relative to government data. This story misses the strategic interplay between the NGO and the government, however. When the costs of investigating increase, two effects emerge in equilibrium. In the direct effect, the NGO invests less effort, leading to greater underreporting bias in NGO data. In the indirect effect, the government anticipates the direct effect and also becomes less truthful, leading to greater underreporting bias in government data. Thus, both data sources become more biased after an increase in investigative costs, but the indirect effect dominates under the sufficient condition in Implication 1. In other words, as investigative costs increase, both government and NGO reports will exhibit more underreporting bias, but the effect will be larger for the government. For similar reasons, $ {\kappa}^{\ast } $ can be decreasing in $ \lambda $ —that is, the proportion of NGO publication benefits that depends on releasing information regardless of cover-ups, as illustrated in Figure 2’s right panel.

Overall, the analysis suggests two important considerations for conflict researchers. First, it establishes conditions under which NGO data should exhibit less underreporting bias relative to government data: (a) when NGO investigations are relatively inefficient (large $ \rho $ ) and (b) when NGOs rely heavily on surprise dividends (small λ). As mentioned above, the first condition likely holds when NGOs do not have long-term, robust funding or when NGOs operate in countries without transparency institutions. The second likely holds with substantial competition among NGOs for influence and attention when, for example, there are many NGOs per capita.

Second, underreporting bias in NGO and government data should be positively correlated across cases. When NGOs are substantially underreporting illegitimate violence, there are few incentives for governments to truthfully disclose illegitimate violence, as the likelihood of being exposed in a cover-up is small. Inversely, when NGOs correctly report illegitimate violence, then the government has stronger incentives to tell the truth to avoid cover-ups. Thus, the model suggests that combining government and NGO data will have limited benefits when addressing underreporting bias. When one source consistently misses violence incidents, it is likely the other source will as well.

Illegitimate Violence and Support

Recent work in the counterinsurgency literature estimates the effect of noncombatant casualties on local support for the side responsible. Broadly, state-caused collateral damage can depress support for the government, but the effect is attenuated when examining insurgent-caused damage and support for insurgent groups (Condra and Shapiro Reference Condra and Shapiro2012; Lyall, Blair, and Imai Reference Lyall, Blair and Imai2013; Shaver and Shapiro Reference Shaver and Shapiro2021). To measure violence against noncombatants, researchers use self-reported exposure in surveys (e.g., Lyall, Blair, and Imai Reference Lyall, Blair and Imai2013) or NGO-reported conflict events (e.g., Condra and Shapiro Reference Condra and Shapiro2012; Shaver and Shapiro Reference Shaver and Shapiro2021). In addition, Lyall, Shiraito, and Imai (Reference Lyall, Shiraito and Imai2015) measure exposure to violence using data from the International Security Assistant Force, a coalition of NATO governments charged with securing Afghanistan against the Taliban insurgency (842). With these data, they find “no consistent association between indirect exposure to violence and individual attitudes” (844–5).Footnote ¹⁴ Inspired by these studies and our cases, we compare the observed effect of illegitimate violence on equilibrium support to the true effect when governments strategically report illegitimate violence.

We begin by assuming that researchers observe government messages $ m $ and final support $ {s}_2 $ from several draws from one equilibrium.Footnote ¹⁵ For example, they observe whether the government reports causing collateral damages or not and the resulting level of civilian support. With such data, researchers can compare expected support after the government reports illegitimate violence (noncombatant causalities in this context) to expected support after the government reports no illegitimate violence, all else equal.Footnote ¹⁶ Definition 1 states this comparison formally.

Definition 1. Given a strategy profile $ \sigma $ , the observed effect of illegitimate violence using government data is $ \mathrm{E}\left[{s}_2|m\ne 1,\sigma \right]-\mathrm{E}\left[{s}_2|m=1,\sigma \right]\equiv \Gamma \left(\sigma \right). $

The observed effect underestimates the distaste of illegitimate violence when $ \Gamma \left(\sigma \right)<\gamma $ and correctly estimates the distaste when $ \Gamma \left(\sigma \right)=\gamma $ .

Table 1 computes the observed effect of illegitimate violence in the truthful and partially truthful equilibria. In the never-admit-fault equilibrium, the government never sends message $ m=1 $ , so $ \Gamma $ is undefined. The rows enumerate all possible combinations of messages and violence states. Given $ \left(m,v\right) $ , the column $ \mathrm{E}\left[{s}_2\left|m,,,\hskip-0.35em ,v,,,\hskip-0.35em ,\sigma \right.\right] $ refers to the expected level of support following message $ m $ and violence state $ v $ . The NA values correspond to pairs $ \left(m,v\right) $ that never appear on the equilibrium path. In the truthful equilibrium, government disclosures completely reveal its type so observed support includes no distaste of lying. In the partially truthful equilibrium, if the government admits illegitimate violence, then it is truthful and the observer correctly anticipates illegitimate violence. In contrast, if the government sends the business-as-usual message, then it is potentially lying. In this case, unobserved support is biased downward when violence was legitimate but biased upward when violence was illegitimate. Expected support after each message then follows from the law of total expectation.

Table 1. Observed Effect of Illegitimate Violence on Equilibrium Support

Note: Rows denote all possible message-violence pairs in the truthful (top) and partially truthful (bottom) equilibria, and NA denotes message-violence pairs that do not emerge in equilibrium. Columns denote the values used to compute the observed effect of illegitimate violence on support Γ. The value Γ is not defined in the never-admit-fault equilibrium.

Thus, the observed effect of illegitimate violence on support correctly estimates $ \gamma $ only when the government is truthful. In the partially truthful equilibrium, however, the observed effect is smaller than the true value because the observer tempers their support after the business-as-usual message because the government may be concealing illegitimate violence. It becomes particularly important to know under what conditions the government will be truthful and the difference between the true effect, $ \gamma, $ and its observed counterpart, $ \Gamma $ . Recall that by Lemma 2, when $ g $ is concave, there exists a $ \bar{\kappa}\hskip0.35em \in \hskip0.35em $ R such that a truthful equilibrium exists if and only if $ \kappa \hskip0.35em \ge \hskip0.35em \bar{\kappa} $ . So when $ \bar{\kappa} $ becomes larger, government disclosures are more likely (in the set inclusion sense) to provide incorrect estimates of $ \gamma $ in the case of the partially truthful equilibrium or infeasible estimates in the case of the never-admit-fault equilibrium.

Implication 2. Assume $ g(s)=s $ . Then $ \bar{\kappa}=\gamma \left(\frac{\left(1+\delta \right)\rho }{\delta \lambda}-1\right) $ , and the truthful equilibrium becomes less likely in the set inclusion sense as the distaste for illegitimate violence $ \gamma $ increase—that is, $ \frac{\partial \bar{\kappa}}{\partial \gamma }>0 $ . Moreover, in the partially truthful equilibrium $ \left(\sigma, \mu \right) $ , the difference between the observed and the true distaste for illegitimate violence $ \Delta =\gamma -\Gamma \left(\sigma \right) $ is increasing in $ \gamma $ —that is, $ \frac{\mathrm{\partial \Delta }}{\partial \gamma }>0 $ .

A dilemma thus arises when estimating the effects of illegitimate violence on popular support using government reports. If the distaste of illegitimate violence, $ \gamma $ , is small, then the government is truthful. This means that the observed level of support will not be biased due to strategic reasons (though it might not be easily detectable in smaller samples). If this distaste is large, then the government is unlikely to be truthful, and the observed effect will be biased toward zero. The magnitude of this attenuation increases in the size of the true effect. Likewise, the bias emerges even though government disclosures and popular support are observed without measurement error. The result indicates that the estimates associated with the government-provided data in Lyall, Shiraito, and Imai (Reference Lyall, Shiraito and Imai2015) could be interpreted as a lower bound on the degree to which civilians punish governments for exposure to violence.

Finally, the result also indicates that the truthful equilibrium is more likely to occur (in the set inclusion sense) when NGOs have small investigative costs, $ \rho, $ and the government cares about long-term support— $ \delta $ is large. Thus, the observed effect $ \Gamma $ should correctly estimate the parameter $ \gamma $ in environments with well-funded NGOs, strong transparency institutions, and governments that prioritize long-term support.

Implication 2 focuses on the relationship between illegitimate violence and observed equilibrium support. Our model also includes a parameter $ \beta $ describing the government’s baseline popularity absent illegitimate violence and cover-ups. We can therefore explore the relationship between popularity and the government’s propensity to disclose illegitimate violence, which means government transparency can be assessed via government baseline popularity, a potentially observable quantity.

Implication 3. Assume $ g $ is strictly concave. As the government’s baseline popularity, $ \beta $ , increases, the following hold:

1. 1. The truthful equilibrium becomes less likely in the set inclusion sense—that is, $ \frac{\partial \bar{\kappa}}{\partial \beta }>0 $ .

2. 2. The never-admit-fault equilibrium becomes more likely in the set inclusion sense—that is, $ \frac{\partial \underset{\_}{\kappa }}{\partial \beta }>0 $ , if and only if

   (6) $$ \frac{g^{\prime}\left(\beta -\gamma -\underline{\kappa}\right)-{g}^{\prime}\left(\beta -\left(\gamma +\underline{\kappa}\right)q\right)}{g^{\prime}\left(\beta -\gamma \right)-{g}^{\prime}\left(\beta -\left(\gamma +\underline{\kappa}\right)q\right)}>\frac{\rho \left(1+\delta \right)}{\delta \left(q+\left(1-q\right)\lambda \right)}. $$

In other words, the government generally becomes less truthful as its baseline popularity increases if the decreasing marginal returns to support are sufficiently strong. Specifically, if $ g $ is strictly concave, then higher levels of baseline support imply a smaller set of parameters sustaining the truthful equilibrium (Implication 3.1). In addition, the left-hand side of Equation 6 is a measure of the strength of decreasing marginal returns.

The intuition for this is straightforward. With strong decreasing marginal returns to support, the loss of support that follows an exposed cover-up is more detrimental to a government with low baseline popularity. Thus, the government can more easily afford the costs of lying when it enjoys broad baseline support. Therefore, the truthful equilibrium becomes more difficult to sustain and the never-admit-fault equilibrium becomes easier to sustain as the baseline support increases. Thus, the result suggests that conflict researchers should have greater concerns about underreporting bias from government data when the government enjoys a high baseline popularity from the observer, all else equal.

How and When NGOs Benefit Governments

Scholars have sought to explain why governments create transparency institutions at all given the benefits of controlling information about its behavior (Grigorescu Reference Grigorescu2003). Several study the variation in FOI laws (Berliner Reference Berliner2014), but transparency institutions include broader legal and regulatory frameworks that facilitate civil society’s access to information (as in Egorov, Guriev, and Sonin Reference Egorov, Guriev and Sonin2009; Lorentzen Reference Lorentzen2014). Understanding the drivers and effects of these institutions is especially important in this domain of national security, as governments are especially reticent to disclose information (Colaresi Reference Colaresi2012).Footnote ¹⁷ In the Naxalite case, for example, the government imposed significant costs on NGOs investigating the conflict via the Chhattisgarh Special Public Security Act of 2005. Those convicted of contacting suspected Naxalite rebels faced six years in prison. This policy and others that determine press protections affect investigative costs, $ \rho $ , and the equilibrium strategies capture the transparency behavior of the government. Thus, we use the model to study the effects of transparency institutions (via smaller $ \rho $ ) on government truthfulness and the conditions under which the government would have incentives to manipulate NGO investigative costs through changes to transparency institutions.

Lemma 3. In the partially truthful equilibrium, the government becomes less likely to disclose illegitimate violence as NGO investigative costs, $ \rho $ , increase—that is, $ \frac{\partial {\sigma}_G(1)}{\partial \rho }<0 $ and $ \frac{\partial {\mu}_0}{\partial \rho }>0 $ . In the other equilibria, the government’s strategy and thus beliefs are constant in $ \rho $ .

Because transparency institutions reduce investigative costs, they encourage government disclosures in the partially truthful equilibrium. This is illustrated in Figure 3’s left panel. Notice that transparency institutions are not necessary for government truthfulness, however. Even in their absence, as long as $ \rho <\infty $ , NGO investigations still expose cover-ups in equilibrium, which means the government could truthfully disclose illegitimate violence when the importance of long-term support, $ \delta $ , and the distaste of cover-ups, $ \kappa $ , are large.

Figure 3. Effects of NGO Efficiency on the Government’s Strategy and Payoffs

Note: Left panel graphs the government’s equilibrium probability of truthfully reporting illegitimate violence, $ {\sigma}_G(1) $ , as a function of the NGO’s cost of effort, $ \rho $ . Right panel graphs the government’s ex ante expected utility as a function of $ \rho $ . Dashed vertical lines demarcate the three types of equilibrium behavior: truthful (small $ \rho $ ), partially truthful (moderate $ \rho $ ), and never admit fault (large $ \rho $ ). Graphs generated assuming $ g(s)=\log s $ , $ \beta =2 $ , $ \kappa =1 $ , $ \gamma =0.95 $ , $ \delta =2 $ , and $ q=0.25 $ .

Recall that uninformed support after message $ m=0 $ depends on the probability that the government lied, $ {\mu}_0 $ . By increasing the equilibrium probability that governments disclose illegitimate violence, efficient NGOs create positive belief spillover effects to governments after legitimate violence via enhanced uninformed support. The next implication states when this effect can increase the government’s ex ante expected utility.

Implication 4. If $ g $ is strictly concave, then the following hold:

1. 1. In the partially truthful equilibrium, the government’s ex ante expected utility is strictly decreasing in NGO investigative costs, $ \rho $ , if $ \lambda \hskip0.35em \ge \hskip0.35em \frac{\rho \left(1+\delta \right)-2 q\delta}{\delta \left(1-2q\right)} $ . This inequality always holds if $ q\hskip0.35em \le \hskip0.35em \frac{1}{2} $ .

2. 2. In the never-admit-fault equilibrium, the government’s ex ante expected utility is strictly increasing in $ \rho $ .

3. 3. In the truthful equilibrium, the government’s ex ante expected utility is constant in $ \rho $ .

In other words, when $ g $ is strictly concave, governments can benefit ex ante from more efficient NGOs—that is, smaller $ \rho $ produced from transparency institutions—only in the partially truthful equilibrium. Implication 4 states two sufficient conditions for this to happen: the probability of illegitimate violence is small or the NGO is sufficiently motivated to investigate events regardless of the surprise dividend. To see the intuition, notice that, in the partially truthful equilibrium, the government wants to commit to telling the truth ex ante. After illegitimate violence, the government is mixing and thus indifferent between lying and telling the truth, the latter entails a payoff of $ \left(1+\delta \right)g\left(\beta -\gamma \right) $ , which is independent of $ \rho $ . After legitimate violence, the government sends message $ m=0 $ and would like the message to be believed with certainty, and Lemma 3 shows that the message becomes more believable with more efficient NGOs. Thus, increasing the efficiency of NGOs via transparency institutions can weakly increase the expected utility of both types of government as the business-as-usual message $ m=0 $ becomes more believable.

In contrast, in the never-admit-fault equilibrium, more efficient NGOs decrease the government’s expected payoffs. Here, the government expects three levels of final support: uninformed $ {s}_2=\beta -\left(\gamma +\kappa \right)q $ with probability $ 1-{\sigma}_N(0) $ , informed after legitimate violence $ {s}_2=\beta $ with probability $ {\sigma}_N(0)\left(1-q\right) $ , and informed after illegitimate violence $ {s}_2=\beta -\gamma -\kappa $ with probability $ {\sigma}_N(0)q $ . As the NGO faces higher investigative costs, there is greater probability that final support will be uninformed, reducing uncertainty from an ex ante perspective. When the government is risk averse ( $ g $ is strictly concave), this increases the government’s expected utility. In the truthful equilibrium, government disclosures remove uncertainty about the type of violence, so the NGO’s report and thus the NGO’s cost of effort does not affect its payoffs.

Overall, whether the government benefits from transparency institutions and more efficient NGOs depends on exactly how truthful the government becomes after their adoption. If the government does not become very truthful, then the NGO will better expose cover-ups, meaning the government is worse off. If the government becomes very truthful, then uninformed support increases, benefiting the government and minimizing the chances of being caught in a cover-up. These competing effects produce the nonmonotonic relationship between investigative costs $ \rho $ and the government’s expected payoffs in Figure 3’s right panel. Here, the government is worse off with moderately efficient NGOs, $ \rho \hskip0.35em \approx \hskip0.35em 6 $ , and would prefer either more or less efficient investigating NGOs.

Connections to Our Cases

Several implications are born out in our cases. First, recall that NGO and government data exist for the Naxalite conflict, specifically in Chhattisgarh during 2005–07 and that substantial differences arise between lists. Implication 1 suggests that one list is likely to be a more accurate depiction of the illegitimate violence in conflict than the other. In the Naxalite case, this is because at least one of the NGOs was especially interested in catching the government in a lie given the competition for attention and resources among NGOs.Footnote ¹⁸ This places the Naxalite context along the light-gray line in Figure 2, suggesting that the NGO list is likely to exhibit less underreporting bias than the SATP list of encounters. Regarding the number of civilians killed, we would expect the NGO list to more accurately represent the nature of the conflict.

We can also observe the relationship between baseline popularity and truth telling. India’s long-running National Congress Party was in power and widely popular between 2004 and 2008, although it was in a coalition government. Marginal returns to additional support were minimal. Consequently, the resulting loss of support from an exposed cover-up would impose a smaller cost than it would have for a less popular governing party, which can explain the differences between the government and NGO accounts.

Implication 3 helps explain the emergence of the Chhattisgarh Special Public Security Act in 2005, which drastically increased the cost of NGO investigations, $ \rho $ , by introducing harsh penalties for affiliating or communicating with suspected Naxalites. Figure 3’s left panel illustrates that such a change in $ \rho $ can move behavior into a never-admit-fault equilibrium from a partially truthful equilibrium. Figure 3’s right panel illustrates that if the initial $ \rho $ was not too small and the subsequent increase in $ \rho $ was large, then the government is strictly better off by having passed the 2005 Act.

In the US targeted-killings program, we can think of this case as exhibiting two different periods: before the release of any data by the administration and after the release of the first report in 2016. In the first period, only NGO data are available and the government’s list is effectively zero, with the administration operating in the never-admit-fault equilibrium. In the later period, it is likely operating in the partially truthful equilibrium, releasing reports that convey only a portion of noncombatant deaths resulting from the drone strikes. This difference in equilibrium could be explained by a change in Obama’s time preferences over support, δ. In 2011, δ is arguably small, as Obama was running for reelection and immediate political support was crucial. In the second period, δ increases drastically as Obama becomes more concerned with his legacy than immediate electoral support. Consider Figure 1 to see that an increase in δ could move the government away from the never-admit-fault equilibrium into the partially truthful one.

The effect of baseline popularity is more difficult to interpret in this case. Obama faced lower than average approval ratings throughout most of his presidency; his favorability surpassed 50% only during his fourth and seventh years in office. During the second peak in popularity, the administration acknowledges the targeted-killings program and begins reporting associated civilian casualties. This pattern is inconsistent with the comparative statics in Implication 3, which suggests that the government’s truthfulness should decrease after an increase in baseline support (assuming g is sufficiently concave). Nonetheless, at the end of his second term, Obama may have prioritized his progressive legacy, in which case truthfulness would have increased due to an increase in δ.

Implication 3 helps us understand the effect of the BIJ, which began systematic data collection in 2010, publishing its first list of casualties in 2011. It was a well-funded actor that selectively chose reporting projects. As such, it constitutes a highly efficient NGO (i.e., it has a small $ \rho $ ). As illustrated in the left panel of Figure 3, when the costs of NGO investigations decrease, the government’s likelihood of disclosing illegitimate violence weakly increases. Furthermore, it is possible that such a change could shift the behavior from the never-admit-fault equilibrium to the partially truthful equilibrium. The overall effect of this shift on the government’s expected utility is ambiguous. If such a change sufficiently commits the government to the truth, then it is better off after the BIJ begins its investigations.