COUNTERINSURGENCY AID AND REBEL RESISTANCE

In traditional cases of civil war, where an armed opposition clashes with a government, there is a struggle for the control of territory. Kalyvas (Reference Kalyvas2006) articulates this as “division of sovereignty in civil war.  . . between zones of incumbent control, zones of insurgent control, and zones where control is contested.” Progovernment forces seek to extend their control to contested and insurgent controlled regions, though they may seek a negotiated peace if it becomes too costly.

Insurgents endeavor to achieve the opposite, aiming to expel government military forces and political officials. While their end goal may be to eventually overthrow the government and establish themselves as the sovereign authority, as is the case for the Taliban in Afghanistan, rebels may also have secession or autonomous devolution of power in mind.

Scholars and practitioners have long argued that a key element to establishing control (from the perspective of either side) is winning the goodwill of the civilian population. Galula (Reference Galula1964) and Trinqiuier (Reference Trinquier1964), among others, argue that political power in civil war flows from the population, with the people essentially deciding who wins the conflict based on their evaluation of the competing sides in terms of their own well-being. Berman, Felter, and Shapiro (2011) formalize this logic by presenting the conflict between progovernment forces and insurgents as essentially a contest for information that is adjudicated by the public.

One common tool used to win the support of the population is development aid spending on the part of progovernment actors. Aid has been deployed as a counterinsurgency technique by intervening forces to great fanfare, including the U.S.-led coalitions in Afghanistan and Iraq (Kilcullen Reference Kilcullen2010; U.S. Army 2009a), in the Philippines, Colombia, and a generation earlier in Vietnam and Algeria. The logic is that aid will win over the “hearts and minds” of the civilian population, which will lead them to stop collaborating with insurgents, whether through material support, information, or other means. Berman, Shapiro, and Felter (Reference Berman, Shapiro and Felter2011) also hypothesize that civilians will respond to aid by beginning to share information with counterinsurgents, allowing progovernment forces to become more effective at eliminating militants.

Recent empirical studies have found evidence that as a counterinsurgency strategy aid improves troop security, a key indicator of incumbent territorial control. Berman, Shapiro, and Felter (Reference Berman, Shapiro and Felter2011) find that hearts and minds-oriented aid spending in Iraq led to a short and long term reduction in violence against Iraqi and coalition military forces. Beath, Christia, and Enikolopov (Reference Beath, Christia and Enikolopov2016) find evidence in Afghanistan that civilian development aid improves troop security in surrounding areas, though not in the communities themselves. Crost, Felter, and Johnston (Reference Crost, Felter and Johnston2016) show experimental evidence in the Phillippines that conditional cash transfers reduce local violence. Iyengar, Monten, and Hanson (Reference Iyengar, Monten and Hanson2011) propose a labor market mechanism, finding that aid spending that increases employment reduces “labor-intensive” insurgent violence. Bohnke and Zurcher (2013) do not find any evidence that aid affects perceptions of security, however, their survey gives evidence of an improvement in perceptions of state legitimacy. Two previous studies on counterinsurgency aid in Afghanistan, by Chou (Reference Chou2012) and Child (2015), on the other hand, find no average effect of aid on violence against U.S. military forces.

These accounts, while important contributions, ignore several important strategic dynamics between government and rebel forces.Footnote ¹ Most importantly, when counterinsurgents engage in spending targeted to win over the affections of the civilian population, we should expect insurgents to oppose them—violently, if necessary—whenever possible. Crost, Felter, and Johnston (Reference Crost, Felter and Johnston2014) illustrate this dynamic in the Phillippines, showing that aid projects distributed from the central government increase violence, as opposition groups sabotage projects in their early stages to undermine any goodwill the central government might earn in the local area. A study on a similar program in India by Khanna and Zimmermann (2015) also finds that aid drives short run increases in violence related to Maoist insurgency. Lyall (2014) finds a similar dynamic with respect to U.S. Air Force airstrikes in Afghanistan, with insurgents responding to coalition strikes and shows of force with attacks against progoverment forces to fight back against any loss of reputation among the populace.

A second strategic element is that insurgents, with finite resources, must decide where to carry out acts of sabotage and nonviolent resistance to counterinsurgency projects. Where costs and the likelihood of immediate retaliation are low, as in the Phillippines case, rebels can attack many aid projects, scuttling their impacts. In a more contested environment, like Afghanistan or Iraq, guerillas must make trade-offs. The ability of insurgents to carry out sabotage is in part related to the degree of control that each side has in a given territory (Harmon Reference Harmon1992; Kilcullen Reference Kilcullen2010). The costs of attacking aid projects are similarly related to zones of control; sabotaging a hearts and minds project in an incumbent-controlled area is much more likely to result in rapid retaliation by progovernment forces.

Third and finally, as noted by Kalyvas (Reference Kalyvas2006), citizens stuck between warring sides in a civil conflict often “shift endogenously towards the army” that controls their environs. Particularly when counterinsurgents make costly investments in military infrastructure, bring in equipment and regularly patrol incumbent-controlled areas, the population can quite rationally become ambivalent towards insurgents, even if pre-conflict preferences might predict sympathy towards guerillas. This suggests that the civilian population in progoverment controlled zones should more consistently respond to hearts and minds programs.

Berman et al. (Reference Berman, Felter, Shapiro and Troland2013) find some evidence for this final claim in Iraq, noting that aid and troop concentration are complements in the provision of troop security, while Biddle, Friedman, and Shapiro (Reference Biddle, Friedman and Shapiro2012) suggest that the “surge” of troops was as significant a factor in reducing violence in Iraq as any aid spending.

These three factors point to an important implication: counterinsurgency aid spending on “hearts and minds” projects should provoke violent and nonviolent retaliation from rebels, except in locations where progovernment forces have full military control. As we look towards the Afghanistan case, this implies that counterinsurgency aid would be predicted to have a violence increasing effect in contested and Taliban-controlled districts, while maintaining a violence reducing effect in districts controlled by U.S. forces.

Furthermore, the strategic responses of insurgents to aid should vary with the type of project that is being implemented. Several factors may be influential in the context, including the visibility of the project, whether the project implies an increase in military capacity for progovernment actors, whether insurgents can effectively interfere with the project using the techniques they have access to. We would expect, for example, that insurgents would respond aggressively to projects investing in military infrastructure, or that build the capacity of local government partners. On the other hand, we would not expect them to attack projects involving humanitarian aid, in part because handing out food, water, and tents is difficult to interdict, in part because violence against such a project would be directly against civilians, and lastly because this aid is far less visible to insurgents than, for example, the construction of a new military watchtower by the district government headquarters.

The Afghanistan case provides us with an opportunity to test each of these claims using detailed, geocoded violence data and random variation in counterinsurgency aid spending by the U.S. military during the 2008–10 period. While the specific dynamics of spending, resistance, and violence are unique to Afghanistan, the strategic relationship they illustrate travels well to other civil war contexts. Particularly as international “stabilization” missions of the sort described in the next section continue to be deployed by NATO and others, these insights will only become more relevant.

WARTIME AFGHANISTAN AND THE COMMANDER’S EMERGENCY RESPONSE PROGRAM (CERP)

The seeds for Afghanistan’s present-day conflict were sown as far back as the 1870s, when the second Anglo-Afghan war allowed Britain to take over Afghanistan’s foreign relations and establish a partial protectorate, in opposition to the expanding Russian Empire. A century later, after numerous foreign interventions and proxy battles, the Soviet Union did what British colonial officials feared in the 19th century, invading Afghanistan in December 1979 in support of the new communist government in Kabul.

Since the 1970s a parade of governments have passed through the doors of power in Kabul: royalists, communists, mujahedeen, Pashtun nationalists, fundamentalist Islamists, and finally, the most recent NATO-sponsored administration. Each has, sooner or later, found themselves at odds with violent insurgents. Indeed, when one group is thrown from power, they often become the next leader’s armed opposition.

The past three decades of conflict are typically broken up into four periods: the Soviet/communist war (1979–1992; also referred to as “the jihad”), the “civil war” (1992–1996), the Taliban period (1996–2001), and the current “American” war (2001–present).

The conflict in Afghanistan since 2001 has been marked by the intervention of the United States, which began after the terrorist attacks of September 11, 2001. Soon after, U.S. special forces supported the opposition Northern Alliance in deposing the Taliban regime in Kabul, installing Hamid Karzai as president soon after. Since 2006, growing armed opposition to the Karzai government and its NATO allies has transformed Afghanistan into a battlefield again. This has included the “Neo-Taliban,” Haqqani Network, Hezb-e Islami, local warlords and guerillas, and foreign sponsors of armed groups (Giustozzi Reference Giustozzi2008, Dorronsoro Reference Dorronsoro2009).

To combat growing armed opposition to the Karzai government, the U.S. Congress authorized “hearts and minds” spending by U.S. commanders, as part of a broader counterinsurgency strategy known as COIN. Civilian aid projects administered by U.S. military commanders were previously used in Iraq, under the Commander’s Emergency Response Program (CERP). It is random variation in the administration of the CERP program in Afghanistan, which I detail below, that I will use to identify the effect of aid on violence in contested and controlled Afghan districts.

As put in the U.S. Army’s Handbook “Commander’s Guide to Money as a Weapons System,” CERP is intended as a “nonlethal weapon to urgent, small-scale, humanitarian relief, and reconstruction projects and services that immediately assist the indigenous population.”

“Warfighters at brigade, battalion, and company level in a counterinsurgency (COIN) environment employ money as a weapons system to win the hearts and minds of the indigenous population to facilitate defeating the insurgents” (U.S. Army 2009b).

Between 2004 and 2011, more than $2.64 billion was spent through CERP in Afghanistan, with projects that ranged from road construction, cash-for-work, agricultural assistance to water projects, and militia payoffs (Johnson, Ramachandran, and Walz Reference Johnson, Ramachandran and Walz2011). Table 1 summarizes the frequency of various projects types from May 2008 to December 2010.

TABLE 1.

CERP Project Frequency by Project Type, 2008–2010

The U.S. COIN strategy during this period encompassed a broad range of civilian and military activities, of which CERP was one. Ranging from cultural sensitivity training, coordination with the host government and military, focus on infrastructure development and services, and the “Clear, Hold and Build” method, COIN doctrine is to counter an insurgency in a holistic manner. This includes challenging insurgents with respect to rule of law, governance and public goods provision, far beyond the traditional security sector tasks often assigned to a military occupation.

As part of the overall U.S. counterinsurgency (COIN) approach, the CERP program was ramped up extensively and rapidly in Afghanistan after 2007, increasing in appropriated funds from just over $200 million in 2007 to nearly $1 billion in 2010. As U.S. foreign policy priorities switched from Iraq to Afghanistan, and the so-called “surge” was authorized by President Obama, intense pressure to spend appropriated CERP funds fell on all levels of the military chain of command. Table 2 illustrates the surge in CERP appropriations to Afghanistan during the 2008–2010 years (Cordesman Reference Cordesman2013).

TABLE 2.

Appropriations to CERP Afghanistan

At the level of local commanders, there was additional pressure to produce proposals for CERP projects. How much money a unit could get “out the door” was strongly considered in evaluations for promotion.Footnote ² As it was put in an internal ISAF review in 2011,“current incentives promote spending CERP funds without sufficient accountability” (Weggeland Reference Weggeland2011). The impacts of the projects barely measured, the only observable metric for evaluating contributions to governance was the amount of CERP money a commander had spent. This pressure, in addition to limited local contextual information on the part of overstretched commanders, meant that the decision to put a district into CERP treatment during a particular period or not was pushed up to the bureaucratic level as a slew of projects weaved their way through the approval process (Kilcullen Reference Kilcullen2010; Weggeland Reference Weggeland2011).

On the approval side, pressure to get spending done was not lost on higher level leadership in the U.S. military, who were eager to implement the well-publicized COIN strategy (SIGAR 2011; Weggeland Reference Weggeland2011). Extensive discussions in theater at ISAF headquarters and with civilian aid workers for the U.S. over a six-month period by the author in 2012 indicate that during the 2008–10 period, numerous rejections, delays in project approval, last minute budget changes, or adjustments in the siting of CERP were due to procurement and bureaucratic technicalities, as opposed to strategic considerations.Footnote ³ In addition, the timing of CERP project approvals was reportedly often difficult to predict, according to the office of the Special Inspector General for Afghanistan Reconstruction (SIGAR) in Kabul.Footnote ⁴ Even if projects were known to be coming to an area, it was uncertain when funds would actually arrive, and be able to be disbursed, due to highly technical and legalistic currency transfer and procurement rules.Footnote ⁵

Even if the approval and timing of CERP funds is plausibly independent of local week-on-week violence trends, it is possible that some commanders synched other military actions with the start of CERP projects. For example, a unit might use the start of a CERP project to undertake anti-Taliban clearing operations, or engage in outreach with local government partners. In this case, the “treatment” would be not only aid spending alone, but a bundle of CERP spending and some other activities. In the Mechanisms section, however, I show that CERP spending is not associated with an increase in anti-insurgent raids, airstrikes, or IED clearances by international or national security forces, suggesting that at least visible operations and outreach to security partners were not, on average, synched with CERP project starts.

It is also important to take account for the continuing nature of both violence and aid expenditure. Violence tends not to increase in just a single period, instead following longer term trends, including seasonality, persistant offensives, and pacification efforts. Similarly, aid projects, even if they include some random variation in approval and timing, are distributed over a period of weeks or months. In the empirical specification that follows, I address serial correlation in violence and aid spending, unobserved conditions in Afghan districts, concerns about reverse causality and selection into treatment, in order to remain secure that the variation in aid being exploited is in fact independent of local violence, military control, and other local characteristics.

While many observers have questioned the utility of CERP spending in Afghanistan for its chaotic nature, as scholars this random variation allows us to examine the effect of locally exogenous changes in CERP spending on local violence outcomes. By examining week-by-week changes in CERP expenditures and changes in several classes of violence, we can identify how civilian aid spending affects local level violence.

DATA

Violence is not the only means of measuring the effect of aid on an antigovernment insurgency. The legitimacy and popularity of the insurgency in the eyes of influential civilians and public support for the institutions of the incumbent government are important factors that may dictate the political settlement of a conflict (Lyall, Blair and Imai Reference Lyall, Blair and Imai2013). Unfortunately, they are both difficult to measure at a fine-grained level, and are indeed ephemeral concepts to measure even under favorable conditions.Footnote ⁶ Accordingly, the dependent variables of interest for this study are local level violence of several types. While violence against progovernment (counterinsurgency) forces is important and easy to measure—international forces keep track of it themselves—it is not the only violence of interest. We want to account for insurgency violence against all targets, as well as noninsurgency related violence.

This study introduces a new dataset of fine grained, geocoded violence in Afghanistan during the period of May 2008 to December 2010 that fills this gap. In contrast with previous studies, this dataset includes local violence against all targets during that interval, including bombings not against international or local security forces, as well as operations against insurgents carried out by international and domestic military forces.Footnote ⁷

The new data on bombings and operations by progovernment forces are compiled from detailed weekly incident reports from the Afghanistan NGO Safety Organization, an independent nonprofit organization that has kept track of security incidents throughout Afghanistan since October 2002. With more than 100 staff spread throughout Afghanistan, ANSO collects reported security incidents first hand, from humanitarian and development NGO (foreign and domestic), triangulated SMS and phone-in reports, and local news media.Footnote ⁸ The organization is funded by Swiss Development Cooperation, the Norwegian Ministry of Foreign Affairs, and the European Commission’s Directorate for Humanitarian Affairs and Civil Protection (ECHO) and is registered as a nonprofit and independent charity in the UK.Footnote ⁹ Each weekly report contains the date, province, district, and precise location of each reported incident, along with a one- to two-sentence description of the incident. The incident narratives follow a set of conventions regarding terminology, spelling, acronyms, and shorthand. For example, coalition forces are referred to as IMF, meaning “international military forces.” To illustrate, the following are two entries from the dataset, the first a bombing incident and the second an operation by progovernment forces:

• Date: 2010 April 25

• Location: Paktya Province, Shwak District, Main Gardez-Khost Road

• Incident Narrative: An IED (improvised explosive device) planted on the road detonated while an ANA EOD team was attempting to defuse it.

• Date: 2010 April 6

• Location: Kunar Province, Chapa Dara District, Badigram Area

• Incident Narrative: IMF/ANSF conducted a joint operation targeting suspected AOG locations, killing six suspected AOG.

Using keyword text analysis, the more than 46,000 security incidents that were reported by ANSO during the 138 weeks of the study period (May 2008 to December 2010)Footnote ¹⁰ are coded using regular expressions from ANSO documents.Footnote ¹¹ This study includes the following three categories of violence, and two variables measuring IEDs cleared/defusedFootnote ¹² :

1. 1. bombings and attempted bombings by insurgents (against all targets);

2. 2. operations against insurgents by international military forces and the Afghan National Army;

3. 3. IEDs defused/cleared by the Afghan National Police or Afghan National Security Forces;

4. 4. IEDs defused/cleared by international military forces.

The violence data are collapsed into 138 weekly bins, across Afghanistan’s 398 districts for a total of 53,460 observations in the time series cross section from May 2008 to December 2010.Footnote ¹³ Figure 1 illustrates the geographic distribution of casualty-causing security incidents from the ANSO dataset (annually per 10,000 inhabitants).

FIGURE 1.

Annual Casualty-Causing Security Incidents per 10,000 Inhabitants (ANSO data), Afghanistan, May 2008–December 2010

Data on the CERP treatment come from an unclassified database, entitled “Afghanistan Commanders Emergency Response Program (CERP) Spending Data 2010–2011,” publicly released by the U.S. military’s Central Command (CENT-COM) at the end of 2010. The files come from the Combined Information Data Network Exchange (CIDNE), the U.S. military’s internal management system for collecting tactical data from troops. The CERP dataset includes completed, ongoing, planned, and cancelled CERP projects in Afghanistan; in this study both completed and active projects are included.Footnote ¹⁴

The CERP database includes the start and end dates of CERP projects, the budget, sector, and global positioning of each project. Using GIS software and a project’s latitude and longitude, I coded each CERP project with its appropriate district and province. In the study period, 5,843 CERP projects across all districts of Afghanistan are included. Figure 2 shows CERP spending per capita.

FIGURE 2.

Annual CERP Spending per Capita (U.S. military data), Afghanistan, May 2008–December 2010

In addition to information on CERP spending, the CIDNE database contains information on “Significant Activities” (SIGACT), which are defined as “events of significance in the operational environment,” that are reported by U.S. military units. SIGACT data range from enemy engagements, friendly fire events, medical evacuations, requests for air support from local units and IED (improvised explosive device) discoveries, and explosions. “Enemy actions” and “explosive hazards” are included in this study as the measure of SIGACT-reported violence events. Figure 3 depicts the annual number of SIGACT per 10,000 inhabitants in each Afghanistan district.

FIGURE 3.

Annual Attacks Against U.S. Troops per 10,000 Inhabitants (U.S. military data), Afghanistan, May 2008–December 2010

“Enemy actions” are defined as live fire attacks by insurgents against progovernment troops that are recorded by international military forces. These may be against fixed installations, military units on patrol, or others. “Explosive hazards” refer to IEDs and bombs that are encountered by progovernment forces, whether they explode or not.

In many cases there are several entries in CIDNE that relate to a single violence incident; for example if a U.S. military unit engages in combat with an AOG unit, then calls for air support and then requests a med-evac for an injured soldier. In order to identify the unique number of events, I collapse the SIGACT data, dropping duplicate observations that occurred in the same location at the same time. The study period contains a total of 62,944 unique SIGACT events, of which 44,304 are “enemy actions” or “explosive hazards” (the first coding of the event applies for the duration so that there is no double counting).

Using monthly reports published by the Institute for the Study of War (ISW) on the order of battle in Afghanistan, the positions of battalion-level and larger ISAF installations is coded by month into the time series. A battalion is the smallest sized unit that is considered by the U.S. military to be both “tactically and administratively self-sufficient.”Footnote ¹⁵ With around 1,000 soldiers and typically commanded by a Lieutenant Colonel, a battalion has the resources to control the district around them, including logistics, easy access to air support, regular patrols, and training of local allies. Larger installations, like brigade headquarters—often in provincial capitals, or divisions (in charge of regional commands), have even greater resources to maintain control of the district within which they sit.

The ISW reports indicate where “white” units are positioned, that is, regular military units as opposed to special forces units and other “black” operations. The locations of battalion-level forward operating bases (FOBs) and major installations and their primary listed areas of responsibility (AOR) are coded as “secured” with a dummy variable. These data are available at the district-month level of resolution. During the period under study, only two FOBs are decommissioned, otherwise it is a strictly additive process. The number of districts with battalion-level troop bases increases from 28 in May 2008 to 49 in December 2010.Footnote ¹⁶

Using battalion-level and larger installations as a measure of progovernment troop control is not ideal, as there may be some misclassifications where there are secure areas (progovernment sovereignty) without bases and areas with bases that do not necessarily have progovernment sovereignty. We might worry that as levels of violence change in a district, the ability of the measure to correctly classify progovernment control might change.

Following the logic of Imai and Yamamoto (Reference Imai and Yamamoto2010), I argue that there are three primary reasons why measurement error should not be correlated with the outcome in this case. First, control, as characterized in this study using the Kalyvas (Reference Kalyvas2006) definition of “division of sovereignty,” is slow moving by nature, while violence is deliberately measured in the short term (week-on-week). Sovereignty over a given district, in general, does not swing back and forth on a weekly basis, particularly where occupation forces have major military installations in place. Second, the expectations and sympathies of the population, key to sovereignty, do not typically react to short-term shifts in violence, especially in civil war contexts where endemic violence is a common phenomenon. Last, because the variable (both the conceptual understanding of control and actual military presence) is binary, as opposed to a continuous measure, it is less susceptible to week-to-week fluctuations (see Table 3). I conduct two additional robustness checks in Appendix C to give further evidence in favor of the measurement. Summary statistics for the data used in the study are presented in Table 3.

TABLE 3.

Summary Statistics

Note: Observations are 396 Afghan districts over 138 weeks from 2008 to 2010 and adjusted per 10,000 inhabitants.

EMPIRICAL APPROACH

Identifying a causal relationship in the study of military-led aid is challenging. Unlike civilian development aid, which has been relatively easily manipulated in an field experimental context, there have been no such experimental studies on counterinsurgency aid spending by military forces. As a result, we must rely on observational data to examine the effect of CERP and other programs.

In order to isolate the variation in CERP spending that is independent of local violence trends in the district in which the spending is taking place, I focus the analysis on week-by-week levels of CERP spending that are in part due to the bureaucratic and operational hurdles described two sections ago. To isolate this plausibly exogenous spending, I employ an empirical strategy that has three main features. First, I use individual district-weeks as the unit of analysis, allowing for a fine-grained examination of variation in CERP spending and violence. Second, I employ a lagged variables model (autoregressive distributed lag, or ADL; Beck and Katz Reference Beck and Katz2011) that addresses serial correlation in the time series,Footnote ¹⁷ ensures that previous weeks’ spending and violence are not confounding the estimates, and allows us to observe the dynamic effects of spending on the following period. Third, the model also includes unit and time fixed effects to eliminate confounding from any remaining non-time-varying characteristics of districts and nationwide trends in spending and violence.Footnote ¹⁸

To verify this approach I carry out a battery of robustness checks, located in Appendix C. In addition, I carry out a placebo test at the end of the Results section to confirm that there is no selection into treatment or “reverse-causality.”

For the purposes of each district-week observation, the presence or absence of a battalion-size or larger ISAF installation is treated as a covariate, which is interacted with CERP aid spending. In order to avoid post-treatment bias concerns, the “secured” variable is lagged by one period.Footnote ¹⁹ While long-term violence and aid trends may be endogenous to the decision-making process regarding where and when to extend large U.S. military installations, such decisions are not made with a week-to-week turnaround. That is, changes in violence in a given district in a given week should not make that district any more or less likely to have a large U.S. military installation put in place or taken away.

I estimate the effect of CERP spending, moderated by FOB presence, on three violence outcomes using the following specification, using OLS:

where Y_it is the violence outcome in levels per capita for district i in week t, β₁ and β₂ are the coefficients of interest for the first period, $\text{CERP}_{it}$ is CERP spending per capita in levels, $\text{CERP}^{\ast}\text{secured}_{it-1,t-2}$ are the interaction of CERP spending with the troop dummy, and $\text{secured}_{it-1,t-2}$ are dummies for whether a district had a battalion FOB or larger installation in a weeks t − 1 and t − 2 District and week fixed effects follow, along with ε _it , the district-week error term.

The effects of interest are then β₁ for the effect of CERP spending in unsecured districts and β₁ + β₂ for the secured districts in the first period. For the second period effects, the coefficient of interest is β₄ + (β*₇β₁) for unsecured districts and β₄ + β₅ + [β*₇(β₁ + β₂)] for secured. In order to estimate the predicted effects of a given project, for example CERP spending worth $500,000 over four weeks, the period one effects are summed with period two effects for each week of spending, providing a predicted cumulative effect. Standard errors for these predicted cumulative effects are estimated using simulation.Footnote ²⁰

SUPPLEMENTARY MATERIAL

To view supplementary material for this article, please visit http://dx.doi.org/10.1017/S0003055416000356