Threat Misestimations and the Role of NGOs in International Risk Management

1. The Waseda-Australia Conference on Political Economy (The Center for Positive Political Economy, Waseda University) Threat Misestimations and the Role of NGOsin International Risk Management 11 March 2019 Toshihiro Ihori (National Graduate Institute for Policy Studies) Martin C. McGuire (University of California-Irvine) Shintaro Nakagawa (Konan University)

2. We investigate the impacts on collective risk management of mistakes made in estimating the severity of a threat. 1. Introduction> 2 > 3 > 4 >5 Introduction

3. Existing literature on the voluntary provision of public goods reports that “ambiguity” in the contribution by other players mitigates the free-riding effect. • Eichberger and Kelsey (2002) • The amount of a public good voluntarily provided by players increases with ambiguity. • Bailey, Eichberger, and Kelsey (2005) • If ambiguity concerning the contribution by other players persists, the provision of public good increases with the population of an economy. • Kelsey and le Roux (2017) • Impacts of ambiguity in the voluntary provision of best-shot or weakest-link public goods. • However, It seems more plausible to assume that allies are uncertain about the threat to their security more than others’ security expenditures. 1. Introduction> 2 > 3 > 4 >5 Literature

4. Although the governments intend to collect precise information on threats, the collected information can contain significant errors and is also often biasedin bureaucratic administrative processes. Moreover, interest groups try to influence the evaluation of the information and the policymaking process through lobbying. Because of such threat misestimates, countries may overprovide or underprovide public goods for international security. 1. Introduction> 2 > 3 > 4 >5 Difficulty in threat estimation Threat Information & errors Bureaucratic administrative process Interest groups Misestimation of threat Under/over-provision

5. The US insisted that Saddam Hussein was hiding weapons of mass destruction. However, the US could not find the weapons after its invasion of Iraq. If Saddam had owned such weapons and was connected to terrorists, his potential threat could have been devastating. In short, the US government overestimated Saddam’s threat. 1. Introduction> 2 > 3 > 4 >5 Example: Iraq War Source: https://en.wikipedia.org/wiki/Saddam_Hussein#/media/File:Iraq,_Saddam_Hussein_(222).jpg

6. In the 1930s, the UK and other European countries underestimated a remilitarized Germany under Adolf Hitler. In the late 1950s, the US overestimated the threat of the USSR’s intercontinental ballistic missiles (Missile Gap). In the 2000s, the US might have underestimated the North Korea’s ability of developing nuclear weapons. 1. Introduction> 2 > 3 > 4 >5 Other examples of over/under- estimation of threat

7. We also investigate the influence of interest groups on threat estimates. Although various interest groups may affect the government in the process of threat estimation, we hypothetically assume the existence of an international NGO (Non-Governmental Organization) located outside the alliance which can affect governments’ behaviors when they estimate losses. 1. Introduction> 2 > 3 > 4 >5 Interest groups and threat misestimation Interest group (international NGO) Affect the government in the process of threat estimation by lobbying Alliance Country Country

8. Each allied country may offer foreign aid to developing countries not only to make them friendly to the alliance but to prevent humanitarian crisis in these countries, (which could lead to a surge of refugees to the allied countries). Because of free-riding incentives, such aid would be less than the socially optimal level. International NGOs might extract additional aid or support to developing world from our allied governments by emphasizing the threatof humanitarian crisis. 1. Introduction> 2 > 3 > 4 >5 Example: Foreign aid and NGOs Refugee camp in Darfur (Chad) By Mark Knobil from Pittsburgh, usa - Camp, CC BY 2.0, https://commons.wikimedia.org/w/index.php?curid=2173345

9. How do misestimates concerning a threat affect burden-sharing in an alliance? ->Model 1 Can misestimation maximize the utilitarian social welfare of individual allies? -> Model 2 Could our hypothetical NGO effectively induce an “optimal” level of bias such that in Nash equilibrium the allies provide a socially optimal amount of public good? -> Model 3 1. Introduction> 2 > 3 > 4 >5 Research questions

10. Introduction Model 1: Burden Sharing and Exogenous Misestimation Model 2: A Normative Analysis of Misestimation Model 3: Endogenous Misestimation and the role of NGO Conclusion 1. Introduction> 2 > 3 > 4 >5 Plan of the presentation

11. We consider an alliance of two countries, A and B. • We assume that there are two states of the world: good and bad. • The nature stochastically determines the state of the world. • The probability of a good state is . • The probability of a bad state is 1 > 2.Model1: Burden Sharing and Exogenous Misestimation > 3 > 4 >5 2.Model 1: Burden Sharing and Exogenous Misestimation

12. With misestimation, the government of country A maximizes its welfare based on biased information of loss in the bad state, or “estimated expected” welfare. • “Estimated expected” welfare of country A is given by • : country A’s estimated expected utility • : country A’s estimated consumption if the state of the world is good • : A’s estimated consumption if the state is bad • : Utility function. , Country B’s utility function is identical to A’s. 1 > 2.Model1: Burden Sharing and Exogenous Misestimation > 3 > 4 >5 Welfare

13. Following Ehrlich and Becker (1972), we consider multiple pure public goods in the sense that “security” is disaggregated into self-protection and self-insurance. • Self-protection, , reduces the probability of a disastrous event • Self-insurance, , reduces the loss from the event 1 > 2.Model1: Burden Sharing and Exogenous Misestimation > 3 > 4 >5 Self-protection and self-insurance

14. The amount of self-protection public good is given by the sum of the contributions of allied countries as follows: • : the total amount of the self-protection public good • : country A’s contribution to the public good • : B’s contribution to the public good • The probability of the good state is given by: where for any 1 > 2.Model1: Burden Sharing and Exogenous Misestimation > 3 > 4 >5 Self-protection public good

15. When government of country A determines its self-insurance and self-protection expenditures, its budget constraint is given as follows where : country A’s income, :its estimated loss in the bad event, : its contribution to the self-insurance public good, : the self-insurance benefit in the bad state, : the self-insurance input in the bad state. 1 > 2.Model1: Burden Sharing and Exogenous Misestimation > 3 > 4 >5 Budget constraint

16. The estimated loss may be formulated as the sum of the true loss and the bias in estimation: where :the true loss in the bad state : the overestimation of that loss (which is given exogenously in this section) 1 > 2.Model1: Burden Sharing and Exogenous Misestimation > 3 > 4 >5 Threat misestimation

17. The self-insurance benefit function is increasing and concave. The marginal product or benefit of self-insurance is not higher than unity: • The price of self-insurance is actuarially fair. Thus the price is . Then, we have where . 1 > 2.Model1: Burden Sharing and Exogenous Misestimation > 3 > 4 >5 Self-insurance benefit

18. If the state is bad, the true loss is revealed. The ex post budget constraints of country A are thus given by the following: where : A’s consumption in the good state : Consumption in the bad state 1 > 2.Model1: Burden Sharing and Exogenous Misestimation > 3 > 4 >5 The ex post budget constraint

19. The first order conditions for interior solution are given as follows: • We assume that the second order conditions for the expected welfare maximization are satisfied. • Country A’s best response function is given as follows: and 1 > 2.Model1: Burden Sharing and Exogenous Misestimation > 3 > 4 >5 Individual optimization

20. The Nash equilibrium of this model is defined as the solution to the following system: 1 > 2.Model1: Burden Sharing and Exogenous Misestimation > 3 > 4 >5 Nash equilibrium

21. The estimated consumptions in the good and bad states (under Nash equilibrium allocations to self-insurance and self-protection) are given as follows: 1 > 2.Model1: Burden Sharing and Exogenous Misestimation > 3 > 4 >5 Estimated consumptions under Nash equilibrium allocations

22. Suppose that all elements of the Nash equilibrium vector of contributions are positive and that and (26) where is absolute risk aversion. Then, estimated consumptions in Nash equilibrium satisfy and 1 > 2.Model1: Burden Sharing and Exogenous Misestimation > 3 > 4 >5 Proposition 1

23. According to Proposition 1, if both countries contribute to both public goods and if the absolute risk aversions of both countries are sufficiently decreasing with consumption, then estimated consumptions become identical regardless of the difference in their national incomes. 1 > 2.Model1: Burden Sharing and Exogenous Misestimation > 3 > 4 >5 Implication of Prop. 1

24. The true (or ex post) consumptions in good and bad states under the Nash equilibrium are given as follows: • From Prop.1, we obtain and . Thus, and 1 > 2.Model1: Burden Sharing and Exogenous Misestimation > 3 > 4 >5 Ex post consumptions

25. Suppose that Eq.(26) is satisfied. Suppose also that the Nash equilibrium is an interior solution. Then, we have the following: if and only if 1 > 2.Model1: Burden Sharing and Exogenous Misestimation > 3 > 4 >5 Proposition 2

26. According to Proposition 2, if Nash equilibrium is interior, the country with the larger overestimation bias consumes more in the bad state than the other country. This implies that the country with larger overestimate enjoys a higher true expected welfare. 1 > 2.Model1: Burden Sharing and Exogenous Misestimation > 3 > 4 >5 Implication of Prop.2

27. Suppose that Eq. (26) is satisfied. Suppose also that the Nash equilibrium to be an interior solution. Then, we have the following: 1 > 2.Model1: Burden Sharing and Exogenous Misestimation > 3 > 4 >5 Proposition 3

28. The difference in total security expenditure between allies does not depend on biases in estimates. • The biases in estimates of loss affect the composition of security expenditure. • For example, let us suppose that country A overestimates its loss in the bad state more than country B. • Then, the difference in self-protection contributions is smaller, while that in self-insurance contributions is larger than in the absence of mistaken estimates. • The shrinking of the gap in self-protection expenditure is canceled out by the widening of the gap in the self-insurance expenditure. 1 > 2.Model1: Burden Sharing and Exogenous Misestimation > 3 > 4 >5 Implication of Prop. 3

29. We specify the utility function as a CRRA function: where is the parameter representing the relative risk aversion of the country. • We also specify the probability function following Tullock’s contest success function: where and are parameters. • We specify the self-insurance benefit function as , where is a constant. 1 > 2.Model1: Burden Sharing and Exogenous Misestimation > 3 > 4 >5 Numerical example: specification

30. The values of the parameters are summarized as follows: 1 > 2.Model1: Burden Sharing and Exogenous Misestimation > 3 > 4 >5 Numerical example: parameters

31. 1 > 2.Model1: Burden Sharing and Exogenous Misestimation > 3 > 4 >5 Numerical example: results Green numberis higher than the baseline. Red number is lower than the baseline.

32. Research Question 1: How do misestimates concerning a threat affect burden-sharing in an alliance? We showed that The difference in total security expenditure between allies does not depend on biases in estimates. The biases in estimates of loss affectthe composition of security expenditure. 1 > 2.Model1: Burden Sharing and Exogenous Misestimation > 3 > 4 >5 Summary of section 2

33. Here we will further investigate the normative role of misestimation to alleviate the free riding outcome of public good provision. For the sake of simplicity, we omit self-insurance and investigate the impacts of bias in estimation exclusively on self-protection and implied welfare. 1 >2> 3.Model2: A Normative Analysis of Misestimation > 4 >5 3. Model 2: A Normative Analysis of Misestimation

34. Country A determines its provision of self-protection to maximize expected welfare subject to the following budget constraints: We assume that the second order condition is satisfied. From the first order conditions, we obtain country A’s best response function as. 1 >2> 3.Model2: A Normative Analysis of Misestimation > 4 >5 Country A’s maximization problem

35. We define the Nash equilibrium as , Consider a symmetric case, where . The symmetric Nash equilibrium is given as . 1 >2> 3.Model2: A Normative Analysis of Misestimation > 4 >5 Nash equilibrium

36. subject to , , with respect to . 1 >2> 3.Model2: A Normative Analysis of Misestimation > 4 >5 The social planner’s problem in a symmetric case

37. We denote the solution of as We also define as the solution of and denote the solution of as and define as . 1 >2> 3.Model2: A Normative Analysis of Misestimation > 4 >5 1st and 2nd order conditions for the social planner’s problem

38. 1 >2> 3.Model2: A Normative Analysis of Misestimation > 4 >5 Socially optimal bias If This point does not satisfy the 2nd order condition. Self-protection is overprovided in the Nash equilibrium These points are socially optimal.

39. 1 >2> 3.Model2: A Normative Analysis of Misestimation > 4 >5 Socially optimal estimation bias and the true loss The lower increases with . If is large, . Thus, does not exist. If is small, . Thus, .

40. Research Question 2 : Can misestimation maximize the utilitarian social welfare of individual allies? Yes, it can. There may exist multiple levels of the socially optimal overestimation. The lower level of the socially optimal overestimation increases with the true loss, while the higher value decreases with the loss. If the true loss is small, the social optimal is achieved in the Nash equilibrium without any overestimation. 1 >2> 3.Model2: A Normative Analysis of Misestimation > 4 >5 Summary of section 3

41. We first conduct a positive analysis of the behavior of the NGO. Consider two identical allied countries. We incorporate a hypothetical NGO into our model. 1 >2> 3>4.Model3: Endogenous Misestimation and the role of NGO >5 4. Model 3: Endogenous Misestimation and the role of NGO

42. The NGO benefits from the provision of the self-protection public good. • It maximizes its net benefit (=its benefit - its lobbying cost). • For example, additional foreign aid facilitates activities of humanitarian-NGOs. Then, we will argue that such NGOs benefit from foreign aid. • Its net benefit is given as follows: :a coefficient of the benefit of self-protection :the constant unit cost of lobbying. 1 >2> 3>4.Model3: Endogenous Misestimation and the role of NGO >5 NGO’s objective

43. 1 >2> 3>4.Model3: Endogenous Misestimation and the role of NGO >5 Time structure An international NGO determines its lobbying efforts in the two allied countries to maximize its net benefit. Lobbying biases the loss estimation by the allied countries with estimated loss of each country increasing with the NGO’s lobbying effort in that country. Period 0 Period 1 Each country independently and simultaneously determines its purchase of self-protection to maximize its “estimated expected” welfare based on its estimate of losses. Period 2 The state of the world is stochastically determined based on the self-protection provided in Period 1. The consumptions of households in both countries are realized.

44. 1 >2> 3>4.Model3: Endogenous Misestimation and the role of NGO >5 Backward inductions Period 0 An international NGO determines its lobbying efforts. subject to Period 1 Each country determines its purchase of self-protection. The Nash equilibrium on this period is given as Period 2 The state of the world is determined. If the state is good, . If the state is bad,

45. The NGO’s decision on its lobbying effort depends on th utility coefficient and the unit cost of lobbying. • The unit cost of lobbying may depends on • information and communication technology • political openness to NGOs (or restrictions on political activities) • If the governments open the political arena to NGOs, the lobbying cost will fall. • We define the optimal unit cost of lobbying as a cost such that the NGO voluntarily (in its own interest) chooses the socially optimal degree of estimation-bias for the alliance. 1 >2> 3>4.Model3: Endogenous Misestimation and the role of NGO >5 Socially optimal lobbying cost

46. CRRA utility function: where is the parameter representing the relative risk aversion of the country. • Tullock’s contest success function: where and are parameters. • Parameters: 1 >2> 3>4.Model3: Endogenous Misestimation and the role of NGO >5 Numerical example: specification

47. 1 >2> 3>4.Model3: Endogenous Misestimation and the role of NGO >5 Numerical example: results Socially optimal lobbying cost Green numberis equal to the social optimum. Red number is lower than the social optimum.

48. 1 >2> 3>4.Model3: Endogenous Misestimation and the role of NGO >5 Socially optimal lobbying cost and the true loss We focus on the lower , which increases with . Thus, decreases with . If is small, . Thus,

49. Research Question 3: Could our hypothetical NGO effectively induce an “optimal” level of bias such that in Nash equilibrium the allies provide a socially optimal amount of public good? If the true loss is in a range, it could. There is a range of loss such that over this range, there exists a socially optimal lobbying cost. For losses larger than the upper bound of the range, there exists no socially optimal unit cost of lobbying. For losses smaller than the lower bound of the range, any lobbying or estimation bias is not beneficial. 1 >2> 3>4.Model3: Endogenous Misestimation and the role of NGO >5 Summary of section 4

50. In this paper, we have investigated the impacts of misestimates of the severity of a threat on collective risk management. Here, we formulated such misestimation as a bias in the estimation of a loss in the bad event. 1>2>3>4>5. Conclusion 5. Conclusion