Third-person Effect and Financial Contagion in the Context of a Global Game

Abstract

In this paper we present a psychological channel of financial contagion. We incorporate this new channel of financial contagion in the global game. Our basic assumption is that agents are overestimating the influence of negative messages they ascribe to others, and are thus acting on the basis of this perception. We resort to the psychological studies on the so-called third-person effect to justify this assumption. We show that the third-person effect is rationalizable. Our model has the feature that a crisis in a foreign country can be transmitted to the domestic country, even though there has been no changes in domestic fundamentals. Our model also provides intuitive explanations to the empirical observations that many governments have lost in a confidence game in the past crisis episodes.

Appendices

Appendix A

The third-person effect, proposed by Davison (1983) and discussed mainly in the mass communication literature, refers to a tendency for people to perceive that the media messages have a greater impact on the beliefs and behaviors of others than on themselves. Examples of third-person effect can be found in voter behavior, fluctuations in the stock market, hoarding of goods when supplies of consumer goods are irregular, and the phenomenon of censorship. The third-person effect is mediated by the nature of the comparison other and the type of media content. The effect is more pronounced when people consider potential impact of negative media content such as violence, sexism, and racism, and when people compare themselves with vague and distant others (Duck and Mullin 1995). We have mentioned in the main text the conditions that facilitate the third-person effect. In this Appendix, we describe the processes through which the third-person effect operates.

The first psychological explanation to the processes that underlie the third-person effect is downward comparison. Perloff and Fetzer (1986) argue that downward comparison makes an individual to perceive himself as invulnerable to negative messages. When confronted by the question of whether negative messages have a greater impact on him or on the others, an individual tends to compare himself to a group of ‘lower than average’ people. The attributes of these people make them more susceptible to the threat of victimization.

What motivates an individual to compare downward? A possible reason is an ego-defensive function, namely, such a comparison helps to reduce self-anxiety and to preserve control and self-esteem. For instance, when asking an individual whether he is more likely to be influenced by violence in the media than others, refusing the idea that he is more vulnerable to the media than others will help to sustain self-esteem and alleviate the pressures that he is a victim of violence in media. Another reason is cognitive. An individual tends to compare himself to a stereotype of people who have a greater risk of becoming the victims of the negative messages. A vivid example is to ask an individual whether he is more likely to get cancer than others. The individual being questioned usually compares his risk of getting cancer to the risk of elders or people addicted to smoking. This phenomenon is more likely to happen when the questioner does not clearly specify who the others are. The same mechanism also makes people judge themselves as less likely than others to get divorced.

The second psychological explanation is based on attribution theory. In general, attribution theory refers to the study of processes people use to infer causes of behavior. It is postulated that there is a widespread tendency for people to attribute their actions to situational (or external) factors and to attribute the same actions of others to dispositional (or internal) factors. Applied to a media message, people assume themselves being aware of situational factors and are less influenced by the message, while others do not take account of situational factors regarding the message and are more likely to be affected by it. The third-person effect arises from this consistent bias in estimating the situational response.

Appendix B

We follow Morris and Shin (2003) to prove the existence of a unique equilibrium. The proof consists of two steps. First, we show that there is a strategy that survives n rounds of iterated elimination of dominated actions. Second, we show that there is only one strategy that solves the model. Following the main text, we assume that the expected payoff function v(x _i , k) is continuous in both x _i and k. It is monotonically increasing in x _i and monotonically decreasing in k. A strategy survives n rounds of iterated elimination of dominated actions if and only if

$$ \begin{array}{ccc} s\left( x_{i}\right) =1 & if & x_{i}\leq \underline{\xi }_{\;n} \\ s\left( x_{i}\right) =0 & if & x_{i}>\overline{\xi }_{n} \end{array} $$

where s(·) indicates investor i’s behavioral action, s = 0 denotes the continuation of the investment and s = 1 denotes investment withdrawal. We define $\underline{\xi }_{\;n}$ and $\overline{\xi }_{n}$ recursively as:

$$ \underline{\xi }_{\;n+1}=\min \left\{ x_{i}:v\left( x_{i},\underline{\xi } _{\;n}\right) =0\right\} $$

$$ \overline{\xi }_{n+1}=\max \Big\{ x_{i}:v\Big( x_{i},\overline{\xi } _{n}\Big) =0\Big\} $$

where $\underline{\xi }_{\;0}=-\infty$ and $\overline{\xi }_{0}=\infty$. We first show that there is only one value of $\underline{\xi }_{\;n}$ and $\overline{\xi }_{n}$, respectively, that survives n rounds of iterated elimination of dominated actions. Let us start from n = 0 and suppose $\underline{\xi }_{\;0}=-\infty <\underline{\theta }$ and $v\left( \underline{ \theta },\underline{\xi }_{\;0}\right) <0$. It is possible to find a $\underline{\xi }_{\;1}$ such that $v\left( \underline{\xi }_{\;1},\underline{ \xi }_{\;0}\right) =0$. Since $v\left( x_{i},k\right)$ is increasing in x _i and decreasing in k, $\underline{\xi }_{\;1}$ must satisfy the condition that $\underline{\xi }_{\;0}<\underline{\theta }<\underline{\xi } _{\;1}$. We can proceed a step further and find a $\underline{\xi }_{\;2}$ such that $v\left( \underline{\xi }_{\;2},\underline{\xi }_{\;1}\right) =0$. Since $v\left( \cdot \right)$ is decreasing in k, it must be the case that $\underline{\xi }_{\;1}<\underline{\xi }_{\;2}$. We can employ the same argument and start from $\overline{\xi }_{0}$. Suppose $\overline{\xi }_{0}=\infty > \overline{\theta }$ and $v\left( \;\overline{\theta },\overline{\xi } _{0}\right) >0$. It is possible to find a $\overline{\xi }_{1}$ such that $\overline{\xi }_{\;0}>\overline{\theta }>\overline{\xi }_{1}$ and $v\left( \;\overline{\xi }_{1},\overline{\xi }_{0}\right) =0$. And so forth. The above argument demonstrates that $\underline{\xi }_{\;n}$ is an increasing sequence and $\overline{\xi }_{n}$ is a decreasing sequence. Thus, as n approaches ∞, $\underline{\xi }_{\;n}$ will approach $\underline{\xi }$ and $\overline{\xi }_{n}$ will approach $\overline{\xi }$. An equilibrium requires that there exists a fixed point such that $v\left( \underline{\xi }, \underline{\xi }\right) =0$ and $v\left(\; \overline{\xi },\overline{\xi } \right) =0$. This completes our first step of proving the existence of equilibrium.

The second step is fairly intuitive in that, we only have to show that there is a single solution to the expected payoff function. This has already been done in Section 3 of our main text. Therefore, $\underline{\xi }$ is just $\overline{\xi }$, and there is only one strategy remaining after eliminating all iteratively dominated strategies.