Grossman Helpman (2001) - Special Interest Politics Chapters 4 And 5

• This page is referenced in BPP Field Exam Papers

Reference(s)

Grossman, Gene and Elhanan Helpman (2001), "Special Interest Politics", Chapters 4 and 5, MIT Press pdf

Abstract

No abstract available - these are book chapters.

Summary

These chapters cover:

• One Lobby
  • Two states of the world
  • Three states of the world
  • Continuous states of the world
  • Welfare considerations
• Two Lobbies
  • Like Bias
  • Opposite Bias
  • Multidimensional Information
• More General Lobbying

The Model(s)

In general there is a policy maker who choses a policy to implement [math]p\,[/math], based on some facts about the state of the world [math]\theta\,[/math]. There is also a Special Interest Group (SIG) who observes the facts about the state of the world but has a bias [math]\delta \gt 0\,[/math]. The utility functions of both types of players are inverse quadratic (i.e. quadratic loss functions).

Utility of the policy maker:

[math]G(p,\theta) = -(p - \theta)^2\,[/math]

Utility of the SIG:

[math]U(p,\theta) = -(p - \theta - \delta)^2\,[/math]

The policy maker sets [math]p=\theta\,[/math] when the SIG reveals the true state of the world and [math]p=\mathbb{E}\tilde{\theta}\,[/math] otherwise.

One Lobby - Two States

There are two states of the world:

[math]\theta_H \gt \theta_L\,[/math]

Given that the bias is positive the SIG never has any incentive to misrepresent the high state, that is a report of [math]\theta_H\,[/math] will be trusted by the policy maker who will implement [math]p=\theta_H\,[/math].

Supposing that the true state is [math]\theta_L\,[/math], then we can use the distance from ideal points to see for what levels of bias the SIG will truely report this. Specifically the sig prefers to truthfully report if:

[math](\theta_L + \delta) - \theta_L \le \theta_H - (\theta_L + \delta)\,[/math]

[math]\therefore \delta \le \frac{\theta_H - \theta_L}{2}\,[/math]

When the bias satisfies this criteria there is informative lobbying and we can have full relevation, however this is not the sole equilibrium. Suppose the policy maker distrusted the SIG, then the policy maker would implement:

[math]p=\frac{(\theta_L+\theta_H)}{2}\,[/math]

Knowing this the SIG has no incentive to report truthfully - this is the Babbling Equilibrium and it always exists.

However, there is an equilibrium refinement by Farrel where the SIG makes a speech essentially saying "I have no incentive to lie". The SIG prefers [math]\theta_L\,[/math] to the policy maker's distrust implementation if is closer to his ideal point of [math](\theta_L+\delta)\,[/math]:

[math](\theta_L+\delta) - \theta_L \le \frac{(\theta_L+\theta_H)}{2} - (\theta_L+\delta)\,[/math]

[math]\therefore \delta \lt \frac{(\theta_H- \theta_L)}{4}\,[/math] provides the criteria for not trusting the SIG.

One Lobby - Three States

[math]\,[/math]