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Grossman Helpman (2001) - Special Interest Politics Chapters 4 And 5 (view source)
Revision as of 18:17, 26 April 2010
, 18:17, 26 April 2010no edit summary
*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 [http://www.edegan.com/pdfs/Grossman%20Helpman%20(2001)%20-%20Special%20Interest%20Politics%20Chapters%204%20And%205.pdf pdf]
**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 > 0\,</math>. The utility functions of both types of players are inverse quadratic.
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 > \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>\threfore \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 < \frac{(\theta_H- \theta_L)}{4}\,</math> provides the criteria for not trusting the SIG.
===One Lobby - Three States===
:<math>\,</math>
