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Grossman Helpman (2001) - Special Interest Politics Chapters 4 And 5 (view source)
Revision as of 19:24, 26 April 2010
, 19:24, 26 April 2010no edit summary
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===
:<math>\therefore \delta < \frac{(\theta_H- \theta_L)}{4}\,</math> provides the criteria for not trusting the SIG.
===One Lobby - Three States===
This allows for an equilibrium with partial transmission of information - this can be possible when the bias conditions for full transmission are violated.
===One Lobby - Continuous States===
As the number of states grows it becomes harder to get full relevation - the bias must be less than half of the distance between two states and this tends to zero as the number of states tends towards infinity. However, we can partition a continuous range of information and report credible with range the true state of the world falls in.
Suppose that:
:<math>\tilde(\theta)~U[\theta_{min},\theta_{max}]\,</math>
The SIG then reports <math>\theta_1\,</math> if <math>\theta_{min} \le \theta \le \theta_1\,</math> and so forth. The policy maker getting such a report implements <math>\frac{(\theta_{min} + \theta_1)}{2}\,</math>. The temptation to lie is greatest when <math>\theta\,</math> is on the boundary of <math>\theta_1\,</math>, and <math>\theta_2\,</math> is the greatest temptation (all other higher values greater exagerate the outcome and will overshoot the bliss point). Credibility therefore requires:
:<math>\frac{(\theta_1 + \theta_2)}{2} - (\theta_1 + \delta) \ge (\theta_1 + \delta) - \frac{(\theta_{min} + \theta_1}{2}\,</math>
:<math>\,</math>
