De Figueiredo (2002) - Electoral Competition Political Uncertainty And Policy Insulation

• This page is referenced in BPP Field Exam Papers

Reference(s)

de Figueiredo, R. J. P., Jr. (2002), Electoral Competition, Political Uncertainty, and Policy Insulation, American Political Science Review 96, 321-333. pdf

Abstract

Scholars argue that electoral uncertainty is a crucial factor that influences policy implementation: current holders of public authority, nervous that they might lose their position, seek to insulate the agencies they create so that policies will survive their creators. These theories, however, ignore crucial variation in the electoral prospects of groups competing for public authority. In this paper, I examine the effect of electoral volatility on the degree to which groups in power will dismantle their opponent’s agencies and programs and insulate their own policies from such destructive behavior. Through the analysis of two repeated games, I derive four propositions which fully characterize the conditions under which cooperative behavior can provide stability in the face of electoral uncertainty and instability. First, I show that if gains from cooperation are sufficiently large, compromise and cooperation can occur in the face of uncertainty. Second, I show that electoral uncertainty increases the possibility of cooperation, a result counter to the informal literature. Third, when electoral uncertainty is low, only one group - that with a low probability of electoral success - will insulate their programs. Finally, as electoral uncertainty increases, a wider set of the parameter values support the extreme cases of either both insulating or not insulating. I conclude by discussing some implications, examples and potential further extensions of the models.

The Reciprocity Game (RG)

The game in an infinitely repeated two-player game.

In each period:

• Nature selects player [math]A\,[/math] to move with probality [math]\gamma \in (0,1)\,[/math] and [math]B\,[/math] to move with [math]1-\gamma\,[/math]. [math]\gamma\,[/math] is the probability of being elected.
  • Political uncertainty is modelled by [math]\gamma\,[/math] close to [math]\frac{1}{2}\,[/math]. With [math]\gamma=1\,[/math] or [math]\gamma=0\,[/math] [math]A\,[/math] or [math]B\,[/math] are certain to be elected.
  • Political uncertainty is decreasing in [math]|\gamma - \frac{1}{2}|\,[/math]
• If elected a player implements their program with certainty.
• A player may also choose [math]A_it=\{O, NO\}\,[/math], that is [math]Overturn\,[/math] or [math]Not\,Overturn\,[/math] with respect to the other players program if one is in place.

Stage payoffs are calculated as:

[math] u_{At} = \begin{cases} (1,0) & \mbox{ if only A program is in place} \\ (0,1) & \mbox{ if only B program is in place} \\ (\beta ,\beta ) & \mbox{ if both A and B programs are in place} \\ \end{cases} \,[/math]

And likewise for [math]B\,[/math], where [math]\beta \in (0,1)\,[/math]. Note that for [math]\beta \gt 0.5\,[/math] choosing NO is welfare improving as [math]\beta+\beta \gt 1\,[/math].

The total payoffs to the game are the discounted sums of the players stage payoffs:

[math]U_it = \sum_{t=0}^{\infty} \delta^t u_it \quad i \in \{A,B\}\,[/math]

A player's strategy at [math]t\,[/math] describes what he will do given all possible histories [math]H_t\,[/math], where [math]H_t\,[/math] is made up of the choices of nature [math]N_t\,[/math] and the action sets of both players [math]A_{At}\,[/math] and [math]A_{Bt}\,[/math], where [math]N_t = (n_1, \ldots, n_t)\,[/math] and [math]A_{At} = (A_{A1},\ldots, A_{A(t-1)}\,[/math], and likewise for [math]A_{Bt}\,[/math]. The game is one of complete information.

The cooperative equilibrium is one where both players play [math]NO\,[/math] in every stage. This can be sustained by a Grim Trigger where a player plays [math]O\,[/math] for all time if either player has played an [math]NO\,[/math] at any time previous, provided that [math]\delta,\gamma \mbox{ and } \beta\,[/math] are sufficiently high. To prove this, recall that the sum of a geometric series is given by:

[math]s \;=\; \sum_{k=0}^\infty ar^k = \frac{a}{1-r}\; \mbox{ or }\; \sum_{k=m}^\infty ar^k=\frac{ar^m}{1-r}[/math]

provided that [math]r\,[/math] is less than 1 (which is needed for convergence).

Then one can solve for [math]\beta_A^*\,[/math], the threshold [math]\beta\,[/math] if [math]A\,[/math] defects as:

[math]\underbrace{\sum_{t=0}^{\infty} \delta^t \beta}_{\mbox{Cooperate}} \ge \underbrace{1 + \sum_{t=1}^{\infty} \delta^t \gamma}_{\mbox{Defect and prob(elected)}=\gamma \,}\,[/math]

[math]\therefore \beta \ge 1-\delta + \delta \gamma\,[/math]

And likewise for [math]\beta_B^*\,[/math]:

[math]\beta \ge 1 - \delta \gamma\,[/math]

Then cooperation can be sustained iff:

[math]B \ge max( \beta_A^*, \beta_B^*)\,[/math].

Note that cooperation can not be sustained if [math]\beta \lt \frac{1}{2}\,[/math].

[math]\beta\,[/math] could be high because:

• Groups value policy continuity ([math]\beta\,[/math] is endogenously high)
• Groups are risk averse
• Policies could be more effective with lower policy volatility
• Much political bargaining takes place across many dimensions - if players care about two dimensions and their indifference curves are elliptical then compromise positions will yield benefits.

The paper then considers the comparative statics of the relationship between uncertainty and cooperation. The results include:

• As [math]\gamma\,[/math] approaches [math]\frac{1}{2}\,[/math] cooperation can be sustained over a wider range of parameters.
  • Therefore as political uncertainty increases it is easier to sustain cooperation.