Bureaucratic beliefs and law enforcement

“A fish rots from the head down.”.

—An ancient proverb.

Abstract

Why are laws and contracts effectively enforced in some developing countries but shelved, undermined, or sabotaged in others, even when formal institutions are in place? We develop a model to explore the interaction between the ruler, front-line bureaucrats, and civilians. We emphasize that bureaucrats’ beliefs play a vital role in determining law enforcement outcomes. Bureaucrats’ beliefs about the ruler’s type determine their expectations about whether the ruler would launch an investigation when observing law non-enforcement, which then shapes their incentive to enforce laws. The ruler’s discretion to pursue personal interests has a signaling value as to his or her type. Our game generates a unique separating equilibrium, wherein ruler types differ in whether to exercise discretion to advance personal interests and the bureaucrats enforce the law if and only if not observing the ruler’s discretion. The game also yields two pooling equilibria where different ruler types choose the same strategy. We illustrate the theoretical insights with a comparative discussion of rulers in weak states and in developmental states.

Appendices

Appendix 1: Uniqueness of separating equilibrium

We consider whether a separating equilibrium different from Proposition 1 exists, in which the type-H ruler exercises discretion and the type-L ruler does not. Suppose that such an equilibrium exists. Then, $\mu \left( D \right) = 1$ and $\mu \left( \emptyset \right) = 0$ constitute a belief system consistent with the ruler’s strategy. The bureaucrat enforces the law upon observing the ruler exercise discretion and does not enforce the law otherwise. Given Lemma 1, production occurs in both rounds of the social game when the type-H exercises discretion, and fighting occurs in both rounds of the social game when the type-L does not exercise discretion. Therefore, the type-L ruler’s payoff is

$$\frac{{\alpha_{L} }}{2} \times 2 \times \left( {2d} \right) = 2\alpha_{L} d.$$

However, if the type-L ruler mimics the type-H ruler by exercising discretion, the law is enforced, production takes place in both rounds of the social game and the type-L ruler’s payoff is

$$\frac{{\alpha_{L} }}{2} \times 2 \times \left( {2a} \right) + B = 2\alpha_{L} a + B.$$

Obviously, $2\alpha_{L} a + B > 2\alpha_{L} d$ because $a > d$, implying that the type-L ruler has an incentive to deviate by mimicking the type-H ruler. Therefore, a separating equilibrium does not exist in which the type-H ruler exercises discretion and the type-L ruler does not.

Appendix 2: Proofs

Proof

(Proposition 2) We analyze the following cases using the equilibria of the subgames in stages 2 through 5.

If $p \ge \frac{E}{W}$: On the equilibrium path, the bureaucrat enforces the law after observing the exercise of discretion and so production takes place in both rounds of the social game. No type of ruler has an incentive to deviate. Part (a) of the proposition is proved.

If $p < \frac{E}{W};\mu \left( \emptyset \right) < \frac{E}{W}$: Given the belief system, the bureaucrat does not enforce the law in any case. The ruler’s discretion loses its signaling value, so neither type of ruler has an incentive to deviate in stage 1 to not exercising discretion. Fighting occurs in both rounds of the social game under the type-L ruler, while the type-H ruler launches an investigation in stage 4 and so fighting occurs in the first round, but production occurs in the second round of the social game.

If $p < \frac{E}{W};\mu \left( \emptyset \right) \ge \frac{E}{W}$: The bureaucrat does not enforce the law if he or she observes the ruler exercising discretion and enforces the law otherwise. For the type-H ruler to have no incentive to deviate to not exercising discretion, we need

$$\begin{aligned} & \frac{{\alpha_{H} }}{2}\left( {2a + 2d} \right) - C + B \ge \frac{{\alpha_{H} }}{2} \times 2 \times \left( {2a} \right) \\ & \quad \Leftrightarrow a - d \le \frac{B - C}{{\alpha_{H} }}, \\ \end{aligned}$$

where on the first line the left-hand side is the type-H ruler’s equilibrium payoff and the right-hand side is his or her payoff by deviating. In equilibrium, the bureaucrat does not enforce the law and so fighting occurs in the first round of the social game and the type-H ruler launches an investigation to shift the social equilibrium to the producing equilibrium in the second round. With deviation, the bureaucrat enforces the law and so production occurs in both rounds of the social game. For the type-L ruler to have no incentive to deviate, we need

$$\begin{aligned} & \frac{{\alpha_{L} }}{2} \times 2 \times \left( {2d} \right) + B \ge \frac{{\alpha_{L} }}{2} \times 2 \times \left( {2a} \right) \\ & \quad \Leftrightarrow a - d \le \frac{B}{{2\alpha_{L} }}, \\ \end{aligned}$$

where on the first line the left-hand side is the type-L ruler’s equilibrium payoff and the right-hand side is the payoff with deviation to not exercising discretion. In equilibrium, the bureaucrat does not enforce the law and fighting occurs in both rounds of the social game because the type-L ruler does not investigate the bureaucrat. With deviation, the bureaucrat enforces the law and so production occurs in both rounds of the social game.

Combining the analyses in the last two paragraphs, part (b) of the proposition is proved.

Proof

(Proposition 3) We analyze the following cases by relying on the equilibria of the subgames in stages 2 through 5.

If $p \ge \frac{E}{W};\mu \left( D \right) \ge \frac{E}{W}$: Given the belief system, the bureaucrat enforces the law in any case. So, the choice of whether to exercise discretion loses its signaling value. Both types of ruler have an incentive to deviate and exercise discretion.

If $p \ge \frac{E}{W};\mu \left( D \right) < \frac{E}{W}$: Given the belief system, the bureaucrat enforces the law if and only if he or she does not observe the ruler exercising discretion. For the type-H ruler to have no incentive to deviate to exercising discretion, we need

$$\begin{aligned} & \frac{{\alpha_{H} }}{2} \times 2 \times \left( {2a} \right) \ge \frac{{\alpha_{H} }}{2}\left( {2d + 2a} \right) + B - C \\ & \quad \Leftrightarrow a - d \ge \frac{B - C}{{\alpha_{H} }}, \\ \end{aligned}$$

where on the first line the left-hand side is the type-H ruler’s equilibrium payoff and the right-hand side is the payoff with deviation. In equilibrium, the bureaucrat enforces the law and so production occurs in both rounds of the social game. With deviation, the bureaucrat does not enforce the law and the type-H ruler launches an investigation, so fighting and production occur in the two rounds of the social game, respectively. For the type-L ruler to have no incentive to deviate to exercising discretion, we need

$$\begin{aligned} & \frac{{\alpha_{L} }}{2} \times 2 \times \left( {2a} \right) \ge \frac{{\alpha_{L} }}{2} \times 2 \times \left( {2d} \right) + B \\ & \quad \Leftrightarrow a - d \ge \frac{B}{{2\alpha_{L} }}, \\ \end{aligned}$$

where on the first line the left-hand side is the type-L ruler’s equilibrium payoff and the right-hand side is the payoff with deviation. In equilibrium, the bureaucrat enforces the law and so production occurs in both rounds of the social game. With deviation, the bureaucrat does not enforce the law and the ruler does not investigate the bureaucrat, so fighting occurs in both rounds of the social game.

If $p < \frac{E}{W}$: The bureaucrat does not enforce the law upon observing that the ruler does not exercise his or her discretion. Both types of the ruler have an incentive to deviate to exercising discretion for the private gains $B$ and for a possibly better chance of law enforcement.

Combining the analyses on the above cases, the proposition is proved.

Appendix 3: Equilibrium refinement

Suppose $p < \frac{E}{W}$ and $\frac{B - C}{{\alpha_{H} }} < a - d < \frac{B}{{2\alpha_{L} }}$. According to Proposition 2(b), pooling equilibria exist in which both types of ruler exercise discretion and the bureaucrat does not enforce the law because he or she operates under the belief system $\mu \left( D \right) = p < \frac{E}{W}$ and $\mu \left( \emptyset \right) < \frac{E}{W}$. Consider deviation by the ruler to not exercising discretion. According to the intuitive criterion, the bureaucrat knows that the deviation is not done by the type-L ruler because the type-L ruler’s payoff from the deviation under even the most favorable belief $\left( {\mu \left( \emptyset \right) = 1} \right)$ is less than his or her equilibrium payoff:

$$\frac{{\alpha_{L} }}{2} \times 2 \times \left( {2a} \right) < \frac{{\alpha_{L} }}{2} \times 2 \times \left( {2d} \right) + B$$

because $a - d < \frac{B}{{2\alpha_{L} }}$. If the type-H ruler deviates to not exercising discretion and is believed by the bureaucrat to be type-H, the ruler’s payoff is higher with deviation from the equilibrium payoff:

$$\frac{{\alpha_{H} }}{2} \times 2 \times \left( {2a} \right) > \frac{{\alpha_{H} }}{2} \times \left( {2d + 2a} \right) + B - C$$

because $\frac{B - C}{{\alpha_{H} }} < a - d$. Thus, the type-$H$ ruler has an incentive to deviate, showing that the intuitive criterion rules out the pooling equilibria in Proposition 2(b) with $\mu \left( \emptyset \right) < \frac{E}{W}$ when $\frac{B - C}{{\alpha_{H} }} < a - d < \frac{B}{{2\alpha_{L} }}$.