Moral hazard in the agenda-setter model.

• Author: Lee, Kangoh

1. Introduction

The paper considers a model of sponsor-bureau relations in an environment where incentives for bureaucratic efforts are important. The bureau provides output for the sponsor in exchange for the budget that finances the Cost of providing output. While the cost is technologically determined by a cost function, casual observation suggests that the bureau may also influence the cost by exerting effort. For instance, in procuring supplies for the military, the bureau may design and examine a contract carefully and negotiate prices with supplying firms in an attempt to cut costs. The bureau may also search for an alternative less expensive way of completing a project. Effort, however, involves disutility for the bureau, and the bureau need not have incentives to make such effort that would decrease the cost.

To model this environment, we assume that the cost of providing output decreases on average with the bureau's effort. In such environment, the budget and the bureau's effort will jointly determine the output level the sponsor enjoys. In particular, the level of output increases with the bureau's effort given a budget. Thus, the sponsor would like the bureau to exert effort while the bureau dislikes effort that involves disutility. The sponsor, however, cannot observe or control effort, causing a moral hazard problem.(1) Therefore, the sponsor should induce the bureau to exert effort through the budget. Consequently, the ideal (second-best) budget the sponsor can choose in the presence of moral hazard would differ from the one without moral hazard. The relevant question concerns then how the equilibrium budget determined through a budgetary process between the sponsor and the bureau compares to the sponsor's ideal budget when bureaucratic incentives for effort are considered.

In explaining the relationship between the equilibrium budget and the sponsor's ideal budget, the literature [14; 17] typically assumes that the bureau maximizes its budget and has the monopoly power to propose a budget that the sponsor can only accept or reject. These assumptions about the bureau's preferences and the budgetary process lead to the proposition that the bureau obtains a budget that exceeds the sponsor's ideal budget. This is one of the main results in the literature on bureaucracy. The key assumption driving this proposition is that the bureau has its own objectives such as maximization of its budget. In our model, however, the presence of moral hazard also creates a difference between the equilibrium budget and the sponsor's ideal budget. The reason is that the sponsor should take into account the incentive constraint in choosing the ideal budget. Therefore, even if the bureau does not wish to maximize its budget, the equilibrium budget may be still too large according to the sponsor's preferences due to moral hazard.

A critical assumption in the analysis is that the budget and effort cannot be determined independently due to moral hazard. Instead, the bureau's choice of effort depends on the budget through the incentive constraint. The sponsor may have complete knowledge of the incentive constraint in some circumstances such as routine projects. That is, the sponsor may learn through time how the bureau adjusts effort to changes in the budget. In the case of new projects, however, this assumption of complete knowledge of the incentive constraint may not be appropriate. The question concerns then how asymmetric information between the sponsor and the bureau affects the equilibrium budget when moral hazard is present. While the bureau may take advantage of its private information in obtaining a budget it prefers, the sponsor attempts to infer private information from the bureau's proposal. Thus, private information does not necessarily enable the bureau to achieve a more preferable budget. However, whether the sponsor can correctly infer bureau's private information or whether the bureau can credibly signal its private information depends crucially on the existence of a separating equilibrium. The analysis shows that separating equilibria exist for a range of the reversion budget. Consequently, the bureau's budget proposal alleviates the sponsor's information problem, and hence improves the ability to make a correct decision as to whether to accept or reject a proposal. This may partially explain why the sponsor grants the bureau the monopoly power to control the agenda. It is Banks [1] who first considers this question in a model where no moral hazard is present and the sponsor is uncertain about the status quo budget. In contrast to our results, no separating equilibrium exists in his model, and the bureau's proposal does not play as an effective signal.

The plan of the paper is as follows. The next section presents the model. Section III analyzes the equilibrium budget in the presence of moral hazard. Section IV considers the effect of asymmetric information on the equilibrium budget. The final section offers a conclusion.

2. The Model

   The model involves a sponsor and a bureau that provides a quantity z of a public output in exchange for a budget x. For simplicity, we write the cost of providing z as cz, with c denoting the constant marginal cost. Due to the unforeseen events such as uncertain production technology and input prices, the marginal cost is stochastic. The probability distribution of c is influenced by bureau's action, a, that cannot be observed by the sponsor. The bureau's unobservable action may be interpreted as effort. Let F(c : a) denote the distribution function of c and let f (c : a) denote the corresponding density function with support [c, c]. It is assumed that

   [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

   where [F.sub.a](c : a) [[is greater than]0 for some c. The first inequality means that an increase in a generates a more favorable distribution of c (puts more weight on the lower tail) in the first-order stochastic dominance sense. The second one roughly means that there are decreasing returns to scale with respect to action, which suffices to satisfy second-order conditions for some optimization problems below. It is also assumed that the support of the distribution is independent of a, which is a standard assumption.(2)

   The sponsor wishes to maximize the difference between the benefits from output, denoted W (z), and the budget used to finance the cost of output. The sponsor's utility may then be given by

   W([Zeta]) - [Chi] = W([Chi]/C) - [Chi], (2)

   where W([Zeta]) is increasing and concave. W([Chi]/C) - [Zeta] may be interpreted as net benefits from a budget [Chi] enjoyed by the sponsor. The bureau provides output supposedly in the interests of the sponsor. The bureau, however, may pursue its own objectives that may differ from the sponsor's objectives, and we write the bureau's utility as

   [Alpha]W([Chi]/c) - [Beta][Chi] - Q(a), (3)

   where Q(a) is increasing and convex.(3) Since we will work mainly with expected utility, we write the sponsor's expected utility and the bureau's expected utility, given [Chi] and a, as

   [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

   where the upper and lower limits of integration, c and c are omitted.

   This specification of the bureau's preferences reflects following two assumptions. First, effort involves disutility for the bureau, but not for the sponsor. Second, the bureau and the sponsor may derive different net benefits from a given budget [Chi], and may desire different budgets. This is the case as long as [Alpha] [is not equal to] [Beta]. In particular, it is straightforward to verify that the bureau desires a budget greater (less), given a, than the sponsor desires if a [is greater than]) ([is less than])[Beta]. The most considered case in the literature is a [Alpha] [is greater than] [Beta] = 0, meaning that the bureau seeks to simply maximize its budget or that the bureau desires an infinite budget. This is a basis of the proposition that the public sector budget tends to be too large according to the sponsor's preferences.

   This paper assumes that [Alpha] = [Beta] = 1. The reason for this assumption is that a goal of the analysis is to show that moral hazard may create a bias towards an excessive equilibrium budget even when the bureau and the sponsor derive the same net benefits from a given budget (or even when the bureau does not wish to maximize the budget). With this assumption, the bureau's preferences coincide with the sponsor's preferences except effort. Consequently, we write the bureau's expected utility as

   [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

   The results, however, can be extended to the case where [Alpha] [is not equal to] [Beta] [is not equal to] 1, as demonstrated below.

   Since we assume [Beta] = 1 [greater than] 0, this assumption is at odds with the traditional Niskanen-type bureau in the sense that the bureau here does not pursue a maximum budget. This assumption, however, is not without precedent. First, the careers of senior bureaucrats at least are tied to the sponsor's evaluation of their performance, as argued by Breton and Weintrobe [4]. Thus, given large mobility among bureaus in government organizations, bureaucrats who care about advancement would not simply maximize their budget for their own interest. Second, as in Courant and Rubinfeld [7], since public employees or bureaucrats are also taxpayers, they would not pursue a maximum possible budget that results in large taxes.

3. Moral Hazard and the Equilibrium Budget

   To investigate the role of moral hazard in determining the relationship between the equilibrium budget and the sponsor's ideal budget, we begin with the sponsor's ideal budget. The sponsor achieves an ideal outcome if the sponsor can decide on the level of x and a. Given the presence of moral hazard, however, the sponsor cannot choose x and a independently, but should take into account the fact that the bureau will select its utility-maximizing effort. Thus, the...