Ability, openness, and managerial decision making.

Introduction

Managerial decision making is very important for various kinds of organizations. Companies spend significant amounts of resources to find CEOs to match their needs. As a manager plays a leading role to his subordinates, the ability of a manager is a concern. (1) Even though a manager has a high level of ability, he usually does not have the time or sufficient amount of information to make a decision. Thus whether a manager is open to opinions of others is relevant to the quality of the decision made. (2) There am some interesting questions about managerial decision making. First, how is the behavior of a manager affected by his ability and his degree of openness? Second, how is the behavior of subordinates affected by the personalities of the managers? Third, what kind of personality is desirable for a manager? Finally, if we have to choose among different merits of good manager, which merit is most desirable?

In this paper, we study the impact of the ability and the degree of openness of a manager on decision making. A manager plays many roles, including decision making, supervision of subordinates, and participation in production directly. Here we emphasize the decision making role of a manager rather than other roles of a manager. For a manager with a large number of subordinates, this emphasis on decision making is appropriate. For example, for the CEO of the General Motors, the decision as whether or not to keep or develop a new brand of cars, is much more important than engaging in the production of cars directly. One contribution of this paper is that we study the information aggregation role of a manager in a formal model. In this paper, a manager needs to estimate the true value of a parameter. A manager may rely on his information only or also consult the information of his subordinates. A more able manager is modeled as a manager with a more precise estimate of the parameter needed for decision making, while a more open manager is modeled as a manager who is more likely to consult subordinates for information.

First, when the degree of precision is exogenous and a leader chooses the number of followers optimally, we show that a more able manager consults a lower number of subordinates. The number of subordinates consulted does not change with the degree of openness of the manager. Second, when the number of subordinates is exogenously given and the level of precision is determined by effort level, a sufficient condition for the manager's effort to increase, and the subordinate's effort to decrease with the ability of the manager is that the quality of prior information is relatively good. When the manager is more open, the effort of the manager decreases and the effort of a subordinate increases. Third, we study the case that both the number of subordinates and the level of precision are optimally chosen. We show that a less open manager exerts a higher level of effort. A higher level of prior precision decreases the effort level of the manager. When prior information is relatively accurate, the number of subordinates consulted decreases with the ability of the manager and the effort of the manager increases. Overall, a more capable manager is more desirable. Interestingly, decision cost is not a monotonic function of the degree of openness. When the decision stake is low, it may be profitable to choose a less open manager to save the wage cost paid to subordinates. When the prior information is relatively inaccurate, it is more desirable to have a more open manager.

In the literature on a manager's vision, Rotemberg and Saloner (1993) study a model in which contracts between the firm and mangers are incomplete. In Rotemberg and Saloner (2000), a manager with a vision biases him in favor of certain projects. This affects the type of projects implemented and thus affects the incentives of subordinates because subordinates can be compensated for their innovative ideas only when their ideas get implemented. In Van den Steen (2005), after knowing the preferences of the managers, workers choose companies to work for. A manager with strong beliefs about the right course of action will attract subordinates with similar beliefs. This alignment of beliefs between managers and workers in the same company gives direction to the firm and affects incentives and coordination. In the above models, the role of a manager is significantly different from that in this paper.

The rest of the paper is organized as follows. First, we specify the model. Second, we examine the optimal choice of the number of subordinates when the degree of precision is exogenously given. Third, we address the impact of ability and openness on behavior when higher effort levels improve the degree of precision. Fourth, we study effort levels when the number of subordinates and the level of precision are all optimally chosen. Optimal selection of a manager is also discussed. Finally, we discuss some generalizations of the model and conclude.

Specification of the Model

In this section, we specify the model. There is a manager and a pool of subordinates. A decision needs to be made and the quality of the decision depends on the estimation of the true value of an unknown parameter [eta]. The decision may be whether to initiate a new investment project. The parameter to be estimated is the profitability of the project. There are alternative interpretations of the manager and the subordinates. For example, the configuration can be a president deciding how many advisors to consult before making a decision.

The prior belief about the parameter [eta] is that it follows a normal distribution with mean [mu] and a specified value of the precision [tau] [tau]>0. (3) Let [theta] denote a positive constant. The manager has one observation with a precision of [theta][p.sub.m] , where [p.sub.m] is a positive number. (4) A manager with a higher value of [theta] is viewed as more capable or with a higher level of ability. There is an unlimited supply of subordinates. The number of subordinates actually consulted by the manager is n. It is assumed that observations between the manager and any subordinate are independent. It is also assumed that observations among subordinates are also independent. Each subordinate has one observation with a precision of [p.sub.s], [p.sub.s]>0.

The manager is assumed to be risk neutral and his objective is to minimize the total cost which is the sum of the decision loss and the opportunity cost of the manager and possible payments to subordinates. For a denoting a positive constant, the loss function is assumed to be quadratic: a([??] - [eta]).sup.2]. Here, [??] is the estimation of the parameter. As argued in DeGroot (1970, p. 228), when the loss depends only on the difference [??] - [eta], a motivation of using the quadratic loss form is that it is an acceptable approximation in a wide variety of situations: Let X denote the amount of information available. From DeGroot (1970), it can be shown that the Bayes decision to minimize the quadratic function is given by [??] = E([eta]). With this decision rule, the minimum loss is [[rho].sup.*] - E[var([eta]|X)].

For t [member of] [0, 1], suppose that the manager uses both his information and the information from his subordinates t percent of the time and uses his information only for the rest of the time. The value of t is determined by the personality of the manager and it may be viewed as the style of the manager. Here, t is a parameter used to measure the manager's degree of openness or tolerance (t stands for tolerance). With this view in mind, t is assumed to be exogenous in this model. When t is equal to zero, the manager does not put any weight on the information gathered by the subordinates. In this case, the manager is viewed as not open. This possibility can be rationalized by arguing that the manager does not trust the information provided by the subordinates. When t is equal to one, the manager puts equal weight on his own observation and the observation provided by the subordinates. In this case, the manager is viewed as completely open. This configuration can apply when the manager views himself as a member of a committee and each member of the committee plays equal role. With the above specification, the degree of openness increases with t. The manager knows the value of t himself. The manager may also determine the number of subordinates to consult.

Total cost is the sum of expected loss and the opportunity cost of the manager and payment to the subordinates. The opportunity cost of the manager is u. The wage rate paid to a subordinate is w. When the manager relies on his own information only, the manager will set the estimation equal to the expected value and the posterior precision is [tau]+[theta][p.sub.m] and the decision risk is a/([tau] + [theta][p.sub.m]). No payment to followers needs to be made. When the manager relies on both his information and the n subordinates, the manager will set the estimation equal to the expected value and the posterior precision is [tau]+[theta][p.sub.m] + n[p.sub.s] and the decision risk is a/([tau]+[theta][p.sub.m] + n[p.sub.s]). The wage cost is nw. Thus the total expected cost for a manager with a degree of openness t is equal to

a(1 - t)/[tau] + [theta][p.sub.m] + a t/ [tau]+[theta][p.sub.m] + n[p.sub.s] + u + t n w. (1)

In the following three sections, we study the impact of the manager's ability and the degree of openness under different configurations.

Optimal Choice of the Number of Subordinates

In this section, the levels of the precisions of individuals are exogenous.

The manager chooses the number of subordinates to consult to minimize total expected cost. From (1), the first order condition for the optimal choice of the number of subordinates is (6)

[OMEGA] [equivalent to] w - a[p.subs.]/([tau]+[theta][p.sub.m] + n[p.sub.s]).sup.2] = 0. (2)

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