Baker Gibbons Murphy (1999) - Informal Authority In Organizations

• This page is referenced in PHDBA602 (Theory of the Firm)

Reference(s)

Baker, G, R Gibbons, and K.J. Murphy (1999), "Informal Authority in Organizations", Journal of Law, Economics & Organization, 15, March pp. 56-73. pdf

Abstract

We assert that decision rights in organizations are not contractible: the boss can always overturn a subordingate's decision, so formal authority resides only at the top. Although decision rights cannot be formally delegated, they might be informally delegated through self-enforcing relational contracts. We examine the feasibility of informal authority in two informational environments. We show that different informations structures priodcute different decusions not only because different information is brought to bear in the decision-making process, but also because different information creates differenty temptations to renege on relational contracts. In addition, we explore the implications of formal delegation achieved through divestitures.

The Basic Model

The is a boss and a subordinate. The boss gets payoffs [math]Y\;[/math], and the subordinate gets payoffs [math]X\;[/math]. Both benefits can take two values:

[math]Y_H \gt 0 \gt Y_L \quad \mbox{and} \quad X_H \gt 0 \gt X_L\;[/math]

The subordinate searches for projects, with the intensity of search affecting the probability of discovering a project that he likes.

[math]a = Pr(X = X_H)\;[/math]

The conditional probability that the boss gets payoff [math]Y_H\;[/math] when an [math]X_H\;[/math] project is found is:

[math]p = Pr(Y = Y_H | X=X_H)\;[/math]

The conditional probability that the boss gets payoff [math]Y_H\;[/math] when an [math]X_L\;[/math] project is found is:

[math]q = Pr(Y = Y_H | X=X_L)\;[/math]

Therefore the joint probabilities are:

[math]Pr(Y = Y_H, X=X_H) = ap\;[/math]

[math]Pr(Y = Y_L, X=X_H) = a(1-p)\;[/math]

[math]Pr(Y = Y_H, X=X_L) = (1-a)q\;[/math]

[math]Pr(Y = Y_L, X=X_L) = (1-a)(1-q)\;[/math]

The timing is as follows:

1. The boss pays the subordinate [math]s (which may be negative) #The subordinate searches by choosing a, where \lt math\gt c(a) = \gamma a^2\;[/math]
2. The subordinate observes the payoffs [math](X,Y)\;[/math], if the payoff is [math]X_L\;[/math] the project is ignored, otherwise the project may be recommended.
3. If the project is recommemded then the boss either implements or rejects the project (perhaps seeing the payoffs).

The next two sections give two simple benchmarks.

Informed Centralization

In this model, the boss is informed of the payoff and then makes the decision. The subordinate knows that the boss will reject decisions with a payoff of [math]Y_L \lt 0\;[/math] and therefore maximizes the expected utility:

[math]\max_a s+ apX_H - c(a)\;[/math]

This solves to:

[math]c'(a^C) = pX_H\;[/math]

The search intensity that maximizes joint welfare conditional on selecting only [math](X_H,Y_H)\;[/math] projects solves:

[math]\max_a ap(X_H + Y_H) -c(a)\;[/math]

Which gives:

[math]c'(a^*) = p(X_H + Y_H)\;[/math]

so [math]a^C\;[/math] is less than efficient. The paper doesn't use the given cost function to make the comparison (any convex cost function would do), but using it gives:

[math]a^C = \frac{1}{\gamma}\cdot pX_H\;[/math]

[math]a^* = \frac{1}{\gamma}\cdotp(X_H + Y_H)\;[/math]

[math]\therefore a^* \gt a^C \; \forall Y_H \gt 0\;[/math]

The expected welfare to the boss under informed centralization is:

[math]a^c p Y_H - s\;[/math]

Total expected welfare is therefore:

[math]V^C = a^C p (X_H + Y_H) - c(a^C)\;[/math]

Contractible Delegation

Now suppose that the boss has contractually delegated the rights to make decisions to the subordinate.

Then the subordinate searches to maximize:

[math]\max_a s + a X_H - c(a)\;[/math]

which solves:

[math]c'(a^D) = X_H\;[/math]

Because [math]c''(\cdot) \gt 0\;[/math] and [math]p \lt 1\;[/math], it must be that delegation increases the incentives to search.

Explicitly this can be seen because:

[math]a^D = \frac{1}{\gamma}\cdot X_H \gt a^C = \frac{1}{\gamma}\cdot pX_H\;[/math]

Note that it might increase them too much. The efficient incentives under delegation are given by:

[math]c'(a^*) = p(X_H + X_L) + (1-p)\cdot \max(0,X_H+Y_L)\;[/math]

which can imply either higher or lower incentives.

The expected payoff to the boss under contractible delegation is:

[math]a^D(pY_H + (1-p)Y_L) -s\;[/math]

So total welfare is:

[math]V^D = a^D p(X_H + Y_H) + a^D(1-p)(X_H + Y_L) - c(a^D)\;[/math]

The following points should be made:

• Parties would agree to delegate if [math]V^D \gt V^C\;[/math] and would leave this right with the boss otherwise.
• Ex-ante incentives are stronger under delegation
• Ex-post project choice and its efficacy differ under the two schemes. Which is better depends on the sign of [math]X_H+Y_L\;[/math] - if this is positive then delegation is better, otherwise centralization is better.
• When p is high (interests are aligned) and [math]-Y_L\;[/math] (the cost from delegation) is small, then delegation is more likely.

Models of Informal Authority

In the following models, formal authority can not be delegated within organisations. However, informal authority can be given in a repeated game framework.

In the first model, the boss becomes informed before ratitfying the project, but has a reputation for not interfering to maintain. In the second model the boss is only informed about historic payoffs, and must either rubber stamp or veto the project.