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Baker Gibbons Murphy (1999) - Informal Authority In Organizations (view source)
Revision as of 20:38, 10 December 2010
, 20:38, 10 December 2010no edit summary
Now suppose that the boss has contractually delegated the rights to make decisions to the subordinate.
Then the subordinate doesn't worry whether the boss gets <math>Y_H\;</math> or <math>Y_L\;</math> and searches to maximize:
:<math>\max_a s + a X_H - c(a)\;</math>
*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 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.
===Informal Delegation===
In this model the boss "promises" to ratify all of the subordinates decisions and then may renege. The subordinate, in turn, has to believe that the boss will honour the decisions. This is the '''informal delegation''' model.
This model would be appropriate when:
*Projects that require careful analysis (increased search) so that the benefits may out weigh the costs of allowing a poor decision through
*The boss may feel regret at allowing a decision yet not overturn it
If the boss promises and the subordinate believes, then the subordinate will choose <math>a^D\;</math>, and the boss will get both <math>Y_H\;</math> and <math>Y_L\;</math> projects. We call these <math>Y^D\;</math> payoffs, and the subordinate gets <math>X^D\;</math> (<math>=X_H\;</math>). The joint surplus is therefore <math>V^D\;</math>.
When the boss gets <math>Y_L\;</math> projects she will be tempted to renege. If she breaks her promise, then subordinate will be playing the informed centralization game from then on, and the payoffs will be <math>X^C\;</math> (<math>=X_H\;</math>) and <math>Y^C\;</math> (<math>=Y_H\;</math>), for a joint surplus of <math>V^C\;</math>.
Therefore the boss (with a discount rate of <math>r) will honour the promise if:
:<math>Y^L + \frac{1}{r} Y^D > \frac{1}{r} Y^C \quad \therefore Y^D - Y^C > -r Y_L\;</math>
The subordinate will accept delegation if:
:<math>X^D - X^C > 0\;</math>
Together these give the necessary and sufficient condition that for delegation:
:<math>V^D - V^C > -r Y_L\;</math>
Of course delegation is efficient if:
:<math>V^D - V^C > 0\;</math>
As <math>Y_L\;</math> is negative, this gives the result that there are times when it would be efficient to delegate authority informally, but that are not feasible because the boss will renege. There are two other important results:
*The attractiveness of delegation over centralization depends solely on the expected surplus
*The feasibility of informal delegation depends on the extreme payoffs - that is holding the expected surplus constant the feasibility is affected by the spread betweem <math>Y_H\;</math> and <math>Y_L\;</math>.
===Informal Authority with an Uniformed Boss===
In this model the boss doesn't know the payoffs of this period, only the past payoffs, and must either "Rubber Stamp" all projects or "Veto" all projects.
This model would be appropriate when:
*The subordinate has expertise the boss must rely on
*Small decisions that do not merit monitoring
*Decisions that must be made quickly
The bosses expected benefit from "Rubber Stamping" a project is:
:<math>\mathbb{E}(Y|X_H) = pY_H + (1-p)Y_L\;</math>
The bosses expected benefit from vetoing a project is <math>0\;</math>, and the boss would prefer to veto if:
:<math>\mathbb{E}(Y|X_H) <0\;</math>
Now the suppose that the subordinate is granted informal authority to propose projects that pay <math>Y_H to the boss, and the boss will threaten to retract this authority and either rubber stamp or veto projects is she ever finds that a <math>Y_L\;</math> project has been proposed. This is the '''informal authority''' model. In this model it is the subordinate, not the boss, who is tempted to renege.
====Rubber Stamping====
When the fall back is rubber stamping we know that:
:<math>\mathbb{E}(Y|X_H) > 0\;</math>
The sole question remaining is whether:
:<math>V^D > V^C \;</math>
Or whether delegation or centralization is more efficient. When delegation is more efficient that is exactly what happens. When centralization is more efficient, we can determine the knife edge case for when informal authority can occur.
Informal authority can occur if the present value from honouring it exceeds the present value from abusing it. If it is abused, we get the rubber stamp payoffs, which are the same as those to delegation (either <math>Y_L\;</math> or <math>Y_H\;</math> projects can be proposed and will be accepted). Formally we get informal authority if:
:<math>\frac{1}{r} X^C > X_H + \frac{1}{r} X^D \quad \therefore \X^C-X^D > r X_H\;</math>
The boss will grant informal authority (over rubber stamping) if:
:<math>Y^C - Y^D > 0 \;</math>
Combining terms gives the nec. and suff. conditions for informal authority:
:<math>V^C - V^D > r X_H\;</math>
The general result is that holding the expected surplus (<math>V^C - V^D\;</math>) constant, informal authority becomes less feasible as the temptation to renege (<math>r X_H\;</math>) increases.
====Veto====
As with the rubber stamping, the interesting case is when we are trying to achieve centralization through informal authority. Now the conditions are that the subordinate must prefer honouring to abusing:
:<math>X^C > r X_H\;</math>
And the boss will grant informal authority iff:
:<math>Y^C > 0\;</math>
Together these constraints give:
:<math>V^C > rX_H\;</math>
Which does not depend on <math>Y_L\;</math> at all.
==Divestiture as Contractible Delegation==
The paper concludes by noting that in a similar vein, firms may divest spin-offs in order to prevent themselves from reneging - that is from retrating informal delegation.
