Return to the setting of Example 17.3. Now assume the firm, rather than the manager, privately…

Return to the setting of Example 17.3. Now assume the firm, rather than the manager, privately observes y ∈ {g, b} after the manager acts but before output is observed. Determine an optimal contract that will simultaneously motivate the manager to supply input H and the firm to self-report its observation. Also write a short paragraph describing the equilibrium specification in the various incentive compatibility constraints.

((Example 17.3: Let’s try this with the setting in Examples 17.1 and 17.2. The optimal solution to program (17.2) is displayed in Table 17.3. For comparison purposes, the Table also displays the optimal contract when the additional measure is publicly observed (though you have to remember it is based on variable y, as opposed to variable y in our notational setup).

Relative to the public case, the information is used less aggressively. This is reflected in the fact the largest payment occurs in the public case, as does the lowest payment. The information is used in a mooted fashion in order to maintain candor in the communication. This also shows up in the noted risk premium. Here we are better off relative to having no additional information, but not as well off were this additional measure public.

Table 17.4 reports the manager’s (net) certainty equivalent for each of the 8 strategies displayed in Table 17.2. The last two (supply L and report via stuck on b or perversely) are, in fact, the binding constraints in the design program. These are the control hot spots. We continue to have concern for the manager’s choice of input, but also now have concern for his candor.4

Some benchmarking is in order. We are contrasting two cases: one where all performance evaluation information is public and another where some of it is privately observed and self-reported by the manager. As noted in laying out the self-reporting design program in (17.2), the self-reporting program consists of the public information design program coupled with a number of additional (incentive compatibility) constraints. This carries two important implications. First, self-reporting cannot improve on the public information case. In general, preserving the integrity of the self-report forces us to use the self-reported information less aggressively than its public counterpart. This is key to maintaining its integrity, just as restricted recognition rules are key to maintaining the integrity of the accounting library.

Second, the firm always has the option of not listening to the self-report (given it can so commit). To illustrate, Table 17.4 also displays the manager’s (net) certainty equivalent if the contracting arrangement ignores his communication, and thus reverts to contracting based on output alone. The I ∗ x solution is always feasible in the private information case, given the information arrives after the manager supplies his input. This implies listening is never deleterious in this setting.5 The deeper question, then, is when does listening to the manager actually improve the contracting arrangement, when, so to speak, does self-appraisal improve the arrangement? Example 17.3 suggests optimism, while the following example is less encouraging.))

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