Parallel Testing

Under a parallel testing strategy, the firm assigns a different expert to each design i ∈ I = {1, . . . , n}, and all experts then perform their testing activities simultaneously. This setup allows the firm to receive refined information on each design’s value and to use this information to select, ex post, the most promising alternative for development. The firm’s overarching goal is to maximize expected profits, which amount to the expected market value of the developed design net of development costs and compensation paid to experts.

Formally, the firm solves the following optimization problem P (the mathematical derivation

8We endogenize the firm’s choice of design alternatives in Section 2.5.1.

and all other formal proofs, has been relegated to the Appendix):

Although complex at first sight, this optimization problem P has an intuitive structure.

As a starting point, note that y^(j)_i is an indicator variable that reflects whether design i is the firm’s jth most preferred alternative (constraint (2.6) ensures that this mapping is indeed one-to-one). That is, if y_i^(j)= 1 then the firm chooses design i for development only if it receives an unfavorable recommendation for all designs with a lower ranking j⁰ < j. Clearly, a design’s attractiveness is not exogenously given and instead depends endogenously on the offered compensation scheme. This fact is reflected by (2.5), which guarantees that the firm makes an ex post optimal selection decision. Conditions (2.2)–(2.4) represent each expert’s incentive compatibility constraints, which depend on the relative attractiveness of the design she has been assigned to evaluate. Thus (2.2) and (2.3) ensure that each expert truthfully reveals, respectively, a “good” and a “bad” signal. These constraints eliminate the adverse selection problem during the recommendation phase. Condition (2.4) similarly negates the moral hazard problem during the design-testing phase because it ensures that each expert prefers high-effort to low-effort testing. Finally, experts are protected by limited liability; hence (2.7)

ensures that all wage payments are nonnegative. The following proposition characterizes—

under mild conditions on the properties of designs in I—the optimal incentive structures for parallel testing and the resulting firm profits.⁹

Proposition 2.1 (Parallel Testing). Suppose the designs in I can be ordered such that qivi ≥ qi+1vi+1 + 2ⁱ⁺¹c[qi/(2qi− 1) − 2qi+1/(2qi+1 − 1)]⁺ for all i ∈ I\{n}, where [x]⁺ = max{0, x}. Then the following statements hold.

(i) Under a parallel testing strategy, the optimal contract that induces truth telling and high-effort testing for each design satisfies u_ig = 2ⁱ⁺¹c/(2q_i − 1), u_ib = 0, u_ia = 0, and u_it= 2ⁿ⁺¹(1 − q_i)c/(2q_i− 1) for all i ∈ I. Moreover, u_it/u_ig = 2ⁿ(1 − q_i)/2ⁱ< 2ⁿ⁻ⁱ⁻¹ ≤ 2ⁿ⁻² for all i ∈ I.

(ii) Ex ante, the firm’s expected profit is Π_P =Pn

i=1((q_iv_i− K)/2ⁱ− 2c/(2q_i− 1)).

Perhaps the most remarkable aspect of this proposition is the simplicity of the optimal contract’s structure. For each design (and thus for each expert) i ∈ I, the firm need offer only two payments: a success bonus u_ig if design i is successfully developed, and a termination bonus u_it if none of the design alternatives is chosen for development (i.e., if test outcomes indicate that all designs are technologically unfeasible). But what respective roles do these payments play in the firm’s incentive system? As (2.4) reveals, the primary purpose of u_ig is to motivate expert i to engage in high-effort testing. Put differently, uig is a purely individual incentive that resolves each expert’s moral hazard concern. In contrast, u_it is a common (or shared) incentive that collectively compensates the experts if all designs are considered to be technologically unfeasible. It therefore decreases the likelihood of an expert giving a positive recommendation despite receiving a negative test outcome—and thereby induces truth telling; see constraint (2.3).

It is intuitive that, when effort becomes less rewarding (i.e., effort costs c increase) and recommendations become less reliable (the signal quality qi decreases), expert i becomes more reluctant to invest high effort and to report test outcomes truthfully. Under these circumstances, the firm must provide stronger incentives; this explains why u_ig and u_it are increasing in c and decreasing in q_i. Conversely, in the extreme case of perfect testing (q_i = 1), expert i has no incentive to misrepresent the test outcomes because such a false recommendation would be easily detected by the firm and so would not benefit him. It follows that if testing is perfect then the firm can forgo payment of any shared incentives (u_it = 0).

9The condition in Proposition 2.1 holds unless I contains a design for which the test is of excep-tionally low efficiency.

Whereas neither u_ig nor u_it depends directly on a design’s inherent economic potential v_i, these terms are affected by the total number n of designs to be tested and by a design’s relative value, which we also index via i. In particular, u_ig increases with i because, with a higher index i, it becomes more likely for tests to indicate that a design with a smaller index is technologically feasible—which would render futile the expert’s testing efforts. Similarly, with a higher n it becomes less likely that all n designs are technologically unfeasible; hence the termination bonus u_it is correspondingly less likely to be paid out. To compensate the experts for this reduced payment probability, the firm must offer a higher u_it.

Proposition 2.1(i) also sheds light on the severity of adverse selection—as compared with moral hazard—when the firm employs a parallel testing strategy. For designs that are ex-tremely promising ex ante (i.e., those with a small index i), the ratio u_it/u_ig is high; the implication is that, for these designs, the firm’s central concern is to incentivize truth telling.

For ex ante less promising designs (those with a large index i) the ratio is low; in that event, the firm becomes relatively more concerned with incentivizing experts to exert high effort.

This shifting priority of the optimal compensation scheme has an appealing explanation.

From an expert’s perspective, admitting that her own testing outcome is bad increases the odds of receiving no payments. This conclusion follows from the extreme unlikelihood of all tested designs being pronounced technologically unfeasible. The firm’s concern on this point is especially strong for designs that show the most promise. At the same time, an expert as-signed to a promising design has a significant intrinsic motivation to exert high effort because the potential rewards from receiving a good test outcome are high. In contrast, an expert assigned to a less promising design fears that her efforts are futile because, in all probability, a more promising design will receive a good recommendation and so the results of her testing could be irrelevant to the firm. Therefore, relatively higher individual incentives must be offered to the experts who are assigned to test less promising designs.

Finally, Proposition 2.1(ii) reveals that the firm’s expected profit is decreasing in c and increasing in qi. The reason is that, with a higher c and a lower qi, expert i is less willing to exert high effort and to disclose the test outcomes truthfully. Hence the incentive mis-alignment between the firm and expert i widens, which enables the expert to extract higher information rents.