This talk consists of two parts. In the first half, we propose an MPEC approach for solving moral-hazard problems. In particular, we consider deterministic contracts as well as contracts with action and/or compensation lotteries, and formulate each case as a mathematical program with equilibrium constraints (MPEC). We investigate and compare solution properties of the MPEC approach to that of the linear programming (LP) approach with lotteries. We propose a hybrid procedure that combines the best features of both. The hybrid procedure obtains a solution that is, if not global, at least as good as an LP solution. It also preserves the fast local convergence property by applying an SQP algorithm to MPECs. The numerical results on an example show that the hybrid procedure outperforms the LP approach in both computational time and solution quality in terms of the optimal objective value.

In the second half, we present a novel application in designing executive compensation contracts. We formulate the problem of finding the optimal mix of fixed salary, at-the-money stock options and restricted stock in an executive compensation contract as a moral-hazard model and apply the MPEC/hybrid approach to solve for an optimal contract. Our analysis produces three important results. First, we find that stock options are an important part of the optimal CEO compensation contract. Second, restricting the compensation contract to fixed salary, at-the-money stock options, and restricted stock produces roughly the same expected payoff to owners as the unrestricted second-best compensation contract. This result suggests that simple observed compensation contracts are robust. Finally, the incentive effects of fixed salary, at-the-money stock options, and restricted stock for some CEOs is dominated by the level and composition of the executive's pre-existing wealth. For these CEOs, the choice of compensation contract is essentially the amount of fixed salary that is necessary to satisfy the outside reservation wage.

The first part of the talk is based on the paper "Computational of Moral-Hazard Problems", jointly with Kenneth L. Judd (Hoover Institution and NBER). The second part is based on "Stocks Options and Chief Executive Officer Compensation", jointly with Christopher S. Armstrong and David F. Larcker, both at Stanford Graduate Business School.

Che-Lin Su is a post-doctoral research fellow in the Center for Mathematical Studies in Economics and Management Science (CMS-EMS) at Kellogg School of Management, Northwestern University. Starting from November 2006, he is also a postdoc researcher at the National Bureau of Economic Research (NBER) and a guest faculty at the Argonne National Laboratory. His research focuses on computational optimization with applications in economics. He was awarded a graduate student paper prize by the Society of Computational Economics in 2005. In 2001, he worked as a manager of strategic planning and portfolio management in the Pharmaceutical Research Institute at Bristol-Myers Squibb Company. He received a Ph.D. in Management Science and Engineering from Stanford University in 2005.