Three Essays on Professional Advising.

Abstract

This dissertation considers three topics in professional advising and forecasting. Chapter 1 examines a principal's optimal contracting with experts. In an environment where experts have heterogeneous private signal distributions and type dependent reservation utilities, we show that the first-best outcome is achieved through a compensation scheme. In the class of independent linear payoff function with respect to a specific performance measure, we derive the optimal payoff function. It is shown that the performance measure should be more sensitive to the error as the reservation utility gets more concave. We then propose a recruiting procedure which leads to the optimal employment under full information.

Chapter 2 explores the optimal employment for a principal who wishes to gather information from multiple experts. When the principal minimizes the expected mean squared error and each expert’s reservation utility is proportional to the marginal single information contribution, it is shown that the optimal employment set follows a cut-off property, which implies a simple algorithm finds the optimum. We then present some extensions with a general submodular set production function. The cut-off property is proved to hold when the function exhibits decreasing curvature. An efficient algorithm to find the global optimum is also discussed.

Chapter 3 analyses forecasting behavior when a new signal arrives with uncertain timing. In addition to the consensus, a forecaster observes a signal which may have been observed by past forecasters. The forecaster then needs to infer the arrival time to figure out whether the signal is new or is already reflected in the consensus. Under a Gaussian specification, it is shown that the forecaster places more weight on the new signal when it moves away from the consensus, believing that the signal more likely to be new. The result sheds light on recent empirical studies on a herding or anti-herding bias. Without resorting to behavioral assumptions or unusual payoff functions, our model shows that statisticians may observe forecasters placing more weight on private information rather than the consensus.