Econometric methods for implementing decision functions

Thesis

This thesis develops econometric methods for implementing data-based decisions. Decisions are viewed as functions of parameters which are estimated from the data. Standard methods focus on providing precise estimates of parameters ignoring intention to use them in decisions. My thesis focuses on designing methods to minimize the expected error in decision functions. The first chapter develops model averaging estimators in multiple regressions that minimize the mean squared error (MSE) of a chosen decision function. Our motivating example is implementing a portfolio choice rule that depends on variables included in assets' returns specification. We characterize the asymptotic MSE of decisions functions based on different models and then describe model-selection and averaging estimators that enable improvements in the MSE. The performance of our method is demonstrated with extensive simulations and empirical applications to futures data. The second chapter describes the risk improvements for a model averaging using two models. This type of averaging is known as shrinkage. Since the risk improvement is over the function of parameters, this shrinkage is referred to as focused shrinkage. The estimator is a weighted average between unrestricted and restricted models. The latter is a minimum distance estimator and requires selecting a projection matrix. The risk improvement of our shrinkage estimator over maximum-likelihood for arbitrary projection matrices is derived. I then show in an application to portfolio choice, that for a specific choice of projection matrix, this improvement can be substantial. The third chapter considers an application of the focused shrinkage estimator to the Global Minimum Variance (GMV) portfolio. Implementing the GMV portfolio requires estimating a covariance matrix and the literature has offered several estimators. Focused shrinkage is particularly suitable here because it can be used to directly minimize the MSE of the GMV portfolio. We illustrate the benefits of our estimator by conducting extensive simulations and empirical applications.

Authors: Klimenka, F; Wolter, J

• DOI: 10.5287/ora-kemg68qnd
• Type of award: DPhil
• Level of award: Doctoral
• Awarding institution: University of Oxford