Estimation of Econometric Models by Risk Minimization: A Stochastic Quasigradient Approach

Abstract

The paper presents a risk minimization approach to estimate a flexible form that meets a priori restrictions on slope and curvature by means of constraints on both the estimated parameters and the function values. The resulting constrained risk minimization combines parametric and nonparametric estimation and contains integrals and implicit constraints. Within econometrics, simulation has become a common tool to solve problems of this kind. However, it appears that in our case, the simulation approach only applies when the model is linear in parameters, has simple constraints on parameters and a quadratic risk function. To deal with other cases, we use a stochastic optimization technique known as the stochastic quasi-gradient method for stationary and nonstationary problems with Cesaro averaging. This method is also applicable to an expanding series of random observations, and produces asymptotically (weakly) convergent estimates