Econometrics

We continued exploring the class of optimization based estimators via-among others-the examination of the semi-parametric linear model with instrumental variables.

In the general case we commented on issues of existence of the estimator, based on properties of the underlying empirical criterion and the parameter space. We examined a generalization of the estimator enabling the consideration of optimization errors, that among others are usually met in numerical procedures.

We begun the exploration of asymptotic properties of such-like estimators, having in mind the usual linear model. We reminded ourselves of the high level conditions that ensure weak consistency of the OLSE when the parameter space is maximal. We asked whether this remains true in the general case when the parameter space is arbitrary yet the true parameter value lies in it. In such cases we generally do not have at our disposal an analytical form of the estimator as a measurable function of the sample. Thus we work with limiting properties of the criterion that are relevant to optimization. 

We begun working with the general case, and examine the mode of locally uniform convergence in probability.

Notes for the above can be found here (v. 24/01/23) and here (v. 24/01/23).