# Linear Programming-Based Estimation & Inference

Project: Research

## Description

Data on different entities (e.g. companies, countries or individuals) collected at a single time period are called cross-sectional data. Cross-sectional data can be used to study relationships among economic variables by studying differences across entities at a single period in time. It is useful to model cross-sectional observations as realizations of independent, identically distributed random variables. This assumption is satisfied if the entities are sampled by simple random sampling. A useful class of models for describing cross-sectional data is provided by linear regressions.In contrast to cross-sectional data, time series data are data for a single entity collected over a period of time (e.g. unemployment measures or exchange rates). Time series data can be used to study the evolution of economic variables over time and to forecast future values of those variables. It is useful to model an observed time series as a realization of a random process. More specifically, to allow for the unpredictable nature of future observations it is assumed that each observation is a realized value of a random variable. A useful class of models for describing the dynamics of a time series is provided by autoregressive (AR) processes.In practice, the parameters of an economic model are unknown and need to be estimated using actual data. The linear regression and AR models described herein are usually estimated by the method of ordinary least squares (OLS). In regression analysis, it is well known that the OLS estimator is inconsistent (may not be close to the true parameter values with high probability even when the data set is very large) for the regression parameters when the error term is correlated (linearly associated) with the explanatory variables in the regression. Similarly, in time series analysis, it is known that the OLS estimator is inconsistent for the AR parameters in an AR process with serially correlated errors. Under certain restrictions, a promising alternative to OLS is linear programming (LP) based estimators. Recent research show that these estimators can be superconsistent in the above mentioned situations and, hence, preferable to OLS. This project has two parts which relate to LP-based estimators and their applications in economics and finance. The first part concerns estimation and inference in a class of restricted linear regression models. The second part involves estimation and inference in a, for economics, recently introduced class of restricted nonlinear time series models.

## Detail(s)

Project number 9042007 ECS Finished 1/01/14 → 22/12/15