Estimating Functions and Equations: An Essay on Historical Developments with Applications to Econometrics

The idea of using estimating functions goes a long way back, at least to Karl Pearson's introduction to the method of moments in 1894. It is now a very active area of research in the statistics literature. One aim of this chapter is to provide an account of the developments relating to the theory of estimating functions. Starting from the simple case of a single parameter under independence, we cover the multiparameter, presence of nuisance parameters and dependent data cases. Application of the estimating functions technique to econometrics is still at its infancy. However, we illustrate how this estimation approach could be used in a number of time series models, such as random coefficient, threshold, bilinear, autoregressive conditional heteroscedasticity models, in models of spatial and longitudinal data, and median regression analysis. The chapter is concluded with some remarks on the place of estimating functions in the history of estimation.