Chapter 10 The Method of Maximum Likelihood Introduction The method of moments is not the only fundamental principle of estimation, even though the estimation methods for regression models discussed up to this point (ordinary, nonlinear, and generalized least squares, instrumental variables | Chapter 10 The Method of Maximum Likelihood Introduction The method of moments is not the only fundamental principle of estimation even though the estimation methods for regression models discussed up to this point ordinary nonlinear and generalized least squares instrumental variables and GMM can all be derived from it. In this chapter we introduce another fundamental method of estimation namely the method of maximum likelihood. For regression models if we make the assumption that the error terms are normally distributed the maximum likelihood or ML estimators coincide with the various least squares estimators with which we are already familiar. But maximum likelihood can also be applied to an extremely wide variety of models other than regression models and it generally yields estimators with excellent asymptotic properties. The major disadvantage of ML estimation is that it requires stronger distributional assumptions than does the method of moments. In the next section we introduce the basic ideas of maximum likelihood estimation and discuss a few simple examples. Then in Section we explore the asymptotic properties of ML estimators. Ways of estimating the covariance matrix of an ML estimator will be discussed in Section . Some methods of hypothesis testing that are available for models estimated by ML will be introduced in Section and discussed more formally in Section . The remainder of the chapter discusses some useful applications of maximum likelihood estimation. Section deals with regression models with autoregressive errors and Section deals with models that involve transformations of the dependent variable. Basic Concepts of Maximum Likelihood Estimation Models that are estimated by maximum likelihood must be fully specified parametric models in the sense of Section . For such a model once the parameter values are known all necessary information is available to simulate the dependent variable s . In Section .
