290 The Basics of financial economeTrics
■ (^) The weighted least squares (WLS) estimator, used when residuals have
different variance, minimizes a weighted sum of squared residuals.
■ (^) The generalized least squares (GLS) estimator, used when residuals
have different variance and are correlated, minimizes a weighted sum of
squared residuals.
■ (^) The maximum likelihood method estimates parameters by maximizing
the probability of the distribution on the data.
■ (^) The maximum likelihood method assumes the form of the distribution
is known.
■ (^) If variables are normally distributed, the maximum likelihood and least
squares methods give the same results.
■ (^) When residuals are correlated with regressors, we cannot use the OLS
method and instead we might use the instrumental variables (IV)
approach.
■ (^) The IV approach replaces regressors correlated with the residuals with
new variables that are correlated with the regressors but uncorrelated
with the residuals.
■ (^) The method of moments equates empirical and theoretical moments.
■ (^) The generalized method of moments uses more conditions than param-
eters and replaces exact determination of parameters with optimization.