What are the three methods of estimation? Discuss.

In econometrics, the estimation of parameters is essential to conduct empirical analysis. There are three main methods of estimation used in econometrics:

1. Ordinary Least Squares (OLS) Estimation: OLS estimation is the most commonly used method of estimation in econometrics. It is used to estimate the unknown parameters of a linear regression model. The OLS estimator minimizes the sum of squared residuals, which is the difference between the observed values and the predicted values of the dependent variable. The OLS estimator is unbiased and has minimum variance under certain assumptions.

2. Maximum Likelihood Estimation (MLE): MLE is a general method of estimation used to estimate the parameters of any statistical model, not just linear regression models. The MLE estimator is the value of the parameter that maximizes the likelihood function, which is a function of the data and the parameter. MLE is an efficient estimator that asymptotically achieves the minimum variance.

3. Generalized Method of Moments (GMM): GMM is a method of estimation that can be used when the assumptions of OLS and MLE are violated. GMM is a nonparametric method of estimation that does not require the specification of a complete statistical model. The GMM estimator is based on moment conditions, which are functions of the data and the parameter. The GMM estimator is consistent and efficient under certain assumptions.

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