Maximum likelihood estimation (MLE)

You must know this. It's a ubiquitous workhorse in statistics.

If you can specify the likelihood function then parameters of the likelihood function can be estimated by maximizing the likelihood function. In certain special cases, (eg. linear regression with conditionally normal error terms) the OLS estimator is the MLE estimator. You've undoubtedly encountered MLE estimation before if you've estimated a logit model.

There are issues with applying MLE to economic models though. Often we know that an overall model is wrong and doesn't match the data, but we'd still like to test particular predictions.

GMM is another broad method for estimating parameters based upon moment conditions. Hayashi's book Econometrics develops ordinary least squares regression, instrumental variables, maximum likelihood, and other methods as special cases of GMM with different moment conditions.

A John Cochrane ode to GMM is here.

Matching methods for estimating causal effects are common in certain areas of economics.

The idea is to match a treated entity with an untreated entity based upon observable characteristics. A widely used technique for example is propensity score matching

Broader classes of linear methods (shrinkage estimators):

The idea here is to start with ordinary least squares but then to bias coefficient estimates towards zero to reduce overfitting and improve out of sample prediction.

• Ridge regression
• Lasso

Maximum likelihood estimation (MLE)

You must know this if you continue doing statistics. It's a ubiquitous workhorse.

If you can specify the likelihood function then parameters of the likelihood function can be estimated by maximizing the likelihood function. In certain special cases, (eg. linear regression with conditionally normal error terms) the OLS estimator is the MLE estimator. You've undoubtedly encountered MLE estimation before if you've estimated a logit model. MLE is all over physics, engineering, and the sciences.

There are issues with applying MLE to economic models though. Often we know that an overall economic model is false. A model will imply certain facts that are entirely fallacious. Forcing the model to match the data in a maximum likelihood sense may not induce a useful choice of parameters. GMM can be used as an alternative approach to selectively test certain predictions of a model.

GMM is another broad method for estimating parameters based upon moment conditions that in expectation should be zero. Hayashi's book Econometrics develops ordinary least squares regression, instrumental variables, maximum likelihood, and other methods as special cases of GMM with different moment conditions. OLS can be thought of as GMM using the orthogonality condition of the regressors and the error terms. MLE can be derived as GMM on the score.

A John Cochrane ode to GMM is here.

Matching methods for estimating causal effects are common in certain areas of economics.

The idea is to match a treated entity with an untreated entity based upon observable characteristics. A widely used technique for example is propensity score matching

There are all kinds of variations on classic linear methods:

The idea here is to start with ordinary least squares but then to bias coefficient estimates towards zero to reduce overfitting and improve out of sample prediction.

• Ridge regression
• Lasso