## Wednesday, May 1, 2013

### Finite Sample Properties of GMM

In a comment on a post earlier today,  Stephen Gordon quite rightly questioned the use of GMM estimation with relatively small sample sizes. The GMM estimator is weakly consistent, the "t-test" statistics associated with the estimated parameters are asymptotically standard normal, and the J-test statistic is asymptotically chi-square distributed under the null. But what can be said in finite samples?

Of course, this question applies to almost all of the estimators that we use in practice - IV, MLE, GMM, etc. Indeed, lots of work has been done to explore the finite-sample properties of such estimators. For instance, consider my own work on bias corrections for MLEs (see here, here, and here). So, I'm more than sympathetic to the general point that Stephen made.

### Estimating an Euler Equation Using GMM

In one of my grad. econometrics courses we cover Generalized Method of Moments (GMM) estimation. I thought that some readers might be interested in the material that I use for one of the associated lab. classes.

The lab. exercise involves estimating the Euler equation associated with the "Consumption-Based Asset-Pricing Model" (e.g., Campbell, 1993, 1996.) This is a great example for illustrating GMM estimation, because the Euler equation is a natural "moment equation".

The basic statement of the problem is given below, taken from the handout that accompanies the lab. class exercises: