It is a complete suite to estimate models based on moment conditions.
It includes the two step Generalized method of moments (GMM) of Hansen(1982), the iterated GMM and continuous updated estimator (CUE) of Hansen-Eaton-Yaron(1996) and several methods that belong to the Generalized Empirical Likelihood (GEL) family of estimators, as presented by Smith(1997), Kitamura(1997), Newey-Smith(2004) and Anatolyev(2005).
In a comment on a post earlier today, Stephen Gordon quite rightly questioned the use of GMM estimation with relatively small sample sizes.
Continuous updating gmm estimator
Is this enough for the asymptotics to "kick in" for GMM estimation of an Euler equation of the type I was considering?
My first reaction was: "let's just bootstrap this thing and find out." My second reaction was: "there has to be plenty of evidence out there already, so let's not re-invent the wheel." Indeed, this is the case. Tauchen considers sample sizes of 50 and 75 - much smaller than I was using.
Several studies have examined the performance of GMM in precisely the context that I was using it in my own example. Among his conclusions (p.397): So, where does that leave us?
Three relevant studies are those of Tauchen (1986), Kocherlakota (1990), and Hansen et al. I'm glad that I used the continuous-updating version of the GMM estimator in my illustration.
With T = 175, I'm in a somewhat better position than those considered in the simulation studies I've just cited.
However, the results should be treated very cautiously.
On the other hand, what are you going to do in practice?
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).