Cons
less parametric than maximum likelihood which requires assumptions about the moment condition than distributions.
What is moment condition
Method of moments estimator
OLS and Maximum likelihood estimator can both be motivated as a special case of a MM estimator
Source of moment conditions
- (Number of moment conditions must equal the number of parameters)
- Economic model (demand and supply first-order condition)
- instrument
- model fit (predicted result equal realized result)
- statistical assumptions
When L moments > K parameters:
we will seek to simultaneously get as close as possible to solving all L sample moments
Optimal GMM estimator
The choice of weighting matrix can influence the variance of the estimator:
Logit model with GMM
Moment conditions:
