When to use Generalized Method of Moments (GMM)?
One should use Generalized Method of Moments (GMM) when:
1. Endogeneity is present
GMM is commonly used to address endogeneity, especially when:
- You have multiple endogenous variables
- You have valid instruments (like lagged variables or external instruments)
2. Model has more moment conditions than parameters
GMM allows estimation even when you have more instruments than endogenous variables (over-identified model), which is helpful for testing instrument validity.
3. Heteroskedasticity or autocorrelation is suspected
Unlike traditional methods (like 2SLS), GMM does not require homoskedastic or uncorrelated errors, making it robust under more flexible assumptions.
4. Panel data with dynamic models
For example, in the Arellano-Bond estimator, GMM is used in dynamic panel models where:
- The lagged dependent variable is a regressor
- Fixed effects and endogeneity need to be controlled
Typical use case:
You have panel data like:
y_it = α + β1*y_{it-1} + β2*x_{it} + u_it y_{it-1} is endogenous. GMM uses its past lags as instruments to consistently estimate β1.In summary:
| Use GMM When… | Why |
|---|---|
| Endogeneity | To get consistent estimates |
| You have valid instruments | GMM handles multiple instruments well |
| There’s heteroskedasticity/autocorrelation | GMM is robust to these |
| You use dynamic panel data | GMM is a go-to method (e.g., Arellano-Bond) |