I am studying GMM methods for two-pass regression (time series regression for beta estimation and then cross-sectional regression for lambda estimation). I get that we can use GMM for cross-sectional regression and derive the estimates & standard errors for lambdas and pricing errors. Also, GMM easily accounts for heteroskedasticity and autocorrelation in the error structure.
There are three confusing points:
- Heteroskedasticity and autocorrelation that GMM deals here are the ones for the time series error structure, not for the cross-sectional error (pricing error), right? (I think I get why autocorrelation matters more for asset pricing model estimation in this sense. It's because we are imposing assumption to the time series regression, where autocorrelation matters way more than heteroskedasticity (ofc, unless it is highly volatile), right?)
- So two-pass regression assumes nothing about the pricing error structure. That is, the second stage cross-sectional regression assumes nothing for its error structure because using estimated betas from the first stage implicitly assigns the time series error structure assumption, right?
- Could you give me an intuition for understanding the effect of "estimated regressor"?
