GMM Inference in Two-Pass Asset Pricing Regressions

Summary

The document raises questions about generalized method of moments (GMM) in two-pass asset pricing regressions. In the first pass, time-series regressions estimate asset betas; in the second, a cross-sectional regression uses those betas to estimate factor risk premiums, or lambdas, and pricing errors. The author asks which error structure GMM addresses and how to understand the impact of using estimated betas as regressors.

These are important inference issues because the second-stage explanatory variables are estimated rather than observed, and the uncertainty from the first stage can affect standard errors and pricing conclusions. The question also distinguishes dependence and changing variance in time-series residuals from the cross-sectional pricing errors. However, the document contains no answers or derivation, so it does not resolve whether particular assumptions hold or how a specific covariance estimator should be constructed. It serves as a conceptual prompt about joint estimation and inference, rather than a complete guide to GMM implementation.

Key ideas

• A two-pass asset pricing procedure first estimates betas from time-series regressions and then estimates risk premiums cross-sectionally.
• GMM can be used to estimate risk premiums and pricing errors while accounting for specified error dependence.
• Using estimated betas in the second pass introduces uncertainty that can affect inference.
• The document poses questions about error structures but provides no answers or estimator details.

Tags

# GMM methods for two-pass regression


# GMM methods for two-pass regression












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"?

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