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The Fama-Macbeth regression is a method used to estimate parameters for asset pricing models such as the Capital asset pricing model (CAPM). The method estimates the betas and risk premia for any risk factors that are expected to determine asset prices. The method works with multiple assets across time (panel data). The parameters are estimated in two steps:
1.First regress each asset against the proposed risk factors to determine that asset's beta for that risk factor.
2.Then regress all asset returns for a fixed time period against the estimated betas to determine the risk premium for each factor.
Eugene F. Fama and James D. MacBeth (1973) demonstrated that the residuals of risk-return regressions and the observed "fair game" properties of the coefficients are consistent with an "efficient capital market" (quotes in the original).

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