  This paper re-examines the problem of estimating risk premia in linear factor
pricing models. Typically, the data used in the empirical literature are
characterized by weakness of some pricing factors, strong cross-sectional
dependence in the errors, and (moderately) high cross-sectional dimensionality.
Using an asymptotic framework where the number of assets/portfolios grows with
the time span of the data while the risk exposures of weak factors are
local-to-zero, we show that the conventional two-pass estimation procedure
delivers inconsistent estimates of the risk premia. We propose a new estimation
procedure based on sample-splitting instrumental variables regression. The
proposed estimator of risk premia is robust to weak included factors and to the
presence of strong unaccounted cross-sectional error dependence. We derive the
many-asset weak factor asymptotic distribution of the proposed estimator, show
how to construct its standard errors, verify its performance in simulations,
and revisit some empirical studies.
