On the statistical properties of tests of parameter restrictions in beta-pricing models with a large number of assets

with Amedeo Andriollo and Giulio Rossetti, 2023, working paper.

[paper] We study the size and power properties of t-tests of parameter restrictions for newlydesigned
methods that aim at reliably estimating risk premia in linear asset pricing
models when the cross-sectional dimension is large. By simulating a variety of empirically
calibrated data generating processes for sample sizes that are typically encountered
in empirical work, we evaluate the finite-sample performance of the test
statistics for scenarios where the factor structure is (i) strong and pervasive; (ii) spurious;
(iii) weak/semi-strong and pervasive; (iv) weak/semi-strong and not pervasive;
and (v) sparse. PCA-based methods such as those of Lettau and Pelger (2020), Giglio
and Xiu (2021), and Giglio et al. (2022) work best when the factors are strong and pervasive,
and they continue to exhibit good finite-sample properties when the factors are
spurious. However, when the factor structure is semi-strong and pervasive, the splitsample
estimator of Anatolyev and Mikusheva (2021) performs substantially better
than the PCA-based estimators listed above. In the case of sparse loadings or when
the factors are semi-strong and not pervasive, none of the candidate methods displays
satisfactory finite-sample properties.