Confidence intervals in regressions with estimated factors and idiosyncratic components

- Recent models use both the factors and idiosyncratic components estimated from a big dataset.
- We derive the distribution of the OLS estimates of these model parameters.
- HAC standard errors must be adjusted to allow for the factor and idiosyncratic estimation error.
- This is in contrast to existing results in the literature where estimation error vanishes when T∕N→0.

This paper shows that HAC standard errors must be adjusted when constructing confidence intervals in regressions involving both the factors and idiosyncratic components estimated from a big dataset. This result is in contrast to the seminal result of Bai and Ng (2006) where the assumption that T∕N→0 is sufficient to eliminate the effect of estimation error, where T and N are the time-series and cross-sectional dimensions. Simulations show vast improvements in the coverage rates of the adjusted confidence intervals over the unadjusted ones.