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.