  We consider continuous-time models with a large panel of moment conditions,
where the structural parameter depends on a set of characteristics, whose
effects are of interest. The leading example is the linear factor model in
financial economics where factor betas depend on observed characteristics such
as firm specific instruments and macroeconomic variables, and their effects
pick up long-run time-varying beta fluctuations. We specify the factor betas as
the sum of characteristic effects and an orthogonal idiosyncratic parameter
that captures high-frequency movements. It is often the case that researchers
do not know whether or not the latter exists, or its strengths, and thus the
inference about the characteristic effects should be valid uniformly over a
broad class of data generating processes for idiosyncratic parameters. We
construct our estimation and inference in a two-step continuous-time GMM
framework. It is found that the limiting distribution of the estimated
characteristic effects has a discontinuity when the variance of the
idiosyncratic parameter is near the boundary (zero), which makes the usual
"plug-in" method using the estimated asymptotic variance only valid pointwise
and may produce either over- or under- coveraging probabilities. We show that
the uniformity can be achieved by cross-sectional bootstrap. Our procedure
allows both known and estimated factors, and also features a bias correction
for the effect of estimating unknown factors.
