  This paper presents a new approach for the estimation and inference of the
regression parameters in a panel data model with interactive fixed effects. It
relies on the assumption that the factor loadings can be expressed as an
unknown smooth function of the time average of covariates plus an idiosyncratic
error term. Compared to existing approaches, our estimator has a simple partial
least squares form and does neither require iterative procedures nor the
previous estimation of factors.
  We derive its asymptotic properties by finding out that the limiting
distribution has a discontinuity, depending on the explanatory power of our
basis functions which is expressed by the variance of the error of the factor
loadings. As a result, the usual ``plug-in" methods based on estimates of the
asymptotic covariance are only valid pointwise and may produce either over- or
under-coverage probabilities. We show that uniformly valid inference can be
achieved by using the cross-sectional bootstrap. A Monte Carlo study indicates
good performance in terms of mean squared error. We apply our methodology to
analyze the determinants of growth rates in OECD countries.
