The main contribution of this paper is to propose and theoretically justify bootstrap methods for regressions where some of the regressors are factors estimated from a large panel of data. We derive our results under the assumption that √T/N→c, where 0≤c<∞ (N and T are the cross-sectional and the time series dimensions, respectively), thus allowing for the possibility that factors estimation error enters the limiting distribution of the OLS estimator. We consider general residual-based bootstrap methods and provide a set of high level conditions on the bootstrap residuals and on the idiosyncratic errors such that the bootstrap distribution of the OLS estimator is consistent. We subsequently verify these conditions for a simple wild bootstrap residual-based procedure.Our main results can be summarized as follows. When c=0, as in Bai and Ng (2006), the crucial condition for bootstrap validity is the ability of the bootstrap regression scores to mimic the serial dependence of the original regression scores. Mimicking the cross sectional and/or serial dependence of the idiosyncratic errors in the panel factor model is asymptotically irrelevant in this case since the limiting distribution of the original OLS estimator does not depend on these dependencies. Instead, when c>0, a two-step residual-based...</∞>

In this paper we give a brief survey of penalized spline smoothing. Penalized spline smoothing is a general non-parametric estimation technique which allows to fit smooth but else unspecified functions to empirical data. While penalized spline regressions are quite popular in natural sciences...

What is considered to be fair depends on context. Using a modified version of the Ultimatum Game, we demonstrate that both fair behavior and perceptions of fairness depend upon beliefs about what one ought to do in a situation - that is, upon normative expectations. We manipulate such...