Economists must often control for unobservable factors when estimating idiosyncratic equations using cross-section dependent panel data. Based on a factor structure of crosssection dependence, we suggest a new method for estimating idiosyncratic equations and demonstrate that the proposed method works under more general conditions than those required by existing idiosyncratic estimators, such as Pesaran's (2006) common correlated effects estimator and Baifs (2005) iterated principal component estimator. Via Monte-Carlo study the propoed estimation method is shown to work well in the finite sample. Applying the method to the Feldstein-Horioka puzzle, we find that the correlation between the log investment ratio and the log saving ratio is not significantly different from zero for a panel of 29 developed countries over the 1980 to 2004 period.