While there is an extensive literature concerning forecasting in a datarich environment, i.e. when the column dimension N of the input matrix X is large relative to T, there are but few attempts to allow for non-linearity in such cases. A non-linear extension, for example extending with X with X2, inflate the ratio N/T and requires specific econometric considerations. Using macroeconomic data, we show that accuracy gains are achieved by allowing for both squares and first level interactions of the original explanatory variables. When interactions are considered the ratio N/T is extremely high. We propose a modification to the two-stage “screen and clean” procedure which facilitates estimation. In the first stage, perform a set of univariate regression to screen for truly interesting effects, controlling the False Discovery Rate. In the second step, perform a standard bridge regression. Preliminary results suggest a substantial improvement over existing alternatives.