The traditional Vector Autoregression (VAR) method is widely used to trace out the effects of monetary policy innovations on the economy. However, this method suffers from the curse of dimensionality, so that in practice VARs are estimated on a limited number of variables, leading to a potential missing information problem. In this article we use the method of structural factor analysis to evaluate the effects of monetary policy on key macroeconomic variables in a data rich environment. This methodology allows us to extract information on monetary policy and its impact on the economy from a much larger data set than is possible with the traditional VAR method. We propose two structural factor models. One is the Structural Factor Augmented Vector Autoregressive (SFAVAR) model and the other is the Structural Factor Vector Autoregressive (SFVAR) model. Compared to the traditional VAR, both models incorporate information from hundreds of data series, series that can be and are monitored by the central bank in setting policy. Moreover, the factors used are structurally meaningful, a feature that adds to the understanding of the ‘black box’ of the monetary transmission mechanism. Both models generate qualitatively reasonable impulse response functions. For the SFVAR model, both the price puzzle and the liquidity puzzle are eliminated.