Factor Models for Non-Stationary Series: Estimates of Monthly U.S. GDP

This paper presents a novel dynamic factor model for non-stationary data. We begin by constructing a simple dynamic stochastic general equilibrium growth model and show that we can represent and estimate the model using a simple linear-Gaussian (Kalman) filter. Crucially, consistent estimation does not require differencing the data despite it being cointegrated of order 1. We then apply our approach to a mixed frequency model which we use to estimate monthly U.S. GDP from May 1969 to January 2017 using 171 series with an emphasis on housing related data. We suggest our estimates may, at a quarterly rate, in fact be more accurate than measurement error prone observations. Finally, we use our model to construct pseudo real-time GDP nowcasts over the 2007 to 2009 financial crisis. This last exercise shows that a GDP index, as opposed to real time estimates of GDP itself, may be more helpful in highlighting changes in the state of the macroeconomy.