Summary. The paper develops a method for producing current quarter forecasts of gross domestic product growth with a (possibly large) range of available within-the-quarter monthly observations of economic indicators, such as employment and industrial production, and financial indicators, such as stock prices and interest rates. In light of existing evidence of time variation in the variances of shocks to gross domestic product, we consider versions of the model with both constant variances and stochastic volatility. We use Bayesian methods to estimate the model, to facilitate providing shrinkage on the (possibly large) set of model parameters and conveniently generate predictive densities. We provide results on the accuracy of nowcasts of realtime gross domestic product growth in the USA from 1985 through 2011. In terms of point forecasts, our proposal improves significantly on auto-regressive models and performs comparably with survey forecasts. In addition, it provides reliable density forecasts, for which the stochastic volatility specification is quite useful.