Is maximum likelihood suitable for factor models in large cross-sections of time series? We answer this question from both an asymptotic and an empirical perspective. We show that estimates of the common factors based on maximum likelihood are consistent for the size of the cross-section (n) and the sample size (T), going to infinity along any path, and that maximum likelihood is viable for n large. The estimator is robust to misspecification of cross-sectional and time series correlation of the idiosyncratic components. In practice, the estimator can be easily implemented using the Kalman smoother and the EM algorithm as in traditional factor analysis.

We compare sparse and dense representations of predictive models in macroeconomics, microeconomics, and finance. To deal with a large number of possible predictors, we specify a prior that allows for both variable selection and shrinkage. The posterior distribution does not typically concentrate on a single sparse model, but on a wide set of models that often include many predictors.

Vector autoregressions (VARs) are flexible time series models that can capture complex dynamic interrelationships among macroeconomic variables. However, their dense parameterization leads to unstable inference and inaccurate out-of-sample forecasts, particularly for models with many variables. A solution to this problem is to use informative priors in order to shrink the richly parameterized unrestricted model toward a parsimonious naıve benchmark, and thus reduce estimation uncertainty. This paper studies the optimal choice of the informativeness of these priors, which we treat as additional parameters, in the spirit of hierarchical modeling. This approach, theoretically grounded and easy to implement, greatly reduces the number and importance of subjective choices in the setting of the prior. Moreover, it performs very well in terms of both out-of-sample forecasting—as well as factor models—and accuracy in the estimation of impulse response functions.

This paper describes how we constructed a real-time database for the euro area. The database covers more than 200 series regularly published in the European Central Bank Monthly Bulletin, as made available to the Governing Council members for their first monthly meeting. We study the properties of the real-time data flow and data revisions in the euro area, also providing comparisons with the United States and Japan. We illustrate how revisions contribute to the uncertainty surrounding key macroeconomic ratios and the non-accelerating inflation rate of unemployment.

We study the conditional distribution of GDP growth as a function of economic and financial conditions. Deteriorating financial conditions are associated with an increase in the conditional volatility and a decline in the conditional mean of GDP growth, leading the lower quantiles of GDP growth to vary with financial conditions and the upper quantiles to be stable over time. Upside risks to GDP growth are low in most periods while downside risks increase as financial conditions become tighter. We argue that amplification mechanisms in the financial sector generate the observed growth vulnerability dynamics.