Search Results
Working Paper
Common Factors, Trends, and Cycles in Large Datasets
This paper considers a non-stationary dynamic factor model for large datasets to disentangle long-run from short-run co-movements. We first propose a new Quasi Maximum Likelihood estimator of the model based on the Kalman Smoother and the Expectation Maximisation algorithm. The asymptotic properties of the estimator are discussed. Then, we show how to separate trends and cycles in the factors by mean of eigenanalysis of the estimated non-stationary factors. Finally, we employ our methodology on a panel of US quarterly macroeconomic indicators to estimate aggregate real output, or Gross ...
Working Paper
Dynamic Factor Models, Cointegration, and Error Correction Mechanisms
The paper studies Non-Stationary Dynamic Factor Models such that: (1) the factors Ft are I(1) and singular, i.e. Ft has dimension r and is driven by a q-dimensional white noise, the common shocks, with q < r, and (2) the idiosyncratic components are I(1). We show that Ft is driven by r-c permanent shocks, where c is the cointegration rank of Ft, and q - (r - c) < c transitory shocks, thus the same result as in the non-singular case for the permanent shocks but not for the transitory shocks. Our main result is obtained by combining the classic Granger Representation Theorem with recent ...
Working Paper
Quasi Maximum Likelihood Estimation and Inference of Large Approximate Dynamic Factor Models via the EM algorithm
We study estimation of large Dynamic Factor models implemented through the Expectation Maximization (EM) algorithm, jointly with the Kalman smoother. We prove that as both n and T diverge to infinity: (i) the estimated loadings are sqrt{T}-consistent and asymptotically normal and equivalent to their Quasi Maximum Likelihood estimates; (ii) the estimated factors are sqrt{n}-consistent and asymptotically normal and equivalent to their Weighted Least Squares estimates. Moreover, the estimated loadings are asymptotically as efficient as those obtained by Principal Components analysis, while ...
Working Paper
Non-Stationary Dynamic Factor Models for Large Datasets
We study a Large-Dimensional Non-Stationary Dynamic Factor Model where (1) the factors Ft are I (1) and singular, that is Ft has dimension r and is driven by q dynamic shocks with q less than r, (2) the idiosyncratic components are either I (0) or I (1). Under these assumption the factors Ft are cointegrated and modeled by a singular Error Correction Model. We provide conditions for consistent estimation, as both the cross-sectional size n, and the time dimension T, go to infinity, of the factors, the loadings, the shocks, the ECM coefficients and therefore the Impulse Response Functions. ...
Working Paper
Measuring the Euro Area Output Gap
We measure the Euro Area (EA) output gap and potential output using a non-stationary dynamic factor model estimated on a large dataset of macroeconomic and financial variables. From 2012 to 2023, we estimate that the EA economy was tighter than the European Commission and the International Monetary Fund estimate, suggesting that the slow EA growth is the result of a potential output issue, not a business cycle issue. Moreover, we find that credit indicators are crucial for pinning down the output gap, as excluding them leads to estimating a lower output gap in periods of debt build-up and a ...
Discussion Paper
Do National Account Statistics Underestimate US Real Output Growth?
In this note, we introduce a new estimate of GDO obtained from a Non-Stationary Dynamic Factor model estimated on a large dataset of US macroeconomic indicators.
Discussion Paper
The Euro Area has a growth problem
The decomposition of GDP into potential output—the level of output consistent with current technologies and "normal" use of capital and labor—and the output gap—the percentage deviation of GDP from its potential—is a fundamental task for policymakers. Potential output tells us how fast an economy can grow in the long run; the output gap helps assess the cyclical position of the economy and, thus, potential inflationary pressures (Jarociński and Lenza, 2018).