Updating or estimating regional input–output tables is a challenging task addressed with non-survey methods. These can be classified into two groups: location quotient (LQ) methods and constrained matrix-balancing methods. This paper focuses on the second group and, specifically, on the performance of the cross-entropy method (CE). The most important finding is that the RAS method slightly outperforms the CE method on average, but its efficiency varies greatly from country to country. On the contrary, the performance of the CE method is more stable over countries and time. More interestingly, a fair implementation of the CE method boosted by the Flegg location quotient (FLQ) method outperforming the competing CE approach in terms of accuracy.

The recent availability of high frequency data has permitted more efficient ways of computing volatility. However, estimation of volatility from asset price observations is challenging because observed high frequency data are generally affected by noise-microstructure effects. We address this issue by using the Fourier estimator of instantaneous volatility introduced in Malliavin and Mancino 2002. We prove a central limit theorem for this estimator with optimal rate and asymptotic variance. An extensive simulation study shows the accuracy of the spot volatility estimates obtained using the Fourier estimator and its robustness even in the presence of different microstructure noise specifications. An empirical analysis on high frequency data (U.S. S&P500 and FIB 30 indices) illustrates how the Fourier spot volatility estimates can be successfully used to study intraday variations of volatility and to predict intraday Value at Risk.