ECONOMICS SEMINAR SERIES (ESS) - 2025/2026

Speaker: Anna Simoni (ENSAE and Ecole Polytechnique)

Title: Impulse Response Function with functional approaches and mixed-frequency data

Abstract:  Prediction and causal models often involve economic time series sampled at different frequencies. In this paper, we propose a continuous-time Impulse Response Function (IRF) designed to measure the impact of a high-frequency input signal on a low-frequency target variable. We express this impact as the convolution of the continuous-time IRF and the input signal. Our approach is particularly suited to scenarios with large gaps in sampling frequencies, such as daily and quarterly data. Such gaps commonly arise when combining series from standard and non-standard sources, like the internet or newspapers. Unlike the local projections approach – which requires estimating a regression model for each forecast horizon – our method constructs the entire IRF in a single step. The estimation problem falls within the class of ill-posed inverse problems, and we address this challenge using a penalized least squares estimator with a Sobolev norm penalty. We establish the consistency of our estimator and derive its rate of convergence as the number of observations T grows to infinity. A Monte Carlo study demonstrates the excellent performance of our approach in finite samples. Finally, we apply our method to estimate the IRFs of quarterly business investment in equipment for the U.S. economy for high-frequency uncertainty shocks.