High-Dimensional Mixed-Frequency IV Regression

Abstract

This paper introduces a high-dimensional linear IV regression for the data sampled at mixed frequencies. We show that the high-dimensional slope parameter of a high-frequency covariate can be identified and accurately estimated leveraging on a low-frequency instrumental variable. The distinguishing feature of the model is that it allows handing high-dimensional datasets without imposing the approximate sparsity restrictions. We propose a Tikhonov-regularized estimator and study its large sample properties for time series data. The estimator has a closed-form expression that is easy to compute and demonstrates excellent performance in our Monte Carlo experiments. We also provide the confidence bands and incorporate the exogenous covariates via the double/debiased machine learning approach. In our empirical illustration, we estimate the real-time price elasticity of supply on the Australian electricity spot market. Our estimates suggest that the supply is relatively inelastic throughout the day.

Keywords: Tikhonov regularization, real-time price elasticity, electricity supply, confidence bands, double/debiased machine learning

JEL Classification: C14, C22, C26, C58