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 derive the convergence rate of its mean-integrated squared error 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 estimate the real-time price elasticity of supply on the Australian electricity spot market. Our estimates suggest that the supply is relatively inelastic and that its elasticity is heterogeneous throughout the day.