A new selection method for high-dimensionial instrumental setting: application to the Growth Rate convergence hypothesis

TL;DR

This paper introduces LOLA, a novel variable selection method for high-dimensional instrumental variable models, demonstrating its effectiveness in empirically testing the growth rate convergence hypothesis.

Contribution

The paper presents LOLA, an automatic, threshold-based selection algorithm for high-dimensional instrumental variable models, with proven consistency and practical effectiveness.

Findings

LOLA performs well in simulations under sparsity.

LOLA effectively handles irrelevant instrumental variables.

Empirical analysis supports the convergence hypothesis.

Abstract

This paper investigates the problem of selecting variables in regression-type models for an "instrumental" setting. Our study is motivated by empirically verifying the conditional convergence hypothesis used in the economical literature concerning the growth rate. To avoid unnecessary discussion about the choice and the pertinence of instrumental variables, we embed the model in a very high dimensional setting. We propose a selection procedure with no optimization step called LOLA, for Learning Out of Leaders with Adaptation. LOLA is an auto-driven algorithm with two thresholding steps. The consistency of the procedure is proved under sparsity conditions and simulations are conducted to illustrate the practical good performances of LOLA. The behavior of the algorithm is studied when instrumental variables are artificially added without a priori significant connection to the model. Using our algorithm, we provide a solution for modeling the link between the growth rate and the initial level of the gross domestic product and empirically prove the convergence hypothesis.