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This paper investigates the problem of selecting variables in regression-typemodels for an "instrumental" setting. Our study is motivated by empiricallyverifying the conditional convergence hypothesis used in the economicalliterature concerning the growth rate. To avoid unnecessary discussion aboutthe choice and the pertinence of instrumental variables, we embed the model ina very high dimensional setting. We propose a selection procedure with nooptimization step called LOLA, for Learning Out of Leaders with Adaptation.LOLA is an auto-driven algorithm with two thresholding steps. The consistencyof the procedure is proved under sparsity conditions and simulations areconducted to illustrate the practical good performances of LOLA. The behaviorof the algorithm is studied when instrumental variables are artificially addedwithout a priori significant connection to the model. Using our algorithm, weprovide a solution for modeling the link between the growth rate and theinitial level of the gross domestic product and empirically prove theconvergence hypothesis.

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