  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.
