Choosing the optimal set of instruments from large instrument sets

It is well known that instrumental variables (IV) estimation is sensitive to the choice of instruments both in small samples and asymptotically. Recently, a simple method has been suggested in the literature for choosing the instrument set. The method involves minimising the approximate mean square error (MSE) of a given IV estimator where the MSE is obtained using refined asymptotic theory. An issue with this method is the fact that when considering large sets of valid instruments, it is not clear how to order the instruments in order to choose which ones ought to be included in the estimation. A possible solution to the problem using nonstandard optimisation algorithms is provided. The properties of the algorithms are discussed. A Monte Carlo study illustrates the potential of the new method.