• Effect estimation;
  • High-dimensional data;
  • Model selection;
  • Robustness

Summary  A problem encountered in some empirical research, e.g. growth empirics, is that the potential number of explanatory variables is large compared to the number of observations. This makes it infeasible to condition on all variables in order to determine whether a variable of interest has an effect. We assume that the effect is identified in a high-dimensional linear model specified by unconditional moment restrictions. We propose a new method that provides a consistent estimator of the effect when the variable of interest is conditional mean independent of excluded variables. Existing methods are consistent when excluded variables do not explain the outcome, but not under the conditional mean independence assumption. We also demonstrate that the new method has good properties in a Monte Carlo study.