Two-step estimation in linear regressions with adaptive learning

Weak consistency and asymptotic normality of the ordinary least-squares estimator in a linear regression with adaptive learning is derived when the crucial, so-called, gain' parameter is estimated in a first step by nonlinear least squares from an auxiliary model. The singular limiting distribution of the two-step estimator is normal and in general affected by the sampling uncertainty from the first step. However, this generated-regressor’ issue disappears for certain parameter combinations.