  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.
