  We study a linear random coefficient model where slope parameters may be
correlated with some continuous covariates. Such a model specification may
occur in empirical research, for instance, when quantifying the effect of a
continuous treatment observed at two time periods. We show one can carry
identification and estimation without instruments. We propose a semiparametric
estimator of average partial effects and of average treatment effects on the
treated. We showcase the small sample properties of our estimator in an
extensive simulation study. Among other things, we reveal that it compares
favorably with a control function estimator. We conclude with an application to
the effect of malaria eradication on economic development in Colombia.
