Usage of an estimated coefficient as a dependent variable

Two-step estimation with large panel data sets generally involves estimating vectors of individual-specific coefficients in a first-stage. In a second-stage estimation a vector of estimated coefficients is used as the dependent variable. Potential problems of heteroskedasticity in the second stage may be mitigated by weighting all independent observations by the inverse of the variance of the dependent variable, which is obtained from the first stage estimation. This approach needs to be modified if the dependent variable in the second stage is a non-linear function of the estimated coefficient.