# Imposing ex-post shares on linear regression estimates

Say I have a panel data model with several waves:

$Y= \beta_0 + \beta_1 * female + \beta_2 * employment + \beta_3 * wave + \epsilon$

where female is a dummy that takes 1 if $female$ and 0 otherwise and $employment$ is a dummy that takes 1 if employed and 0 otherwise.

I am using an OLS model to calculate the predicted values, which would be just $\hat{\beta_0}+\hat{\beta_1}*female + \hat{\beta_2}*employment + \hat{\beta_3}*wave$

However, I want to impose some ex-post gender-employment-time-specific shares (weights) : e.g. say I want to impose a particular share for males that have been employed in all waves (say .6) than for males that have been employed only half of the time (say .4). Similarly, for for females that have been employed in all waves (say .4) compared to those only in half of the waves (say .6).

Would it be correct to use this formula for the expectation?

$E(Y|X) = male_{times_{employed}} * (\beta_0 + \beta_1 * female + \beta_2 * employment + \beta_3 * wave) + female_{times_{employed}} * (\beta_0 + \beta_1 * female + \beta_2 * employment + \beta_3 * wave)$