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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?

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

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OLS is inappropriate for this data to begin with. Because you have several observations per subject, the observations weren't sampled independently. The standard approach to this is to use a mixed model, with per-subject random intercepts.

As for weighting, I don't know why you would want to weight subjects differently according to how consistently they were employed. Isn't investigating the effect of employment why you have employment as a predictor?

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  • $\begingroup$ With regards to weighting, I am interested not only how the current employment affects Y but also how considerations of the past influence Y. This is why I wanted to weight. $\endgroup$ – Rebecca Mar 26 '17 at 20:06
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    $\begingroup$ @Rebecca Then it seems like you should add lagged covariates (i.e., terms not only for current employment but for past employment). $\endgroup$ – Kodiologist Mar 26 '17 at 20:07
  • $\begingroup$ I think lags are not what I am looking for. In this example, lags would inform how the predicted Y is influenced by the individual's past status rather the times he has been in a particular status in the past. It is the latter that interests me. $\endgroup$ – Rebecca Mar 26 '17 at 20:11
  • $\begingroup$ @Rebecca How about a predictor that counts the number of times the subject has been employed in previous waves, then? $\endgroup$ – Kodiologist Mar 26 '17 at 20:17
  • $\begingroup$ Yes, I thought about that. But what I am not sure about is whether that is just an alternative way of predicting Y or the correct way. What I mean is: should I necessarily put that as a predictor in the regression, or could I just multiply after the betas as I mentioned above in my question. $\endgroup$ – Rebecca Mar 26 '17 at 20:22

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