I'm trying to get caught up in some notes, and the topic is pooled, cross-sectional data. If we have the regression: $$\log{wage_i}=\beta_0+\beta_1\text{married}_i+\delta_0\text{yr10}_i+\delta_1\text{married}_i\times \text{yr10}_i+\varepsilon_i$$ Where $\text{married}$ is a dummy variable which $=1$ if a person is married and $0$ if not, and $\text{yr10}$ is a dummy variable indicating whether the observation was recorded in the year 2010, as opposed to being recorded in the year 2000. There's a blank spot in the notes that I didn't get, and it asks: How do we interpret $\delta_1$?

I think it's correct to say that $\delta_1$ measures how the return on whether or not someones married has changed in the past $10$ years. Is that correct? Or am I wrong? I read a little bit in my textbook and I think that's what it's saying.

  • $\begingroup$ Nice question and nice answer from @scortchi. But why are some coefficients $\beta$ and some $\delta$? (Just curious). $\endgroup$
    – Peter Flom
    Dec 5 '12 at 11:50
  • $\begingroup$ @PeterFlom that is just the way my professor likes to distinguish between new variables that she is adding. We originally had a simple regression without the $yr10_i$ and the interaction term. Then just to make a clear distinction she added the $\delta$'s. $\endgroup$
    – Kyle
    Dec 5 '12 at 16:54
  • $\begingroup$ @PeterFlom Actually I didn't explain that very precisely. My professor adds the $\delta$'s depending on the topic. Here it happened to be panel cross sectional data and she used the $\delta$ for the year as a dummy variable (because it was either observed in 2000 or 2010. And anything associated with the $\delta$ she also uses $\delta$ as a coefficient. Not that this is the most important thing, I just wanted to be more correct. $\endgroup$
    – Kyle
    Dec 5 '12 at 17:11

You're correct & that's a nice way of putting it. Perhaps worth adding that it's a multiplicative return because the independent variable is log wage. If you want to convince yourself put some numbers into the equations.

More precisely $\mathrm{e}^{\delta_1}$ is the ratio of the factor by which changing year from 2000 to 2010 increases wage for married people to the factor by which changing year from 2000 to 2010 increases wage for unmarried people.

  • $\begingroup$ Yes I agree wih Peter +1 for the second sentence. $\endgroup$
    – Kyle
    Dec 5 '12 at 17:45
  • $\begingroup$ A little more precision would help this answer, because I'm sure you don't mean that either the wage or the log wage are multiplied by $\delta_1$! More subtly, it also is not the case that the wage is multiplied by $1 + \delta_1$. $\endgroup$
    – whuber
    Feb 26 '14 at 19:41

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