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I'm trying to get caught up in some notes, and the topic is pooled cross sectional data. If we have the regression: $$lwage_i=\beta_0+\beta_1married_i+\delta_0yr10_i+\delta_1married_i\times yr10_i+\varepsilon_i$$ Where $lwage$ is the log wage, $married$ is a dummy variable which $=1$ if a person is married and $0$ if not, and $yr10$ 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.

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Nice question and nice answer from @scortchi. But why are some coefficients $\beta$ and some $\delta$? (Just curious). – Peter Flom Dec 5 '12 at 11:50
@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. – Kyle Dec 5 '12 at 16:54
@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. – Kyle Dec 5 '12 at 17:11

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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.

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Yes I agree wih Peter +1 for the second sentence. – Kyle Dec 5 '12 at 17:45

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