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I am trying to reproduce the result found in an old paper by Harvey S. Rosen, titled "Tax Illusion and the Labor Supply of Married Women Author", using a different dataset. The model that is estimated looks as follows:

$$ Hours_j = B_1 Wage_j - B_1 ρ(t_j Wage_j)+ ∑B_i X_{ij} +u_j$$

Where:

$Hours_j$ is the amount of hours worked of person $j$.

$Wage_j$ is the wage per hour of person $j$.

$ρ$ is a coefficient of tax perception (this coefficient can be calculated because of the constraint that the first two Betas to be equal).

$t_j$ is the marginal tax rate of person $j$

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The idea is that $Wage_j$ has a positive effect on hours worked, where $t_j Wage_j$ has a negative effect on the hours worked.

Problem

When trying to reproduce the result I often see that the signs switch on these two variables (while nevertheless being very significant).

I have the feeling that this has a lot to do with the fact that obviously one is a ratio of the other. Nevertheless, the GVIF of these variables is below 1.5.

Economically obviously switched signs do not make any sense at all. There is no sound reason for the wage having a negative effect and the tax having a positive (even when there would be a huge income effect, they should both be positive).

Could someone perhaps elaborate on why the signs might be switching. Obviously confounding factors are a possibility, but I did cover the variables used in the paper.

What I hope to achieve by this post is getting some fresh ideas to deal with this issue. So please feel free to comment even when you are not completely sure.

Tom
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  • "I often see that the signs switch" okay this happens when what? Are we talking different data sets or different control variables in the vector X? Is wage really defined as "the amount of hours worked of person j"? "one is a ratio of the other" ... yeah which one and what other? "Obviously confounding factors are a possibility, but I did cover the variables used in the paper." okay so maybe the theory is just wrong ... – Jesper for President Aug 25 '20 at 15:04
  • I corrected wage to: the wage per hour of person j. The sign switches for example dependent on the sample used. But also when instrumenting wage. Not so much depending on control variables. The theory might be imperfect, and theoretically yes it could be wrong. Nevertheless, that would be unlikely. – Tom Aug 25 '20 at 15:16
  • I am thinking this could be collinearity. Is there much variation in the marginal rates in your data? Or what is the correlation between $w$ and $t \cdot w$? – dimitriy Aug 25 '20 at 17:49
  • Thank you for your comment. There is indeed not a lot of variation in the marginal tax rates (about 3-4 levels for a year). This is why I checked the GVIF (and actually expected it to be large). I will provide more exact details on this in the morning. – Tom Aug 25 '20 at 18:00

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