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I am using a fixed effects model with household fixed effects. I just added a year dummy for year fixed effects. Here below is the Stata result screenshot from running the regression. In the regression results table, should I report R-squared as 0.2030 (within) or 0.0368 (overall)?

Thanks!

enter image description here

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All three of these values provide some insight into your model, so you may need to report all three, but the within value is typically of main interest, as fixed-effects is known as the within estimator. At least in Stata, it comes from OLS-estimated mean-deviated model:

$$ \left ( y_{it} - \bar{y_{i}} \right ) = \left ( x_{it} - \bar{x_{i}} \right )\boldsymbol{\beta } + \left ( \epsilon _{it} - \bar{\epsilon _{i}} \right ) $$

The definition of each of R-squared value is below:

  • Within: How much of the variation in the dependent variable within household units is captured by your model (i.e., how well do your explanatory variables account for changes in DV within each of the households over time). As I said above, in Stata it comes from the OLS-estimated mean-deviated model and is calculated as squared correlation between actual and predicted values of DV (which, in OLS case, is equal to the the ratio of their variances - the formal definition of R-squared).
  • Between: How much of the variation in the dependent variable between household units is captured by your model (i.e., how well do your explanatory variables account for differences in DV between households).
  • Overall: weighted average of the two

More detailed information (calculation of each one) can be obtained from the Stata manual: https://www.stata.com/manuals13/xtxtreg.pdf

Also, if you don't already know, if you are using xtreg, fe for your estimation, the within R-squared is obtained in a manner that assumes that groups (households, in your case) are fixed quantities, so their effects are removed from the model. There is also areg procedure that estimates coefficients for each dummy variable for your groups. More information can be found at:

https://www.stata.com/support/faqs/statistics/areg-versus-xtreg-fe

https://kb.iu.edu/auur

https://dss.princeton.edu/training/Panel101.pdf

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    $\begingroup$ Very helpful (+1). The latest version of the Stata manual entry (version 15 at the time of writing) is stata.com/manuals/xtxtreg.pdf It seems to be an artefact of Google that Stata 13 manual entries are often suggested in a search. I doubt that there is any substantial difference in this case. $\endgroup$
    – Nick Cox
    Apr 5, 2019 at 9:10

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