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I am analyzing a panel data set with 55 countries. The coefficient of my variable of interest is not naturally interpretable. Hence, I thought of demeaning and standardizing my dependent and independent variable.

My questions are: 1) Is it okay to standardize only the dependent and independent variable? Do I need to standardize the control variables in my model when running the regression? 2) When running the regression with demeaned and standardized variables, is it correct to use "reg" instead of "xtreg" in Stata?

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  • $\begingroup$ Welcome. What do you mean by it’s not naturally interpretable? Do you want to conduct a fixed effects regression? If you’re using xtreg, then you’re demeaning your data. $\endgroup$
    – Thomas Bilach
    Commented Apr 29, 2020 at 2:59
  • $\begingroup$ Hi Thomas, thanks for the reply. My dependent variable is firm equity issuance (aggregated at the country level) and my independent variable is aggregate stock market liquidity. I initially ran a panel regression with fixed effects (xtreg), but since the scales of the two variables are different, the coefficients are not directly interpretable. I recently saw in a paper that demeaning and standardizing variables allows meaningful interpretation of the coefficients, that's why I used the demeaning approach. $\endgroup$
    – Ama Perera
    Commented Apr 29, 2020 at 4:36
  • $\begingroup$ To get interpretable coefficients, maybe taking the log of the dependent and main independent variable would be enough? $\endgroup$
    – Alexandre C-L
    Commented Apr 29, 2020 at 9:59
  • $\begingroup$ Be careful when demeaning yourself. Save a mistake from me, xtreg demeans, but il also applies necessary corrections to the standard errors. $\endgroup$
    – Alexandre C-L
    Commented Apr 29, 2020 at 10:01
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    $\begingroup$ Just to be clear, there is no requirement in a regression context that the units of your independent variable correspond to the units of your dependent variable. Is it that your interpretation of the relevant variables in their 'level form' doesn't make sense, or is awkward? $\endgroup$
    – Thomas Bilach
    Commented Apr 29, 2020 at 21:57

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I am not a proponent of standardizing coefficients in panel data contexts. But, hopefully others will offer their input.

Is it okay to standardize only the dependent and independent variable?

You can, but what is your justification for doing this? For instance, you already noted that you intend to demean your data. By construction, you are restricting attention to "within-country" effects. Standardizing your coefficients (i.e., calculating $\beta$ coefficients) after the "within transformation" would inevitably be a "pooled" standard deviation that incorporates cross-country information.

In other words, you begin with a fixed effects estimation strategy to center each country around a "within-country" time average, but then you use the entire panel to standardize your coefficients. It seems paradoxical.

  1. When running the regression with demeaned and standardized variables, is it correct to use "reg" instead of "xtreg" in Stata?

I am unaware of any built-in Stata commands to standardize your demeaned data within each panel unit. In my opinion, you must be very clear about what variation you are using to identify your effects. In your case, one transformation uses within-country variation, while the other invariably uses between-country variation. It is unclear what variation will dominate in your regression.

Consistent with Alex's comments, I would investigate the interpretive value of a log-log model. Proportional percentage changes might ease the interpretability of the model coefficients.

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