Demeaning and standardizing variables in panel regression

[Ama Perera]

Hello everyone,

I am analyzing a panel data set with 55 countries. 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 as below,

xtreg equity liquiditity $controls i.year, fe vce(robust) // (1st regression)

However, since the scales of the two variables are different, the coefficients are not naturally interpretable. I recently saw in a paper that demeaning and standardizing variables allows meaningful interpretation of the coefficients. To try this, I ran the following command which creates a new set of standardized variables with the prefix "c_".

by country: center equity liquiditity , standardize

reg c_equity c_liquidity $controls i.year, vce(robust) // (2nd regression)

My questions are;
01) Is it Ok to standardize only the dependent and independent variable? Do I need to standardize the control variables in my model when running the 2nd regression?
02) When running the regression with demeaned and standardized variables, is the code stated above correct; is it correct to use "reg" instead of "xtreg"?
03) Even though I did not standardize the control variables, the coefficients and the p values of those control variables in the 2nd regression are different from the 1st regression. Is that to be expected?

Any help is much appreciated. Thank you.

[Phil Bromiley]

You are making this much harder than it has to be. As has been discussed on this listserv, standardization is probably not a great idea when the variables have meaningful values or scales. Just because the scales of the right-hand side variables differ from the scale of the dependent variable is no problem. You still get results like a one unit increase in liquidity results in a x unit increase in predicted equity. This is completely understandable.

When you start standardizing, you lose this ease of interpretation. If you standardize everything across the entire sample, you can talk about one standard deviation increase in liquidity influencing an x standard deviation increase in the dependent variable, but no one really deals in standard deviations for such variables.

The problem becomes even more difficult if you standardize by country. Then, what a standard deviation means will vary across each panel. This becomes incredibly difficult to understand. Since your rescaling with different weights for each panel, this probably will also change your statistical significance and could even change parameter signs. Your standardization by country will automatically be changing the weights placed on the different countries and any change weights will change parameters and significance.

I don't think standardization by panel is a good way to estimate a fixed effects estimator. While you can estimate a fixed effects estimator by subtracting the panel means, you would have to do this for all the variables not just the ones you care about, but this does nothing except make your life more difficult. xtreg is much much easier. You have rescaled some of the variables but not others and you switched from a panel estimator to a non-panel estimator, so it is not surprising that you're getting different parameters.

While in simple regression if you standardize everything, the statistical significance levels shouldn't change, I don't think it a lot of that interpretation transfers directly into a panel estimator and certainly not if you're standardizing by panel.

[Ama Perera]

Phil Bromiley , Thanks a lot for your helpful comments. I understand that standardizing is less preferable to using xtreg with fe. But the issue is with the interpretation. For instance, if the dependent variable is firm competition, a one unit increase in liquidity results in a 0.2 increase in firm competition doesn't make sense. In that situation, I think Interpreting in terms of standard deviation will make more sense. I hope to do the standardization only as a robustness test. My main analysis is based on the results from xtreg.