Estimating linear trends over time with standardized outcome variables - what's the best method to normalize?

[Kate Schneider]

Hello,
This is really just a statistics question. I have a panel dataset over 20 years of 50 variables for every country in the world. We want to get a simple estimate of whether the linear trend over time is different from 0 so we are regressing the indicator on time with country fixed effects. But right now the indicators are all in different units. We want to standardize the outcome variables so my question is given that the application is regressing the result on time, when we calculate the standardized values (z-scores or min-max), should we be pooling the data for every indicator over all years or calculating for each year separately? And following that, is there any argument for why z-scores or min-max would be preferred or easier to interpret?

Thanks for your help!
-Kate

[George Ford]

I'd say separately by outcome, but it depends on what your question is. You can't do it by year, since there is no estimate in time for one year.

I think if you include a fixed effect (reghdfe) for country and outcome, you can get one t-stat and slope.

[Kate Schneider]

Thanks so much George, so you're saying normalize all the data per outcome? I want to run separate regressions by outcome so that i only have to deal with the coefficient on year and then we visualize as a coefficient plot.

Thanks so much for your help!!

[George Ford]

If you estimate in levels, then the coefficient will reflect differences in levels.

You could divide the outcomes by the first observation so that they all start at 1

by outcome: g y_1 = y / y[1]