How to interpret an index of values between -2.5 and +2.5 (an independent variable) in a regression? I am in the proccess of writing my Master's Thesis and I'm performing a multivariate regression (OLS). One of my independent variables is Chinn-Ito Index (financial openness index) which takes values from -2.5 to +2.5.
The coefficient is .261. And the dependent variable is in log.
Normally, we would interpret this coefficient as:
-> one unit increase in Financial Openness Index increases the dependent variable by 26.1%.
I'm worried this interval (-2.5 and +2.5) might cause some extreme value in my coefficient as other control variables are in different units.
I am not sure what is 1 unit increase in this case?
Does this mean that an increase from, for instance, -2 to -1 increases the dependent variable by 26.1%? Seems kind of odd to me.
Should I maybe normalize the index somehow? I have seen a paper when they normalized this index between 0 and 1. If this is the solution, how to do it in Stata?
And if normalizing is appropriate in this case, how to interpret a coefficient?
Thank you in advance for taking the time to answer my questions.
Victoria
Edit:
I am trying to get some results on what explaines the crypto adoption.
Logcrypto is the log transformation of the crypto index, and the rest are independent variables.


Look at this post to see how to normalize between 0, 1 with Stata. And this post for the general idea.
The coefficient for f_opennavg is $-0.261$, so assuming your model looks like $log(y)=\beta_0 + \beta_1x + u$, the interpretation would be: "An increase in $x$ by one unit is associated with a change in $y$ by $100* \beta_1$% approximately, on average, all other things equal."
So when f_opennavg changes from $1$ to $2$, you would expect that this leads to a change of $-26.1$% in whatever is your $y$. Keep in mind that the model is linear which implies that a change from -2 to -1 has the same marginal effect as a change from -1 to 0 etc.
This is not neccessarily a reasonable assumption, i.e. in cases where you have "bunching" around -1 and 1 (or so) and few "extreme" observations at the top/bottom end of the scale (e.g. North Korea would be extremely "closed" and at the same time is very different to most other countries). You could try to use a dummy to differentiate "extreme" cases from others (or more technically speaking: to "control for the effect of extreme values in openness").
You could also use a GAM model (as described here) to see if the effect of f_opennavg on $y$ can be assumed to be linear. There seem to be GAM models for Stata as well.
When you change the scale of $x$ (e.g. by squeezing it into the interval 0,1), the OLS coefficient will be "scaled" as well (but will not change its fundamental meaning). So putting $x$ on a scale between 0 and 1 will not change the overall result.
Data:
  y  x
1 1  0
2 5  0
3 4  5
4 3  5
5 6  5
6 8 10

Regression:
Coefficients:
            Estimate Std. Error t value Pr(>|t|)
(Intercept)   2.5882     1.2255   2.112    0.102
x             0.4588     0.2269   2.022    0.113

Data with $x$ in range 0,1:
  y   x
1 1 0.0
2 5 0.0
3 4 0.5
4 3 0.5
5 6 0.5
6 8 1.0

Regression:
Coefficients:
            Estimate Std. Error t value Pr(>|t|)
(Intercept)    2.588      1.225   2.112    0.102
x              4.588      2.269   2.022    0.113

So the coefficient for $x$ is simply "sclaed" $\beta*10$ (the former max value in my data)
R-Code:
df = data.frame(y=c(1,5,4,3,6,8), x=c(0,0,5,5,5,10))

summary(lm(y~x,df))

xs = (df$x- min(df$x)) / (max(df$x)-min(df$x))
dfs = data.frame(y=df$y, x=xs)

summary(lm(y~x,dfs))

