Interpretation

[Koen Wolters]

Dear community,

I have a question regarding the interpretation of the size of a coefficient.
e.g. I have a variable in my data called Equity, it measures the ratio of equity/total assets.

The dependent variable in my data set is fragility which is also measured as a ratio.
The coefficient is for equity is -0.713 in one of the models and is statistically significant

So I conclude that a 1% increase in equity decreases fragility by 0.713%.

The standard deviation of equity is 6.1%.

Would it be correct to say that fragility decreasing by 0.713 is a relatively small change as the standard deviation of equity is 6.1%?

Kind regards,
Koen

[Phil Bromiley]

You'll increase your chances of a useful answer by following the FAQ on asking questions - provide Stata code in code delimiters, readable Stata output, and sample data using dataex. In your case, for example, you don't tell us what estimator gave you the coefficient or whether the ratios are percents or factions.

I will assume you did a simple regression and that both ratios are percents (it is often a good idea to have descriptive names - in a program with equity and assets, naming a variable Equity is just asking for misunderstanding. Often folks will also stay with all lowercase variable names - just so they don't have to remember what variables start with capital letters.)

Often, it is easiest to use the margins command to do predictions and then discuss those. After the regression, you might run margins, at(Equity=(0 1))

If both Equity and fragility are in percents and you've used simple regression, then your interpretation is of the .7% decrease is right. Whether a .7% is small or large depends on your view and the substantive context. It is over 10% of the standard deviation in y. Often, folks will use a one standard deviation change in x and relate the predicted change to the standard deviation in y. In your case, suppose the standard deviation in Equity is 10, then 1/10 of a standard deviation change in x changes predicted y by .7/6.1 of a standard deviation so a one standard deviation change in x would result in a 10*.7/6.1 change in predicted y, which is a large effect in almost any context.

[Eric de Souza]

Since both Equity and fragility are percentages, it would be: a one percentage point increase in Equity decreases fragility by 0.713 percentage points,
to the extent that one can give the relationship a causal interpretation

[Marcos Almeida]

You may wish to deal with - margins - plus elasticities. If so, please read this text.

[Koen Wolters]

Dear Phil,

I have a question, you said "In your case, suppose the standard deviation in Equity is 10, then 1/10 of a standard deviation change in x changes predicted y by .7/6.1 of a standard deviation so a one standard deviation change in x would result in a 10*.7/6.1 change in predicted y, which is a large effect in almost any context."

I am confused as to why you supposed the standard deviation in equity is 10, but then proceed to use 6.1 while calculating the predicted value of y.

Below I have added an example of my data

 sum Zinverse Equity ROAA

[CODE}


Variable | Obs Mean Std. Dev. Min Max
-------------+---------------------------------------------------------
fragility| 1,779 -14.97297 11.13423 -94.15739 14.32847
Equity | 1,782 9.765002 6.191295 -41.58431 85.37
ROAA | 1,779 1.338891 2.566942 -47.4304 21.79407

[/CODE]


-----------------------

* Example generated by -dataex-. To install: ssc install dataex
clear
input float(fragility Equity ROAA)
 -3.36828      6.67        .01
-6.397102  4.079976   8.606809
 -6.21302 10.270158  2.0515535
 -4.85535  8.771732   .8574384
 -5.12184    9.5092   .6484755
-4.385345  7.638911  1.0581414
-3.895388  6.924237   .8011279
-4.468364  7.237186  1.6245085
-3.979657  6.645245  1.2472435
-4.300331  6.962866  1.5655864
-5.303912  8.790968  1.7277932
 -5.78045   10.1922  1.2716347
-5.981434 10.605012  1.2574164
-6.170702 10.826555    1.41123
-5.343085  9.713322   .8831294
-8.363056  4.764364  .24567308
-6.816705  3.855009  .22865845
-8.564076  4.897561   .2329008
end

------------------

 xtreg fragility Equity ROAA, fe robut

             coefficient  stad err robust
equity      -.713    .120
ROAA      .108       .17

thank you all for the quick replies!