Impact on probability of one standard deviation increase in predictor variables (Logit)

[Sofi Gomes]

Hello,

I am using the following code:

logit bnkr gndr nita tlta cntr, vce(cluster id)
margins, dydx (gndr nita tlta cntr) atmeans

In which, bnkr is a bankruptcy indicator which equals 1 for a bankruptcy and 0 otherwise and it is my dependent variable. My explanatory variables are gndr is a dummy for managers' gender which equals 1 when there is a female and 0 where there are only male; nita is net income/total assets; and tlta is total liabilities/total assets. And cntr represents country and is a control variable.
I do this study using panel data, of 40 periods for 13,000 companies (which is my id).

My problem is with interpretating the margins.
The output of the margins command is the following:

Expression : Pr(bnkr1), predict()
dy/dx w.r.t. : gndr nita tlta cntr
at : gndr = .0733237 (mean)
nita = -.0569804 (mean)
tlta = .5282768 (mean)
cntr = 1.795103 (mean)

	dy/dx	Delta-method Std. Error	z	P>|z|	[95% Confi	dence Interval]
gndr	0.0001926	0.0000743	2.59	0.010	0.0000469	0.0003382
nita	-3.43e-08	0.0000974	-0.00	1.000	-.000191	0.0001909
tlta	0.000701	0.0000899	7.80	0.000	0.0005249	0.0008772
cntr	0.0003884	0.0000885	4.39	0.000	0.0002149	0.000562

If I understand correctly, for instance, for the variable gndr, the interpretation of these results would be the following: "everything else constant, a firm with female managers is only 0.019 percentage points more likely to file for bankruptcy than a firm with only men in these positions". Is that correct?

But how can I make similar interpretations for continuous variables? And is there a way of doing so stating the impact on the bankruptcy probability of one standard deviation increase in the explanatory variables?
On this regard, I found someone mentioning that a possible interpretation could be "one standard deviation increase of the variable nita decreases the bankruptcy probability by 5.89e-07 %" (5.89e-09 = -3.43e-08 (dy/dx of nita) * 0.1718386 (std. deviation of nita displayed when doing - sum nita -). Is this correct? How would it go from "percentage points" in the interpretation of dummies to "percentage" in the interpretation of continuous variables?

Thank you in advance!

[Clyde Schechter]

My problem is with interpretating the margins.

No. You haven't even shown any margins here. The questions you ask about all concern marginal effects, not margins. I'm being pedantic, but unclear use of language leads to unclear thinking, which leads to bad analysis.

If I understand correctly, for instance, for the variable gndr, the interpretation of these results would be the following: "everything else constant, a firm with female managers is only 0.019 percentage points more likely to file for bankruptcy than a firm with only men in these positions". Is that correct?

Actually, it's not correct because you didn't use factor variable notation correctly. Because your -logit- command mentioned gndr without any prefix, and without including it in any interaction terms, Stata interprets gndr as a continuous variable and the -margins- command calculates the marginal effect as d(Prob(bankruptcy))/d gndr. So it is not the incremental change in probability associated with the higher value of the gender variable. It is probably fairly close, but unlikely the same. Even worse, I notice you have a variable cntr which, you state, gives the country. This should not be a continuous variable and even your -logit- regressions will be wrong unless, as it happens, the country variable is dichotomous and is coded with two consecutive integers. The code should be:

logit bnkr i.gndr nita tlta i.cntr, vce(cluster id)
margins, dydx (gndr nita tlta cntr) atmeans

When you do that, the i. prefix signals Stata that gndr and cntr are categorical variables, and so -margins- will correctly calculate the difference in outcome probability for them.

The continuous variables are handled correctly (although, if cntr signals more than just two countries, then the error in the specification of country means that everything in the -logit- output is wrong.) The meaning of a marginal effect is that it is the first derivative of outcome probability with respect to the predictor variable. So for tlta it is the rate of increase in the probability of bankruptcy per unit of increase in the total liabilities:total assets ratio. It is often said, as an abuse of language, that it is the change in bankruptcy probability associated with a 1 unit increase in the total liabilities:total assets ratio, but that is not strictly correct. That is like saying that you will travel 60 km in the next hour when what is really happening is that at this particular moment your speedometer reads 60 km/hr.

On this regard, I found someone mentioning that a possible interpretation could be "one standard deviation increase of the variable nita decreases the bankruptcy probability by 5.89e-07 %" (5.89e-09 = -3.43e-08 (dy/dx of nita) * 0.1718386 (std. deviation of nita displayed when doing - sum nita -). Is this correct?

Yes, it's technically correct. But why would you want to obfuscate your results in this way? Who on earth, besides you and the readers of this post, will ever know or understand what the standard deviation of nita in this study was? To an audience who has not worked through the analysis with you this statement is just bewildering and meaningless. It's accurate, but uninformative.

So just state the unvarnished truth: the rate of increase in the probability of bankruptcy per unit increase of tlta is 0.000701, or if you prefer to denominate it in percentage points, then say it is 0.0701 percentage points per unit increase of tlta. And it doesn't go from percentage points to percentage.

The other clarification I suggest you make in your language is to say explicitly "other variables held constant at their mean values" rather than just "everything else constant."

[Sofi Gomes]

Dear Clyde,

That was very helpful and answered all my questions and more!

I am very grateful to you!