1. Interpretation of marginal effects

I have a question to the interpretation of marginal effects in a certain paper, maybe someone is familiar

On p.2626 it is written: A decrease in DEratio of 0.244 from the mean of 0.561 increases the probability that an offer will be successful by 1%.

I know how to calculate marginal effects with Stata and how to get to the change in probability when the indep.var. deviates from its mean. However, I only know it if an indep. var. (e.g. DEratio) increases by 1 unit from the mean, not by 0.244 as in the example. So, I can say: A one-unit decrease in DEratio from the mean of 0.561 increases the takeover probability by X%. (The coeff of DEratio is not important here!)
However, this interpretation has its weaknesses because probit models sometimes only work well for small changes in the indep.variable.

Unfortunately, the paper does not explain how it computes the decrease of 0.244 from the mean of 0.561 which results in a 1%-increase of successful takeover completion.

Does somebody know how can compute the deviation of 0.244 for a 1%-increase in probability in Stata?

2. Re: Interpretation of marginal effects

Maastricht:

As you probably know, the marginal effect of the k-th variable for logit is given by

I'm not positive, but I think one way to get your result is to work backward. Suppose all covariates are set to their means (or some representative value), except the . Let

Now we are explicitly saying that there is some change in that leads to a .01 change in . Insert that result into the first equation and rearrange to get:

where I use overbars to denote means. Then use the inverse logit function to solve for

Again, I could be wrong, but this is how I would get that number. I don't think that Stata's margins command is capable of doing it. It would have to be done by hand or in another statistical package.

3. Re: Interpretation of marginal effects

Hello, thanks for your help, but I probably I will use a way to calculate it with Stata automatically

4. Re: Interpretation of marginal effects

Well, like I said, there's no Stata command that does what you're asking. Margins could calculate the marginal effect at a specified point, but not over an interval. Instead, you'd probably want to use nlcom after running the regression.

nlcom (invlogit(.01/_b[DE]) - xb)/_b[DE]

where xb would be your estimate . That would also give you delta method standard errors for the estimate.

5. Re: Interpretation of marginal effects

thanks, I actually I will do the probit model and just apply the margins at means and calculate the marg effect on probability after one-unit change in the indep.var., I know that probit is a non-linear model, but it is easier for me and I need to finish this work...
I am not familiar with this command -nlcom-

6. Re: Interpretation of marginal effects

- help nlcom - will tell you everything you need to know. It's just calculates a specified non-linear combination of the estimated paraemters and gives a delta-method standard error. Its cousin is - lincom - .

7. Re: Interpretation of marginal effects

thank you, but can you provide a brief example of nlcom, for instance for the -nlcom- command after this probit model:
probit takeovercompleted Sales1yrgr Liquidity DEratio MBratio PEratio

8. Re: Interpretation of marginal effects

I'll give a more abstract example using logit, since we already derived the result above. Probit is the same, just use the inverse standard normal, instead.

Suppose you want to estimate a logit model where y is a dichotomous outcome variable and x is a continuous explanatory variable. You would estimate

. logit y x

-logit- returns a vector of coefficient estimates e(b), which can be accessed by by _b[x] and _b[_cons]

Now, suppose you want to know the magnitude and direction by which you would need to change x (from its mean) in order to induce a .01 increase in the probability of observing y = 1. You would first find the mean of x:
. sum x, meanonly
. local xmean = r(mean)

And then you could issue the following command, which as I showed above is the the change in x from its mean required to induce a .01 change in the probability of y:

. nlcom (invlogit(.01/_b[x]) - xmean' - _b[_cons] )/_b[x]

Instead of the mean, you could use some other representative value.

9. Re: Interpretation of marginal effects

thanks a lot, it is working now.
However, I fitted a probit model before because I thought Stata11 knows invprobit as well. Stata11 only seems to know invlogit and not invprobit, but I guess this does not matter since the results are very similar. I also did not find -invprobit- under -ssc describe- . So I guess only -invlogit- is possible here.

probit takeovercompleted gindex
sum gindex, meanonly
local gindexmean = r(mean)

Output:
nlcom (invlogit(.01/_b[gindex]) - gindexmean' - _b[_cons] )/_b[gindex]

nlcom (invlogit(.01)/ -.0248432) - 8.841709 - .7122677 / -.0248432

_nl_1: (invlogit(.01)/ -.0248432) - 8.841709 - .7122677 / -.0248432

------------------------------------------------------------------------------
takeoverco~d | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
_nl_1 | -.3980415 . . . . .

Thus, gindex must decrease by -0.39 from the mean of 8.84 to induce a 1% increase in takeover likelihood!

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