multinomial logistic - interpreting the economic effects

[Truong Quoc Phan]

Hello statalist
When I replicate this paper, "Corporate cash shortfalls and financing decisions.", I encounter the issue with the term "Economic Effect" of the multinomial logistics model.

Table 6, see the green highlight.

My question is:
1. What is the economic effect of logistics regression? Is the same as marginal effect?
2. How to get this in Stata? (I successfully got mlogit coefficients, but I got stuck with the economic effect that the authors show in the paper)

Thank you

[Carlo Lazzaro]

Truong:
why not emailing authors directly?

[Truong Quoc Phan]

Carlo Lazzaro : I did 3 weeks ago but still no reply from them

[Hong Il Yoo]

Truong Quoc Phan

(1) Sounds like this is the average marginal effect of changing the value of x from an initial level, which is its observed value minus one standard deviation, to a new level, which is its observed value plus one standard deviation. To evaluate this average marginal effect, you'll first have to calculate the standard deviation of x in the usual manner (e.g., -summarize-). Then, for each observation, you calculate the predicted probabilities at the two different levels of x, keeping other independent variables at their observed values, and take the difference between the two probabilities. The average marginal effect is the average of these differences.

(2) I'm not familiar enough with the -margins- command to tell whether one can use this command for (1). But I'm aware that if you're ready to apply some elbow grease, you'll be able to calculate this using -predictnl- and obtain relevant standard errors. For example, suppose that you're estimating a trinomial model with three outcomes Red, Blue, and Green (omitted category). Suppose further that your variable x has a standard deviation of 2 and you're interested in the "economic effect" of x on the probability of Red. Then, your command line will look something like:

predictnl MEx_coef = exp(xb(Red) + _b[Red:x] * 2) / (1 + exp(xb(Red) + _b[Red:x] * 2) + exp(xb(Blue) + _b[Blue:x] * 2)) - ///
                                  exp(xb(Red) - _b[Red:age] * 2) / (1 + exp(xb(Red) - _b[Red:x] * 2) + exp(xb(Blue) - _b[Blue:x] * 2)), se(MEx_SE)
summarize MEx_coef MEx_SE

[Truong Quoc Phan]

Hong Il Yoo : thank you so much