Help with interpretation of margins

[Alina Faruk]

Dear All,

Will someone please kindly inform me if I am interpreting the following Average Adjusted Prediction (AAP) and Average Marginal Effect (AME) correctly? Most predicted probabalitly examples I found online are using the atmeans option.

use http://fmwww.bc.edu/RePEc/bocode/o/oaxaca.dta, clear

svyset [pw=wt]

gen lnwage2 = lnwage > 3 if lnwage < .

svy, subpop(lfp): probit lnwage2 c.age##c.age female educ exper tenure
margins, subpop(lfp)
margins, dydx(*) subpop(lfp)

Predictive margins Number of obs = 1,434
Subpop. no. obs = 1,434
Model VCE : Linearized

Expression : Pr(lnwage2), predict()

------------------------------------------------------------------------------
| Delta-method
| Margin Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
_cons | .8068882 .0100654 80.16 0.000 .7871603 .8266161
------------------------------------------------------------------------------


Interpretation: An average labor force participant has an 80.7% chance of earning a log hourly wage greater than 3.

Average marginal effects Number of obs = 1,434
Subpop. no. obs = 1,434
Model VCE : Linearized

Expression : Pr(lnwage2), predict()
dy/dx w.r.t. : age female educ exper tenure

------------------------------------------------------------------------------
| Delta-method
| dy/dx Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
age | .007352 .0014939 4.92 0.000 .004424 .01028
female | -.1404273 .0207117 -6.78 0.000 -.1810214 -.0998331
educ | .0380656 .0066568 5.72 0.000 .0250186 .0511126
exper | .0028385 .0016122 1.76 0.078 -.0003214 .0059983
tenure | .0021601 .0017968 1.20 0.229 -.0013616 .0056818
------------------------------------------------------------------------------
.
Interpretation: Being female reduces the average probability of having a log hourly wage greater than 3 by 14.0% compared to being male. A 1 year increase in age increase the average probability of lnwage2=1 by 0.7%.

Thank you in advance.

[Clyde Schechter]

I think you have the general idea, but some of your wording is incorrect.

Interpretation: An average labor force participant has an 80.7% chance of earning a log hourly wage greater than 3.

I think people will generally understand what you mean, but if you think about it, there probably is no such thing as an average labor force participant. What is actually being calculated is the average probability (or, if you prefer, chance) of a worker earning a log hourly wage > 3. So I would phrase this as: within subpopulation lfp, the expected probability of earning a log hourly wage > 3, adjusted for age, sex, education, experience, and tenure, is 80.7%

Interpretation: Being female reduces the average probability of having a log hourly wage greater than 3 by 14.0% compared to being male. A 1 year increase in age increase the average probability of lnwage2=1 by 0.7%.

There are two problems with this wording. First, you are using causal language, which is not justified unless you have external evidence that these effects are actually causal--which I doubt. Second, you are stating the unit of the marginal effect as percent, but the correct unit is percentage point, or in the case of the marginal effect of a continuous variable is percentage points per unit of the continuous variable. (Changes denominated in percent are multiplicative changes, by definition. But marginal effects, by definition, are additive changes and their unit is percentage points.) So I would rephrase this as: In subpopulation lfp, the average adjusted probability of having a log hourly wage > 3 is 14.0 percentage points lower among females than among males, and the average rate of decrease in this probability with increasing age is 0.7 percentage points per year.

[Alina Faruk]

I think you have the general idea, but some of your wording is incorrect.


I think people will generally understand what you mean, but if you think about it, there probably is no such thing as an average labor force participant. What is actually being calculated is the average probability (or, if you prefer, chance) of a worker earning a log hourly wage > 3. So I would phrase this as: within subpopulation lfp, the expected probability of earning a log hourly wage > 3, adjusted for age, sex, education, experience, and tenure, is 80.7%


There are two problems with this wording. First, you are using causal language, which is not justified unless you have external evidence that these effects are actually causal--which I doubt. Second, you are stating the unit of the marginal effect as percent, but the correct unit is percentage point, or in the case of the marginal effect of a continuous variable is percentage points per unit of the continuous variable. (Changes denominated in percent are multiplicative changes, by definition. But marginal effects, by definition, are additive changes and their unit is percentage points.) So I would rephrase this as: In subpopulation lfp, the average adjusted probability of having a log hourly wage > 3 is 14.0 percentage points lower among females than among males, and the average rate of decrease in this probability with increasing age is 0.7 percentage points per year.

Thank you very much. This was really helpful.