Stata provides an average marginal effect of 0.1 for South (region = 3) vs Northeast (region = 1). Does this mean that the difference between the predicted probability of the outcome is 0.1 percentage points when assuming everyone has a value of region = 3 vs region = 1 (holding age category at its observed value)?
Yes. More precisely, it gives the average of each individual difference, since the effect varies with the age category.
Stata provides an average marginal effect is 0.5. Does this mean that the change in predicted probability of the outcome is 0.5 percentage points for all possible one-unit increments in agecategory: 2 vs 1, 3 vs 2, 4 vs 3, 5 vs 4?
No. The effect of the variable on the probability is not assumed to be linear in a logit. It will vary across observation with the value of the age category and of the other variable.
It calculates the average marginal effect, that is, the average change in the probability among all observation in the sample.
If you want to look at how this predicted effect changes at different values of the agecategory, you can use the at option of the margin command.
My hunch would be - without having checked Wooldridge - that he refers to a situation in which there also are individual (country, in your example)-specific effects next to the time effects.
I ran
library(plm)
plm(y ~ x1 + country_age, data = Panel, effect = "twoways", model = "within")
plm(y ~ x1 + country_age, data = Panel, effect = "time", model = "within")
on your first set of data, and do get a coefficient on country_age in the latter case, but not in the former.
> plm(y ~ x1 + country_age, data = Panel, effect = "twoways", model = "within")
Model Formula: y ~ x1 + country_age
Coefficients:
x1
2409669178
> plm(y ~ x1 + country_age, data = Panel, effect = "time", model = "within")
Model Formula: y ~ x1 + country_age
Coefficients:
x1 country_age
2409669178 91766658
Notice that including an individual-specific fixed effect amounts to unitwise demeaning of all regressors (see e.g. here). If the changes of one regressor are constant over time across units, the demeaned variable will be collinear with the unitwise demeaned time effects.
Consider the following artificial regressor matrix of a panel data model with both individual-specific effects (the first two columns, i.e. two "countries"), the time effects (3rd to 6th column) and the constant-changes regressors with different starting points (7th column).
We observe that the regressor matrix has rank 5, so that even with different starting points, the time effects and the constant change regressor are collinear (one rank is lost due to collinearity of individual and time effects, which is why Wooldridge already drops the time dummy for the first year). Equivalently, even with different starting points and dropping column 3, we can combine columns 1, 2, 4, 5 and 6 into column 7 via
$$6\times x_1+7\times x_2+2\times x_4 +2\times x_5+2\times x_6.$$
X <- matrix(c(rep(1,4), rep(0,4), rep(0,4), rep(1,4), # dummies for the units
rep(c(1,0,0,0),2), rep(c(0,1,0,0),2), rep(c(0,0,1,0),2), rep(c(0,0,0,1),2), # dummies for the time points
seq(6, by=2, length.out=4), seq(7, by=2, length.out=4)), ncol=7) # constant-increase regressor
X
[,1] [,2] [,3] [,4] [,5] [,6] [,7]
[1,] 1 0 1 0 0 0 6
[2,] 1 0 0 1 0 0 8
[3,] 1 0 0 0 1 0 10
[4,] 1 0 0 0 0 1 12
[5,] 0 1 1 0 0 0 7
[6,] 0 1 0 1 0 0 9
[7,] 0 1 0 0 1 0 11
[8,] 0 1 0 0 0 1 13
> qr(X)$rank
[1] 5
This also shows why time effects and same starting points (modify the last four elements of the last column to 6, 8, 10, 12 to try) cannot both be estimated even without individual-specific effects: just as individual-specific effects do not go together with time-invariant regressors, regressors require variation across units when being fitted next to time effects.
Now, with the same starting point and the same increases, the regressor takes the same value across units for each point in time and hence gets dropped when fitting time effects:
> lm(y~X[,3:7]-1)
Call:
lm(formula = y ~ X[, 3:7] - 1)
Coefficients:
X[, 3:7]1 X[, 3:7]2 X[, 3:7]3 X[, 3:7]4 X[, 3:7]5
-1.16909 -0.51927 0.02666 0.41310 NA
Equivalently, columns 3 to 6 alone can then be linearly combined into column 7.
Best Answer
Coefficients in fixed effects models are interpreted in the same way as in ordinary least squares regressions. For the categorical variables,
i.mar_statgenerates dummies for the observed marital status and Stata omits one of these dummies which will be your base/reference category. In this case this reference group are people who are never married. So a coefficient of 0.2599 means that divorced individuals have 0.2599 "more health" (the exact interpretation depends on how this health status is measured) compared to those who were never married. However, when you look at the p-value of this coefficient you will notice that it is not significant. For this reason you can't say that divorced individuals have a better health status than those who were never married because your test rejects the hypothesis that 0.2599 is significantly different from the reference group.Another side-note on your methodology: when you interpret your coefficients it's also important to remember that you are only estimating a correlation between marital status and health, not a causal one. Consider someone who is in such bad health that no girl wanted to marry him in the first place, then his health status is lower than those of divorced individuals but this has nothing to do with his marital status but because he was in poor health to begin with. So you might have an endogeneity problem here.