Margins with effects

[Miguel Olivo-Villabrille]

I am estimating an equation
\[
Y_{ist} = \alpha D_{ist} + \beta \cdot x_{ist} + \gamma_s + \lambda_t + \delta_i + \varepsilon_{ist},
\]
where ist denotes individual, state and time. I am estimating it with

xtset i t
xtreg Y D `xx' i.s i.t, fe

The macro `xx' is a list of covariates. I am now trying to get the mean prediction but setting D to zero:
\[
\mathbb{E}[Y_{ist} \mid D_{ist} = 0]
\]
I want to prediction to include the effects \delta_i. Notice that margins, at(D = 0) gives me the mean prediction without the effects \delta_i.

[Phil Bromiley]

You'll increase your chances of a useful answer by following the FAQ on asking questions - provide Stata code in code delimiters, readable Stata output, and sample data using dataex.

I don't understand what \delta.i means. Are you asking for the effect if D=0 and D=1? that just takes an at statement - see the margins documentation.

[Miguel Olivo-Villabrille]

Hi Phil,

delta_i is the individual-specific fixed-effect. Similarly, gamma_s and lambda_t are are state-specific, and time-specific fixed-effects.

Like I said, what I want to get is the mean prediction of Y given that D = 0. I could get the prediction with

predict, xbu

and I can work with that to get the mean prediction, but I was wondering if there is a Stata command that would give me what I am after, along with perhaps confidence intervals. Like you mention, I could use

margins, at(D = 0)

but like I mentioned, that ignores the individual effects delta_i, that is, it gives the expression
\[
\mathbb{E}[Y_{ist} \mid D_{ist} = 0, \delta_i = 0].
\]

[Clyde Schechter]

Since this is a linear model, you can re-run it as:

regress Y D `xx' i.s i.t i.i

after which

margins, at(D = 0)

will give you what you want, if I understand you correctly.

[Miguel Olivo-Villabrille]

The problem with that solution

regress Y D `xx' i.s i.t i.i

is that when there are a large number of individuals, it becomes unfeasible. I could use areg, but with that I can't use the "trick" below to obtain the mean prediction I'm after.

But more fundamentally, consider

webuse nlswork
xtset idcode year
xtreg ln_w grade age c.age#c.age ttl_exp c.ttl_exp#c.ttl_exp tenure c.tenure#c.tenure 2.race i.not_smsa i.south i.year, fe
keep if e(sample)

margins, at(not_smsa = 0 south = 0)

Predictive margins                              Number of obs     =     28,091
Model VCE    : Conventional

Expression   : Linear prediction, predict()
at           : not_smsa        =           0
               south           =           0

------------------------------------------------------------------------------
             |            Delta-method
             |     Margin   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
       _cons |   1.726847   .0053209   324.54   0.000     1.716418    1.737276
------------------------------------------------------------------------------

clonevar not_smsa2 = not_smsa
clonevar south2 = south
replace not_smsa = 0
replace south = 0
predict xb, xb
predict xbu, xbu
sum xb xbu


    Variable |        Obs        Mean    Std. Dev.       Min        Max
-------------+---------------------------------------------------------
          xb |     28,091    1.726847    .1805905   1.258244   2.484918
         xbu |     28,091    1.677103    .3975748          0    3.98918

Notice that margins gives the answer for xb, rather than xbu. Why is that? and how can I obtain the mean prediction given not_smsa = 0 and south = 0 with fixed-effects?

[Clyde Schechter]

Notice that margins gives the answer for xb, rather than xbu. Why is that?

Well, -help xtreg postestimation- says that the default prediction for -margins- after -xtreg- is based on xb. It goes even further and says that -xbu- is not permitted, even though -predict, xbu- does exist. I do not know why. Usually when Stata doesn't support some calculation there is a good reason why it can't or shouldn't be done. But I can't think of such a reason in this instance.

and how can I obtain the mean prediction given not_smsa = 0 and south = 0 with fixed-effects?

Well, you have in fact already done it. Your own calculations , copied here, do exactly that:

clonevar not_smsa2 = not_smsa
clonevar south2 = south
replace not_smsa = 0
replace south = 0
// predict xb, xb
predict xbu, xbu
summ /*xb*/ xbu

[Miguel Olivo-Villabrille]

I mean to ask how I can do it with margins, so that I can get standard errors and confidence intervals as side effects, hehe...

[Clyde Schechter]

OK, I see. Well, I have to say I'm stumped here. I can't think of anything other than the -regress... i.i ...- approach, which your data set is not compatible with.

[Miguel Olivo-Villabrille]

I found this answer:
https://www.stata.com/support/faqs/s...on-unsuitable/

It seems I can use

margins, at(not_smsa = 0 south = 0) predict(xbu) force

[Clyde Schechter]

Thank you.