Calculate the CI/SE/p-value of an inverse transformed variable in Stata after regression

[Uma Ravi]

This problem halfway between Stata and Statistics - which is why I am putting it here.

In this modelling problem, I have X = log (wage_educated/wage_uneducated) and Y = log (labor_educated/labor_uneducated)
After I do this:

reg Y X

The elasticity of substitution is the inverse of the coefficient of X. Now I need to also calculate the Confidence Interval, Std. Error and p-value for this elasticity. How do I use Stata commands to do them?

I do need help with this for a thesis I am writing. And, as I said this, I know this problem is halfway between Stata and Stats, so, do let me know if you want me to take this question down.

[Maarten Buis]

help nlcom

[Joro Kolev]

What Maarten said, but explicitly:

. sysuse auto, clear
(1978 Automobile Data)

. reg price mpg

      Source |       SS           df       MS      Number of obs   =        74
-------------+----------------------------------   F(1, 72)        =     20.26
       Model |   139449474         1   139449474   Prob > F        =    0.0000
    Residual |   495615923        72  6883554.48   R-squared       =    0.2196
-------------+----------------------------------   Adj R-squared   =    0.2087
       Total |   635065396        73  8699525.97   Root MSE        =    2623.7

------------------------------------------------------------------------------
       price |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         mpg |  -238.8943   53.07669    -4.50   0.000    -344.7008   -133.0879
       _cons |   11253.06   1170.813     9.61   0.000     8919.088    13587.03
------------------------------------------------------------------------------

. nlcom 1/_b[mpg]

       _nl_1:  1/_b[mpg]

------------------------------------------------------------------------------
       price |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
       _nl_1 |   -.004186     .00093    -4.50   0.000    -.0060088   -.0023631
------------------------------------------------------------------------------

[Uma Ravi]

OMG. Thanks so much, both of you. This was far easier than the manual calculation I was doing.

[Uma Ravi]

Joro Kolev Maarten Buis One more additional question - how do I store the confidence intervals/SE/p-value/t-value that I get from nlcom? I type in

return list

and I don't see the place where Stata has stored the values for CI/SE/p/t values. I type

ereturn list

and all I get are the list from the original regressions not from nlcom.

[Joro Kolev]

Yes, indeed, these are a little bit hard to retrieve. You might want to file a complaint with Stata Corp.

You can get them manually like this:

. nlcom 1/_b[mpg]

       _nl_1:  1/_b[mpg]

------------------------------------------------------------------------------
       price |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
       _nl_1 |   -.004186     .00093    -4.50   0.000    -.0060088   -.0023631
------------------------------------------------------------------------------

. dis "Point estimate = " el(r(b),1,1)
Point estimate = -.00418595

. dis "Lower Bound = " el(r(b),1,1) - 1.96*sqrt(el(r(V),1,1))
Lower Bound = -.00600879

. dis "Upper Bound = " el(r(b),1,1) + 1.96*sqrt(el(r(V),1,1))
Upper Bound = -.00236311

Joro Kolev Maarten Buis One more additional question - how do I store the confidence intervals/SE/p-value/t-value that I get from nlcom? I type in

return list

and I don't see the place where Stata has stored the values for CI/SE/p/t values. I type

ereturn list

and all I get are the list from the original regressions not from nlcom.

[Maarten Buis]

There is a Stata tip that discusses what Joro just did: https://journals.sagepub.com/doi/pdf...867X0800700408