You need to use the post
option, like this:
. sysuse auto
(1978 Automobile Data)
. reg price mpg weight
Source | SS df MS Number of obs = 74
-------------+------------------------------ F( 2, 71) = 14.74
Model | 186321280 2 93160639.9 Prob > F = 0.0000
Residual | 448744116 71 6320339.67 R-squared = 0.2934
-------------+------------------------------ Adj R-squared = 0.2735
Total | 635065396 73 8699525.97 Root MSE = 2514
------------------------------------------------------------------------------
price | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
mpg | -49.51222 86.15604 -0.57 0.567 -221.3025 122.278
weight | 1.746559 .6413538 2.72 0.008 .467736 3.025382
_cons | 1946.069 3597.05 0.54 0.590 -5226.245 9118.382
------------------------------------------------------------------------------
. nlcom ratio: _b[mpg]/_b[weight], post
ratio: _b[mpg]/_b[weight]
------------------------------------------------------------------------------
price | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
ratio | -28.34844 58.05769 -0.49 0.625 -142.1394 85.44254
------------------------------------------------------------------------------
. di _se[ratio]
58.057686
This standard error is the square root of the entry from the variance matrix r(V):
. matrix list r(V)
symmetric r(V)[1,1]
ratio
ratio 3370.6949
. di sqrt(3370.6949)
58.057686