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If you have two separate regressions, you have all the ingredients for the formula that Glen_b linked to, other than the covariance term. You can assume it's zero if that makes sense with your model, or you can estimate the two equations as a system, which will give you cross-equation covariances between the coefficients. It's hard to know which is better without the details. One way (out of several possible ways) to do the latter is with Seemingly Unrelated Regression:

If you have two separate regressions, you have all the ingredients for the formula that Glen_b linked to, other than the covariance term. Here you have two choices. You can assume it's zero if that makes sense with your model and do the calculation "manually". Or you can estimate the two equations as a system, which will give you cross-equation covariances between the coefficients. It's hard to know which is better without the details. One way (out of several possible ways) to do the latter is with Seemingly Unrelated Regression:

If you have two separate regressions, you have all the ingredients from the formula that Glen_b, other than the covariance term. You can assume it's zero if that makes sense with your model, or you can estimate the two equations as a system. It's hard to know for sure without the details. One way to do the latter is with Seemingly Unrelated Regression:

If you have two separate regressions, you have all the ingredients for the formula that Glen_b linked to, other than the covariance term. You can assume it's zero if that makes sense with your model, or you can estimate the two equations as a system, which will give you cross-equation covariances between the coefficients. It's hard to know which is better without the details. One way (out of several possible ways) to do the latter is with Seemingly Unrelated Regression:

Added in response to the OP's comment below:

If you have two separate regressions, you have all the ingredients from the formula that Glen_b, other than the covariance term. You can assume it's zero if that makes sense with your model, or you can estimate the two equations as a system. It's hard to know for sure without the details. One way to do the latter is with Seemingly Unrelated Regression:

. webuse regress

. sureg (eq1:y x1 x2) (eq2:y x1 x3)

Seemingly unrelated regression
----------------------------------------------------------------------
Equation          Obs  Parms        RMSE    "R-sq"       chi2        P
----------------------------------------------------------------------
eq1               148      2     4.54006    0.3758      91.48   0.0000
eq2               148      2    3.770546    0.5694     211.94   0.0000
----------------------------------------------------------------------

------------------------------------------------------------------------------
             |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
eq1          |
          x1 |   7.472932     .98949     7.55   0.000     5.533568    9.412297
          x2 |  -.4768772   .7799875    -0.61   0.541    -2.005625     1.05187
       _cons |  -1.374358   2.883296    -0.48   0.634    -7.025514    4.276798
-------------+----------------------------------------------------------------
eq2          |
          x1 |   4.338581   .7852935     5.52   0.000     2.799434    5.877728
          x3 |  -.0026865   .0003774    -7.12   0.000    -.0034261   -.0019468
       _cons |   16.32873   3.214735     5.08   0.000     10.02797     22.6295
------------------------------------------------------------------------------
    
. nlcom ratio:[eq1]_b[x1]/[eq2]_b[x1]

       ratio:  [eq1]_b[x1]/[eq2]_b[x1]

------------------------------------------------------------------------------
             |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
       ratio |   1.722437   .2773696     6.21   0.000     1.178803    2.266071
------------------------------------------------------------------------------