 »  Home »  Resources & support »  FAQs »  Estimation commands and omitted variables

## Why do estimation commands sometimes omit variables?

 Title Estimation commands and omitted variables Author James Hardin, StataCorp

When you run a regression (or other estimation command) and the estimation routine omits a variable, it does so because of a dependency among the independent variables in the proposed model. You can identify this dependency by running a regression where you specify the omitted variable as the dependent variable and the remaining variables as the independent variables. Below we generate a dependency on purpose to illustrate:

. sysuse auto
(1978 automobile data)

. generate newvar = price + 2.4*weight - 1.2*displ

.  regress trunk price weight mpg foreign newvar displ
note: weight omitted because of collinearity.

Source         SS           df       MS      Number of obs   =        74
F(5, 68)        =     12.03
Model    626.913967         5  125.382793   Prob > F        =    0.0000
Residual    708.707655        68  10.4221714   R-squared       =    0.4694
Total    1335.62162        73  18.2961866   Root MSE        =    3.2283

trunk   Coefficient  Std. err.      t    P>|t|     [95% conf. interval]

price    -.0017329   .0006706    -2.58   0.012    -.0030711   -.0003947
weight            0  (omitted)
mpg    -.0709254   .1125374    -0.63   0.531    -.2954903    .1536395
foreign     1.374419   1.287406     1.07   0.289    -1.194561    3.943399
newvar     .0015145   .0005881     2.58   0.012     .0003411     .002688
displacement      .007182   .0092692     0.77   0.441    -.0113143    .0256783
_cons     4.170958   5.277511     0.79   0.432    -6.360151    14.70207



The regression omitted one of the variables that was in the dependency that we created. Which variable it omits is somewhat arbitrary, but it will always omit one of the variables in the dependency. To find out what that dependency is, we can run the regression using the omitted variable as our dependent variable and the remaining independent variables from the original regression as the independent variables in this regression.

. regress weight price mpg foreign newvar displ

Source         SS           df       MS      Number of obs   =        74
F(5, 68)        >  99999.00
Model    44094178.4         5  8818835.68   Prob > F        =    0.0000
Residual    6.9847e-07        68  1.0272e-08   R-squared       =    1.0000
Total    44094178.4        73  604029.841   Root MSE        =     .0001

weight   Coefficient  Std. err.      t    P>|t|     [95% conf. interval]

price    -.4166667   2.11e-08 -2.0e+07   0.000    -.4166667   -.4166667
mpg     4.40e-06   3.53e-06     1.25   0.217    -2.65e-06    .0000115
foreign      .000041   .0000404     1.02   0.314    -.0000396    .0001217
newvar     .4166667   1.85e-08  2.3e+07   0.000     .4166667    .4166667
displacement     .4999999   2.91e-07  1.7e+06   0.000     .4999993    .5000005
_cons    -.0002082   .0001657    -1.26   0.213    -.0005388    .0001224



The regression that we ran where the omitted variable was the dependent variable has an R-squared value of 1.00 and the residual sum of squares is zero (well, nearly). Also, the coefficients of the regression show the relationship between the price, newvar, and displ variables. The output of this regression tells us that we have the dependency

weight = -.4166667*price + .4166667*newvar + .4999999*displacement


which is equivalent to the dependency that we defined above.