Does offset have a specific functionality?

[Alfonso Sánchez-Peñalver]

Hi all,

As I finish polishing the functionality of a new command I have been programming (coming shortly I hope), I am wondering if there is a particular functionality for the offset(varname) option that cannot be equally obtained with the use of constraints. Consider the following

. clear all
. set more off
. sysuse auto
(1978 Automobile Data)

. gen wgt = -weight/1000

. const def 1 wgt = 1

. probit foreign mpg wgt, nolog

Probit regression                                 Number of obs   =         74
                                                  LR chi2(2)      =      36.38
                                                  Prob > chi2     =     0.0000
Log likelihood =  -26.84419                       Pseudo R2       =     0.4039

------------------------------------------------------------------------------
     foreign |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         mpg |  -.1039503   .0515689    -2.02   0.044    -.2050235   -.0028772
         wgt |   2.335544     .56605     4.13   0.000     1.226107    3.444982
       _cons |   8.275464   2.554142     3.24   0.001     3.269437    13.28149
------------------------------------------------------------------------------

. probit foreign mpg, offset(wgt) nolog

Probit regression                                 Number of obs   =         74
                                                  Wald chi2(1)    =       0.00
Log likelihood = -30.278258                       Prob > chi2     =     0.9718

------------------------------------------------------------------------------
     foreign |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         mpg |   .0010781   .0304492     0.04   0.972    -.0586012    .0607575
       _cons |   2.280349   .7161614     3.18   0.001     .8766982    3.683999
         wgt |          1  (offset)
------------------------------------------------------------------------------

. probit foreign mpg wgt, const(1) nolog

Probit regression                                 Number of obs   =         74
                                                  Wald chi2(1)    =       0.00
Log likelihood = -30.278258                       Prob > chi2     =     0.9718

 ( 1)  [foreign]wgt = 1
------------------------------------------------------------------------------
     foreign |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         mpg |   .0010781   .0304492     0.04   0.972    -.0586012    .0607575
         wgt |          1  (constrained)
       _cons |   2.280349   .7161614     3.18   0.001     .8766981    3.683999
------------------------------------------------------------------------------

You can see how the results using offset and the constraint are identical, so it baffles me.

Thanks for throwing any light.

Alfonso.

[Richard Williams]

Offset is easier and probably less error prone.

[Alfonso Sánchez-Peñalver]

Hi Richard, I found that you can also offset a variable that you already have as an explanatory variable, and the coefficient gets the 1 subtracted from it. Clearly you can also achieve this by adding 1 to the variable you want to offset, but as you mention using -offset- is easier, and you don't have to alter the data. Not so sure about the practical applications in economics. -exposure- on the other hand can be useful if you're trying to do a quick test of whether an elasticity is equal to 1 or not, since the coefficient on the natural log of the variable you're applying -exposure- to will be the difference from 1, and if not significant you can claim unit-elasticity. Of course you can always do -offset- of the natural log of the variable, but you're changing data again.

Thanks Richard!

[Richard Williams]

Exposure in count models makes a lot of sense to me, when the length of exposure to risk varies across individuals (e.g. older researchers have had more time to publish articles). Offset can do the same as exposure by using the log of a variable. Other than that I don't know of many occasions when offset is handy -- it seems especially odd to me in a logit or probit. As you say, I guess it is one way of testing whether or not a coefficient equals 1, if that is a hypothesis that makes sense to test.