st: Negative Binomial: Exposure vs. Offset

["Downey, Patrick" <PDowney@urban.org>]

Hello,

I'm using a negative binomial regression through the nbreg command in Stata
to estimate crimes committed by a certain population. Different
observations were "on the street" different lengths of time, so I want to
account for that.

I'm confused about the difference between the exposure option and the
offset option. They appear to be doing the same thing. In the online
documentation, it says:

    offset(varname) specifies that varname be included in the model with
the
        coefficient constrained to be 1.

    exposure(varname) specifies a variable that reflects the amount of
        exposure over which the depvar events were observed for each
        observation; ln(varname) with coefficient constrained to be 1 is
        entered into the log-link function.

Could someone please explain the difference between the two or send some
documentation which formalizes the difference mathematically.

Thanks,
Mitch

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