Interpreting coefficients when using the exposure/offset function

[Brenden Beck]

Hi all,

I am running a fixed effects model predicting numbers of arrests in different cities and I am using population as an exposure variable. How does using Stata's exposure or offset function change the interpretation of the coefficients? E.g. if variable 1's coefficient is 0.05, does that mean that a 1% increase in variable 1 is associated with a 0.05 arrest increase per person?

Thanks!

[Carlo Lazzaro]

Brenden:
without reading what you typed and what Stata gave you back (as per FAQ), the best advice that springs to my mind is to take a look at Example 1 under -poisson- entry in Stata .pdf manual.

[Brenden Beck]

Hi Carlo,
Thanks for your reply. My code and Stata's output are below. I couldn't find much in the Stata user guide about exposure. I'd like to interpret the coefficient of "percent in poverty" as "A 1% increase in the percent in poverty in a city is associated with an increase in 0.01 arrests per person in the city." Any advice you have would be greatly appreciated!
- Brenden

xtset cityid year
xtnbreg arrests pctpov year if flag==1, nolog fe vce(oim) exposure(pop)

Conditional FE negative binomial regression     Number of obs      =      7534
Group variable: fipsplace                       Number of groups   =      1038

                                                Obs per group: min =         2
                                                               avg =       7.3
                                                               max =         8

                                                Wald chi2(2)       =   2052.04
Log likelihood  = -31808.402                    Prob > chi2        =    0.0000

------------------------------------------------------------------------------
     arrests |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
      pctpov |   .0117664   .0019442     6.05   0.000     .0079558     .015577
        year |  -.0339315    .000776   -43.73   0.000    -.0354525   -.0324106
       _cons |   59.26344   1.550597    38.22   0.000     56.22432    62.30255
     ln(pop) |          1  (exposure)
------------------------------------------------------------------------------

[Carlo Lazzaro]

Brended:
I think that your interpretation is correct. 1% increase in -pctpov- is correlated with a 1% increase in arrest.
I would have examined the contributions of -year- differently, though, using the factor variable notation -i.year-.

[Brenden Beck]

Thanks, Carlo. That makes sense, to think about it as a percent increase.