A COMPANION TO Theoretical Econometrics
Practical Considerations
Those with experience of nonlinear least squares will find it easy to use packaged software for Poisson regression, which is a widely available option in popular econometrics packages like LIMDEP, STATA, and TSP. One should ensure, however, that reported standard errors are based on (15.17) rather than (15.6). Many econometrics packages also include negative binomial regression, also widely used for cross section count regression, and the basic panel data models. Statistics packages such as SAS and SPSS include count regression in a generalized linear models module. Standard packages also produce some goodness-of-fit statistics, such as the G2-statistic and pseudo-P2 measures, for the Poisson (see Cameron and Windmeijer, 1996).
More recently developed models, such as finite mixture models, most time series models and dynamic panel data models, require developing one's own programs. A promising route is to use matrix programming languages such as GAUSS, MATLAB, SAS/IML, or SPLUS in conjunction with software for implementing estimation based on user-defined objective functions. For simple models packages such as LIMDEP, STATA, and TSP make it possible to implement maximum likelihood estimation and (highly desirable) robust variance estimation for user-defined functions.
In addition to reporting parameter estimates it is useful to have an indication of the magnitude of the estimated effects, as discussed in Section 2.2. And as noted in Section 2.4, care should be taken to ensure that reported standard errors and f-statistics for the Poisson regression model are based on variance estimates robust to overdispersion.
In addition to estimation it is strongly recommended that specification tests are used to assess the adequacy of the estimated model. For Poisson cross section regression overdispersion tests are easy to implement. For time series regression tests of serial correlation should be used. For any parametric model one can compare the actual and fitted frequency distribution of counts. Formal statistical specification and goodness-of-fit tests based on actual and fitted frequencies are available.
In most practical situations one is likely to face the problem of model selection. For likelihood-based models that are nonnested one can use selection criteria, such as the Akaike and Schwarz criteria, which are based on the fitted loglikelihood but with degrees of freedom penalty for models with many parameters.
