Appendix
Marginal effects in count data models
The marginal effect of any explanatory variable xij on the conditional mean
of the dependent variable yi is given by
dE(yi∖xi) 0 om n NB
—— = eχp(xiβ)βj = Yj
for the negative binomial model and by
dE (yi∖xi) = eχp(xiβ) β = ZINB
∂xij (1 + exp(xiβ))2 Y γi
for the zero-inflated negative binomial model, in the case where the vector
of explanatory variables x0i is identical in the inflation model and the main
equation. The marginal effects depend on the explanatory variables and need
to be evaluated at some value. We evaluate them at the sample mean.
The standard errors of the marginal effects were computed according to
the asymptotic variance formulas
Asy.Var[γ]NB = (exp(χ0∕3))2[Ik + exp(X0∕3)∕3x0] V [Ik + exp(x0 ∕3)x∕30]
and
. , ... . . , г» . . . . ^ . . . ^
Asy.Var[γ∖ziNB = [Л(1 - л)] [Ik + (1 - 2Л)вх ]V[Ik + (1 - 2Л)х/3 ]
where x is the K × 1 vector of sample means, / is the K × 1 vector of parameter
estimates, Ik is an identity matrix of dimension K , V is the K × K estimated
asymptotic covariance matrix of ∕ and Λ = exp(x0∕)∕(1 + exp(x0∕3)) is a
scalar.
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