How Low Business Tax Rates Attract Multinational Headquarters: Municipality-Level Evidence from Germany

Appendix

Marginal effects in count data models

The marginal effect of any explanatory variable x_ij on the conditional mean
of the dependent variable yi is given by

^dE(yi∖xi)        0 o_m n NB

—— = e^χp(xi^β)^βj = Yj

for the negative binomial model and by

^dE (yi∖xi) =    ^eχp(xi^β)    _β = ZINB

∂xij      (1 + exp(xiβ))2 ^{Y   γ}i

for the zero-inflated negative binomial model, in the case where the vector
of explanatory variables x⁰_i 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» .              .               . . ^                            .               . . ^

A^sy.V^ar[γ∖ziNB = ^{[Л(1 - л)]} [Ik ^{+ (1 -} 2^{Л)вх ]V}[Ik ^{+ (1 -} 2^Л)х/3 ^]

where x is the K × 1 vector of sample means, / is the K × 1 vector of parameter
estimates, I_k 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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