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Published in:
27-02-2017 | Erratum
Erratum to: Analyzing the effect of dynamically assigned treatments using duration models, binary treatment models, and panel data models
Published in: Empirical Economics | Issue 2/2018
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Excerpt
The first displayed (unnumbered) equation on page 11 in Abbring and van den Berg (2004) gives an expression for \(\hbox {Pr}(T_{m}> t, T_p > t_{p}|x)\) that is incorrect. Under the assumption (implicit in the paper) that the distribution of \(T_{p}|x\) is not defective,
$$\begin{aligned} \hbox {Pr}(T_{m}>t, T_{p}>t_{p}|{x})= {\mathop {\int }\nolimits _{t_{p}}^{\infty }} \frac{\partial \hbox {Pr}(T_{m}>t, T_{p}\le u|x)}{\partial {u}} du, \end{aligned}$$
$$\begin{aligned}&\frac{\partial \hbox {Pr}(T_{m}>t, T_{p}\le t_{p}|x)}{\partial {t_{p}}}\\&\quad ={\mathop {\int }\nolimits _{0}^{\infty }} {\mathop {\int }\nolimits _{0}^{\infty }} \exp (-\phi _{m}(x)v_{m}[\Lambda _{m}(\hbox {min}\{t,t_{p}\})+\hbox {I}(t>t_{p})\Delta (t|t_{p},x)]) \\&\qquad \times \phi _{p} (x)v_{p}\lambda _{p}(t_{p})\exp (-\phi _{p}(x)v_{p}\Lambda _{p}(t_{p}))dG(v_{m},v_{p}). \end{aligned}$$