  Recently, Hirsch (2019a) proposed a new variant of the h index called the
$h_\alpha$ index. He formulated as follows: "we define the $h_\alpha$ index of
a scientist as the number of papers in the h-core of the scientist (i.e. the
set of papers that contribute to the h-index of the scientist) where this
scientist is the $\alpha$-author" (p. 673). The $h_\alpha$ index was criticized
by Leydesdorff, Bornmann, and Opthof (2019). One of their most important points
is that the index reinforces the Matthew effect in science. We address this
point in the current study using a recently developed Stata command (h_index)
and R package (hindex), which can be used to simulate h index and
$h_\alpha$index applications in research evaluation. The user can investigate
under which conditions $h_\alpha$ reinforces the Matthew effect. The results of
our study confirm what Leydesdorff et al. (2019) expected: the $h_\alpha$ index
reinforces the Matthew effect. This effect can be intensified if strategic
behavior of the publishing scientists and cumulative advantage effects are
additionally considered in the simulation.
