  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. 
Does the $h_\alpha$ index reinforce the Matthew effect in science?   Agent-based simulations using Stata and R