  We propose a simple microscopic model to numerically investigate the
stability of a two dimensional fractional topological insulator (FTI). The
simplest example of a FTI consists of two decoupled copies of a Laughlin state
with opposite chiralities. We focus on bosons at half filling. We study the
stability of the FTI phase upon addition of two coupling terms of different
nature: an interspin interaction term, and an inversion symmetry breaking term
that couples the copies at the single particle level. Using exact
diagonalization and entanglement spectra, we numerically show that the FTI
phase is stable against both perturbations. We compare our system to a similar
bilayer fractional Chern insulator. We show evidence that the time reversal
invariant system survives the introduction of interaction coupling on a larger
scale than the time reversal symmetry breaking one, stressing the importance of
time reversal symmetry in the FTI phase stability. We also discuss possible
fractional phases beyond $\nu = 1/2$.
