Some countries have adopted an Inflation Targeting (IT) regime to reduce inflation and inflation uncertainty: two factors the literature suggests firms put positive weight on when making outlay decisions that may affect aggregate domestic investment. This observation naturally leads to the question of whether domestic investment responds to IT. We apply the synthetic control method to developed and developing IT and non-IT countries to estimate the IT regime's causal effect on the domestic investment over time while addressing country heterogeneity. Adopting an IT regime had no short or long-run effect, at conventional levels of significance, on domestic investment in 21 out of 29 treated countries; this dominant pattern appears consistent with recent works on rational inattentive behaviour of firms. However, IT induced mainly long-run heterogeneous changes in domestic investment prices in 9 targeters, suggesting that supply constraints external to firms can also weaken the link between IT and domestic investment.