Yi = + Di + 1Zi + 2DiZi + ei where Yi is the outcome of interest, Zi is the distance from the border, Di is an indicator of the cultural group membership, and ei is an unobserved disturbance (i.e., all unmodelled 35

Published online by Cambridge University Press (13) factors affecting Yi). The main parameter of interest is (i.e., the effect of being in one or the other cultural group), while 1 measures if the distance from the border associates with the outcome on one side of the border, and the parameter 2 allows for a different effect of distance from the border on the other side of the border. Of course, more complex versions of this model are also possible (e.g., powers of Zi, see, e.g., Angrist & Pischke, 2014). As the identifying assumption of spatial regression discontinuity design (as well as the logic of the conditional local geographic ignorability design) can be valid only in the vicinity of the threshold, this regression should only be run on observations that lie in the vicinity of the cultural border and not over the entire domain of the score. To show the robustness

e., Kernel regression). Concerning statistical inference, calculations of standard errors in spatial regression discontinuity design are a rather delicate matter; we, thus, re-direct readers interested in this topic to Cattaneo and Titiunik (2022) or Cattaneo et al. (2020). 36 Published online by Cambridge University Press

Technical box # 4: Regression discontinuity design Let Zi be the running variable. Units are assigned either to the cultural group Di = 1 if Zi c or to Di = 0 otherwise, where c denotes the cutoff point/border. In this scenario, unconfoundedness holds trivially, because Di is a deterministic function of the running variable Zi. However, positivity never holds, because P [Di = 1|Zi = z] is either 0 or 1 (Imbens & Lemieux, 2008). Identification, thus, relies on a different assumption, known as continuity (Hahn et al., 2001): E[Yi(1)|Zi = c] and E[Yi(0)|Zi = c] are continuous in z at c (14) Formally, the continuity assumption allows us to define the estimand of interest as, E[Yi(1) Yi(0)|Zi = c] (15) which is identified by lim E[Yi|Zi = z] lim E[Yi|Zi = z] zc zc (16)