First Stage (Regression Discontinuity)

The Garg et al. (2021) RDD is fuzzy: crossing the population threshold increases the probability of receiving a road but does not guarantee it. Before running the fuzzy RD, we need to verify that the first stage is strong — that the threshold indicator actually predicts road construction.

• Define a global for the baseline controls:

* baseline controls
    global      blcontrols primary_school med_center elect ///
                    tdist irr_share ln_land pc01_lit_share ///
                    pc01_sc_share bpl_landed_share ///
                    bpl_inc_source_sub_share bpl_inc_250plus

• Run the first-stage regression: regress receivedroad on t left right $blcontrols using reghdfe, with triangular kernel weights [aw = kernel_tri_ik], absorbing year and dist_thresh_id fixed effects, and clustering standard errors at village_id. Store as fs.

1. Use rdplot to visualize the first stage. Plot receivedroad against v_pop with the cutoff at 0. Restrict to abs(v_pop) <= 250 and use 20 bins per side. Export the figure and import it into your Overleaf document.

2. What is the coefficient on t? Interpret it in words: by how many percentage points does crossing the threshold increase the probability of receiving a road?

3. Is the first stage strong? Check the F-statistic against the conventional rule-of-thumb threshold of $F > 10$.