/* REGRESSION DISCONTINUITY DESIGN Bicocca, 6 - 13 Maggio 2022 */ ** open DTA file ** use "C:\Users\Mara\Dropbox\DIDATTICA\Bicocca 2022\esercizio stata_spatial rdd.dta", clear /* in the dataset there is the sample of municipalities belonging to the italian regions sharing the policy-change boundary for the EU Regional policy during the period 2000-2006 we want to estimate the impact of the Objective 1 treatment on the employment variation in a spatial RDD framework: treat ==1 for municipalities belonging to Objective 1 regions; 0 otherwise y is the employment variation between 2006 and 2010 (post policy) the policy-change bondary is the discontinuity between Objective 1 regions and non-Objective 1 regions policy-change boundary dummies: one dummy for each of the 4 segments of which the boundary is composed (b1 b2 b3 b4) rastervalu: centered distance from each municipality's centroid and the policy-change boundary x_coord y_coord: the longitude and latitude coordinates of the municipality's centroid trasf91: total amount of other public resources addressed to municipalities in the same period of the EU Regional Policy funds (placebo treatment) */ /****************************************** Border Strategy estimation ******************************************* restrict the sample to municipalities countiguos to the policy-change boundary and run: */ reg y ob1 b1 b2 b3 b4 /* how do this result change with respect to an OLS analysis that would not account of the discontinuity from a methodological point of view? do the two approaches lead to different conclusions on the policy's impact on employment? */ /****************************************** Parametric estimation ******************************************* need to refer to the whole sample of municipalities and include in the model the polynomio of the forcing variable the forcing variable is the centered distance between each municipality's centroid and the policy-change boundary construct the polynomial function of the distance as forcing variable polynomial forcing variable Angrist 6.1.4 */ gen forc_2=rastervalu^2 gen forc_3=rastervalu^3 /* interaction polynomial forcing variable * treatment dummy Angrist 6.1.6 */ gen tf=ob1*rastervalu gen tf_2=ob1*forc_2 gen tf_3=ob1*forc_3 * different polynomial degrees from 1 to 3 *** treat varying, no treat == 1 *poly 1 1 reg y ob1 tf rastervalu estimates store model1_1 *poly 2 1 reg y ob1 tf rastervalu tf_2 estimates store model2_1 *poly 3 1 reg y ob1 tf rastervalu tf_2 tf_3 estimates store model3_1 *** treat varying, no treat == 2 *poly 1 2 reg y ob1 tf rastervalu forc_2 estimates store model1_2 *poly 2 2 reg y ob1 tf rastervalu tf_2 forc_2 estimates store model2_2 *poly 3 2 reg y ob1 tf rastervalu tf_2 forc_2 tf_3 estimates store model3_2 *** treat varying, no treat == 3 *poly 1 3 reg y ob1 tf rastervalu forc_2 forc_3 estimates store model1_3 *poly 2 3 reg y ob1 tf rastervalu tf_2 forc_2 forc_3 estimates store model2_3 *poly 3 3 reg y ob1 tf rastervalu tf_2 forc_2 tf_3 forc_3 estimates store model3_3 * let the Akaike criteria identifying the best specification estimates table model1_1 model2_1 model3_1 model1_2 model2_2 model3_2 model1_3 model2_3 model3_3, stats(r2 r2_a aic bic N) b(%7.3g) se(%6.3g) t(%6.3g) p(%4.3f) ** model 1_2: poly 1 2 - reg y ob1 tf rastervalu forc_2 /****************************************** Balancing properties ******************************************* balancing properties on the observables assure that the policy-change boundary lead to identify a treated (Objective 1) and a not treated group (non-Objective 1) of municipalities for which observable characteristics are equally distributed. To ensure that treated and not treated municipalities are similar in everything except for the treatment (Black, 1999) it remains to verify that no other phenomena are distributed across space in the same way as the EU Regional Policy and correlated to this same policy. In this case their role would remain hidden and included in the estimated policy impact as a confounding factor. In order to deal with this: - are the total financial resources transferred from the regions to the municipalities smoothly distributed across the boundary? */ reg trasf91 ob1 b1 b2 b3 b4 /* since I cannot reject H0: beta=0, the total financial resources transferred from the regions to the municipalities do not significantly change across the policy-change boundary (memo on p value: The p-value is the probability of estimating the coeff b given that the beta=0. If the p-value is lower than the significance level, set by convention at 0.05, we can reject the hypothesis H0 of beta = 0 and conclude that the coefficient is statistically different from 0 at the 5% level) is the result supportive? ******************************************* Additional Placebo ******************************************* - do the total financial resources transferred from the regions to the municipalities have any effect on employment at the policy-change boundary? */ reg y trasf91 b1 b2 b3 b4 /* since I cannot reject H0: beta=0, the total financial resources transferred from the regions to the municipalities do not significantly affect the employemnt variation at the boundary is the result supportive? ******************************************* Graphical Analysis *******************************************/ cmogram y rastervalu, cutright histopts(bin(180))lfit scatter cutpoint(0)