Randomization Inference (Standard Errors)

If standard errors are theoretically messy or you want a fully non-parametric p-value, you can bypass the standard error calculation entirely using Randomization Inference (RI). RI randomly permutes the treatment variable thousands of times, generating a distribution of placebo coefficients. Your actual coefficient is then compared against this distribution.

• Using Michler_JEEM.dta (maize only), first run the OLS regression of lnyield on CA with the same controls (lnbasal lntop lnseed lnaream2 pdate pdate2 i.year), clustering standard errors at rc, and save the true coefficient on CA in a global called true_b.
• Run ritest to permute CA 1,000 times setting the seed at 0 and then save (saving) the permutation distribution in a file called ri_yield.
• Finally, save the p-value from the randomization inference in a global called ri_p. Use globals rather than locals because use, clear wipes locals from memory.

* save ri p-value
	matrix          pvalues = r(p)
	global          ri_p = pvalues[1,1]
	global          ri_p : di %5.3f ${ri_p}

1. Load the saved permutation data and create a kernel density plot of the placebo distribution, marking the true coefficient and the RI p-value and output it to your Overleaf file.

* plot permutation distribution
	twoway          (kdensity _pm_1, lwidth(medthick) ///
	                    lcolor(sky) lpattern(dash)), ///
	                    ytitle("Density") ///
	                    xtitle("Hypothetical treatment effect") ///
	                    title("CA effect on yield (t/ha)") ///
	                    xscale(range(${true_b})) ///
	                    xline(${true_b}, lpattern(solid) ///
	                        lwidth(thin) lcolor(sky)) ///
	                    text(.18 `=${true_b} - .01' "CA TE", ///
	                        color(sky) j(left) size(vsmall) ///
	                        place(nw) orient(vertical)) ///
	                    text(2.2 `=${true_b} - .01' ///
	                        "p-value = ${ri_p}", color(sky) ///
	                        j(left) size(vsmall) place(nw) ///
	                        orient(vertical)) ///
	                    legend(off)

2. What is the RI p-value?

3. How does the RI p-value compare to the p-value from the standard ivreg2 regression?