Robust & Clustered Standard Errors (Standard Errors)

In this exercise you will compare different approaches to calculating standard errors for the conservation agriculture IV regression from Michler_JEEM.dta. The base specification is a pooled IV model using ivreg2 with household fixed effects.

Run the panel IV regression with default (uncorrected) standard errors.
Run the same specification but with the robust option.
The bw(1) kernel(tru) options require the data to be tsset. Since the data has multiple plots per household-year, generate a unique observation ID (gen obs_id = _n) and tsset obs_id before running this specification.
Run the same specification but using the Bell-McCaffrey corrections bw(1) kernel(tru).
Run the same specification but with the standard error option cluster at the household (rc) level.

1. Export a four-column comparison table and put it in your Overleaf file:

* compare standard error methods
	esttab      def robust hc2 cluster ///
	                using "$answ/13-se-hc2.tex", replace ///
	                b(3) se(3) keep(CA) nomtitles ///
	                star(* 0.10 ** 0.05 *** 0.01) ///
	                stats(N, labels("Observations") fmt(0)) ///
	                noobs booktabs nonum collabels(none) ///
	                nobaselevels nogaps fragment label ///
	                prehead("\begin{tabular}{l*{4}{c}} " ///
	                    "\\[-1.8ex]\hline \hline \\[-1.8ex] " ///
	                    "& \multicolumn{1}{c}{Uncorrected} & " ///
	                    "\multicolumn{1}{c}{Robust} & " ///
	                    "\multicolumn{1}{c}{HC2} & " ///
	                    "\multicolumn{1}{c}{Clustered} " ///
	                    "\\ \midrule") ///
	                postfoot("\hline \hline \\[-1.8ex] " ///
	                    "\multicolumn{5}{p{0.9\linewidth}}{\small " ///
	                    "\noindent \textit{Note}: Dependent variable " ///
	                    "is log maize yield. CA instrumented with " ///
	                    "wardNGO. All models include input controls " ///
	                    "and year FE. " ///
	                    "* p$<$0.10, ** p$<$0.05, *** p$<$0.01.} " ///
	                    "\end{tabular}")

1. Compare the standard error on CA across HC1, HC2, and the panel FE specifications. Does adjusting for leverage (HC2) increase or decrease the standard error?

2. How do the clustered standard errors compare to the robust standard errors? What does this suggest about within-household correlation in this panel?