suggests that there may not be any issues related to weak instruments, the large differences between the OLS and IV estimates raises concerns other concerns of the relevance of the instruments.(Kiviet, 2020, 2022; Kripfganz and Kiviet, 2021).<sup>18</sup> As a first step, we employ the KLS estimator as an additional estimator to help reinforce our results. Because the KLS estimator does not rely on instruments, we are able to use it along with the 2SLS estimation to test for any potential exclusion restriction violation in our just-identified model. In particular, it allows the user to assess the validity of previously untestable just-identifying exclusion restrictions. The KLS estimator therefore serves as both a complement to the IV-estimation as well as a validation tool.

5.4.3 KLS RESULTS Because the correlation coefficient, _ρ_ , is unknown, the KLS requires the postulation of admissible correlation of the regressors with the error term within plausible bounds. To do so, we combine information from the OLS and IV estimates in previous sections for guidance. The coefficients of _Voice_ from the OLS and IV estimations in Tables 4 and 5 respectively suggest that the OLS estimator is downward biased in our case. To this end, we specify a negative sign for the correlation as well as a reasonable interval of -0.6 to -0.2 for the unknown correlation coefficient, _ρ_ . Given that the KLS requires a postulated interval, as a more illuminating approach, the KLS plots the estimated coefficient with their corresponding 95% confidence intervals over the chosen range of endogeneity correlations (i.e., -0.6 to -0.2). This shows immediately for which values of the correlation coefficient we can reject (or not reject) the null hypothesis that a coefficient of interest equals a certain value. Furthermore, we are able to check whether the coefficient is statistically significantly different from zero. We also report formal exclusion test for our instrumental variable from postestimation tests from the KLS estimator.<sup>19</sup> Figure 1 presents the results. The top row of the figure, Panels A and B, reports the estimates of the effect of _voice_ on access to sanitation from the KLS estimator and the IV-regression. The light gray shaded area is the 95% confidence for the 2SLS estimator and the solid black line is the point estimate from the 2SLS estimator of _Voice_ , _β_ 1 _,IV_ . The dark gray shaded area in Panels A and B is the 95% confidence interval for the KLS estimate and the dashed lines are the KLS point estimates ( _β_ 1 _,KLS_ ) of _Voice_ corresponding to the postulated correlation coefficients given between -0.6 and -0.2. Panel A is the specification with no control variables and Panel B is the model with control variables. Both specifications include the regional dummies. The bottom figures, Panel C and D report the respective exclusion tests for the instrument used in the IV regressions in Panel A and B.

It is clear from panels A and B of figure 1 that for plausible range of the postulated values of the correlation coefficient, _Voice_ has an unambiguous and statistically significant effect on access to sanitation. Two notable points need further highlighting: First, the effect of _Voice_ from the KLS is decreasing in the postulated values of the correlation coefficient. Recall that the OLS estimates of the coefficient of voice and accountability are biased downwards. Hence, because the KLS estimator coincides with the OLS estimator at _ρ_ = 0, it is intuitive to see that as the postulated endogeneity gets closer to zero, the KLS estimates of the effect of _Voice_ will get closer to the OLS estimate.<sup>20</sup> Second, at approximately -0.56 and -0.52 for the postulated correlation coefficient in panel A and B, respectively, the estimates from the KLS coincides with the estimate from the 2SLS (i.e., _β_ 1 _,KLS_ = _β_ 1 _,IV_ ). Additionally, for most of the postulated values, the KLS confidence lies within the confidence interval associated with the IV-estimation. This

> 18We thank Aart Kraay and S. Kripfganz for raising this issue. We intend on further investigating this issue and expanding the KLS postulated correlation interval to include positive correlation. The analysis is ongoing.

> 19We use the Stata command `kinkreg` developed by Kripfganz and Kiviet (2021) to implement the KLS estimations and postestimations. 20 Indeed, Kripfganz and Kiviet (2021) show that the KLS estimator _β_ 1 _,KLS_ is by construction, point-symmetric around _ρ_ = 0 and that _β_ 1 _,KLS_ is a monotonically decreasing function in _ρ_ . See also Kiviet (2020) and Kiviet (2022) for additional details.

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