We have some prior information from the IV-KLS analysis from above that informs us about the sign of the endogeneity. The KLS estimates in Figure 1 suggests that the plausible range of the correlation coefficient lies approximately between -0.6 to -0.1; this also lies within the confidence interval of the IV estimates. For our panel estimation we specify a negative sign for the endogeneity coefficient, _ρ_ , and restrict is to lie between zero and -0.2.<sup>22</sup> We now estimate the panel data equivalent version of Equation 1 given as where the subscript _i_ refers to countries and _t_ refers to time in year, _αi_ and _δ_ are country fixed-effects and time effects respectively, and all other variables as defined above.

**Figure 2:** KLS Panel-data estimates of the effect of voice & accountability on access to sanitation

<!-- Start of picture text --> Panel A : Total access to sanitation<br>Panel B : Urban access to sanitation<br>−.2 −.15 −.1 −.05 0 −.2 −.15 −.1 −.05 0<br>Postulated endogeneity of Voice & Accountability Postulated endogeneity of Voice & Accountability<br>KLS >=95% CI KLS estimate KLS >=95% CI KLS estimate<br>Panel B : Rural access to sanitation Panel D : Rural-Urban gap in access to sanitation<br>−.2 −.15 −.1 −.05 0 −.2 −.15 −.1 −.05 0<br>Postulated endogeneity of Voice & Accountability Postulated endogeneity of Voice & Accountability<br>KLS >=95% CI KLS estimate KLS >=95% CI KLS estimate<br>.25<br>.3<br>.2<br>.15 .2<br>.1<br>.1<br>.05<br>Estimated Voice & Accountability Coefficient 0 Estimated Voice & Accountability Coefficient 0<br>.3<br>.3<br>.2<br>.2<br>.1<br>.1<br>0<br>Estimated Voice & Accountability Coefficient 0 Estimated Voice & Accountability Coefficient −.1<br><!-- End of picture text -->

**Notes:** The light gray shaded area in Panel A is the 95% confidence for the KLS estimate and the solid blue line is the coefficient point estimates of voice and accountability corresponding to the postulated correlation coefficient, _ρ_ set between -0.2 and 0. We control for country-specific effects and time-specific effect. The estimation comprise 73 countries over the period 2002-2020 with a total number of observation of 1,378.

Figure 2 depicts the results for the KLS panel estimates. For the admissible range of correlation coefficients ( _ρ <_ 0), we find strong evidence that _Voice_ has a positive and statistically significant impact on access to sanitation (Panel A, B, and C). Additionally, Panel D in the figure shows that _Voice_ helps to close the rural-urban gap in access to sanitation. These panel-data results complements the findings from the cross-sectional analysis.

assumptions. As pointed out by the authors, in several applications, it might be easier to specify a credible range for the correlation of an endogenous regressor with the error term than to convincingly present strong and valid instruments. However, on one hand, if the postulated endogeneity range is too narrow, it may not include the true correlation value, potentially leading to serious bias. In contrast, if it is too wide, the resulting confidence intervals could be less informative than those from a 2SLS estimation with strong and valid instruments.

> 22We conduct preliminary estimation with _ρ_ specified between (-0.6, 0). We found that the corresponding confidence intervals for _ρ_ values less than -0.25 are extremely wide. We therefore rule out these values for the purpose of inference.

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