_Figure 8: The development of idiosyncratic versus covariate shocks_ <!-- Start of picture text --> Idiosyncratic over covariate shock ratio (2016-2019)<br>4.0<br>3.4<br>2.9<br>3.0 2.5 2.6 2.5<br>2.2<br>1.9 1.9 1.8 1.9<br>2.0 1.7 1.7<br>1.0<br>0.0<br>2016 2017 2018 2019<br>All Rural Urban<br><!-- End of picture text --> _Source: World Bank estimates based on EHPM (2016-2019)_

**To sum up, the decrease in vulnerability to poverty over time is connected to a parallel decrease in poverty.** Given the decrease in poverty, the share of households close to the poverty line is lower. Related to this development, a lower share of households switched their poverty status, which then also lowers the rate of households being vulnerable. Poverty-induced vulnerability decreased and risk-factors play a more significant role in vulnerability to poverty. These developments are not in contrast to parallel increases in operational vulnerability (Robayo-Abril and Barroso, 2022), given that operational vulnerability takes a static perspective towards vulnerability to poverty. Operational vulnerability and ex-ante vulnerability therefore do not reflect the same group of people.

# **6. Robustness Tests and Sensitivity Analysis**

**To validate our findings, we conduct several robustness tests and a sensitivity analysis.** First, we estimate several model specifications and compare their results to each other. Next, we account for potential measurement errors in the underlying income variable. We then take advantage of the fact that 50 of the included municipalities are autorrepresentative, meaning direct estimates from the household survey are representative for these 50 municipalities, given their sample size. This analysis is useful for the estimation of covariate vulnerability. Lastly, we conduct a sensitivity analysis by applying an alternative probability threshold, which defines if a person is vulnerable or not. The following subsection details the main findings and conclusions from these validity checks.

## 6.1. Different Model Estimations and Vulnerability Estimates

**We investigate the robustness of our findings to different model specifications.** These model specifications account for some of the shortfalls of our baseline specification. Table 4 illustrates the results. We conduct these robustness tests for the 2019 survey year. The first colum reports the baseline estimate. We first present the total vulnerability rate for the overall population, and those for the urban and rural populations separately. Column 2 refers to a model specification which excludes the educational variable in order to increase the underlying sample size. Row 1 reveals that the vulnerability rate is slightly higher than the one from the baseline specification (29.5 percent versus 23.7 percent). These differences remain when restricting the sample by urban/rural status.

**Our risk measures are self-reported and could be subject to reporting biases; we account for this potential shortcoming by measuring exposure to hazards via external data sources.** There are two possibilities to measure hazards. First, one can rely on self-reporting of exposure to shocks by households. Second, it is possible to rely on data collected externally, as for example weather or remote-sensed data. Both approaches are subject to potential limitiations and biases. While external data sources might suffer from so-called basis risks, self-reporting is endogenous and subjective (Nguyen & Nguyen, 2020). Column 3 presents results for a model specification which relies on external data sources to measure risk exposure and excludes the educational variable. Column 4 relies on external data sources to measure risk exposure and

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