represents a vulnerability line within the US$ 8 and US$ 11 dollar-a-day in 2005 PPP interval (i.e. US$ 10 to US$ 14.9 dollar-a-day in 2011 PPP). The second exercise shows that the vulnerability line would belong to an interval between US$ 8.7 and US$ 13.6 dollar-a-day in 2005 PPP (i.e. U$S 11.5 and U$S 17.8 dollara-day in 2011 PPP) for a 10 percent probability of falling into poverty considering all models and time intervals. Moreover, previous research on the value of the vulnerable group and the middle class finds that the value of the vulnerability line is around US$ 9.5 to US$10 (i.e. US$ 12.6 and US$13.2 dollar-a-day in 2011 PPP) (see Pabon and Perez, 2016; Lopez-Calva and Ortiz-Juarez, 2014).

The interval values for the vulnerability line estimated in previous exercises and research overlap within a range of U$S 8 and US$ 14 dollar-a-day 2005 PPP. However, this is not enough for identifying the vulnerability line. To do so, we first restrict the findings only to the 2008-10 synthetic panel, because it is the closest period when the official poverty lines were estimated. The range still is around US$ 8.4 and US$ 13.4 dollar-a-day 2005 PPP based on the sensitivity analysis and the adapted Lopez-Calva Method. The last assumption consists in taking the simple average of these lines to get a single number, and the result is a vulnerability line of US$ 10.1 dollar-a-day in 2005 PPP or US$ 13.2 dollar-a-day in 2011 PPP. Even though the results presented in the next section are based on the US$ 10 dollar-a-day 2005 PPP vulnerability line, welfare dynamics were estimated using other vulnerability lines for the 30 percent vulnerability index in other years (i.e. US$ 9 and US$ 11.3 dollar-a-day 2005 PPP) showing no significant differences.<sup>15</sup> We would like to offer some further reflections about identifying the vulnerability line. This task depends to a large extent on the specific context of the country, and subjective judgment.<sup>16</sup> Thus it can be useful to combine details from both the contextual background, as well as findings from previous studies to construct the vulnerability line. This process ensures that different economic and societal factors are fully taken into account. Our discussion above did so and suggests that a vulnerability index of 30 percent could be appropriate for Colombia. But we will also examine other robustness checks in future research, for example, by investigating mobility patterns when the vulnerability lines are varied.<sup>17</sup>

# **5. Results: “Monetary welfare” dynamics**

This section presents mobility estimates for Colombia during four pairs of years (i.e. 2008-2010, 2010-2012, 2012-2014 and 2014-2016) relying on the synthetic panel methodology proposed in Dang and

> 15 Transition matrices as well as profiles are available upon request.

> 16 Notably, the construction of the poverty line is also full of arbitrary choices, for example over the composition of the food basket or how to add the non-food expenditure component.

> 17 In a quick review, the transition matrices are not statistically different if we use the vulnerability line associated to a vulnerability index of 32 and 28 percent. All these transition matrices are available upon request.

15