Pavon and Perez, 2016).<sup>11</sup> Even though these results based on the ELCA were informative, they raised several concerns since the poverty figures were not only different from official estimates but also reflected a different poverty line (i.e. international poverty lines were used in this exercise). However, the main requirement the Lopez-Calva and Ortiz-Juarez (2014) methodology has is the existence of longitudinal information or panel data, which are not currently available in Colombia.

It is important to note that, for the Dang and Lanjouw (2017) approach, there is no close solution for �� that can be obtained from the equations of the “insecurity” and “vulnerability” indexes. However, given household income in both periods, the poverty line z, and some pre-determined value for either the insecurity or vulnerability index, it is possible to empirically solve for the vulnerability line ��. The construction of the vulnerability lines can be approached as a two-step process: the first is to identify the appropriate poverty lines (which are usually given; for example, the international poverty line); the second step is to iterate upward from the given poverty line, until we reach a value of the vulnerability line that provides the specified vulnerability index.

This method produces a set of vulnerability lines for a set of vulnerability indexes, posing the challenge for policy makers or society to choose a number from that set. The rule of thumb used under this approach for developing countries is to set a vulnerability index between 15 and 30 percent (or as desired by the social development objectives). This identification difficulty is not particular to this approach. For instance, under the Lopez-Calva and Ortiz-Juarez (2014) method, a figure is defined according to a “certain” risk level of falling back into poverty, which is usually 10 percent; some other rules have been used to define the middle class.<sup>12</sup> There is no clear consensus in the literature on how to objectively identify this line; instead it looks more like an arbitrary decision either to choose the likelihood level to fall into poverty or a number from a set of vulnerability indexes. Two exercises are presented to better inform this crucial decision: the first one consists on a sensitivity analysis of vulnerability lines when the base year is changed; and the second one is inspired by the method by Hertova, Lopez-Calva and Ortiz-Juarez (2010).

# **4.1. Estimation of the vulnerability line**

Poverty lines are sensitive to the base year used for their estimation. These lines are drawn from particular welfare distributions that change over time given the underlying development process in which many

> 11 The vulnerability to poverty approach can be divided in three steps. The first stage focuses on identifying the characteristics associated with the transition to and from the poverty condition. The second stage seeks to model the probability of falling into poverty, based on a series of observable variables, using a logistic model. The third step uses the variables that explain the probability of falling into poverty to predict the expected income associated with each level of probability. The third stage allows to identify the level of income associated with a 10 percent probability of falling into poverty (per the stylized facts reported by Cruces et al., 2011).

> 12 Lawrence (1984), Blackburn & Bloom (1987), Horrigan & Haugen (1988), Kosters & Ross (1989), Birdsall, Graham & Pettinato (2000) and D'Ambrosio et al (2002), Atkinson, A. and Brandolini, A. (2011) to quote a few.

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