Dang _et al_ . (2014) propose both a parametric and a non-parametric approach to construct synthetic panels and estimate an upper-bound (assuming zero correlation between error terms) and a lower-bound (assuming perfect positive correlation between error terms) for the transitions using two rounds of cross sections. In addition, in Dang and Lanjouw (2013, 2016) the authors extend this method further and calculate point estimates of poverty mobility based on the synthetic-panels (relying on the key assumption that the residual terms of the income equations in two periods are distributed according to a bi-normal distribution).<sup>2</sup> In addition to the analysis of the transitions in and out of poverty using synthetic-panels, Dang and Lanjouw (2017) estimate vulnerability lines to analyze welfare dynamics in India (note that the authors also use true panel data from Vietnam and the United States to illustrate their method to assess vulnerability), connecting the specification of the vulnerability line to the risk of falling into poverty.

The purpose of this paper is twofold. First, define the vulnerability lines, and second analyze the short-run transitions between poverty, vulnerability and middle class in Colombia, relying on an application of the synthetic panel methodology proposed by Dang and Lanjouw (2013, 2016) and Dang _et al_ . (2014) using as few as two rounds of cross-section surveys and relatively parsimonious modeling assumptions. The approach models income or consumption using only time-invariant covariates common to two (or more) surveys. The procedure assumes that the underlying populations being sampled in both rounds of the survey are the same, such that the time-invariant household characteristics in one round of the survey would be the same in the following round. The main implication of this assumption is that households interviewed in the second period of the survey with characteristics similar to those of households interviewed in the first period would have achieved similar levels of income or consumption in the initial period and vice versa, providing the linkage between household income or consumption in both periods.

One of the cross-cutting strategies envisioned to achieve the strategic development objectives of the country per the National Development Plan of Colombia for the 2014-2018 period<sup>3</sup> is promoting social mobility. In this context, the National Development Plan highlights the need to deepen the analysis of inequality and welfare dynamics in Colombia. Information on the dynamics of income allows to identify the characteristics associated with economic mobility, as well as identify the segment of the population more vulnerable to return to poverty. For the Latin America region, the World Bank defines the middle class as those individuals with a per capita income from US$10 to US$50 per day in purchasing power parity (PPP) at 2005 international prices, values estimated using the vulnerability to poverty approach proposed by Lopez-Calva and Ortiz-Juarez (2014). This methodology assumes that households with incomes above the poverty line but with a probability of falling into poverty higher than 10 percent should

> 2 In addition, a recent paper by Bourguignon and Moreno (2015) discusses using two cross sections to construct synthetic panels relying on pseudo-panel, matching and calibration techniques.

> 3 See the National Development Plan at: <u>https://colaboracion.dnp.gov.co/CDT/PND/PND%2020142018%20Tomo%201%20internet.pdf</u>

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