estimating their expected value; which they claim are more easily interpreted and exposited than the utility-based measures.

Along this strand, Cafiero and Vakis (2006) have suggested an approach based on an “augmented” poverty line, which in addition to including basic consumption goods and services it incorporates a basic “basket of insurance” against risks. In this line, Lopez-Calva and Ortiz-Juarez (2014) argue that it is possible to find the income level associated with a set of assets and socioeconomic characteristics that would allow the households to be less vulnerable to fall into poverty due to idiosyncratic and asymmetric shocks, and interpret it as an “augmented” poverty line. From that perspective, they explore the link between income and vulnerability to poverty in Mexico.<sup>5</sup> This paper follows their procedure, summarized in next section.

No single best approach exists to measure vulnerability (Ligon and Schechter, 2004). So far, different measures and approaches to estimate vulnerability have been proposed, depending on the priorities of the researcher and on nature of the data (along with the opportunities and problems it carries over). The proposed definition by Lopez-Calva and Ortiz-Juarez (2014) employed in this paper does at least conform to the widespread sense of what the nature of the concept of vulnerability should be.

# **2.2. Estimation**

The vulnerability-to-poverty estimates (as an approach to middle classes) were constructed in three stages as follows. The first stage exploited longitudinal data to analyze movements in and out of poverty during 2002-05 using the international poverty line of $4 a day. The data were taken from the _Mexican Family Life Survey_ (MxFLS) for the rounds of 2002 and 2005 with representativeness at the national, regional, urban and rural levels. The first wave includes 8,440 households, while the second includes 7,572 of the original households (attrition rate of 10%); however, only 6,129 households reported income in both waves. These datasets allowed to construct poverty transition matrices of households classified into four categories: 1) _never poor_ , if a household never felt under the poverty line during 2002-05; 2) _always poor_ , if it was poor in both years; 3) _out of poverty_ , if it was poor in 2002, but exited poverty in 2005; and 4) _entered poverty_ , if it was non-poor in 2002 but fell into poverty in 2005.

These transitions were used in a second stage to estimate probabilities of falling into poverty through logistic models identifying actual characteristics associated with movements in or out of poverty. The observable characteristics included demographic indicators, labor market resources, and self-reported shocks affecting the household—such as death, illness or accident of any

> 5 For rural Mexico, de la Fuente (2009) tried, in an eclectic fashion, to bring together core elements from various approaches that have been proposed to define and obtain explicit quantitative outcome-based measures of vulnerability, that is, adopting of a normative, welfarist, utility-based approach to measure vulnerability, but taking into account some kind of threshold like the poverty line employed by the FGT measures, so that higher levels of consumption above a given welfare threshold do not increase vulnerability.

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