and Nuñez, 2004]) compared to regional standards (the sixth highest in absolute terms from a total of 19 countries studied in Cunningham [2007: 32]).

Despite these widely acknowledged design shortcomings of the Colombian social protection system, no study has systematically provided a quantification of the magnitude of their distortive consequences. The next section provides an analytical framework to quantify such magnitudes.

# **3. Analytical Framework of the Interrelations between the Labor Market and Social Protection in Colombia**

By extending the partial equilibrium model developed by Levy (2007, 2008), this paper assumes a labor market made up of formal and informal workers, according to whether or not they receive legally-defined benefits, specifically those associated with social security. Workers are divided into four groups: formal salaried workers, formal self-employed workers, poor informal workers and nonpoor informal workers. For simplicity, this conceptual analysis merges poor and nonpoor informal workers into one category, but when applied to Colombia, the distinction between poor and nonpoor informal workers is resumed. In Colombia, this distinction –instrumented with a means-test index, Sisben–<sup>4</sup> determines whether or not households qualify as beneficiaries for certain assistance programs. As we will see below, income levels of formal workers also determine (small) additional social security contributions, but the high income threshold (four minimum wages) limits the size of this group in practice.<sup>5</sup> As a result, formal workers will not be differentiated by income or socioeconomic levels in the analysis.

The proposed theoretical setup is based on a traditional partial equilibrium analysis (see Albrecht, Navarro, and Vroman, 2009, for a recent review, and Kugler and Kugler, 2009, for an arithmetical representation of payroll taxes), in which the labor market reaches equilibrium when the marginal cost of work is equal to its marginal product. This constitutes the optimal solution to maximize both worker utility and the employing enterprises’ profit function. For an algebraic presentation of this kind of model, see Levy (2008). Suppose that this point of equilibrium reaches an ideal situation at points A and B of Figure 3, which will determine a labor distribution without unemployment of among formal salaried workers, formal self-employed individuals, and informal workers, ( _Lo_<sup>_A_</sup> _, Lo_<sup>_C_</sup> _, Lo_<sup>_I_</sup> respectively). The labor market efficiently assigns the work factor among the differing occupations and it is only supply and demand, and the availability of each type of occupation within that economy, that determines this assignation.

The economy can move away from this equilibrium for diverse reasons, among which the most interesting ones to analyze in this paper are: (i) the imposition of a minimum salary differing from “W,” the efficient level at which marginal costs and productivity are equal; (ii) the inclusion of labor benefits and their respective costs, “T”—that might be different for each kind of worker—and; (iii) for the workers’ different valuations of received benefits, “β.” Figure 3 shows the consequences of each one of them. The position of the minimum salary above “W” will determine the aggregate demand for formal employment, as well as its distribution between salaried and self-employed

> 4 Sisben, _Sistema de Identificación de potenciales Beneficiarios de Programas Sociales_ (System for the identification of potential beneficiaries of social programs), is an index that ranks families in six categories (1 the lowest, 6, the highest) according to a principal components related weighted average of housing conditions, access to public services, education and social security services, household demographics and incomes. Updated versions of Sisben excluded income and social security coverage in the construction of the index.

> 5 Formal workers earning more than four minimum salaries are only 5% of total formal workers in Colombia (Fedesarrollo, 2008).

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