Occupational Choice and Investments in Human Capital in Informal Economies

As defined in Schneider, Buehn, and Montenegro (2011), the shadow economy is “all market-based legal production of goods and services that are deliberately concealed from public authorities … to avoid paying taxes or meeting certain standards or complying with certain administrative procedures”.

Van der Sluis, Van Praag, and Vijverberg (2008) and Parker and Van Praag (2006) review the evidence about the effects of education on the returns to entrepreneurship and conclude that there exists a positive association, a relationship also found in Caliendo, Fossen, and Kritikos (2014) and Caliendo, Goethner, and Weißenberger (2020).

Similar figures can be obtained for alternative measures of the size of the informal economy across countries, like the share of vulnerable employment over total employment, according to the definition in the WDI (World Development Indicators, World Bank).

The definition of informality used is based on the productive characteristics of the occupations, according to which informal workers or entrepreneurs are those individuals who work in firms with less than five employees, irrespective of whether they contribute to social security systems, which corresponds to a more legalistic definition of informality. However, both ways of defining informality produce measures that are very much correlated.

Parker (2004), Hartog, Van Praag, and Van Der Sluis (2010), Block Hoogerheide, and Thurik (2011), Caliendo, Fossen, and Kritikos (2014), and Caliendo, Goethner, and Weißenberger (2020), among others, present evidence showing how education affects positively the returns to entrepreneurship.

Individuals know their innate ability at the beginning of the first period of their lives, and this characteristic is public information.

For instance, for a model economy with a period-length of 20 years (in which agents are born at age 20) the value t e S can be set to 1/4, averaging a period of time invested in post-secondary education of five years.

As described next, investing in skills in the first period is costly not only due to the forgone income when young, but also due to a direct cost c per unit of time spent to education.

Labor supplies of young individuals is denoted by adding the subscript indicating the stage of their life for these decisions (subscript 1 for young and 2 for old individuals). Hence, the notation for labor supplies becomes: l _1u , l _2u , l _2s . Notice that young individuals are not yet allowed to supply skilled labor since the investment in education takes place when young, so l _1s is not defined for this economy. Additionally, notice that the focus is on equilibria in which wages are constant over time, so w _s and w _u are the right notations for wages.

For instance, the production technology can take the form of a nested CES with perfect capital-skill complementarity: y = m γ F ( k , l u , l s ) 1 − γ = m γ [ min { b l s , k } ] α ( 1 − γ ) l u ( 1 − α ) ( 1 − γ ) .

The proceeds from taxation are dissipated.

The exact equilibrium occupational choices for each ability level will depend on the values of the parameters values of the parameters characterizing preferences (β), the technology for human capital formation ( t e S , θ, and the direct costs of education, c), the distribution of innate ability (μ _z and σ z ), and the technology for producing goods (γ, α and b, where b is the technical coefficient in a nested CES with perfect capital-skill complementarity such as y = m γ [ min { b l s , k } ] α ( 1 − γ ) l u ( 1 − α ) ( 1 − γ ) . Occupational choices will of course also depend on the exact functional forms of preferences and technologies. The key technological assumption for the results is that there is a sufficiently high degree of capital-skill complementarity in the production function of goods.

The LHS in (9) is a linear increasing and concave function of d, given a, m and the parameters τ , η . The RHS is increasing in d up to the level of optimal use of capital, k * ( m ) -which results from solving the unconstrained version of the maximization problem in (3)-, and for all d > k * ( m ) the LHS is constant. Since the objective function is also increasing in d, the demand for loans d (a, h; η, τ) can be found in the intersection between the LHS and the RHS.

This is a result of the shape of the technology for human capital formation (stated in Eq. (1)), in which for z → 1 the contribution of education to increase m is close to zero. Anecdotically, one can think in Bill Gates or Steve Jobs as two examples of highly productive and formal entrepreneurs that are college dropouts.

This is true as long as informal managers are not too able, that is, as long as they lie in the “middle” of the support for innate ability. This condition is likely to be fulfilled because both types of formal managers (skilled and unskilled) have higher levels of innate ability z, and therefore they lie closer to 1 in the support of z.

Let the remaining three cases be: (i) case 2, the order is: z ˆ U , W U , I , M , z ˆ U , I , M S , W , z ˆ S , W S , I , M , z ˆ S , I , M S , F , M , and z ˆ S , F , M U , F , M ; (ii) case 3, the order is: z ˆ U , W U , I , M , z ˆ U , I , M S , I , M , z ˆ S , I , M S , W , z ˆ S , W S , F , M , and z ˆ S , F , M U , F , M ; (iii) case 4, the order is: z ˆ U , W U , I , M , z ˆ U , I , M S , I , M , z ˆ S , I , M S , F , M , z ˆ S , F , M S , W , and z ˆ S , W U , F , M .

The analysis of the three remaining cases can be found in the Appendix.

Note that the change analyzed here is of moderate size in the sense that η does not become as low as to make the formal sector disappear, that is, the increase in the cost of enforcing contracts has to be such that an equilibrium with a positive mass of individuals in the six occupations (as under the conditions in Proposition 4.4) is still possible.

Notice for instance that W (a (z), m (z); η, τ) is increasing in η while W ( a ( z ) , m ( z ) ; 0 , 0 ) is independent of η.

Note that these comparative statics effects will trigger other of general equilibrium on the values for the rest of occupations. However, the changes in the values of formal managers and skilled workers are of first order and will likely quantitatively dominate.

Notice that Figure 10 omits considering the underlying distribution of z-types, which would be needed to properly account for the shares of individuals who choose one or the other occupation, educational level or sector. One way to easily incorporate in this figure the distribution of z is to assume an uniform distribution. However, the results hold true for other well-behaved (unimodal) distributions.

While the value for z ˆ S , W U , I , M is reduced, the value of z ˆ S , I , M S , F , M increases, leading to this result.