Presentación día típico del supervisor de acarreo

In this section we want to concentrate on policy functions connected to the educational mechan- ics in the model, in particular, we focus on the interplay of human capital investments, vivos transfers and the college decision. Human capital has an impact on several aspects in our model. Regardless of the college decision, it determines the likelihood for all households which pro- ductivity type they will draw (see equation (33)) in their respective qualification group. If the household decides to go to college, human capital also influences the likelihood of succeeding in graduating (see equation (31)). Finally, students have to spend time on studying, which is deducted from their time endowment during college (see equation (32)).

All functions are chosen such that it has no added value, should a human capital greater than one be achieved, which makes it the natural upper bound for hja. In addition, this implicitly sets

an upper limit for parents’ investments in human capital. Further, the substitution elasticity of the human capital function has a major impact on investment behavior. Following Cunha and Heckman (2007), we have chosen a function that exhibits a higher elasticity during primary education than during secondary education.

Furthermore, due to dynamic complementarity, high human capital can not be built up in a single period without investing in education before and after. If investments during primary education are insufficient, the resulting gaps in the subsequent secondary education phase can not be easily compensated by high investments. On the other hand, the fruits must be harvested during secondary education if they have been sown early on, since otherwise they will expire.33 These are roughly the mechanisms of human capital formation and they are also reflected in the policy functions of our model.

Figure 7 shows human capital investments during primary and secondary education as a function of parents’ cash-on-hand. While all other characteristics of parents and the human capital of their children are kept constant, parents differ with respect to their current idiosyn-

33_{In Appendix A.1 we give a more detailed overview of the six empirical facts of the literature on human capital}

(a) Investments of parents in primary education (b) Investments of parents in secondary education

Figure 7: Parental Investments in Primary and Secondary Edu.

Note: Age in both figures refers to model age of parents. Respective model age of kids is 2 and 14 in terms of real age.

cratic shock (yc) and their productivity type (kc).34 _{It is worth noticing, that the underlying}

investment level of the government is positive (ig_j > 0 for all j = 0, . . . , 3), so that a certain level of education is provided, even if parents do not invest additionally.

First of all, it is noticeable that given cash-on-hand investments in primary education are higher than in secondary. This is related to human capital being more malleable in this phase and coincides with both the data of human capital literature.35 In both periods, parents already start to invest with minimum cash-on-hand. Thereafter, investments gradually increase until a certain point is reached. As indicated, this upper bound comes from the fact that investments leading to human capital above a certain level are not worthwhile, as they neither increase the likelihood of drawing the better productivity type, nor complete college, or make studying less time-consuming.

Two other aspects in Figure 7 are interesting: (i) investments are decreasing after a certain level of income is reached and (ii) this is happening sooner for households with better financial conditions (kc=2 and yc=2). We have to work this out in two steps.

34_{For both shocks “one” stands in for the negative and “two” for the positive realization}

(a) Investments Low Productivity Parents in Sec- ondary Edu.

(b) Investments High Productivity Parents in Sec- ondary Edu.

Figure 8: Secondary Investments Given Abilities

Note: Age in both figures refers to model age of parents. Respective model age of kids is 14 in terms of real age.

Figure 8 represents parents’ investments (again ceteris paribus) as a function of cash-on- hand, given four different human capital levels of children. The acquired human capital (aec) level of 5 represents the upper bound described above. It is defined as the level at which, even with zero parental investments (given the current, positive investment level of the government), in the next period the highest reasonable human capital will be reached. Thus, for aec = 5 we have zero investments for all cash-on-hand levels.36 It should be said that this upper level is of a more theoretical nature and the fraction of households at this level will be close to zero in the calibrated model.

At the lower end of the human capital spectrum, parents’ investments also stay at zero, but for a completely different reason. We are in the secondary education period: the elasticity of substitution is low, but we have to invest so that the sown fruits do not expire. In order to explain the missing investments of parents, the government comes into play, because the level it provides is already sufficient. Last but not least - and this is the most important area for the calibrated version of the model - it is noticeable that more is invested in kids with higher human

36_{This will help us in the computation of the model in defining reasonable investment grids, which is further}

capital (aec = 4) than for the lower (aec = 3). It can be explained by dynamic complementarity: ∂2_f

j(hj, Ij)

∂hj∂Ij

> 0.

As the return on investments is higher, when the child is more able (e.g. due to higher invest- ments during primary education), the acquired human capital level has a positive impact on today’s investments.

(a) Vivos transfers (b) College Choice Probability

Figure 9: Vivos Transfers and the College Decision

Note: Age in both figures refers to model age of parents. Respective model age of kids is 18 in terms of real age.

Finally, we are able to bridge the gap between Figure 9 and Figure 7, which explains the hump-shaped course of human capital investments. Figure 9(a) shows parents’ transfers as a function of their cash-on-hand. Figure 9(b) shows the college decision probability (which will be explained in detail in Section 3.3) as a function of assets, which at that point is determined by parents’ vivos transfers. There are different phases to be distinguished: first of all, a certain asset level is necessary so that young households can generally afford to attend college. If this is exceeded, the college decision depends primarily on the skills of the respective household. But for extremely high cash-on-hand levels, the choice probability of attending college is de- creasing, which has a rather theoretical background and will play only a very limited role for the calibrated model:

The incentive to reach for higher education in our model is purely driven by the prospect on higher wages. However, if the household receives extremely high transfer payments from parents, work, and in turn education, becomes less important. Therefore, in Figure 9(b), the likelihood of going to college drops off at some point, and this also explains the drop in human capital investment in Figures 7 and 8: extremely rich parents know that they will later make large transfer payments and therefore invest less in the human capital their children.

Again, the fraction of these special cases in the distribution of the calibrated model will be negligible. The purpose for this description was to analyze the different model mechanisms very precisely.