Casos de uso

Our ultimate goal is to compute child productivity per day of farm labor. There are different ways to do this. First, in the specification where child and adult labor are perfect substitutes (eq. 1.4), γ_cis a measure of the productivity rate of children compared to adults. If we know the adult wage rate and assuming that the labor market equates the marginal productivity to the wage, then we can compute the child marginal productivity

18In this specification, we adjust the translog function to impose our hypothesis that the substitution between labor and other inputs is constant equal to 1. We provide robustness tests for that assumption.

by: w_c = γ_cw_a where w_a is the adult wage. However, this series of assumptions (perfect substitutes and perfect labor market) is doubtful.

In addition, we may not be interested in the marginal productivity but rather on the average productivity. Indeed, if marginal returns are decreasing, marginal productivity informs us on the production obtained with the last day of work. A cash transfer would aim to reduce substantially, and maybe even suppress, child labor. In order to achieve this, families would have to be compensated for a larger number of days and average productivity on those days is the relevant concept.

As a consequence, we will provide for each specification the average semi-elasticity of output with respect to days of child labor. More precisely, our estimates of equations (1.4), (1.5) and (1.6) allow us to compute the expected production in absence of child labor, using the actual number of days of child labor for each farm, based on the households’

use of the other inputs. We then compute for each household:

E_{Y cit}= logY^c_it(L_c= L^o_cit) − logY^c_it(L_c= 0)

L^o_cit (1.7)

where L^o_cit is the number of days of child labor observed in household i at date t. The numerator is therefore the predicted difference in the production (expressed in logs) between the situation where the child does not work and the situation where he works the actual number of days. E_{Y cit} is the average labor productivity of children in household i at date t, provided that all other inputs remain the same. Obviously, this can only be estimated for households that use child labor, but this is our sample of interest (in spite of the fact that we use all farming households for the estimation).

We then weight households by amount of child labor and average the individual semi-elasticities to obtain an aggregate measure of child labor productivity:

E_{Y c} = 1

Because adult productivity is a benchmark against which child productivity should be

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evaluated, we compute that as well. Adult on-farm labor is rarely null, so to compute the average productivity on a meaningful margin, we take as a base the 10th percentile of adult labor that is observed in our sample.¹⁹ The adult semi-elasticity E_{Y a} is computed as:

where L_a is the the 10th percentile of adult labor (38 labor days per year for a farm).²⁰

1.3.3 Inputs

The inputs that are included in the estimation are the following ones: adult labor, child labor, cultivated land size, use of organic and inorganic fertilizer, spending on pesticides, erosion of the plot, irrigation of the plot and productive assets. Non-household labor days are aggregated with household adult labor days (no non-household child labor is used on the farms). Several inputs such as child labor, fertilizers and pesticides have frequently null values, which raises a problem for our specifications in logs. In order not to restrict the sample to the households who have positive values of all inputs, which would lead to selection bias, we follow MacKinnon and Magee (1990); Burbidge et al. (1988); Pence (2006) by using a modified function of the logarithm that is defined in 0:

log^M(x) = log1 2

x +√

1 + x^2 (1.11)

This function behaves similarly to the log function when x is large. As a consequence, for all inputs that have large values, the estimated coefficient reflects the increase in the production (expressed as a percentage) associated to an increase by 1% of the input. Given that child labor is often equal to 0 in our data, we cannot use this approximation for the

19The estimated production function fits the data only for the range of adult labor that is observed.

We do not want to extrapolate outside of this range.

20More precisely, in this computation, we discard the observations with less than 38 adult labor days.

interpretation of the coefficient. The same holds as well for the other inputs that tend to be close to zero. The semi-elasticities of production with respect to labor are computed taking into account that the log^M function (instead of log) is used for the estimation. The details for these computations are provided in Appendix1.7.3.

In the data, we also have a non negligible number of households who declare a null production, despite non-zero inputs. This is due to disasters such as droughts and pests.

We choose to keep these observations with null production in order to avoid a selection bias. We therefore use the same modified function. Given that the expected value of output is always large, we consider our function to be well approximated by the logarithm function and interpret it accordingly (the effect of one additional unit of input is expressed as a percentage increase in the production).