Child labor is a relevant problem in developing countries because it may have a negative impact on economic growth. Policy makers and government agencies need information to correctly allocate their scarce resources to deal with this problem. Although there is research attempting to predict the causes of child labor, previous studies have used only linear statistical models. Non-linear models may improve predictive capacity and thus optimize resource allocation. However, the use of these techniques in this field remains unexplored. Using data from Peru, our study compares the prediction capability of the traditional logit model with artificial neural networks. Our results show that neural networks could provide better predictions than the logit model. Findings suggest that geographical indicators, income levels, gender, family composition and educational levels significantly predict child labor. Moreover, the neural network suggests the relevance of each factor which could be useful to prioritize strategies. As a whole, the neural network could help government agencies to tailor their strategies and allocate resources more efficiently.
Child labor is a critical problem in developing
countries because it could negatively affect
economic growth
According to the International Labor
Organization (ILO), in Latin America this phenomenon
reached 12.5 million children and teenagers
between 5 and 17 years old in 2014
Child labor can not only lead to gaps among
countries but also within a country. In Peru, for
example, the child labor rate in rural areas is twice
as high as in urban areas
Table 1 shows a summary of the issues covered by previous research in this field. All these studies used traditional techniques; to the best of our knowledge, in this field there are few studies using modern techniques such as neural networks. For example, Rodrigues, Prata, and Silva (2015) used data from Brazil and decision trees to search for patterns in the variables explaining child labor. The objective of the present study is to compare the predictive power of traditional and modern models in regard to child labor (i.e., correctly identify those children who work). It is expected that our results will shed light on the difference between models in terms of predictive power. By identifying the antecedents to child labor and the technique with the best predictive power, we will be able to provide recommendations to the Peruvian government. 2
Classification problems such as the child labor issue can be addressed by several techniques, both parametric and non-parametric. Parametric techniques (e.g., discriminant analysis, the logit model) require the prior specification of a function (or model) that relates the independent variables (Xi) with the dependent variable (Y ). In practical terms, this function may be known grounded in theory or assumed. These techniques use observations of Y and Xi to estimate the parameters of the function. Once the parameters have been estimated, they can be used for prediction with new participants. One disadvantage of the parametric techniques is that they have a rigid structure (the mathematical function does not change and it only allows for estimating the parameters). Thus, these techniques may not be appropriate to represent phenomena that do not follow well-known mathematical functions.
In contrast, non-parametric techniques (e.g.,
artificial neural networks) do not assume a function a
priori but instead approximate the function based
on observation. Once the function has been
approximated, it can be used to predict new cases.
One relative advantage of these techniques is that
they can represent complex non-linear
mathematical functions. In other research arenas, this
flexibility of non-parametric techniques has, under
certain conditions, demonstrated the superiority of
its predictive power over that of parametric
techniques
Our research compares the logit model (parametric technique) with artificial neural networks (non-parametric technique) in the field of child labor. The application of these models for predictive purposes involves the following steps: • The sample is randomly divided into two subsamples. • The parameters of the model are estimated with one of the subsamples. • The predictive capacity of the model (number of hits over total observations) is assessed. • With these estimated parameters, prediction of the dependent variable for the other subsample is conducted. • The predictive capacity of the model (with the test data) is assessed. 2.1
The logit model is a method that uses
independent variables to estimate the probability of
occurrence of a discrete outcome in the dependent
variable
The logit model has a straightforward and closed functional form that is easily estimated using maximum likelihood methods (Lattin et al.,
Rodr´ıguez (2002) Emerson and Souza (2002) Sapelli and Torche (2004) Lavado and Gallegos (2005) Garc´ıa (2006) Gunnarsson, Orazem, and Snchez (2006) Alca´zar (2008) Rodr´ıguez and Vargas (2008) Rodr´ıguez and Vargas (2009)
2003, p. 475). The logit technique does not
assume restrictions on the normality of the
distribution of variables
The logit model is defined by the following function:
pi 1 pi ! Logit(pi) = Ln = ↵ + XiT + "i (1) where pi is the probability that an observation takes a specific outcome of the dependent variable, ↵ is the constant term; is the corresponding vector of the coefficients; and "i is the error term. 2.2
A neural network is, in a general sense, a
machine designed to model the way in which the
brain performs a particular task or function of
interest
According to their topology, neural networks
can be feedforward or feedback networks. In the
former, the mapping goes from an input to an
output layer instantaneously since there is no delay
between them. This type of network is
characterized by its lack of feedback which implies that the
neural network has no explicit connection between
layers
Another typology of neural networks is
related to the learning paradigm which distinguishes
between supervised learning and non-supervised
learning. The first implies that the knowledge of
the environment available to the teacher is
transferred to the neural network through training as
fully as possible
This research uses a Multilayer Perceptron
neural network with a back-propagation algorithm
which consists of applying a family of
gradientbased optimization methods to find the optimal
value of the weights based on minimizing the error
norm between the desired output and the output
calculated by the neural network
The concept of child labor varies from country to country depending on the cultural context. According to the ILO, child labor refers to a work that is dangerous and harmful to the physical, mental, or moral wellness of the child, interfering with his/her education.
In the case of Peru, the minimum age for a child
to be allowed to legally work is 14 years old, as
long as these activities do not harm their integrity
nor negatively impact their studies
According to the National Housing Survey, child labor between 6 and 13 years old in rural areas (67.5%) is twice as prevalent as child labor in urban areas (32.5%). However, in the range from 14 to 17 years old, the values are similar (49.7% and 50.3% for rural and urban areas, respectively). Another important issue is that child labor rates significantly differ between cities. For example, Huancavelica is the city with the highest rate of child labor with 79.0%, followed by Puno, Huanuco, and Amazonas with 69.0%, 65.0%, and 64.0% respectively. Trujillo has the lowest child labor rate, at about 5.0%, which is significantly lower than the others. Not surprisingly, the cities with the highest rates of child labor are also those with the lowest incomes per capita. Furthermore, according to the National Institute of Statistics and Informatics (INEI in Spanish), economic activity for females (63.3%) is considerable lower than for males (81.4%).
Based on the above paragraph, we included
variables capturing: 1) age and gender; 2) type of
residence area such as urban/rural, region, stratum,
and schooling available; and 3) socioeconomic
variables such as expenses, education of the
family head, type of housing, housing ownership, and
housing status (adequacy, coverage of basic needs,
sanitation). In addition, following
Data were collected from the Peruvian National Housing Survey (ENAHO) for the year 2014. We eliminated the data for the months of January, February and March to eliminate seasonality. The rationale is that those months are holidays in Peruvian schools and thus the probability of child labor is high but does not imply that children stop studying to carry it out. Data include children between 12 and 17 years old at the national level who meet the following criteria: 1) is the son/daughter of the head of the family, and 2) he/she has not yet finished school.
For analysis, we used logit and neural networks techniques to find the antecedents to child labor and to classify children according to the probability of becoming a worker. We used these two techniques to compare predictive power because a correct prediction may allow governments to correctly allocate resources to deal with this problem. The first technique is based on linear relationships, while the latter can manage non-linear effects. Thus, differences in their results are expected. In the case of the logit model, we randomly divided the full sample into 2 subsamples: 1) a training subsample consisting of 85% of the full sample, and 2) a test subsample made up of the remaining 15%. We used the training subsample to calibrate the model (i.e., estimate the parameters of the function), and the test subsample to assess the predictive power of these results. In the case of neural networks, we randomly divided the sample into 3 subsamples: 1) a training subsample (70% of the total data), 2) a validation subsample (15% of the total data), and 3) a test subsample (15% of the total data). We used the training and validation subsamples together to estimate the parameters of the model. To avoid overfitting and guarantee that the results of this stage could be generalized, we validated the predictive quality of the model with only the validation subsample every 1000 interactions. This process allows a better estimation of the weights of the network. Finally, we assessed the predictive power of the model with the test subsample. 4 4.1
We conducted a preliminary analysis including all 17 independent variables. Results show that only 9 variables were statistically significant (variables with coefficients with p-value less than 0.05) in explaining the variance of our dependent variable (WORK). The other 8 variables (p-values higher than 0.05) were not considered in the subsequent analysis given that they do not have any impact on the dependent variable. Retained variables are divided into 6 categorical variables: URBAN, AREA, STRATUM, OWN, ADEQ, and UNMET; and 3 continuous variables: EXPENSE, EDU HEAD, and SIBLINGS. We calculated the coefficients of the model using equation (1), where pi is the probability that child i becomes a worker.
We assessed whether assumptions of logistic
regression were met. Assumptions 1, 2, and 3 were
determined by the model and data collection. For
assumption 4, we conducted a linear regression
to obtain VIF values. All VIF values were lower
than 5 (the independent variable URBAN has the
highest VIF value at 2.274). Therefore, there is
no evidence of multicollinearity problems in our
model
Age (AGE) Education of the family head (EDU HEAD) Younger siblings (SIBLINGS)
Level of schooling of the head of the family (in years) Number of children under 5 years old in the family Ratio of the number of adults (18 years old or older) to the number of children (younger than 18 years old) in the family Ratio of the number of education centers to the number of schoolage children in the province of residence of the family Natural logarithm of the total monthly expense per family member Categorical Independent Variables 1 = If the child is male 0 = If the child is female 1 = If the residence of the family is located in the urban area 0 = If the residence of the family is located in a non-urban area 1 = If the child is the oldest in the family 0 = If the child is not the oldest in the family 1 = If the child presents school backwardness 0 = If the child does not present school backwardness 1 = North Coast 2 = Center Coast 3 = South Coast 4 = North Highlands 5 = Center Highlands 6 = South Highlands 7 = Jungle 8 = Lima Metropolitan Area 1 = More than 100,000 dwellings 2 = From 20,001 to 100,000 dwellings 3 = From 10,001 to 20,000 dwellings 4 = From 4,001 to 10,000 dwellings 5 = From 401 to 4,000 dwellings 6 = 400 dwellings or fewer 7 = Composite rural area 8 = Simple rural area 1 = Independent house 2 = Apartment in building 3 = Chalet 4 = Neighborhood house 5 = Shack or cottage 6 = Improvised housing 7 = Non-housing premises 8 = Other
1 = Rented 2 = Owned by the family, totally paid 3 = Owned by the family, as result of squatting 4 = Owned by the family, paying off a loan 5 = Given by the workplace of one of the members 6 = Given by other family or institution 7 = Other 1 = If the housing is inadequate 0 = If the housing is adequate 1 = If the housing has unmet basic needs 0 = If the housing has not unmet basic needs 1 = If the house does not have sanitation 0 = If the housing has sanitation values were over the value of 0.0038 and thus our model satisfied the linearity assumption. For the sixth assumption, we found 4 outliers of concern which were not considered in subsequent analysis. Results of the logistic model are presented in Table 3. Our model is statistically significant ( 2 = 2300.885, df = 25, p = 0.000), and explains between 33.2% and 47.8% of the variance in child labor.
In terms of predictive value, our model correctly predicted 82.61% of cases, with 55.80% of correct positive classifications (sensitivity) and 93.02% of correct negative classifications (specificity). Accordingly, our model has an efficiency (average of sensitivity and specificity) of 74.41% and a mean absolute percentage error (MAPE) of 17.39%. Although our model has an adequate overall predictive power, the Hosmer and Lemeshow goodness of fit test was significant ( 2 = 39.889, df = 8, p = 0.000) showing that it is poor at predicting the categorical outcomes. The reason for this finding may be the difference between sensitivity and specificity. Finally, coefficients (B) were found to be significant based on the Wald test. Table 3 also shows the standard error (SE) of the coefficients and their odd ratio (OR). We then assessed the model with our test subsample. Our model correctly predicted 80.64% of all the cases in this sample, with a sensitivity of 52.78%, a specificity of 91.88%, an efficiency of 72.33%, and a MAPE of 19.36%. 4.2
For purposes of comparison, we chose a simple
neural network. Accordingly, we used a hidden
layer with activation functions Hyperbolic
tangentsigmoidy, and an output layer with activation
functions Log-sigmoid. The value of weights and
bias are updated according to gradient descent
momentum and an adaptive learning rate. The
training parameters of the neural network were:
Maximum number of epochs to train: 40000, learning
rate: 0.01, momentum constant: 0.7, performance
goal: 10-5. These values were set following
current literature
The first neural network used the 17 proposed independent variables (inputs). With the training and validation subsamples we obtained the best neural network made up of 38 neurons in the hidden layer and 1 neuron in the output layer. This model predicted 88.26% of all the cases, with a sensitivity of 90.97% and specificity of 87.21%. The efficiency of the model was thus 89.09%, and the MAPE was 11.74%. When applying this model to the test subsample, it predicted 85.11% of all the cases, with a sensitivity of 90.02%, a specificity of 79.42%, an efficiency of 84.72%, and a MAPE of 14.89%.
In addition, by analyzing the weight of the inputs of the neural network, we ranked the independent variables from the highest to the lowest effect: AREA (7.7), EXPENSE (7.4), HYGIENIC (7.4), STRATUM (7.0), MALE (6.2), OWN (6.0), SIBLINGS (5.9), TYPE (5.9), OLD CHI (5.9), AGE (5.7), EDU HEAD (5.5), COMPO (5.5), ADEQ (5.1), DELAY (5.0), CENTER (4.9), URBAN (4.6), and UNMET (4.4).
The second neural network used only the 9 variables that were statistically significant in the logit
*p < 0.05, **p < 0.01, ***p < 0.001 B=Coefficients; SE=Standard error; OR=Odds ratio SS=Skipped for simplicity. (For categorical variables with more than 2 categories, there is a coefficient for each category. We are choosing not to report them all because our focus is the predictive power of the model.) model for a straight comparison. In this model, with the training and validation subsamples we obtained the best neural network made up of 30 neurons in the hidden layer and 1 neuron in the output layer. Our model achieved 84.45% of correct total predictions, with a sensitivity of 79.61%, a specificity of 86.34%, an efficiency of 82.97%, and a MAPE of 15.55%. When using our models parameters on the test subsample, it predicted 81.69% of all the cases, with a sensitivity of 78.86%, specificity of 84.23%, efficiency of 81.55%, and a MAPE of 18.31%.
For this model, the ranking of the inputs according to their weights is: AREA (12.9), STRATUM (12.6), EDU HEAD (12.4), SIBLINGS (12.3), URBAN (10.9), ADEQ (10.6), UNMET (9.7), OWN (9.5), and EXPENSE (9.1). 4.3
The results of the previous section are summarized in Table 4. Considering that the logit model used 9 variables (8 were not considered because they have no significant impact on the dependent variable), the neural network used these same 9 variables and the same instances to ensure a fair comparison. In addition, Table 4 shows the results of the neural network technique with the complete 17 variables to assess if this non-linear model could extract important information from those 8 variables without a linear impact on the dependent variable. This table shows that overall neural network technique performed better than the logit model. In fact, the neural network obtained the highest values of accuracy (correct total - positive and negative - predictions). Also, considering that it is more important to predict when a child has high probabilities of becoming a worker than to predict that a child will be non-worker, sensitivity stands as our most important metric when comparing models. By an inspection of Table 4, sensitivity of the neural network technique was superior to the values obtained from the logit model. In spite of these results, the logit model was superior in terms of specificity. However, specificity is a metric for correct predictions of non-workers, which is not relevant in our case. In addition, Figure 1 shows the ROC curve of prediction for these techniques. Overall, the results show that the neural network technique surpasses the logit model in predictive capacity of child labor (sensitivity). Indeed, this phenomenon may have a more complex structure than is assumed by the logit model. In consequence, the neural network (which adopts nonlinear relationships) could capture sources of variation that are not identified by the logit technique. An accurate prediction of this phenomenon could be used by policy makers and government agencies to design adequate strategies or to invest scarce resources efficiently to deal with this problem.
Also, our findings show that the neural network model with 17 variables performed better than the 9-variables models (logit or neural network). This result suggests that this additional set of variables capture an important variability in explaining child labor. In other words, the neural network model with 17 variables does not ignore information that is relevant to the prediction. This result could be used by decision makers to avoid discarding relevant factors when dealing with this phenomenon.
Another important result is that the neural network model shows that geographical indicators, income levels, gender, family composition and educational levels significantly predict child labor. These results are aligned with those of the logit model showing that stratum, geographic area, and housing conditions have a significant impact on our dependent variable. These results can be used to determine the relevance of each factor. In turn, this relevance-based ranking of factors could further help government agencies to better allocate their resources and implement their strategies to reduce child labor.
Finally, previous studies in this field have used linear statistical models to predict child labor. Our study shows that the use of computational intelligence techniques, such as the neural network, could provide better predictions, which leads to better decision making.