Breaking down the gap

Accurately measuring the GPG is relevant to assess how far we are from equality since it is a symbol of women’s position in the workforce in comparison to men. However, the unadjusted (raw) GPG is a complex indicator. Although it provides an overall picture of the difference between men and women salaries, it could mask the fact that this difference can be attributed not only to direct discrimination through ‘unequal pay for equal work’, but also related to many other factors equally or more powerful determinants of male-female earnings differentials, including social and historical factors, such as the concentration of one gender in certain activities ('segregation') ,and the ease of access to higher paid hierarchical positions (‘glass ceiling’) ^{(Karamessini and Ioakimoglou, 2007: 31)} . Therefore, being able to decompose the GPG and to determine the contribution of its different components is important to design appropriate policies for reducing it. In this regard, some efforts have been made, typically through regression models that are based on Mincer-type wage equations, Oaxaca-Blinder decompositions or further developments of this method, or the Wellington approach to estimate the GPG along time, among other proposals ^{(Karamessini and Ioakimoglou, 2007: 31; Chernozhukov et al., 2013: 2205} ; ^{Blau and Kahn, 2017: 789} ; ^{Töpfer, 2017}; ^{Amado et al., 2018: 357} ; ^{European Commission. Statistical Office of the European Union, 2018)}.

Traditionally, economists’ approaches to understand the GPG have rested on two sets of economic theories: human capital model and models of labor market discrimination^{(Grybaitė, 2006}: 85; ^{Ospino et al., 2010: 237)} .

The human capital model is usually used to analyze the so-called explained part of the GPG (adjusted GPG), the one that can be attributed to differences in qualifications. The basic idea is that every person has some form of human capital, i.e., the abilities and skills acquired through education, training and working experience. According to this model, if women have less human capital than men, they should rightfully receive lower wages ^{(Mincer and Polachek, 1974: S76} ; ^{Polachek, 1981: 60; Grybaitė, 2006: 85)} . On average, making this assumption is valid and there are numerous reasons to explain it. For instance, women tend to have lesser labor market experience because they work part-time and intermittently due to the traditional division of labor by gender, maternity and the hourly dedication to housework and childcare. Moreover, all of these factors result in fewer incentives to invest in education and training ^{(Becker, 1985: S33} ; Grybaitė, 2006: 85). It is important to point out, as several studies have already done, that human capital factors are based on broad assumption and does not take into account the fact that women and men cannot be studied as individuals independently from material and social frameworks since all decisions are made in a normative context where there are pre-established ideas about what women and men ought to do ^{(Grybaitė, 2006: 85)}.

Although the human capital model plays an important role in explaining the GPG, it does not account for the total gap. The remaining portion of the GPG, that is the unexplained part of the gap, is generally presumed to be due to labor market discrimination and refers to difference in salaries for workers that have the same abilities, experience and training. Therefore, it can be defined as direct discrimination since it accounts for ‘unequal pay for equal work’ ^{(Grybaitė, 2006: 85)} . There are several models aimed at trying to understand this portion of the gap, such as the statistical discrimination model proposed by Edmund ^{Phelps (1972: 659)} , other statistical models ^{(Becker, 1971}; ^{Bergmann, 1974: 103} ; ^{Aigner and Cain, 1977: 175} ; Lundberg and Startz, 1983: 340), or the overcrowding model developed by Barbara ^{Bergmann (1974: 103)}. However, none of these models, while helpful in understanding some of the reasons behind the unexplained part of the GPG, manage to fully encompass it or propose ways to resolve inequity.

Both contributions to the GPG have varied over time. For instance, in the USA, by 2010, conventional human capital variables (education and labor-market experience) that were an important part of the GPG decades before, have decreased in importance probably due to the reversal of the gender difference in education and the substantial reduction in the experience gap ^{(Blau and Kahn, 2017: 789)}. However, the persistence of an unexplained GPG suggests that labor-market discrimination continues to contribute. In 2014, the average adjusted GPG for the EU was 11.5% with a variation from 2.5% in Belgium to 24.2% in Lithuania. Notably, in many EU countries, the adjusted GPG is higher than the unadjusted figure. This means that women are expected to earn more than men due to better, on average, characteristics in the labour market ^{(European Commission, 2018)}.

Since the unexplained part reflects differences in salaries of subjects with supposedly identical characteristics aside from gender, it could be claimed to reflect direct discrimination ^{(Goldin, 2014: 1091)} .

To estimate the unexplained (adjusted) GPG, that is the pay penalty of being female is not an easy task since it is necessary to control for all relevant factors that are simultaneously correlated with salaries and gender ^{(Fortin et al., 2011)} , such as experience, educational level, abilities, position ^{(Goldin, 2006: 1} ; ^{Mandel and Semyonov, 2014: 1597} ; ^{Blau and Kahn, 2017: 789} ; ^{Töpfer and Brieland, 2022)} .

Machine Learning, a novel approach

As ^{Qin and Chiang (2019: 465)} point out, over the last 20 years there has been a revolution in statistical science given the possibility of ‘extracting important patterns and trends, and understanding “what the data says”’, so-called “learning from data” thanks to big data analysis and machine learning (ML).

Machine learning (ML) is a branch of artificial intelligence (AI) in which algorithms -that is sequences of statistical processing steps- are trained to find patterns in massive amounts of data in order to make decisions, inferences, and predictions. The resulting trained algorithm is the ML model.

There are four basic steps for building a ML model:

The whole process is an iterative one.

In this regard, ML methods could offer a new approach to estimate the adjusted GPG ^{(Karimian et al., 2019}; ^{Bonaccolto-Töpfer and Briel, 2022)} . In the literature, relevant variables to control for the estimation of the adjusted GPG are typically chosen based on economic reasoning. However, there is a limited understanding of the functional form, which includes identifying relevant interactions and polynomials ^{(Bonaccolto-Töpfer and Briel, 2022)}. Additionally, certain character skills may have a nonlinear impact on wages. Estimating the adjusted GPG becomes particularly complicated when there is a lot of heterogeneous data since numerous factors may contribute to pay differences between genders, and their relevance may vary depending on the wage level being considered. ML methods provide a more systematic approach to avoid arbitrary selection of variables ^{(Bonaccolto-Töpfer and Briel, 2022)}.

Being able to perform a GPG decomposition controlling simultaneously for several factors, even in heterogeneous samples could help clarify the different effect each of the variables have to diminish this gap, and globally understand how each of the components vary over time.

Undoubtedly, the most effective approach for assessing the level of discrimination would be to compare an individual's salary with what they would earn in the exact same conditions if they were of the opposite gender ^{(Alatrista-Salas et al., 2017)} . However, this method is unrealistic since it is impossible to observe someone's characteristics as the opposite gender. Nevertheless, by utilizing ML, we can simulate this scenario to some extent and that is what we attempted to do in this research.

In this article, we will show how through a ML model and based on specific information (gender, age, years of experience, number of employees at their company, position, etc.), provided by a population of 5,742 IT-related workers through an anonymous online survey conducted by a community called Sysarmy we can infer with certain degree of precision, this person’s salary. Based on this model, we will propose a decomposition approach for the GPG to find out the value for the unexplained GPG considering size sample disparity and the factors determinants of male-female earnings differentials in the explained part of the GPG.

Phase I. Characterization of the sample

Our original idea was to generate a salary predictor for IT-related workers. To do that, a ML model was developed from real salary data provided by an open and anonymous survey on IT-related workers. The answers were from a self-selected population, and therefore did not represent the entire IT population of Argentina, but it allowed us to analyze trends.

The salary values mentioned in the article correspond to Argentine pesos. Between December 2019 and 2020 —the period during which the information was collected—, on average, in Argentina, one US dollar was equivalent to 63 Argentine pesos. The inflation indexes for these months were 3.7% and 2.3%, respectively. This could bring some variability to the analysis because we did not have the date of each record to normalize the values if there were any salary adjustments.

Data preparation

First, we tried to detect and eliminate anomalies —that is, extreme values that did not make sense for salaries, number of employees, age, etc.— that were introduced maybe intentionally due to typing errors or misunderstanding of the questions. For instance, someone answered that their company had over a billion employees, clearly an outlier. Many other workers entered that their salaries were $1, perhaps unemployed people who still wanted to participate in the survey. A person indicated that he had been employed by the same company for 2000 years; it was probably someone who misinterpreted the statement and understood that he was being asked since what year he had been working for his current company.

From a total of 5,982 responses, we finally considered 5,766 in the present analysis, that is, 96% of the total. We were, then, faced with two types of data: numerical (e.g., years of experience and salary) and categorical, that is non-numerical (e.g., gender and province), which had to be transformed into numerical variables.

Numerical data. Despite the fact that it was possible to operate directly with these values, it is important to take into account that they do not necessarily follow a linear progression.

Regarding experience, for example, we might think that it does not have the same effect on salary to go from having no experience to having 1 year, that to go from having 10 to 11 years. That is to say, the more years of experience a person has, the less impact in the salary will have the addition of a new one. A good way to adjust this behavior is by using a logarithmic function. We could also apply logarithm to the salary values themselves because it is not the same to earn $1,000 more for someone who earns $10,000 than for a person who receives $200,000. It is important to note that monotonic transformations of the inputs do not affect the result in a tree model, like the one we used.

Categorical data. To transform non-numerical into numerical data, we created a matrix assigning binary values to each of the categorical characteristics.

Argentina is made up of 24 jurisdictions: 23 provinces and the Autonomous City of Buenos Aires (CABA). Since the cost of living in each jurisdiction is quite uneven, salaries tend to be too. Although people from different provinces responded to the survey, some of the districts had very few answers and that made generalization difficult. So, we decided to group them into larger blocks based on the average salary for each province and cultural similarities that we expected to cause their indicators to behave similarly. Based on this analysis, we divided the provinces as follows:

Therefore, for geographical data, we used one column for each region and assign each person a binary value for each column. It is important to note that, when grouping, information is lost on provinces that had public technology development policies such as Tierra del Fuego and San Luis.

This approach had the advantage of accounting for features that are not mutually exclusive, such as programming languages: multiple options could be selected in the question and that information could be reflected in the matrix. Consequently, a man from CABA, who uses Java and JavaScript in his work, will be represented by the values shown in Table 2.

Sample characterization

In order to adequately describe the original sample, we chose certain features of the Sysarmy form that we considered most relevant (some of which would later be used to interpret the explained part of the GPG, see Phase IV), and we analyzed the wage distribution according to these features: age, career, level of education attained, institution where the person studied, specific occupation within the company, number of employees in the company, number of dependents (workers they coordinate), years of experience, and geographical distribution.

Phase II. Creating the salary predictor

Then, we moved towards the construction of the model itself: from the actual data collected we wanted to build a model that would be able to estimate wages from new inputs. The construction of a model requires two steps, (1) training and (2) prediction. In the training stage, the model received data with labels that represent the ‘correct’ result, in this case, the salary. In the prediction step, the ‘correct’ result was unknown and the model had to predict it. It would be very easy to make a model that memorizes the ‘correct’ answers and gives them as outputs whenever it is asked, but despite being able to perfectly predict these values, this model would have little predictive capacity in the face of unknown data that do not fit exactly those from whom it learned.

So, what we needed was to train the model with a set of known data and evaluate another set of data, also known, but that the model had never ‘seen’. This would allow us to know how good the model was. Since we had relatively little data, we chose a technique called cross validation (leave one out method), which consists of dividing the data into several groups and training the model many times. At each of those times, a different group is excluded from the training and used for the prediction. In this way, if we cross-validate with five groups, we are going to train five different models (models A1 to A5), each with four fifths of the data, and we are going to ask each model to infer the data, that is predict the salary, of the remaining group. Thus, once the process is finished, we will have a prediction for each value, reached by the model that did not ‘see’ that data when training, and we could estimate how close to the ‘correct’ result the predictions were through a coefficient of determination (R²). For example, if one person earns $100 and the model estimates $110 and for another that earns $200 it predicts $180, then R² is 0.9 because it has a 10% error in each estimate. The best possible coefficient is 1, equivalent to say that all the predictions were correct.

Using XGBoost², a model based on decision trees that tends to work best in ML. We obtained R² for models A1-A5. The code is publicly accessible in Github ^{(Waisbrot, 2022)} .

Then, it was time to obtain the salary predictor (model A). We created it by training on the whole dataset and using the architecture that had been validated in the previous step (with the five groups A1-A5) ^{(Waisbrot, 2020)} .

Phase III. Adjusting the GPG

When sharing the salary predictor with the public through social networks to test how well it worked, some users noticed that changing gender from "male" to "female" but keeping all other variables exactly the same often led to a decrease in salary. We decided to explore this situation.

From here onwards, we worked only with the data of those individuals who had identified themselves as male or female (5,742 responses) and deliberately excluded the category "others" because, unfortunately, there were very few data (24 responses).

First, we calculated the unadjusted GPG from the actual salaries reported by the IT workers in the survey through comparing the median values ​​for the salary of men and women. Then, we tried to estimate whether there were differences exclusively by gender, that is the adjusted GPG.

To do that, we constructed the same structure as for model A and trained it with the same data but reversing the gender for each entry yielding five models (B1-B5) and ten expected outcomes: each person had an outcome with a model that accounts for their gender and one outcome with the model that include their gender reversed. Thus, we learned how much the model predicted it should pay, keeping all the variables the same (education, experience, etc.) except gender.

We also considered the difference in the sample size: we had six times more responses from men than from women. Accordingly, we created another model that compensated for this skew (model C).

Access to the code for the construction of each model is public in Github ^{(Waisbrot, 2020)} .

Phase IV. Analyzing the explained part of the GPG

To analyze the explained part of the GPG we used model A -as it considered the whole dataset- to establish which of the features the prediction model considered relevant, that is which were the more important salary predictors. With this information, we looked at what the variation in salary by gender was for each of these features in the original data set (characterization of the sample in Phase I). It should be noted that it is not enough just to look at the distribution of the data. We must also consider the number of responses in each group. If there were a large pay gap in a group where there are few people, its impact on the total gap would not be significant. Therefore, both variables were analyzed in each case through different methods of plotting numeric data.

Accounting for the sample size disparity

There were approximately six times more data from men than from women (4922 responses vs. 820 responses, respectively). This disparity brought with it a problem: the model was more unfair to women, i.e., it was less penalized when making a mistake with women. To compensate for this asymmetry, we built model C.

Model C architecture was similar to that of model B (gender reversal) but in order to train it, we "cloned" each woman five times so that each of them was worth six. By giving more "weight" to the data collected from women, the model became fairer, equally penalizing errors for men and women. Thus, the adjusted GPG decreased from 6.92% to 5.77%. Why do we say that the model is fairer? Because if we use it to estimate the salary a woman should receive in a company, it will show that, instead of paying her 6.92% less, we should pay her “only” 5.77% less than men. There is still a gap due to gender alone, but now it is smaller.

Salary predictors: the explained part of the GPG

To estimate salaries, the prediction model A takes as main characteristics years of experience, degree, number of employees in the company, profession, age, level of education attained, college they attended, whether they had finished their degree, and number of people that person has in charge (Figure 3) .

Since these characteristics seem to be the most important contributors to a person's salary, we decided to analyze them for the original sample data to better understand the explained part of the GPG.

Features that significantly contribute to de GPG

Features that do not significantly contribute to de GPG