Sources of information

This research took as a source of information the National Household Income and Expenditure Survey [Spanish ENIGH] which is performed by the National Institute of Statistics and Geography [Spanish INEGI], whose objective is to provide statistics about the behavior (amount, origin and distribution) of income and spending in households. This is in addition to the occupational and sociodemographic characteristics of household members, and the house’s infrastructure and equipment. The data corresponding to the years 1994, 1996, 1998, 2000, 2002, 2004, 2006, 2008, 2010, 2012, and 2014 were used.²

Creating the pseudo-panel

In order to analyze income profile as a result of age, the LHC was taken as a theoretical reference point, which involves tracking information from one individual over time. However, it is difficult to obtain a series of consecutive observations of the same person, given that the ENIGH is a tool for transversal measurements. In an effort to solve this problem, ^{Browning et al. (1985)} propose the creation of a pseudo-panel. This method is based on the creation of n synthetic cohorts (groups of individuals) defined based on one fixed characteristic, for example, birth year, and for a constant interval. This allows for the tracking of behavior depending on the variables of interest for each cohort in successive surveys.

For the purposes of this research, 17 cohorts were created, defined by birth year of the head of household in intervals of five years. Cohort 1 is comprised of heads of household that were between 80 and 84 years old, that is to say, who were born between 1910-1914. This was followed until cohort number 17, with heads of household born between 1990-1994 and corresponding ages between 20 and 24 years old in 2014. The sample is restricted to heads of household whose minimum age is 20 years old and maximum age is 85 years old, given that before and after this age range there are few recorded observations.

Definition of variables

The principal variable in this study is income, given the importance that it has as a mechanism of economic security. Specifically, the behavior of monetary, work, and transfer income patterns are analyzed. Monetary income is the sum of: work income, comprised of subordinate or independent work, in addition to other jobs; property rentals, including income deriving from cooperatives, companies and businesses, and the leasing of tangible assets and finances; income from transfers, such as retirement, pensions and compensations, grants, donations, remittances, benefits from governmental programs, and the like; and other revenue streams. Incomes were deflated using the National Consumer Price Index database of 2014.

The control variables are: 1) Households with and without children. Within this, three groups are analyzed: a) with children exclusively under 6 years old; b) with children exclusively between 6 and 12 years old, and c) without children under 13 years old. And, 2) Formal education level. Three levels are established: a) low, with elementary school studies or less; b) middle, with middle school studies or incomplete high school studies; and c) having completed high school, a technical, bachelor’s or postgraduate degree.

Specifications and calculation of income profile during the life-cycle

In order to examine the income profile during the life cycle of Mexican households, a semiparametric model was estimated, being linear in two phases, following ^{Speckman (1988)}, and ^{Fernández-Villaverde and Krueger (2004}, ²⁰⁰⁷⁾. The semiparametric regression has two components: a parametric form, obtained from ordinary least squares, and a non-parametric form, derived from a Kernel function.³ The specifications are the following:

Y_it = π_i cohorte_i + π_t tiempo_t + m (edad_it) + ε_i (1)

Where Y _it represents household income, in cohort i and year t. The cohort and time variables are dichotomous for each cohort and year of the study, calculated in a parametric form. The residual ɛ _it is random and independent of the explanatory variables. Function m (age _it ) is a smooth function of age _it estimated in a non-parametric manner. To calculate it, the framework of ^{Gutiérrez et al. (2003)} is utilized, using local polynomials, based on the model Y _i = m (X _i ) + ɛ _i where X = age and Y is the dependent variable.⁴ The equation for an approximation of X ₀ can be defined as:

Where K _k represents a Kernel function that gives more weight to households with heads whose ages are near the values of X ₀ . Based on equation 2, for each X ₀ point an approximation m (X ₀ ) is calculated.⁵ To analyze household income patterns in this study, a Kernel Epanechnikov function is used with a zero-degree polynomial.

One of the problems that presents itself when calculating equation (1) is that the effects of cohort, time and age are linearly dependent, causing perfect multicollinearity by including all of the equation’s variables. Accordingly, to avoid this problem this study follows ^{Deaton’s (1997)} proposal and assumes that the dichotomous variables for each year t of the survey do not correlate to a tendency of time and the sum of dichotomous variables is zero. In this way, the proposed equation allows for the creation of artificial dichotomous variables based on dichotomies by year:

Where d _t is a dichotomous variable for each year, and is equal to 1 if the year is t and 0 in the opposite case. For this study, t =1 indicates the year of the first survey that was used, that is, 1994; t =2 corresponds to the second survey, 1996; up until t = n which refers to 2014.

Adjusting the data with equivalency scales

With the goal of calculating the effect of composition and size of household on income patterns, the data were adjusted using equivalency scales.⁶ Regarding this thematic, the scales created by the Organization for Cooperation and Economic Development [Spanish OCDE] have been widely used in the empirical literature. Accordingly, in the present work the most up-to-date scale offered by the organization is used, which involves dividing income between the root squared of the household size, due to the assumption that necessities increase less than proportionally with household size (^{OCDE, 2008)}.⁷

Sociodemographic characteristics of Mexican households over time

Mexico has seen important demographic changes over time. Based on data from the ENIGH (1994-2014), the dynamics observed for households shows an increase in family units with female heads of household, along with a decrease in number of members, and an increase in the average age of those female heads of household. In 1994, there were 19.2 million households; only 15.4% were headed by women and 85% were headed by men. In 2014, the percentage of female-headed households increased significantly, representing 25.7% of 31.6 million households, and therefore the percentage of male heads of household decreased to 74.3%.

Additionally, the average number of household members went from 4.6 in 1994 to 3.8 in 2014. This average has been less for female-headed households, in comparison to male-headed ones. Furthermore, the percentage of households with minors has decreased across time, though there are important differences according to the gender of the household head. The percentage of male-headed households with children younger than 6 years old or between 6 and 12 years old is greater than those with female heads, across all of the years being analyzed. Thus, as an effect of the increase in life expectancy, the average age of heads of household shows a rising tendency between 1994 and 2014. This highlights the fact that female heads of household are older than male heads of household by an average of between 5 and 8 years.

Another important factor that has a direct effect on income earnings is education. In Mexico, important gender gaps can be seen by education level; in 1994 around 30% of female heads of household did not have any level of formal instruction. Although this percentage has been decreasing, in 2014 it was still almost double the percentage of male heads of household without formal instruction. The highest level reached for the majority of heads of household is elementary school, and only a small percentage end up with bachelor’s degree or postgraduate studies. For example, in 1994 only 8 out of every 100 male heads of household and 4 out of every 100 female heads of household had completed higher studies.

The foregoing data gives a brief panorama of Mexican household dynamics over time. The description of these variables is important because it helps to explain income patterns. According to ^{Tepichin (2011)}, women’s participation in earning income is determined by the life cycle of the family unit: presence of minors, a partner, other women who help with domestic and care work, and adults who perform remunerated activities.

In this context the significant presence of female-headed households in Mexico may come with more vulnerability, given gender inequalities that are present both in public and private spaces, and to other factors such as household structure. Since female-headed households headed report fewer members, an important percentage have single parentage, and as ^{Buvinic states (1991)}, women may be taking on the totality of household expenditures. On the other hand, age is an important factor that also explains income patterns. The LHC establishes that people earn their highest income in middle age. Nonetheless, women’s work trajectories are distinct from those of men, and can involve an early retirement from the job market.

Evolution of income in Mexico

The evolution of household incomes in Mexico has been characterized by fluctuations influenced by the economic cycle. Between 1994 to 1996, a period of financial crisis, a fall in average household income stream was observed, to then show a mild recuperation in 2008. As a consequence of the global crisis, in 2010 another decrease was observed. From 2010 to 2014, a degree of stability in income levels was observed (^{INEGI, 1994-2014)}.

An initial approach to explain income patterns is to analyze its components. Table 1 demonstrates that the principal income source for Mexican households is work. Still, there are important gender gaps in terms of the percentage of income that female-headed households earn in this way, compared to what is seen for those with male heads of household. The widest gap was seen in 2000, when this percentage was lower by 20 points.

Another difference is observed in income from transfers: households headed by women obtain a higher percentage by this account in comparison to what is seen for men; this tendency is consistent across the years of analysis. It is important to note the increasing relevance of transfers as a source of income across time; in 1994 they represented 11.6% of the income stream for female-headed households, while in 2012 it made up 20.2% of that income.

For income earned from property rentals, an important asymmetry can also be seen, although in this case in favor of male-headed households, given that they earn a higher percentage by this means, than those headed by women. The foregoing leads to the thought that households headed by men have greater access to monetary assets and may be owners of certain capital goods.

Descriptive statistics demonstrate import gender asymmetries in terms of income sources that can impact household income patterns. The greatest inequality is seen in income earnings from work, which can be explained by factors such as lower education level, household structure, unequal distribution of household tasks, and even employment discrimination (^{Tepichin, 2011}; ^{Valenzuela, 2003}; ^{Salles and Tuirán, 2002}).

Income profiles for Mexican households

Below are presented the results for the calculation of the age effect on the behavior of income across the life cycle of households in Mexico. The main objective is to visualize the differences between female-headed and male-headed households, taking family structure and education as control variables, and to ascertain if both household types conform to the LHC.

Figure 1 shows income patterns for Mexican households. To obtain this, monetary income and three of its principal components were analyzed: 1) work; 2) property rentals, and 3) transfers. It can be seen that both monetary income and work income evidence an inverted U profile. Monetary income at the beginning (20 years old) and at the end (85 years old) of the life cycle is on average 4,500 pesos per month. The highest income level, slightly over 6,100 pesos per month, is reached between 50 and 52 years of age, the point at which it also begins to decrease. The average work income reaches its highest point between 45 and 50 years of age, but after this decreases significantly.

*Monthly amount in 2014 pesos adjusted with OCDE equivalency scales.

Source: prepared by the authors based on the ^{INEGI (1994-2014)}

Figure 1 Household Income Profiles* 

If the LHC indeed is directed to work income, the monetary resources obtained through transfers increase in relevance at advanced ages. In this way it can be observed that income from this avenue is low between 20 and 40 years of age, although it is high when the heads of household reach the age of 85, since it represents around 30% of household monetary income. This result coincides with that obtained by ^{Campos and Meléndez (2013)}, who found that income from transfers represents 30% around 70 years of age, and reaches approximately 50% for people at 90 years of age.

Finally, it can be observed that income by property rentals, that is to say, income originating from the possession of financial or tangible assets, is almost null across the life cycle in Mexican households. The amount of income for this rubric is low and has a relatively linear behavior.

Effects of family structure on income patterns

The inverted U profile established by the LHC is not met in every case, given that a variety of factors exist which affect income patterns. The presence of children (between 0 and 5 years old) in the household represents an increase in unpaid domestic and care work, given that they are completely dependent. This means that female heads of households devote less time to the labor market, and as a consequence it is predicted that the function for incomes from these households does not comply with what is established by the LHC.

a) Income profiles of households with children exclusively under 6 years old

Income patterns for female-headed households with children under 6 years old do not show an inverted U form, as demonstrated by Figure 3, part A, where the figures are flat; the income levels, both monetary and from work, are low and do not present notable variations across the life cycle. The highest level, slightly observable, is reached at an average of 43 years old, a lower age compared to that of the female-headed households in general that reach this point around 50 years old. With respect to income from transfers, they have a linear form and gradually decrease, though in terms of percentage, they continue to represent an important source of income for female-headed households.

*Monthly amounts in 2014 consistent pesos, adjusted by OCDE equivalency scales.

Source: prepared by the authors based on the ^{INEGI (1994-2014)}.

Figure 3 Income Profiles for Households with Children Exclusively Under 6 years Old by Head of Household Gender* 

In male-headed households, family structure appears not to have an effect on income patterns, as demonstrated by part B of Figure 3. Both monetary and work income form an inverted U shape, as established by the LHC. With respect to income from transfers, it is under 2% of monetary income at the beginning of the life cycle, but later tends to grow, until it ends up representing one fifth of monetary income.

The presence of minors in the household demands more time performing domestic and care work, usually done by women-a situation which limits their participation in the labor market. The foregoing suggests the necessity of supporting public policies that help balance work with family life, and of carefully incorporating redistributive policies. To this end, it would be recommendable, as proposed by UN Women (2018): to recognize care work as an important factor in social wellbeing and the functioning of the economy; to redistribute unpaid domestic and care work in an equitable way between men and women; and to reduce care work via national care-providing systems.

b) Income profiles for households with children between 6 and 12 years of age

Just like female-headed households with children exclusively under 6 years old, the results presented in Figure 4, part A, indicate that the profile projected in the LHC is not met by households with children between 6 and 12 years old, given that the income patterns have a flat shape.

*Monthly amounts in 2014 consistent pesos, adjusted with OCDE equivalency scales.

Source: prepared by the authors based on the ^{INEGI (1994-2014)}.

Figure 4 Income Profiles of Households with Children Exclusively Between 6 and 12 Years of Age by Head of Household Gender* 

The highest monetary income level is reached at 47 years of age, and for work income at 45 years old. Since a decrease in monthly amount is registered for both income types at the end of the life cycle, in terms of percentages, said reduction is minimal due to said income not showing important changes during the cycle. Additionally, income from transfers represents approximately 30% of the monetary income at the beginning of the life cycle, although it diminishes slightly at advanced ages, to ultimately represent around 23% of monetary income.

In the case of male-headed households, the presence of children between 6 and 12 years old does not have an effect either on income patterns; the inverted U shape maintains the same pattern as Figures 2 and 3, part B. The foregoing can be explained by the presence of a spouse or partner as part the household, which may mean double income, and further, allow the heads of household to stay for more time on the labor market. By contrast, in the majority of female-headed households, there is generally not a spouse that can contribute to the family income. In this sense, ^{Sánchez et al. (2016)} show that the presence in the household of another woman older than 14 years old increases the possibility of women integrating themselves in the labor market, and with it the possibility of paid work hours.

For households with children exclusively between 6 and 12 years old, having a better-defined income profile was expected, given that children of this age are not completely dependent. Nonetheless, in both cases, the income levels obtained for female-headed households are low and are not consistent with the LHC.

The results demonstrate that the income profile of female-headed households is affected in a significant way by household structure. In this context, households with children under 6 years of age are more vulnerable. Accordingly, it is important for Mexico to attend to the recommendation given by ^{OCDE (2017)} which asserts the necessity of performing an analysis of budgets for each Secretary and level of government, from a gender perspective, to gain a more effective visualization of gender differences in policies and programs, considering the differentiated impact that allocations have on men and women. Further, it is highly important to perform evaluations and accordingly to implement redistributive policies to ensure better allocation of public spending in favor of gender equality.

Under these circumstances, it would be a priority to attend to and offer resources to groups like female-headed households with minors, and to female heads of household of advanced age that find themselves in one-person households and whose income depends primary on transfers

c) Income profiles of households without children between 0 and 12 years old

Like the previous cases, the LHC appears to not be met by female-headed households without children under 13 years old, given that the shape of the monetary income function-if it presents an ill-defined highest point around 30 years old and after that begins to decrease-does not have an inverted U profile. At the same time, for work income a slight “hump” shape can be identified, though not sufficiently clear to confirm that it conforms to the LHC. Once again, the relevance of transfers for female-headed households is evident, given that at the end of the life cycle, the amount gained by this means reaches a point slightly greater than work income.

Another important result, demonstrated in part A of Figure 5, is that these households reach a higher level of monetary income, by between 70 and 90%, compared to what is registered for households with children only under 6 years old, and children between 6 and 12 years old, respectively. Similar findings are found by ^{Montes and Villagómez (2002)}, and although their analysis is not divided by head of household gender, they find that in households without children the income is higher than for families with children.

*Monthly amounts in 2014 consistent pesos, adjusted with OCDE equivalency scales.

Source: prepared by the authors based on the ^{INEGI (1994-2014)}.

Figure 5 Income Profiles for Households Without Minors Less than 13 years Old by Head of Household Gender* 

Although monetary and work income patterns in male-headed households without minors under 13 years old show a slight “hump” form, and are much more defined that that of female-headed households, they do not reach a concave form in its totality. In part B of Figure 5, it is evident that although the income amounts of these households are higher, a greater loss at the end of the life cycle is also registered; at this stage work income and income from transfers contribute the same percentage as monetary income.

Effects of education on income profiles

Gender differences are seen in various contexts, of which education is one. During the years analyzed in this study, it is shown that the percentage of female heads of household without any level of instruction is higher than that of male heads of household at the same time. It was also determined that the percentage of female heads of household that reached university level education is minimal. Thus, there is evidence that gender inequalities experienced at young ages affect future wellbeing in a significant way.

Various authors (^{Ceballos, 2018}; ^{Campos and Meléndez, 2013}; ^{Duval and Orraca, 2011}; ^{Fuentes and Villagómez, 2001)} have noted that income and savings rates are higher when the head of household has a higher education level. Accordingly, it is expected that households with the same level of formal education have a similar income profile, which conforms to what is proposed by the LHC. This section only makes reference to work income, given that a greater participation by women in the labor market is assumed, based on the rate of increase of their education level.

In Figure 6, part A, one can see that the female heads of household with high education levels (high school graduates or higher), come to have a work income of close to 6,500 pesos per month, at the beginning of their life cycle. This amount represents slightly more than double the income observed for a female head of household with mid-level education (partially completed middle school or high school), and more than triple what is earned by a female household head with a low education level (elementary school or less). The income forms a concave shape, although more open, in comparison with the income shape of male-headed households. The highest point is reached between 53 and 55 years of age, with high to medium levels of education, and between 50 and 53 years old, with a low level.

Upon analyzing the work income profile for male-headed households, in Figure 6, part B, it can be seen that this income is greater compared to female-headed households, from the beginning to the end of the life cycle, in all three levels of education. The case of households with a high level of education stands out, where the highest point is reached at 55 years of age, which is the same for female heads of household, but the amount of income calculated is greater by approximately 3,000 pesos per month compared to the maximum income earned by female-headed households.

*Monthly amounts in 2014 consistent pesos, adjusted with OCDE equivalency scales.

Source: prepared by the authors based on the ^{INEGI (1994-2014)}.

Figure 6 Work Income Profiles for Households by Level of Education According to Head of Household Gender* 

These final results are relevant because it was expected that the income profile of female-headed households would be similar to male-headed households when controlling for the same formal education level. Regardless, even when the female heads of household have a high level of education, their income is still lower across their life cycle in comparison to male heads of household. The foregoing suggests that there is horizontal and vertical segregation in the labor market that affects income patterns for female-headed households.

Accordingly, it is necessary to support the empowerment of women and to assure an equal remuneration to men when performing the same jobs. Furthermore, it would be opportune to incentivize policies that prevent school dropouts, in particular at the upper middle level, given what was observed in the descriptive analysis: the largest percentage of heads of household have elementary school as their highest level of study, and only a small percentage reach higher studies. As such, the graduation rate must be boosted for higher levels of education.