How the wage-education profile got more convex: evidence from Mexico

A1 The Mexican employment survey (ENEU)

The ENEU (Encuesta Nacional de Empleo Urbano) is the Mexican employment survey collected yearly by the Mexican national statistical office, INEGI. It is available yearly from 1987 to 2004 and it covers only urban areas with municipalities being the primary sampling units. The sampling scheme has changed over time with a number of smaller municipalities having progressively entered the sample. The ENEU is a quarterly household survey with a rotating panel structure similar to the US Current Population Survey: households are interviewed for five consecutive quarters and in each quarter 20% of the households are replaced by new households that are interviewed for the first time. The survey reports detailed employment information on individuals at least 12 years old with several questions on occupation status, type and characteristics of employment, sector of main and secondary job, contract type, working hours, monthly earnings, unemployment status and duration, and social security taxes paid by the worker’s employer in the private and public sector. Importantly for the analysis in this paper, the ENEU accurately reports earnings for each individual in each of four consecutive quarters. For those paid by the week the survey transforms weekly earnings into monthly earnings by multiplying the former by 4.3. Similar adjustments are used for workers paid by the day or every 2 weeks. Hourly wages are computed as the ratio between monthly earnings and hours worked in the main occupation.

The definition of earnings in the ENEU refers to monthly earnings received from the main job net of all labour taxes and social security contributions paid in either public or private funds. The use of after-tax earnings to study the convexification could be problematic in the presence of changes in the tax system that affected some wage percentiles more than others.

Tanzi (2000) provides a comprehensive study of the changes in personal income tax rates between 1985 and 2000 in 17 Latin American countries including Mexico, and shows that all Latin American countries experienced a fall in the highest tax rate: between 1986 and 2000 the highest tax rate fell, on average, by more than 20 percentage points. We can take a further look at tax changes in Mexico by looking at the data directly. Yearly historical data on top marginal personal income tax rates are available from the Urban Institute and Brooking Institution Tax Policy Center,^[32] which collects the evidence from the World Tax Database.^[33] The data for Mexico show that between 1987 and 1990 the top marginal income tax rate dropped from 55% to 35%, it remained constant until 1998, and it then increased by 5% for next 3 years to be back to 35% in 2002. Therefore, it is unlikely that changes in taxation played an important role to explain the wage convexification, which happened in the decade of the 1990s when the tax rate was fixed at 35% with the exception of the last 2 years of the decade.

However, tax changes could have affected wages at the end of the 1980s when the top marginal taxation rate dropped from 55% to 35%. In particular, the high marginal income tax rate of 55% in 1987 could have affected real top wages and induced a redistribution effect from the top to the bottom of the wage distribution. Tanzi (2000) argues that the drop in the top marginal tax rate did not induce substantial distributional effects from the top to the bottom of the income distribution since Latin America taxation system is characterised by very high personal exemptions and deductions and very small or no taxes on capital gains and incomes from financial sources.

Shome (1999) provides a comprehensive discussion of all the details on exemptions, deductions and taxes on capital gains in Latin America in the decade of the 1990s. For Mexico Shome (1999) shows three important facts: first, in the 1990s the top marginal taxation rate decreased but personal exemption levels for the top income also decreased substantially falling from around 21 in 1986 to around 5 in 1997; second, corporate income tax decreased from 42% in 1986 to 34% 1997; third, taxation on capital remained low with capital gains taxed at normal income tax rates throughout the 1990s. Net of all exemptions, in 1986 one would have to have an income 21 times the per capita income of the country before being subject to the highest marginal tax rate of 55%. As discussed by Shome (1999), people who have incomes so high as 21 times the average per capita income are very few and if they do have such high incomes, the incomes probably come from untaxed sources or from sources that are difficult to identify. As a consequence, the very high taxation rate of 55% did apply to very few to almost no individuals, so that it hardly affected net wages.

A2 The Mexican education system and the construction of the education groups

The Mexican education system consists of four main cycles: pre-school, primary, secondary, and post-secondary education. Pre-school education is between age 3 and 6 and is provided free of charge. Primary education starts at age 6, lasts 6 years and has always been compulsory. Secondary education comprises two main levels: lower and upper secondary. Lower secondary lasts between 3 and 4 years, depending on the program. Upper secondary lasts 3 years. Both levels of secondary education includes an “academic” and a “vocational” branch that paves the way, respectively, to university and non-university education. In 1993 lower secondary education became compulsory. This policy change mainly affected rural areas with a large increase in the construction of schools and corresponding increasing attainment rates at lower secondary education in these areas. Post-secondary education comprises universities, 2 and 4-years technical institutes, and graduate education. By far the majority of undergraduate students are enrolled in universities and a very small proportion is enrolled in 2-years technical institutes. University takes 4–5 years and graduate education lasts between 2 and 4 years.

I have aggregated the schooling levels as follows: the “basic education” group includes those with up to uncompleted upper secondary education, the “intermediate education” group includes those completed upper secondary and up to uncompleted university education, and the “higher education” group includes those with completed university education or more. In the 1990s average attainment rates were above 90% at primary education nationwide; at lower secondary they were above 80% in urban areas and below 40% in rural areas. Since the ENEU only covers urban areas I group primary and lower secondary education into “compulsory basic education.” Finally, following Manacorda, Sanchez-Paramo, and Schady (2010), I combine the academic and vocational branch of secondary education by considering in the “intermediate education” group all that have completed any of the two branches.

B1 Household decision problem

The household’s decision problem model can be solved recursively by simple backwards induction from the last to the first period of adult life.

Step 1. Set an initial guess for the vector of skill prices [p₁, p₂, p₃] and assume that future prices equal current prices.

Step 2. Solve the optimisation problem in the last period of work life before retirement (a=a̅).

Define with Va¯Sch(jP, ja¯C, Aa¯, p(a¯), η, za¯) and with Va¯Work(jP, ja¯C, Aa¯, p(a¯), η, za¯), respectively, the conditional value function of sending the child to school and to work and denote with Wa_Sch(ja_P, Aa_, p(a_), η, za_) and Wa_Work(ja_P, Aa_, p(a_), η, za_) the initial guess for child lifetime utility as an adult conditional on having sent the child, respectively, to school and to work in the last period of coresidence. A̅ denotes the age of the parent in the first period of adult life.

Given Wa_Sch(.) and Wa_Work(.), Va¯Sch(.) and Va¯Work(.) take the following expressions:

(24)Va¯Sch(jP, ja¯C, Aa¯, p(a¯), η, za¯)=maxca¯{U(ca¯)+λβEza_Wa_Sch(ja_P,Aa_,p(a_),η,za_)}s.t.   ca¯=Aa¯(1+r)+wjP,a¯−FjC−Aa¯+1 (24)

(25)ja_C=(ja¯C+1)=ja_P (25)

(26)Va¯Work(jP, ja¯C, Aa¯, p(a¯), η, za¯)=maxca¯{U(ca¯)+λβEza_Wa_Work(ja_P, Aa_, p(a_), η, za_)}s.t.  ca¯=Aa¯(1+r)+wjP,a¯+wjC,a¯−Aa¯+1 (26)

(27)ja_C=ja¯C=ja_P (27)

where r is the fixed real interest rate on financial assets, F_jC denotes the fixed costs of schooling for child education level j^C and w_jP,a̅ and w_jC,a̅ are, respectively, parental and child wage at age a̅ given parental (child) education level j^P(j^C). λ denotes the degree of parental altruism and expectations are taken over next period shock to earnings, z. Equations (25) and (27) describe the evolution of child education that increases by one unit if the child is sent to school. The level of child education at the end of the last period of coresidence defines the (fixed) education level throughout adulthood (ja_C=ja_P=jP). For simplicity I do not report the credit constraints and the terminal condition.

Step 3. Solve the conditional maximisation problems in the third, second and first period of adult life.

In the third period child education is a choice variable. The conditional maximisation problems read:

VaSch(jP, jaC, Aa, p(a), η, za)=maxca{U(ca)+βVa+1(jP, jaC+1, Aa+1, p(a+1), η, za+1)}s.t. ca=Aa(1+r)+wjP,a−FjC−Aa+1ja+1C=(jaC+1)

VaWork(jP, jaC, Aa, p(a), η, za)=maxca{U(ca)+βVa+1(jP, jaC, Aa+1, p(a+1), η, za+1)}s.t. ca=Aa(1+r)+wjP,a+wjC,a−Aa+1ja+1C=jaC

where F_jC is the fixed cost of child schooling level j^C and Va+1(jaC+1,.) and Va+1(jaC,.) define, respectively, the expected value over the maximum between the conditional value functions of the schooling and work alternative in the next period given the decision of sending the child, respectively, to school or to work in the current period.

They take the following expressions:

   Va+1(jP, jaC+1, Aa+1, p(a+1), η, za+1)≡Eza+1 max[Va+1Sch(jP, jaC+1, Aa+1, p(a+1), η, za+1), Va+1Work(jP, jaC+1, Aa+1, p(a+1), η, za+1)]

  Va+1(jP, jaC, Aa+1, p(a+1), η, za+1)≡Eza+1 max[Va+1Sch(jP, jaC, Aa+1, p(a+1), η, za+1), Va+1Work(jP, jaC, Aa+1, p(a+1), η, za+1)]

In the second period the child is sent to compulsory basic education. The maximisation problem is given by:

Va(jP, Aa, p(a), η, za)=maxca{U(ca)+βVa+1(jP, 1, Aa+1, p(a+1), η, za+1)}s.t.  ca=Aa(1+r)+wjP,a−F1−Aa+1

where F₁ denotes the fixed costs of basic education and V_a+1(1,.) defines the expected value over the maximum between the conditional value functions of the schooling and work alternative in the next period given that the child has completed compulsory basic education in the current period:

   Va+1(jP, 1, Aa+1, p(a+1), η, za+1)≡Eza+1max[Va+1Sch(jP, jaC=1, Aa+1, p(a+1), η, za+1), Va+1Work(jP, jaC=1, Aa+1, p(a+1), η, za+1)]

where jaC=1 denotes completed basic education.

In the first period of adult life the child is in pre-school. Child education is normalised to zero. The parent solves the following maximisation problem:

Va_(jP, Aa_, p(a¯), η, za_)=maxca_{U(ca_)+βEza_+1Va_+1(jP, Aa_+1, p(a_+1), η, za_+1)}s.t.  ca_=Aa_(1+r)+wjP,a_−Aa_+1

Step 4. Compute the new initial guesses for Wa_Sch(.) and Wa_Work(.).

The solution of the model in steps two and three provides the complete set of value functions and optimal saving rules for any combination of the state space variables. The optimal value function in the first period of adulthood, V_a̅, provides a new initial guess for child lifetime utility. Denoting with ja¯C the level of education of the child at the end of the last period of coresidence, Va_(jP=(ja¯C+1), Aa_, p(a_)) provides the new initial guess for Wa_Sch(.) and Va_(jP=ja¯C, Aa_, p(a_)) provides the new initial guess for Wa_Work(.). Given the new initial guesses for Wa_Sch(.) and Wa_Work(.), I repeat steps two and three above.

Given the conditional value functions for the work and schooling alternative, the child is sent to school when the expected value of investing in schooling is at least as high as the expected value of sending the child to work, that is when the following condition holds:

VaSch(jP, jaC, Aa, p(a), η, za)≥VaWork(jP, jaC, Aa, p(a), η, za)  ∀  a=a_ed, ...a¯

where a_ed denotes parental age when child education becomes a choice variable.

Step 5. Repeat steps two to four until the following two conditions are satisfied:

||Va_Sch_Iter(jP, Aa_, p(a_), η, za_)−Va_Sch_(Iter−1)(jP, Aa_, p(a_), η, za_)||≤ε||Va_Work_Iter(jP, Aa_, p(a_), η, za_)−Va_Work_(Iter−1)(jP, Aa_, p(a_), η, za_)||≤ε

where ε is an arbitrarily small number and ||·|| denotes the distance between the conditional value functions in the first period of adulthood in two consecutive iterations.

B2 Computational algorithm

The solution of the model proceeds in the following four consecutive steps:

1. Take the value of the fixed real interest rate, r, the distribution of ability and of the idiosyncratic shocks, and make an initial guess on the vector of education prices, p̅≡[p₁, p₂, p₃]. Also take the initial distribution of assets at age a̅, and the distribution of education among the adults and the young.

2. Solve the household’s problem described in Section B.1 at the given prices p̅ and r. The solution gives optimal decision rules for education, consumption, saving, and parental bequests of financial assets.

3. Simulate the life-cycles of 10,000 agents who start with initial wealths given by the initial distribution of assets at age a. Each of the 10,000 simulated agents is exogenously matched with another agent who represents her child. The abilities of the parents and children in these matches are the same since the model assumes that ability is perfectly transmitted from the parents to the children. These matches are fixed across iterations so that the bequests of financial assets given by the parent in the match converges to the initial wealth of the child in the match. Aggregate the decisions of the 10,000 simulated agents to check market clearing conditions and update prices appropriately.

4. If updates were required in step (3), go back to step (2) and proceed with the updated guesses. Otherwise, exit because a fixed point of the algorithm has been achieved.