International job search: Mexicans in and out of the US

Abstract

It is argued that migration from Mexico to the US and return migration are determined by international wage differentials and preferences for origin. We use a model of job search, savings and migration to show that job turnover is a crucial determinant of the migration process. We estimate this model by Simulated Method of Moments (SMM) and find that migration practically disappears, it goes down from 19 to 0.5%, had Mexico US arrival rates while employed. A lower decrease in migration, to 7%, occurs by an increase in Mexican wage offers. On the other hand, doubling migration costs reduces migration rates from 19 to 5%, while subsidizing return migration in $300 reduces migration rates only to 14%.

Appendix

1.1 Proof of Propositions 1 and 2

Proof of Proposition 1

At age t = T, V ^e _t (A _t , ω, k) is monotonically increasing in ω. This follows from the fact that the utility function is increasing in consumption and a higher ω increases consumption at time T. Then W ^e _T (A _T , ω, k) defined in is also increasing in ω. Now, functions V ^e _t (A _t , ω, k) and W ^e _t (A _t , ω, k) at t < T preserve monotonicity in ω. Thus the reservation wage property exists both for reservation and retention wages □

Proof of Proposition 2

If π ^k _t  < λ ^k _t , then W ^u _t (A _t , k) > W ^e _t (A _t , ω^*(A _t , k), k) and from the definition of retention wages we know that W ^e _t (A _t , ω^**(A _t , k), k) = W ^u _t (A _t  − c ^k, 1 − k).

Then I ^m _t (A _t , k) = 1 is equivalent to W ^u _t (A _t  − c ^k, 1 − k) > W ^u _t (A _t , k) and because of transitivity W ^e _t (A _t , ω^**(A _t , k), k) = W ^u _t (A _t  − c ^k, 1 − k) > W ^u _t (A _t , k) > W ^e _t (A _t , ω^*(A _t , k), k). Hence ω ^** _t (A _t , k _t ) > ω ^* _t (A _t , k _t ). Similarly, ω ^* _t (A _t , k _t ) > ω ^** _t (A _t , k _t ) is equivalent to W ^e _t (A _t , ω^*(A _t , k), k) > W ^e _t (A _t , ω^**(A _t , k), k) and because of transitivity W ^u _t (A _t , k) > W ^e _t (A _t , ω^*(A _t , k), k) > W ^e _t (A _t , ω^**(A _t , k), k) = W ^u _t (A _t  − c ^k, 1 − k). Hence, I ^m _t (A _t , k) = 0. □

1.2 Numerical solution of the model

As mentioned in the main body of the paper, the model is solved on a discretized state space. The table below gives further details of this discretization, based on Rendon (2006).

	Discretization of variables
	Assets	Wages
Original variable	A	ω
Discretized variable	A(i)	ω(j)
Gridpoints	i = 1,..., N A	j = 1,..., N w
Number of gridpoints	N A  = 251	N w  = 51
Lower bound	$\underline{A}=0$	$\underline{w}=50$
Upper bound	$\overline{A}=150,000$	$\overline{w}=20,000$
Gridsize	$\Updelta_{A}={\frac{\overline{A}-\underline{A}}{N_{A}}}=598$	$\Updelta_{w}={\frac{\ln\overline{w}-\ln\overline{w}}{N_{w}}}=392$

The discrete probability for a wage draw ω(j) is

$$ \widehat{f}\left( j,k\right) ={\frac{\Upphi\left( {\frac{\ln\omega (j)+\Updelta_{w}/2-\mu^{k}} {\sigma_{w}^{k}}}\right) -\Upphi\left( {\frac{\ln \omega(j)-\Updelta_{w}/2-\mu^{k}} {\sigma_{w}^{k}}}\right) }{\Upphi\left( {\frac{\ln \overline{w}-\mu^{k}}{\sigma_{w}^{k}}}\right) -\Upphi\left( {\frac{\ln \underline {w}-\mu^{k}}{\sigma_{w}^{k}}}\right) }}. $$

Wage as a function of age w _t (ω, k) is also discretized and becomes w(j, k, t) = ω(j) exp(α ^k₁ t + α ^k₂ t ²). Arrival and layoff rates are $q\left( k,t\right) ={\frac{\exp\left( \alpha_{q}^{0k}+\alpha_{q}^{k}t\right) }{1+\exp\left( \alpha_{q}^{0k}+\alpha_{q}^{k}t\right) }}, q=\{\lambda,\pi,\theta\}.$

The numerical solution proceeds in the following steps:

• 1. For t = T + 1 define the discretized value functions:

  $$ \begin{aligned} V^{u}[i,k,t] & =V^{R}[i,k,t],\hbox { and} \\ V^{e}[i,j,k,t] & =V^{R}[i,k,t], \end{aligned} $$

  where V ^R[i, k, t] is the discretized value of being retired:

  $$ V^{R}[i,k,t] =\max\limits_{m}\left\{ U\left( A_{s}(i)-{\frac{A_{s+1}(m)}{ 1+r}}\right) +(1-k) \psi +\beta V^{R}[i,k,t+1] \right\}, $$

  with $A_{{T_{F} }} + 1 = 0.$

• 2. Integration. Define the discretized expected values

  $$ \begin{aligned} W^{u}\left[i,k,t\right] =&\lambda \left( k,t\right) \sum_{j=1}^{N_{w}}\hbox{max} \left[V^{e}\left[i,j,k,t\right],V^{u}\left[i,k,t\right] \right] f(j,k)+ \left[1-\lambda \left( k,t\right) \right] V^{u}\left[i,k,t\right] ; \\ W^{e}\left[i,j,k,t\right] =&\left[1-\theta \left( k,t\right) \right] ( \pi \left( k,t\right) \sum_{l=1}^{N_{w}}\hbox{max} \left[V^{e}\left[i,j,k,t \right],V^{e}\left[i,l,k,t\right],V^{u}\left[i,k,t\right] \right] f(l,k) \\ & \left. +\left[1-\pi \left( k,t\right) \right] \hbox{max} \left[ V^{e}\left[i,j,k,t\right],V^{u}\left[i,k,t\right] \right] \right) \\ & +\theta \left( k,t\right) (\pi \left( k,t\right) \sum_{l=1}^{N_{w}}\hbox{max} \left[V^{e}\left[i,l,k,t\right],V^{u}\left[i,k,t\right] \right] f(l,k) \\ & +\left[1-\pi \left( k,t\right) \right] )V^{u}\left[i,k,t\right] . \end{aligned} $$

• 3. Compute the value function for the previous period

  $$ \begin{aligned} V^{u}\left[i,k,t\right] =&\max\limits_{m}\left\{ U\left( A(i)+b^{k}-{\frac{A(m)}{ \left( 1+r\right) }}\right) +\left( 1-k\right) \psi \right. \\ & \left. +\beta \hbox{max} \left[W^{u}\left[m,k,t+1\right],W^{u}\left[h\left( m,k\right),1-k,t+1\right] \right] \right\}, \\ V^{e}\left[i,j,k,t\right] =&\max\limits_{n}\left\{ U\left( A(i)+w(j,k,t)-{\frac{ A(n)}{\left( 1+r\right) }}\right) +\left( 1-k\right) \psi \right. \\ & \left. +\beta \hbox{max} \left[W^{e}\left[n,j,k,t+1\right],W^{u}\left[h\left( n,k\right),1-k,t+1\right] \right] \right\}, \end{aligned} $$

  where h(m, k) = {h |A(h) ≥ A(m) − c ^k > A(h − 1)}. The maximizers to these problems are m ^* = m ^*(i, k, t) and n ^* = n ^*(i, j, k, t); and the reservation wage is j ^*(i, t) = {j | V ^e[i, j, k, t] ≥ V ^u [i, k, t] > V ^e[i, j − 1, k, t] }.

• 4. Go to step 2. This process goes backwards and it is repeated until reaching period t = 1.

1.3 Sample selection and construction of variables

The first data set used in this paper is the Mexican Migration Project 124; the files used in this paper are the longitudinal files, which include 17,764 individuals. After applying our selection criteria, only males 15–45 years old who are not disabled or incarcerated, our sample reduces to 9,225 individuals, as seen in Table 5

Table 5 Sample selection (individuals)

.

The MMP 124 includes all individuals surveyed in the communities that reaches, which generates three types of observations: those who never migrate and provide their labor history in Mexico; those who migrate, return home, and provide their labor and migration history; and those who migrate, stay in the US, and have some family members in Mexico that provide part of their data. For these individuals, the MMP sends surveyors to the US and interviews those individuals to obtain their labor and migration histories. Consequently, the MMP only loses individuals that belong to households that migrated entirely to the US or to another community in Mexico. The longitudinal files of MMP124 are constructed by interviewing individuals and asking them retrospective questions about their migratory history and entire job search history. They are also asked about their first and last wages in both Mexico and the US. The major disadvantage of the MMP124 data set is the potential measurement error due to recall bias, as well as the fact that over time changes are due not only to individual changes, but they are also due to changes in the communities sampled. Our measure of job to job transition can also miss unemployment spells that lasted less than a year.

The second data set is a 10% sample of the 2000 Mexican Census. Here we are using the files containing 4.9 million observations on Mexican males. Once we restrict attention to individuals 15–45  years old and exclude disabled people we are left with 1.7 million observations, as shown in Table 5. ¹⁸ We obtain annual wage income multiplying by twelve the monthly income reported in the Mexican census and then dividing it by the PPP rate.

The third data set is a 5% sample of the US census (IPUMS data base), which has 234 thousand observations on individuals that claim to be born in Mexico. Once we restrict the sample to males 15–45  years old and exclude disabled individuals we are left with 134 thousand observations (see Table 5).

The fourth data set used in the paper is the ENEU 1999 first quarter to fourth quarter waves. ENEU is representative of urban Mexico. It includes a total of 495 thousand individuals. Once we restrict attention to males between 15 and 45 years old and exclude the disabled, we are left with 112 thousand individuals. ¹⁹ To measure unemployment, we consider employed only those individuals that answered to have done paid work in the previous week. We also considered employed individuals if they were not present at work and they claim to have been temporarily ill, or in vacations. Every other individual is considered not employed, including those out of the labor force. The unemployment rate used in the paper is the proportion of observations that are unemployed in the sample by age. The proportion of individuals exiting unemployment is obtained as the proportion of individuals that exit unemployment from one quarter to another by age. Then we obtained the weighted average of this measure for the year. The proportion of individuals losing their jobs is obtained as the proportion of individuals that lost their job from one quarter to another, then we obtained the weighted average for this measure in the year. With this information we estimate the annual transition probabilities. The major advantage of this data set is that transitions between employment and non-employment are obtained quarter to quarter at the individual level. The major disadvantage of the data set is that it only represents the urban population of Mexico.

The fifth source of data is the CPS 1999 January to December waves. They are a representative data set of the US population. It provides also with a rotating panel on employment status, employment transitions and wages of individuals. We only include in the study individuals that claim they born in Mexico, which in total are 7.5 thousand individuals. The sample used in the study includes only males 15–45 years old, which are not disabled, which let us with 3.4 thousand individuals. Individuals are considered employed only if they answered to have done paid work in the previous week. They were also considered employed if they were not present at work and they claim to have been temporarily ill, or in vacations. Every other individual is considered not employed. The unemployment rate is then calculated as the proportion of observations unemployed in the sample by age. The proportion of individuals exiting unemployment is obtained as the proportion of individuals that exit unemployment from 1 month to another by age. Then we obtained the weighted average of this measure for the year. The proportion of individuals losing their jobs is obtained as the proportion of individuals that lost their job from 1 month to another, then we obtained the weighted average for this measure in the year. With this information we estimate the annual transition probabilities. The major advantage of the CPS is that it provides with month to month transitions between employment and non-employment at the individual level. The major disadvantage is that the CPS potentially undercounts illegal Mexican migrants to the US.

Table 6 shows the number of periods that individuals appear in our different panels: the MMP124, ENEU, and the CPS. In MMP124 most observations are observed for more than 5 years. In ENEU, the individuals are distributed evenly among 2, 3 and 4 periods. In the CPS most observations are found 2–4 periods, while very few are observed for more than 5 periods.

Table 6 Balance of the panels (individuals)

1.4 Choice of sources

In principle, we can get all the information we need for this paper from the MMP124 data set. However, a comparison with the Mexican Census, the US census, ENEU and CPS shows that the data for wages, employment, job loss and exit from unemployment look very different, as Table 7 illustrates.

Table 7 Descriptive statistics

Available wages in the MMP124 are the first wage in the US, the last wage in the US and the last wage in Mexico. Wages in the US are transformed into 1,999 dollars using the consumer price index. They are first transformed into annual wage income depending on their periodicity. Wage that are reported for Mexico are first transformed into annual wages depending on their periodicity, then transformed into US dollars using the exchange rate in the given year, and, finally, transformed into 1,999 dollars by the consumer price index. All the wages come from the life files in the data set.

For wages we use Census data for both countries. We did not use ENEU data set for wages in Mexico, because this source only contains urban data, and we wanted to have a picture for the average migrant. We calculate wages from the ENEU and compare them to the wages from the Mexican census. Wages for ENEU where obtained form the wages reported in the survey, which were either monthly, biweekly, weekly or daily. They were transformed to annual income. Then divided by 9.7, which was the average exchange rate in 1999.

We use US census wages and not those of the CPS, to be consistent with the choice of data for measuring wages for Mexico. Additionally, most of the research on migration from Mexico to the US has used Census data. We compare wages for Mexicans measured in the CPS with wages measured in the US census. Wages for CPS where obtained from the weekly income reported in the survey and then multiplied by 52. In general wages in the US census are smaller than wages in the CPS Wage information from the MMP124 is very noisy, which could be related to recall bias, since these data are retrospective.

For employment rates and employment we can use the data from MMP124 life data set on occupations reported by the individuals. This is retrospective information on the employment history of the individuals. However, we observed that unemployment rates were smaller than expected which is due to the fact that the MMP124 is an annual data set, in which short spells of unemployment may be not reported. Thus, we prefer to use the employment surveys for Mexico and the US, ENEU and CPS.

1.5 Comparison with other sources

Our estimations of the migration rate are comparable to those of Chiquiar and Hanson (2005: 246). They show that the migration rate in 2000 for males Mexicans 16–25 years old was 17.58, which is above the MMP124 migration rate of 11%. For males 26–35 years old they estimate the migration rate at 15.49, which is below the MMP124 migration rate of 16%. Finally, for males 36–45 years old they estimate a migration rate of 12.21%, while the MMP124 migration rate is 14%. Our estimations of the unemployment rate seem higher to what has been reported in the literature, because we are including as unemployed individuals out of the labor force. Once we take into account this difference our numbers are comparable to those in the literature. Blau and Kahn (2007) report an unemployment rate for males in the US of 13%, and that 6% of Mexican males in the US are out of the labor force. Their estimations are based on the CPS 1994–2003 March waves. We report an unemployment rate of 19%, but this number includes individuals who are both unemployed and out of the labor force. We merge these categories to simplify our analysis.

Our estimations of probabilities of exit from unemployment and job loss probabilities are comparable to those shown by Calderon-Madrid (2000), once we take into account differences in sample and frequency reported. He shows that job loss in a given quarter of 1997 was 10.91%, among males and females between 14 and 77 years old in Mexico, while the exit rate from unemployment was 12.31%. In annual terms, job loss amounts to 30.66% and exit from unemployment to 34.59%. Our reported job loss is smaller and our exit from unemployment higher because we look at males 15–45 years old. If we use Calderon-Madrid (2000) sample selection rules for 1999 the job loss is equal to 33.73%, while exit from unemployment is 46.66% for 1999.

Card and Lewis (2007) show that the mean hourly wage for Mexicans in the 2000 US census was 12.89 dollars per hour for males 16–45 years old. Using our sample, which is different from their sample in that we exclude disabled individuals, generates an average annual wage income of $16,816 for that year. If individuals worked 52  weeks and 40 h per week, that annual wage income is equivalent to approximately 8.08 dollars per hour. We believe this implies that leisure choices are potentially important, since it is obvious that individuals must be working less than full time shifts. However, and in-depth analysis is beyond the scope of this paper and is left for future research.