Robustness Checks and Threats to Identifi cation

turns to documented and undocumented migration experience that are similar to those in Column 2. In Column 5, when we add relevant experience, we again fi nd a large and statistically signifi cant extra return to a year of relevant experience 0.033. Add- ing relevant experience cuts the coeffi cient on documented experience by more than half from 0.047 to 0.023, and it is now imprecisely estimated. Even in this specifi ca- tion, we continue to estimate a signifi cant return to undocumented migration experi- ence of 0.014. These results suggest that the extra return to legal experience might be due to the fact that documented experience is more likely to be job- relevant than undocumented experience. Indeed, summary statistics reveal this to be the case. On average, among migrants with some undocumented migration experience, 30 percent of undocumented migration experience was relevant for their current occupation in Mexico. By contrast for the average migrant with some documented migration experi- ence, about 56 percent of their documented migration experience was job relevant. Taken together, the results in Table 10 suggest that the relationship between docu- mented migration experience and earnings back in Mexico is stronger than the rela- tionship between undocumented migration experience and earnings, but the impreci- sion of our estimates prevents us from drawing fi rm conclusions under our preferred specifi cation with community fi xed effects. The data also suggest that this disparity may be related to the importance of relevant job experience. Furthermore, there ap- pears to be a signifi cant degree of heterogeneity in the returns to documented migra- tion experience. Short- term agricultural visas do not appear to offer many opportuni- ties for skill upgrading compared with other forms of legal experience. Obviously, our analysis here does not take into account the endogeneity of legal status, and it could certainly be the case that more complicated patterns of selection into documented and undocumented migration are driving these results. A full exploration of such issues is beyond the scope of this paper, but the patterns documented here are suggestive of the importance of legal status in shaping the returns to work experience. It is also note- worthy that even when legal status is taken into account, job- relevant experience still appears to be an important channel.

E. Robustness Checks and Threats to Identifi cation

1. Alternate Specifi cations In Table A4 of the Appendix, we present some alternate specifi cations that test the robustness of our fi ndings to the inclusion of alternate control variables or specifi ca- tions. Our results appear to be robust to the inclusion of more fl exible controls for age, education, and past Mexican work experience. We also check to see if the returns to migration experience vary depending on the migration rate out of a particular commu- nity. We fi nd a slightly smaller return for individuals from high- migration communi- ties, but this interaction effect is not statistically signifi cant. 2. Self- Employment and Business Ownership In our preferred specifi cations, we restrict the sample to exclude workers who are self- employed or own businesses. We have done this in order to simplify the inter- pretation of our results, since the relationship between migration experience and the outcomes of business owners is potentially more complex than the standard case. In addition to building human capital, past migration also might allow individuals to overcome credit constraints and either start new businesses or fi nance capital invest- ments in existing ventures Mesnard 2004. In this section we explore the robustness of our main results to the inclusion of these individuals in the sample. This is particu- larly important in a country like Mexico, which features an exceptionally high self- employment rate. To carry out this robustness exercise, we defi ne a new sample using the same cri- teria as our main sample, but now we include self- employees and business owners. As before, we exclude those who are not in the labor force, trim top and bottom one percent of monthly income observations, and trim the top one percent of migration experience observations. It is important to distinguish entrepreneurs, who own and make substantial capital investments in a business and may hire other employees, from the larger category of the self- employed, which may include informal workers, and those with small, subsistence enterprises. The MMP survey directly asks individuals whether they own a business, and this question likely includes both self- employees and entrepreneurs. However, we can learn something more about the nature of the businesses owned by looking at the MMP’s occupation question. Several occupation categories are clearly linked to entrepreneurial business ownership factory owners, owners of a service establishments, entrepreneurs, retail business owners. We defi ne someone as being an entrepreneur if they are engaged in one of these occupations. We defi ne someone as being self- employed if they are an entrepreneur or if they own a business of any kind. Table A3 in the appendix presents summary statistics for this sample. The percent of individuals in the entire sample who have ever migrated is similar to that in our main sample 28 percent. Coincidentally, about 28 percent of the sample is also self- employed or owns a business. However, only about 6 percent of workers are engaged in entrepreneurship based on our defi nition. The successive pairs of columns of Table A3 focus on mutually exclusive subsamples: wage workers not self- employed, self- employed but not entrepreneurs, and entrepreneurs. There are very large differences in the unconditional incomes of these three groups, with the self- employed earning incomes that are 17 percent higher than those of wage workers, and entrepreneurs earning about 42 percent higher incomes. In part this refl ects differences in demo- graphics, as self- employees and entrepreneurs tend to be older and have higher levels of education. If we look only at the return migrants in the three groups, we see that there are clear differences in average accumulated migration experience across these groups. Whereas return migrants who are paid employees have accumulated about 2.71 years of experience on average, those who are self- employed have accumulated about 3.30 years on average, and those who are entrepreneurs have accumulated about 4.17 years on average. In Column 1 of Table 11, we replicate our preferred basic specifi cation Column 3 in Table 3 using the sample that includes the self- employed and entrepreneurs. Here we estimate an average return of about 2.1 percent per year of migration experience, which is almost the same as our estimate without the self- employed. In Column 2, we modify the specifi cation to include a dummy variable for Self- Employment this includes entrepreneurs and nonentrepreneurial self- employees. We also interact this Self- Employment dummy with the U.S. dummy and migration experience to allow for different patterns of selection into migration by self- employment status and different estimated returns to experience across these groups. The coeffi cient on USExp now rises to about 0.024, and there appears to be a lower return to migration experience for the self- employed, with the coeffi cient on the interaction term SExUSExp estimated to be −0.010. These coeffi cient estimates still suggest a sizable extra return to migration experience for the self- employed 1.4 percent per year, although this is smaller than the large return for paid employees 2.8 percent. In Column 3, we take the specifi ca- tion in Column 2 but add a dummy for Entrepreneurship, and interact this dummy with US and USExp, thus fl exibly allowing for different returns to migration experience across all three groups. Interestingly, we fi nd that that the extra return to migration Table 11 Regressions including the Self- Employed and Entrepreneurs 1 2 3 USExp 0.021 0.024 0.024 0.005 0.007 0.007 SExUSExp –0.010 –0.014 0.009 0.010 EntrexUSExp 0.022 0.018 US –0.085 –0.063 –0.066 0.022 0.026 0.026 SExUS –0.087 –0.051 0.048 0.051 EntrexUS –0.146 0.099 SE 0.195 0.143 0.020 0.022 Entre 0.225 0.044 Age 0.038 0.035 0.035 0.004 0.004 0.004 Age2 –0.041 –0.038 –0.038 0.005 0.005 0.005 Educ 0.055 0.054 0.054 0.002 0.002 0.002 Married 0.056 0.051 0.051 0.025 0.025 0.024 Observations 8,521 8,521 8,521 R 2 0.344 0.358 0.363 Note: Stars signify the following: signifi cant at the 0.01 level, signifi cant at the 0.05 level, signifi cant at the 0.1 level. Standard errors are reported in parentheses. All columns contain MMP community effects which subsume survey time effects, as well as controls for years of education, marriage, and a quadratic in age. experience appears to be large for paid employees and entrepreneurs 2.4 percent and 3.2 percent, respectively, but is smaller for nonentrepreneurial self- employees about 1 percent. Taken together, the results in Table 11 tell a story that is quite consistent with the results from the basic sample. When we include the self- employed and consider our basic specifi cation, we estimate a coeffi cient on USExp that is nearly identical to the basic estimate. When we allow the for different returns to migration experience among paid employees, self- employees, and entrepreneurs, we fi nd that paid employees and entrepreneurs appear to face similar returns to migration experience, but the nonentre- preneurial self- employed face a smaller return. 3. Employment and Labor Force Participation Our results describe the relationship between migration experience and earnings for the group of individuals that are observed working and earning income at the time of the MMP survey. We have ignored unemployment and the labor- force participation decision, and this could induce sample selection bias in our estimates. To give just one possible scenario for bias, suppose that return migrants with several years of migration experience are less likely to be employed than those with less experience. This could arise if high- experience return migrants have accumulated more assets and are more likely to choose not to work and live off of their savings. If this is the case, then the high- experience return migrants might only decide to work if they receive particularly high income draws in Mexico, inducing a positive correlation between migration ex- perience and observed income. In the following analysis, we defi ne our sample to be all male household heads, aged 18–65, observed in Mexico, with nonmissing demographic and migration vari- ables. This differs from our basic sample in that we now include those who are un- employed and out of the labor force, as well as those who are self- employed. This sample also includes individuals who are working but do not report an income value. Since income is not observed for many people in this sample, we no longer drop the top and bottom 1 percent of income observations. However, as before, we drop the top 1 percent of the migration experience distribution. Return migrants have a slightly higher employment rate than nonmigrants 0.948 vs. 0.943, but they are more likely to be unemployed 0.024 rate vs. 0.014. The relevant exercise for our purposes is to compare high- experience migrants with low- experience migrants. In Table 12, we regress an employment dummy on the set of regressors used in our basic earnings specifi cation Column 3 in Table 3. The results in Column 1 suggest that while re- turn migrants are more likely, on average, to be employed, there is a negative and statistically signifi cant relationship between years of migration experience and the probability of employment. A one- year increase in migration experience is associated with a decline in the employment probability of about 0.004. Compared to the base nonemployment probability of about 0.055, an extra year of migration experience is associated with a 7.3 percent increase in the nonemployment probability. This relation- ship is even larger if we restrict our attention to prime age workers. In Column 2 of Table 12, we again replicate this employment regression for individuals who are no more than 40 years old. In this sample, a one- year increase in migration experience is associated with a decline in the employment probability of 0.007. As Columns 3–4 demonstrate, a similar pattern holds for the probability of unemployment, conditional on labor force participation. If we had a valid exclusion restriction, we could jointly estimate the parameters of an employment equation and an income equation. Unfortunately, we do not believe that such a valid restriction exists in this case. However, we argue that while return mi- grants with more experience are less likely to be employed, the selection bias induced by such a correlation is likely to be minimal. First, note that the absolute difference in employment probabilities is still quite small. A 30- year- old individual with 0.75 years of migration experience approximately the 25th percentile of the migration experi- ence distribution is predicted to have an employment probability that is very close to one. By contrast, if the same migrant had four years of migration experience 75th percentile, we would predict an employment probability of about 0.986. It seems unlikely that such small differences could be driving the results. Although we do not have suffi ciently rich data to identify the degree of self- selection bias that arises from these differential employment rates, we can learn some- thing about the magnitude of this bias that would result under different assumptions about the degree of selection into employment on the basis of unobserved skill. In Figure 2, we estimate the return to migration experience under different assumptions about the degree of selection into nonemployment. That is, we assume that the income of those who are not working would differ from the earnings of observationally equiv- alent workers who are working by some log- income penalty for instance 0.25. Then Table 12 Regressions Explaining Employment and Unemployment Employed Employed Age ≤ 40 Unemployed Unemployed Age ≤ 40 USExp –0.004 –0.007 0.003 0.007 0.001 0.003 0.001 0.003 US 0.008 0.004 0.002 –0.008 0.007 0.006 0.005 0.005 Age 0.019 0.007 –0.005 –0.002 0.002 0.005 0.001 0.004 Age2 –0.028 –0.011 0.006 0.004 0.002 0.008 0.002 0.006 Educ 0.001 0.000 –0.001 –0.001 0.001 0.000 0.000 0.000 Married 0.020 0.011 –0.008 –0.007 0.008 0.006 0.005 0.005 Observations 13,437 5,966 12,968 5,934 R 2 0.114 0.040 0.037 0.050 Note: Stars signify the following: signifi cant at the 0.01 level, signifi cant at the 0.05 level, signifi cant at the 0.1 level. Standard errors are reported in parentheses. All columns contain MMP community effects which subsume survey time effects. we do the following: 1 We regress Mexican income on our standard set of regressors for the subsample with observed income. 2 Using the resulting coeffi cient estimates, we predict income for the observations in our larger sample with missing income data either because of nonemployment or nonresponse. Let ω i represent the predicted value for individual i. 3 We modify the predicted values of those who are unem- ployed by subtracting off some amount that refl ects an assumed degree of negative self- selection bias. For example, if we assume a log- income penalty of 0.25, we would take ω i − 0.25 as our predicted log- income level for someone who is not employed. 4 We run our basic regression again, taking the predicted values as data for the observa- tions who are not employed or who have missing income data. Figure 2 plots how the estimated coeffi cient on USExp plotted with the 95 percent confi dence bands would change as the assumed nonemployment penalty ranges from 0 to 2. Without any assumed penalty, we estimate a return to migration experience of about 0.027. Increasing the assumed penalty decreases the estimated coeffi cient, as we would expect. However, even if we assume extreme differences in the incomes of the employed and nonemployed, the data would still suggest a substantial return to migra- tion experience that is in line with our previous results. For example, if the penalty is a full log point different, we would estimate a coeffi cient of about 0.023. Even under the extreme assumption of a full two log point difference, we would still estimate a Estimated Return to Migration Experience Assumed Income Penalty for those not Employed –0.005 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.5 1 1.5 2 Figure 2 Estimates with Imputed Data for those without Income Note: The dashed lines present the bounds of the 95 percent confi dence interval associated with each point estimate. statistically signifi cant coeffi cient of 0.019. Our conclusion is that self- selection into employment does not explain an economically signifi cant fraction of the return to migration experience. 4. A Comment on Persistent Shocks and Selective Return Migration One possible explanation for the correlation between accumulated migration experi- ence and earnings involves persistent wage shocks and selective return migration. Consider a model with the following elements. Suppose that individuals receive ran- dom wage offers each period in both the United States and Mexico, and that these wage rates persist if accepted. In any cohort of new migrants, there will be some with relatively low wage offers and others with relatively high wage offers. Suppose that individuals stay in the United States until they receive a wage offer in Mexico that exceeds some reservation wage, which is an increasing function of their U.S. wage offer. If these assumptions hold, then individuals with high U.S. wage offers will stay abroad for a longer period of time than those with low wage offers, because it will take more time for them to randomly draw a Mexican wage offer that exceeds their reservation wage. Furthermore, the Mexican wage offers that induce these high U.S. wage migrants to return will necessarily be higher than the wages accepted by those who were less lucky in the United States. Such a model would then predict a posi- tive correlation between accumulated migration experience and the earnings of return migrants, even without skill upgrading or permanent differences in skill. While persistent wage shocks and selective return migration could theoretically produce a positive relationship between migration experience and Mexican earnings, we believe that this is an unlikely explanation for the patterns that we observe in the data. Indeed, such a model would be inconsistent with the empirical results of the previous two sections. First, if the experience- earnings relationship were being driven by persistent shocks, then controlling for the wage on the last migration should reduce this correlation. However, the results in Table 4 using U.S. wage residuals suggest that this is not the case. Furthermore, if selection on persistent wage shocks were the only mechanism at play, then it would suggest that there should only be a correlation between current Mexican earnings and migration experience accumulated on the last migratory trip. Migration experience accumulated on prior trips would not be corre- lated with current Mexican earnings because once an individual draws a wage offer on a new trip, this is all that matters for jointly determining return migration and Mexican earnings upon return. However, this is inconsistent with the results in Table 6, which suggest that last- trip migration experience is not more positively correlated with earn- ings than total migration experience. Taken together, these patterns in the data cast doubt on an explanation for the experience- earnings relationship driven primarily by persistent wage shocks and selective return migration.

F. Policy Implications and Conclusion