PERSPECTIVAS DE LOS ESTUDIANTES

The data on undocumented Thai migrants in Sobieszczyk (2000) allows us, in fact, to extract the value of α for those who worked in Japan.²³ The Sobieszczyk (2000) study covers a total of 29 migrants who worked illegally in Japan between 1986 and 1997.

We shall use 1995 as the benchmark year for our calibration as the data for most of the required parameters is readily available for this year (except for the deportation rate and the price ratio for which only the data in 2000 is available). For the purpose of retrieving the value of α on the basis of this sample, we calibrate the following parameters: w^∗/w, p^∗/p, r^∗, r, λ, and τ.

Wage ratio. For the 29 migrants, the average monthly wage in Japan was equal to $1^′378.11 (in current dollars). Unfortunately, Sobieszczyk (2000) does not provide information on the wage earned in Thailand before or after migration. However, we know that the average monthly wage of an unskilled worker in Thailand in the mid

23The full sample contains information on 104 temporary migrants who worked in various destination countries including Japan, Hong-Kong, Singapore, Taiwan, Brunei, South Korea and Malaysia. However, due to the lack of data on deportation rates, we are only able to analyze the case of migration to Japan.

1990s was 6^′267 baht, which is equal to $250.68 at the exchange rate of 25 baht per dollar in 1995-1996 (Jones and Pardthaisong 1999, footnote to Table 6). This value of the monthly wage rate is consistent with the ILO data on wages in Thailand in 1995 ($250.56). Dividing $1^′378.11 by $250.68 we obtain the wage ratio w^∗/w = 5.49.

Price ratio. The data on the price ratio is taken from OECD Comparative price levels for 2000 (data for 1995 are not available, although one may expect that in 1995 the price dierential was larger than in 2000). The value of the index for Japan was 164 and for Thailand it was 40, implying that p^∗/p = 164/40 = 4.1.

Interest rates. The real interest rate in 1995 was equal to 4% in Japan and 7.3%

in Thailand (World Bank Data²⁴). Thus we have r^∗ = 0.04 and r = 0.073. Since the benchmark time period used in the model simulation is one month, these values will be divided by twelve in the calculations below.

Deportation rate. The Japanese Ministry of Justice provides information on the number of deportations and the estimated stocks of illegal immigrants as of 1999. The ratio of annual deportations of undocumented Thai nationals to the stock of illegal aliens from Thailand residing in Japan is on average 0.144 for the seven years from 1999 to 2005.²⁵ I therefore set λ = 0.144.

Deportation penalty. According to the Revised Immigration Control and Refugee Recognition Act (1999), the penalty for illegal stay in Japan is imprisonment of up to 3 years or a ne of up to 3 hundred thousand yen.²⁶ This monetary penalty is equal to $2^′638, applying the average exchange rate in 1999 of 113.71 yen per dollar.²⁷ Given that the average earnings of a migrant were $1^′378.11 per month, the penalty represents

24http://data.worldbank.org/indicator/FR.INR.RINR?page=3

25For each of these years, the ratio is reported to be as follows: 3886/30065 = 0.1292 in 1999, 3359/23503 = 0.1429in 2000, 2552/19500 = 0.1308 in 2001, 2391/16925 = 0.1412 in 2002, 2272/15693 = 0.1447 in 2003, 2521/14334 = 0.1758in 2004, and 1895/12787 = 0.1481 in 2005 (Japanese Ministry of Justice, 2005, 2011).

26http://www.jca.apc.org/apfs/nyukan_rev_e.html

27I use the Board of Governors of the Federal Reserve System release on monthly dollar-yen exchange rate to calculate the average. The data is available at http://research.stlouisfed.org/fred2/data/EXJPUS.txt

approximately 1.91 times the monthly wage.

Trip duration. The average duration of stay abroad of the 29 undocumented Thai migrants in Japan was 60.19 months or 5.015 years, which is in fact less than the hypo-thetical expected stay (given the deportation rates) of 1/λ = 6.9 years.

If we use these data to characterize the economic environment facing an undocu-mented Thai migrant and calculate the optimal duration of stay in Japan in the absence of homesickness (i.e., by setting α = 0), we obtain τ = 8.88 years. This is almost 4 years longer than the observed average length of stay. The value of the homesickness param-eter which is consistent with the observed average migration duration of 5.015 years is α = 0.0117, assuming the benchmark elasticity of marginal utility θ = 0.9. Column 2 of Table 3 reports the value of α for θ ranging from 0.75 to 3. These estimates are, of course, a result of a rough calculation based on a small sample and should be only considered as suggestive. They allows us, nonetheless, to interpret the utility loss due to homesickness in more concrete terms if we relate it to the utility enjoyed from the consumption of commodities. That is, we can calculate the consumption-equivalent loss due to social isolation. Using as the point of reference the optimal consumption rate in the last month of the undocumented stay, we calculate that the impact of homesickness on utility is identical to a 17 - 89% cut in the consumption rate (see Table 2, column 5), depending on the degree of concavity of the utility function (θ ranging from 0.75 to 3).

Our results are undoubtedly sensitive to the chosen specication of the homesickness function. One might argue that homesickness increases with time spent abroad following a linear trend. Or, alternatively, homesickness increases but at a decreasing rate due to better assimilation, for example, or even declines over time. The latter case is, however, highly unlikely for illegal Thai migrants in Japan as they typically do not learn the Japanese language and restrain from being seen in public. We consider two alternative specications of the ht function: linear (ht= αt) and concave (ht= t^α− 1), where the

HHHH HH

θ

h_t

exponential,30 linear,30 concave,30 exponential,60 linear,60 concave,60

θ = 0.75 55.67 65.63 83.11 89.81 89.86 89.93

θ = 0.9 37.59 43.69 59.75 68.32 68.37 68.45

θ = 1.25 20.20 22.47 32.89 40.51 40.53 40.60

θ = 3.00 7.40 7.69 11.79 16.88 16.88 16.92

Table 2: Consumption-equivalent loss at 30th and 60th month for alternative homesickness functions.

latter captures decaying marginal homesickness eect. In the absence of homesickness (α = 0) all the three functions are normalized to zero. In each case, the parameter α is extracted from the data on undocumented Thai migrants in Japan. The predicted consumption-equivalent loss is reported in Table 2 for alternative values of θ and two consumption reference points: the 30th month (half average trip duration) and the 60th month. The results are remarkably similar across all the three specications. If we consider the 30th month as the point of reference, then the eect of homesickness is equivalent to a 7.4% (θ = 3) to 55.6% (θ = 0.75) cut in the migrant's consumption rate in that month when htis exponential, a 7.7% to 65.6% cut when htis linear, and a 11.8%

to 83.1% cut when htis concave. Logically, the convex functional form yields a relatively smaller loss than the linear form which in turn yields a smaller loss than the concave function. If we consider the last month of the trip as the point of reference, then the eect of homesickness translates into approximately a 17% (θ = 3) to 89% (θ = 0.75) decline in the consumption rate for all the three specications. Homesickness thus appears to be a powerful element inuencing return decisions of undocumented foreign workers, as suggested by descriptive studies (see, e.g., Kibria 2004).

One may go a step further to measure the inuence of homesickness in relation to other pull-back factors, such as, for example, the expected rate of return on investments in Thailand. How large would this rate have to be in the absence of the homesickness eect in order to induce undocumented Thai migrants to return after spending 5 years

in Japan? The model predicts that the real interest rate in Thailand would need to be 15.5% (instead of the observed rate of 7.3%), implying an increase of 8.2 percentage points. The sensitivity of this result to variations in the elasticity of marginal utility (θ) can be seen in the 3d column of Table 3, which shows that, within a realistic range of values of θ, the overall eect of homesickness is equivalent to that of a 5.07 to 9.63 percentage-point increase in the rate of return on investment in the sending country.

As the nal step, we examine the predicted impact of a change in λ on undocumented Thai migrants' duration of stay in Japan. Given the estimated value of the homesickness

Inverse Homesickness Equivalent increase Reduction in τ due Reduction in τ due of EICS intensity in interest rate,% to doubling of λ,% to tripling of λ,%

θ = 0.75 α = 0.014438 9.63 2.07 3.89

θ = 0.85 α = 0.0125347 8.68 2.62 4.72

θ = 0.9 α = 0.011715 8.24 3.01 5.14

θ = 0.95 α = 0.010973 7.83 3.03 5.56

θ = 1.05 α = 0.0096935 7.15 3.81 6.38

θ = 3.00 α = 0.0028235 5.07 8.74 13.95

Table 3: Exponential homesickness function, ht= e^αt− 1.

Inverse Homesickness Equivalent increase Reduction in τ due Reduction in τ due of EICS intensity in interest rate,% to doubling of λ,% to tripling of λ,%

θ = 0.75 α = 0.0230045 9.63 2.59 4.58

θ = 0.9 α = 0.0170148 8.24 3.40 5.78

θ = 3.00 α = 0.0030764 5.07 8.89 14.18

Table 4: Linear homesickness function, ht= αt.

Inverse Homesickness Equivalent increase Reduction in τ due Reduction in τ due of EICS intensity in interest rate,% to doubling of λ,% to tripling of λ,%

θ = 0.75 α = 0.212093 9.63 3.40 5.98

θ = 0.9 α = 0.17209 8.24 4.35 7.37

θ = 3.00 α = 0.041477 5.07 10.74 16.93

Table 5: Decaying homesickness function, ht= t^α− 1.

parameter, the model implies that a doubling of the deportation rate to 0.2882 reduces the optimal τ by 2 - 8.74% or 1.25 to 5.26 months (depending on the choice of θ), as shown in the forth column of Table 3. The fth column shows the change in τ following a 3-times increase in the deportation rate. It amounts to a decline in the duration of stay of 2.5 (θ = 0.75) to 8.5 months (θ = 3). Not surprisingly, the higher is the elasticity of intertemporal consumption substitution (1/θ), the smaller is the implied change in τ.

Tables 4 and 5 report similar results for the linear and, respectively, concave specication of the ht function. Column 2 shows the extracted value of α for three representative values of θ. Column 3 shows the required increase in the real interest rate to induce a voluntary return after 5 years in the absence of the homesickness eect (identical to the values in Table 3). Columns 4 and 5 show the change in τ following a two-fold and, respectively, a three-fold increase in the deportation rate. The concave ht function captures a relatively fast-growing negative impact of homesickness at the beginning of the trip and a subsequent slow-down. The linear function captures a steady increase, while the convex function captures a slowly growing homesickness at the beginning of the trip but an explosively high growth at longer durations. The eect of an increase in the deportation rate on the change in the optimal-return date is thus more pronounced for a concave specication (regardless of θ) since the marginal impact of homesickness (the slope of ht) is larger for t < τ. For instance, a doubling of λ reduces τ by 6.5 months if h_tis concave and only by 5.26 months if it is convex (assuming θ = 3). The dierence of 5 weeks may seem to be negligible but one should keep in mind that in certain countries tolerance towards illegal immigrants is minimal and an overstay of even a few weeks is punished by heavy monetary penalties or imprisonment or a ban on reentry.

In closing our discussion on the role of homesickness in a model of temporary mi-gration we would like to emphasize that it allows us to improve our understanding of undocumented migrants' behavior and, in particular, their incentives to return to the

country of origin. Homesickness is only one of the drivers of return decision but its role is reinforced in environments characterized by sharp intolerance of illegal immigration and strict deportation policies. This is, for example, the case in East-Asian economies and the Gulf States. It is relevant to a lesser extent for illegal Mexican migrants in the United States, where deportations are fairly rare.

We have shown that taking into account the risk of deportation allows us to obtain more realistic values for optimal trip durations of undocumented migrants than those arising from standard deterministic models of temporary migration. Incorporating the homesickness phenomenon allows to further rene those results and thus reduce the potential for erroneous policy prescriptions. It is clear that when the migration du-ration of undocumented workers is overestimated, an overly restrictive policy may be introduced which may not only result in a gap in labor supply in certain sectors (if not accompanied by relevant legal migration programs) but also in an unnecessary burden on the immigration authorities' budget. The present model has no ambition of comparing eectiveness of various immigration policies, as this would require information on the numbers of deterred entries and relative costs of each policy. We can, however, conclude that deportation policy (i) has a non-negligible indirect eect of reducing the stock of illegal immigrants by inducing them to leave the host country sooner and (ii) acts as a homesickness catalyst which in turn is a powerful pull-back factor that may speed-up voluntary return even when economic incentives (such as rate of return on investment, for instance) are relatively weak.

4 Conclusion

The present paper develops a framework for the analysis of temporary illegal immi-gration. Its main contribution is three-fold. Starting with the characterization of the

solution for the optimal timing of return to the source country when the event of de-portation follows a stochastic process, we show that a more vigorous dede-portation policy advances the date of voluntary return. This helps explain why undocumented immi-grants choose to remain for only a relatively short period of time in countries with very strict deportation measures, such as Japan, South Korea, Singapore, Malaysia and the Gulf States, while tending to stay for longer durations or even permanently in countries with a more lenient stance, such as the U.S.A. or the EU. A higher deportation risk creates stronger incentives for voluntary return by operating through two channels: ac-celeration of wealth accumulation and "homesickness". In addition, it is found that the risk of deportation may trigger voluntary return under conditions that would otherwise make a permanent undocumented stay optimal.

An important policy implication of this analysis is that for any given ow of undoc-umented workers, a host country with stricter deportation policies will have a smaller stock of illegal immigrants at each point in time. This is not only because it physically removes more undocumented aliens, but also because the policy indirectly induces those who are not apprehended to voluntarily leave the country sooner. In addition to these direct and indirect eects which contribute to a reduction in the stock of illegal aliens for a given ow, deportations obviously have a deterrent eect on the inow.

The paper also shows that consideration of just the economic pull-back factors, such as international return-on-investment or cost-of-living dierentials, which have been ex-tensively studied in the literature on temporary migration, is not sucient to account for the observed behavior of undocumented aliens. Although these factors do play an im-portant role in drawing migrants back to their country of origin, they do not explain why deportable illegal immigrants return voluntarily after only 2 to 5 years of work abroad.

Accounting, in addition, for the eects of "homesickness" and using the evidence on the behavior of undocumented Thai migrants in Japan, enables us to measure the inuence

of these psychological and social factors on the timing of voluntary return. They are found to be just as important as economic considerations. On average, the loss of wel-fare associated with family separation and social isolation experienced by undocumented Thai migrants during their last month in Japan is equivalent to a change in utility asso-ciated with a 17 to 68% cut in the consumption rate abroad (in the empirically relevant range of the intertemporal substitution elasticity). For illegal immigrants in countries with very strict deportation measures, the degree of social isolation and separation from other family members is indeed unique across the spectrum of migrant types. It therefore deserves particular attention in both theoretical and empirical studies.

Our calibration of the model for the case of undocumented Thai migrants in Japan also allows us to draw conclusions on the eectiveness of a change in the intensity of deportations in terms of its impact on the optimal duration of an undocumented stay.

Our model predicts that while stricter deportation measures can be quite eective in building on the incentives for voluntary return at relatively low rates of deportation, it is also true that, after a certain point, a further tightening of this policy becomes less eective. In the case of Japan, we nd that doubling the deportation rate from its level in the late 1990s would have reduced the optimal duration of stay of illegal aliens from Thailand by about 1.25 to 8.5 months, depending on the intertemporal substitution elasticity and the shape of the homesickness function.

References

[1] Auriol, E., and A. Mesnard. 2012. "Sale of Visas: A Smuggler's Final Song?" mimeo, Toulouse School of Economics.

[2] Bandyopadhyay, S., and S.C. Bandyopadhyay. 1998. "Illegal Immigration: A Supply Side Analysis," Journal of Development Economics, vol. 57, pp. 343-360.

[3] Bond, E.W, and T.-J. Chen. 1987. "The Welfare Eects of Illegal Immigration,"

Journal of International Economics, vol. 23, pp. 315-328.

[4] Businessweek. 2005. "A Chilly Reception for Guest Workers in South Korea," avail-able at http://www.businessweek.com/magazine/content/05_06/b3919082.htm [5] Cornelius, W.A. 2005. "Controlling 'Unwanted' Immigration: Lessons from the

United States, 1993-2004," Journal of Ethnic and Migration Studies, vol. 31, pp. 775-794.

[6] Dixit, A.K., and R.S. Pindyck. 1994. Investment Under Uncertainty. Princeton Uni-versity Press.

[7] Djaji¢, S. 1997. "Illegal Immigration and Resource Allocation," International Eco-nomic Review, vol. 38, no. 1, pp. 97-117.

[8] Djaji¢, S. 2010. "Investment Opportunities in the Source Country and Temporary Migration," Canadian Journal of Economics, vol. 43, no. 2, pp. 663-682.

[9] Djaji¢, S. 2011. "Asylum Seeking and International Migration," mimeo, The Gradu-ate Institute, Geneva.

[10] Djaji¢, S. 2013. "Some Essentials of a Workable Guest-Worker Program," Interna-tional Economic Review, vol. 54, no. 2, pp. 739-766.

[11] Djaji¢, S. and A. Mesnard. 2013. "Guest Workers in the Underground Economy,"

CReAM Discussion Paper 24/13.

[12] Djaji¢, S., and R. Milbourne. 1988. "A General-Equilibrium Model of Guest-Worker Migration: The Source Country Perspective," Journal of International Economics, vol.

25, pp. 335-351.

[13] Djaji¢, S., and A. Vinogradova. 2011. "Immigration Policies and the Choice between Documentes and Undocumented Migration," mimeo, The Graduate Institute, Geneva.

[14] Djaji¢, S., and A. Vinogradova. 2013. "Undocumented Migrants in Debt," Labour Economics, vol. 21, pp. 15-24.

[15] Epstein, L.G., and S.E. Zin. 1991. "Substitution, Risk Aversion, and the Temporal Behavior of Consumption and Asset Returns: An Empirical Analysis," The Journal of Political Economy, vol. 99, no. 2, pp. 263-286.

[16] Ethier, W.J. 1986. "Illegal Immigration: The Host-Country Problem," The Ameri-can Economic Review, vol. 76, no. 1, pp. 56-71.

[17] Eurelings-Bontekoe, E.H.M., E.P.M. Brouwers, and M.J. Verschuur. 2000. "Home-sickness among Foreign Employees of a Multinational High-Tech Company in the Netherlands," Environment and Behavior, vol. 32, pp. 443-456.

[18] Gaytan-Fregoso, H., and S. Lahiri. 2000. "Foreign Aid and Illegal Immigration,"

Journal of Development Economics, vol. 63, pp. 515-527.

[19] Global Envision. 2006. "Hard Work, Furtive Living - Illegal Immigrants in Japan,"

available at http://www.globalenvision.org/library/3/986

[20] Hamilton, K. 2013. "How Obama Could (but Probably Won't) Stop Deporting Illegal Immigrants Today," available at

http://www.theatlantic.com/politics/archive/2013/03/how-obama-could-but-probably-wont-stop-deporting-illegal-immigrants-today/274352/

[21] Hansen, L.P., and K.J. Singleton. 1982. "Generalized Instrumental Variables Esti-mation of Nonlinear Rational Expectations Models," Econometrica, vol. 50, no. 5, pp.

1269-1286.

[22] Hanson, G. 2006. "Illegal Migration from Mexico to the United States," Journal of Economic Literature, vol. 44, pp. 869-924.

[23] Hill, J.K. 1987. "Immigrant Decisions Concerning Duration of Stay and Migratory Frequency," Journal of Development Economics, vol. 25, pp. 221-234.

[24] Human Development Report. 2009. "Overcoming Barriers: Human mobility and development." United Nations Development Programme. Palgrave Macmillan, New York.

[25] Ignacio-esteban, Ma. Angelina. "The Dynamics of Illegal Migra-tion: The Philippines-South Korea Case," viewed April 4, 2012

http://www.lipiniana.net/publication/the-dynamics-of-illegal-migration-the-philippines-south-korea-case/13197759176933/8/1

[26] Jones, H., and T. Pardthaisong. 1999. "The Impact of Overseas Labor Migration on Rural Thailand: Regional, Community and Individual Dimensions," Journal of Rural Studies, vol. 15, no. 1, 35-47.

[27] Kibria, N. 2004. "Returning International Labor Migrants from Bangladesh: The Experience and Eects of Deportation". Working Paper No. 28, Mellon-MIT Inter-University Program on NGOs and Forced Migration.

[28] Kirdar, M. 2013. "Source Country Characteristics and Immigrants' Migration Du-ration and Saving Decisions," IZA Journal of MigDu-ration, vol. 2, 8.

[29] McCormick, B., and J. Wahba. 2001. "Overseas Work Experience, Savings and Entrepreneurship Amongst Return Migrants to LDCs," Scottish Journal of Political

[29] McCormick, B., and J. Wahba. 2001. "Overseas Work Experience, Savings and Entrepreneurship Amongst Return Migrants to LDCs," Scottish Journal of Political