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Ec-980u: Self-Selection of Immigrants

Ec-980u: Self-Selection of Immigrants. George J. Borjas Fall 2010. 1 . Hourly wage differentials between immigrant and native men in 2000, by national origin. 2 . The migration decision.

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Ec-980u: Self-Selection of Immigrants

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  1. Ec-980u: Self-Selection of Immigrants George J. Borjas Fall 2010

  2. 1. Hourly wage differentials between immigrant and native men in 2000, by national origin

  3. 2. The migration decision • What determines whether to migrate or not? Basic economic model: person migrates if the income gain from migrating exceeds the migration cost • Let V1 be present value of earnings (income) if one migrates to, say, the US • Let V0 be the present value of earnings if one stays in the sending country • Migration occurs if V1 –V0 > C , where C measures the cost of migration

  4. 3. The selection problem • The immigrant flow is a non-random sample of the population from the countries of origin • The immigrant flow is self-selected: Not all persons from a particular source country wish to migrate to the United States • Which persons leave the country of origin and which persons stay there?

  5. 4. Ad hoc theories of selection • Benjamin Franklin, 1753: German immigrants are “the most stupid of their own nation.” • George Patton, 1943: “When we land, we will meet German and Italian soldiers whom it is our honor and privilege to attack and destroy. Many of you have in your veins German and Italian blood, but remember that these ancestors of yours so loved freedom that they gave up home and country to cross the ocean in search of liberty. The ancestors of the people we shall kill lacked the courage to make such a sacrifice and continued as slaves.”

  6. 5. More ad hoc theories of selection • Chiswick (1978): immigrants are “more able and more highly motivated” than natives. • Carliner (1980): immigrants “choose to work longer and harder than nonmigrants”

  7. 6. Types of selection Frequency Negatively-Selected Immigrant Flow Positively-Selected Immigrant Flow sN sP Skills

  8. 7. Theory of selection: The Roy model • Two-country model: a sending country (0) and a receiving country (1); e.g., Mexico and the U.S. • Log earnings in the sending country are given by: • Think of ε0 as the de-meaned value of worker’s skills in the sending country. • If everyone from 0 were to migrate to 1, their log earnings distribution would be (ignoring any general equilibrium effects!):

  9. 8. Migration costs • Assume the costs of migration are equal to C. Define “time-equivalent” migration costs as Π=C/w0. Suppose time-equivalent migration costs are constant. • A person chooses to migrate from country 0 to country 1 if:

  10. 9. Probability of migration The random variable v is normal with standard deviation σv; Φ is the cumulative distribution function of the normal. Note that the larger z, the lower is the probability of migration. Hence:

  11. 10. A definition • The correlation between the ε component of sending and receiving country earnings is: • Where σ01 is the covariance between ε0 and ε1, and σj is the standard deviation of εj.

  12. 11. Self-selection • Question: how do the out-migrants do in the source country prior to migration? • This depends on mean earnings in the source country, on the ε error terms, and implicitly on the correlation between these error terms.

  13. 12. A property of normal random variables • Suppose x and y are normal random variables. Then the conditional expectation is linear and the coefficient is the regression coefficient: • This implies we can write the “population” regression between standard normal random variables as:

  14. 13. Let’s use this property • The “*” denote standard normal random variables. Note that λ(z) must be a positive number.

  15. 14. And to simplify further:

  16. 15. Self-selection, part 2 • Question: how do the immigrants do in the receiving country after migration?

  17. 16. Types of selection • Suppose μ0 = μ1, so that we can isolate the selection in the distribution of skills, as measured by Q0 and Q1. There are four possibilities: • Case 1: Q0>0 and Q1>0. • Case 2: Q0<0 and Q1<0. • Case 3: Q0<0 and Q1>0. • Case 4: Q0>0 and Q1<0.

  18. 17. Case 1: Positive selection • Q0>0 and Q1>0. • Since λ(z) is always a positive number this requires that:

  19. 18. Case 2: Negative selection • Q0<0 and Q1<0. • This requires that:

  20. 19. Case 3: Refugee sorting • Q0<0 and Q1>0. • This requires that:

  21. 20. Case 4: Impossible • Q0>0 and Q1<0. • This requires that: • This type of selection requires that the correlation coefficient exceeds 1, which is impossible. The reason is that income maximization would never lead to an outcome where high-income people migrate to become low-income people.

  22. 21. A graphical version of the Roy model • There is a linear relationship between wages and “skills” in each country: log wagej = aj + rjS • The intercept aj gives the earnings of a person with little (zero) skills; the slope rj gives the rate of return to skills in country j. • “Skills” increase earnings in both the country of origin and in the United States. • There are no migration costs

  23. 22. Positive selection Log wage U.S. Source Country aS aUS Do Not Move Move sP Skills

  24. 23. Negative selection Log wage Source Country U.S. aUS aS Do Not Move Move sN Skills

  25. 25. Impact of a decline in U.S. incomes (with positive selection) Log wage U.S. Source Country aS aUS sP Skills s*

  26. 26. Impact of a decline in U.S. incomes (with negative selection) Log wage Source Country U.S. aUS aS sN s* Skills

  27. 27. Adjusted entry wage of immigrants and per-capita GDP in source country

  28. 28. Entry wage of immigrants and income inequality in the source country

  29. 29. Trends in emigrant share, by education, Mexico (Chiquiar-Hanson)

  30. 30. Chiquiar-Hanson and Fernandez-Huertas • Chiquiar-Hanson use Census data • Fernandez-Huertas uses the ENET: • “The ENET is the household survey…used to calculate the official employment statistics for Mexico from the second quarter of 2000 until the end of 2004…The ENET is very similar to the Current Population Survey in the United States…Since every household is interviewed five times, with one of the five panels dropping out of the sample each quarter, a researcher can match the data on wages or schooling of an individual in a quarter in which she lives in Mexico with the migration behavior of that individual in the following quarter.”

  31. 31. Wage distributions of migrants and non-migrants (Fernandez-Huertas, 2009)

  32. 32. Degree of selection (diff in wages) (Fernandez-Huertas, 2009)

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