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 Country of origin% of immigrant workforce Log wage gap All immigrantsNew arrivals Mexico China India Philippines Vietnam El Salvador Cuba United Kingdom Canada Korea Russia Dominican Republic Guatemala Germany Jamaica

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 V 1 be present value of earnings (income) if one migrates to, say, the US Let V 0 be the present value of earnings if one stays in the sending country Migration occurs if V 1 – V 0 > C, where C measures the cost of migration

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?

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.”

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”

6. Types of selection Positively-Selected Immigrant Flow Frequency Negatively-Selected Immigrant Flow Skills sPsP sNsN

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 ε 0 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!):

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

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

10. A definition The correlation between the ε component of sending and receiving country earnings is: Where σ 01 is the covariance between ε 0 and ε 1, and σ j is the standard deviation of ε j.

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.

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:

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

14. And to simplify further:

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

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

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

18. Case 2: Negative selection Q 0 <0 and Q 1 <0. This requires that:

19. Case 3: Refugee sorting Q 0 0. This requires that:

20. Case 4: Impossible Q 0 >0 and Q 1 <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.

21. A graphical version of the Roy model There is a linear relationship between wages and “skills” in each country: log wage j = a j + r j S The intercept a j gives the earnings of a person with little (zero) skills; the slope r j 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

22. Positive selection Skills Log wage Do Not Move Move aSaS a US sPsP Source Country U.S.

23. Negative selection Skills Log wage Do Not Move Move sNsN aSaS a US Source Country U.S.

24. “Refugee” sorting Skills Log wage Do Not Move Move sRsR U.S. and source country prior to revolution Source country after revolution

25. Impact of a decline in U.S. incomes (with positive selection) Skills Log wage aSaS a US sPsP Source Country U.S. s*s*

26. Impact of a decline in U.S. incomes (with negative selection) Skills Log wage sNsN aSaS a US Source Country U.S. s*s*

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

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

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

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

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