Ec-980u: Aging, Cohort, and Period Effects

George J. BorjasHarvard University

Fall 2010

2. Chiswick model

log w = Xb + δA + θI + αy + ε where w is the wage rate; X includes

education; A is “age”; I is a foreign-born dummy; y is years-since-migration.

Chiswick also includes quadratics in age and y (so the equation is building from the Becker-Mincer human capital model)

3. Chiswick results, 1970 Census

4. Cross-section age-earnings profiles, 1970

5. Cross-section age-earnings profiles, 1990

6. Interpretation #1: Cohort differences

Carl C. Brigham’s Study of American Intelligence (1923). Described the trends in immigrant intelligence as measured by the scores in IQ tests given to army recruits during World War I.

Fact: Foreign-born recruits who had been in the United States for less than five years had an “average mental age” of eleven years, while recruits who had been in the country for at least twenty years had an average mental age of almost fourteen years.

Interpretation: “The average intelligence of succeeding waves of immigration has become progressively lower.”

7. Interpretation #2: Assimilation

Urban Institute’s Immigration and Immigrants: Setting the Record Straight (1994). Compares the incomes of various immigrant waves as of 1990.

Fact: “For households headed by immigrants entering the U.S. before 1980, household income averages about $40,900 a year—almost 10 percent greater than native households. But income for households headed by immigrants who entered in the 1980s averages only $31,100.”

Interpretation: “… immigrant socioeconomic status improves with time in the United States … data for immigrants who have been in this country for at least 10 years suggest that over time immigrants increasingly resemble natives.”

8. Assimilation versus cohort effects

Two different questions are being answered with the same type of data: How do the skills of the immigrant

waves admitted now compare to the skills of the waves admitted earlier?

What happens to the skills (or economic performance) of immigrants as they assimilate into the United States?

9. The identification problem

20 40 60 Age

Wage

1990 cohort

1950 cohort

1970 cohort and natives

10. Borjas model

where w gives the wage of person in cross-section τ; X gives a vector of socioeconomic characteristics; A gives the worker’s age at the time the cross-section survey is observed; C gives the calendar year in which the immigrant arrived in the host country; y gives the number of years that the immigrant has resided in the host country (y =τ - C)

11. One definition of assimilation

Other definitions are possible. For example, LaLonde-Topel argue that “assimilation occurs if, between two observationally equivalent [foreign-born] persons, the one with greater time in the United States typically earns more” [LaLonde and Topel (1992), p. 75].

The LaLonde-Topel definition is simply the parameter α, the coefficient of years-since-migration in the immigrant earnings function.

12. Identification restriction

13. Model with age-at-migration

14. Trends in the earnings of recent immigrants (Lubotsky, 2007)

15. Trends in immigrant earnings (Borjas, 1995)

16. Tracking across cohorts (Borjas, 1995)

17. Repeated cross-sections

18. Aging-cohort-period model

19. Selective out-migration

Lubotsky argues that the repeated cross-section method is still biased because of selective out-migration.

Suppose that the least-skilled immigrants drop out of a U.S. census sample. That filtering will increase the average earnings of a particular cohort over time even if there are no differences across cohorts.

So you may need longitudinal data.

20. What assimilation effect does longitudinal data measure?

Nature of Lubotsky data: 1994 cross-section data (SIPP or CPS) as well as prior Social Security earnings history.

So it measures the wage growth experienced by stayers from a specific cohort.

A different question: what is the wage growth experienced by the typical immigrant from a specific cohort? Longitudinal data cannot help with that.

longitudinal data provides an unbiased estimate of earnings growth among the immigrants who are in the United States in 1994. (p. 834)

21. Impact of selective out-migration on assimilation