Immigration

Immigration is migration across national borders. Who migrates depends on how much each country pays for skills (self-selection). An inflow of immigrants who compete with native workers lowers those workers’ wage in the short run, by less or not at all once capital adjusts, and raises natives’ total income by the immigration surplus.

Who migrates: the Roy model

Countries differ in how steeply earnings rise with skill. Where skills are well paid, the skilled gain most from going; where wages are compressed, the less skilled do.

Let $s$ be a worker’s skill. Earnings are $w_0 = \alpha_0 + \delta_0 s$ in the source country and $w_1 = \alpha_1 + \delta_1 s$ in Canada, where $\delta_0$ and $\delta_1$ are the returns to skill. Migrating costs $C$, the same for everyone. A worker migrates if $w_1 - C > w_0$. The two lines cross at the cut-off skill

$$\begin{aligned} \alpha_1 + \delta_1 s^* - C &= \alpha_0 + \delta_0 s^* \\ (\delta_1 - \delta_0)\, s^* &= \alpha_0 - \alpha_1 + C \\ s^* &= \frac{\alpha_0 - \alpha_1 + C}{\delta_1 - \delta_0} . \end{aligned}$$

• If $\delta_1 > \delta_0$, workers with $s > s^*$ migrate: positive selection. Immigrants are more skilled than the average worker who stays.
• If $\delta_1 < \delta_0$, workers with $s < s^*$ migrate: negative selection.

The direction of selection depends only on the relative returns to skill; the intercepts and $C$ move $s^*$, changing how many migrate but not which end of the skill distribution they come from. George Borjas applied this model, due to A. D. Roy, to immigration and found that the earnings of US immigrants with the same measured skills differ systematically with conditions in their home countries at the time they migrated.¹²

Migration cost, C

$15k

Cut-off when δ₁ > δ₀ (most skilled migrate)

3.3

Cut-off when δ₁ < δ₀ (least skilled migrate)

7.5

Open in Graph Lab

Figure 1. Source-country earnings (red) against net earnings in Canada under two wage structures, with a $15,000 migration cost. When Canada pays more for skills ($\delta_1 > \delta_0$) workers above $s_P = 3.3$ migrate; when it pays less ($\delta_1 < \delta_0$) workers below $s_N = 7.5$ migrate. A higher migration cost shrinks both groups of migrants without changing which workers are selected.

The prediction: holding costs fixed, immigrants from countries with more earnings inequality than Canada (a higher $\delta_0$) tend to be negatively selected, and immigrants from more equal countries positively selected.

Key idea

Skills flow toward the country that pays more for them. Positive selection requires $\delta_1 > \delta_0$; a higher average wage in Canada attracts more immigrants but does not change their type.

Assimilation and cohort effects

Immigrants’ earnings usually start below those of comparable natives and grow faster as they gain language skills and local experience: assimilation.

Cross-section studies compare earlier and recent arrivals in one census. Starting with Barry Chiswick’s work on the 1970 US census, they implied that immigrants caught up with natives within 10 to 15 years.³⁴ But a cross-section mixes two things: how a cohort’s earnings grow (assimilation) and how cohorts differ at entry (cohort effects). If earlier cohorts were more skilled at arrival, the gap between old and new arrivals overstates the growth any cohort experiences. Following the same arrival cohort across censuses separates the two. Doing that with the 1970 and 1980 censuses, Borjas found that for most immigrant groups within-cohort earnings growth was significantly smaller than the cross-section predicted, consistent with a decline in the skills of successive cohorts.⁴ Selective return migration biases the cross-section the same way if the less successful are the ones who leave.

Canada shows the same pattern. Entry earnings of successive immigrant cohorts fell from the late 1960s through the 1990s. For immigrant men, Abdurrahman Aydemir and Mikal Skuterud found that shifts in official-language knowledge and region of origin explain no more than a third of that decline, and that a falling return to work experience gained abroad, concentrated among immigrants from non-traditional source countries, explains roughly another third.⁵

The labour market impact

Short run: perfect substitutes, fixed capital

Assume a competitive labour market in which immigrants and natives are perfect substitutes, capital is fixed, native labour supply slopes up, and $M$ immigrants work at any wage. Supply shifts right by $M$. The wage falls, total employment rises, and native employment falls, because natives whose reservation wage exceeds the new wage leave the market.

Immigrants, M (thousands)

20k

Wage

$44.0k

Total employment

72.0k

Native employment

52.0k

Natives who leave the market

8.0k

Open in Graph Lab

Figure 2. Short run, immigrants and natives perfect substitutes, capital fixed. Twenty thousand immigrants shift supply from $S_0$ to $S_1$: the wage falls from $50,000 to $44,000, total employment rises from 60,000 to 72,000, and native employment falls to 52,000.

Long run: capital adjusts

Cheaper labour raises the return to capital, so firms invest, which raises the value of the marginal product of labour and shifts labour demand right. With constant returns to scale, investment continues until the capital-labour ratio, and with it the wage, returns to its original level. In the long run natives’ wage and employment are unchanged and the economy is simply larger (see long-run labour demand).

Capital adjustment completed

100%

Wage

$50.0k

Total employment

80.0k

Native employment

60.0k

Open in Graph Lab

Figure 3. Short run vs long run. At $E_1$ capital is fixed and the wage is $44,000. With constant returns to scale, capital accumulates until demand shifts from $D_0$ to $D_1$: at $E_2$ the wage is back at $50,000, native employment is back at 60,000, and total employment is higher by the 20,000 immigrants.

Complements. If immigrants complement a native group (immigrant labourers and native supervisors), the inflow raises that group’s value of marginal product, wage and employment. Each native group’s outcome depends on whether immigrants substitute for or complement its skills.

The immigration surplus

Hold native labour supply fixed at $N$ and add $M$ immigrants who are perfect substitutes. The wage falls from $w_0$ to $w_1$. Native workers lose $(w_0 - w_1)N$ to the owners of firms. Firms also gain the triangle between demand and $w_1$ over the immigrants’ employment, because each immigrant adds the value of their marginal product but is paid only $w_1$. That triangle,

$$\text{immigration surplus} = \tfrac{1}{2}(w_0 - w_1)M ,$$

is the net gain to natives as a whole. It exists only because the wage falls, so it comes with a redistribution from native workers to employers.

Immigrants, M (thousands)

20k

Wage

$40.0k

Transfer from native workers to firms

$600m

Immigration surplus

$100m

Open in Graph Lab

Figure 4. The immigration surplus with native labour supply fixed at 60,000 workers. Twenty thousand immigrants lower the wage from $50,000 to $40,000. Native workers lose the rectangle, $600 million a year, which goes to the owners of firms; the triangle, $100 million a year, is the net gain to natives.

Worked example

Labour demand is $w = 80 - 0.5E$ and native labour supply is $w = 5 + 0.75E$, with $w$ in thousands of dollars a year and $E$ in thousands of workers. Twenty thousand immigrants arrive.

1. Before. $80 - 0.5E = 5 + 0.75E$ gives $E_0 = 75/1.25 = 60$ and $w_0 = 80 - 30 = 50$.

2. Short run. Total supply is $w = 5 + 0.75(E - 20) = -10 + 0.75E$. Setting $80 - 0.5E = -10 + 0.75E$ gives $E_1 = 90/1.25 = 72$ and $w_1 = 80 - 36 = 44$.

3. Natives. Native employment is $E_1 - M = 52$, or from native supply, $(44 - 5)/0.75 = 52$: 8,000 natives leave the market.

4. Long run. With constant returns, demand shifts right by 20: $w = 90 - 0.5E$. Then $90 - 0.5E = -10 + 0.75E$ gives $E_2 = 80$ and $w_2 = 90 - 40 = 50$, with native employment back at $80 - 20 = 60$.

5. Surplus. With native supply fixed at 60, the wage falls to $80 - 0.5(80) = 40$. Native workers lose $(50 - 40) \times 60 = 600$, that is $600 million a year, to employers; the surplus is $\tfrac{1}{2} \times 10 \times 20 = 100$, or $100 million.

Second example: in a 2000 census, immigrants who arrived in 1975 earn 5 percent more than comparable natives, and those who arrived in 1995 earn 20 percent less. In the 1980 census, the 1975 arrivals earned 15 percent less. Separate assimilation from the cohort effect.

Show the solution

The cross-section in 2000 attributes the 25-point gap between the two cohorts to 20 years in Canada. Following the 1975 cohort, its relative earnings rose from $-15$ to $+5$ between 5 and 25 years after arrival: 20 points of assimilation. Five years after arrival the 1995 cohort stood at $-20$, 5 points below the 1975 cohort at the same stage; that is the cohort effect. The cross-section overstates assimilation by those 5 points.

Evidence

Comparing cities with more and fewer immigrants understates wage effects: immigrants settle where demand is growing, natives move away from areas receiving immigrants, and capital flows in, spreading the effect across the national market. Researchers therefore look for natural experiments, inflows driven by events unrelated to local labour markets.

The Mariel boatlift. Almost 125,000 Cubans reached the United States between April and September 1980, most settling in Miami.⁶ David Card found that the inflow raised Miami’s labour force by about 7 percent, yet compared with other cities there was virtually no effect on the wages of non-Cuban workers or the unemployment of less-skilled Black workers.⁷ Borjas later focused on high school dropouts, the group the Marielitos most resembled (at least 60 percent had not finished high school), and found that their wage in Miami fell by 10 to 30 percent.⁸ Giovanni Peri and Vasil Yasenov, using a synthetic control group of cities, found no significant difference for Miami’s high school dropouts in 1981 to 1983.⁶ Michael Clemens and Jennifer Hunt traced the conflict to the data: the racial composition of the small Current Population Survey subsamples changed sharply in Miami around 1980 for reasons unrelated to the boatlift.⁹ A natural experiment is only as good as its comparison group and its data.

National estimates. Comparing education-experience groups across the whole US labour market, Borjas estimated that a 10 percent increase in a group’s supply lowers its wage by 3 to 4 percent.¹⁰ With Aydemir, he found a similar response in Canada, Mexico and the United States, although immigration narrowed wage inequality in Canada while it widened it in the United States.¹¹ A US National Academies panel concluded that over ten years or more the effect on native-born workers’ wages overall is very small, with any negative effects concentrated on earlier immigrants and native-born workers without a high school diploma.¹²

Canada’s points system

Canada selects many economic immigrants by points. Regulations adopted in 1967 scored independent applicants on factors including education, occupation, age, language, arranged employment and relatives in Canada, and admitted those with at least 50 of 100 points.¹³ The Federal Skilled Worker Program still uses a 100-point grid with a pass mark of 67: language up to 28 points, education 25, experience 15, age 12, arranged employment 10 and adaptability 10.¹⁴

Since January 1, 2015, Express Entry has managed applications to the federal economic programs (Federal Skilled Worker, Federal Skilled Trades and Canadian Experience Class).¹⁵ Candidates in the pool are ranked by the Comprehensive Ranking System (CRS): up to 500 points for core human capital (age, education, official languages, Canadian work experience; 460 plus up to 40 for a spouse’s factors), up to 100 for skill transferability and up to 600 additional points, for a maximum of 1,200. A provincial nomination alone is worth 600 points.¹⁶ IRCC invites the top-ranked candidates in rounds, some restricted to categories such as French-language proficiency, healthcare and social services, STEM, trades and education.¹⁷ Point values change often: IRCC has announced new rules for scoring Canadian work experience and job offers from November 3, 2026.¹⁶

A points system selects directly on observable skills, so it raises immigrants’ average measured skill whatever the source country’s wage structure. It cannot screen on unobserved skills or ensure that skills acquired abroad are rewarded: returns to foreign experience have fallen, and résumé experiments show Canadian employers discounting foreign work experience and immigrant-sounding names.

Common mistakes

Traps on exams

• Selection from average wages. Whether immigrants are positively or negatively selected depends on the relative returns to skill ($\delta_1$ against $\delta_0$), not on which country has higher average wages.
• Reading a cross-section as assimilation. Comparing early and recent arrivals in one census mixes assimilation with cohort effects.
• One answer for all horizons. With perfect substitutes the wage falls in the short run; with constant returns it returns to $w_0$ in the long run; complementary natives gain in both.
• Counting the rectangle as the surplus. The rectangle $(w_0 - w_1)N$ is a transfer from native workers to employers. Only the triangle is the net gain, and native workers lose.

On the exam

For the Roy model, draw both earnings lines against skill, mark $s^*$ where $w_1 - C$ crosses $w_0$, and shade the migrants. For the labour market, draw $S_0$, $S_1 = S_0 + M$ and demand; label $w_0$, $w_1$, native employment $N_1$ and total employment $E_1$; then shift demand for the long run.

Check yourself

1.

In the Roy model, earnings are $w_0 = \alpha_0 + \delta_0 s$ in the source country and $w_1 = \alpha_1 + \delta_1 s$ in Canada, and every worker faces the same migration cost. When are immigrants positively selected, that is, more skilled than the workers who stay?

Migration cost, C

$15k

Cut-off when δ₁ > δ₀ (most skilled migrate)

3.3

Cut-off when δ₁ < δ₀ (least skilled migrate)

7.5

1When $\delta_1 > \delta_0$, so Canada pays more for skills than the source country2When $\alpha_1 > \alpha_0$, so Canada pays more to a worker with no skills3When average earnings in Canada are higher than in the source country4When the migration cost is high

Check answer

2.

Immigrants and natives are perfect substitutes, capital is fixed, and native labour supply slopes upward. In the short run, an inflow of immigrants who will work at any wage

Immigrants, M (thousands)

20k

Wage

$44.0k

Total employment

72.0k

Native employment

52.0k

Natives who leave the market

8.0k

1lowers the wage, raises total employment and lowers native employment2lowers the wage and lowers total employment3leaves the wage unchanged, because labour demand rises one for one with supply4raises natives' wage, because immigrants take the least attractive jobs

Check answer

3.

Labour demand is $w = 80 - 0.5E$, with $w$ in thousands of dollars a year and $E$ in thousands of workers. Native labour supply is fixed at 60 thousand workers. Ten thousand immigrants who are perfect substitutes for natives arrive. What is the immigration surplus, in millions of dollars a year?

Immigrants, M (thousands)

20k

Wage

$40.0k

Transfer from native workers to firms

$600m

Immigration surplus

$100m

Your answer (millions of dollars a year)

Check answer

Practise more questions on this topic

Sources

1. Roy, A. D. (1951). Some thoughts on the distribution of earnings. Oxford Economic Papers, 3(2), 135 to 146. ↩

2. Borjas, G. J. (1987). Self-selection and the earnings of immigrants. American Economic Review, 77(4), 531 to 553. NBER working paper 2248. ↩

3. Chiswick, B. R. (1978). The effect of Americanization on the earnings of foreign-born men. Journal of Political Economy, 86(5), 897 to 921. ↩

4. Borjas, G. J. (1985). Assimilation, changes in cohort quality, and the earnings of immigrants. Journal of Labor Economics, 3(4), 463 to 489. ↩ ↩²

5. Aydemir, A. and Skuterud, M. (2004). Explaining the deteriorating entry earnings of Canada’s immigrant cohorts: 1966 to 2000. Statistics Canada, Analytical Studies Branch Research Paper Series, no. 225. Statistics Canada. Published in the Canadian Journal of Economics, 38(2), 641 to 672 (2005). ↩

6. Peri, G. and Yasenov, V. (2019). The labor market effects of a refugee wave: Synthetic control method meets the Mariel boatlift. Journal of Human Resources, 54(2), 267 to 309. NBER working paper 21801. ↩ ↩²

7. Card, D. (1990). The impact of the Mariel boatlift on the Miami labor market. Industrial and Labor Relations Review, 43(2), 245 to 257. NBER working paper 3069. ↩

8. Borjas, G. J. (2017). The wage impact of the Marielitos: A reappraisal. ILR Review, 70(5), 1077 to 1110. NBER working paper 21588. ↩

9. Clemens, M. A. and Hunt, J. (2019). The labor market effects of refugee waves: Reconciling conflicting results. ILR Review, 72(4), 818 to 857. NBER working paper 23433. ↩

10. Borjas, G. J. (2003). The labor demand curve is downward sloping: Reexamining the impact of immigration on the labor market. Quarterly Journal of Economics, 118(4), 1335 to 1374. NBER working paper 9755. ↩

11. Aydemir, A. and Borjas, G. J. (2007). Cross-country variation in the impact of international migration: Canada, Mexico, and the United States. Journal of the European Economic Association, 5(4), 663 to 708. ↩

12. National Academies of Sciences, Engineering, and Medicine (2017). The Economic and Fiscal Consequences of Immigration. Washington, DC: The National Academies Press. Report summary. ↩

13. Canadian Museum of Immigration at Pier 21, Immigration Regulations, Order-in-Council PC 1967-1616, 1967. ↩

14. Immigration, Refugees and Citizenship Canada, Six selection factors: Federal Skilled Worker Program, accessed October 2026. ↩

15. Citizenship and Immigration Canada (2015). Recruiting in-demand, skilled immigrants to Canada, news release, January 1, 2015. ↩

16. Immigration, Refugees and Citizenship Canada, Comprehensive Ranking System (CRS) criteria: Express Entry, accessed October 2026. ↩ ↩²

17. Immigration, Refugees and Citizenship Canada, Express Entry: category-based selection, accessed October 2026. ↩