Immigration in America: Understanding the Numbers

This presentation is available at http://www.macalester.edu/~bressoud/talks

June 21–25, 2004

David Bressoud, Mathematics, Macalester College

Kathy Fennelly, Immigration & Public Policy, Humphrey Institute of Public Affairs, U MN

Steve Holland, Economics & Political Science, Macalester College

lit·er·ate adj.

1. Able to read and write

2. Educated, knowledgeable

lit·er·ate adj.

1. Able to read and write

2. Educated, knowledgeable

nu·mer·ate adj.

1. Able to do arithmetic and simple geometry

2. Educated, knowledgeable

Quantitatively literate citizenship:

•Understand comparative magnitudes of risk and significance of very small numbers (10 ppm)

•Understand that unusual events can easily occur by chance (eg. Cancer clusters)

•Analyze economic and demographic data to support or oppose policy proposals

•Understand difference between rates of change and changes in rates, between average and marginal rates, and between linear and exponential rates of growth

•Appreciate common sources of bias in surveys

"Numeracy is not the same as mathematics, nor is it an alternative to mathematics. Rather, it is an equal and supporting partner in helping students learn to cope with the quantitative demands of modern society. Whereas mathematics is a well-established discipline, numeracy is necessarily interdisciplinary. Like writing, numeracy must permeate the curriculum. When it does, also like writing, it will enhance students' understanding of all subjects and their capacity to lead informed lives."

Lynn Arthur Steen, Mathematics and Democracy: The Case for Quantitative Literacy, NCED, 2001.

"Numeracy is not the same as mathematics, nor is it an alternative to mathematics. Rather, it is an equal and supporting partner in helping students learn to cope with the quantitative demands of modern society. Whereas mathematics is a well-established discipline, numeracy is necessarily interdisciplinary. Like writing, numeracy must permeate the curriculum. When it does, also like writing, it will enhance students' understanding of all subjects and their capacity to lead informed lives."

Lynn Arthur Steen, Mathematics and Democracy: The Case for Quantitative Literacy, NCED, 2001.

"Numeracy is not the same as mathematics, nor is it an alternative to mathematics. Rather, it is an equal and supporting partner in helping students learn to cope with the quantitative demands of modern society. Whereas mathematics is a well-established discipline, numeracy is necessarily interdisciplinary. Like writing, numeracy must permeate the curriculum. When it does, also like writing, it will enhance students' understanding of all subjects and their capacity to lead informed lives."

Lynn Arthur Steen, Mathematics and Democracy: The Case for Quantitative Literacy, NCED, 2001.

Quantitative Methods for Public Policy

• Goals of the programProvide a useful, quantitative education to students throughout the College, including those who are utterly uninterested in mathematics.

Bring together faculty from varied disciplines, including those disciplines that avoid quantitative work, to send a clear message to students about the advantages of examining issues from a quantitative perspective

Assist faculty from all disciplines to understand the relevance of quantitative methods to their own scholarship, and enable them to make connections to quantitative methods in their classes.

Is a big population good or bad?

• Increased drain on fixed natural resources• Crowding, congestion, traffic• Lower wages (supply exceeds demand)BUT• Larger economy => economies of scale

– E.g., public transportation requires high density– Larger markets for movies, books, newspapers =>

diversity• Greater specialization of workers

– Benefits of open markets/free trade

Is population increase good or bad?

• Depends on whether we are above or below the ideal target population.

• Too fast an increase stresses infrastructure.• Demographic issues: age structure of population, wage

structure for workers.• Cultural issues: assimilation and tolerance• Can we benefit from “draining the brains” and capital of

other countries?• Growth as a component of planning [adding without

cutting]

Population

• One way to estimate what our ideal population should be is to look at countries that we admire, and copy them.

Populations of Largest Countries

China 1,246,871,951

India 1,000,848,550

United States 272,639,608

Indonesia 216,108,345

Brazil 171,853,126

Russia 146,393,569

Pakistan 138,123,359

Bangladesh 127,117,967

Japan 126,182,077

Nigeria 113,828,587

Mexico 100,294,036

Germany 82,087,361

Philippines 79,345,812

Vietnam 77,311,210

Egypt 67,273,906

Turkey 65,599,206

Iran 65,179,752

Thailand 60,609,046

Ethiopia 59,680,383

United Kingdom 59,113,439

France 58,978,172

Italy 56,735,130

Congo, Democratic Republic of the 50,481,305

Ukraine 49,811,174

Burma 48,081,302

Korea, South 46,884,800

South Africa 43,426,386

Colombia 39,309,422

Spain 39,167,744

Poland 38,608,929

Hong Kong 6571

Singapore 5540

Gaza Strip 3091

Bahrain 1015

Bangladesh 949

Taiwan 685

Korea, South 477

Netherlands 466

Puerto Rico 434

Lebanon 348

Belgium 337

Japan 337

India 337

Rwanda 327

West Bank 286

Israel 283

El Salvador 282

Philippines 266

Haiti 250

Jamaica 245

United Kingdom 245

Vietnam 238

Germany 235

Cyprus - Turkish Sector 225

Italy 193

Switzerland 183

Nepal 178

Korea, North 178

Pakistan 177

China 134

Poland 127

Denmark 126

Persons per square km

Tanzania 35

Cameroon 33

Eritrea 33

Estonia 33

Yemen 32

Guinea 31

Liberia 30

United States 30

Faroe Islands 29

Zimbabwe 29

Indonesia 118

Uganda 114

Guatemala 114

Kuwait 112

Slovakia 111

Hungary 110

France 108

Portugal 108

Malawi 106

Serbia 103

Egypt 68

Ethiopia 53

Mexico 52

Iraq 52

Jordan 51

Somalia 11

Congo, Republic of the 8

Canada 3

Australia 2

Population Density is Uneven

A Population Question

The population of the US is approximately 300M.

The population of Mexico is approx. 100M.

The US added about 30M in population over the last decade and Mexico added about 20M.

QUESTION: If this sort of growth continues in both countries, will the population of Mexico ever exceed that of the US?

Arithmetic Growth Model

• Add a constant amount each time period.

• Rate is described in terms of a number per time period: e.g., 30M per decade

• This is an intuitive form of growth: water into a bathtub, distance travelled at a constant velocity, age of a child.

Arithmetic Growth Model

0

100

200

300

400

500

600

700

2000 2010 2020 2030 2040 2050 2060 2070 2080 2090 2100

year

population (millions)

US population

Mexican population

Geometric Growth Model

• Growth is proportional to size.• Growth rate is described as a proportion or

percentage per time period.• Examples:

– Population– Bank interest– Inflation

• For geometric growth, the quantity doubles in a fixed period of time, the “doubling time.”

• More modern term, “Exponential growth.”

Doubling Time and the US Population

US Census data

Doubling time: 25 years

(today, the doubling time of the US population is about 70 years)

year Population

1790 3,929,827

1800 5,305,925

1810 7,239,814

1820 9,638,151

1830 12,866,020

1840 17,062,566

Geometric Growth Model

0

200

400

600

800

1000

1200

1400

200020102020203020402050206020702080209021002110212021302140

year

population (millions)

US population

Mexican population

Doubling Time: Rule of 72

• To approximate the doubling time corresponding to small growth rates, divide 72 by the rate in percent.

• US: approximately 1% per year, corresponds to a doubling time of 72 years.

• Mexico: approximately 1.8% per year; doubling time of 40 years.

• In 140 years, US would double twice, Mexico about 3 and a half times: 2*2*2*√2 ≈ 12 times the original population!

Thus time alone relieves a debtor nation, so long as its population increases faster than unpaid interest accumulates on its debt.

This fact would be no excuse for delaying payment of what is justly due [compensation for owners(!) of slaves to be emancipated in the year 1900], but it shows the great importance of time in this connection – the great advantage of a policy by which we shall not have to pay until we number 100,000,000 what by a different policy we would have to pay now, when we number but 31,000,000.

-Abraham LincolnState of the Union Address 1862