Math AA Internal Assessment Example, High school final essays of Mathematics

Things to imporve on this assessment: Math IA Improvements: - Cut out Spain and Japan - Add more data in the US (put in appendix) - Test for linear by doing the vertical line test - R squared formula for best trend line (after pearson) look for other trend lines - LINEA POTENCIAL - Do Chi Square test to show correlation instead of causation - Remove screenshots - fix tables and equation editor problems - Show standard deviation - Quantitative predictions in conclusion + reflections

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Is Migration Good for The
Economy?
The aim of my investigation is to determine the relationship
between net migration and GDP per capita in the USA, Japan
and Spain.
Word Count: 3374
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Is Migration Good for The

Economy?

The aim of my investigation is to determine the relationship

between net migration and GDP per capita in the USA, Japan

and Spain.

Word Count: 3374

Introduction

There has been a rise of politicians who like to sell the idea that migrants negatively

affect the economy (Goldin et al. 2018). These views risk hindering efforts to

implement migration policies for the upcoming demographic and economic changes

facing many countries (OECD 2014). Most of my family are immigrants from Ecuador

to Spain and have received severe discrimination from it. But what’s the reality? To

solve the question, the aim of my investigation is to determine the relationship between

net migration and GDP per capita in the USA, Spain and Japan.

  1. Personal Interest

I have chosen to analyse Spain due to my own personal connection to the country. I was

born in Ecuador, but have lived in Spain for most of my life. There is a growing anti-

migration sentiment across Europe (Goldin et al. 2018), and this has given rise to many

political parties, such as Vox in my country, who campaign for the expulsion of

immigrants, specifically Muslim (Casals 2019). They are gaining popularity and,

thereby, excusing hate crimes and religious intolerance, which have seen an alarming

120% increase in 2017 (Ansa 2019). The most common myth spread by the media and

leaders is that immigrants hurt the country financially (Anti- Defamation League 2019).

I can’t help but wonder how close to the truth this statement lies.

  1. The US Migration

To further investigate this relationship, I selected two demographically opposite

countries: the US and Japan. The United States has the most immigrants out of all the

countries in the world. Immigrants account for 13.6 % of the nation’s population.

However, the country has seen a fall of new arrivals due to the decrease in number of

GDP is divided by the population of the country, the GDP per capita is calculated

(Codrington 2017). This shows that the people living in the country are getting

wealthier not the countries aggregate economic growth (Kopf 2018), which is far more

important for my investigation. This also allows me to compare countries, as less

populated countries would be negatively affected in terms of its GDP in total.

Net migration stands for “the estimated rate of net migration (immigration – emigration)

per 1,000 people” (Population Reference Bureau 2019). The figure is especially

valuable because it can be estimated without the data for specific migration streams

(Lieberson 1980). In epidemiologic research, rates are typically expressed per 1000

population as it reflects the “actual experience” of a population (Bains 2019). Thus, for

my exploration I wanted to incorporate a widely used measure that accurately represents

the difference between the movement into and out of a country. The data for the net

migration is only measured after a 5-year period, this is because information about the

country of residence is collected 5 years before the census to provide a reference date to

international migration during a definite point in the past. Consequently, I also had to

select the GDP per capita data within a 5-year period (USCB 2019).

Table 1

Data collected of GDP per Capita ($) and Net Migration per 5 years from 1962 to 2017

in the US (World Bank Data Set)

Year GDP per capita (US$) Net Migration

Table 1 shows that in the US, as time passes and the net migration increases, so does the

GDP per capita. The lowest net migration in 1967 was correspondent to one of the

lowest GDP per capita value recorded on the table. Moreover, the lowest value for GDP

per capita in 1962 had the second lowest net migration of 1556054. In 2007, the table

shows the highest net migration of the data and a GDP per capita of over 47,975$. The

highest GDP per capita measured on Table 1 is in 2017, with a net migration of over 4

million immigrants which is a significant improvement of the net migration in 1962 of

1,835,728. In the 1990s, the number of immigrants entering the United States each year

grew exponentially, and hit a peak at the end of the decade with a substantial decline

after 2001. By 2002, the net migration had dropped by almost half and the immigration

flows have since been significantly below the peak values of 1999-2000. Between 1995

and 2000 the GDP per capita grew at a faster rate than ever before, and the slope

decreased after the 2000s. This could show a correlation between the immigration flows

and the improvement of the economy.

Due to the fact that I am researching the correlation, a plot

graph would be the most suitable to represent the data. As it shows each individual

point and the relationship between them. A trend line was chosen to show the best fit.

y = ax + b

Where:

- y is the dependent variable - x is the independent variable

  • a is the gradient, gives the rate of change of the dependent variable
  • b is the y-intercept, value of the dependent variable when x=

To solve for a, the formula goes as follows:

a =

y 2 − y 1

x 2 − x 1

Then, I substitute my values:

a =0. 0064

The gradient of the line is positive; this means it increases, therefore, migration has a

positive effect on GDP per capita. However, the value is under 1 which shows a weak

effect. To verify, I placed the data on the calculator to check the values for a, as seen in

Figure 2, the data matches the information given.

Figure 2 Image showing the a value of the function f(x)=0.0064x-904.537 and the graph

(Created by the Author on Casio calculator)

However, the gradient can not show the linear correlation between the two variables.

For this I will use the Pearson Correlation Coefficient, which measures strength

between the different variables and their relationships. The values can range from +1 to

-1, where +1 demonstrates a perfect positive relationship between the variables, the -

demonstrates a perfect negative, and a 0 value indicates no correlation (Verwey 2019).

Pearson’s Correlation Coefficient is as follows (WallStreetMojo 2019):

r =

n ( Σ xy )−( Σ x )( Ey )

Where:

  • r= Pearson Correlation Coefficient
  • n= number of the pairs of the stock
  • Σ xy = sum of products of the paired stocks
  • Σx = sum of the x values

Σ y = sum of the y values

Σ x

2

= sum of the squared x values

Σ y

2

= sum of the squared y values

Then, I substituted my values:

r =0.

As you can observe in Figure 2, this value was also verified. The r value indicates a

moderate fit, as it lies between the ranges of ±0.20 < r < ±0.85 (Verwey 2019). The

Pearson Correlation Coefficient has not only indicated the absence or presence of a

correlation, but the extent to which the variables are correlated. This demonstrates a

positive correlation between net migration and GDP per capita in the US, which proves,

to a certain extent, that the influx of migrants into the US does not jeopardize the

economy.

Year GDP per capita (US$) Net Migration

Table 2 shows that in Japan, until 2017, as time passes GDP per capita increases and net

migration fluctuates but increases overall by 206,449. The lowest GDP per capita value

on the graph corresponds to the second lowest net migration. The highest net migration

of 822,703 shows a big increase in GDP per capita from 1962 to 1967, where both the

net migration and GDP per capita remained high after then. A decrease of GDP per

capita in 1997 to 2002 of 2,732.37$ is correlated to a significant decrease in net

migration in 1997. Moreover, in 2012 to 2017 there is a decrease in both GDP per

capita and net migration. Then, as seen above, to show correlation more effectively I

made a plot graph:

-400000 -200000 0 200000 400000 600000 800000 1000000

0

10000

20000

30000

40000

50000

60000

Japan GDP per capita and Net Migration Relation

Net migration

GDP per capita

Figure 3. Graph showing the relationship between GDP per capita (US$) and Net

Migration in Japan from 1962 to 2017 (Created by Author on Excel)

As seen in Figure 3, the graph is not similar to Figure 1. The trend line has negative

gradient and the standard deviation from most values is significantly high. The

anomalies are the majority of the points in the graph under the trend line, they show that

as net migration increases GDP per capita decreases. However, all of these points are

from the year 1962 to 1982 which are relatively close to the end of World War 2, in

which Japan suffered from its worst recession (Crawford 1998). Japan’s economy began

to take off in the 70s, but then was struck by its first oil-price shock and the nation’s

industrial industrial production decreased by 20%. In addition to raising the price from

3 dollars to 13 dollars, there was a second oil-shock in 1978 which raised the price of

oil to 39.5 dollars (Business Inter, 1978). Japan started having a stable economy in the

1980s. After exploring the background knowledge of the anomalies in terms of GDP per

a =0,

The Pearson Correlation Coefficient is:

r =0.

This correlation coefficient is a strong moderate fit, close to a strong fit. Shows a

significant correlation between Net Migration and GDP per capita in Japan.

  1. Spain Migration

In the last half of the 1990s, immigration started to become a vital issue for politicians

and the Spanish public. The nation’s transition into a country of immigration was part of

a larger phenomenon. At the end of the 1980s, in the middle of the economic crisis,

Southern European countries of the Mediterranean, such as Italy, Greece and Portugal

became receiving countries instead of the so-called “waiting rooms” (Ortega 2003).

According to the United Nations, immigrants compromise 12.8% of the population in

Spain (Rolfe et al. 2018). When the migrant surge began in 2015, much of Western

Europe was welcoming, however, since then many of the countries have closed their

border and supported anti-migrant politicians. The most significant exception is Spain.

In the beginning of the year 2018, almost 49,000 refugees/ migrants landed in Spain

(Rolfe et al. 2018). The anti-migrant party Vox had 9,000 people attend a rally in

Madrid last month and has won a seat in parliament, but the party is still relatively

weak. The data to be analysed will show the effects of this ‘heavy’ influx and could

serve as a role model for other countries to continue to open their borders.

  1. Data Analysis – Spain

The data collected will be represented like in Tables 1 and 2, and graphed like in

Figures 1 and 3 for easier comparison and illustration of information.

Table 3

Data collected of GDP per capita (US$) and net migration per 5 years from 1962 to

2017 in Spain (World Bank Data Set).

Year GDP per capita (US$) Net Migration

Table 3 shows that as time increases, GDP per capita increases and, even though net

migration fluctuates throughout the years, it increases overall by 6,193. Increases in net

migration during 1962 to 1977 see an increase in GDP per capita. There is a significant

increase of 1,342,776 in the years between 1997 and 2007 which correspond to an

exponential increase in GDP per capita. From 1992 to 2002, the number of people with

origins in developing countries increases 214% by year (Ortega 2003). There is a

significant increase in the 1990s due to the closing of borders of neighbouring countries

who were traditionally opening, for example, Germany and Switzerland (Perez 2003).

Both values go through a fall in 2012, and GDP per capita continues decreasing whilst

net migration rises in 2017.

Correlation Coefficient falls smaller than the countries calculated previously and is a

moderate fit:

r =0.

The fluctuation of net migration may have lowered the correlation, as the US data of net

migration shows a constant increase (Table 1), and the Figure 4 of Japan also shows a

relatively stable increase.

Conclusion

After analysing the data from the US, Japan and Spain I have reached the conclusion

that the influx of migrants does not hinder the GDP per capita. All the correlations, after

certain adjustments, were positive and above moderate fit. There was no evidence for

causation. Therefore, I have met my aim to demonstrate the relationship between net

migration and GDP per capita in the USA, Spain and Japan.

There were several anomalies in each table and graph, this is due to a limitation of the

GDP per capita. To understand the impact of immigration on an economy more factors

should be assessed. The OECD recommends three main areas: the public purse, the

labour market and economic growth. Investigating these elements of an economy would

give a broader perspective than GDP per capita (OECD 2014). Such understanding is

essential to design policies that maximise the benefits of migration, which is

fundamental in coming decades as rapid aging populations increase the demand for

migrants to replace the workforce.

Works Cited

“About Us.” Data World Bank , World Bank , data.worldbank.org/about.

“Alarm in Spain over Increase in Hate Crimes, Islamophobia.” InfoMigrants , ANSA, 25

Mar. 2019, www.infomigrants.net/en/post/15886/alarm-in-spain-over-increase-in-

hate-crimes-islamophobia.

Bains, Namrata. “Standardization of Rates .” Standardization of Rates , 2009,

core.apheo.ca/resources/indicators/Standardization

%20report_NamBains_FINALMarch16.pdf.

McCurry, Justin. “Japan under Pressure to Accept More Immigrants as Workforce

Shrinks.” The Guardian , Guardian News and Media, 26 Nov. 2015,

www.theguardian.com/world/2015/nov/26/japan-under-pressure-to-accept-more-

immigrants-as-workforce-shrinks.

Measuring Migration in a Census. United States Census Bureau , Feb. 2019,

www.unfpa.org/sites/default/files/resource-pdf/measuring-migration.pdf.

“Myths and Facts About Immigrants and Immigration (En Español).” Anti-Defamation

League , Anti-Defamation League, www.adl.org/resources/fact-sheets/myths-and-

facts-about-immigrants-and-immigration-en-espanol.

Plumer, Brad, et al. “New Research Suggests an Aging Workforce Is Holding Back

Economic Growth: The New New Economy.” Vox.com , www.vox.com/a/new-

economy-future/aging-population-slow-growth.

Pérez, Nieves Ortega. “Spain: Forging an Immigration Policy.” Migrationpolicy.org , 2

Mar. 2017, www.migrationpolicy.org/article/spain-forging-immigration-policy.

Radford, Jynnah. “Key Findings about U.S. Immigrants.” Pew Research Center , Pew

Research Center, 17 June 2019, www.pewresearch.org/fact-tank/2019/06/17/key-

findings-about-u-s-immigrants/.

“Rise, Peak and Decline: Trends in U.S. Immigration 1992 - 2004.” Pew Research

Center's Hispanic Trends Project , Pew Research Center, 1 Apr. 2013,

www.pewresearch.org/hispanic/2005/09/27/rise-peak-and-decline-trends-in-us-

immigration-1992-2004/.

Rolfe, Pamela, and James McAuley. “Spain Is the Most Welcoming Country in Europe

for Migrants. Will It Last?” The Washington Post , WP Company, 28 Oct. 2018,

www.washingtonpost.com/world/europe/spain-is-the-most-welcoming-country-

in-europe-for-migrants-will-it-last/2018/10/27/73aa0c0a-c0e9-11e8-9f4f-

a1b7af255aa5_story.html.

Stokes, Bruce, and Kat Devlin. “Japanese Views on Immigrants, Immigration,

Emigration.” Pew Research Center's Global Attitudes Project , Pew Research

Center, 12 Nov. 2018, www.pewresearch.org/global/2018/11/12/perceptions-of-

immigrants-immigration-and-emigration/.

Verwey, Victoria Mathematics Teacher

Wallace, Ben Mathematics Teacher