Immigration Growth and GDP per capita growth: A Statistical Analysis

By: Nate Burr

Introduction

Introduction

In this research study, I will be analyzing the potential statistical relationship between immigration growth and per capita GDP growth. The United States of America is a country of immense wealth. Among many other attractions, it is a country that offers seemingly limitless opportunity. Consequently, foreign nationals from all over the world apply to become legal residents, students, and laborers here. Some have been waiting in line, so to speak, for decades; I personally know a family that waited fifteen years before being granted a green card. Comparatively, because they were sponsored by family members living in America, fifteen years was a rather quick response. (Continue next slide)

Introduction

Nevertheless, this long and enduring wait implies two things: firstly, there is a shortage of green cards made available during any given year to meet the corresponding number of applicants; and secondly, the United States Immigration Department, understandably, does have a limit and/or quota on annual immigration growth (my forthcoming descriptive analysis might numerically suggest what, exactly, that “limit” is). The goal of this paper is to derive some evidence, one way or the other, as to whether migrant growth and GDP growth have been correlated over the preceding thirty years. It’s important to note, however, I will not be investigating a causal relationship between these two variables; rather, I will simply test a possible correlation between them – and the intensity of that presumed correlation. With that said…

• Is immigration growth correlated with income per capita growth? Let’s attempt to find out! But first, allow me to present some conventional perceptions, and then my personal theory.

Polarized Philosophies• Pros• Immigrants come

equipped with fresh ideas• They create new

innovations• They spur job growth

Polarized Philosophies• Cons• Immigration floods

our labor market• They would decrease

the capital per unit of labor – lowering wages.• They take American

jobs

My Philosophy:

Just as I do not believe immigration has harmed the United States’ economy (by most measures), similarly, I do not believe migrant growth props up our economy either. I am suggesting that any statistical relationship between these two variables will be very weak, if not negligible; and this lacking would suggest some other – unknown – variable/s is at play. Furthermore, I do not believe immigration growth has outpaced capital investment growth over the last thirty years – an important argument of the immigration growth opposition. Similarly, it’s crucial to remember that an economy does not have a fix number of jobs that an ever increasing number of people are all vying for – job creation takes place. (Continue next slide)

My Philosophy:

In summary, I will be conducting and presenting a statistical study in an attempt to provide evidence denouncing both extreme, and oppositional, theories regarding immigration growth and its effects on America’s economy. I believe there is no statistical relationship between economic growth and immigration growth – at least in the short run – and that there are other unknown variables at work.

Methodology:Operational Definitions of my Variables

Operational Definitions:

Immigration Growth – the annual percentage change in United States net migration growth (migration inflows minus migration outflows), using 1978 as a base year (with a migration base of 13 million), and collecting data up to 2008 (the most recent data available). To mathematically derive the percentage change in migration I will use the following formula:

Operational Definitions:

Real GDP per capita growth – percentage change in real GDP per capita year-over-year, that is, nominal output per-capita adjusted for inflation. I’ll use 1978 as a base year and will be adjusting the annual per capita figures using a 2005 dollars index. To mathematically derive the percentage change in per capita GDP I will use the following formula:

Methodology:

Each of my data sets will be comprised of thirty observations (the years 1978 through 2008). This sample was drawn because I believe it provides the most telling and relevant data for my purposes, unlike the alternative earlier data sets. The year 1978 became my base year as it defined the thirty-year mark per reverse chronology from the year 2008. Moreover, a minimum of thirty observations is necessary to ensure a normal distribution that satisfies the Central Limit Theorem (a principle in statistics that attempts to sample out any randomness in data collection as to more accurately depict a true population mean). The Bureau of Economic Analysis and The United States Census Bureau are my two prevailing secondary sources of data.

A Statistical AnalysisDescriptive Breakdown

Descriptive Analysis: Immigration Growth• Mean• 3.533333• Standard Error• 0.186396• Median• 3.2• Mode• 3.2• Standard Deviation• 1.02093• Sample Variance• 1.042299• Kurtosis• 4.163631• Skewness• 1.976257• Range• 4.5• Minimum• 2.5• Maximum• 7• Sum• 106• Count• 30

The average percentage growth in migration over the 1978-2008 time periods was 3.53% per year. However, because the median percentage growth was 3.2% we know the data is positively skewed as a result of a few higher extremes. This is reinforced with a +1.98 skewness statistic. The mode here is 3.2%, which implies this percentage is the most frequently observed growth rate in my sample. On average, a single observation in my sample varies from the mean (of 3.53 percent) by 1.02 percent. The highest growth rate in my sample was 7% (in 1991), and the lowest was 2.5% (in 2008).

As the above line chart depicts, there were some unusually high migrant growth rates to begin each of the last two decades. Omitting these extremes, we can see that over the past thirty years immigration growth has been rather stable at, or around, our median of 3.2% per

annum. This may provide some gauge as to what exactly our government’s implicit growth target is.

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Descriptive Analysis: GDP per capita growth• Mean• 1.803• Standard Error• 0.335617• Median• 2.05• Mode• 1.5• Standard Deviation• 1.838251• Sample Variance• 3.379167• Kurtosis• 1.293615• Skewness• -0.50689• Range• 9.2• Minimum• -2.9• Maximum• 6.3• Sum• 54.09• Count• 30

The mean percentage growth in GDP per capita over the 1978-2008 time span was 1.8% per annum. However, the median growth rate was 2.05%, meaning the data is negatively skewed as a result of a few low extremes (likely during economic recessions). This is reinforced with a negative skewness statistic. We have a mode of 1.5%, meaning this growth rate was most frequently observed in our sample of thirty years. On average, an individual observation in this sample varies from the mean (1.8%) by roughly 1.84%. The lowest growth period recorded a 2.9% decline in per capita GDP (in 1982), with the highest growth period recording a 6.3% increase in output per capita (in year 1984). These extremes are indicative of the 1982 recession and subsequent economic expansion.

The above bar chart illustrates the thirty-year trend of GDP per capita growth. The downward sloping trends represent recessions, with the low points depicting

troughs (the ending of a recession). The upward sloping trends represent economic expansions, with the high points representing business cycle peaks (the

ending of an expansionary period). We can clearly see the downward trend, beginning in 2004, and leading to the 2008 financial crisis and recession.

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Correlation Bivariate Analysis The Conclusive Test

Bivariate Analysis:• This is the critical stage of my study. Here, we will more

conclusively examine the correlation of my two variables using the following formula:

• We will be testing at the 5% level of significance; a level that provides strong and credible evidence.

• With our results, we will be enabled to compare the test data with my initial theory (nonexistent statistical correlation).

Bivariate Analysis:

• Ho: ρ = 0 becomes are null hypothesis, where 0, or any number that is statistically similar to 0, would suggest no linear association between our two variables.

• HA: ρ ≠ 0 becomes our alternative hypothesis, where any number other than 0 would suggest some linear association between our two variables.

• Our critical values become: -2.0484 and 2.0484. These values are located on what’s termed a “t-chart,” and are determined by our level of significance (5%) and our sample size (30). Any number outside of this range allows us to reject the null, and conclude there is a linear association between immigration growth and GDP per capita growth – discrediting my argument.

Bivariate Analysis: Correlation and Covariance Statistics

Correlation:  -0.3266

Covariance:-.5925

Bivariate Analysis: Correlation and Covariance Statistics

In the preceding slide, I have used Excel to derive the covariance and correlation of my two variables. The covariance measures the direction of a potential linear relationship between two numerical variables. In this study’s case, the covariance is -.5925. The negative measure suggests that my sample data are negatively related – this is somewhat inconsistent with my initial theory that these variables are not related – let’s dig deeper. To measure the strength of this supposed negative relationship, we compute the correlation – similar to the covariance measure in that it measures the direction of a potential linear relationship of two numerical variables, however, it also measures the strength of that relationship (a derivation of “1” meaning the two variables are perfectly correspondent, while a derivation of “0” suggests absolutely no relation between the two variables). With a correlation measure of -.3266, we once again have evidence that there is a negative relationship between the two variables in this sample; once again weakening my hypothesis. However, -.3266 is a rather weak correlation and should not be taken for granted just yet.

The Irrefutable Test:• Using our Bivariate Correlation formula:

≈ -1.82847338657 ≈ -1.83

• Because our test result (-1.83) is inside of our critical range, we can accept the null and conclude there is no statistically significant linear relationship between our two variables at the 5% level of significance. That is, -2.0484 < -1.83 < 2.0484.

• This is a noteworthy finding. Through this analysis, I have found strong evidence against both polarizing philosophies regarding immigration. According to our descriptive analysis (correlation and covariance), we may be inclined to assume an inverse correlation between our variables, albeit weak, but a more thorough analysis discredits this presumption and provides statistically-irrefutable evidence that there is not a statistically significant linear relationship between migrant growth and GDP per capita growth.

• The earliest our test statistic (-1.83) allows us to reject the null hypothesis is at the 10% level of significance, but at this level the evidence is considerably weaker than at more accurate levels. We will accept our 5% level hypothesis test, where we accept the null.

Summary and Conclusions• Having completed a thorough statistical analysis of a possible

linear correlation between immigration growth and GDP per capita growth, and using the results to test my original thesis (that these two variables are not associated), we can conclude – based on strong evidence, but no proof – that there, in fact, may be a slightly negative correlation between these two variables. However, further analysis suggests that any correlation is most likely just random, or by chance, and provides evidence to suggest that there is no statistically significant relationship between migrant growth and GDP per capita growth.

Thank You for Viewing!The End

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• "Population Estimates." Census Bureau Home Page. Web. 10 Apr. 2011. <http://www.census.gov/popest/national/national.html>.

• "Statistics Help - Free Math Help." Free Math Help - Lessons, Tutoring, Message Board and More. Algebra, Geometry, Trig, Calculus... Whatever Level You're Studying! Web. 10 Apr. 2011. <http://www.freemathhelp.com/statistics.html>.

• U.S. Bureau of Economic Analysis (BEA) - Bea.gov Home Page. Web. 10 Apr. 2011. <http://www.bea.gov/>.

• USCIS Home Page. Web. 10 Apr. 2011. <http://www.uscis.gov/portal/site/uscis>.