Download Immigration Growth and GDP per capita growth: A

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 Analysis
Descriptive Breakdown
Descriptive Analysis: Immigration
Growth
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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).
Annual Change in Migration
8
7
6
% Change
5
4
3
2
1
0
78
80
82
84
86
88
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92
94
96
98
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02
04
06
08
Year
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.
Descriptive Analysis: GDP per
capita growth
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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.
% change in GDP per capita
8
% change in GDP per capita
6
4
2
0
78
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93
98
03
08
-2
-4
Year
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.
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
Bibliography/References
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Inflation Rates, Saving Calculator, Relative Value, worth of a Dollar,
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<http://www.measuringworth.com/datasets/usgdp/result.php>.
• "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>.