FE550 A2: GDP and FX Rates

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<H1> FE 550 Assignment 2 </H1>
<H2 class="italic"> Robert McAllister </H2>
<H2 class="italic"> June 18, 2017 </H2>
<H1> Exploring Relationship Between Country's GDP Growth and Currency Strength</H1>
<H2> Introduction </H2>
<p class="text"> GDP and FX Rate are both assumed to be indicators for the strength of a country's economy. GDP is an indication of internal production while an FX Rate shows the strength of the local currency relative to the rest of the world. Given how tied both are to an economy, this paper will explore whether there is a relationship between them, the annual change in a country's GDP and the country's FX rate. Specifically, is there a significant historical correlation between the growth rate of a country's GDP and the strength of its currency's FX rate?

As a benchmark, we will use the US' GDP growth rate, and for FX rates all will be relative to USD. We will use data from 1980 through 2015 for this analysis and will use a sample of developed and emerging market economies across the globe.

<H2>Data</H2>
<p class="text">As stated in the introduction, we will be using a sample of countries from across the globe including both developed and developing economies. The data was sourced from the United States Department of Agriculture: Economic Research Service. Here, they maintain a set of historical economic data for countries across the globe.
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<a href="https://www.ers.usda.gov/data-products/international-macroeconomic-data-set/international-macroeconomic-data-set/#Historical">USDA ERS Historical Macroeconomic Data</a>
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From here, I will use two specific data sets: GDP and FX Rates. Using Excel and some basic manipulation we extracted the historical GDP Value, Growth Rates, FX Rates, and FX Growth Rates. 
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We selected the following countries (in these regions) for this analysis:
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<ul style="list-style-type:circle" class="text">
	<li> Canada (Americas)</li>
	<li> Mexico (Americas)</li>
	<li> Brazil (Americas)</li>
	<li> France (Europe)</li>
	<li> Greece (Europe)</li>
	<li> Ireland (Europe)</li>
	<li> Italy (Europe)</li>
	<li> Spain (Europe)</li>
	<li> UK (Europe)</li>
	<li> Switzerland (Europe)</li>
	<li> Russia (Eastern Europe)</li>
	<li> China (Asia)</li>
	<li> Hong Kong (Asia)</li>
	<li> Japan (Asia)</li>
	<li> Korea (Asia)</li>
	<li> Singapore (South Asia)</li>
	<li> India (South Asia)</li>
	<li> Australia (Oceania)</li>
	<li> South Africa (Africa)</li>
</ul>
</p>
<p class="text">
The FX Rates were already relative to the US Dollar (values are the direct USD to Local rates), but we needed to create a GDP Growth Rate value relative to the US for our analysis. To do this, we created a new value which is the difference in GDP Growth percentage in the local country to the GDP growth percentage of the US. The data went from 1980 through 2015, so for our analysis we wull be using 1981 through 2015 (no change data for 1980).
</p>
<H2> Analysis </H2>
<p class="text">
To start, we will use a single economy, the United Kingdom, for an initial analysis. The below highlights the GDP values in both the US and the UK over our selected time period
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<script src="USAandUKGDPScatter.js"></script>
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<p class="text">
As we look at the chart, we can see consistent growth in GDP for both countries. The slope indicates a sharper increase in the US GDP, and overall more muted changes in the UK as is evident in 2009 when both look to decrease with the US's decline being much more severe.
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As we are interested in the relationship of the changes between the two, lets now look at a plot of the plot of both country's GDP percentage changes
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<script src="USAandUKGDPChangeScatter.js"></script>
<p class="text">
Despite in absolute values the US seeming to be growing more than the UK, when looking at the percentage changes the chart suggests that the US is not growing at a faster rate (nor declined more in 2009) when looked at from a percentage standpoint. Both countries had dispersed years of greater positive and negative percent changes. Given our analysis is looking at these changes relative to one another, the below visualizes the relative percentage change in GDP over this period (UK GDP Percent Change less US GDP Percent Change)
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<script src="UKRelativeGDPChangeScatter.js"></script>
<p class="text">
When looking at these relative numbers, we can see the previous observation plotted outright. Throughout this period, the relative growth rate in GDP between the UK and US fluctuated between positive and negative values with a range between -5 and 4%. Now that we see differences exist in these relative GDP Growth Rates, lets now look at the change in the FX Rates (USD/GBP). The below chart highlights the percentage change in USD/GBP FX Rate over this same time period.
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<script src="UKFXRateChangeScatter.js"></script>
<p class="text">
When we look at FX Rate changes, we can see the same type of variability, both positive and negative changes, like we saw with the GDP changes. The big question, and what we want to understand, is whether these positive and negative changes in both indicators is correlated. The below plots the FX Rate % Change for each year to the same year's Relative GDP Growth Rate.
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<script src="UKFXRatetoGDPChangeScatter.js"></script>
<p class="text">
Looking at this chart, we can see that there is no visual indication of correlation between these two economic indicators. A positive FX Rate Change did not necessarily mean the GDP Growth Rate in the UK increased relative to the US (and vise versa).
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We have confined our analysis to a single country initially, but now lets expand this and view the same plot but now include all of the countries in our analysis.
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<script src="AllFXRatetoGDPChangeScatter.js"></script>
<p class="text">
When looking at this, we can still see now visibly significant correlation between a positive relative change in GDP to a positive change in FX rate. One interesting thing that can be noted from this though is that the highest concentration of points seems to be around the 0% Relative GDP Change indicating the US GDP Growth not being significantly higher (or lower) than that of the rest of the world
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The chart separates out the data by region as well. One insight that can be gained from this is that the Asia and South Asia Relative GDP Values had a higher concentration in the greater than 5% range indiciating this part of the world has grown significantly over this time period.
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Rather than just looking at this from a visual standpoint, lets look at the actual statistics. Using R, we calculated the Correlation between the FX Rate Changes and the Relative GDP Changes, and overall across all countries this value was -.1745, indicating almost no correlation (and the small bit of correlation was on the negative side).
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While overall we see almost no correlation between these two indicators, if we examine the correlations across regions we see something interesting.
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<script src="RegionCorr.js"></script>
<p class="text">
While individually, each region had a negative correlation between the two indicators, South Asia and the rest of the Americas had a somewhat high negative correlation, with -.505 and -.426 respectively. Since these regions are made up of more than one country. Let's dig into the composition of these to see if individual countries were the cause of these high negative values.
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<script src="CountryCorr.js"></script>
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<p class="text">
Looking at the individual country correlations, 5 stick out in particular. Mexico (-.421) and Brazil (-.469) from the Americas, Korea (-.473) from Asia, and Singapore (-.620) and India (-.449) from South Asia. These all had high negative correlation values. If we look at the FX Rate Change and Relative GDP Growth Rate plots for a subset of these, we can see patterns.
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In Brazil, we see a similar plot to what we had in the UK plot, however the change values were more volatile on either side.
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<script src="BrazilFXRatetoGDPChangeScatter.js"></script>
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<p class="text">
In Singapore, you can see that there was a fairly consistent positive relative GDP growth, however this was not indicative of the same positive increase in FX Rate. This seems to be indicative of a growing economy in an emerging market. The FX rate seems to be relatively stable despite this growth.
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<script src="SingaporeFXRatetoGDPChangeScatter.js"></script>
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<p class="text">
And finally in Korea, in all but one year there was a higher GDP growth rate than in the US. This again did not signal that the other indicator, FX Rate, would have a positive increase though.
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<script src="KoreaFXRatetoGDPChangeScatter.js"></script>
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<H2> Conclusion </H2>
<p class="text">
After going through the analysis, there was not a significant relationship between the change in a country's local currency FX Rate and the relative GDP growth rate with the US as a benchmark. Not only was there no significant correlation, those that did have some statistical significance had a negative correlation due to a growing economy (GDP) relative to the US with a stagant (or reversing) FX Rate. 
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Now while this answers our original question, this analysis was done with the FX Rate and GDP Growth being compared at the same time (in this case year), but a future analysis could be done to see if GDP Growth Rate has a correlation to the future FX Rate change. The rationale for this could be that GDP growth could be indicator, however confidence needs to be instilled in sustained growth before the FX Rate adjusts for this positive GDP growth.
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