Introduction:
In this report we will be examining three economic indicators real GDP growth, the unemployment rate and the inflation rate from the 1929 to 2017. We will be specifically focusing on the real GDP growth rate and the unemployment rate in the US and how the two variables affect each other. We will also look at future forecasts and measure the accuracy of these forecasts using different methods and calculating the errors.
Cleaning the data
We put all the cleaned data into percentages. This is because we believe that it helps to make the data easier to interpret and is a better match since we are talking about rates of change. The first variable we looked at was the inflation rate this can be described as an increase in the prices of goods, the cost of living and a decrease in the value of money. As the inflation rate increases prices, interest rates for banks increase too and can result in a higher level of unemployment due to business’s failing. Another variable in which we looked at is the unemployment rate which is those that are able to work but currently do not, expressed as a percentage. A consistently high unemployment rate can cause many issues such as an decrease in disposable income, which would lead to a decrease in consumer spending. The last variable that we looked at was the GDP growth rate (Gross Domestic Product) which is the market value of the entirety of the goods and services produced in a country over a particular time period. A high GDP would suggest that a country is increasing the amount of production and services that it is supplying and citizens should have a higher income. The cleaned data can be seen in Figure 1.
Descriptive Statistics
Figure 2: Descriptive Statistics
GDP
Inflation
Unemployment
Mean
6.35%
3.15%
7.15%
Median
6.13%
2.80%
5.70%
Standard Deviation
6.87%
4.03%
4.70%
Sample Variance
0.47%
0.16%
0.22%
Kurtosis
5.9271
3.9766
4.4907
Skewness
-0.7855
0.2803
2.1561
Range
51.43%
28.40%
23.70%
Minimum
-23.09%
-10.30%
1.20%
Maximum
28.34%
18.10%
24.90%
Count
88
88
88
Here are some descriptive statistics for all the variables. With the cleaned data we used a full sample to calculate these statistics. The first statistic that we calculated was the mean. The mean is affected by extreme values which does not make it very effective when there are outliers. When the mean is larger than the median the graph will have a positive skew. From this we can identify that all there of the variables GDP, inflation and unemployment will have a positive skew. We then looked at the standard deviation and sample variance. The standard deviation tells you how much the data varies from the mean, helping to tell you how accurate the mean is. The sample variance tells you how varied the data is. Kurtosis is used to describe the distribution of data. All kurtosis values are greater than 3, all the graphs will be leptokurtic. We also calculated the skewness of the data which can tell you how the distribution differs from a normal distribution. The range gives you an idea of the spread of the data but is affected by outliers.
Figure 3: Graph of the percentage change of the inflation, unemployment and GDP rate from 1929 to 2017
From the line graph that we have created here you can see how the inflation, unemployment and GDP growth rate has changed over the years 1929 to 2017. During the first few years all the variables fluctuate a lot, this suggests uncertainty in the economy, from 1929 to 1953. At the start where the GDP growth rate and the inflation rate had a large decrease in percentage change while the unemployment rate was increasing shows that there is a strong negative correlation between the variables GDP and unemployment as well as inflation rate and unemployment. This correlation becomes weaker as the graph progresses. However, after this time period the variables seem to be less susceptible to change and all the variables seem to increase and decrease at a similar level, this could be due to a stronger economy.
GDP Growth Rate and Unemployment Rate
Figure 4: A graph to show the correlation between GDP and unemployment rate
Regression Statistics
Multiple R
0.3157
R Square
0.0997
Adjusted R Square
0.0881
Standard Error
0.0683
Observations
80
We then compared the GDP growth rate to the unemployment rate. From this scatter diagram here you can see the negative correlation between the two variables although a weak correlation it is still evident on the graph. We have also made some statistics for the regression line of this graph which show the R squared value of 0.0997 also called the coefficient of determination, which can give you an indication as to how accurate the line of best fit is, as the value is not close to 1, where the regression line fits the data, the regression line is not the best estimate for future predictions as the data is not very close to the regression line. The correlation coefficient of this graph is -0.4613, it is weak negative correlation.
Figure 5: Regression Statistics
Coefficients
Intercept
0.0994
Unemployment X
-0.4613
By using the least squares model we were able to calculate the equation of the regression line for the data which is y = -0.4613(X) + 0.0994. The slope of this regression line is -0.4613 and the Y-intercept is 0.0994. The regression line can be used to help predict future outcomes.
Figure 6: Regression Line
Forecasting Analysis
Date
Unemployment Rate %
GDP Growth Rate %
Forecast GDP
Error
Absolute Value of Error
Squared Error
2010-01-01
9.30%
3.76%
5.65%
-1.89%
1.89%
0.04%
2011-01-01
8.50%
3.67%
6.02%
-2.35%
2.35%
0.06%
2012-01-01
7.80%
4.21%
6.34%
-2.13%
2.13%
0.05%
2013-01-01
6.70%
3.63%
6.85%
-3.22%
3.22%
0.10%
2014-01-01
5.60%
4.39%
7.36%
-2.97%
2.97%
0.09%
2015-01-01
5.00%
3.98%
7.63%
-3.65%
3.65%
0.13%
2016-01-01
4.70%
2.68%
7.77%
-5.09%
5.09%
0.26%
2017-01-01
4.02%
4.16%
8.09%
-3.93%
3.93%
0.15%
Figure 7: Forecasting
MSE
Mean Squared Error
0.11%
MAD
Mean Absolute Deviation
3.15%
TS
Tracking Signal
-8
RMSE
Root Mean Square Error
0.0331
By using the last 8 observations to create an out of sample analysis we worked out an estimated forecast and calculated the accuracy of this forecast. As the coefficient of determination is not very strong the forecast was not likely to be very accurate but can still be a useful way to predict upcoming trends in the economy. In this table it shows you the actual value of the GDP and the forecasted value with another column to show the level of error in the prediction. We also calculated the root mean standard deviation of the residuals, the RMSE, this can give you an idea of how close the data is to the line of best fit. Another measure we used to see how accurate the forecasting was the MSE, mean squared error. The smaller the value for the MAD the more accurate the forecast is. The tracking signal here is above the average which is -4 to 4 suggesting that the data does have some bias.
Figure 8: Forecasting Errors
Conclusion
Overall we think that the forecast predictions for the out of sample data were not very accurate however, we believe that they can still be used to help predict future trends in the economy along with other models. The weak correlation between the two variables made forecasted predictions of the GDP growth rate and unemployment rate inaccurate. However we were still able to identify using the in sample analysis, using all the data given to us that there is a negative correlation between the two variables, as the GDP growth rate increases the unemployment decreases. This correlation also makes sense in economic terms as when a country is producing more goods more jobs should be made available.
References:
Economicshelp.org. (2018). [online] Available at: https://www.economicshelp.org/macroeconomics/inflation/definition/ [Accessed 25 Nov. 2018].
Seth, S. (2018). Inflation Definition | Investopedia. [online] Investopedia. Available at: https://www.investopedia.com/terms/i/inflation.asp [Accessed 25 Nov. 2018].
FocusEconomics | Economic Forecasts from the World’s Leading Economists. (2018). What is the unemployment rate?. [online] Available at: https://www.focus-economics.com/economic-indicator/unemployment-rate [Accessed 25 Nov. 2018].
Appendix:
Figure 1: Cleaned Data
Observation date
GDP(billions of dollars)
Inflation Rate %
Unemployment rate %
GDP Growth Rate %
1930-01-01
92.1600
-6.40%
8.70%
-11.86%
1931-01-01
77.3910
-9.30%
15.90%
-16.03%
1932-01-01
59.5220
-10.30%
23.60%
-23.09%
1933-01-01
57.1540
0.80%
24.90%
-3.98%
1934-01-01
66.8000
1.50%
21.70%
16.88%
1935-01-01
74.2410
3.00%
20.10%
11.14%
1936-01-01
84.8300
1.40%
16.90%
14.26%
1937-01-01
93.0030
2.90%
14.30%
9.63%
1938-01-01
87.3520
-2.80%
19.00%
-6.08%
1939-01-01
93.4370
0.00%
17.20%
6.97%
1940-01-01
102.8990
0.70%
14.60%
10.13%
1941-01-01
129.3090
9.90%
9.90%
25.67%
1942-01-01
165.9520
9.00%
4.70%
28.34%
1943-01-01
203.0840
3.00%
1.90%
22.38%
1944-01-01
224.4470
2.30%
1.20%
10.52%
1945-01-01
228.0070
2.20%
1.90%
1.59%
1946-01-01
227.5350
18.10%
3.90%
-0.21%
1947-01-01
249.6160
8.80%
3.90%
9.70%
1948-01-01
274.4680
3.00%
4.00%
9.96%
1949-01-01
272.4750
-2.10%
6.60%
-0.73%
1950-01-01
299.8270
5.90%
4.30%
10.04%
1951-01-01
346.9140
6.00%
3.10%
15.70%
1952-01-01
367.3410
0.80%
2.70%
5.89%
1953-01-01
389.2180
0.70%
4.50%
5.96%
1954-01-01
390.5490
-0.70%
5.00%
0.34%
1955-01-01
425.4780
0.40%
4.20%
8.94%
1956-01-01
449.3530
3.00%
4.20%
5.61%
1957-01-01
474.0390
2.90%
5.20%
5.49%
1958-01-01
481.2290
1.80%
6.20%
1.52%
1959-01-01
521.6540
1.70%
5.30%
8.40%
1960-01-01
542.3820
1.40%
6.60%
3.97%
1961-01-01
562.2100
0.70%
6.00%
3.66%
1962-01-01
603.9210
1.30%
5.50%
7.42%
1963-01-01
637.4510
1.60%
5.50%
5.55%
1964-01-01
684.4600
1.00%
5.00%
7.37%
1965-01-01
742.2890
1.90%
4.00%
8.45%
1966-01-01
813.4140
3.50%
3.80%
9.58%
1967-01-01
859.9580
3.00%
3.80%
5.72%
1968-01-01
940.6510
4.70%
3.40%
9.38%
1969-01-01
1017.6150
6.20%
3.50%
8.18%
1970-01-01
1073.3030
5.60%
6.10%
5.47%
1971-01-01
1164.8500
3.30%
6.00%
8.53%
1972-01-01
1279.1100
3.40%
5.20%
9.81%
1973-01-01
1425.3760
8.70%
4.90%
11.43%
1974-01-01
1545.2430
12.30%
7.20%
8.41%
1975-01-01
1684.9040
6.90%
8.20%
9.04%
1976-01-01
1873.4120
4.90%
7.80%
11.19%
1977-01-01
2081.8260
6.70%
6.40%
11.12%
1978-01-01
2351.5990
9.00%
6.00%
12.96%
1979-01-01
2627.3340
13.30%
6.00%
11.73%
1980-01-01
2857.3070
12.50%
7.20%
8.75%
1981-01-01
3207.0420
8.90%
8.50%
12.24%
1982-01-01
3343.7890
3.80%
10.80%
4.26%
1983-01-01
3634.0380
3.80%
8.30%
8.68%
1984-01-01
4037.6130
3.90%
7.30%
11.11%
1985-01-01
4338.9790
3.80%
7.00%
7.46%
1986-01-01
4579.6310
1.10%
6.60%
5.55%
1987-01-01
4855.2150
4.40%
5.70%
6.02%
1988-01-01
5236.4380
4.40%
5.30%
7.85%
1989-01-01
5641.5800
4.60%
5.40%
7.74%
1990-01-01
5963.1440
6.10%
6.30%
5.70%
1991-01-01
6158.1290
3.10%
7.30%
3.27%
1992-01-01
6520.3270
2.90%
7.40%
5.88%
1993-01-01
6858.5590
2.70%
6.50%
5.19%
1994-01-01
7287.2360
2.70%
5.50%
6.25%
1995-01-01
7639.7490
2.50%
5.60%
4.84%
1996-01-01
8073.1220
3.30%
5.40%
5.67%
1997-01-01
8577.5520
1.70%
4.70%
6.25%
1998-01-01
9062.8170
1.60%
4.40%
5.66%
1999-01-01
9630.6630
2.70%
4.00%
6.27%
2000-01-01
10252.3470
3.40%
3.90%
6.46%
2001-01-01
10581.8220
1.60%
5.70%
3.21%
2002-01-01
10936.4180
2.40%
6.00%
3.35%
2003-01-01
11458.2460
1.90%
5.70%
4.77%
2004-01-01
12213.7300
3.30%
5.40%
6.59%
2005-01-01
13036.6370
3.40%
4.90%
6.74%
2006-01-01
13814.6090
2.50%
4.40%
5.97%
2007-01-01
14451.8600
4.10%
5.00%
4.61%
2008-01-01
14712.8450
0.10%
7.30%
1.81%
2009-01-01
14448.9320
2.70%
9.90%
-1.79%
2010-01-01
14992.0520
1.50%
9.30%
3.76%
2011-01-01
15542.5820
3.00%
8.50%
3.67%
2012-01-01
16197.0070
1.70%
7.80%
4.21%
2013-01-01
16784.8510
1.50%
6.70%
3.63%
2014-01-01
17521.7470
0.80%
5.60%
4.39%
2015-01-01
18219.2970
0.70%
5.00%
3.98%
2016-01-01
18707.1890
2.10%
4.70%
2.68%
2017-01-01
19485.3940
2.10%
4.02%
4.16%
SYMMARY STATISATICS
REGRESSION OUTPUT FROM EXCEL
ANYTHING ELSE
ANOVA
df
SS
MS
F
Significance F
Regression
1
0.0403
0.0403
8.6338
0.0043
Residual
78
0.3640
0.0047
Total
79
0.4043
Coefficients
Standard Error
t Stat
P-value
Lower 95%
Upper 95%
Lower 95.0%
Upper 95.0%
Intercept
0.0994
0.0137
7.2680
0
0.0722
0.1266
0.0722
0.1266
Unemployment X
-0.4613
0.1570
-2.9383
0.0043
-0.7738
-0.1487
-0.7738
-0.1487
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