Question of MACROECONOMIC ANALYSIS

The following table presents the Real Gross Domestic Product (GDP) of the United States (chained 2012 dollars) from 1999 to 2019. Please finish the questions below.

Year	Real GDP	ln(GDP)	GR-1	GR-2
1999	12610.5	9.442	NA.	NA.
2000	13131.0	9.483	0.041	Fill in here
2001	13262.1	Fill in here	Fill in here
2002	13493.1
2003	13879.1
2004	14406.4
2005	14912.5
2006	15338.3
2007	15626.0
2008	15604.7
2009	15208.8
2010	15598.8
2011	15840.7
2012	16197.0
2013	16495.4
2014	16912.0
2015	17432.2
2016	17730.5
2017	18144.1
2018	18687.8
2019	19091.7

Note: Real GDP, annual real GDP of the United States, unit: Billions of Chained 2012 Dollars, Not Seasonally Adjusted. Ln(GDP) is the natural logarithm of real GDP. GR-1 is the growth rate of real GDP calculated using the method in part (2) as below. GR-2 is the growth rate of real GDP calculated using method in part (3). Data: https://fred.stlouisfed.org/series/GDPCA

(1) Transform the real GDP (the 2nd column) into natural logarithm (Ln) values (in the 3rd column). There are two example years of 1999 and 2000. You may use calculator, spreadsheet or other devices to calculate the natural logarithm values. Please fill in the blanks of blue color in the third column.

(2) Calculate real GDP growth rate (GR-1) in each year and complete the blanks in the fourth column (pink color). You can use the formula as below. GDP growth rate in year t equals,

GRt = (GDPt – GDPt-1) / GDPt-1;

In the table, real GDP growth rate in the year 2000, between 1999 and 2000, is given as an example (t = 2000). You can follow the example and fill in all the blanks in pink color. Please make sure to keep three decimal digits for your answers of GR-1 (as the example).

(3) An alternative approach, we can use the difference of natural logarithm to calculate growth rate (GR-2). It is relatively easier than the calculation above (GR-1). Here we will skip some technical details. In sum, for a small growth rate, we can use natural logarithm to calculate GDP growth rate. For GDP growth rate over one year, GR-2 can be calculated as,

GRt = Ln(GDPt) – Ln(GDPt-1); (I)

For the average growth rate of N years (GRN),

GRN = [Ln(GDPt+N) – Ln(GDPt)]/N; (II)

Now use formula (I) in this part to calculate real GDP growth rate (GR-2) of each year. Fill the blanks in the last column with green color and compare the results with annual growth rates computed by the method of GR-1. Are the values in the two columns close enough or not? Please make sure to keep three decimal digits for your answers.

(4) Use the annual real GDP growth rates from 2015 to 2019 and calculate the average growth rate over these five years. How much in the average growth rate? Please make sure to keep three decimal digits for your answer.

(5) With the average growth rate computed above, how many years it takes for the US to double its real GDP. Try to use both the “Rule of 70” and the logarithm method in your lecture note. Compare the results from these two methods, are they close or not. Please make sure to keep three decimal digits for your answer.