Question

5. The US DP growth rate for 2007-2017 is reported on the following chart. Determine the consecutive three year period between 2007 and 2017 with the largest growth rate Develop a model to predict the US DP growth rate for December 31, 2020 Value Date Dec 31, 2017 4.49% Dec 31, 2016 3.40% Dec 31 , 2015 2.89% Dec 31, 2014 4.42% Dec 31, 2013 4.43% Dec 31, 2012 3.56% Dec 31, 2011 3.65% Dec 31, 2010 4.19% Dec 31, 2009 0.47% Dec 31, 2008-0.83%

Answer 1

As shown in the table given in the question, the consecutive three years between 2007 and 2017 with the largest growth rate is:

Year	Growth rate
31-Dec-12	3.56%
31-Dec-13	4.43%
31-Dec-14	4.42%

Now, develop a regression model in which the growth rate is function of time.

Assume t=0 for Period 31-Dec-2007

Thus, the required table is:

Year	t	Growth rate
31-Dec-07	0	4.59%
31-Dec-08	1	-0.83%
31-Dec-09	2	0.47%
31-Dec-10	3	4.19%
31-Dec-11	4	3.65%
31-Dec-12	5	3.56%
31-Dec-13	6	4.43%
31-Dec-14	7	4.42%
31-Dec-15	8	2.89%
31-Dec-16	9	3.40%
31-Dec-17	10	4.49%
31-Dec-18	11
31-Dec-19	12
31-Dec-20	13

The regression model is:

Thus the model is:

Growth_rate = 0.020727273 + 0.002265455 * t

For Dec 31, 2020, the value of t=13

Hence, the predicted growth rate in Dec 31, 2020 is:

= 0.020727273 + 0.002265455 * t

=0.020727273 + 0.002265455 * 13

=0.050178182

=5.0178%