II. Suppose that the national debt is 75 percent of GDP at the end of 2017 (so t
ID: 1117631 • Letter: I
Question
II. Suppose that the national debt is 75 percent of GDP at the end of 2017 (so the debt ratio is 0.75). Suppose that in 2018, the government runs a deficit equal to 5 percent of GDP (so the deficit ratio is 0.05).
(a) Suppose that real GDP growth in 2018 is 2 percent, while the inflation rate is zero. What is the growth rate of nominal GDP? What is the debt ratio at the end of 2018?
(b) Re-do part (a), assuming the inflation rate is 5 percent, holding other things equal.
Hint: use the following formula for the evolution of the debt ratio given in class and in chapter 16, where g is the nominal GDP growth rate in year T, and the debt ratio, deficit ratio and nominal GDP are expressed as decimals (so that a debt ratio of 75 percent is expressed as 0.75, and nominal GDP growth of 2 percent is 0.02):
Debt Ratio = (1/1+g) * Debt Ratio + Deficit Ratio
at end of Year T at end of Year T-1 in Year T
(c) Explain in words what happened to the actual debt ratio in the United States between 1946 and 1976, using the formula above as a reference. Did the debt ratio rise or fall over time? Why did it rise or fall?
Explanation / Answer
Debt Ratio at end of Year T = (1/1+g) * Debt Ratio at end of Year T-1 + Deficit Ratio in Year T
a. nominal GDP growth rate, g = real GDP growth rate + inflation rate = 2 + 0 = 2%
Debt ratio in year 2018 = 0.75/(1+0.02) + 0.05 = 0.78 = 78%
b. nominal GDP growth rate, g = real GDP growth rate + inflation rate = 2 + 5 = 7%
Debt ratio in year 2018 = 0.75/(1+0.07) + 0.05 = 0.75 = 75%
c. The US debt ratio in 1946 was over 100% due to heavy military spending by the govt. However, it kept coming down till 1976 due to a high nominal growth rate of GDP. This same result is reflected by the above formula. The debt ratio showed a declining trend between 1946 and 1976 and it was largely because of higher nominal growth rate of GDP. Also, the instances of higher deficit ratio were not as common as it has been after 1976.
Thus we notice that debt ratio fell between 1946 and 1976. The reason behind its fall was largely due to limited govt spending and a higher nominal growth rate fuelled by private investment.