Dynamics of government debt

Question 1

What do the terms in the equation mean:

Bⁿ_t+1 - Bⁿ_t = i_tBⁿ_t+ Gⁿ_t- Tⁿ_t

Answer 1

Gⁿ_t - Tⁿ_t represents the primary deficit

Gⁿ_t - Tⁿ_t + i_tBⁿ_t represents the overall deficit

i_tBⁿ_t the interest payment on outstanding debt, and the entire expression stands for the overal deficit, which corresponds to the change in debt going forward.

Question 2

What is the relationship between i, π, and r?

Answer 2

(1+i_t)/(1+π) = 1 + r

Because trade-off of a dollar in real terms is 1/P_t goods today versus (1+i_t)/P_t+1 goods tomorrow. Since rate of return is 1+ r, 1+r = goods tomorrow/goods today

Question 3

What is another way of expressing bⁿ_{t ,}the debt to GDP ratio?

Answer 3

y_t*N_t

Question 4

What is another way of expressing B^’_nt/P_t?

Answer 4

B^’_t/B_t + π_t

Question 5

Express the growth of debt as a percent of GDP (b_t)using its components

Answer 5

B’_t/B_t -y’_t/y_t - N’_t/N_t

Or

B’_t/B_t -g_t-n_t

Question 6

What is another way to express B’_t/B_t?

Answer 6

b’_t/b_t + π_t + n_t

Question 7

What can we conclude about the forces that contribute to a growing debt to gdp ratio?

Answer 7

Given that the growth of the debt ratio, b’t/tb=(Gt-Tt)/Bt + r - (g + n)

we can say that a combination of the primary deficit and high interest rates and low gdp growth and low population growth contribute to a growing debt/gdp ratio

Doesn’t matter whether gdp per capita growth or pop growth is low here, both affect the equation

Question 8

What happens to debt ratio (bt) of a country with a balanced primary budget, a small amount of debt and positive but constant rates of g + n and r, such that r > g + n?

Answer 8

It grows exponentially at a rate of r - g -n

Question 9

What should the government do for a government to run a balanced primary budget, but maintain a small amount of debt given constant rates of g + n and r, such that r > g + n?

Answer 9

Make sure the debt to gdp ratio growth (b’t/bt) <= 0

That means (Gt-Tt)/Bt <= -r + ( g + n

or that (Tt-Gt)/Bt => r - g - n

run a surplus that compensates for high interest rates and low growth

Question 10

What is the definition of the size of debt in debt:GDP ratio and GDp terms?

Answer 10

B_t = b_t * Y_t

Question 11

Use the law of motion to explain whether a government can run primary and total fiscal deficits forever

Answer 11

Using the law of motion, we know that b’_t/b_t = (G-T)/Y + [r_t -(g_t + n_t)]b_t

We can add the interest payment component to get the expression for total debt

b’_t/b_t = (G-T + iB_t)/Y + [-(g_t + n_t)]b_t

Question 12

What is the Law of Motion for debt to GDP ratio?

Answer 12

(G-T)/Y + [r - (g + n)*b]_t

Question 13

What is the law of motion for the overall deficit?

Answer 13

(G-T+ _iB)/Y = -(π + g + n)*b_t

Question 14

What are the two ways to express the law of motion for the debt to gdp ratio?

Answer 14

b’_t/b_t = (G_t-T_t)/B_t + r_t - (g_t+n_t)

this is the growth rate of the debt to gdp ratio

change in debt to gdp ratio is b’_t = (G_t-T_t)/Y_t + [r_t = (g_t+n_t)]*b_t

or manipulate it by multiplying by bt and expressing Bt as bt*Yt

Question 15

What is the expression for the growth rate of debt?

Answer 15

B’t/Bt = it + (Gt - Tt)/Bt

Question 16

What expression do you use to answer whether the government can run primary fiscal deficits forever?

Answer 16

b’ = (G-T)/Y + [r-(g+n)]*b

or bt+1 - bt = (G-T)/Y + [r-(g+n)]*b

Question 17

What is the expression you use to see whether you can run total (overall) fiscal deficits forever?

Answer 17

b’ = (G-T + iB)/Y -(π + g + n)*b

Question 18

What does the law of motion tell us about what are sustainable primary fiscal deficits and overall deficits?

Answer 18

It tells us that for primary deficits, (G-T)/Y <= (-r + g+n)*b so that the primary deficit must be less than the product of the current debt to gdp ratio and the gap between the interest rate and real GDP growth/

and that for the overall deficit,

(G-T+iB)/Y <= (π + gt +n)*b the total deficit as percent of gdp cant exceed the nominal growth of GDP times debt to gdp ratio

Question 20

If you have the debt to gdp ratio b and also r, g and n, how do you figure out what the minimum level of “toughness” the government should apply, e.g. your target for the primary deficit so that it doesn’t grow out of control?

Answer 20

Use the (G-T)/Y = (r -g-n)*b formula by plugging in b, r g and n numbers to figure out what the size of the deficit should be

Question 21

What minimum toughness should the government impose on the overall deficit to ensure that debt stabilizes at a given level of r, g, n, and b?

Answer 21

Use the (G - T + iB)/Y <= (π+g+n)*b

Question 22

What is a quantitative way to express nominal long-run GDP growth?

Answer 22

π + g + n , can use this when determining the rules for stablizing debt