Chapter 14: The Government BudgetTest Bank
Chapter 14: The Government Budget
Multiple Choice Questions
Question 1
The reported budget deficit refers to
a)The debt of the federal government.
b)Government expenditures plus transfers net of tax revenues.
c)Interest payments on the primary budget deficit.
d)The primary budget deficit plus interest payments on government debt.
Answer: D
Question 2
If government expenditures are $11 billion, transfers are $7 billion and tax receipts are $9 billion then the primary budget deficit is
a)$9 billion.
b)$5 billion.
c)$27 billion.
d)Cannot calculate, need figures for interest payments.
Answer: A
Question 3
The steady state of a difference equation is said to be stable, if
a)The state variable always increases over time irrespective of the starting value.
b)The state variable always decreases over time irrespective of the starting value.
c)The state variable always moves towards the steady state, no matter where it starts out from.
d)The state variable always moves away from the steady state, unless it starts exactly at the steady state.
Answer: C
Question 4
Suppose the nominal interest rate is 2% and the growth rate of GDP is 7%. If the government maintains a policy of running a constant deficit equal to d% of GDP every year, what is the approximate value of d consistent with a steady state value of debt equal to twice the GDP?
a)42.
b)5.
c)8.
d)9.
Answer: D
Question 5
Ricardian Equivalence says that it does not matter whether the government finances increased expenditure by borrowing or by raising taxes because
a)The government must pay back its debt by borrowing more.
b)Households correctly anticipate that if the government borrows today, it will have to pay back the debt by raising future taxes.
c)Households who pay taxes are not the ones who hold government debt.
d)None of the above.
Answer: B
Analytical Questions
Question 6
Distinguish between a stock and a flow variable using the example of government debt and deficit.
Answer:
Debt is a stock and deficit is a flow.
Question 7
Explain, using the concept of a state variable, what is meant by a difference equation.
Answer:
A difference equation describes how a state variable evolves through time. For instance, Figure 14.1 in the text is a difference equation that describes the evolution of nominal government debt.
Question 8
What is a steady state of a difference equation? What do you mean by the stability of that steady state? Explain using a diagram.
Answer:
A steady state is a value of the state variable such that when the dynamical system reaches that value, it continues to stay there forever. The steady state is called stable if the system converges towards it starting from any initial value of the state variable.
Question 9
(a)Let Bt denote the government debt in year t, Dt denote the budget deficit in year t, i denote the nominal interest rate and n denote the growth rate of nominal GDP. Use these symbols to write down a relationship showing how nominal government debt evolves over time (given the budget deficit every year).
(b)Using nominal GDP as the deflator, rewrite the difference equation with nominal debt-to-GDP ratio as the state variable. Why is this a better way of analyzing a country's debt situation than using the relationship from (a)?
Answer:
(a)
(b). This relationship takes care of the government's ability to pay back its debt obligations, relative to the size of GDP.
Question 10
(a)Write down a simple difference equation showing how the debt-to-GDP ratio evolves over time if the government runs a constant budget deficit-to-GDP ratio of d (> 0) every year.
(b)Draw the difference equation obtained in (a).
(c)Clearly label the steady state. Distinguish the case where the steady state is stable from the case where it is not.
(d)Starting from any value of the debt-to-GDP ratio, trace out the time path of the state variable.
Answer:
(a).
(b)The graph of the equation is steeper or flatter than the 45o line depending upon whether (1+i)/(1+n) is bigger or smaller than 1. Refer to Figure 12-4 in the text.
(c)The steady state is stable if (1+i)/(1+n) < 1, unstable otherwise.
(d)The time path will converge to the steady state if it is stable and diverge from the steady state if it is unstable.
Question 11
Distinguish between the primary budget deficit and the reported budget deficit. Which one is more helpful for economists to analyze the government debt situation?
Answer:
The primary budget deficit refers to the value of government expenditures plus transfer payments minus the value of government revenues. The reported deficit is the primary deficit plus interest payments on outstanding government debt.
The primary budget deficit is more useful in analyzing the evolution of public debt.
Question 12
Briefly describe how the federal debt and budget deficits have behaved in the 1980's, and why it has caused so much concern.
Answer:
See discussion in Section 4, Chapter 14 of the text.
Question 13
When would you say that the government debt is sustainable? Use a diagram of the budget equation to explain.
Answer:
The debt is sustainable if the economy is able to grow out of its indebtedness. This is true if the difference equation has a stable steady state.
Question 14
What is a balanced budget policy? What does it imply for the primary budget deficit?
Answer:
A balanced budget policy sets the reported deficit equal to zero. This means that the government has to run a (primary) budget surplus every year to pay back the interest on outstanding debt.
Question 15
Suppose that the budget equation describing the evolution of the debt-to-GDP ratio has an unstable steady state. If the government can change neither the interest rate nor the growth rate in the short run, can you think of a policy that may temporarily solve the problem? (Hint: Consider how you might change the steady state by altering the budget deficit. Use a diagram of the budget equation.)
Answer:
Consider the diagram above. Suppose that the difference equation describing the evolution of the debt-to-GDP ratio is the one which goes through A. If the economy is at b0 today, such a situation is clearly unsustainable since the debt-to-GDP ratio would increase over time, moving away from the steady state. One solution would be to run a budget surplus today, so that the difference equation shifts down to pass through point B (note that the intercept is negative for this line). Point B becomes the steady state for the new system.
Question 16
Explain the propositionof Ricardian equivalence.
Answer:
Ricardian equivalence is a proposition that says it does not matter whether the government finances increased expenditure by borrowing or by raising taxes because households correctly anticipate that if the government borrows today, it will have to pay back the debt by raising future taxes.
Question 17
(a)How does the pre-1979 government debt situation in the U.S. differ from the post-1979 situation?
(b)Using the budget equation, can you think of two reasons why this change may have happened?
Answer:
(a)Refer to discussion in Section 4, Chapter 14.
(b)The situation changed after 1979 because the interest rate was consistently higher than the growth rate, and the government was running higher budget deficits.
Question 18
It is widely believed that the government debt in the 1980's rose to alarming proportions in the U.S. because nominal interest rates consistently exceeded the growth rate of nominal GDP. But this feature is something common to all the G-7 countries. Although in analyzing the budget equation we assume that the interest rate is given from outside, can you think of any reason why increased borrowing by the U.S. government in the 1980's might have contributed to rising interest rates in the U.S. and in the rest of the G-7 countries?
Answer:
See discussion in Section 5, Chapter 14 of the text. Higher borrowing by the U.S. government drove up interest rates not only in the U.S. but in other countries as well, because their currencies are in practice tied to the U.S. dollar.
Question 19
Suppose that instead of borrowing from the public, the government were to lend to the public. Let b denote the ratio of government lending to GDP, and let d represent the government surplus to GDP ratio. How does this affect the government budget equation?
Answer:
Same as the usual case (for instance, equation 14.2 in the text), except that the variables have a different interpretation. b now denotes the ratio of government lending to GDP (instead of government borrowing to GDP), whereas d represents government surplus to GDP ratio (instead of government deficit-to-GDP ratio).
Numerical Questions
Question 20
(a)If the government earns $300 billion in tax revenues this year, and incurs an expenditure of $335 billion in addition to making transfer payments of $50 billion, what is the primary budget deficit?
(b)Suppose the government has outstanding debt obligations of $400 billion from last year. If the nominal interest rate is 5%, what is the value of the reported deficit?
Answer:
(a)$85 billion.
(b)$105 billion.
Question 21
Consider the budget equation: Bt = (1+i)Bt-1 + Dt, where the symbols have their usual meaning.
(a)If the government earns $300 billion in tax revenues this year, and incurs an expenditure of $235 billion in addition to making transfer payments of $100 billion, what is the value of Dt in the current year?
(b)If the nominal interest rate is 10%, and the government has an outstanding debt of $500 billion from last year, how much does it have to borrow today?
Answer:
(a)$35 billion.
(b)$585 billion.
Question 22
For each of the following difference equations, draw a graph of xt against xt-1. Label the steady state, find its value and explain whether it is stable or unstable.
(a)xt = 2 + (1/3)xt-1.
(b)2xt = 2 + (3/2)xt-1.
(c)xt = -2 + 4xt-1.
Answer:
(a)3, stable.
(b)4, stable.
(c)2/3, unstable.
Question 23
For each of the following difference equations, draw a graph of xt against xt-1. Label the steady state, find its value and explain whether it is stable or unstable.
(a)xt = 3 + xt-1.
(b)xt = 1/2 + (3/2)xt-1.
(c)xt = -7 + (5/4)xt-1.
Answer:
(a)No steady state.
(b)-1, unstable.
(c)28, unstable.
Question 24
Consider the difference equation: yt = A + Byt-1, where A and B are constants, and A, B > 0.
(a)What is the value of the steady state in terms of A and B?
(b)When is this steady state positive? When is it stable?
(c)Now suppose A = 1 and B = 1/4. Calculate the steady state value of y. If the starting value of y is y0 = 1/2, what will be the value of y after 3 periods? Is it closer to or farther away from the steady state? What does this say about the stability of the steady state?
Answer:
(a)A/(1 - B).
(b)B < 1 required for both.
(c)The steady state is 4/3, which is approximately equal to 1.33. After 3 periods, the value of y is 1.32. Hence it is closer to the steady state (the steady state is stable).
Question 25
Consider the difference equation:
(1)
with initial condition X0 = 0.5.
(a)Find the steady state value of X.
(b)Explain what will happen to X over time if its path is described by equation (1).
(c)Suppose now that X represents the ratio of government debt to GDP. Explain what happened after 1979 in the U.S. to cause a problem for the government budget, using an equation similar to (1).
Answer:
(a)-1.
(b)X will diverge away from the steady state value of -1.
(c)a would represent the government deficit-to-GDP ratio - it increased after 1979. b would represent the ratio (1+i)/(1+n) - it became bigger than 1.0 after 1979, so that the steady state became unstable.
Question 26
Suppose the government debt to GDP ratio obeys the difference equation
where the symbols have their usual meaning.
Consider first the case where d = 0.05, i = 4%, n = 5%.
(a)Calculate the steady state value of b.
(b)If the government has outstanding debt of 100% of GDP from last year, what will be its debt obligations at the beginning of next year?
Now suppose that the interest rate jumps to 6% from tomorrow.
(c)Calculate the new steady state and explain why it is not stable.
(d)Is the debt situation sustainable in the future if the interest rate continues to be 6% from tomorrow?
Answer:
(a)5.25.
(b)1.04 times the GDP.
(c)New steady state value of b is -5.25.
(d)No.
Question 27
Suppose you borrowed $1,000 from your credit card company today at a nominal interest rate of 5% per annum. Also suppose that you do not need to borrow any money in the next couple of years. Letting B denote your borrowing, use a difference equation to illustrate how your indebtedness to the credit card company changes over time. Use this equation to estimate how much you will have to pay back at the end of two years.
Answer:
Bt = (1 + i) Bt-1. You will have to pay back (1.05)2 $1,000 = $1,102.50 at the end of two years.
Question 28
Suppose the government of Xanadu has no public debt outstanding at the beginning of 1998. It earns $100 in taxes in 1998, but has to make transfer payments of $55 and spend $75 in current goods and services.
(a)Calculate the primary budget deficit in 1998.
(b)If the government were to borrow today, at an annual interest rate of 10%, to pay for the deficit, what will be its outstanding debt obligations at the beginning of 1999?
(c)Suppose that the growth rate of nominal GDP is 12% per year, and the nominal GDP in 1998 is $400. Assuming that the government of Xanadu runs a zero primary deficit in 1999, what is its debt obligation in 1999 as a fraction of nominal GDP?
Answer:
(a)$30.
(b)$33.
(c)7.37% of GDP.
Question 29
In Econoland, the government is running a budget deficit equal to 10% of GDP. The nominal interest rate is 5% and the growth rate of nominal GDP is 6%. Calculate the steady state ratio of debt to GDP.
Answer:
10.6
Question 30
In Xanadu, the government is running a budget deficit equal to 5% of GDP.
(a)If the nominal interest rate is 3% and the growth rate of nominal GDP is 4%, calculate the steady state ratio of debt to GDP.
(b)Suppose that the maximum that the government can possibly raise in taxes is equal to 25% of GDP. Assume again that the interest rate equals 3% and the nominal growth rate of GDP equals 4%. At what value of the deficit will the interest payments on the steady state debt exceed the government’s ability to finance these payments through taxes?
Answer:
(a)5.2.
(b)i (104 d) = 0.25, hence, d = 8% of GDP.
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