Deficit, national debt, and the underground economy

Define federal budget deficit and national debt, and explain their relationship: why is the deficit said to be a flow and debt a stock? Use the analogy of the faucet and the bathtub.

A state spends $500,000$ million dollars and receives revenue of $470,000$ million.

1. a) Calculate its annual deficit.
2. b) Explain where the state can get the difference from.

Distinguish between a budget surplus, balance, and deficit. Calculate the balance of a state that receives $200,000$ million and spends $190,000$ million, and of another that receives the same amount and spends $215,000$ million. Which of the two will have to borrow?

Distinguish between a cyclical deficit (it appears with the recession and disappears with the recovery) and a structural deficit (it exists even in the good years). Give an example of each and explain why the second is more worrying.

The figure shows the annual public deficit of an imaginary country over six years, as a percentage of GDP.

1. a) State in which years the government spent more than it received and in which years it saved.
2. b) Explain what happens to the country's total debt during those years even if the deficit is decreasing.

A country's public debt rises from $80\ \%$ to $100\ \%$ of its GDP, which is $1,200,000$ million dollars.

1. a) Calculate the debt in dollars at each moment.
2. b) Explain why the debt-to-GDP ratio can rise even if the annual deficit is falling: what role do the denominator (GDP) and the accumulated stock play?

Who lends money to the federal government? Explain what a Treasury bond or bill is, who usually buys them (banks, funds, individuals, other countries) and what the buyer receives in return (interest and repayment of the principal).

What is the risk premium? Explain in simple words what it measures (the extra interest investors demand from one country compared with the safest one) and what it indicates if it rises sharply.

A country accumulates a debt of $1,000,000$ million dollars at an average interest rate of $3\ \%$.

1. a) Calculate annual interest expenditure.
2. b) Compare that figure with an education budget of $40,000$ million and draw a conclusion about the "cost" of the debt.

A state has a debt of $100,000$ million dollars at an average interest rate of $2\ \%$.

1. a) Calculate the annual interest expenditure.
2. b) If each year it pays that interest by borrowing new debt and repays nothing, explain what happens to the debt in the long run (the snowball effect) and why interest rates matter so much.

Debt sustainability depends on the race between the growth of the economy and the interest rate the federal government pays.

1. a) Explain in simple words why a debt is easier to sustain if the economy grows faster than the interest it pays (the denominator grows faster than the debt).
2. b) Reason what happens if rates stay above growth for years and what options the federal government has left.

A country presents the following macroeconomic data in its public accounts:

• Debt-to-GDP ratio: $125\,\%$.

• Primary deficit (budget balance excluding interest payments): $1.8\,\%$ of GDP.

• Average nominal interest rate demanded by markets to roll over its debt ($r$): $5.2\,\%$.

• Nominal GDP growth rate ($g$): $1.5\,\%$.

1. a) Explain why, when $r > g$, the Debt-to-GDP ratio tends to shoot up on its own even if the federal government does not increase its primary deficit ("snowball effect"). Detail the spiral that is triggered if investors lose confidence.
2. b) An international organization recommends that this country implement an immediate cut in social spending equivalent to $4\,\%$ of GDP in a single year to calm the markets. Justify, using the fiscal multiplier and the denominator effect, why this shock adjustment could end up raising the Debt-to-GDP ratio instead of lowering it.
3. c) Design the main guidelines of a multi-year fiscal consolidation plan (four years) that makes the debt sustainable by acting on both the numerator (revenue and expenditure) and the denominator ($g$), evaluating its social equity implications.

During a budget debate, an analyst argues: "Public debt is an intergenerational scam: we are living beyond our means and condemning young people who have not even been born yet to pay the bill." In response, another economist states: "Public debt does not impoverish future generations because it is a debt that society owes to itself."

1. a) Critically evaluate both statements, distinguishing between debt held by residents and debt held by foreign creditors. In which case is there a true net transfer of wealth abroad in the future?
2. b) Imagine that one government issues $10,000$ million dollars in debt to finance an energy transition and digital infrastructure program, while another issues the same amount to cover the structural deficit of pensions and current spending by government departments. Using the intergenerational balance sheet (inherited assets versus liabilities), justify which of the two operations is sustainable and fair to future taxpayers.
3. c) Under what financial condition (relationship between the real interest rate on debt and GDP growth) can a high debt ratio stabilize without the need to implement immediate cuts or tax increases? Reason your answer.

Compare the financial position and sovereign risk of two economies:

• Country J: Has a public debt of $240\,\%$ of GDP, issues debt in its own sovereign national currency, and $88\,\%$ of the securities are held by domestic savers and financial institutions.

• Country E: Belongs to a monetary union (such as the Eurozone), has a debt of $110\,\%$ of GDP, and $55\,\%$ of its bonds are held by foreign investment funds.

1. a) Despite having a significantly lower debt ratio, why is Country E much more vulnerable to a risk premium crisis and a liquidity panic than Country J? Justify your answer considering the nationality of the creditors and monetary sovereignty.
2. b) Explain the dilemma of the monetary union's central bank in the face of Country E's debt tensions: what risk does intervening as a lender of last resort by purchasing its debt generate (moral hazard and inflation), and what risk does refusing to intervene generate?
3. c) What distinct consequences would it have for the citizens of both countries if the government of Country E carried out a restructuring with a haircut compared to the monetization of debt through inflation in Country J? Analyze who bears the real cost in each option.

The federal government must address two extraordinary spending needs of $12,000$ million dollars each:

• Project A: Emergency aid campaign and direct subsidies to households and small businesses to cushion the temporary loss of income caused by a health or war crisis over six months.

• Project B: Construction of a railway infrastructure network and freight logistics hubs with an estimated useful life of $50$ years.

Congress debates whether each project should be funded through an extraordinary tax hike in the current year or through the issuance of $30$-year government bonds.

1. a) Apply the principle of intergenerational equity and the "golden rule of public finance" (which links debt to investment) to justify which of the two financing methods is economically and ethically most suitable for each of the projects.
2. b) A member of Congress argues that financing Project A with debt "costs current citizens nothing because the money is provided by voluntary investors." Refute their argument by explaining two real economic costs that the massive issuance of debt immediately transfers onto the current economy.
3. c) Based on the Ricardian equivalence theorem, predict how household saving and consumption will react if the federal government decides to finance Project A with debt instead of taxes, and what consequences this response has on the effectiveness of fiscal policy.

European fiscal rules ask countries to keep the deficit below $3\ \%$ of GDP and debt below $60\ \%$.

1. a) What do those rules seek (market confidence, sustainability, common discipline in a shared currency)?
2. b) What problem do they have in the middle of a recession (forcing cuts when the economy is weak: a pro-cyclical effect)? Reason through the debate.

Observe the budgetary data of a country during the first year of an economic recession:

• Real GDP falls by $3.2\,\%$.

• Tax revenue (federal income tax and sales tax) decreases from $120,000$ to $106,000$ million dollars.

• Spending on unemployment benefits increases from $14,000$ to $21,000$ million dollars.

• The remaining public spending items remain frozen at $110,000$ million dollars.

• The federal government has not passed any tax laws or discretionary budgetary changes.

1. a) Demonstrate, using these data, how the automatic stabilizers have operated and calculate the change in the budget balance (deficit or surplus). What macroeconomic function do they serve regarding aggregate demand during the fall in GDP?
2. b) Suppose that the Secretary of the Treasury, alarmed by the resulting deficit, decides to implement a procyclical policy by cutting public spending on healthcare and infrastructure to force an immediate budget balance. Predict the impact this decision will have on GDP, unemployment, and future tax revenue (paradox of thrift / paradox of austerity).
3. c) Distinguish between cyclical deficit and structural deficit in this scenario. Why can trying to eliminate the cyclical deficit through spending cuts worsen the crisis?

A country's Treasury announces a record issuance of public debt to finance its negative budget balance. Analyze the impact of this measure in two different macroeconomic contexts:

• Scenario A: The economy operates close to full employment ($4\,\%$ unemployment), private savings remain stagnant, and the Federal Reserve pursues a restrictive monetary policy to curb inflation.

• Scenario B: The economy goes through a deep recession ($19\,\%$ unemployment), there is high precautionary savings stagnant in banks, and the Federal Reserve maintains interest rates at $0\,\%$ with bond-buying programs.

1. a) Predict in which of the two scenarios a "crowding out" effect on private investment is highly likely to be triggered and in which one it is not. Justify the financial mechanism by explaining what will happen in each case to interest rates and credit to small businesses.
2. b) A commentator states: "Every public deficit automatically reduces private investment." Refute this statement drawing upon the concept of "crowding in" for Scenario B.
3. c) If you were the director of analysis at the Department of the Treasury, what three financial variables or indicators would you monitor to confirm whether public debt is crowding out the productive sector or not?

Fictitious headline: "The federal government breaks its revenue record and still closes the year in deficit."

1. a) Explain how this is possible (spending grows even faster than revenue).
2. b) What data do you need to judge whether that deficit is worrying (the size of GDP, the cost of the debt, economic growth, what it is spent on)? Justify each one.