Lecture 3: Public Expenditures/Debts and Sovereign Default

What channels does government policy influence economic outcomes through?

Fiscal and regulatory channels

When does the First Welfare Theorem hold?

What does the FWT imply about markets and the equilibrium?

Why would the government intervene in the provision of public goods?

Why would the government intervene in markets that are not complete and competitive?

Why would the government intervene in markets regarding inequality?

How many periods are in our model?

Two-period representative household model

What is the aim of the model?

Add government debt and abstract from capital to show conditions under which debt is irrelevant

When can the government issue debt in the model?

t = 1

What does the debt finance?

Lump-sum transfer T₁

What is T₁ financed by?

Issuing debts B₁

How are the debts B₁ paid back?

Lump-sum tax τ₂

How are preferences defined in the model?

What is the population size?

Normalised to 1

What do households do in each period?

By abstracting from savings, what are the budget constraints of the household in each period?

When would debts change the decisions of the household?

If they affect their lifetime budget constraint

Aggregate the two budget constraints and simplify

What condition must second-period tax satisfy?

Second-period tax must cover the payments for bonds to finance the first period transfer payments

What is the lifetime budget constraint when τ₂ = T₁ = 0?

Lifetime budget constraint unaffected

What must the household’s decisions be identical to?

Those in the situation of zero taxes and transfers

How much does the household reduce c₁ by and what does that amount correspond to?

What does the reduction in consumption (increase in savings) exactly match?

What factors does Ricardian Equivalence rely on regarding taxes, credit and transfers?

What does it not hinge on?

There being no capital

What time horizon does the result extend to?

An infinite-horizon economy

Are taxes lump-sum in reality?

No, they are distortionary

What would productive expenditures do to households?

Change the household’s intertemporal budget constraint

What might governments do with their debt?

May choose to default

What is the budget constraint of the government?

What does each term represent?

What happens if expenditures exceed revenues?

What then happens if B_t > B_t-1?

Public debt rises

How do we define the stock of debt at any point in time?

The cumulative sum of net deficits run by a government through history

How does government spending differ across countries on average?

How has US government expenditure and revenues changed over time?

How have various taxes imposed by the US government changed over time?

How has the US primary deficit and net interest payment changed over time?

How has total US government debt changed over time?

What is the equation for B_t which focuses on the government’s primary deficit?

Divide through by nominal GDP

Rewrite this term using the real growth rate of GDP and the inflation rate

Substitute back into the equation for B_t/Yⁿ_t

Relabel terms that are shares of nominal GDP using lowercase letters

What is the equation for the real interest rate?

Substitute the real interest rate into the relabelled equation

What does this tell us?

How the debt-to-GDP ratio evolves

What does the change in the debt-to-GDP ratio depend on?

The difference between the real growth rate and real interest rate

When d_t = 0, when does b_t increase/decrease?

What is the equation for b_t - b_t-1?

When is b_t - b_t-1 > 0?

What does this tell us?

The debt-to-GDP ratio is increasing for primary deficits exceeding the LHS of the expression

What is the equation for the debt-to-GDP ratio that can sustained for a given primary deficit?

Suppose the growth rate is projected to 3%, the long-run real interest rate is 2%, and the primary deficit is projected at 3%; what is the sustainable debt-to-GDP ratio?

Is it realistic that a debt-to-GDP ratio of 309% is sustainable?

What does the sustainability of debt measure ignore?

The incentive to default, which is increasing in the size of the debt

Given we ignore the incentives of the government to default, what may happen?

Who/what does the government tax and what does that fund under distortionary taxes?

The government taxes labour and capital incomes to finance government consumption and maybe transfers

What is the equation for the balanced budget of the government?

What do households do in the first period of their life?

Households offer labour, consume, and save in their first period of life

What are we assuming with log-linear utility?

No effect of interest rate changes on savings (IE and SE of interest rate changes offset each other)

What is the lifetime utility of a two-period OLG household for distortionary taxes?

What are the household’s budget constraints?

What is the Euler equation?

What is the impact of capital income tax on the Euler equation?

Reduces the RHS of the Euler equation

How does this impact consumption?

What then happens to c_2t+1, s_1t and k?

What is the production function for firms under distortionary taxes?

Profit maximisation under perfect competition implies the equations for MPK and MPL are what?

What is the impact of a decline in capital intensity from the higher capital income tax?

Wages shrink and pre-tax interest rate increases

What is the impact of the fall in wages on labour supply?

What is the impact of a labour income tax rather than a capital income tax?

Similar to the capital income tax; likely decline in labour supply and a reduction in savings due to lower disposable incomes

What do taxes distort regarding equilibriums?

Taxes distort the equilibrium distortion relative to the market equilibrium with zero taxes

What does this constitute regarding welfare?

Pareto optimum and a welfare maximum

Hence, what do distortionary taxes do to welfare?

Reduce welfare

Why do distortionary taxes reduce welfare?

Only reason to raise taxes was to finance government consumption (and transfers) since there are no externalities or public goods to provide

Why does Ricardian Equivalence tend to fail?

Lump-sum taxes are considered unfair since poorer households pay proportionally more

What did Aschauer (1989) indicate about movements in public investment on private-sector output?

What framework do we adapt to showcase productive government expenditures?

Barro (1990)

How do we denote productive government expenditures financed by labour income taxes?

G

How do we denote the balanced budget of the government?

How many firms are there?

Continuum of identical firms, i ∈ [0,1], operating under perfect competition

How do we denote the technology of the firms?

How do we denote the profit maximised by firm i under perfect competition?

How do we denote w_t and (1+r_t) given the FOC?

How do we denote the lifetime utility of the household?

What is it maximised subject to?

How do we then denote c_1t and s_1t after maximisation?

From the balanced budget constraint and aggregating over time, what is the equation for Y_t?

If wages must be equal in equilibrium, what is the equation for w_t?

Using the equation for w_t, how can we adapt the aggregate balanced budget constraint?

Therefore, what is the aggregate output in equilibrium?

How can we rewrite w_t and (1+r_t) using the aggregate output in equilibrium?

What do they tell us about the impact of an increase in τ?

Wages and interest rates are increasing in τ

When assessing dynamic behaviour at the equilibrium of productive government expenditures, what do we assume about population sizes and growth?

Abstract on population growth and normalise L_t = 1

Given that capital depreciates entirely, what is k_t+1 the same as?

k_t+1 = K_t+1 = s_1tL_t = s_1t

Using the household optimal s_1t, what does k_t+1 become?

Substituting w_t into k_t+1 gives what?

Dynamic equation

What are the two opposing effects of τ on available incomes and capital accumulation?

Why is τ = 0 not advisable?

Implies G = 0 → Y = 0