1. L11200 Introduction to Macroeconomics 2009/10
Lecture 22: Public Debt I
Reading: Barro Ch.14
22 March 2010

2. Introduction
Last time: effect of different forms of taxation on real activity
Labour income and asset income taxes both proved ‘distortionary’
Cost to society was lower output and income
Today: the ‘public budget’
Governments’ budgets and debt

3. Public Debt
So far, considered how government raise income (tax) and spend revenue
Governments can also amass assets / incur debts
Call the government’s budget position the ‘public budget’
U.K./U.S. governments currently have large public deficits (expenditure > income) and also large public debts.

4. Government Bonds Government can borrow by issuing ‘bonds’
An i.o.u. from the government, bought by households
So households can either buy private bonds, or government bonds
In aggregate, Bt=0, so aggregate household bond holdings are equal to

5. Government Budget Constraint
Previous government budget constraint
With borrowing/saving this becomes
government spending + government transfers = tax revenue + real revenue from money creation
spending + transfers + interest payments = tax revenue + real debt issue +real revenue from money creation

6. Government Budget Constraint
If Mt and Pt do not change over time, simplifies to:
If , government is saving, and vice-versa
So real government saving given by:

7. ‘National Saving’ So saving of an economy is given by:
Total private saving (household lending to other households cancels out)
Total private capital investment
Government saving
So government saving and private saving cancel out (just a flow of money between the two)

8. Public Debt and Household Budget
Household multiyear budget constraint:
Now add household government bond holding
present value of consumption = value of initial assets + present value of wage incomes + present value of transfers net taxes
present value of consumption = value of initial assets + present value of wage incomes + present value of transfers net taxes

9. Government Borrowing and Taxation
Now assume government has zero debt, and no transfers but decides to lower taxes without lowering spending
With no debt or transfers, government has no initial interest payments, so

10. Government Borrowing and Taxation
In period 2, government repays all of its debts
For simplicity, assume borrowing was 1 unit
So, interest due is r multiplied by ‘1’, bond to be repaid is ‘1’:
Hence:

11. Impact on households How does this impact on households?
T1 falls by 1, T2 rises by 1+r
Present value
Decrease in year 1’s real taxes + present value of increase in year 2’s taxes

12. Debt Neutrality
So effect of cutting taxes, then increasing taxes again is 0
Household pay lower tax in the first period
But then have to pay higher taxes in the second period
No change to present value (cost of debt interest offset by present value deduction)

13. Ricardian Equivalence
This famous result is known as ‘Ricardian Equivalence’
Households view a cut in real taxes as equivalent to an increase in the real budget deficit, and hence higher future taxation
So the real budget deficit is equivalent to the present value of real future tax rises

14. Crucial Result for Public Policy
Ricardian Equivalence implies
Cutting taxes now to finance government spending has no impact on the economy – households ‘internalise the debt’ save more now
Borrowing more now to finance government spending has no impact on the economy – households anticipate tax rises and save more now

15. ‘Fiscal Stimulus’ No role for a fiscal stimulus
Idea: government should borrow and spend more now to ‘keep up demand’ during a recession
Problem: government borrowing means future tax rises for households
Households anticipate this, and save more now
Net effect (we have shown) is zero

16. Summary Government has an asset/debt position, just like households
Debts eventually have to be paid-off by lower spending or more taxation
Households know this, and offset govt activity
Next time: intertemporal effects
Taxes distorted output decision
Intertemporal tax/spend policy distorts household activity as well