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

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

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.

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

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

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:

‘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)

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

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

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:

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

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)

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

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

‘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

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