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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 Btg Bt Btg – In aggregate, Bt=0, so aggregate household bond holdings are equal to Btg Government Budget Constraint • Previous government budget constraint Gt Vt Tt (M t M t 1 ) / Pt government spending + government transfers = tax revenue + real revenue from money creation • With borrowing/saving this becomes Gt Vt it 1 ( B / Pt ) Tt ( B B ) / Pt ( M t M t 1 ) / Pt g t 1 g t g t 1 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: Gt Vt rt 1 ( Btg1 / P) Tt ( Btg Btg1 ) / P g g ( B B • If t t 1 ) , government is saving, and vice- versa • So real government saving given by: ( Btg Btg1 ) / P ‘National Saving’ • So saving of an economy is given by: g g ( B B – Total private saving t t 1 ) / P (household lending to other households cancels out) – Total private capital investment K t K t 1 g g – Government saving ( Bt Bt 1 ) / P – 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: C1 C2 / (1 r1 ) ... (1 r0 ) ( B0 / P K0 ) (w / P)1 L (w / P)2 L / (1 r1 ) ... s 1 s 2 (Vt T1 ) (V2 T2 ) / (1 r1 ) (V3 T3 ) /[(1 r1 ) (1 r2 )] ... present value of consumption = value of initial assets + present value of wage incomes + present value of transfers net taxes • Now add household government bond holding C1 C2 / (1 r1 ) ... (1 r0 ) ( B0 / P BoG / P K0 ) (w / P)1 L1s (w / P)2 Ls2 / (1 r1) ... (Vt T1 ) (V2 T2 ) / (1 r1 ) (V3 T3 ) /[(1 r1 ) (1 r2 )] ... 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 Gt Vt rt 1 ( Btg1 / P) Tt ( Btg Btg1 ) / P • With no debt or transfers, government has no initial interest payments, so G1 T1 ( B ) / P g 1 Government Borrowing and Taxation • In period 2, government repays all of its debts G2 r ( B1g / P) T2 ( B2g B1g ) / P • For simplicity, assume borrowing was 1 unit • So, interest due is r multiplied by ‘1’, bond to be repaid is ‘1’: G2 r T2 1 • Hence: T2 G2 1 r Impact on households • How does this impact on households? C1 C2 / (1 r1 ) ... (1 r0 ) ( B0 / P BoG / P K0 ) (w / P)1 L1s (w / P)2 Ls2 / (1 r1) ... (Vt T1 ) (V2 T2 ) / (1 r1 ) (V3 T3 ) /[(1 r1 ) (1 r2 )] ... • T1 falls by 1, T2 rises by 1+r • Present value 1 (1 r ) / (1 r ) 1 1 0 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
