Lecture 5-Chapter 8

Chapter 8 –cont. Chong-En Bai and Binzhen WuCompetitive Equilibrium for an Economy without Firm and Work DecisionAssume there are N consumers.T=Nt, T’=Nt’; S P=Σi s iCompetitive conditions:Actors: consumers and the government1) Given r, y, y’, t, t’, consumers choose c, c’, s tomaximize utility s.t. budget constraints2) The government’s budget constraints hold in bothperiods3) Markets clearCredit market clears: B=S p= Σi s i(S g+S P=0)Market for current consumption goods clears: Y=C+GIn the current period, there are only two markets. When creditmarket is clear, good market must also be clear.Market for future consumption goods clears: Y’=C’+G’Effects of Tax Cuts -Ricardian Equivalence TheoremRET: If current and future government spending are held constant, then financing the government by debt is equivalent to financing it by taxes, in the sense that the equilibrium real interest rate, the consumption and welfare of individuals are the same.Financing the government by debt means issuing debt to financea tax cut.A tax cut in the current period implies, in the future, thegovernment will have to raise taxes to pay off the debt and theaccumulated interest.A tax cut does not reduce consumers’ lifetime tax burden.A forward-looking consumer understands theseRET: given G and G’,a change in the timing of taxes is neutral: no effect on consumption, market real interest rate, and welfare. The tax changes do affect private saving and government saving.The national saving keeps the same.A key assumption: consumers are forward-lookingRicardian Equivalence Theorem-ProofCurrent period ∆T, G and G’ keep the same.1) G=T+B and G’= T’-(1+r)B⇒∆B=-∆T, ∆T’= ∆T(1+r).If there is a cut in current taxes, ∆T<0, the government must issue more debt today to finance the tax cut (because G=T+B), and it will have toincrease taxes in the future to pay off this higher debt (because G’=T’-(1+r)B).2) Consumers: ∆t = ∆T/N; ∆t’ =∆T’/N= ∆T(1+r)/Nwe=y-y’/(1+r)-t-t’/(1+r)⇒∆we = 0, although endowment point changes Given r, the optimal choices for c and c’ do not changeTotal consumption C= Σi c i does not changeS p=Σi s i= Y-C-T ⇒∆S = -∆TForward-looking consumers anticipate future tax will increase, so they save all of the current tax cut to pay higher future taxes.3)∆S p = ∆B; new S p=new B, so the credit market still clears;The market for current good also clears: Y=C+G still holdsThe original equilibrium is also the equilibrium after the tax change.Figure 8.17 Ricardian Equivalence with a Cut in Current Taxes for a BorrowerRicardian Equivalence Theorem: ImplicationsA change in the timing of taxes or in the form of financinggovernment spending is neutralA tax cut is not a free lunch: consumer must pay for the currenttax cut by bearing higher taxes in the future, no better off.Reality: changes in the timing of taxes may affect consumers’ consumption-savings decision and welfare, and thus r.1)Tax cut may affect the distribution of wealth acrossgenerations or across individuals. Some consumers receivehigher tax cuts than others, but do not have a higher share of burden of government debt. The lifetime wealth for theseconsumers is changed.2) The credit market is not perfect. The behavior and welfare ofcredit-constrained consumers are affected.3) Proportional taxes cause distortion. Smoothing tax rates overtime can improve welfare.4) People may be myopia (not forward-looking enough)Traditional View about the effects of tax cuts , Chapter 9Test the Ricardian Equivalence Theorem Bush’s tax withholding reduction: defer tax payment in 1992 to 19931968 tax surcharge in US: a temporary (one-year) tax increase intending to reducing aggregate demandReagan tax cut of 1981The data shows some evidence consistent with the Ricardian Equivalence Theorem. However, the evidences are mixed.Pay-As-You-Go Social SecurityN’=(1+n)Nn: growth rate of population; N’: the number of the young, N: the number of the oldNb=N’tPay-as-you-go: the benefit for the old is financed by taxes on the young in the same period.b: benefit for the old, t: the tax on the young⇒t=b/(1+n)Return rate of social security b/t = 1+nIf the return rate of social security is higher than the private market rate 1+r, everybody is better-off.The consumers who are old when the program was introduced gain most.The existence of social security program also makes people born after the program was introduced better off if n>r.Fully-Funded Social SecurityEssentially a forced savings program: require consumers to save for retirement, and the rate ofreturn is just the rate of return in the credit market. It changes consumers’ behavior and welfare only if the program mandates a higher level of saving than the consumer would choose without such a program. Consumers are no better-off than they are in the absence of such program.Fully-funded system is often associated with the “privatization” of social security. This can beefficiency enhancing, but not necessarily so.A transition from a pay-as-you-go system to a fully-funded system can be welfare-improving for allgenerations, if government borrowing is notconstrained. Again, this is not necessarily so.RET: Change the model: credit constraint Two forms of borrowing/liquidity constraint: The amount of borrowing can not be larger than s0 The interest rate for borrowing is higher than theinterest rate for savingQuestion: how borrowing constraints affect the conclusions we derived from the baseline model.For the borrowing-constrained consumers, currentconsumption is determined by the current income.Holding G and G’ constant, a tax cut in the currentperiod does not affect lenders, but increase currentconsumption and welfare for credit-constrainedborrowers.on the amount of borrowing c’c’= –(1+r)c+we(1+r)EcY+son amount of borrowing“The borrowingconstraint is not binding” means choices are not affected by the constraint. “Thec’The borrowing constraint isnot bindingconstraint is binding” means……Because of the borrowing constraint, more people stay at the kink.For borrowing-constrained consumers,y + s 0determines c. y’does not matter.c y+s 0E The borrowing constraint is bindingAn numerical example –problem 8Q1: Lifetime budget constraintInterceptions:vertical: we(1+r)=267.96horizontal: we= 255.2Endowment point: (160, 100)Credit constraint: s ≥0, c ≤160Q1: Indifference curveQ2: Choice: 1) c = c‘; 2)c+0.95c'=255.2c = c' = 130.7; s=y−t−c=29.3; alender, the constraint is notbindingQ3: t=20, t’=71B.C: we= 255.2;E: (180, 89)160c ≤y-t=180Choices: c = c' = 130.7;s=y−t−c=49.3; a lenderAn numerical example –problem 8Q4: y=100, t=40, t’=50, y’=150we=155.2; E 1=(60, 100); s ≥0 Optimal choice: any point on the line segment BE 1, c =60, s = 0The constraint is binding, a credit-constrained borrowerQ4: y=100, t=20, t’=71, y’=150we=155.2; E 1=(80, 79); s ≥0 Optimal choice: c = c ' = 79.5; s = 0.5.The constraint is no longer binding, ∆c< ∆t.For tax cuts that leave lifetimewealth unchanged, lenders will not change their c, but credit-constrained borrowers will increase c and be better-off.Borrowing Constraint (2): Different Lending and Borrowing Rates111101'1'1'0s ifwe r t t r y y r c c s if<≡+−−++=++>22221'1'1'we r t t r y y r c c ≡+−−++=++r 1<r 2:Borrowing is more expensive than saving.The budget constraint has a kink at the endowment pointBorrowing Constraint (2): Different Lending and Borrowing RatesCompared with themodel where r 1=r 2=r 0, more people stay at the endowment point. For the peoplec’choosing the kink point, current income determines current consumption regardless of the lifetime incomeQ: how does a tax cut affect the choices?cEEffects of a Tax Cut for a Consumer with Different Borrowing and Lending RatesAfter the tax cut, thebudget constraint movesfrom AE1B to AE2FHolding G and G’constant, a current taxcut will increase c andwelfare of credit-constrained borrowersc increases by theamount of the tax cut ifthe borrower isconstrained after the tax-cut.Case Study: the High Japanese Saving Rate Japan has historically had one of the world’s highest saving ratesGood or bad?A key to the rapid growth Japan has experiencedafter World War IIContribute to Japan’s slump during the 1990sWhy Japanese like to save a lotIt is hard for households to borrow in JapanNeed to save a lot to buy a home (40% downpayments + high housing price)Tax system encourages savings by taxing capitalincome very lightlyCultural difference: more risk averse, more patientPolicy Implication –Government Debt Most economists oppose a strict rule requiring the government to balance its budget.Intergenerational redistribution to improve welfare Relaxing credit constraintsSmoothing taxesStabilizationsA balanced-budget rule would revoke the automaticstabilizing powers of the system of taxes and transfers.Fighting depressionsTax cut may stimulate aggregate demand.Coordinate with monetary policyGovernment debt can potentially have negative effects.Policy Implication –Government Debt Government debt can potentially have negative effects.A higher level of government debt may lead tomonetary expansion by printing money, whichlead to great inflation.It may also risk capital flight.The possibility of running budget deficits mayencourage politicians to press unduly burdenon future generations.Allowing government debt gives a soft budgetconstraint that makes the governmentspending too easy to be approved.ReviewA intertemporal model without firm (investment) andworking decisionConsumers’ problemLifetime budget constraint; preference (desire tosmooth consumption); choicesComparative statics: changes in incomes or rConsumption functionGovernment (lifetime) budget constraintsRicardian Equivalent TheoremTheorem; implications; when it is violatedRedistribution Across Generation:Social securityChange the setup of the model: credit constraint。