Government &Tax Policies in 2-Period CE Model Government Expenditures Ricardian Equivalence Capital Market Imperfections Social Security

2-Period Model w/ Government Recall effect of taxes in one-period model: G = T Consider two-period CE model w/ exogenous income. Government Budget Constraint Period 1: Period 2: Government’s Lifetime (Intertemporal) BC: PDV of Government Expenditures = PDV of Taxes

Households Budget Constraint: Period 1: Period 2: Lifetime BC: we = Present Discounted Value of C

Optimal Consumption: MRS c1,c2 = (1+r) Note: For a given interest rate r, only changes in we will affect consumption and welfare. Market Clearing:B = s y 1 = c 1 + G 1 y 2 = c 2 + G 2 Remark – Consistency between BC and Market Clearing.

Effects of Government Expenditures Government BC  changes in PDV of G must be balanced by PDV of T. Household BC  PDV of G creates income effects. Increase in G 1 (temp)  Higher equilibrium r Increase in G 2 (future)  Lower equilibrium r Permanent increase in G  Small effects on r.

Effects of Permanent Changes in Government Expenditures Permanent changes in G: Historical growth in size of government G/GDP8%20% Gov Spend/GDP10%33% Real Interest Rate4.5%5%

Government Spending Shocks and Interest Rates

Taxes Ricardian Equivalence Proposition: Financing a given amount of G by T or B are equivalent. For a given level of G, a current tax cut (which increases BD) has no effect on equilibrium consumption, interest rates, or welfare. Result also holds with labor market & production under lump-sum taxation.

Application: G.H.W. Bush and the Tax Withholding Reduction Beginning of $25 billion withholding reduction. No overall tax reduction for No evidence that real consumption increased between 1992:Q1 and 1993:Q1. Supports Ricardian Equivalence.

Figure 8.25 Real Consumption of Services, 1991–1993

Evidence (Mixed) (i)Temporary tax rebates do little to affect aggregate consumption. (supports) (ii)Public is aware of “burdens” of national debt on future generations. (supports) (iii)Large Tax cuts (even temporary) do tend to stimulate consumption and lead to higher long-term interest rates. (conflicts) (iv)Large budget deficits in 1980s and economic expansion conflicts with Ricardian Equivalence. (conflicts)

Ricardian Equivalence says that tax policies by themselves are irrelevant (only G matters). Problems with Ricardian Equivalence: (1)Unequal Tax Burdens – redistributes income. (2)Taxes are NOT lump-sum – may have substitution effects. (Need production & labor market in model). (3)Intergenerational Transfers (4)Capital Market Imperfections

Capital Market Imperfections How do individuals react to tax cuts when they face different borrowing and lending rates? Lending rate = r < r H = borrowing rate Consumer is lender (s > 0): Consumer is borrower (s < 0)

Graphically, there’s a “kink” in the budget constraint. Government borrows at r < r H. Example:  T 1 = -1 and  T 2 = (1+r) Lender  Ricardian Equivalence Borrower  Ricardian Equivalence fails! Tax cuts for “constrained” borrowers work like a low interest loan. Hence  we > 0 and increases current consumption.

Intergenerational Transfers Two types of Social Security Programs (1)Pay-As-You-Go Benefits to old generation financed by taxing current young generation. (2)Fully Funded Government sponsored saving accounts which are retained until retirement.

Pay-As-You-Go Two period “overlapping generations” model Definitions: N Y = young population N O = old population n = population growth rate N Y = (1+n)N O S = social security tax paid by each young. B = social security benefits paid to each old.

Two Period Overlapping Generations: Period 1  Young (“Y”) Period 2  Old (“O”) Assume in each period (except initial) G = 0 and there are zero net taxes  T = 0. Zero Net Taxes: Total SS Taxes = Total SS Benefits: SN Y = BN O  S = B/(1+n) Question: Can such a pure transfer (no net change in taxes) affect consumption and welfare?

Initial Generation: subject to Anticipated Program:   B > 0  increases (each by less than B) and unambiguously welfare.

Unanticipated Program: constant increases by B Welfare unambiguously increases (but by less than anticipated program).

Figure 8.17 Pay-As-You-Go Social Security for Current Old

Future Generations: subject to Lifetime BC: Effect of B > 0:

Figure 8.18 Pay-As-You-Go Social Security for Future Generation

US Population Growth:

US Real Interest Rates:

Remarks: (1)Population growth has been declining. (2) Low (real) interest rate policies benefit the PAYG system. (3) Less restrictive immigration policy may allow PAYG system to be Pareto improving. (4)PAYG system discourages private saving.

Fully Funded SS A fully funded program that simply sets aside a required level of s g. Consumer’s Problem: subject to FF program only improves welfare relative to pay-as-you-go if n < r. In theory, FF program can do no better than “free market” choices. Practical issue – FF can only improve welfare relative if government can do better than individuals (“free market”) at choosing s g.

Even if n < r, there are other issues when transitioning from PAYG to FF: (1)Benefits current young generation but hurts current old. (2)Current old benefits can be financed by running budget deficits and taxing future generations. Possibly Pareto improving.