Fiscal Policy Presentation

Fiscal Policy Craig Burnside Duke University October 11, 2023 Fiscal Policy 1 Government expenditure on goods, services, and transfer payments 2 Taxation 3 Government deficits and debt Fiscal Policy Look at historical data Discuss the effects of changes in government purchases of goods and services I this is “G” in the NIPA Discuss the effects of changes in tax rates I I consumption, labor income and capital taxation optimal taxation Linking changes in G to changes of taxes Supply side view of taxation Government debt and deficits I Ricardian equivalence Government revenue in the U.S. (% of GDP, 1929–2022) 35 State & local (net of federal transfers) Federal All government 30 % of GDP 25 20 15 10 5 0 1930 40 50 60 70 80 90 2000 10 20 Federal government revenue (% of GDP, 1929–2022) 30 Personal taxes Customs & excise Corporate income tax Social insurance contributions Other 25 % of GDP 20 15 10 5 0 1930 40 50 60 70 80 90 2000 10 20 State & local government revenue (% of GDP, 1929–2022) 20 Personal taxes Sales taxes Property taxes Transfer receipts Other % of GDP 15 10 5 0 1930 40 50 60 70 80 90 2000 10 20 Federal government expenditure (% of GDP, 1929–2022) 50 Military C+I Non-military C+I Transfer payments Other Interest % of GDP 40 30 20 10 0 1930 40 50 60 70 80 90 2000 10 20 Federal expenditure on transfers (% of GDP, 1929–2022) 25 Social security Medicare Veterans benefits Other social transfers Other transfers % of GDP 20 15 10 5 0 1930 40 50 60 70 80 90 2000 10 20 State & local government expenditure (% of GDP, 1929–2022) 30 Consumption and investment Transfer payments Other Interest 25 % of GDP 20 15 10 5 0 1930 40 50 60 70 80 90 2000 10 20 Gross public debt (% of GDP, 1930–2022) 140 State Local Federal 120 % of GDP 100 80 60 40 20 0 1930 40 50 60 70 80 90 2000 10 20 Federal government deficits (% of GDP, 1929–2022) 30 Federal primary deficit Federal deficit 25 % of GDP 20 15 10 5 0 -5 1930 40 50 60 70 80 90 2000 10 20 A Simple Model of Fiscal Policy The government buys goods and services, makes transfers to households, and pays for these by taxing households. I I I I gt : Government purchases of goods and services (widgets) vt : Government transfers to households τt : Tax revenue raised by the government Measure these variables in per-household terms Government budget constraint: gt + vt = τt Taxes and transfers are assumed to be lump-sum We don’t make assumptions about how the government comes to its decisions about how much to spend and tax Households take the government’s decisions as given Household Preferences Revisited We assume that the instantaneous utility function is now U(ct , `t ) + Ψ(gt ) Households get utility from government purchases, but they are neither a substitute for, nor a complement to private consumption or leisure Household Budget Constraint ct + it + bt+1 = wt hts + rkt kt + vt − τt + (1 + rt−1 ) bt Same as our previous budget constraint but transfers are added to income and taxes are subtracted The government budget constraint implies that vt − τt = −gt and since the household takes all of these as given we can just write the budget constraint as ct + it + bt+1 = wt hts + rkt kt − gt + (1 + rt−1 ) bt Household Lifetime Budget Constraint The lifetime budget constraint works exactly like before ∞ ∞ ∑ qt [ct +kt+1 −(1−δ )kt ] = t=0 ∑ qt (wt hts +rkt kt +vt −τt )+(1+r−1 )b0 . t=0 (1) The household chooses {ct , hts , kt+1 }∞ t=0 to maximize lifetime utility ∞ ∑ β t [U(ct , 1 − hts ) + Ψ(gt )] t=0 subject to (1). Household Optimality Conditions In addition to its budget constraint the optimality conditions for the household are U` (ct , 1 − hts ) = wt MRS`t ct = Uc (ct , 1 − hts ) MRSct+1 ct = s ) β Uc (ct+1 , 1 − ht+1 1 = s Uc (ct , 1 − ht ) 1 + rt rkt+1 − δ = rt and, of course, the lifetime budget constraint. Since you don’t see gt anywhere other than the lifetime budget constraint this suggests that changes in government purchases will primarily affect household decisions via their effect on lifetime income. Firm’s Optimality Conditions The firm’s problem is unchanged: At Fh (ktd , htd ) = wt At Fk (ktd , htd ) = rkt Equilibrium Conditions If you impose factor market clearing and goods market clearing you get the following equations At Fh (kt , ht ) = U` (ct , 1 − ht ) Uc (ct , 1 − ht ) Uc (ct , 1 − ht ) = β Uc (ct+1 , 1 − ht+1 )[At+1 Fk (kt+1 , ht+1 ) + 1 − δ ] ct + kt+1 − (1 − δ )kt + gt = At F (kt , ht ) The last equation, which is the market clearing condition for widgets, is the only one which is different than what we saw in the chapter on investment. A Temporary Change of Government Purchases Shifts of Aggregate Demand and Supply Assume that in period 0, government purchases increase by an amount ∆g I Government pays for this increase with an equal sized increase in taxes (or a cut in transfer payments). If it’s strictly temporary (and the increase is not very big) the income effect is very small I We’ll approximate this with no shift of C D and no shift of hs (due to the income effect) in the labor market diagram No effect on I D as the change of g0 does not affect the MPK schedule in period 1. So Y D shifts right by ∆g, given that government purchases are part of aggregate demand No shift of Y S A Temporary Change of Government Purchases The Goods Market Output rises, the interest rate rises, and consumption and investment both fall (a) Goods Market (b) Labor Market A Temporary Change of Government Purchases The Labor Market In the labor market, hd is unaffected because MPH0 is unaffected The labor supply curve, hs , shifts down (to the right) because c ↓ ⇒ Uc ↑ ⇒ MRS`c ↓ Equilibrium labor rises (consistent with what happens in the goods market) and the wage rate falls (a) Goods Market (b) Labor Market A Permanent Change of Government Purchases Assume that in period 0, government purchases increase by an amount ∆g and that the change is permanent I Again, the government pays for this increase with an equal sized increase in taxes (or a cut in transfer payments). We expect a larger negative income effect which will decrease consumption demand and increase labor supply It turns out that in order to figure out what happens to Y D and Y S , and the size of their relative shift, it is useful to consider what happens in the long-run A Permanent Change of Government Purchases Long-Run Steady State c ↓, h ↑ due to the income effect Intertemporal condition in the long-run steady-state: ρ = r Long-run rental rate of capital: rk − δ = r ⇒ rk = ρ + δ Optimal capital condition in the long-run steady state: AFk (k, h) = rk = ρ + δ I But this condition says that AFk (k/h, 1) = ρ + δ I So, k/h doesn’t change in the long-run: ⇒ k ↑ proportionally to h ↑. A Permanent Change of Government Purchases Short-Run Shift of Aggregate Supply Let ∆h > 0 and ∆k > 0 be the long-run changes of labor and capital If the economy is initially in a steady state with r = ρ, this suggests that at time 0, holding the interest rate fixed, the increase of labor supply—via the income effect—will be ∆h0 ≈ ∆h. Given that the capital stock does not change at time 0, expect the rightward shift of Y S to be ∆Y S ≈ MPH · ∆h. A Permanent Change of Government Purchases Short-Run Shift of Aggregate Demand In the long-run the household’s gross income increases by approximately MPK · ∆k + MPH · ∆h Because depreciation also increases, by δ ∆k, income net of depreciation increases by approximately (MPK − δ ) · ∆k + MPH · ∆h = ρ · ∆k + MPH · ∆h Household has to pay more taxes to pay for increased government spending so change of net income is ρ · ∆k + MPH · ∆h − ∆g Households decrease in consumption in the long-run, and the shift of C D in the short-run (at the old interest rate) should be ∆C D = ρ · ∆k + MPH · ∆h − ∆g < 0 I Negative as long as consumption is a normal good A Permanent Change of Government Purchases Short-Run Shift of Aggregate Demand ∆C D = ρ · ∆k + MPH · ∆h − ∆g Shift of investment demand at the old interest rate is ∆I D = ∆k So shift of aggregate demand is ∆Y D = ∆C D + ∆I D + ∆g = (1 + ρ) · ∆k + MPH · ∆h > ∆Y S A Permanent Change of Government Purchases The Goods Market Output rises, the interest rate rises, consumption falls, investment rises (shift dominates the interest rate effect) (a) Goods Market (b) Labor Market A Permanent Change of Government Purchases The Labor Market In the labor market, hd is unaffected because MPH0 is unaffected The labor supply curve, hs , shifts down (to the right) because income effect and interest rate rises both imply c ↓ ⇒ Uc ↑ ⇒ MRS`c ↓ Equilibrium labor rises (consistent with what happens in the goods market) and the wage rate falls. (a) Goods Market (b) Labor Market Taxes We introduce three types of taxes that distort household decisions I I I Labor income tax Consumption tax Capital income tax 1 What are the economic consequences of these distortions? 2 What type of tax is optimal? 3 What are the effects of a permanent increase in g, financed with these taxes? Labor Income Tax Assume that τt = τh wt hts Proportional (flat) tax on labor income Household’s lifetime budget constraint can be written as ∞ ∞ t=0 t=0 ∑ qt (ct + it ) = ∑ qt [(1 − τh )wt hts + rkt kt + vt ] + (1 + r−1 )b0 . Changes the intratemporal condition governing the consumption-leisure decision: (1 − τh )wt = U` (ct , 1 − hts ) Uc (ct , 1 − hts ) Other optimality conditions remain the same Long-Run Effects of the Labor Income Tax The Intratemporal Substitution Effect Starting in a steady state, with ρ = r , suppose the government increases the labor income tax rate but rebates back the extra revenue it raises to households as lump-sum transfers This is like the Robinson-Crusoe experiment where we isolate the substitution effect of a change of technology The higher tax distorts the consumption-labor margin without inducing an obvious income effect Relative price of leisure is (1 − τh )wt so it falls suggesting that c ↓ `↑ h↓ But there are other effects as well Long-Run Effects of the Labor Income Tax Consider the long-run steady state conditions r =ρ I I I rk − δ = r AFk (κ, 1) = rk ⇒ AFk (κ, 1) = ρ + δ Means the capital-labor ratio is unaffected by the increase tax rate in the long-run (also means rk and w unaffected in the long run) With h ↓ this means k ↓ which means pre-tax household income is lower Suggests an implied negative income effect c ↓ with a somewhat offsetting effect on h The income effect cannot completely offset the substitution effect because c + δ k + g = AF (k, h) ⇒ c + g = [AF (κ, 1) − δ κ] h so that c and h must move in the same direction. Short-Run Effects of the Labor Income Tax Because c + δ k + g = AF (k, h) we know that the change of consumption, between the initial steady state and the eventual one must be ∆c ≈ (MPK − δ )∆k + MPH∆h where ∆k and ∆h are the long-run changes in k and h If we hold r0 = ρ we should expect the leftward shift of C D to be approximately ∆C D = (MPK − δ )∆k + MPH∆h = ρ∆k + MPH∆h We should expect the leftward shift of I D to be approximately equal to ∆I D = ∆k Therefore ∆Y D ≈ (1 + ρ)∆k + MPH∆h It is also reasonable to assume households wish to smooth leisure in which case we might expect ∆Y S ≈ MPH∆h Means demand shifts by more than supply: r0 ↓ and y0 ↓ Short-Run Effects of the Labor Income Tax Consumption Taxes Assume that τt = τc ct Proportional tax on consumption purchases Household’s lifetime budget constraint can be written as ∞ ∞ t=0 t=0 ∑ qt [(1 + τc )ct + it ] = ∑ qt (wt hts + rkt kt + vt ) + (1 + r−1 )b0 . Changes the intratemporal condition governing the consumption-labor decision: wt U` (ct , 1 − hts ) = 1 + τc Uc (ct , 1 − hts ) Other optimality conditions remain the same Effects of the Consumption Tax Suppose the government increases the consumption tax and rebates increased revenue back to households as transfers Because the tax rate distorts the same intratemporal condition as the labor tax all the qualitative effects that the tax has are qualitatively the same as the effects of the labor income tax. However, this does not mean that a consumption tax that raises the same amount of revenue as a labor income tax will have exactly the same effect on the economy. Capital Income Tax Assume that τt = τk (rkt − δ )kt Proportional tax on capital rental income net of depreciation Household’s lifetime budget constraint can be written as ∞ ∑ qt (ct + it ) = t=0 ∞ ∑ qt {wt hts + rkt kt − τk (rkt − δ )kt + vt } + (1 + r−1 )b0 . t=0 The after-tax rate of return on capital income becomes (1 − τk ) (rkt+1 − δ ) No arbitrage conditions now says rt = (1 − τk ) (rkt+1 − δ ) All other optimality conditions remain unchanged. Long-Run Effects of the Capital Income Tax Consider the long-run steady state conditions r =ρ (1 − τk )(rk − δ ) = r ⇒ I I I I AFk (κ, 1) = AFk (κ, 1) = rk ρ +δ 1 − τk Means the capital-labor ratio falls when τk ↑ Intuition: Capital become less attractive as a way of savings, so households are less willing to own it Given that κ ↓ it follows that AFk (κ, 1) ↑ so rk ↑ Given that κ ↓ it follows that AFh (1, κ −1 ) ↓ so w ↓ Other effects are hard to sign because κ isn’t invariant to the tax rate Long-Run Effects of the Capital Income Tax Other Effects Intratemporal condition says w= I U` (c, 1 − h) Uc (c, 1 − h) Given that w ↓ this suggests an additional intratemporal substitution effect: c ↓, ` ↑, h ↓ However the market clearing condition for goods says c + g = [AF (κ, 1) − δ κ] h I I If κ ↓ the term in square brackets falls suggesting a negative income effect that would make c ↓, and h ↑ Unclear what the net effect is on h Optimal Taxation Suppose that the government has particular spending plans that need to be financed What is the utility maximizing way for the government to finance this spending? I I I If the initial condition of the economy is taken into account this is called a Ramsey planning problem If lump-sum taxes were feasible they would be the best way to raise revenue, since lump-sum taxes are non-distorting Without lump-sum taxes, the answer to the question depends on the set of tax instruments available. If you ignore initial conditions you can compare the steady states of two economies with the same g and v , but different tax systems, and ask “In which economy would households prefer to live?” I Generally, this will give a different answer Quantitative Experiments with Tax Systems The next slide considers three experiments 1 Replace lump-sum taxes completely with a labor income tax 2 Replace lump-sum taxes completely with a consumption tax 3 Replace lump-sum taxes completely with a capital income tax Set up an example with U(c, `) = ln c + θ ln ` y = Ak α h1−α Set δ = 0.02, α = 0.4, ρ = 0.01, θ = 2.454, A = 0.8152 I I This is meant to mimic quarterly data, so the steady state interest rate is about 4% and the steady state depreciation rate is about 8%. Implies that y = 1 (a normalization) and h = 0.25 Let g = 0 and v = 0.1, so transfers are 10% of GDP Optimal Taxation: A Quantitative Example Economic Outcomes and Utility Under Different Tax Systems Lump-Sum 0.1 n/a 53.3 0.25 0.73 1 13.3 0.27 Labor 0.1 0.20 53.3 0.21 0.62 0.84 11.3 0.23 Consumption 0.1 0.15 53.3 0.22 0.66 0.90 12.0 0.24 Capital 0.1 0.65 24.1 0.23 0.55 0.66 5.5 0.11 U(c, 1 − h) −1.02 Consumption Equivalent −1.06 4.6% −1.04 2.6% −1.23 23.6% v Tax Rate κ h c y k i Optimal Taxation: A Quantitative Example The “consumption equivalent” tells you how big a percentage increase in consumption would be needed for the household to be indifferent between living in the economy with the tax, and the economy with lump-sum taxes I Comparing utils isn’t really that useful The consumption tax has the smallest “consumption equivalent”, suggesting that this is the least distorting tax that can be used to finance transfers The capital tax has a much larger distortionary effect than the labor income and consumption taxes I A large literature on optimal taxation provides similar results in more thorough analyzes that solve the full optimization problem Important to recognize that this analysis of optimal taxation does not take into account possible differential impacts of taxes on different households I Incidence of consumption taxes, especially taxes on essential goods, can be highly regressive The Time Consistency Problem The theory of optimal taxation I’ve described assumes that the government can commit to its tax policies. I This means that the government sticks to any tax rates it announces. Suppose the government announces a zero capital tax. Suppose the government reneges on this promise after households have made their savings decisions. Taxing capital income completely in the next period could be the optimal policy, because at that point it is a non-distorting tax. In this case, a zero capital tax is called time-inconsistent. For this reason, the theoretical models usually assume commitment, and assume no taxation of capital income at date 0. Government Spending and Taxes in the Long-Run Consider a permanent increase in government purchases, financed by a permanent increase in the labor tax rate In essence this is a combination of I I An increase in g, financed by an increase in lump-sum taxes A decrease in lump-sum taxes paid for by an increase in the labor income tax rate We’ve already studied these two experiments in isolation, so the net effect is the sum of the effects in the two experiments I I I The increase of g financed by lump-sum taxes lowers c, and increases h via the income effect The increase of τ h to pay for larger transfers, lowers c and h via the intratemporal substitution effect Neither experiment affects the capital-labor ratio Net effect of the combined experiment is ambiguous, so we need a quantitative model Government Spending and Taxes in the Long-Run Red: Lump-sum tax case Blue: Labor income tax case Consumption 1 Labor Income Tax Rate 1 0.4 0.8 0.6 0.3 0.6 0.4 0.2 0.4 0.2 0.1 0.2 0 0 c h 0.8 0 0.1 0.2 0.3 0.4 2 0 0 g Output 0.1 0.3 0.4 0.5 0 0.4 15 0.3 0.1 0.2 g 0.3 0.4 0.1 0.2 0.3 0.4 0.3 0.4 g Investment 0.5 i 10 0.2 5 0.1 0 0 0 20 k 1 0.2 g Capital 25 1.5 y Labor 0.5 0 0 0.1 0.2 0.3 0.4 0 0.1 g 0.2 g The substitution effect, in this example dominates I The income effect, on it’s own, is captured by the red line. The Laffer Curve and Supply Side Economics In the 1980s economist Arthur Laffer popularized the idea that increases in tax rates do not necessarily increase government revenue. In fact, he argued, cutting taxes can actually increase revenue because of their effect on the tax base Basic idea in the case of labor income taxes: I I Revenue is τ h wh. Cutting taxes decreases τ h , but it might increase h enough to offset the decline of τ h In our model the effects of increasing τ h depend on whether this finances an increase in transfers or an increase of government purchases. Once again, we need our quantitative model I We will increase τ h and use the revenue to finance either g or v . The Laffer Curve Red: Government purchases Labor 0.2 0.1 0 1 0.6 0.75 0.4 0.5 0.2 0.25 0 0 0.5 1 1 0 0 Total Wages 0.5 1 0 Capital 20 0.8 v or g k 10 0.4 5 0.5 1 0.3 0.2 0.1 0 0 1 0.4 0.6 0 0.5 Government Spending 0.5 15 0.2 Output 1.25 c h 0.3 wh Consumption 1 0.8 y 0.4 Blue: Transfers 0 0 0.5 1 0 0.5 1 When taxes finance g, c falls more, and h falls less I Increasing g adds an income effect that partially offsets the substitution effect of the higher tax The Laffer Curve Red: Government purchases Labor 0.2 0.1 0 0.8 1 0.6 0.75 0.4 0.5 0.2 0.25 0 0 0.5 1 1 0 0 Total Wages 0.5 1 0 Capital 20 0.8 v or g k 10 0.4 5 0.5 1 0.3 0.2 0.1 0 0 1 0.4 0.6 0 0.5 Government Spending 0.5 15 0.2 Output 1.25 c h 0.3 wh Consumption 1 y 0.4 Blue: Transfers 0 0 0.5 1 0 0.5 1 The negative income effects bolsters the tax base when taxes are paying for g, so the limits on government spending are higher if taxes are paying for g The peak of the Laffer curve is at a very high tax rate Government Debt Assume that the government borrows and lends in the same bond market as households, and faces the same competitively determined interest rate. The government’s budget constraint is: vt + gt + (1 + rt−1 )btg = τt + btg+1 btg represents the government’s net debt to households The government’s fiscal balance is revenue minus expenditure: I τt − (vt + gt + rt−1 btg ) I A deficit is a negative fiscal balance An important alternative concept is the primary balance, which is government revenue minus non-interest expenditure: τt − (vt + gt ) Like households, the government has a lifetime budget constraint (1 + r−1 )b0g = ∞ ∑ qt [τt − (vt + gt )] t =0 Government Debt When the government can borrow, the primary balance in any period can be positive (a surplus) or negative (a deficit) τt − (vt + gt ) But over its lifetime, if the government has initial debt (b0g ) then it must run a sequence of primary balances that is in surplus in present value terms: ∞ (1 + r−1 )b0g = ∑ qt [τt − (vt + gt )] t=0 Holding b0g fixed, if the government decides to run a deficit in the short run, it must run some combination of bigger balances in the future to offset this Household Behavior with Government Debt The household budget constraint is the same as before: ct + it + bt+1 = wt hts + rkt kt + vt − τt + (1 + rt−1 ) bt . The household’s lifetime budget constraint is: ∞ ∞ t=0 t=0 ∑ qt (ct + it ) = ∑ qt (wt hts + rkt kt + vt − τt ) + (1 + r−1 )b0 Parse out the part to do with government behavior: ∞ ∑ qt (ct + it ) = t=0 ∞ ∞ t=0 t=0 ∑ qt (wt hts + rkt kt ) + (1 + r−1 )b0 + ∑ qt (vt − τt ) Household Behavior with Government Debt The Lifetime Budget Constraint ∞ ∞ ∞ ∑ qt (ct + it ) = t =0 ∑ qt (wt hts + rkt kt ) + (1 + r−1 )b0 + ∑ qt (vt − τt ) t =0 t =0 (1 + r−1 )b0g = ∞ ∑ qt [τt − (vt + gt )] t =0 We know that the timing of transfers and taxes doesn’t matter to households ... only their present value matters Households take all government variables as given, so we can just as easily replace ∞ ∑ qt (vt − τt ) t =0 ∞ with −(1 + r−1 )b0g − ∑ qt gt t =0 Also, if the government has any initial debt, it is held by households: b0 = b0g So we can write the lifetime budget constraint of the household as ∞ ∞ ∞ t =0 t =0 t =0 ∑ qt (ct + it ) = ∑ qt (wt hts + rkt kt ) − ∑ qt gt Ricardian Equivalence The only government-related variable that appears in the rewritten household budget constraint is gt . Government debt does not appear there, and taxes and transfers do not appear there This implies that the level of government debt and the timing of taxes (and hence, deficits) are completely irrelevant to household decision making! Ricardian Equivalence If You are Still Not Convinced Think through any experiment where {gt } is unchanged Examples: I Government cuts taxes now, and raises taxes in the future to pay off increased government debt I Government increases transfers now, and raises taxes in the future to pay off increased government debt F F I No effect because PV of taxes is unchanged No effect because PV of taxes next of transfers is unchanged Suppose households own more government debt at time 0 F F Means PV of taxes net of transfers in the future must be larger So households don’t feel richer because they hold more government bonds All that matters is {gt }! When Does Ricardian Equivalence Fail? Distortionary Taxes If taxes are distortionary, then the government’s ability to borrow and lend, and the timing of taxes both matter Typically, government spending on transfers rising during recessions and other government spending tends to be acyclical I Without the ability to borrow, the government would have to increase taxes to pay for the increased public spending. I In a world with lump-sum taxes this would not matter because households only care about the present value of taxes I In a world with distorting taxes, the government would have to raise tax rates during the recession, which would make the recession worse. Suppose taxes are cut today, but raised later to pay for today’s cut I In a world with lump-sum taxes this would not matter because households only care about the present value of taxes I In a world with distorting taxes, an income tax cut today makes people work harder today, and an increase in the future makes them work less in the future through substitution effects. When Does Ricardian Equivalence Fail? Finite Lives / Intergenerational Effects Suppose households have finite lives and don’t care about future generations. A tax cut now can make a household feel wealthier if the future tax increase that will pay for the tax cut is expected to take place far into the future. If the household feels wealthier, the tax cut stimulates consumption demand and labor supply falls. There are, of course, additional effects if the tax cut is not lump sum. When Does Ricardian Equivalence Fail? Borrowing-Constrained Households Suppose some households are unable to borrow and would like to. If they receive a tax cut today, it is as if they received a loan from the bank that they have to pay back in the future (in this case, in the form of higher future taxes). Households who are borrowing-constrained and receive the tax cut will have a high propensity to spend the entire tax cut Households who are not borrowing-constrained are unlikely to change their behavior in response to receiving the tax cut.