MAGYAR NEMZETI BANK MINI-COURSE

Transcription

1 MAGYAR NEMZETI BANK MINI-COURSE LECTURE 3. POLICY INTERACTIONS WITH TAX DISTORTIONS Eric M. Leeper Indiana University September 2008

2 THE MESSAGES Will study three models with distorting taxes First draws on Gordon-Leeper (2005,2006): growth model w/ transactions demand for money Second draws on Leeper-Yun (2006): provides micro foundations for FTPL Once models completely solved out, can understand price-level determination more deeply Emphasizes the role of asset substitution, which is absent from simple models Gets us away from the fiscal theory story about wealth effects Useful models to keep in your head: roll your own policies Characterize eqm as function of general sequences of policy variables

3 FIRST MODEL Growth model w/ capital, money, nominal government debt arbitrages among assets determine their relative demands returns to real balance holdings and after-tax returns to capital determine the relative values of real and nominal assets expected macro policies determine expected returns on real and nominal assets so price level depends on interactions among current and expected future MP & FP Quantity theory and fiscal theory emerge as special cases QT & FT employ common money demand M d P = h(i, y) how can this be?

4 THE MODEL We exploit the analytic convenience that comes with log prefs, C-D technology, complete depreciation of capital none of the general points depend on these simplifying assumptions Aggregate resource constraint c t + k t + g t = f(k t 1 ) Goods producing firm rents k at rental rate r and pays taxes levied against sales of goods to solve max k t 1 D Gt = (1 τ t )f(k t 1 ) r t k t 1 Transactions services producing firm hires labor l at wage rate w to solve max l t D T t = P T t T (l t ) w t l t

5 THE MODEL Household owns firms and pays taxes on capital income HH has income I t = r t k t 1 + D Gt + w t l t + D T t + z t where z t 0 is lump-sum transfers from the government HH s expenditures on c & k must be financed with real money balances, M t 1 /P t, or with transactions services, T t, to satisfy the constraint M t 1 P t + T t (c t + k t ) c t + k t T t gives fraction of expenditures financed w/ transactions services

6 THE MODEL HH s problem max E 0 {c t,l t,t t,m t,b t,k t} t=0 β t U(c t, 1 l t ), 0 < β < 1 where 1 l t is leisure, subject to the finance constraint, the budget constraint c t + k t + M t + B t P t + P T t T t I t + M t 1 + R t 1 B t 1 P t and 0 l t 1 Future government policy is the sole source of uncertainty; the operator E denotes equilibrium expectations of private agents over future policy

7 THE MODEL The government finances expenditures on goods, g t, and transfer payments, z t, by levying taxes, issuing new debt, and creating new money to satisfy: τ t f(k t 1 ) + M t M t 1 P t + B t + R t 1 B t 1 P t = g t + z t Assume the following functional forms: f(k t 1 ) = kt 1, σ 0 < σ < 1 T (l t ) = 1 (1 l t ) α, α > 1 U(c t, 1 l t ) = log(c t ) + γ log(1 l t ), γ > 0

8 SOLVING THE MODEL State at t depends on assets and expectations of macro policies denote state by z t = (k t 1, M t 1, (1 + i t 1 )B t 1, {E t ρ j, E t τ j, E t s g j } j=t) ρ t = M t /M t 1, s g t = g t/f(k t 1 ) emphasizes that a complete specification of policy must allow agents to form expectations over infinite future of policies

9 SOLVING THE MODEL First-order conditions firms household s 1 + r t = σ(1 τ t )k σ 1 t 1 ϕ t + λ t = 1 + λ t Tt d c t γ = w t ϕ t 1 l t ϕ t P T t = λ t (c t + k t ) [ ϕ t ϕt+1 + λ t+1 = βe t P t ϕ t P t = β(1 + i t )E t w t = α(1 l t ) α 1 P T t P t+1 [ ϕt+1 P t+1 ϕ t + λ t = λ t T d t + βe t (1 + r t+1 )ϕ t+1 ] ]

10 EQUILIBRIUM Characterize eqm in terms of policy expectations functions (µ t, η t ), government claims to goods, s g t, and assets, (k t 1, M t 1, (1 + i t 1 )B t 1 ) Solution maps policy expectations into portfolio choices of course, policy expectations are restricted to policy paths that are consistent with eqm η and µ capture portfolio balance effects of policies η measures direct tax distortion on investment & extent to which gov t expends are financed by taxing output µ reflects expected inflation & the expected return on nominal assets Assume (similar to Monetary Doctrines ) ρ t+j = ρ F, j > 0 τ t+j = τ F, j > 0 s g t+j = sg F, j > 0

11 EQUILIBRIUM Two dynamical equations to solve: real asset & nominal assets k Euler equation in terms of s t = k t /(c t + k t ) yields 1 1 s t = σβe t whose solution is where [ ( [ 1 τt+1 1 )]+E 1 s g t 1 σβ γ ] 1 τ t+1 t+1 1 s t+1 α 1 s g t s t = η t [ η t E t (σβ) i d η i 1 σβ γ ] 1 τ t+i+1 α 1 s g i=0 t+i+1 i 1 d η i = ( ) 1 τt+j+1 1 s g, d η 0 = 1 t+i+1 j=0

12 EQUILIBRIUM Euler equation for M yields d.q. in velocity, 1 T t [ ] { [ (1 T t ) = β 1ρt E t (1 T t+1 ) 1 1 s t γ α whose solution is [ 1 (1 T t ) γ ] 1 s t α where 1 1 s t+1 γ α = µ t ρ t ] + γ } α µ t β γ α E t β i d µ i, dµ i i=0 i 1 j=0 1 ρ t+j+1, d µ 0 = 1

13 EQUILIBRIUM Imposing the stationary policy assumptions yields the policy expectations functions ) η t ( ( ) (+) 1 σβ γ τ F, s g F ) = α ( 1 σβ β γ α ( 1 τ F 1 s g F 1 τ F 1 s g F µ t ( ( ) ρ F ) = 1 β/ρ F Eqm capital stock is ( k t = 1 1 ) ) (1 s g t )f(k t 1 ) η t Eqm real money balances are ( ) M t µ t = (1 s g t )f(k t 1 ) P t η t γ/α )

14 PRICE-LEVEL DETERMINATION Can think of price level being determined through eqm real balances M t P t = t (1 s g t )f(k t 1 ) where with t ( ( ) ρ F, (+) ( ) τ F, s g F ) = t = µ t η t γ/α β γ α 1 γ/α ( 1 σβ 1 τ F 1 s g F 1 β/ρ F ) 1/ t is velocity; it gives the value of nominal assets t depends on expected MP & FP

15 THE ROLE OF POLICY EXPECTATIONS µ and η capture 3 distinct influences of expectations on P 1. µ: the marginal value of real money balances; higher expected money growth lowers µ and induces substitution away from money, raising P 2. η: direct tax distortion that alters return on investment; higher expected taxes reduce return on investment and induces substitution away from k into c and into M (Tobin effect), raising money demand and lowering P 3. η summarizes composition of expected fiscal financing; higher η reflects increase in expected nominal liability creation & reduction in relative role of real taxation To see (3), note terms (1 τ)/(1 s g ) in η and write gbc as 1 τ t 1 s g t = 1 + (M t M t 1 + B t (1 + i t 1 )B t 1 )/P t (1 s g t )f(k t 1 )

16 JOINTLY CONSISTENT (EQUILIBRIUM) POLICIES Dynamic interactions among policies current policies constrain future policy options expected fiscal financing constrains current policies expected policies affect P t & real value of gov t liabilities How do jointly consistent combinations of current & future policies affect P? 1. Which policies are consistent with eqm given current expectations (µ & η)? 2. How do current policy changes affect the set of future policies that are consistent with eqm?

17 JOINTLY CONSISTENT POLICIES 1. Which policies are consistent with eqm given current expectations (µ & η)? 2. How do current policy changes affect the set of future policies that are consistent with eqm? Eqm government b.c. at t [ ( ) ρt 1 B i t 1 ρ t M ρ t t ( ) ] B t = sg t τ t M t 1 1 s g t where (B/M) s B s /M s and t summarizes given expected policies Eqm government b.c. in future t = ( s g F τ ) F 1 s g ( F B ) M F 1 β 1 ( ( ) B M )t + ρ F 1 ρ F

18 M t P t = β γ α MONEY DEMAND ( ) 1 + it 1 η t γ/α (1 sg t )f(k t 1) i t In general, both MP and FP affect P When is P determined by MP alone? Under policy assumptions that dichotomize real & nominal sides Balanced net-of-interest surplus: τ t = s g t all t Now η t = (1 σβγ/α)/(1 σβ) and M d is M t P t = h(i t, c t + k t ) P independent of FP but not of debt money growth must finance interest obligations higher B higher debt service higher P & π In general, cannot rid M/P of η

19 UNPLEASANT MONETARIST ARITHMETIC Open-market sale of B t, holding M t + B t fixed Fix (s g t, s g F ) and τ t B/c B t, some future policy must adjust either τ F or ρ F 1. suppose τ F : η t, k t P t (but future P ) 2. suppose ρ F : µ t, tend to make P t (but future P ) But M t, so ultimate effect on P t can go either way, depending on B/M Monetary policy is constrained by the government s fiscal obligations works through seigniorage

20 CANONICAL FTPL Bond-financed tax cut: τ t, B t Fix (ρ F, τ F, s g F ) and sg t B/c B t rises, if M t unchanged, (B/M) t rises and some future policy must adjust By ass n no future policy can adjust Only eqm policy is for M t to rise in proportion to the B t increase so that (B/M) t unchanged Required increase in M t is exactly enough so increase in future seigniorage (b/c the level of money supplied is now higher) suffices to service higher debt The fixed policies peg i t and M t /P t, so P t Monetary policy is constrained by the government s fiscal obligations works through nominal asset revaluation

21 PURE FISCAL EFFECTS FP can affect P independently of MP Consider a debt-financed tax cut to which future taxes adjust Fix (ρ t, ρ F, s g t, s g F ) Lower τ t & higher (B/M) t higher τ F Lower return on capital induces substitution away from real assets toward nominal assets With M t fixed, P t falls This Tobin effect gives debt a natural role in determining P Quite non-keynesian: current fiscal expansion reduces nominal demand and price level Note that even though money growth is unchanged, because M/P rises, seigniorage revenues rise

22 COUNTERCYCLICAL FISCAL POLICIES Extend previous models in several ways add human capital, h: f(k, h), f CRS incomplete depreciation of both k and h total investment, x = x k + x h, and consumption enters finance constraint calibrate to U.S. data Need to compute expectations functions, {η t, µ t } assume perfect foresight use data on {s g t, sz t, τ t, ρ t } handle infinite sum in a couple of ways Simulate time paths of investment & velocity

23 COUNTERCYCLICAL FISCAL POLICIES Basic intuition: economic downturn: g/y and T/y debt-financed deficit if agents expect higher future taxes, return on investment investment in the downturn declines more than in absence of countercyclical policy capital stock lower than in absence of countercyclical policy downturn is deeper and more prolonged that in absence of countercyclical policy

24 COUNTERCYCLICAL FISCAL POLICIES Capital accumulation ) k t + h t = (1 1ηt (1 δs g t )f(k t 1, h t 1 ) s g t capital η t plays two roles 1. heavy dependence of direct taxation η high elasticity of capital wrt/ s g t is high 2. if future taxes rise, η t rises further raising elasticity of capital wrt/ s g t How countercyclical policies are expected to be financed influences their effectiveness

25 COUNTERCYCLICAL FISCAL POLICIES U.S. Policy Variables Purchases as Share of Output Transfers as Share of Output Tax Revenues as Share of Output Seigniorage as Share of Output

26 COUNTERCYCLICAL FISCAL POLICIES Portfolio Choices (U.S. Data) Cyclical 0.10 Xk/(C+Xk) X/Y

27 COUNTERCYCLICAL FISCAL POLICIES Portfolio Choices (U.S. Data) Cyclical Velocity of C+Xk Velocity of Y

28 COUNTERCYCLICAL FISCAL POLICIES Model Portfolio Choices Cyclical Xk/(C+Xk) X/Y

29 COUNTERCYCLICAL FISCAL POLICIES Model Portfolio Choices Cyclical 0.03 Velocity of C+Xk Velocity of Y

30 THIRD MODEL Seek to provide micro foundations for the FTPL Elastic labor supply; fixed capital stock Proportional tax levied against labor income has both supply and demand effects FTPL typically focuses only on demand effects Complete contingent claims, fiat currency, nominal government debt CRS production in labor Derive effects of tax policies on balance sheets of HHs

31 Preferences E 0 THE MODEL t=0 β t [u(c t, m t ) + v(1 h t )] HH budget constraint [ ] B t,t+1 c t +m t +E t Q t,t+1 (1 τ t )(w t h t +Φ t )+ B t 1,t + M t 1 P t P t Q t,t+1 is stochastic discount factor (nominal value at t of $1 at t [ + 1; Φ t is real dividends B E t Q t,t+1 t,t+1 is real value at t of nominal contingent claims P t ] 1 + i t = 1 E t [Q t,t+1 ], Q t,t+1 = q t,t+1 P t P t+1

32 THE MODEL Rewrite the HH s flow b.c. as c t + i t 1 + i t m t + E t [q t,t+1 a t+1 ] (1 τ t )(w t h t + Φ t ) + a t a t = B t 1,t + M t 1 P t, value of nominal assets HH s present-value b.c. is E 0 t=0 [ q t c t + i ] t m t (1 τ t )(w t h t + Φ t ) a i t with lim t E 0 [q t a t ] = 0

33 First-order conditions THE MODEL β t u c (c t, m t ) = λq t ( ) β t it u m (c t, m t ) = λq t 1 + i t where λ = u c (c 0, m 0 ) v (1 h t ) u c (c t, m t ) = (1 τ t)w t Use these in PV b.c. E 0 t=0 βt [u c (c t, m t )c t + u m (c t, m t )m t (1 τ t )y t u c (c t, m t )] = a 0 u c (c 0, m 0 ) Note: LHS entirely in terms of allocations When allocations are unique, have a unique real value of nominal assets, a 0 = B 1,0+M 1 P 0

34 EQUILIBRIUM E 0 t=0 βt [u c (c t, m t )c t + u m (c t, m t )m t (1 τ t )y t u c (c t, m t )] u c (c 0, m 0 ) = a 0 Under rational expect, HH knows a 0 when it optimizes This is an eqm balance sheet relation, where LHS is PV of HH s assets at time 0 Get cond in policy variables, subst y t = c t + g t in relation E 0 t=0 β t u c(c t, m t ) u c (c 0, m 0 ) Noting that q t = β t u c(c t,m t) u c(c 0,m 0 ) E 0 t=0 An equilibrium condition! [ (τ t y t g t ) + u m(c t, m t ) u c (c t, m t ) m t q t [ (τ t y t g t ) + i t 1 + i t m t ] = a 0 ] = a 0

35 A FISCAL THEORY EQUILIBRIUM E 0 t=0 [ q t (τ t y t g t ) + i ] t m t = a i t Suppose: τ t y t are lump-sum tax revenues; y & g exogenous, then q given; let MP peg i t = ī m t = h(y t ) independent of MP & FP; let FP set {τ t } exogenously Under these ass ns, LHS a number, call it P V S, so P 0 = B 1,0 + M 1 P V S At t = 0, B 1,0 + M 1 given, so this determines P 0 Can think of 1/P V S as price of nominal assets, which plays the same role as 1/ in earlier model

36 POLICY EXPERIMENTS 1. Expect lower τ t+k P V S P 0 2. Reduce current τ 0 P V S P 0 ī 3. Expect lower m P V S P 1+ī 0 (3) seems perverse relative to standard theory lower expected seigniorage iff lower ī lower π e in most monetary models higher expected return to M M d P 0 what s going on? in standard models, the ubiquitous eqm condition is present but it doesn t restrict the nature of the eqm b/c it is assumed that taxes adjust to alter the P V S for any given P 0 ī in FTPL, lower m less backing for nominal assets, 1+ī so nominal assets are worth less, meaning 1/P 0 Whether the ubiquitous eqm condition should be treated as a constraint or an eqm condition is at the heart of Buiter s critique of the FTPL

37 A PRICE-THEORETIC VIEW OF THE FTPL Follow public finance to extend Slutsky-Hicks decomposition to include a third effect FT works through a type of wealth effect that arises when P revalues nominal assets in HH portfolios Decompose impacts of tax change as total effect = substitution effect + wealth effect + revaluation effect Let y F t be Becker s full income (dividend income + maximum labor income if HH works entire time endowment 1 unit) y F t = (1 τ t )w t 1 + Φ t HH takes yt F as given and from it purchases consumption, real balances, leisure

38 A PRICE-THEORETIC VIEW OF THE FTPL HH flow b.c. c t + i t 1 + i t m t + (1 τ t )w t (1 h t ) + E t [q t,t+1 a t+1 ] y F t + a t HH present value b.c. E 0 t=0 [ q t c t + i ] t m t + (1 τ t )w t (1 h t ) a 0 + v i t with lim t E 0 [q t a t ] = 0, lim t E 0 [q t y F t ] = 0 v 0 is expected PV of full income flows, v 0 = E 0 t=0 [q ty F t ] HH takes both a 0 and v 0 parametrically

39 A PRICE-THEORETIC VIEW OF THE FTPL Lagrange multiplier on the PV b.c. is λ = e 0 a 0 +v 0 e 0 = E 0 t=0 β t [u c (c t, m t )c t + u m (c t, m t )m t + v (1 h t )(1 h t )] e 0 is expected PV of expenditures (including leisure) λ is shadow price of wealth wealth rises (a 0 + v 0 ) λ expenditures rise (e 0 ) λ Demand functions ( qt c t = c β, i t, a ) 0 + v 0 t 1 + i t m t = m h t = h ( qt e 0 i t 1 + i t, a 0 + v 0 β, ( t (1 τ t) w t, q t β, t e 0 ) i t 1 + i t, a 0 + v 0 e 0 )

40 A PRICE-THEORETIC VIEW OF THE FTPL Conventional wealth effect vs. revaluation effect suppose B 1,0 + M 1 = 0 revaluation effect is zero (a 0 = 0) conventional wealth effect still operates through v 0 & e 0 Of course, taxes can affect P 0 even if FTPL not operative suppose τ 0 substitution effect reduces labor supply wealth effect raises labor supply final impact depends on relative sizes but then the resulting P 0 and a 0 imposes restrictions on {τ t } t=1 necessary for eqm

41 SUBSTITUTION, WEALTH & REVALUATION Suppose {τ t } t=0 changes to {τ t } t=0 Problem (*) s.t. Problem ( ) s.t. max {c t,m t,h t} t=0 t=0 E 0 β t [u(c t, m t ) + v(1 h t )] t=0 [ E 0 q t c t + i ] t m t + (1 τt )w t (1 h t ) a 0 + v i t yields {c t, m t, h t, w t, a t, v t, e t, P t, q t, R t, Φ t } t=0 max {c t,m t,h t} t=0 t=0 E 0 β t [u(c t, m t ) + v(1 h t )] t=0 [ E 0 q t c t + i ] t m t + (1 τ t 1 + i )w t(1 h t ) a 0 + v 0 t yields {c t, m t, h t, w t, a t, v t, e t, P t, q t, R t, Φ t } t=0

42 SUBSTITUTION EFFECT Set lump-sum transfers, T s 0, so HH can achieve same level of utility it would have obtained under the (*) tax even though it optimizes under the ( ) tax Problem (Substitution) max E 0 {c t,m t,h t} t=0 [ s.t. E 0 c t + t=0 q t t=0 i t β t [u(c t, m t ) + v(1 h t )] 1 + i m t + (1 τ t )w t (1 h t ) t ] a 0 + v 0 + T s 0 constraining prices to be eqm prices under ( ) tax budget line of this problem tangent to HH s indifference surface under ( ) tax

43 A HICKSIAN DECOMPOSITION Problem (No Revaluation) s.t. max E 0 β t [u(c t, m t ) + v(1 h t )] {c t,m t,h t} t=0 t=0 [ ] E 0 q t c t + i t 1 + i m t + (1 τ t )w t (1 h t) t t=0 a 0 + v 0 HH assumes revaluation does not result from the tax change, so assets have value a 0 = a 0 under ( ) tax

44 A HICKSIAN DECOMPOSITION Set lump-sum transfers, T w 0, so HH can achieve the same level of utility it would have obtained under the ( ) tax, with and without asset revaluation Problem (Revaluation) max E 0 {c t,m t,h t} t=0 [ s.t. E 0 c t + t=0 q t t=0 i t β t [u(c t, m t ) + v(1 h t )] 1 + i m t + (1 τ t )w t (1 h t ) t ] a 0 + v 0 + T w 0 T0 w permits Problem (No Revaluation) and Problem (Revaluation) to achieve the same level of utility Total Effect: Problem (*) vs. Problem ( ) Substitution Effect: Problem (*) vs. Problem (Substitution) Revaluation Effect: Problem (No Revaluation) vs. Problem (Revaluation) Wealth Effect = Total Substitution Revaluation

45 A HICKSIAN DECOMPOSITION Solutions to optimization problems are cons demands ( q ( ) : c t = c t β t, ( ( ) : c t = c q t β t, i t 1 + i t i t, a 0 + v 0 e 0, a 0 + v 0 e i t ( ) (Substitution) : c t u0 =u = c q t 0 β t, i t 1 + i, a 0 + v 0 + T 0 s t e 0 u0 =u 0 ( ) (Revaluation) : c q t t u0 =u 0,a = c 0=a 0 β t, i t a i, + v 0 + T 0 w t e 0 u0 =u 0,a 0=a 0 c t u0 =u : planned consumption under ( ) tax, with utility at 0 u 0, the level under (*) tax c t u0 =u 0,a : planned consumption without revaluation 0=a 0 under ( ) tax with utility at u 0, the level under ( ) tax ) )

46 A HICKSIAN DECOMPOSITION The full decomposition ( ) c t log c t total effect ( = log + log + log c t u 0 =u 0 c t ) substitution ( effect ( c t u 0 =u 0,a 0 =a 0 c t u 0 =u 0 wealth effect c t c t u 0 =u 0,a 0 =a 0 revaluation effect ) )

47 AN EXAMPLE ECONOMY Assume log preferences u(c, m) + v(1 h) = log c + log m + log(1 h) Then e 0 = 3 1 β ( ) ( ) 1 β β t c t = (a 0 + v 0 ) 3 q ( ) ( t ) ( ) 1 β β t 1 + it m t = (a 0 + v 0 ) 3 q t i ( ) ( t ) 1 β β t h t = 1 (a 0 + v 0 ) 3 (1 τ t )w t q t Then can compute all the objects in the decomposition Assume MP pegs i t to satisfy: β(1 + i t ) = 1, t 0 See Leeper-Yun (2006) for details and case of lump-sum

48 AN EXAMPLE ECONOMY Income taxes set τ t > 0 1 τ t y t = 2 s g τ t q t = β t (1 τ 0) (2 s g τ t ) (1 τ t ) (2 s g τ 0 ) Present value full income flows is v 0 = E 0 t=0 HH present value b.c. β t [ (1 τ0 )(2 s g τ t ) 2 s g τ 0 a 0 + v 0 = 3 (1 τ 0 )(1 s g ) 1 β 2 τ 0 s g A Laffer curve in τ t y t with revenues maximized at τ = 2 s g (2 s g )(1 s g ) ]

49 AN EXAMPLE ECONOMY Suppose taxes constant at τ y & c constant; i pegged; q t = β t v 0 = 1 τ 1 β, a 0 = 1 β 2 s g τ 1 τ 1 2s g + τ Equilibrium price level P 0 = 1 β 1 τ 2 s g τ 1 2s g + τ (B 1 + M 1 ) Note from a 0 = 1 β 2 s g τ, quadratic in τ = Laffer curve 1 τ 1 2s g +τ in sum of PV surpluses + seigniorage Laffer curves in τ t y t and in a 0 can look very different

50 CONVENTIONAL LAFFER CURVE 0.7 τ = 58.6% Units of Goods tax base (real GDP) direct tax revenue flow Income Tax Rate (τ)

51 FISCAL THEORY LAFFER CURVE τ = 26.8% τ = 58.6% primary surplus + seigniorage (present value) Units of Goods tax base (real GDP) direct tax revenue flow Income Tax Rate (τ)

52 TWO LAFFER CURVES Why are these different? Tax bases differ conventional: τ t y t ( fiscal theory: P V τ t y t + ) it 1+i t m t changes in conventional tax base, y t, feed into m t and the seigniorage tax base Should we care about this? presents tradeoffs relevant for inflation-targeting countries to think about the fiscal consequences of MP

53 WRAP UP Fiscal theory has been accused of being incoherent, inconsistent with economic theory, and worse This shows that with the right kind of price-theoretic analysis, the revaluation effect that lies at the heart of the FTPL can be understood as a natural extension in an environment with nominal assets of standard the Slutsky-Hicks decomposition Critics have also accused FTPL of ignoring the government s budget constraint Here we have shown that you can get an eqm condition that determines P 0 without any reference to government variables Introducing distorting taxes to a FTPL analysis reveals a second kind of Laffer curve that has been largely overlooked