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Fiscal Stimulus and Distortionary Taxation Harald Uhlig1 Thorsten Drautzburg2 1 University of Chicago Department of Economics [email protected] 2 [email protected] January 8, 2010 Harald Uhlig (University of Chicago) Fiscal Stimulus and Distortionary Taxation January 8, 2010 1 / 70 Outline 1 Introduction 2 The model 3 The model: Details Equations Parameters 4 Results Comparison to neoclassical growth. No rules-of-thumb, no binding zero lower bound. Including Rule-of-Thumb Consumers. A binding zero Lower Bound. Chemotherapy 5 Conclusions Harald Uhlig (University of Chicago) Fiscal Stimulus and Distortionary Taxation January 8, 2010 2 / 70 Introduction Outline 1 Introduction 2 The model 3 The model: Details Equations Parameters 4 Results Comparison to neoclassical growth. No rules-of-thumb, no binding zero lower bound. Including Rule-of-Thumb Consumers. A binding zero Lower Bound. Chemotherapy 5 Conclusions Harald Uhlig (University of Chicago) Fiscal Stimulus and Distortionary Taxation January 8, 2010 3 / 70 Introduction Question and Answers Question: What is the effect of a fiscal stimulus as the ARRA? What are the resulting fiscal multipliers? Answers: ... Harald Uhlig (University of Chicago) Fiscal Stimulus and Distortionary Taxation January 8, 2010 4 / 70 Introduction Bernstein-Romer, Appendix: Multipliers Romer−Bernstein output effects of a permanent stimulus of 1% of GDP 1.6 government spending 1.4 output effect 1.2 1 0.8 tax cut 0.6 0.4 0.2 0 2009 Harald Uhlig (University of Chicago) 2010 2011 Date 2012 Fiscal Stimulus and Distortionary Taxation 2013 January 8, 2010 5 / 70 Introduction What I do: Build on: Cogan-Cwik-Taylor-Wieland (2009), using Smets-Wouters (CCTW-SW). Lump-sum taxes. This paper: ! ! ! ! Medium-to-long term effects. Distortionary labor taxation ... ... plus: rule-of-thumb consumers. ... plus: binding zero lower bound. Harald Uhlig (University of Chicago) Fiscal Stimulus and Distortionary Taxation January 8, 2010 6 / 70 Introduction Key insights Output response is modest. Fiscal multipliers are typically below 1. Consumption response is typically negative or, at most, feebly positive. In the medium-to-long term: ! ! Pronounced output loss due to increased tax burden. Output losses large relative to initial increase. Note: No or only moderate inflation tax on initial bond holders, i.e. no “stealing from the Chinese”. Harald Uhlig (University of Chicago) Fiscal Stimulus and Distortionary Taxation January 8, 2010 7 / 70 The model Outline 1 Introduction 2 The model 3 The model: Details Equations Parameters 4 Results Comparison to neoclassical growth. No rules-of-thumb, no binding zero lower bound. Including Rule-of-Thumb Consumers. A binding zero Lower Bound. Chemotherapy 5 Conclusions Harald Uhlig (University of Chicago) Fiscal Stimulus and Distortionary Taxation January 8, 2010 8 / 70 The model Smets-Wouters (2007): overview Elaborate New Keynesian model. Continuum of households. They supply household-specific labor in monopolistic competition. They set wages. Wages are Calvo-sticky. Continuum of intermediate good firms. They supply intermediate goods in monopolistic competition. They set prices. Prices are Calvo-sticky. Final goods use intermediate goods. Perfect competition. Habit formation, adjustment costs to investment, variable capital utilization. Monetary authority: Taylor-type rule. Harald Uhlig (University of Chicago) Fiscal Stimulus and Distortionary Taxation January 8, 2010 9 / 70 The model Application to ARRA CCWT: path for government spending. Government consumption. Perhaps additively separable in utility. CCWT: Fed-Funds = 0 for four quarters. “Jump” to “switched-off” Taylor rule. This paper: ! ! ! ! ! Distortionary labor taxation, consumption taxes, capital income taxes. Steady state levels: Trabandt-Uhlig (2009). Details. Eg: all of labor income or without “union profits”? The former. Speed to return to steady state debt level: ψτ ∈ [0, 1]. ... plus: rule-of-thumb consumers: φ ∈ [0, 100%]. ... plus: binding zero lower bound per discount shock, causing recession. Harald Uhlig (University of Chicago) Fiscal Stimulus and Distortionary Taxation January 8, 2010 10 / 70 The model Tax rule Remaining deficit, prior to new debt and labor taxes ... ft = gov.spend.+subs.+old debt repaym.−cons.tax rev.,cap.tax rev. ... needs to be financed: lab.tax rev. + new debt = ft Steady state debt level, steady state taxes: f̄ . Tax rule: lab.tax rev.t − lab.tax rev. = ψτ (ft − f̄ ) Harald Uhlig (University of Chicago) Fiscal Stimulus and Distortionary Taxation January 8, 2010 11 / 70 The model: Details Outline 1 Introduction 2 The model 3 The model: Details Equations Parameters 4 Results Comparison to neoclassical growth. No rules-of-thumb, no binding zero lower bound. Including Rule-of-Thumb Consumers. A binding zero Lower Bound. Chemotherapy 5 Conclusions Harald Uhlig (University of Chicago) Fiscal Stimulus and Distortionary Taxation January 8, 2010 12 / 70 The model: Details Equations Outline 1 Introduction 2 The model 3 The model: Details Equations Parameters 4 Results Comparison to neoclassical growth. No rules-of-thumb, no binding zero lower bound. Including Rule-of-Thumb Consumers. A binding zero Lower Bound. Chemotherapy 5 Conclusions Harald Uhlig (University of Chicago) Fiscal Stimulus and Distortionary Taxation January 8, 2010 13 / 70 The model: Details Equations Extensions of Smets-Wouters (2007): Investment & Consumption Shadow price of investment – original SW with τ k = 0: Q̂t = −q̂tb − (R̂t − Et [πt+1 ]) + 1 × r∗k (1 − τ k ) + δτ k + 1 − δ k × [r∗k (1 − τ k )Et (r̂t+1 ) + (1 − δ)Et (Q̂t+1 )], (1) Consumption growth – SW with τ j = 0, j = l, c and “ex-dividend” wage w∗h instead of w∗ : ĉt = 1 h/µ 1 − h/µ Et [ĉt+1 ] + ĉt−1 − (q̂ b + R̂t − Et [π̂t+1 ]) 1 + h/µ 1 + h/µ σ[1 + h/µ] t [σ − 1][w∗ n∗ /c∗ ] 1 − τ l − (Et [n̂t+1 ] − nt ), (2) σ[1 + h/µ] 1 + τ c Harald Uhlig (University of Chicago) Fiscal Stimulus and Distortionary Taxation January 8, 2010 14 / 70 The model: Details Equations Extensions of Smets-Wouters (2007): Wages Evolution of wages: (1 + β̄µ)ŵt − ŵt−1 − β̄µEt [ŵt+1 ] ! " d τtl (1 − ζw β̄µ)(1 − ζw ) 1 = [ĉt − (h/µ)ĉt−1 ] + ν n̂t − ŵt + ] ζw 1 − h/µ 1 − τl − (1 + β̄µιw )π̂t + ιw π̂t−1 + µ̄Et [πt+1 ] + λ̂w ,t , (3) In the flexible economy: ŵt = d τtl 1 [ĉt − (h/µ)ĉt−1 ] + ν n̂t + . 1 − h/µ 1 − τl Harald Uhlig (University of Chicago) Fiscal Stimulus and Distortionary Taxation January 8, 2010 (4) 15 / 70 The model: Details Equations Extensions of Smets-Wouters (2007): Tax rate and gov’t deficit Financing the current deficit: ! " w∗ n∗ c∗ d τtl + ŵt + n̂t + ,τt c∗ Ȳ τl # $ ψτ b b̂ − π̂ c k ∗ t ∗ ∗ t−1 p = µ[ĝta + ĝ s ] + − µτc ĉt − τ k [r∗k rtk + (rtk − δ)k̂t−1 ] µ π∗ Ȳ Ȳ Ȳ τl Budget: ĝt + 1 b∗ 1 b∗ c∗ [b̂t−1 − π̂t ] = [b̂t − R̂t − q̂tb ] + τc ĉt + µπ∗ Ȳ R∗ Ȳ Ȳ ! l " w∗ n∗ c∗ d τt k∗ p + τl + ŵt + n̂t + τ k [r∗k rtk + (rtk − δ)k̂t−1 ] . (6) c∗ Ȳ τl µȲ Harald Uhlig (University of Chicago) Fiscal Stimulus and Distortionary Taxation January 8, 2010 16 / 70 The model: Details Equations Unchanged SW equations: Cost and pricing equations % t = (1 − α)ŵt + αr̂tk − γt , mc (1 + β̄µιp )π̂t = ιp π̂t−1 + β̄µEt [π̂t+1 ]+ A (7) [1 − ζp β̄µ][1 − ζp ] % t + λ̂p,t . (8) mc ζp 1 − ζp is the probability of (potential) price adjustment. Harald Uhlig (University of Chicago) Fiscal Stimulus and Distortionary Taxation January 8, 2010 17 / 70 The model: Details Equations Unchanged SW equations: Capital services and Capital Stock Cost minimization yields: k̂t = ŵt − r̂tk + n̂t . (9) From the FOC with respect to capacity utilization: r∗k r̂tk = a## (1)ût ⇒ ût ≡ 1 − ψu k r̂ . ψu t (10) The law of motion for capital implies: ! " x∗ x∗ x∗ p p k̂t = 1 − p k̂t−1 + p q̂tx + p x̂t . k∗ k∗ k∗ Harald Uhlig (University of Chicago) Fiscal Stimulus and Distortionary Taxation (11) January 8, 2010 18 / 70 The model: Details Equations Unchanged SW equations: Investment and FedFunds The FOC for investment implies: x̂t = & ' 1 1 x̂t−1 + β̄µEt (x̂t+1 ) + 2 ## [Q̂tk + q̂tx ], µ S (µ) 1 + β̄µ (12) The interest rate rule: R̂t = ρR R̂t−1 + [1 − ρR ][ψ1 π̂t + ψ2 (ŷt − ŷtflex )] + ψ3 [ŷt − ŷt−1 + flex − (ŷtflex − ŷt−1 )] + mst , (13) Here: Introduce wedge between R̂t and the relevant interest rate for the private sector for first periods. Harald Uhlig (University of Chicago) Fiscal Stimulus and Distortionary Taxation January 8, 2010 19 / 70 The model: Details Equations Unchanged SW equations: Production and Expenditure The production technology for final goods: ŷt = Ȳ + Φ [αk̂t + (1 − α)n̂t + γt ], Ȳ (14) Spending identity with costs of capacity utilization: ŷt = ĝt + Harald Uhlig (University of Chicago) c∗ x∗ r k k∗ ĉt + x̂t + ∗ ût . Ȳ Ȳ Ȳ Fiscal Stimulus and Distortionary Taxation (15) January 8, 2010 20 / 70 The model: Details Parameters Outline 1 Introduction 2 The model 3 The model: Details Equations Parameters 4 Results Comparison to neoclassical growth. No rules-of-thumb, no binding zero lower bound. Including Rule-of-Thumb Consumers. A binding zero Lower Bound. Chemotherapy 5 Conclusions Harald Uhlig (University of Chicago) Fiscal Stimulus and Distortionary Taxation January 8, 2010 21 / 70 The model: Details Parameters Parameters: Estimated SW parameters I Parameter δ λw g µ β π∗ α σ Ȳ +Φ = λp Ȳ S ## (µ) h Ξw Value 0.025 1.5 0.18 1 + 0.4312 100 100 0.1657+100 1 + 0.7869 100 0.1901 1.3808 1.6064 0.5187 5.7606 0.7133 0.7061 Harald Uhlig (University of Chicago) Description depreciation rate markup labor market exogenous gov’t spending/GDP trend growth rate discount factor inflation rate capital share in production 1/intertemporal elasticity of substitution fixed cost and goods market markup net exports/gov’t exp. reaction to techn. investment adjustment cost habit persistence calvo parameter labor market Fiscal Stimulus and Distortionary Taxation January 8, 2010 22 / 70 The model: Details Parameters Parameters: Estimated SW parameters II Parameter ν Ξp ιw ιp ψ1 ρR ψ2 ψ3 Value 1.8383 0.6523 0.5845 0.2432 0.5462 2.0443 0.8103 0.0882 0.2247 Harald Uhlig (University of Chicago) Description labor supply elasticity calvo parameter goods market indexation labor market indexation goods market capital utilization elasticity Taylor rule reaction to inflation Taylor rule interest rate smoothing Taylor rule long run reaction to output gap Taylor rule short run reaction to output gap Fiscal Stimulus and Distortionary Taxation January 8, 2010 23 / 70 The model: Details Parameters Parameters: Calibration and Implications Parameter Value Description b Ȳ τk 0.63 0.36 0.28 0.05 0.1059 0.0097 0.2268 0.0335 0.0353 Debt to GDP ratio capital tax wage tax rate consumption tax rate implied transfer payment Interest payments relative to GDP Labor tax revenue relative to GDP Capital tax revenue relative to GDP Consumption tax revenue relative to GDP τl τc Harald Uhlig (University of Chicago) Fiscal Stimulus and Distortionary Taxation January 8, 2010 24 / 70 Results Outline 1 Introduction 2 The model 3 The model: Details Equations Parameters 4 Results Comparison to neoclassical growth. No rules-of-thumb, no binding zero lower bound. Including Rule-of-Thumb Consumers. A binding zero Lower Bound. Chemotherapy 5 Conclusions Harald Uhlig (University of Chicago) Fiscal Stimulus and Distortionary Taxation January 8, 2010 25 / 70 Results Comparison to neoclassical growth. Outline 1 Introduction 2 The model 3 The model: Details Equations Parameters 4 Results Comparison to neoclassical growth. No rules-of-thumb, no binding zero lower bound. Including Rule-of-Thumb Consumers. A binding zero Lower Bound. Chemotherapy 5 Conclusions Harald Uhlig (University of Chicago) Fiscal Stimulus and Distortionary Taxation January 8, 2010 26 / 70 Results Comparison to neoclassical growth. A neoclassical growth model Comparison to a neoclassical growth: standard, but .. ... add distortionary labor taxes, capital income taxes, consumption taxes. Frisch elasticity: 1. Calibration: Trabandt-Uhlig (2009). Consider an anticipated permanent increase in government spending. Harald Uhlig (University of Chicago) Fiscal Stimulus and Distortionary Taxation January 8, 2010 27 / 70 Results Comparison to neoclassical growth. Neoclass. vs SW-DU: announced, ψτ = 0.03. Neoclass. SW-DU Impulse response to gov.spending announcement shock ,ψτ=0.03 government spending (% ini 1 1.5 government spending(%init.output) 0.5 output 1 output τn (wage tax,perc. points) 0 percent percent 0.5 τ (wage tax rate, perc. points) 0 −0.5 consumption −1 −0.5 −1.5 2009 2010 2011 Year Harald Uhlig (University of Chicago) 2012 2013 −1 consumption 2009 2010 Fiscal Stimulus and Distortionary Taxation 2011 2012 year 2013 January 8, 2010 2014 28 / 70 Results Comparison to neoclassical growth. Neoclass. vs SW-DU: perm., ann., ψτ = 0.03. Long run. Neoclass. SW-DU Impulse response to gov.spending announcement shock ,ψ =0.03 τ 1.5 2 government spending(%init.output) output 1 0.5 τn (wage tax,perc. points) 0 0.5 percent percent government spending (% init. output) 1 1.5 0 output τ (wage tax rate, perc. points) −0.5 −0.5 consumption −1 −1 consumption −1.5 −1.5 −2 2010 2015 2020 Year Harald Uhlig (University of Chicago) 2025 2030 2010 2015 Fiscal Stimulus and Distortionary Taxation 2020 2025 year 2030 2035 January 8, 2010 29 / 70 Results No rules-of-thumb, no binding zero lower bound. Outline 1 Introduction 2 The model 3 The model: Details Equations Parameters 4 Results Comparison to neoclassical growth. No rules-of-thumb, no binding zero lower bound. Including Rule-of-Thumb Consumers. A binding zero Lower Bound. Chemotherapy 5 Conclusions Harald Uhlig (University of Chicago) Fiscal Stimulus and Distortionary Taxation January 8, 2010 30 / 70 Results No rules-of-thumb, no binding zero lower bound. Short-run. ψτ = .03 vs lump-sum. ψτ = 0.03 Lump-sum (CCWT) 0.6 0.4 0.2 0.8 Stimulus GDP τ (wage tax rate, perc. points) 0 −0.2 Investment Consumption 0.6 Stimulus GDP 0.4 0.2 0 −0.2 2009 2010 2011 2012 2013 2014 2015 2016 year Harald Uhlig (University of Chicago) % of init. output/perc. points % of init. output/perc. points 0.8 τ (wage tax rate, perc. points) Consumption Investment 2009 2010 2011 2012 2013 2014 2015 2016 year Fiscal Stimulus and Distortionary Taxation January 8, 2010 31 / 70 Results No rules-of-thumb, no binding zero lower bound. Medium-run. ψτ = .03 vs lump-sum. ψτ = 0.03 Lump-sum (CCWT) 0.6 0.4 0.8 Stimulus GDP τ (wage tax rate, perc. points) 0.2 0 −0.2 Investment Consumption 2010 2015 2020 % of init. output/perc. points % of init. output/perc. points 0.8 0.6 GDP 0.4 0.2 Harald Uhlig (University of Chicago) 2030 2035 τ (wage tax rate, perc. points) 0 −0.2 2025 year Stimulus Consumption Investment 2010 2015 Fiscal Stimulus and Distortionary Taxation 2020 2025 year 2030 2035 January 8, 2010 32 / 70 Results No rules-of-thumb, no binding zero lower bound. Fiscal stimulus: medium run. ψτ = 0.03. % of init. output/perc. points 0.8 0.6 0.4 Stimulus GDP τ (wage tax rate, perc. points) 0.2 0 −0.2 Investment Consumption 2010 Harald Uhlig (University of Chicago) 2015 2020 2025 year 2030 Fiscal Stimulus and Distortionary Taxation 2035 January 8, 2010 33 / 70 Results No rules-of-thumb, no binding zero lower bound. Spending increase, short-run output dynamics: various ψτ . 0.5 ψ= 0.03 0.4 0.3 ψ= 0.10 0.2 percent 0.1 0 Lumpsum −0.1 ψ= 0.30 −0.2 ψ= 1.00 −0.3 −0.4 2008 Harald Uhlig (University of Chicago) 2010 2012 year 2014 Fiscal Stimulus and Distortionary Taxation 2016 January 8, 2010 34 / 70 Results No rules-of-thumb, no binding zero lower bound. Spending increase, short-run fiscal multipliers 0.6 ψ= 0.03 0.4 Lumpsum ψ= 0.10 0.2 ψ= 0.30 0 ψ= 1.00 −0.2 −0.4 −0.6 2008 Harald Uhlig (University of Chicago) 2010 2012 year 2014 Fiscal Stimulus and Distortionary Taxation 2016 January 8, 2010 35 / 70 Results No rules-of-thumb, no binding zero lower bound. Spending increase, short-run tax dynamics: various ψτ . 1 percentage points 0.8 ψ= 0.30 0.6 ψ= 0.10ψ= 1.00 0.4 0.2 0 2008 Harald Uhlig (University of Chicago) ψ= 0.03 2010 2012 year Lumpsum 2014 Fiscal Stimulus and Distortionary Taxation 2016 January 8, 2010 36 / 70 Results No rules-of-thumb, no binding zero lower bound. Spending increase, short-run debt dynamics: various ψτ . 6 percent of init. output 5 4 ψ= 0.10 3 2 ψ= 0.03 ψ= 0.30 1 0 2008 Harald Uhlig (University of Chicago) 2010 ψ= 1.00 Lumpsum 2012 year 2014 Fiscal Stimulus and Distortionary Taxation 2016 January 8, 2010 37 / 70 Results Including Rule-of-Thumb Consumers. Outline 1 Introduction 2 The model 3 The model: Details Equations Parameters 4 Results Comparison to neoclassical growth. No rules-of-thumb, no binding zero lower bound. Including Rule-of-Thumb Consumers. A binding zero Lower Bound. Chemotherapy 5 Conclusions Harald Uhlig (University of Chicago) Fiscal Stimulus and Distortionary Taxation January 8, 2010 38 / 70 Results Including Rule-of-Thumb Consumers. Consumption of the two agents Modify consumption Euler equation to account for Rational Agents only: ĉtRA = 1 h/µ 1 − h/µ Et [ĉt+1 ]+ ĉt−1 − (q̂ b + R̂t −Et [π̂t+1 ]) 1 + h/µ 1 + h/µ σ[1 + h/µ] t [σ − 1][w∗ n∗ /c∗RA ] 1 − τ l − (Et [n̂t+1 ] − nt ), (16) σ[1 + h/µ] 1 + τc The consumption of the Rule-of-Thumb consumer is determined from their budget constraint: ! " dτl RoT l w∗ n∗ ĉt = (1 − τ ) RoT ŵt + n̂t − , (17) c∗ 1 − τl using n̂t = n̂tRoT = n̂tRA and n∗ = n∗RoT = n∗RA . Harald Uhlig (University of Chicago) Fiscal Stimulus and Distortionary Taxation January 8, 2010 39 / 70 Results Including Rule-of-Thumb Consumers. Aggregating consumption Aggregate consumption: ĉt = c∗RA c RoT (1 − φ)ĉtRA + ∗ φĉtRoT , c∗ c∗ (18) where w∗ n∗ (1 − τ l ) + s∗ , 1 + τc c∗ − φc∗RoT = . 1−φ c∗RoT = c∗RA Harald Uhlig (University of Chicago) Fiscal Stimulus and Distortionary Taxation January 8, 2010 40 / 70 Results Including Rule-of-Thumb Consumers. Distorting taxation and Rule-of-Thumb Consumers: ψτ = 0.03, φ = 0.50. 0.6 output government spending (% init. output) percent 0.4 0.2 0 τ (wage tax rate, perc. points) consumption −0.2 −0.4 2008 2009 2010 2011 2012 2013 2014 2015 year Harald Uhlig (University of Chicago) Fiscal Stimulus and Distortionary Taxation January 8, 2010 41 / 70 Results Including Rule-of-Thumb Consumers. Medium run. φ=0 φ = 0.5 0.8 0.6 0.6 0.2 0 government spending (% init. output) government spending (% init. output) output 0.4 percent percent 0.4 τ (wage tax rate, perc. points) output 0.2 0 τ (wage tax rate, perc. points) consumption −0.2 −0.2 −0.4 consumption −0.4 2010 2015 2020 2025 year Harald Uhlig (University of Chicago) 2030 2035 2010 2015 Fiscal Stimulus and Distortionary Taxation 2020 2025 year 2030 2035 January 8, 2010 42 / 70 Results Including Rule-of-Thumb Consumers. Comparing consumption patterns, ψτ = 0.03. φ = 0: φ = 0.5: 0.5 0.6 0.4 percent percent output 0 Rule of Thumb output 0.2 0 Rule of Thumb consumption −0.2 Rational Agent consumption −0.4 −0.5 2007 2008 2009 2010 2011 2012 2013 2014 year Harald Uhlig (University of Chicago) Rational Agent 2007 2008 2009 2010 2011 2012 2013 2014 year Fiscal Stimulus and Distortionary Taxation January 8, 2010 43 / 70 Results Including Rule-of-Thumb Consumers. Short run: ψτ = 0.03, vary rules-of-thumb fraction φ. ψτ = 0.03, φ = 0: ψτ = 0.03, φ = 0.25: 0.8 0.8 0.6 0.6 0.2 0 outputgovernment spending (% init. output) government spending (% init. output) output τ (wage tax rate, perc. points) 0.4 percent percent 0.4 0.2 0 −0.2 −0.2 τ (wage tax rate, perc. points) consumption consumption −0.4 2008 2009 2010 2011 2012 2013 2014 2015 year ψτ = 0.03, φ = 0.50: −0.4 2008 2009 2010 2011 2012 2013 2014 2015 year ψτ = 0.03, φ = 0.75: 1 0.6 output output government spending (% init. output) 0.5 0.2 0 τ (wage tax rate, perc. points) consumption percent percent 0.4 government spending (% init. output) consumption 0 τ (wage tax rate, perc. points) −0.2 −0.4 2008 2009 2010 2011 2012 2013 2014 2015 year Harald Uhlig (University of Chicago) −0.5 2008 2009 2010 2011 2012 2013 2014 2015 year Fiscal Stimulus and Distortionary Taxation January 8, 2010 44 / 70 Results Including Rule-of-Thumb Consumers. Short run: φ = 0.75, vary ψτ . ψτ = 0.03 ψτ = 0.10 1 40 output 30 government spending (% init. output) consumption 0 20 percent percent 0.5 τ (wage tax rate, perc. points) 10 τ (wage tax rate, perc. points) government spending (% init. out output 0 −10 −0.5 2008 2009 2010 2011 2012 2013 2014 2015 year Harald Uhlig (University of Chicago) consumption 2008 2009 2010 2011 2012 2013 2014 2015 year Fiscal Stimulus and Distortionary Taxation January 8, 2010 45 / 70 Results A binding zero Lower Bound. Outline 1 Introduction 2 The model 3 The model: Details Equations Parameters 4 Results Comparison to neoclassical growth. No rules-of-thumb, no binding zero lower bound. Including Rule-of-Thumb Consumers. A binding zero Lower Bound. Chemotherapy 5 Conclusions Harald Uhlig (University of Chicago) Fiscal Stimulus and Distortionary Taxation January 8, 2010 46 / 70 Results A binding zero Lower Bound. Zero nominal interest rates Before (and following CCWT): for four quarters, “switch off” Taylor rule and set nominal interest rate to zero instead. SW/CCWT: steady state quarterly nominal interest rate is 1.55% Now: recession per bond-premium-shock q̂tb : Consumers want to save more at any given interest rate (Christiano, Eichenbaum and Rebelo (2009)). Increase half-life of shock to one period (SW: <0.5 periods). Zero lower bound becomes binding with a bond-premium shock of 0.165, implying a (quarterly) change in GDP of -5.46%. Assume shock of 0.20. Harald Uhlig (University of Chicago) Fiscal Stimulus and Distortionary Taxation January 8, 2010 47 / 70 Results A binding zero Lower Bound. Results Extreme scenario. Examine differences between “with” and “without” stimulus. Results are practically the same as before. Erceg-Lindé, 2009. Harald Uhlig (University of Chicago) Fiscal Stimulus and Distortionary Taxation January 8, 2010 48 / 70 Results A binding zero Lower Bound. Without stimulus, ψτ = 0.03. Economic performance: 0 τ (wage tax rate, perc. points) government spending (% init. output) percent −2 −4 output −6 −8 consumption Rates: 0 percentage points (quarterly rate) 2 inflation −0.5 marginal cost implied fed funds −1 −1.5 actual fed funds −2 2007 2008 2009 2010 2011 2012 2013 2014 year Harald Uhlig (University of Chicago) 2005 2006 2007 2008 2009 2010 2011 2012 year Fiscal Stimulus and Distortionary Taxation January 8, 2010 49 / 70 Results A binding zero Lower Bound. With stimulus, ψτ = 0.03. Economic performance: 0 τ (wage tax rate, perc. points) government spending (% init. output) percent −2 −4 output −6 −8 consumption Rates: 0 percentage points (quarterly rate) 2 inflation −0.5 marginal cost implied fed funds −1 −1.5 actual fed funds −2 −10 2007 2008 2009 2010 2011 2012 2013 2014 year Harald Uhlig (University of Chicago) 2005 2006 2007 2008 2009 2010 2011 2012 year Fiscal Stimulus and Distortionary Taxation January 8, 2010 50 / 70 Results A binding zero Lower Bound. Difference between with and without stimulus. 0.8 0.6 percent 0.4 government spending (% init. output) output 0.2 0 τ (wage tax rate, perc. points) −0.2 consumption −0.4 2009 2010 2011 2012 2013 2014 2015 2016 year Harald Uhlig (University of Chicago) Fiscal Stimulus and Distortionary Taxation January 8, 2010 51 / 70 Results A binding zero Lower Bound. SW-DU, Bondpremium-Shock with binding ZLB: Difference, compared to “switching off”. ZLB, ψ = 0.03: “switching off”, ψ = 0.03: 0.6 percent 0.4 0.2 0.8 Stimulus GDP wage tax rate 0 −0.2 Investment Consumption 0.6 0.4 Stimulus GDP τ (wage tax rate, perc. points) 0.2 0 −0.2 2009 2010 2011 2012 2013 2014 2015 2016 year Harald Uhlig (University of Chicago) % of init. output/perc. points 0.8 Investment Consumption 2009 2010 2011 2012 2013 2014 2015 2016 year Fiscal Stimulus and Distortionary Taxation January 8, 2010 52 / 70 Results A binding zero Lower Bound. Rates: Difference between with and without stimulus. 0.1 percent 0.05 0 implied fed funds marginal cost inflation actual fed funds −0.05 −0.1 2009 2010 2011 2012 2013 2014 2015 2016 year Harald Uhlig (University of Chicago) Fiscal Stimulus and Distortionary Taxation January 8, 2010 53 / 70 Results Chemotherapy Outline 1 Introduction 2 The model 3 The model: Details Equations Parameters 4 Results Comparison to neoclassical growth. No rules-of-thumb, no binding zero lower bound. Including Rule-of-Thumb Consumers. A binding zero Lower Bound. Chemotherapy 5 Conclusions Harald Uhlig (University of Chicago) Fiscal Stimulus and Distortionary Taxation January 8, 2010 54 / 70 Results Chemotherapy i = 0 for 0 quarters (ψτ = 0.03). 0.8 0.6 percent 0.4 government spending (% init. output) output 0.2 0 τ (wage tax rate, perc. points) −0.2 consumption −0.4 2009 2010 2011 2012 2013 2014 2015 2016 year Harald Uhlig (University of Chicago) Fiscal Stimulus and Distortionary Taxation January 8, 2010 55 / 70 Results Chemotherapy i = 0 for 4 quarters (ψτ = 0.03). 0.8 0.6 percent 0.4 government spending (% init. output) output 0.2 0 τ (wage tax rate, perc. points) −0.2 consumption −0.4 2009 2010 2011 2012 2013 2014 2015 2016 year Harald Uhlig (University of Chicago) Fiscal Stimulus and Distortionary Taxation January 8, 2010 56 / 70 Results Chemotherapy i = 0 for 8 quarters (ψτ = 0.03). 0.8 output 0.6 government spending (% init. output) percent 0.4 0.2 0 τ (wage tax rate, perc. points) consumption −0.2 −0.4 2009 2010 2011 2012 2013 2014 2015 2016 year Harald Uhlig (University of Chicago) Fiscal Stimulus and Distortionary Taxation January 8, 2010 57 / 70 Results Chemotherapy i = 0 for 12 quarters (ψτ = 0.03). 1.4 output 1.2 1 percent 0.8 0.6 0.4 consumption government spending (% init. output) 0.2 0 −0.2 τ (wage tax rate, perc. points) −0.4 2009 2010 2011 2012 2013 2014 2015 2016 year Harald Uhlig (University of Chicago) Fiscal Stimulus and Distortionary Taxation January 8, 2010 58 / 70 Results Chemotherapy i = 0 for 16 quarters (ψτ = 0.03). 5 output 4 consumption percent 3 2 1 government spending (% init. output) 0 −1 τ (wage tax rate, perc. points) 2009 2010 2011 2012 2013 2014 2015 2016 year Harald Uhlig (University of Chicago) Fiscal Stimulus and Distortionary Taxation January 8, 2010 59 / 70 Results Chemotherapy i = 0 for 20 quarters (ψτ = 0.03). τ (wage tax rate, perc. points) 2 1 government spending (% init. output) 0 percent −1 −2 −3 −4 −5 output consumption −6 2009 2010 2011 2012 2013 2014 2015 2016 year Harald Uhlig (University of Chicago) Fiscal Stimulus and Distortionary Taxation January 8, 2010 60 / 70 Results Chemotherapy i = 0 for 16 quarters (ψτ = 0.03). Long run output 5 4 consumption percent 3 2 1 government spending (% init. output) 0 −1 τ (wage tax rate, perc. points) 2010 Harald Uhlig (University of Chicago) 2015 2020 2025 year 2030 Fiscal Stimulus and Distortionary Taxation 2035 January 8, 2010 61 / 70 Results Chemotherapy i = 0 for 12 quarters (ψτ = 0.03). Long run 1.4 output 1.2 1 percent 0.8 0.6 0.4 consumption government spending (% init. output) 0.2 0 −0.2 τ (wage tax rate, perc. points) −0.4 2010 Harald Uhlig (University of Chicago) 2015 2020 2025 year 2030 Fiscal Stimulus and Distortionary Taxation 2035 January 8, 2010 62 / 70 Results Chemotherapy Comparing binding ZLB, “switching off” with proper ZLB. 12 quarters ZLB, 12 qtrs: 1.4 switching off, 12 qtrs: GDP 1.4 1 percent 0.8 0.6 0.4 Stimulus Consumption 0.2 0 wage tax rate Investment −0.2 2009 2010 2011 2012 2013 2014 2015 2016 year % of init. output/perc. points 1.2 GDP 1.2 1 0.8 0.6 0.4 Stimulus Consumption 0.2 0 τ (wage tax rate, perc. points) Investment −0.2 −0.4 2009 2010 2011 2012 2013 2014 2015 2016 year ( ψτ = 0.03, scaling the interest rate down to 2/3 of actual value in interest rate rule. High persistence, ρb = 0.9. Shocks: 2.38% for 16 qtrs, 2.02% for 12 qtrs, 1.57% for 8 qtrs, 1.43% for 5 qtrs. ) Harald Uhlig (University of Chicago) Fiscal Stimulus and Distortionary Taxation January 8, 2010 63 / 70 Results Chemotherapy Comparing binding ZLB, “switching off” with proper ZLB. 16 quarters ZLB, 16 qtrs: 3 switching off, 16 qtrs: GDP 5 % of init. output/perc. points 2.5 percent 2 1.5 Consumption 1 0.5 Stimulus Investment 0 −0.5 wage tax rate 2009 2010 2011 2012 2013 2014 2015 2016 year GDP 4 3 Consumption 2 1 Stimulus Investment 0 −1 τ (wage tax rate, perc. points) 2009 2010 2011 2012 2013 2014 2015 2016 year ( ψτ = 0.03, scaling the interest rate down to 2/3 of actual value in interest rate rule. High persistence, ρb = 0.9. Shocks: 2.38% for 16 qtrs, 2.02% for 12 qtrs, 1.57% for 8 qtrs, 1.43% for 5 qtrs. ) Harald Uhlig (University of Chicago) Fiscal Stimulus and Distortionary Taxation January 8, 2010 64 / 70 Results Chemotherapy Evaluation What does it take for the ZLB to bind? Disclaimer: based on linear extrapolation of the case of a non-binding ZLB. This is a problem because it neglects the feedback – since the recession is stronger if the ZLB binds, a smaller shock is needed for a given decline in interest rates. Harald Uhlig (University of Chicago) Fiscal Stimulus and Distortionary Taxation January 8, 2010 65 / 70 Results Chemotherapy Necessary initial bond premium shock to make ZLB exactly binding at x quarters Necessary size of bond shock for binding ZLB at x quarters 100 0.3 =0.22 0.1 0.4 80 SW 0.5 0.6 0.7 Shock size (%) ρ 0.8 60 40 20 used values 0.9 0 Harald Uhlig (University of Chicago) 5 10 quarters 15 Fiscal Stimulus and Distortionary Taxation 20 January 8, 2010 66 / 70 Results Chemotherapy With a maximal contraction of 50%, ZLB of x quarters obtains for ... maximum horizon at which ZLB binds if peak GDP contraction < 50% 30 horizon (quarters) 25 20 15 10 SW 5 0 0 Harald Uhlig (University of Chicago) 0.2 0.4 rho 0.6 0.8 Fiscal Stimulus and Distortionary Taxation 1 January 8, 2010 67 / 70 Results Chemotherapy Generating a binding ZLB at x horizons leads to... Peak GDP response if ZLB binds at x quarters 0.9 0.8 0 ρ GDP response (%) −500 =0.22 SW 0.6 0.7 0.3 −1000 −1500 0.40.5 −2000 0.1 −2500 −3000 0 Harald Uhlig (University of Chicago) 5 10 quarters 15 Fiscal Stimulus and Distortionary Taxation 20 January 8, 2010 68 / 70 Conclusions Outline 1 Introduction 2 The model 3 The model: Details Equations Parameters 4 Results Comparison to neoclassical growth. No rules-of-thumb, no binding zero lower bound. Including Rule-of-Thumb Consumers. A binding zero Lower Bound. Chemotherapy 5 Conclusions Harald Uhlig (University of Chicago) Fiscal Stimulus and Distortionary Taxation January 8, 2010 69 / 70 Conclusions Conclusions In the context of this model, the impact of a government spending stimulus ... ... is very sensitive to assumptions about taxes. ... on output is rarely larger than the government spending increase ... is a comparatively larger output loss later on, due to the increased tax burden. Furthermore, Consumption declines. Rules-of-thumb agents do not change the results much. Consumption may be feebly positive, the increase in output is somewhat larger. Binding zero lower bound: does not change the results much, if temporary, and is extreme and fragile, if longer. Therefore: tax considerations and medium-term impacts merit much more attention! Harald Uhlig (University of Chicago) Fiscal Stimulus and Distortionary Taxation January 8, 2010 70 / 70