Optimal fiscal policy Jasper Lukkezen Coen Teulings
Overview Aim Optimal policy rule for fiscal policy How? Four building blocks: 1. Linear VAR model 2. Augmented by linearized equation for debt dynamics 3. Welfare function with non-linearities 4. Discretionary Fiscal Policy measure by IMF (Devries et al., 2011) Properties Our approach is Analytically solvable "Smash the model till mathematics will confess" Empirically grounded Widely applicable (monetary policy?) 2/31
Reduced form model of the economy Reduced-form VAR model model z t+1 = a 0z + A z z t + a z f t + v t+1, Cov [v t+1 ] = V z t : stationary variables describing the economy f t : discretionary policy variable Accounting equation for potentially non-stationary variables d t d t+1 = a 0d + a d z t + d t Stack x t = [ z t d t ] 3/31
Welfare function Optimal policy requires: Objective function: [ ( W t = E t (1 + β) t s 1 y s + θ x t + 1 ) ] s=t 2 x tθx t y t β (h 0 + h x t + 12 ) x thx t y t : pay-off in period t Control variable The policy maker uses f t to maximize W t via x t Non-linearities Θ denotes direct welfare impact, H denotes impact via y t 4/31
Solution Suppose a linear policy rule: Then welfare satisfies f t = b 0 + b x t W(x t, y t ) = w 0 + β 1 y t + w x t + 1 2 x twx t d t explodes for f t = 0, hence f t required to stabilize d t Expressions for the optimal policy rule b 0, b can be derived 5/31
Natural rate The steady state of z t is unaffected by the policy rule for any sustainable policy steady state z t is a function of A, a, a 0, not of the policy rule steady state d t is a function of the policy rule 6/31
Widely applicable z t and d t have not been specified yet Lag length has not been specified Delayed effect of policy possible ( f t impacts x t+2 ) Welfare losses of sub-optimal policy rules can be calculated 7/31
Optimal fiscal policy / the economy VAR model of the economy: z t potential growth unempl constant f t fiscal policy prim surpl/gdp = g t u t s t z t+1 = a 0z + A z z t + a z f t + ν t+1 plus equation for debt dynamics (1 e order Taylor expansion): d t debt/gdp d t+1 = a 0d + a dz z t + d t 8/31
Optimal fiscal policy / welfare Why square root of unempl instead of level? Why potential instead of actual growth? Optimal policy requires non-linearities Welfare Zero lower bound unemployment / capacity constraint Constant determines curvature At high debt levels GDP growth decreases non-linearly (Reinhart and Rogoff, 2010; Checherita-Westphal and Rother, 2012) [ W t = E t (1 + β) (y t s+1 s 1 s=t 2 γu2 s ) ] y t g t 1 2 ψd2 t 1 2 χ u2 t State contingent fiscal multipliers àcambridge la Auerbach University and Gorodnichenko (2011) are introduced via Okun s law 1 χ u 2 9/31
Empirical set-up 1. Set the accounting equation for d t 2. Fix the parameters of the welfare function β, γ, ψ and χ 3. Estimate the VAR for z t 4. Determine the optimal policy rule b 0, b 10/31
Can optimal policy be estimated? Narrative approach distinguishes effects of economy on the budget from effect of budget on the economy No structural modelling, thus: Sims (1980) critique applies: policy likely to be correlated to (un)observed variables Lucas (1976) critique applies: description of the economy (a 0, A and a) might depend on policy rule (b 0, b) But also: Natural rate implies we do not fool all the people all of the time Empirical validity of policy rules CAN be tested 11/31
Data Sources: Annual data for y, u, s and d from the Ameco database Discretionary fiscal policy identified from policy documents Devries et al. (2011) 31 years (1979-2009) 17 developed economies Netherlands, Belgium, Germany, Finland, France, Ireland, Spain, Portugal, Italy, Austria, Sweden, Denmark, Canada, United Kingdom, United States, Australia and Japan Estimation method: Panel VAR model using system GMM All variables forward mean differenced prior to estimation 12/31
Accounting equation and parameters We set: d t+1 = 0.45g t s t + d t We pick: Time preference: β = 0.064 (Cameron and Gerdes, 2005) Welfare loss due to involuntary unemployment: γ = 4.4 Hence 1% of unempl = 2.2% of GDP (Winkelmann and Winkelmann, 1998; Di Tella et al., 2001, 2003) Debt hold-up: ψ = 0.021, Hence 100%-points increase in debt/gdp = -1.0%-points growth (Reinhart and Rogoff, 2010; Checherita-Westphal and Rother, 2012) Okun s law: χ = 2.82 Hence 1% unempl = -1.4% growth (Lee, 2000; Freeman, 2001; Balakrishnan et al., 2010) 13/31
Estimation results g u s L.g 0.577*** -0.411*** 0.361*** L.u 0.082** 1.248*** -0.091*** L.s -0.169** -0.225* 0.746*** L2.g 0.200** -0.011 0.229** L2.u -0.046-0.380*** 0.144*** L2.s 0.123** 0.298*** -0.022 f -0.005-0.735*** -0.178 std 0.015 0.026 0.015 n 402 Standard errors in brackets *** p < 0.01, ** p < 0.05, * p < 0.1 14/31
Estimation results / optimal policy Natural rate: g = 2.4%, u 2 = 8.1% and s = 0.4% Optimal policy rule: f t = 0.68g t + 1.67u t + 0.10s t 0.19d t +0.31g t 1 0.47u t 1 + 0.51s t 1 Positive coefficient on g t explainable from Blanchard and Quah (1989)? g t measures permanent TFP shock u t measures transitory demand shock 15/31
Estimation results / steady state debt d t = 0 maximizes growth, steady state d = 0 In steady state W = 0: short-run benefits of stimulus equal to long-run losses: W f = steady state debt is 16% growth 0.37 unempl. +0.19 Okun s law +0.30 debt 0.74 d 16/31
Alternative policies We evaluate 4 policy rules: Optimal maximizes welfare Delayed idem, but using x t 1 rather than x t Maximize growth disregards the welfare effect of unemployment (γ) Empirical estimated from Devries et al. (2011) 17/31
Growth shock, response of growth 0.005.01.015.02 Optimal.005 0.005.01.015 Optimal, delayed.005 0.005.01.015.02 Maximizing growth.005 0.005.01.015.02 Maximizing growth, delayed.005 0.005.01.015 Empirical
Optimal Growth shock, response of unemployment Optimal, delayed Maximizing growth.006.004.002 0.006.004.002 0.008.006.004.002 0 Maximizing growth, delayed Empirical.01.0050.005.015.01.0050.005
Optimal Growth shock, response of debt Optimal, delayed Maximizing growth.08.06.04.02 0.08.06.04.02 0.08.06.04.02 0 Maximizing growth, delayed Empirical.08.06.04.02 0.08.06.04.02 0
Growth shock, response of discretionary policy Optimal Optimal, delayed Maximizing growth.02.01 0.01.02.01 0.01.02.02.01 0.01.02.03 Maximizing growth, delayed Empirical.02.01 0.01.02.03.002 0.004.006
Unemployment shock, response of growth.02.01 0.01.02.03 Optimal.02 0.02.04 Optimal, delayed.02.01 0.01.02.03 Maximizing growth.02 0.02.04 Maximizing growth, delayed.02.01 0.01.02 Empirical
Unemployment shock, response of unemployment Optimal Optimal, delayed Maximizing growth 0.005.01.015 0.005.01.015.02 0.005.01.015 Maximizing growth, delayed Empirical 0.005.01.015.02.01 0.01.02.03
Optimal Unemployment shock, response of debt Optimal, delayed Maximizing growth 0.01.02.03.04.010.01.02.03.010.01.02.03 Maximizing growth, delayed Empirical.010.01.02.03.15.1.05 0.05
.02 0.02.04.06 Unemployment shock, response of discretionary policy Optimal Optimal, delayed Maximizing growth.04.02 0.02.04.06.02.02.04 0.06 Maximizing growth, delayed Empirical.04.02 0.02.04.06.0050.005
Comparing policy rules Optimal responses pro-cyclical to growth shocks anti-cyclical to unemployment shocks Maximizing growth reacts stronger to growth and debt Delayed policy reacts weaker than optimal policy Effect optimal policy after unemployment shock: recovering half of the shock costs 2 instead of 5 years 26/31
Welfare implications Welfare losses are given in log output times β = 6.4% Welfare losses compared to optimal policy depend on the debt level Welfare losses compared to optimal policy of: using maximizing growth are small: 2.2% to 4.5% using delayed information are smaller: 0.4% to 0.6% using the empirical policy rule are substantial: 3.2% to 5.6% 27/31
Robustness For higher β: Policy rule less activist, unemployment dominates Steady state debt higher Welfare differences with delayed and empirical reduce, with maximizing growth increase For lower ψ: Policy response to debt decreases Steady state debt levels move away from 0 Welfare differences with delayed and empirical reduce, with maximizing growth increase 28/31
Summary A general approach optimal policy with a VAR We apply it on optimal fiscal policy: We find: 3-variable VAR-model with 1 fiscal policy variable and debt accumulation equation Intertemporal welfare function in output and unemployment Empirical evidence for our set-up using a panel VAR model We provide: Prescription for optimal fiscal policy Show the welfare losses of applying suboptimal policy rules 29/31
Discussion Given our model, how should fiscal policy have responded to the crisis? What is discretionary fiscal policy? 30/31
Thank you for your attention! 31/31
Bibliography I Auerbach, A. J. and Gorodnichenko, Y. (2011). Fiscal Multipliers in Recession and Expansion, NBER Working Papers 17447, National Bureau of Economic Research. Balakrishnan, R., Das, M. and Kannan, P. (2010). Unemployment Dynamics during Recessions and Recoveries: Okun s Law and Beyond, IMF World Economic Outlook, 2010 edn, International Monetary Fund, chapter 3. Blanchard, O. J. and Quah, D. (1989). The Dynamic Effects of Aggregate Demand and Supply Disturbances, American Economic Review 79(4): pp. 655 673. 32/31
Bibliography II Cameron, T. A. and Gerdes, G. R. (2005). Individual Subjective Discounting: Form, Context, Format, and Noise. University of Oregon mimeo. Checherita-Westphal, C. and Rother, P. (2012). The Impact of High Government Debt on Economic Growth and its Channels: An Empirical Investigation for the Euro Area, European Economic Review 56(7): 1392 1405. Devries, P., Guajardo, J., Leigh, D. and Pescatori, A. (2011). A New Action-based Dataset of Fiscal Consolidation, IMF working paper 11/128, International Monetary Fund. 33/31
Bibliography III Di Tella, R., MacCulloch, R. J. and Oswald, A. J. (2001). Preferences over Inflation and Unemployment: Evidence from Surveys of Happiness, American Economic Review 91(1): 335 341. Di Tella, R., MacCulloch, R. J. and Oswald, A. J. (2003). The Macroeconomics of Happiness, The Review of Economics and Statistics 85(4): 809 827. Freeman, D. G. (2001). Panel Tests of Okun s Law for Ten Industrial Countries, Economic Inquiry 39(4): 511 523. Lee, J. (2000). The Robustness of Okun s law: Evidence from OECD countries, Journal of Macroeconomics 22(2): 331 356. 34/31
Bibliography IV Lucas, R. J. (1976). Econometric Policy Evaluation: A Critique, Carnegie-Rochester Conference Series on Public Policy 1(1): 19 46. Reinhart, C. M. and Rogoff, K. S. (2010). Growth in a Time of Debt, NBER Working Paper 15639, National Bureau of Economic Research. Sims, C. A. (1980). Macroeconomics and Reality, Econometrica 48(1): pp. 1 48. Winkelmann, L. and Winkelmann, R. (1998). Why Are the Unemployed So Unhappy? Evidence from Panel Data, Economica 65(257): 1 15. 35/31