Tax Smoothing, Learning and Debt Volatility

Transcription

1 Tax Smoothing, Learning and Debt Volatility Francesco Caprioli 1 1 Universitat Pompeu Fabra Conference - November 2008 Caprioli (UPF) Tax Smoothing, Learning and Debt Volatility Conference / 42

2 The question Motivation A key question in fiscal policy is: How to finance government expenditures when taxes are distortionary? Lucas and Stokey (1983) provide an answer Assuming 1. complete markets 2. agents know the tax rule followed by the government then 1. taxes are smooth 2. state-contingent bonds act as an insurance device Caprioli (UPF) Tax Smoothing, Learning and Debt Volatility Conference / 42

3 Motivation Positive issue with Lucas and Stokey Are Lucas and Stokey s implications in line with the data? No L-S Model Data T axratecorrelation Gov.exp.correlation 1 >> 1 Tax rate volatility 0 > 0 Fiscal deficit in "good" times no yes Caprioli (UPF) Tax Smoothing, Learning and Debt Volatility Conference / 42

4 This paper Motivation I assume 1. complete markets 2. agents LEARN the tax rule followed by the government and I get L-S Model This paper data T axratecorrelation Gov.exp.correlation 1 >> 1 >> 1 Tax rate volatility 0 >0 >0 Fiscal deficit in "good times" no yes yes Caprioli (UPF) Tax Smoothing, Learning and Debt Volatility Conference / 42

5 Motivation Normative issue with Lucas and Stokey Does the Lucas and Stokey debt management recipe perform well when agents are boundedly rational? When expenditure shock is correlated, the state-contingent bond rule can induce sizable welfare cost Large bond positions magnify distorted expectations Agents form model-consistent expectations after a very long time (500 years) Caprioli (UPF) Tax Smoothing, Learning and Debt Volatility Conference / 42

6 The economy This paper Production economy with no capital The production function is linear in labour (wage=1) Government expenditure shock Caprioli (UPF) Tax Smoothing, Learning and Debt Volatility Conference / 42

7 Households This paper Optimal behaviour depends on expectations about next period consumption They know 1. the stochastic properties of the government expenditure process 2. the relation between consumption and tax rate They do not know the tax rule followed by the government They use past consumption to forecast future consumption Caprioli (UPF) Tax Smoothing, Learning and Debt Volatility Conference / 42

8 The government This paper It has full knowledge of the model It is benevolent It has a commitment technology It pursues an optimal taxation approach Caprioli (UPF) Tax Smoothing, Learning and Debt Volatility Conference / 42

9 Normative result Results Learning introduces an additional distortion: households expectations The government chooses the fiscal plan to minimise the costs associated to both distortions Active use of fiscal policy to correct distorted expectations Specifically, the optimal fiscal plan is to 1. Lower taxes when agents are pessimistic 2. Increase taxes when they are optimistic Caprioli (UPF) Tax Smoothing, Learning and Debt Volatility Conference / 42

10 Related Literature Optimal fiscal policy incomplete markets (Aiyagari et al. (2002)) Learning and fiscal policy rules (Evans Honkapohja (2003)) Robust optimal fiscal policy (Karantounias, Hansen, Sargent (2007)) Caprioli (UPF) Tax Smoothing, Learning and Debt VolatilityConference / 42

11 Outline Review of Lucas and Stokey (1983) model My model with boundedly rational agents Results Additional implications Conclusions Caprioli (UPF) Tax Smoothing, Learning and Debt VolatilityConference / 42

12 Review of Lucas and Stokey (1983) model The agent problem The representative agent has to s.t. max E 0 β t u(c t, l t ) {c t,l t,b t(g t+1 g t )} t=0 t=0 b t 1 (g t ) = c t (1 τ t )(1 l t ) + The optimality conditions are u l,t u c,t = 1 τ t g t+1 g t p b t(g t+1 g t )b t (g t+1 g t ) p b t(g t+1 g t ) = β u c,t+1(g t+1 g t ) u c,t π(g t+1 g t ) Caprioli (UPF) Tax Smoothing, Learning and Debt VolatilityConference / 42

13 Review of Lucas and Stokey (1983) model The government problem The government has to s.t. 1. Resource constraint 2. Implementability condition max E 0 β t u(c t, l t ) {c t,l t} t=0 t=0 c t + g t = 1 l t E 0 β t (u c,t c t u l,t (1 l t )) = b 1 u c,0 t=0 Caprioli (UPF) Tax Smoothing, Learning and Debt VolatilityConference / 42

14 Review of Lucas and Stokey (1983) model The solution under rational expectations The Lucas and Stokey model has the following features 1. The endogenous variables are time invariant functions of the current period government expenditure shock 2. The tax rate has the same stochastic properties of the government expenditure shock 3. The present does not depend on the past (no history dependence) Caprioli (UPF) Tax Smoothing, Learning and Debt VolatilityConference / 42

15 My model with boundedly rational agents Learning: the agent problem The representative agent has to s.t. max Ẽ 0 β t u(c t, l t ) {c t,l t,b t(g t+1 g t )} t=0 t=0 b t 1 (g t ) = c t (1 τ t )(1 l t ) + The optimality conditions are u l,t u c,t = 1 τ t g t+1 g t p b t(g t+1 g t )b t (g t+1 g t ) p b t(g t+1 g t ) = β ũc,t+1(g t+1 g t ) u c,t π(g t+1 g t ) Caprioli (UPF) Tax Smoothing, Learning and Debt VolatilityConference / 42

16 My model with boundedly rational agents Learning: the fiscal ignorance by agents u c,t+1 (g t+1 ) = 2 τ t+1 (1 τ t+1 )(1 g t+1 ) At t, fully rational agents know that τ t+1 = τ(g t+1 ). Hence E t u c,t+1 (g t+1 ) = 2 τ(g t+1 ) (1 τ(g t+1 ))(1 g t+1 ) Boundedly rational agents do not know the tax rate rule. Hence Ẽ t u c,t+1 (g t+1 ) = 2 Ẽtτ t+1 (1 Ẽtτ t+1 )(1 g t+1 ) If Ẽtτ t+1 > τ(g) agents are pessimistic, and viceversa Caprioli (UPF) Tax Smoothing, Learning and Debt VolatilityConference / 42

17 My model with boundedly rational agents Learning: expectations updating rule The government expenditure shock follows a 2-state Markov process As markets are complete, agents need to forecast their own marginal utility of consumption when the shock tomorrow is low and when it is high As they forecast state-contingent objects, they use state-contingent information Their forecast of marginal utility of consumption when the shock tomorrow is high (low) depends on all past marginal utilities of consumption when the shock has been high (low) Caprioli (UPF) Tax Smoothing, Learning and Debt VolatilityConference / 42

18 My model with boundedly rational agents Why this learning rule? This learning scheme has two nice properties 1. In the long-run agents form model-consistent expectations 2. In the short-run forecast errors are bounded π ɛ,t P ( 1 T T [u c,t Ẽt 1u c,t ] 2 < 1 T t=0 T [u c,t E t 1 u c,t ] 2 + ɛ) > 1 δ t=0 T \ɛ Caprioli (UPF) Tax Smoothing, Learning and Debt VolatilityConference / 42

19 My model with boundedly rational agents The government problem under learning The government has to s.t. 1. Resource constraint max E 0 β t u(c t, l t ) {c t,l t} t=0 t=0 c t + g t = 1 l t 2. Expectations formation mechanism { ũc,t (g ũ c,t+1 (g i ) i ) + α t (u c,t (g i ) ũ c,t (g i )), if g t = g i ũ c,t (g i ). if g t = g j 3. Implementability condition E 0 β t A t (u c,t c t u l,t (1 l t )) = b 1 u c,0 t=0 Caprioli (UPF) Tax Smoothing, Learning and Debt VolatilityConference / 42

20 My model with boundedly rational agents The distortion associated to households beliefs log(a t ) = log(a t 1 ) + log(ũ c,t ) log(u c,t ) (The log of) A t is the sum of all past forecast errors made by agents The higher the initial pessimism the higher A t the lower the interest rate on government debt the lower the taxation distortion (lower government expenditure in Lucas and Stokey) Caprioli (UPF) Tax Smoothing, Learning and Debt VolatilityConference / 42

21 My model with boundedly rational agents The solution under learning The model has the following features The endogenous variables are time invariant functions of 1. current period government expenditure shock 2. previous period expectations about marginal utility of consumption 3. sum of all past forecast errors The tax rate is a decreasing function of previous period expectations about marginal utility of consumption The present depends on the past (history dependence) Caprioli (UPF) Tax Smoothing, Learning and Debt VolatilityConference / 42

22 My model with boundedly rational agents The solution under learning The model has the following features The endogenous variables are time invariant functions of 1. current period government expenditure shock 2. previous period expectations about marginal utility of consumption 3. sum of all past forecast errors The tax rate is a decreasing function of previous period expectations about marginal utility of consumption Intuition: the higher Ẽt 1τ t, the lower τ t to drive expectations in the "right" direction The present depends on the past (history dependence) Caprioli (UPF) Tax Smoothing, Learning and Debt VolatilityConference / 42

23 Examples First example: Constant government expenditure I show that 1. Optimal fiscal policy under rational expectations and learning differ substantially 2. Under learning taxes are more volatile than under rational expectations Caprioli (UPF) Tax Smoothing, Learning and Debt VolatilityConference / 42

24 Optimal allocation Examples 0.41 rational agents Consumption pessimistic agents years Leisure years Caprioli (UPF) Tax Smoothing, Learning and Debt VolatilityConference / 42

25 Fiscal Variables Examples Tax rate Primary Surplus Government Debt rational agents pessimistic agents years Caprioli (UPF) Tax Smoothing, Learning and Debt VolatilityConference / 42

26 Examples Initial beliefs and limiting bond holdings Limiting bond holdings Rational expectation equilibrium 0.5 Optimistic agents Pessimistic agents Initial beliefs over marginal utility of consumption Caprioli (UPF) Tax Smoothing, Learning and Debt VolatilityConference / 42

27 Examples Second example: War I show that 0.1 t < 10 g t = 0.2 t = t > Optimal fiscal policy under rational expectations and learning differ substantially 2. Under learning the government runs a primary deficit during good times Caprioli (UPF) Tax Smoothing, Learning and Debt VolatilityConference / 42

28 Optimal Allocation Examples rational agents Consumption pessimistic agents Leisure years Caprioli (UPF) Tax Smoothing, Learning and Debt VolatilityConference / 42

29 Fiscal Variables Examples tax rate rational agents pessimistic agents primary surplus years Caprioli (UPF) Tax Smoothing, Learning and Debt VolatilityConference / 42

30 Examples Third example: Serially correlated government expenditure shock ( ) πl,l π P = L,H I show that π H,L π H,H 1. Optimal fiscal policy under rational expectations and learning differ substantially 2. Under learning fiscal variables are very persistent Implications for tests on fiscal policy issues (market completeness and debt sustainability) Caprioli (UPF) Tax Smoothing, Learning and Debt VolatilityConference / 42

31 Examples Statistics before convergence of beliefs R.E. Pess. agents Mean St.Dev. Autocorr Mean St.Dev. Autocorr consumption leisure labor tax rate market value of debt primary surplus Caprioli (UPF) Tax Smoothing, Learning and Debt VolatilityConference / 42

32 Additional implications Complete vs. incomplete markets: Persistence tests Scott (2007), Marcet and Scott (2007), Faraglia, Marcet and Scott (2006) Two ways of testing complete vs. incomplete markets 1. Persistence tests 2. Impact tests Complete markets Incomplete markets near unit root tax rate no yes cost of distortionary taxes constant over time time-varying persistenceofgovernmentdebt persistenceofprimarysurplus 1 >> 1 Persistence tests mix evidence of learning with evidence of market incompleteness Caprioli (UPF) Tax Smoothing, Learning and Debt VolatilityConference / 42

33 Additional implications Complete vs. incomplete markets: impact test H 0 :Bond markets are incomplete 1. Unit Root in the tax rate Type II error= Unit Root in the cost of distortionary taxes Type II error= Relative Persistence of primary surplus/gdp and market value of government debt/gdp test Caprioli (UPF) Tax Smoothing, Learning and Debt VolatilityConference / 42

34 Additional implications Complete vs. incomplete markets: impact test H 0 :Bond markets are incomplete 1. Unit Root in the tax rate Type II error= Unit Root in the cost of distortionary taxes Type II error= Relative Persistence of primary surplus/gdp and market value of government debt/gdp test Caprioli (UPF) Tax Smoothing, Learning and Debt VolatilityConference / 42

35 Additional implications Complete vs. incomplete markets: impact test H 0 :Bond markets are incomplete 1. Unit Root in the tax rate Type II error= Unit Root in the cost of distortionary taxes Type II error= Relative Persistence of primary surplus/gdp and market value of government debt/gdp test Caprioli (UPF) Tax Smoothing, Learning and Debt VolatilityConference / 42

36 Additional implications Testing complete vs. incomplete markets Impact test Complete markets Incomplete markets co-movement deficit debt <0 >0 Intuition: complete markets "over-insure" against government expenditure shock H 0 :Bond markets are incomplete Correlation between deficit and government debt gives the right answer!!! Caprioli (UPF) Tax Smoothing, Learning and Debt VolatilityConference / 42

37 Back to Keynes? Keynesian stimulus? Not always A "counter-sentimental" fiscal policy helps stabilising expectations Nevertheless, in many developing countries fiscal policy is procyclical (Alesina at. al. (2007), Ilzetzki and Vegh (2008), Gavin and Perotti (1997)) Positive correlation between optimism and growth rate of the economy What is the effect of an expansionary fiscal policy when a restrictive one is required? Caprioli (UPF) Tax Smoothing, Learning and Debt VolatilityConference / 42

38 Back to Keynes? Keynesian stimulus? Not always Suppose the economy faces "good" shocks and agents are optimistic However, the government wants to stimulate the economy setting low taxes where χ t = 0.7 t T { τ pess τ t = t, t T χ t τ pess t + (1 χ t )τt bb. t > T Caprioli (UPF) Tax Smoothing, Learning and Debt VolatilityConference / 42

39 Back to Keynes? Keynesian stimulus? Not always consumption leisure years years forecast error optimal fiscal policy when agents are optimistic wrong stimulus years Caprioli (UPF) Tax Smoothing, Learning and Debt VolatilityConference / 42

40 Future Research Conclusions Quantitative analysis of the model Policymakers may have a misspecified model (Sargent (2001), Orphanides and Williams (2003), Primiceri (2005), Cogley and Sargent (2005)) Governments alternate in power Caprioli (UPF) Tax Smoothing, Learning and Debt VolatilityConference / 42

41 For notational convenience Ẽ t u c,t+1 ũ c,t+1 { ũc,t (g ũ c,t+1 (g H ) = H ) + α t (u c,t (g H ) ũ c,t (g H )), if g t = g H ũ c,t (g H ). if g t = g L Return { ũc,t (g ũ c,t+1 (g L ) = L ) + α t (u c,t (g L ) ũ c,t (g L )), if g t = g L ũ c,t (g L ). if g t = g H Caprioli (UPF) Tax Smoothing, Learning and Debt VolatilityConference / 42

42 L-S Model This paper data T axratecorrelation Gov.exp.correlation 1 >> 1 >> 1 Tax rate volatility 0 >0 >0 Fiscal deficit in "good times" no yes yes Return1 Caprioli (UPF) Tax Smoothing, Learning and Debt VolatilityConference / 42

43 L-S Model This paper data T axratecorrelation Gov.exp.correlation 1 >> 1 >> 1 Tax rate volatility 0 >0 >0 Fiscal deficit in "good times" no yes yes Return2 Caprioli (UPF) Tax Smoothing, Learning and Debt VolatilityConference / 42

44 L-S Model This paper data T axratecorrelation Gov.exp.correlation 1 >> 1 >> 1 Tax rate volatility 0 >0 >0 Fiscal deficit in "good times" no yes yes Return Caprioli (UPF) Tax Smoothing, Learning and Debt VolatilityConference / 42

45 Persistence under RE Persistence of debt/gdp Persistence of primary surplus/gdp Persistence of government expenditure k Persistence under learning k Persistence of debt/gdp Persistence of primary surplus/gdp Persistence of government expenditure Return Caprioli (UPF) Tax Smoothing, Learning and Debt VolatilityConference / 42