Learning about Fiscal Policy and the Effects of Policy Uncertainty

Transcription

1 Learning about Fiscal Policy and the Effects of Policy Uncertainty Josef Hollmayr and Christian Matthes Deutsche Bundesbank and Richmond Fed

2 What is this paper about? What are the effects of subjective uncertainty about fiscal policy on economic outcomes? To have something to say about this in a general equilibrium setting, we have to take a stand on how to model uncertainty

3 Approach we set up a simple real business cycle model with a rich fiscal sector (similar to Leeper et al.(2))

4 Approach we set up a simple real business cycle model with a rich fiscal sector (similar to Leeper et al.(2)) Agents learn about fiscal policy rule coefficients

5 Approach we set up a simple real business cycle model with a rich fiscal sector (similar to Leeper et al.(2)) Agents learn about fiscal policy rule coefficients - This governs the evolution of policy uncertainty in our model

6 Approach we set up a simple real business cycle model with a rich fiscal sector (similar to Leeper et al.(2)) Agents learn about fiscal policy rule coefficients - This governs the evolution of policy uncertainty in our model Simulate a crisis and how fiscal policy makers may react to it Does learning matter for outcomes?

7 Approach we set up a simple real business cycle model with a rich fiscal sector (similar to Leeper et al.(2)) Agents learn about fiscal policy rule coefficients - This governs the evolution of policy uncertainty in our model Simulate a crisis and how fiscal policy makers may react to it Does learning matter for outcomes? In other words: are previous results in the literature robust to the specification of expectation formation?

8 What to take away Learning matters!

9 What to take away Learning matters! - Outcomes of key macro variables (GDP, consumption and capital etc.) can be several percentage points lower for substantial periods of under learning Very robust trade-off between either lower outcomes or higher business cycle volatility

10 Related Papers Strand of learning Literature Giannitsarou (26) Eusepi and Preston - multiple papers 2 Uncertainty in the economy Bloom et al. (22) Born and Pfeifer (2) Fernandez-Villaverde, Guerron, Kuester and Rubio-Ramirez (22)

11 Model Learning Algorithm Households Each period, households maximize the infinite sum of discounted utility with the period utility function: subject to the budget constraint: U t = C t σ σ L+φ t + φ () C t( + τt C ) + B t + I t = W tl t( τt L ) + ( τt K )Rt K K t + R t B t + Z t (2) and the law of motion for capital: K t = ( δ)k t + I t (3) and subject to their beliefs about fiscal policy (their perceived policy rule)

12 Model Learning Algorithm Firms The production function follows the standard Cobb-Douglas type: Y t = A t K α t L α t (4) with the exogenous process for technology given by: A t = ρ a A t + ɛ A t (5)

13 Model Learning Algorithm Fiscal Sector The government is allowed to run deficits over. The corresponding budget constraint is then given by: B t = B t R t R K t K tτ K t W tl tτ L t C tτ C t + G t + Z t (6)

14 Model Learning Algorithm Fiscal Sector The government is allowed to run deficits over. The corresponding budget constraint is then given by: B t = B t R t R K t K tτ K t W tl tτ L t C tτ C t + G t + Z t (6) The fiscal rules follow Leeper et al. (2) - except for timing: Government Expenditure: Transfers: log(g t) = G c ρ g,y log(y t ) ρ g,b log(b t ) + ɛ G t (7) log(z t) = Z c ρ z,y log(y t ) ρ z,b log(b t ) + ɛ Z t, (8)

15 Model Learning Algorithm Fiscal Sector The government is allowed to run deficits over. The corresponding budget constraint is then given by: B t = B t R t R K t K tτ K t W tl tτ L t C tτ C t + G t + Z t (6) The fiscal rules follow Leeper et al. (2) - except for timing: Government Expenditure: Transfers: log(g t) = G c ρ g,y log(y t ) ρ g,b log(b t ) + ɛ G t (7) log(z t) = Z c ρ z,y log(y t ) ρ z,b log(b t ) + ɛ Z t, (8) Consumption Tax Rate Rule: Other Tax Rate Rules: log(τ C t ) = τ c c + ɛ C t (9) log(τ i t ) = τ i c + ρ i,y log(y t ) + ρ i,b log(b t ) + ɛ i t () with i=l,k

16 Model Learning Algorithm Calibration of Parameters Description Parameter Value impatience β.99 Capital share α.33 Depreciation rate δ.25 CES utility Consumption σ 2 CES utility labor φ 2 coeff. on Y in gov. exp. rule ρg,y.34 coeff. on B in gov. exp. rule ρ g,b.23 coeff. on Y in transfer rule ρz,y.3 coeff. on B in transfer rule ρ z,b.5 coeff. on Y labor tax rule ρ L,y.36 coeff. on B labor tax rule ρ L,b.49 coeff. on Y capital tax rule ρ K,y.7 coeff. on B capital tax rule ρ K,b.39 AR parameter technology ρa.9 Std.deviation technology σa.62 Std.deviation gov. spending σg.3 Std.deviation transfers σz.34 Std.deviation cons.tax σc.4 Std.deviation labor tax σ l.3 Std.deviation capital tax σ k.44 Table : Calibrated Parameters of the model Calibrated parameters of the real economy in line with the literature on US economy. The fiscal parameters are taken from the estimation of Leeper et al. (2).

17 Model Learning Algorithm What do agents know and what do they learn about? Agents know the structure of the economy - this includes the variables entering the fiscal policy rules

18 Model Learning Algorithm What do agents know and what do they learn about? Agents know the structure of the economy - this includes the variables entering the fiscal policy rules The only thing private agents do not know is the vector of coefficients in the fiscal policy rules

19 Model Learning Algorithm Estimation some notation: Ω t represents the vector of coefficients of all fiscal policy rules and τ t the vector of fiscal policy instrument at t firms and households learn via the Kalman filter the state space system is given by: τ t = X t Ω t + η t () Ω t = Ω t + t ν t (2) We assume agents know the volatility of the innovations in the policy rules

20 Model Learning Algorithm What happens under learning? - An illustration Let s focus on one policy rule for simplicity: log(g t ) = G c ρ g,y log(y t ) ρ g,b log(b t ) + ɛ G t

21 Model Learning Algorithm What happens under learning? - An illustration Let s focus on one policy rule for simplicity: log(g t ) = G c ρ g,y log(y t ) ρ g,b log(b t ) + ɛ G t This is the true policy rule

22 Model Learning Algorithm What happens under learning? - An illustration Let s focus on one policy rule for simplicity: log(g t ) = G c ρ g,y log(y t ) ρ g,b log(b t ) + ɛ G t This is the true policy rule agents are going to estimate the coefficients. their perceived policy rule is given by: log(g t ) = G c,t ρ g,y,t log(y t ) ρ g,b,t log(b t ) + ɛ G t

23 Model Learning Algorithm What happens under learning? - An illustration Let s focus on one policy rule for simplicity: log(g t ) = G c ρ g,y log(y t ) ρ g,b log(b t ) + ɛ G t This is the true policy rule agents are going to estimate the coefficients. their perceived policy rule is given by: log(g t ) = G c,t ρ g,y,t log(y t ) ρ g,b,t log(b t ) + ɛ G t note the form of the perceived policy shock ɛ G t : ɛ G t = ɛ G t +G c G ct (ρ g,y ρ g,y,t ) log(y t ) (ρ g,b ρ g,b,t ) log(b t )

24 Model Learning Algorithm Within-period timing Private agents enter period t with beliefs (or point estimate) Ω t, which is the posterior mean coming out of the Kalman filter. They treat estimated parameters as if they were known with certainty and formulate plans accordingly (Kreps 998 calls this anticipated utility ). The fiscal authority sets the systematic part of policy at the beginning of the period. Then shocks are realized, and agents observe the technology shock and the perceived fiscal policy rule shocks. Outcomes are determined in accordance with beginning-of-period plans. After observing outcomes, private agents update estimates and carry them forward to t +.

25 Model Learning Algorithm Perceived Equilibrium Dynamics - How the economy evolves according to private agents A(Ω t )Y t = B(Ω t )E t Y t+ + C(Ω t )Y t + Dε t log-linearized around perceived steady state Conditional on beliefs, this equation can be solved using standard algorithms (e.g. Gensys) Y t = S(Ω t )Y t + G(Ω t )ε t

26 Model Learning Algorithm Solving for actual equilibrium dynamics Some more notation: we modify C(Ω t ) to now include the true policy coefficients. We call this matrix C true (Ω t ) A(Ω t )Y t = B(Ω t )E t Y t+ + C true (Ω t )Y t + Dε t Y t = H(Ω t )Y t + G(Ω t )ε t H(Ω t ) = S(Ω t ) + (A(Ω t ) B(Ω t )S(Ω t )) (C true (Ω t ) C(Ω t ))

27 Simulations Outline of Setup of our experiments Effects of Learning/Uncertainty vs. RE benchmark What would be the effects of different fiscal measures? Do results hold under different specifications?

28 Simulations Setup of the Computational Experiment We start off our simulations at the original steady state In period 9, there is a negative technology shock that puts technology 5% below steady state The following period the government permanently increases government spending by % of initial steady state GDP (unanticipated) The government does so by changing the intercept in the policy rule for government spending policy change represents a 2 standard deviation shock according to agents views

29 Simulations Rational Expectations - Outcomes GDP Cap. Tax Capital Gov. Spending Consumption Labor Debt Transfers Cons. Tax Investment Labor Tax x 3 Interest Rate

30 Simulations Learning - Outcomes: Benchmark Cons. GDP 5 Hours Investment Captax Debt 5 Capital Gov.Spending 2 LE std / RE std, log C.5 LE std / RE std, log GDP LE std / RE std, log debt.2.5 LE std / RE std, log capital G c ρ gy ρ gb Median.34 Upper Lower Actual

31 Simulations A Partial Explanation perceived SS median learning original SS new SS

32 Simulations Learning - Outcomes: Standard Dev Cons. GDP Hours Investment Captax 2 Debt Capital Gov.Spending 2 LE std / RE std, log C.5 5 LE std / RE std, log GDP LE std / RE std, log debt LE std / RE std, log capital G c ρ gy ρ gb Median Upper Lower Actual

33 Simulations Learning - Outcomes: 3 Standard Dev Cons. GDP 5 Hours Investment Captax Debt 5 Capital Gov.Spending 4 LE std / RE std, log C.2 LE std / RE std, log GDP LE std / RE std, log debt LE std / RE std, log capital G c ρ gy ρ gb Median Upper Lower.8 5 Actual

34 Simulations Including Irrelevant Regressors Cons. GDP 5 Hours Investment Captax Debt 5 Capital Gov.Spending 4 LE std / RE std, log C.5 LE std / RE std, log GDP LE std / RE std, log debt.2.2 LE std / RE std, log capital G c ρ gy ρ gb Median Upper Lower Actual

35 Simulations The Case Of No Policy Changes Cons. GDP Hours Investment Captax Debt Capital Gov.Spending.5.5 LE std / RE std, log C.5 LE std / RE std, log GDP LE std / RE std, log debt.2..5 LE std / RE std, log capital G c ρ gy ρ gb Median Upper.34 Lower Actual

36 Simulations Concluding Thoughts Changes in fiscal policy are not as effective under learning as under rational expectations

37 Simulations Concluding Thoughts Changes in fiscal policy are not as effective under learning as under rational expectations 2 Differences can be substantial: either large average differences or increased volatility

38 Simulations Concluding Thoughts Changes in fiscal policy are not as effective under learning as under rational expectations 2 Differences can be substantial: either large average differences or increased volatility 3 robust across a large variety of simulation exercises

39 Different Utility Functions Cons. GDP Hours Investment 2 Captax 5 Debt Capital Gov.Spending 2 LE std / RE std, log C 2 5 LE std / RE std, log GDP LE std / RE std, log debt LE std / RE std, log capital G c ρ gy ρ gb Median Upper.4.2 Lower Actual

40 Different Utility Function II Cons. GDP 2 Hours Investment Captax 2 Debt Capital Gov.Spending LE std / RE std, log C LE std / RE std, log GDP LE std / RE std, log debt LE std / RE std, log capital G c ρ gy ρ gb Median Upper Lower Actual 5 5

41 Learning only about G Cons. GDP 5 Hours Investment Captax Debt 5 Capital Gov.Spending 4 LE std / RE std, log C LE std / RE std, log GDP LE std / RE std, log debt LE std / RE std, log capital G c ρ gy ρ gb Median Upper Lower Actual

42 Capital Tax Decrease Suppose now that capital tax respond by a % (of GDP) decrease 5 2 Cons. GDP Hours Investment Captax Debt Capital Gov.Spending LE std / RE std, log C LE std / RE std, log GDP LE std / RE std, log debt LE std / RE std, log capital Tax kc ρ ky ρ kb Median Upper Lower Actual