## _wp10243

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---

### Introduction — key findings and setup
- Model features and purpose:
  - Estimates a New Keynesian model that accounts for monetary and fiscal policy interactions with Bayesian methods and explicitly includes government debt and fiscal financing to allow for PMAF regimes.
- Policy regime definitions:
  - AMPF: active monetary and passive fiscal policy regime (in Leeper (1991) sense).
  - PMAF: passive monetary and active fiscal policy regime.
- Samples and estimation designs:
  - Samples: 1955Q1-1966Q4, 1967Q1-1979Q2, 1984Q1-2007Q4.
  - Three specifications:
    - P1: prior centered at AMPF but allows both regimes.
    - P2: prior centered at PMAF but allows both regimes.
    - P3: imposes PMAF by not allowing fiscal instruments to respond to debt growth.
- Posterior and model comparison summary:
  - Except when PMAF is imposed (P3), posterior distributions fall in AMPF parameter space regardless of prior.
  - Model comparisons: data least prefer the specification with PMAF imposed.

### Literature and identification challenge
- Prior findings and contrasts:
  - Many studies estimate the inflation coefficient in a Taylor rule as smaller than one (examples: Judd and Rudebusch (1998), Taylor (1999b), Cogley and Sargent (2005), Boivin (2006)).
  - New Keynesian models with passive monetary rules imply indeterminacy for pre-Volcker period (Clarida et al. (2000), Lubik and Schorfheide (2004), Boivin and Giannoni (2006)).
  - Regime-switching work finds monetary policy passive at times in pre-Volcker era (Davig and Leeper (2006), Davig and Doh (2009), Bianchi (2010)).
- Identification difficulty:
  - Many monetary–fiscal combinations can generate the same stochastic processes for observables (Sims (2008)).

### Contribution and main findings
- Estimation strategy:
  - Estimates DSGE model with fixed policy rules that yield AMPF or PMAF depending on parameter values; fixed rules impose identification restrictions.
- Primary empirical result:
  - "The PMAF regime is never favored by the data due to the high volatility the fixed PMAF regime implies for certain observables, particularly hours worked and inflation."
  - Standard New Keynesian model cannot match data features if a fixed PMAF regime is assumed.
- Additional findings:
  - Structural innovations differ substantially between pre- and post-Volcker periods.
  - Contrary to some VAR-based conclusions, no reduction in monetary policy effects on output is found in the post-Volcker period.

### Model structure and solution summary
- Core model elements (preserved terminology and equations summarized):
  - Final goods aggregator: [∫_0^1 y_t(i)^{1/(1+η_p_t)} di]^{1+η_p_t} ≥ Y_t, with η_p_t time-varying markup.
  - Intermediate goods demand: y_t(i) = Y_t (p_t(i)/P_t)^{-(1+η_p_t)/η_p_t}.
  - Production: y_t(i) = A_t^{1−α} k_t(i)^α L_t(i)^{1−α}, α∈[0,1].
  - Technology growth: a_t = (1−ρ_a)γ + ρ_a a_{t−1} + ε_a_t, ε_a_t ∼ i.i.d. N(0, σ_a^2).
  - Price rigidity: Calvo (1983); indexation p_t(i) = p_{t−1}(i) π_{t−1}^{χ_p} π^{1−χ_p}.
  - Household utility: E_t Σ_{s=0}^∞ β^s u_{b,t+s} [ ln(c_{t+s} − θ C_{t+s−1}) − φ L_{t+s}(j)^{1+ν}/(1+ν) ], with β∈(0,1), θ∈(0,1), ν≥0; preference shock ln u_{b,t} AR(1).
  - Monetary rule (percentage deviations): ˆR_t = ρ_r ˆR_{t−1} + (1−ρ_r)(φ_π ˆπ_t + φ_y ˆY_t) + ε_{r,t}, ε_{r,t} ∼ N(0, σ_r^2).
  - Fiscal budget constraint: B_t + τ_t (R_{k,t} K_t + W_t L_t) = R_{t−1} B_{t−1}/π_t + G_t + Z_t.
  - Fiscal reactions to lagged debt ratio b_{t−1} = B_{t−1}/Y_{t−1}:
    - ˆτ_t = ρ_τ ˆτ_{t−1} + (1−ρ_τ) γ_τ ˆs b_{t−1} + ε_{τ,t}.
    - ˆG_t = ρ_g ˆG_{t−1} − (1−ρ_g) γ_g ˆs b_{t−1} + ε_{g,t}.
    - ˆZ_t = ρ_z ˆZ_{t−1} + ε_{z,t}.
  - Goods clearing: C_t + I_t + G_t + ψ(v_t) \bar{K}_{t−1} = Y_t.
- Two parameter regions deliver unique equilibrium: AMPF (monetary authority responds sufficiently to inflation; fiscal stabilizes debt growth) and PMAF (fiscal authority does not stabilize debt; monetary authority stabilizes via prices).

### Estimation samples, observables, and methodology
- Samples: 1955Q1-1966Q4, 1967Q1-1979Q2 ("Great Inflation"), 1984Q1-2007Q4 ("Great Moderation").
- Nine observables: real consumption, investment, wages, government spending, tax revenue, government debt, hours worked, inflation, federal funds rate.
- Estimation details:
  - Parameters assumed independent; prior truncated to determinacy region Θ_D with ˜p(θ) = (1/c) p(θ) I{θ∈Θ_D}.
  - Negative log posterior minimized using csminwel (Christopher Sims) for local mode.
  - Posterior via random walk Metropolis-Hastings:
    - 2.02 million draws; first 20,000 discarded.
    - Thinning every 25 draws → final sample size 80,000.
    - Step size 0.33; acceptance ratio 0.27 to 0.33.
    - Diagnostics: trace plots, chain mixing, Geweke’s Separated Partial Means test.
- Calibration:
  - β = 0.99; α = 0.3; δ = 0.025; η_w and η_p = 0.14.
  - Steady-state fiscal calibrations to sample means (1955Q1 to 2007Q4): tax rate = 0.185; G/Y = 0.104; B/(annual Y) = 0.348.

### Priors and parameterization
- Prior for technology growth 100γ: Normal(mean 0.5, sd 0.03). Data average quarterly growth per capita = 0.47 (1955Q1 to 2007Q4).
- Example calibration: ωw = 0.9; threshold for φπ: φπ ≥0.7 consistent with AMPF when ωw = 0.9.
- Numerical search used to identify parameter-space boundaries for AMPF or PMAF; robustness check: impose passive fiscal policy (γg = γt = 0, transfers’ response to debt = 0.5) to test determinacy.
- Prior-implied probabilities for PMAF:
  - P1: 1.15 percent
  - P2: 99.97 percent
  - P3: 100 percent

### Posterior estimates — key findings and statistics
- Data are informative for most parameters; 90-percent credible intervals differ from priors except for technology growth γ.
- Price and wage stickiness (ωp, ωw) estimated higher under P2 and P3 than typical literature values.
- Fiscal responses γg and γt: 90-percent credible intervals positive in all samples for P1 and P2 (except γg for 1955Q1-1966Q4 under P2).
- Volatility changes:
  - Monetary policy shock standard deviation (under P1) falls from 0.17 in 1967Q1-1979Q2 to 0.14 in 1984Q1-2007Q4.
  - Comparative references: Boivin and Giannoni (2006) interest-rate std dev 0.48 for 1959Q1-1979Q2 and 0.23 for 1979Q3-2002Q2; Smets and Wouters (2007) std dev falls from 0.2 to 0.12 across comparable samples.
- Interest-rate response estimates:
  - φπ: estimated higher in pre-Volcker samples under P1; mean φy = 0.12 in 1984Q1-2007Q4 under P1 (compared with 0.08 in Smets and Wouters (2007)).
- Model limitations noted: distortionary financing raises model volatility making reconciliation with observed variances of inflation and nominal interest rate difficult.

### Regime analysis — posterior regime allocation and model fit
- Posterior allocation under P2 (prior favors PMAF) ends up in AMPF region:
  - 1955Q1-1966Q4: 99.95 percent of posterior draws in AMPF.
  - 1967Q1-1979Q2: 99.85 percent in AMPF.
  - 1984Q1-2007Q4: 100 percent in AMPF.
- P3 posterior concentrated in PMAF by design.
- Bayes-factor/model-fit (data prefer P1 across samples; P3 strongly disliked).
- Mechanism: under P2/P3 priors implying φπ < 1, prior implies high volatility in prices, nominal interest rate, and hours; posterior raises ωp and ωw to damp inflation volatility.
- Differences P2 vs P3:
  - P3 increases hours-worked volatility and covariances much more than data.
  - P2 matches data better because estimated φy is roughly double that under P3, allowing stronger monetary response to output that damps hours-worked volatility.
- φπ behavior:
  - Under P2 most posterior draws imply active monetary policy even though prior mean is below one.
  - Under P3 fixed PMAF forces low φπ (mean estimates 0.23 to 0.4 across samples), limiting volatility reduction.

### Applications — policy experiments and impulse-response findings
- Three applications: evolution of monetary policy effects, government spending increase under PMAF, expansionary effect of income tax cut.
- Evolution of monetary policy effects (exogenous monetary tightening):
  - Under P1 across samples:
    - Output response peak for 1967Q1-1979Q2 and 1984Q1-2007Q4: about 2.5 percent (mean response peaks at about 2.5 percent in both).
    - No evidence that monetary policy effects on output have diminished in the post-Volcker sample.
  - Under P2 for earlier samples:
    - Mean peak output response for the two pre-Volcker samples about 1 percent.
    - If actual responses align with P2, monetary policy appears more effective in post-Volcker sample.
  - Inflation responses under P1:
    - Mean inflation response declines from more than 0.2 percent in 1967Q1-1979Q2 to less than 0.05 percent in 1984Q1-2007Q4.
    - Upper bounds similar across samples; estimation is inconclusive on diminished inflation effects post-Volcker.

### Monetary tightening: dynamics and key parameters
- Main finding: Monetary tightening has little effect on lowering inflation because the central bank responds less than one-for-one to inflation; in 1967-1979 a monetary tightening can even raise inflation in the medium run.
- Persistence ρr (P1 means): 0.83, 0.88, 0.86 for the three samples sequentially.
- Under P2 mean ρr for 1955Q1-1966Q4 and 1967Q1-1979Q2 are 0.79 and 0.70.
- Role of φπ and ωp:
  - Under P1 high φπ damps fall in inflation after tightening; 1984Q1-2007Q4 estimated mean φπ = 2.
  - High ωp reduces monetary effectiveness on inflation; example ωp approaches one → prices nearly fixed; ωp = 0.98 for 1955Q1-1966Q4 under P3 versus 0.78 for 1967Q1-1979Q2.
- Price puzzle under P2 for 1967Q1-1979Q2:
  - High wage stickiness → monetary tightening reduces equilibrium labor, raises wage → slow wage adjustment plus small interest-rate response raises marginal costs → inflation and expectations rise.

### Government spending increase under a PMAF regime
- Under imposed PMAF (P3):
  - Positive consumption response observed for 1967Q1-1979Q2 but negligible for 1955Q1-1966Q4.
  - Explanation hinges on price stickiness: ωp high (0.98) for 1955Q1-1966Q4 implies small slow price level increase → real interest rate does not fall → consumption does not rise.
- Output multipliers (present-value at two years and long-run cumulative):
  - Present-value at two years:
    - 1955Q1-1966Q4: about 0.5 under P1 and 1.1 under P3.
    - 1967Q1-1979Q2: about 0.6 under P1 and 1.2 under P3.
  - Cumulative over 1000 quarters:
    - 1955Q1-1966Q4: −0.7 under P1 and around 1.1 under P3.
    - 1967Q1-1979Q2: −0.7 under P1 and around 1.2 under P3.
  - Comparison: P3 multipliers can exceed 1 but are much smaller than Davig and Leeper (2009) which obtained ∼2.3 under fixed PMAF.
- Shock persistence and habit formation:
  - Government spending shock persistence under P1: ρg = 0.98 for pre-Volcker samples.
  - Habit θ: mean estimates > 0.7 across samples.
  - High persistence induces large negative wealth effect under P1 → negative long-run consumption/output responses.
  - Under AMPF high θ dampens negative consumption response and increases output multiplier; under PMAF high θ prevents consumption from rising much and dampens multiplier.

### Expansionary effect of an income tax cut
- Under P1:
  - Deficit-financed income tax reduction is expansionary: increases labor and output via higher savings and labor supply → capital accumulation → higher labor demand → lower marginal cost and price level.
  - Monetary authority responds more to falling prices than increased output → nominal rate declines.
- Under P2 anomaly:
  - Labor can fall if monetary authority raises nominal rate to counteract output (φy response strong relative to φπ).
  - Estimated mean φy under P2: 0.18 for 1955Q1-1966Q4 and 0.14 for 1967Q1-1979Q2.
  - Estimated φπ under P2 around 0.5–0.6.
- Multipliers:
  - Present-value output multipliers at two years after tax shock are all below 0.1 under P1 or P2 for pre-Volcker samples.
- Caveat: model allows only distortionary financing; absence of transfer adjustments may overstate negative financing effects and understate expansionary impacts.

### Overall conclusions and caveats
- No support for a fixed PMAF regime in any period studied because PMAF implies excessive volatility in hours worked and inflation relative to data.
- Monetary policy effectiveness on output not found to be reduced in post-Volcker samples (contrasting some VAR literature).
- Government spending can increase consumption under PMAF but depends critically on price stickiness.
- Income tax cuts can reduce labor if monetary policy tightens in response to output.
- Methodological caveat: policy parameters fixed (no regime switches); allowing switching or parameter drift could change support for PMAF as expectations of future policy changes may alleviate volatility issues with fixed PMAF.

### Key numeric highlights (preserved exactly)
- Prior-implied PMAF probabilities: P1 = 1.15 percent; P2 = 99.97 percent; P3 = 100 percent.
- Estimation draws: 2.02 million; discarded first 20,000; final sample size 80,000 after thinning every 25 draws.
- Step size 0.33; acceptance ratio 0.27 to 0.33.
- Calibrations: β = 0.99; α = 0.3; δ = 0.025; η_w = η_p = 0.14.
- Steady-state fiscal: tax rate = 0.185; G/Y = 0.104; debt/annual output = 0.348.
- Example posterior φπ (P1 sample means): 1955Q1-1966Q4 = 1.67 [1.39, 1.98]; 1967Q1-1979Q2 = 1.62 [1.27, 1.96]; 1984Q1-2007Q4 = 2.0 [1.67, 2.32].
- Monetary shock std dev under P1 falls from 0.17 (1967Q1-1979Q2) to 0.14 (1984Q1-2007Q4).
- Example data vs model (1955Q1-1966Q4, selected from Table 4):
  - π (inflation): Data 0.27; P1 0.77; P2 0.66; P3 1.86 [0.52, 1.70][0.39, 1.73][0.80, 7.81]
  - R (real interest rate): Data 0.37; P1 0.83; P2 0.78; P3 1.87 [0.59, 1.72][0.52, 1.78][0.85, 7.65]
- Model comparison (Table 5, Bayes factors relative to P1):
  - 1955Q1-1966Q4: P2 = exp[9.8]; P3 = exp[25.3]
  - 1967Q1-1979Q2: P2 = exp[7.9]; P3 = exp[27.9]
  - 1984Q1-2007Q4: P2 = exp[22]; P3 = exp[64]

*Source: _wp10243 - REFERENCES*

### References .............................................................................................................

### _wp10243 - References

### Tables
- Table 1. Estimates for the prior 1 specification (P1), centered at the active monetary and passive fiscal policy regime ...............................................................................................  33
- Table 2. Estimates for the prior 2 specification (P2), centered at the passive monetary and active fiscal policy regime ...........................................................................................  34
- Table 3. Estimates for the prior 3 specification (P3), centered at the passive monetary and active fiscal policy regime ...........................................................................................  35
- Table 4. Standard deviations from data and unconditional standard deviations from the posterior distribution ..........................................................................................................  36
- Table 5. Model fit comparisons ..........................................................................................  37
- Table 6. Standard deviations from the unconditional standard deviations from the prior Distribution .........................................................................................................................  37

### Figures
- Figure 1. Combinations of various parameters that deliver the AMPF regime ..................38
- Figure 2. Prior and posterior bivariate density plots. ..........................................................39
- Figure 3. Prior and posterior bivariate density plots ...........................................................40
- Figure 4. The effects of monetary policy across samples: all samples under P1 ................41
- Figure 5. The effects of monetary policy across samples: 1955Q1-1966Q4 and 1967Q1-1979Q2 are under P2, and 1984Q1-2007Q4 is under P1 ....................................................42
- Figure 6. The effects of a government spending increase for 1955Q1-1966Q4 .................43
- Figure 7. The effects of a government spending increase for 1967Q1-1979Q2 .................44
- Figure 8. The effects of a tax cut for 1955Q1-1966Q4 .......................................................45
- Figure 9. The effects of a tax cut for 1967Q1-1979Q2 .......................................................46

### Introduction — key findings and setup
- Model features and purpose:
  - The paper estimates a New Keynesian model that accounts for monetary and fiscal policy interactions with Bayesian methods.
  - Unlike many estimated New Keynesian models, the specification includes government debt and fiscal financing to allow for the possibility of a PMAF regime.
- Policy regime definitions and context:
  - AMPF: active monetary and passive fiscal policy regime (in the sense of Leeper (1991)); commonly implied by models that omit government debt and assume lump-sum taxes adjust to clear the government budget.
  - PMAF: passive monetary and active fiscal policy regime.
  - Economists generally agree that monetary policy in the post-1984 U.S. has been active, implying the post-1984 U.S. fits an AMPF regime.
- Samples and estimation designs:
  - Three samples are estimated: 1955Q1-1966Q4, 1967Q1-1979Q2, and 1984Q1-2007Q4.
  - For all samples, estimations are conducted under three specifications:
    - Specification 1 (P1): prior centered at an AMPF regime but allows parameter combinations in both regime regions.
    - Specification 2 (P2): prior centered at a PMAF regime but allows parameter combinations in both regime regions.
    - Specification 3 (P3): imposes a PMAF regime by not allowing fiscal instruments to respond to debt growth.
- Posterior and model comparison results:
  - Except for the third specification imposing the PMAF regime, the posterior distributions fall in the parameter space of the AMPF regime, regardless of the prior.
  - Model comparisons indicate that for all three samples, the data prefer least the specification with a PMAF regime imposed.
- Insights on monetary policy parameter estimates:
  - Competing estimates for the Federal Reserve’s response to inflation are found in the pre-Volcker period within the parameter space of an AMPF regime:
    - One where the inflation coefficient is larger than one—when the prior for this variable is larger than one (as in P1).
    - One where the inflation coefficient is smaller than one—when the prior is much below one (as in P2).
  - Although the conventional boundary of the monetary authority’s response to inflation for active monetary policy is (near) one, the boundary can be much below one in medium and large scale New Keynesian models.
  - The result suggests that estimates from New Keynesian models for the pre-Volcker sample are likely to be influenced to a large extent by the prior imposed.
- Debate on drivers of post-Volcker macroeconomic stability:
  - "Good Luck" explanation: Federal Reserve’s response to inflation was sufficient in the pre-Volcker period; reduced economic instability in the post-Volcker period is due to reduced variance of structural disturbances (cited works: Canova and Gambetti (2009), Sims and Zha (2006), Primiceri (2005)).
  - "Good Policy" explanation: persistent high inflation in the pre-Volcker period resulted from the Federal Reserve’s insufficient ability to control inflation.

*Source: _wp10243 - References*

### conclusions are often based on the inflation coefficient in a Taylor-type rule being estimated

### _wp10243 - conclusions are often based on the inflation coefficient in a Taylor-type rule being estimated

### Literature and identification challenge
- Prior literature often finds the inflation coefficient in a Taylor-type rule estimated as smaller than one (examples cited: Judd and Rudebusch (1998), Taylor (1999b), Cogley and Sargent (2005), and Boivin (2006)).
- Papers using New Keynesian models with passive monetary policy rules conclude that pre-Volcker monetary policy implies indeterminacy and that high volatility in inflation and output could be due to sunspot fluctuations (Clarida et al. (2000), Lubik and Schorfheide (2004), and Boivin and Giannoni (2006)).
- Allowing for regime switches yields different conclusions: Davig and Leeper (2006), Davig and Doh (2009), and Bianchi (2010) conclude that monetary policy was passive (and determinate) at times in the pre-Volcker era.
- Identification is challenging because many different monetary and fiscal policy combinations can generate the same stochastic processes for model variables (Sims (2008)).

### Contribution and main findings
- The paper estimates AMPF (active monetary, passive fiscal) and PMAF (passive monetary, active fiscal) regimes in the pre- and post-Volcker periods and evaluates relative fit by estimating a DSGE model with fixed policy rules that deliver AMPF or PMAF solutions depending on policy parameters. The fixed rules impose identification restrictions that allow identification of AMPF and PMAF regimes.
- Primary empirical result:
  - "The PMAF regime is never favored by the data due to the high volatility the fixed PMAF regime implies for certain observables, particularly hours worked and inflation."
  - "The results suggest that the standard New Keynesian model used for policy analysis is not able to match features of the data if a fixed PMAF regime is assumed."
- Structural innovations differ substantially between the pre- and post-Volcker periods.
- Contrary to VAR-based conclusions, the paper does not find reduced monetary policy effects on output in the post-Volcker period (contrasting with Gertler and Lown (1999), Barth and Ramey (2002), and Boivin and Giannoni (2002)).

### Fiscal shocks, price stickiness, and consumption responses
- A PMAF regime can generate a positive consumption response to an increase in government spending, but this depends crucially on the degree of price stickiness.
- Under the imposed PMAF regime (third specification), a positive consumption response following a government spending increase is found for 1967Q1-1979Q2, but the consumption response is almost negligible for 1955Q1-1966Q4.
  - Explanation: estimated degree of price stickiness for 1955Q1-1966Q4 is quite high, so a government spending increase leads to a small and slow increase in the price level and does not lower the real interest rate.
- References documenting similar mechanisms: Kim (2003), Davig and Leeper (2009).

### Policy coordination and tax cuts
- Policy coordination matters for the expansionary effect of a tax cut:
  - If the monetary authority reacts relatively weakly to inflation and strongly to output growth induced by a tax cut, labor can fall and thus dampen the stimulative effect of the tax cut.
  - A monetary tightening can trigger asset substitution between government bonds and physical capital, offsetting the investment incentive from a lower income tax rate.
  - As investment is dampened, firms’ demand for labor weakens; despite households’ desire to increase labor supply given a lower income tax rate, equilibrium labor falls and the expansionary effect of an income tax cut is diminished.

### Model structure and solution summary
- Model: a standard New Keynesian model with a stochastic growth path (as in Del Negro et al. (2007) and Fernandez-Villaverde et al. (2010a)) that also emphasizes fiscal behavior to capture monetary–fiscal interactions.
- Key model features and equations preserved as in source:
  - Final goods technology (Dixit and Stiglitz (1977)):
    - [∫_0^1 y_t(i)^{1/(1+η_p_t)} di]^{1+η_p_t} ≥ Y_t
    - η_p_t denotes an exogenous time-varying markup to intermediate goods’ prices.
  - Intermediate goods demand: y_t(i) = Y_t (p_t(i)/P_t)^{-(1+η_p_t)/η_p_t}.
  - Production technology (Cobb-Douglas): y_t(i) = A_t^{1−α} k_t(i)^α L_t(i)^{1−α}, α∈[0,1].
  - Technology growth a_t = ln A_t − ln A_{t−1} follows AR(1): a_t = (1−ρ_a)γ + ρ_a a_{t−1} + ε_a_t, ε_a_t ∼ i.i.d. N(0, σ_a^2).
  - Price rigidity via Calvo (1983); indexation rule: p_t(i) = p_{t−1}(i) π_{t−1}^{χ_p} π^{1−χ_p}.
  - Labor packer technology and demand with time-varying wage markup η_w_t.
  - Household utility: E_t Σ_{s=0}^∞ β^s u_{b,t+s} [ ln(c_{t+s} − θ C_{t+s−1}) − φ L_{t+s}(j)^{1+ν}/(1+ν) ], with β∈(0,1), θ∈(0,1), ν≥0.
  - Preference shock ln u_{b,t} = (1−ρ_b) ln u_b + ρ_b ln u_{b,t−1} + ε_{b,t}, ε_{b,t} ∼ i.i.d. N(0, σ_b^2).
  - Household budget constraint (units of consumption goods) spelled out (equation (10)), including income tax rate τ_t and components c_t, i_t, b_t, x_t(j), transfers Z_t, profits D_t, and capital utilization costs ψ(v_t).
  - Capital accumulation law (equation (11)): \bar{k}_t = (1−δ)\bar{k}_{t−1} + u_{i,t} [1 − s(i_t/i_{t−1})] i_t.
  - Investment efficiency shock ln u_{i,t} = (1−ρ_i) ln u_i + ρ_i ln u_{i,t−1} + ε_{i,t}, ε_{i,t} ∼ i.i.d. N(0, σ_i^2).
  - Wage setting with Calvo-style wage rigidity and indexation (equation (14)).
  - Monetary policy: Taylor-type rule in percentage deviations (carets): ˆR_t = ρ_r ˆR_{t−1} + (1−ρ_r)(φ_π ˆπ_t + φ_y ˆY_t) + ε_{r,t}, ε_{r,t} ∼ N(0, σ_r^2) (equation (15)).
  - Fiscal budget constraint (equation (16)): B_t + τ_t (R_{k,t} K_t + W_t L_t) = R_{t−1} B_{t−1}/π_t + G_t + Z_t.
  - Fiscal policy reaction functions to lagged debt-to-output ratio b_{t−1} = B_{t−1}/Y_{t−1}:
    - ˆτ_t = ρ_τ ˆτ_{t−1} + (1−ρ_τ) γ_τ ˆs b_{t−1} + ε_{τ,t}, ε_{τ,t} ∼ i.i.d. N(0, σ_τ^2) (equation (17)).
    - ˆG_t = ρ_g ˆG_{t−1} − (1−ρ_g) γ_g ˆs b_{t−1} + ε_{g,t}, ε_{g,t} ∼ i.i.d. N(0, σ_g^2) (equation (18)).
    - ˆZ_t = ρ_z ˆZ_{t−1} + ε_{z,t}, ε_{z,t} ∼ i.i.d. N(0, σ_z^2) (equation (19)).
  - Goods market clearing: C_t + I_t + G_t + ψ(v_t) \bar{K}_{t−1} = Y_t (equation (20)).
- Two distinct parameter regions delivering a unique rational expectations equilibrium: AMPF or PMAF. Definitions:
  - AMPF: monetary authority responds sufficiently to inflation deviations; fiscal authority adjusts government spending or tax policy to stabilize government debt growth.
  - PMAF: fiscal authority does not take sufficient measures to stabilize debt; monetary authority stabilizes debt growth through price adjustments.

### Estimation samples, observables, and methodology
- Samples used: 1955Q1-1966Q4, 1967Q1-1979Q2, and 1984Q1-2007Q4.
  - 1967Q1-1979Q2 corresponds to the “Great Inflation.”
  - 1984Q1-2007Q4 corresponds to the “Great Moderation.”
- Nine observables used: real consumption, investment, wages, government spending, tax revenue, government debt, hours worked, inflation, and the federal funds rate.
- Data linkage to model log-linearized variables given in equation (21), where l and dl denote 100 times logs and log differences; 100γ appears in the mapping for level variables.
- Estimation methodology:
  - Parameters assumed independent; prior product p(θ) truncated to determinacy region Θ_D with joint prior ˜p(θ) = (1/c) p(θ) I{θ∈Θ_D}, c = ∫_{θ∈Θ_D} p(θ) dθ.
  - Equilibrium written in state-space form; negative log posterior minimized using csminwel (Christopher Sims) for local mode search.
  - Posterior constructed via random walk Metropolis-Hastings:
    - 2.02 million draws sampled; first 20,000 discarded.
    - Thinning by every 25 draws leaves final sample size of 80,000.
    - Step size of 0.33 yields acceptance ratio from 0.27 to 0.33 across estimations.
    - Diagnostic checks include trace plots, chain mixing, and Geweke’s Separated Partial Means test.
- Calibration and priors:
  - Calibrated values: β = 0.99; α = 0.3 (labor income share 0.7); δ = 0.025 (annual depreciation rate is 10 percent); η_w and η_p set to 0.14 (steady-state markups 14 percent).
  - Steady-state fiscal calibrations to sample means (1955Q1 to 2007Q4): tax rate = 0.185; ratio of government spending to output = 0.104; ratio of government debt to annual output = 0.348.
  - Three prior specifications (P1, P2, P3) differ in priors for monetary and fiscal parameters φ_π, γ_g, and γ_t:
    - P1 centered at AMPF: monetary authority raises interest rate by more than inflation; fiscal responses γ_g and γ_t ~ Normal(mean 0.15, sd 0.05).
    - P2 centered at PMAF: φ_π ~ Beta(mean 0.5, sd 0.2); γ_g and γ_t ~ Normal(mean 0, sd 0.03).
    - P3 restricted to PMAF: φ_π ~ Beta(...). (specification truncated in source text)

### Implications for policy analysis
- The inability of a fixed PMAF regime within the standard New Keynesian model to match data features—particularly volatility in hours worked and inflation—implies caution when attributing historical macro volatility to PMAF equilibria without allowing regime changes or altering model structure.
- Degree of price stickiness materially affects fiscal multipliers and the sign/magnitude of consumption responses to government spending shocks; policy evaluations should account for estimated nominal rigidities.
- Coordination between monetary and fiscal authorities affects fiscal policy effectiveness (e.g., for tax cuts); weak monetary responses to inflation combined with strong responses to tax-cut-induced output can negate expansionary effects via labor and investment channels.

*Italic: _wp10243 - conclusions are often based on the inflation coefficient in a Taylor-type rule being estimated*

### 0.5 and a standard deviation of 0.2, as in P2.

### _wp10243 - 0.5 and a standard deviation of 0.2, as in P2.

### Priors and parameterization
- Prior for the percentage growth rate of technology (100γ): normally distributed with a mean of 0.5 and a standard deviation of 0.03.
- The tight prior for 100γ is intended to match the average quarterly growth rate of real output per capita, which is 0.47 from 1955Q1 to 2007Q4.
- Other priors follow closely Smets and Wouters (2007) and Justiniano et al. (2010).
- Example calibration used in illustrations: ωw = 0.9 and a threshold for φπ: φπ ≥0.7 is consistent with an AMPF regime when ωw = 0.9.
- Numerical search used to identify parameter-space boundaries that yield AMPF or PMAF regimes; robustness check: impose a passive fiscal policy (γg = γt = 0, transfers’ response to debt = 0.5) to test if determinacy persists, implying active monetary policy if determinacy is preserved.

### Numerical regime identification and prior-implied regime probabilities
- Because the parameter space cannot be characterized analytically, a numerical approach searches boundaries that deliver AMPF or PMAF.
- Probabilities for the PMAF regime under the three prior specifications:
  - P1: 1.15 percent
  - P2: 99.97 percent
  - P3: 100 percent

### Posterior estimates — key findings and statistics
- Data are informative for most parameters; 90-percent credible intervals for most parameters differ from priors, except technology growth rate γ whose posterior closely mimics its prior.
- Degrees of price and wage stickiness (ωp and ωw) are estimated higher under P2 and P3 than typical literature values.
- Fiscal responses:
  - γg and γt 90-percent credible intervals are positive in all samples for P1 and P2 (except γg for 1955Q1-1966Q4 under P2).
  - Adjustments in government spending increasingly used across samples to finance debt.
- Volatility of several shocks decreases over time; example for monetary policy shock under P1:
  - standard deviation falls from 0.17 in the 1967Q1-1979Q2 sample to 0.14 in the 1984Q1-2007Q4 sample.
- Comparison notes:
  - Boivin and Giannoni (2006): standard deviation of the interest rate is 0.48 for 1959Q1-1979Q2 and 0.23 for 1979Q3-2002Q2.
  - Smets and Wouters (2007): estimated mode of standard deviation of monetary policy shock falls from 0.2 in 1966Q1-1979Q2 to 0.12 in 1984Q1-2007Q4.
- Interest-rate response estimates:
  - φπ (interest-rate response to inflation): estimated higher in two pre-Volcker samples under P1 than in some previous studies, but comparable to Bayesian DSGE estimates.
  - φy (interest-rate response to output): mean estimate is 0.12 in 1984Q1-2007Q4 under P1 (compared with 0.08 in Smets and Wouters (2007) for a similar sample).
- Model limitations: standard New Keynesian setup struggles to reconcile estimated variances of inflation and nominal interest rate with data, in part due to distortionary financing of government debt increasing model volatility.

### Regime analysis — posterior regime allocation and model fit
- Posterior regime allocation under P2 (despite P2 prior favoring PMAF):
  - Posterior draws under P2 located in AMPF region:
    - 1955Q1-1966Q4: 99.95 percent
    - 1967Q1-1979Q2: 99.85 percent
    - 1984Q1-2007Q4: 100 percent
- Posterior under P3 is entirely concentrated in the PMAF regime (by design).
- Bayes-factor/model-fit results:
  - Across all three samples, data prefer the P1 specification; evidence favoring P1 over P2 is weak for 1955Q1-1966Q4 and 1967Q1-1979Q2.
  - All samples strongly dislike the P3 specification.
- Mechanism for posterior shifting of stickiness parameters:
  - Under P2 and P3 priors (which imply φπ < 1), the model prior implies high volatility in prices, nominal interest rate, and hours worked.
  - To reconcile with smoother observed inflation, the posterior pushes ωp and ωw to high values (large nominal stickiness), which damps inflation volatility.
- Differences in volatility and hours worked across P2 and P3:
  - P3 increases volatility of hours worked and covariances much more than the data counterpart.
  - P2 matches data statistics better because its estimated φy is approximately double that under P3, allowing monetary policy under P2 to respond more aggressively to output and dampen hours-worked volatility.
- φπ behavior across specifications:
  - Under P2 the majority of posterior draws imply active monetary policy even though mean φπ is centered below one.
  - Under P3 the fixed PMAF regime forces low φπ (mean estimates from 0.23 to 0.4 across samples), limiting ability to reduce volatility of inflation and hours worked.
- Implication: standard New Keynesian model may not match data features under a PMAF regime; a potential extension is including longer maturity horizons for government debt.

### Applications — policy experiments and impulse-response findings
- Three applications studied using the estimated model: evolution of monetary policy effects, effect of a government spending increase under a PMAF regime, and expansionary effect of an income tax cut. (Summary below focuses on the first application reported in the text.)
- Evolution of monetary policy effects (impulse responses to an exogenous monetary tightening):
  - Under P1 specification across samples:
    - Output response peak for 1967Q1-1979Q2 and 1984Q1-2007Q4: about 2.5 percent (mean response peaks at about 2.5 percent in both cases).
    - No evidence found that monetary policy effects on output have diminished in the post-Volcker sample.
  - Under P2 specification for earlier samples (1955Q1-1966Q4 and 1967Q1-1979Q2):
    - Estimated mean peak response of output for the two pre-Volcker samples is about 1 percent.
    - If actual output responses align with P2, monetary policy appears more effective in the post-Volcker sample.
  - Inflation responses:
    - Under P1 conditioning, mean inflation response declines from more than 0.2 percent in 1967Q1-1979Q2 to less than 0.05 percent in 1984Q1-2007Q4.
    - Upper bounds of inflation responses across samples remain quite similar; estimation is inconclusive about diminished inflation effects in the post-Volcker period.

*Italic source: _wp10243 - 0.5 and a standard deviation of 0.2, as in P2.*

### conclusion. Monetary tightening has little effect in lowering inflation, as the central bank

### conclusion. Monetary tightening has little effect in lowering inflation, as the central bank responds less than one-for-one to inflation deviations.

### Monetary tightening: dynamics and key parameters
- Main finding: Monetary tightening has little effect in lowering inflation because the central bank responds less than one-for-one to inflation deviations; in the 1967-1979 sample, a monetary tightening can even drive up inflation in the medium run.
- Persistence of monetary policy shocks (ρr):
  - Under the P1 specification, mean estimates of ρr are 0.83, 0.88, and 0.86 for the three samples sequentially.
  - Under P2, mean estimates of ρr for 1955Q1-1966Q4 and 1967Q1-1979Q2 are 0.79 and 0.70.
  - A more persistent monetary policy innovation implies a stronger effect on output due to intensified asset substitution between government bonds and physical capital; when expected to last long, output contracts more.
- Response of interest rate to inflation (φπ) and price rigidity (ωp):
  - Under P1, a high φπ dampens the fall in inflation following a monetary tightening; the 1984Q1-2007Q4 sample has the estimated mean of φπ = 2.
  - High ωp contributes to reduced effectiveness of monetary policy on inflation in the post-Volcker sample; when ωp approaches one (prices effectively fixed), monetary policy’s ability to influence inflation is almost nil (as estimated under P2 for 1955Q1-1966Q4).
  - Specific ωp estimates cited: ωp = 0.98 for 1955Q1-1966Q4 under P3 (highly sticky) versus 0.78 for 1967Q1-1979Q2.
- Price puzzle in 1967Q1-1979Q2 under P2:
  - Observed small “price puzzle” following a monetary tightening under P2 in 1967Q1-1979Q2.
  - Mechanism: high wage stickiness → monetary tightening reduces equilibrium labor and drives up the wage rate → slow wage adjustment plus small interest-rate response to inflation raises marginal costs → inflation and inflation expectations rise.

### Government spending increase under a PMAF regime
- Context: New Keynesian/neoclassical models typically imply negative consumption response to higher government spending unless many rule-of-thumb consumers are present; previous calibrated work (Kim (2003), Davig and Leeper (2009)) shows positive consumption response under PMAF.
- Empirical impulse-response observations:
  - Under the imposed PMAF regime (P3), a positive consumption response to government spending increase is observed for 1967Q1-1979Q2 but not for 1955Q1-1966Q4 — PMAF is not sufficient for positive consumption response.
  - Under the preferred P1 estimation, responses align with standard New Keynesian/neoclassical intuition: competition for goods raises the real interest rate and the negative wealth effect reduces consumption.
- Output multipliers (present-value and cumulative):
  - Present-value output multiplier at end of two years following the shock:
    - 1955Q1-1966Q4: about 0.5 under P1 and 1.1 under P3.
    - 1967Q1-1979Q2: about 0.6 under P1 and 1.2 under P3.
  - Cumulative output multiplier computed over 1000 quarters:
    - −0.7 (−0.7) under P1 and around 1.1 (1.2) under P3 for the 1955Q1-1966Q4 (1967Q1-1979Q2) samples.
  - Comparison: Multipliers under imposed PMAF (P3) can exceed 1, but are much smaller than Davig and Leeper (2009) which obtained around 2.3 with a fixed PMAF regime.
- Role of price stickiness and shock persistence:
  - High ωp = 0.98 under P3 for 1955Q1-1966Q4 (v.s. 0.78 for 1967Q1-1979Q2) implies small price increase and slowly adjusting future price levels → smaller inflation expectations → the real interest rate can still rise → consumption can decline under P3 for 1955Q1-1966Q4.
  - Real interest rate behavior: under P3, real interest rate remains positive for 1955Q1-1966Q4 (Figure 6), while negative for 1967Q1-1979Q2 (Figure 7).
  - High persistence of the government spending shock drives small or negative cumulative multipliers:
    - Under P1, ρg = 0.98 for the two pre-Volcker samples.
    - Highly persistent shock induces a large negative wealth effect; consumption remains persistently negative even 10 years after the shock.
  - Long-run fiscal adjustments to higher debt-to-output ratio (higher income taxes and lower government spending) push output negative and lead to negative cumulative multipliers under P1; under P3 (PMAF), fiscal policy does not adjust so cumulative multipliers can exceed 1.
- Habit formation:
  - Estimated mean degree of habit formation θ: all mean estimates exceed 0.7.
  - Implications:
    - Under AMPF (P1), high θ dampens the negative consumption response and increases the output multiplier.
    - Under PMAF (P3), high θ prevents consumption from rising much and dampens the output multiplier.

### Expansionary effect of an income tax cut
- Baseline P1 responses:
  - Under P1, a deficit-financed reduction in the income tax rate is expansionary: increases labor and output.
  - Mechanisms: tax reduction encourages savings and labor → higher capital accumulation → higher marginal product of labor → increased labor demand → lower marginal cost and lower price level.
  - Monetary authority responds more to falling price level than increased output, causing nominal interest rate to decline.
- P2 specification anomaly:
  - Under P2 (pre-Volcker period), labor response can be negative.
  - Mechanism: under P2 the monetary authority raises the nominal interest rate to counteract rising output (estimated stronger reaction to output than to inflation).
  - Estimated mean φy:
    - 0.18 for 1955Q1-1966Q4.
    - 0.14 for 1967Q1-1979Q2.
  - Estimated reaction to inflation under P2 is small, around 0.5-0.6; the net policy response can be positive, suppressing investment and labor demand, so equilibrium labor can fall despite tax cuts.
- Aggregate effects and multipliers:
  - Despite negative labor response under P2, a tax cut remains expansionary overall: consumption and investment responses are muted initially but capital utilization rises producing more output.
  - Present-value output multipliers at end of year two after a tax shock are all below 0.1 under either P1 or P2 for both pre-Volcker samples.
  - Model specification only allows for distorting financing; because the government in reality also adjusts transfers, the estimates here likely overstate negative financing effects and under-estimate expansionary effects on output, labor, consumption, and investment.
- Significance: monetary policy accommodation (or lack thereof) critically affects expansionary effects of income tax cuts.

### Overall conclusions and caveats
- Estimated regimes and volatility:
  - No evidence supporting a fixed PMAF regime in any period studied; mainly because estimated volatility of hours worked and inflation under PMAF exceeds that observed in the data.
- Other key findings:
  - Unlike much of the VAR literature, estimation does not find reduced effectiveness of monetary policy on output in post-Volcker samples.
  - A government spending increase can generate positive consumption under PMAF, but this depends on estimated price stickiness.
  - An income tax cut can generate a negative labor response if the monetary authority raises the nominal interest rate to counteract expansionary output effects.
- Caveat on methodology:
  - Estimation fixes policy parameters and does not allow for regime switches.
  - Literature (Davig and Doh (2009), Bianchi (2010), Fernandez-Villaverde et al. (2010b)) finds evidence of monetary policy switching or parameter drift; allowing switching/parameter drift may give more favorable support for PMAF because expectations of future policy changes could alleviate complications the fixed PMAF regime faces in matching data volatility.
  - This extension is left for future research.

*Italicized source: _wp10243 - conclusion. Monetary tightening has little effect in lowering inflation, as the central bank responds less than one-for-one to inflation deviations.*

### REFERENCES

### _wp10243 - REFERENCES

### References list
- Comprehensive bibliography of works cited, including but not limited to: Arestis et al. (2010); Barth and Ramey (2002); Bianchi (2010); Bilbiie, Meier, and Muller (2008); Boivin (2006); Boivin and Giannoni (2002, 2006); Calvo (1983); Canova and Gambetti (2009); Christiano, Eichenbaum, and Evans (2005); Clarida, Gali, and Gertler (2000); Cochrane (1999); Cogley and Sargent (2005); Davig and Leeper (2006, 2009); Del Negro et al. (2007); Dixit and Stiglitz (1977); Erceg, Henderson, Levin (2000); Favero and Monacelli (2005); Fernandez-Villaverde et al. (2010a, 2010b); Flaschel, Franke, and Proano (2008); Gertler and Lown (1999); Geweke (1999, 2005); Greenwood, Hercowitz, and Krusell (1997); Judd and Rudebusch (1998); Justiniano, Primiceri, and Tambalotti (2010); Kim (2003); Leeper (1991); Leeper, Plante, and Traum (2010); Lubik and Schorfheide (2004); Meltzer (2005); Orphanides (2003); Primiceri (2005); Romer and Romer (2002); Schmitt-Grohe and Uribe (2010); Sims (1994, 2001, 2008); Sims and Zha (2006); Smets and Wouters (2003, 2007); Taylor (1999a, 1999b); Traum and Yang (2010); Woodford (2003); Zubairy (2009).

### Prior specifications and parameter estimates (Tables 1–3)
- Tables 1–3 present posterior mean estimates and 90-percent credible intervals ([5, 95]) for a large set of structural parameters, monetary and fiscal policy coefficients, and shock process parameters under three prior specifications:
  - P1: prior 1 specification (centered at the active monetary and passive fiscal policy regime).
  - P2: prior 2 specification (centered at the passive monetary and active fiscal policy regime).
  - P3: prior 3 specification (centered at the passive monetary and active fiscal policy regime).
- Each table reports values across three sample periods: 1955Q1-1966Q4, 1967Q1-1979Q2, and 1984Q1-2007Q4.
- Example entries (from Table 1, P1 specification — structural parameters for each sample):
  - 100γ: prior mean 0.5 [0.45, 0.55]; sample means: 1955Q1-1966Q4 = 0.49 [0.45, 0.54], 1967Q1-1979Q2 = 0.49 [0.44, 0.54], 1984Q1-2007Q4 = 0.49 [0.45, 0.54].
  - ν2: prior [0.95, 3.37]; sample means: 1955Q1-1966Q4 = 2.50 [1.37, 3.92], 1967Q1-1979Q2 = 2.31 [1.16, 3.76], 1984Q1-2007Q4 = 3.19 [1.87, 4.80].
  - θ: prior 0.5 [0.17, 0.83]; sample means: 1955Q1-1966Q4 = 0.89 [0.81, 0.94], 1967Q1-1979Q2 = 0.88 [0.81, 0.94], 1984Q1-2007Q4 = 0.80 [0.74, 0.87].
  - φπ (monetary authority’s response to inflation): prior 1.5 [1.09, 1.91]; sample means: 1955Q1-1966Q4 = 1.67 [1.39, 1.98], 1967Q1-1979Q2 = 1.62 [1.27, 1.96], 1984Q1-2007Q4 = 2.0 [1.67, 2.32].
- Full tables list many additional parameters (ψ, s, ωp, ωw, χp, χw, φy, ρr, γg, γt, ρg, ρt, and extensive shock autoregressions ρa, ρb, ρi, ρp, ρw, ρz and shock standard deviations σa, σb, σr, σi, σp, σw, σg, σt, σz) with their posterior means and [5, 95] credible intervals for each sample and prior.

### Data and model-implied standard deviations (Table 4)
- Table 4 reports observed standard deviations ("Data") and unconditional standard deviations from the posterior distribution under P1, P2, and P3 for key macro series across the three sample periods. Square brackets indicate the 90-percent credible intervals.
- Example for the 1955Q1-1966Q4 sample (selected variables):
  - GGrowth: Data 2.43; P1 2.65; P2 2.78; P3 2.56 [2.31, 3.09][2.39, 3.27][2.24, 2.99]
  - CGrowth: Data 0.53; P1 0.85; P2 0.99; P3 1.20 [0.69, 1.09][0.76, 1.33][1.01, 1.45]
  - IGrowth: Data 4.40; P1 5.12; P2 5.46; P3 7.19 [4.23, 6.41][4.33, 7.00][5.77, 8.89]
  - BGrowth: Data 7.00; P1 8.20; P2 7.87; P3 7.65 [6.82, 10.49][6.60, 9.76][6.50, 9.17]
  - π (inflation): Data 0.27; P1 0.77; P2 0.66; P3 1.86 [0.52, 1.70][0.39, 1.73][0.80, 7.81]
  - R (real interest rate): Data 0.37; P1 0.83; P2 0.78; P3 1.87 [0.59, 1.72][0.52, 1.78][0.85, 7.65]
- Note: analogous rows are reported for the 1967Q1-1979Q2 and 1984Q1-2007Q4 samples in Table 4.

### Model comparison and fit (Table 5)
- Table 5 reports Bayes factors (relative to P1) for model specifications across the three sample periods:
  - 1955Q1-1966Q4: P2 = exp[9.8]; P3 = exp[25.3]
  - 1967Q1-1979Q2: P2 = exp[7.9]; P3 = exp[27.9]
  - 1984Q1-2007Q4: P2 = exp[22]; P3 = exp[64]

### Prior unconditional standard deviations (Table 6)
- Table 6 reports unconditional standard deviations from the prior distribution for the same macro series under P1, P2, and P3, with 90-percent credible intervals in square brackets. Example entries:
  - GGrowth: P1 0.81 [0.32, 3.45]; P2 0.71 [0.27, 3.19]; P3 0.70 [0.26, 3.19]
  - CGrowth: P1 0.58 [0.18, 3.25]; P2 1.25 [0.31, 8.91]; P3 1.26 [0.31, 9.06]
  - π: P1 0.93 [0.24, 8.21]; P2 2.17 [0.60, 15.85]; P3 2.20 [0.61, 16.34]

### Figures and impulse-response summaries (Figures 1–9)
- Figure 1: "Combinations of various parameters that deliver the AMPF regime." X-axis denotes φπ. Note states all non-plotted parameters held at P1 mean values.
- Figures 2–3: Prior and posterior bivariate density plots. Figure 2: x-axis ωp, y-axis STDπ; posteriors from P2 and P3 for 1955Q1-1966Q4. Figure 3: x-axis φy, y-axis STDL; posteriors from P2 and P3 for 1955Q1-1966Q4.
- Figures 4–5: Effects of monetary policy across samples (responses in percentage deviation to steady state; solid lines mean responses, dotted-dashed 90% confidence bands). Figure 4: all samples under P1. Figure 5: 1955Q1-1966Q4 and 1967Q1-1979Q2 under P2, 1984Q1-2007Q4 under P1.
- Figures 6–9: Impulse responses to fiscal shocks (government spending increase and tax cuts) across samples and prior specifications (P1, P2, P3). Y-axis in all cases is percentage deviation to steady state; solid lines mean responses; dotted-dashed lines 90% confidence bands.

*Italic: Content adapted exactly from the provided PDF excerpt (_wp10243 - REFERENCES).*

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