## 1. Selected Estimates for the Augmented DSGE Model of the Euro Area

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### Introduction and purpose
- Purpose: assess effects of government spending shocks on private consumption within a New-Keynesian DSGE framework augmented for non-Ricardian (liquidity-constrained) households.
- Key modeling insight: coexistence of “Ricardian” (optimizing, forward-looking) and “non-Ricardian” (rule-of-thumb, consume after-tax disposable income) households can alter propagation of fiscal shocks; success depends on debt-financing, real-wage response, and fiscal rule.

### Model structure and policy rules
- Agents and aggregation:
  - Four agent types: households (two types), firms, monetary authority, fiscal authority.
  - Household shares: share 1−ω are Ricardian; share ω are non-Ricardian.
  - Aggregation: X_t = (1−ω) X_i,t + ω X_j,t. Only Ricardian households hold bonds and capital: B_t+1 = (1−ω) B_i,t+1; K_t+1 = (1−ω) K_i,t+1.
- Non-Ricardian consumption rule:
  - (1 + τ_c) C_j,t = (1−τ_d)(1 + τ_w) W_t/P_t N_t − T_j,t/P_t.
- Wage and price setting:
  - Calvo wage: reset probability 1−ξ_w; partial indexation γ_w; wage markup λ_w,t = λ_w + η_w,t.
  - Calvo price: reset probability 1−ξ_p; partial indexation γ_p; price markup λ_p,t = λ_p + η_p,t.
- Fiscal authority:
  - Real per-capita budget constraint: G_t + B_t/P_t = τ_d(1+τ_w) W_t/P_t N_t + τ_d R_K,t/P_t Z_t K_t − τ_d δ K_t + τ_d D_t/P_t + τ_c C_t + T_t/P_t + R_t^{−1} B_t+1/P_t.
  - Log-linear fiscal rule for lump-sum taxes: t_t = φ_b b_t + φ_g g_t.
  - Government spending process: g_t = ρ_g g_t−1 + η_g,t.
- Monetary policy:
  - Nominal interest rate rule (log-linear): r_t = φ_r r_t−1 + (1−φ_r)( ̄π_t + φ_π(π_t−1 − ̄π_t) + φ_y(y_t − y*_t)) + φ_Δπ(π_t − π_t−1) + φ_Δy(y_t − y*_t − (y_t−1 − y*_t−1)) + η_r,t.
  - ̄π_t = ρ_{̄π} ̄π_{t−1} + η_{̄π,t} (time-varying inflation objective).

### Estimation approach and data
- Bayesian estimation using Metropolis-Hastings MCMC; Dynare software employed.
- Data: aggregate euro area series (real GDP, consumption, investment, employment, wage income, GDP inflation, short-term nominal interest rate).
- Sample period: 1980Q1 through 1999Q4 (1970Q1–1979Q4 used to initialize unobserved variables).
- Shocks included (ten): serially correlated ε_b,t, ε_n,t, ε_a,t, ε_i,t; serially uncorrelated cost-push η_p,t, η_w,t, η_q,t; government spending η_g,t (with ρ_g); monetary η_r,t and η_{̄π,t}.
- Fixed/calibrated values preserved exactly:
  - β = 0.99
  - α = 0.3
  - δ = 0.025
  - λ_w = 0.5
  - G/Y = 0.18
  - (B/P)/Y = 0.6×4
  - For specifications with distortionary taxes: τ_d = 0.14, τ_w = 0.45, τ_c = 0.20
- Priors highlighted:
  - Prior for ω: Beta with mean 0.5 and standard deviation 0.1.
  - Prior for φ_b: Inverted Gamma with mean 0.1 and degrees of freedom = 2.
  - Prior for φ_g: Normal with mean 0.1 and standard deviation 0.05.
  - Persistence parameters: Beta with uniform mean 0.85 and uniform standard deviation 0.1.
  - Shock conditional sds: Inverted Gamma with two degrees of freedom.

### Selected estimation results and posterior summaries
- Share of non-Ricardian households:
  - Prior mean = 0.5.
  - Posterior mean equals one-fourth or roughly one-third depending on presence of distortionary taxes.
- Preference and consumption parameters:
  - Ricardian households’ estimated intertemporal elasticity of substitution 1/ς is larger than in benchmark; close to unity in specifications with non-Ricardian households.
  - Degree of habit formation θ is significantly smaller in specifications with non-Ricardian households than in benchmark.
- Fiscal parameters:
  - Benchmark and some specifications: φ_b = 1 (periodically balanced), φ_g = 0.
  - Other specifications: posterior mean φ_b = 0.07 or 0.29 depending on distortionary taxes; posterior mean φ_g ≈ 0.12 regardless of distortionary taxes.
- Government spending shock persistence:
  - Posterior estimate ρ_g close to 0.95; impulse analysis uses ρ_g = 0.943.
- Model comparison:
  - Marginal likelihoods: none of augmented specifications with non-Ricardian households outperformed benchmark Smets-Wouters specification.

### Dynamic responses to a government spending shock (impulse experiments)
- Shock used for impulse responses:
  - Government spending shock size: 1 percent of steady-state output.
  - Persistence: ρ_g = 0.943.
- Main aggregate consumption findings:
  - Benchmark (no non-Ricardian households): aggregate consumption falls noticeably on impact and then returns gradually in a hump-shaped path.
  - Augmented specifications (I–III with non-Ricardian households): aggregate consumption falls less on impact relative to benchmark but:
    - None of the augmented specifications generates crowding-in of aggregate consumption.
    - Fiscal multiplier with respect to output does not exceed one in augmented specifications.
    - Any stronger short-lived impact effect is followed by lasting undershooting relative to benchmark consumption.
- Behavioral decomposition:
  - Non-Ricardian households: consumption increases on impact.
  - Ricardian households: consumption declines due to large negative wealth effect amplified by high persistence of government spending shocks.
  - Net effect: aggregate consumption falls less than in benchmark but does not rise; low posterior share of non-Ricardian households limits crowding-in.
- Hours, real wage and monetary reaction:
  - Hours worked increase substantially on impact; real wage rises only very little due to high wage-setting rigidity.
  - Output gap in specifications with non-Ricardian households exceeds benchmark by almost one-tenth of a percentage point.
  - Inflation effect small and comparable across specifications; more sizeable output gap leads to more pronounced monetary tightening, further depressing Ricardian consumption.

### Responses to a monetary policy shock
- Shock specification: unexpected one-quarter increase in the short-term nominal interest rate equal to 25 basis points, with monetary authority following estimated rule thereafter.
- Findings:
  - Rise in short-term nominal interest rate has a comparatively large negative impact on aggregate consumption in specifications with non-Ricardian households.
  - Initial periods see a disproportionate fall in Ricardian household consumption in specifications with non-Ricardian households.
  - Smaller estimated inverse intertemporal elasticity and lower habit increase interest-rate elasticity of consumption in these specifications.
  - Stronger decline in aggregate consumption is partially offset by a more subdued fall in investment.
  - Decrease in hours worked and the real wage is uniformly smaller in specifications with non-Ricardian households.

### Forecast-error-variance decomposition (selected)
- Shocks analyzed: η_g,t, η_b,t, η_n,t, η_w,t, η_r,t.
- Key points:
  - Contributions of selected shocks to forecast-error variance of aggregate consumption broadly similar across benchmark and non-Ricardian specifications.
  - Government spending shock contributions noticeably smaller at short horizons in specification with non-Ricardian households.
  - In short run (Panel B, lump-sum taxation specification):
    - Government spending shocks account for about 3 percent of fluctuations in consumption of non-Ricardian households, and about 0.5 percent for Ricardian households.
    - Preference shocks explain about 15 percent of variation in non-Ricardian consumption across horizons, compared to roughly 60 percent for Ricardian consumption.
    - Wage markup shocks account for more than 25 percent of short-run fluctuations in non-Ricardian households’ consumption.
  - Aggregate implication: estimated ω less than one-fourth explains limited aggregate effects and partial cancellation across household types.

### Sensitivity analysis (single-parameter variations)
- Parameters varied: ω, ρ_g, φ_b, φ_g, ξ_w, γ_w.
- Key threshold and sensitivity results:
  - ω (share of non-Ricardian households):
    - Once ω exceeds 0.35, aggregate consumption response to government spending shock becomes positive while investment response remains broadly unchanged.
  - ρ_g (persistence of government spending):
    - To generate positive aggregate consumption response, ρ_g would need to fall below 0.87.
  - φ_b (responsiveness of lump-sum taxes to debt):
    - Varying φ_b has almost no effect on instantaneous consumption response because government debt is predetermined and builds up slowly.
  - φ_g (share of government spending instantaneously financed by lump-sum taxes):
    - Lowering φ_g bolsters disposable income and consumption, but even φ_g = 0 does not produce positive impact effect.
  - Wage-setting parameters (1−ξ_w, γ_w):
    - Frequency of wage-reset permission and degree of wage indexation have negligible effects on impact responses of consumption and investment.
- Overall conclusion: only a small chance that government spending shocks crowd-in consumption or produce fiscal multiplier > 1 within the estimated DSGE framework given estimated parameter values.

### Policy implications and suggested model extensions
- Current model treats government spending as exogenous and highly persistent; fiscal rule stabilizes government debt but does not endogenize long-run debt response to persistent spending shocks.
- Suggested extensions to mitigate negative wealth effects and better match evidence:
  - Allow agents limited information about future path of exogenous government spending shocks so they must form expectations about unobserved shocks (mechanism referenced: Erceg, Guerrieri, and Gust (2003)).
  - Introduce endogenous responses of the long-run government debt-to-GDP ratio to persistent government spending shocks.
  - Consider alternative fiscal policy rules where distortionary taxes (rather than lump-sum taxes) respond to government spending and debt.

### Selected numeric parameter estimates (posterior means reported)
- Consumption and preference parameters (Table 1, specifications with non-Ricardian households):
  - ω: Benchmark 0.246; Lump-Sum Taxation 0.249; Asym. Lump-Sum Taxation 0.370
  - ς: 1.339, 1.099, 0.985, 1.101
  - θ: 0.597, 0.411, 0.412, 0.412
  - ρ_b: 0.820, 0.840, 0.847, 0.825
  - σ(η_b_t): 0.414, 0.373, 0.346, 0.386
- Labour supply and wage-setting (Table 1):
  - ζ: 2.168, 2.660, 2.638, 2.343
  - ρ_n: 0.889, 0.917, 0.904, 0.894
  - σ(η_n_t): 3.706, 3.361, 3.603, 3.628
  - ξ_w: 0.731, 0.741, 0.739, 0.747
  - γ_w: 0.711, 0.712, 0.731, 0.724
  - σ(η_w_t): 0.291, 0.296, 0.295, 0.296
- Fiscal policy parameters (Table 1):
  - φ_b: 1.000*, 0.074, 1.000*, 0.292
  - φ_g: 0.000*, 0.118, 0.000*, 0.123
  - ρ_g: 0.943, 0.947, 0.952, 0.944
  - σ(η_g_t): 0.323, 0.320, 0.318, 0.319
- Marginal likelihood (Panel D, Table 1):
  - lnL(Y_T|m): -286.10, -296.96, -295.24, -292.00
  - Note: marginal likelihood for specification with distortionary taxes but without non-Ricardian households equals 288.23 (as indicated in source).
- Additional estimation results (Table 5, selected):
  - φ: 0.418, 0.662, 0.629, 0.602
  - υ: 7.293, 7.302, 7.204, 7.386
  - ψ: 0.216, 0.215, 0.225, 0.219
  - ρ_a: 0.794, 0.875, 0.872, 0.849
  - σ(η_a_t): 0.658, 0.521, 0.526, 0.547
  - φ_r: 0.969, 0.961, 0.967, 0.964
  - φ_π: 1.700, 1.684, 1.671, 1.692

### Key quantitative values cited in text and experiments
- β = 0.99
- α = 0.3
- δ = 0.025
- λ_w = 0.5
- G/Y = 0.18
- (B/P)/Y = 0.6×4
- τ_d = 0.14; τ_w = 0.45; τ_c = 0.20 (for distortionary tax specifications)
- Prior mean ω = 0.5; prior sd = 0.1
- Prior for φ_b: Inverted Gamma with mean 0.1 and degrees of freedom = 2
- Posterior mean ρ_g ≈ 0.95; impulse-response used ρ_g = 0.943
- Government spending shock in impulse-response: 1 percent of steady-state output
- Estimated posterior mean of share of non-Ricardian households: one-fourth or roughly one-third (depending on tax specification)
- Fiscal rule form preserved: t_t = φ_b b_t + φ_g g_t
- Monetary policy rule retained exactly as specified in the main text

*Source: _wp05159 - 1. Selected Estimates for the Augmented DSGE Model of the Euro Area, pages 26–34.*

### 1. Selected Estimates for the Augmented DSGE Model of the Euro Area...................26

### 1. Selected Estimates for the Augmented DSGE Model of the Euro Area

### Selected Estimates
- Section title: "Selected Estimates for the Augmented DSGE Model of the Euro Area"
- Location: page 26

### Forecast-Error-Variance Decomposition of Consumption
- Section title: "Forecast-Error-Variance      Decomposition of Consumption"
- Location: page 27

### Prior Distributions for the Augmented DSGE Model for the Euro Area
- Section title: "Prior Distributions for the Augmented DSGE Model for the Euro Area"
- Location: page 28

### Prior Distributions for the Augmented DSGE Model for the Euro Area (cont.)
- Section title: "Prior Distributions for the Augmented DSGE Model for the Euro Area (cont.)"
- Location: page 29

### Further Estimates
- Section title: "Further Estimates for the Augmented DSGE Model of the Euro Area"
- Location: page 30

### Figures included in this unit
- Figure 1: "Selected Dynamic Responses to a Government Spending Shock" — page 31
- Figure 2: "The Responses of Monetary Policy to a Government Spending Shock" — page 32
- Figure 3: "Selected Dynamic Responses to a Monetary Policy Shock" — page 33
- Figure 4: "The Sensitivity of the Impact Multiplier to Variations in Selected Parameters" — page 34

*Source: _wp05159 - 1. Selected Estimates for the Augmented DSGE Model of the Euro Area, pages 26–34.*

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

### _wp05159 - References..............................................................................................................

### Introduction
- Purpose: assess effects of government spending shocks on private consumption within a New-Keynesian DSGE framework augmented for non-Ricardian (liquidity-constrained) households.
- Motivation: standard New-Keynesian DSGE models predict a strong negative consumption response to government spending shocks, whereas empirical literature suggests positive or non-significant negative effects (references cited in source).
- Key modeling insight: allowing coexistence of “Ricardian” (optimizing, forward-looking) and “non-Ricardian” (rule-of-thumb, consume after-tax disposable income) households can alter propagation of fiscal shocks; success depends on debt-financing, real-wage response, and fiscal rule.

### The model (extended Smets-Wouters 2003)
- Structure:
  - Four agent types: households (two types), firms, monetary authority, fiscal authority.
  - Household shares: share 1−ω are Ricardian; share ω are non-Ricardian.
  - Non-Ricardian rule: (1 + τ_c) C_j,t = (1−τ_d)(1 + τ_w) W_t/P_t N_t − T_j,t/P_t.
  - Ricardian households optimize consumption, investment, bonds B_i,t+1, capital K_i,t+1, capital utilization Z_i,t.
- Wage and price setting:
  - Calvo wage setting with probability 1−ξ_w to reset; partial indexation γ_w. Wage markup λ_w,t = λ_w + η_w,t.
  - Calvo price setting with probability 1−ξ_p to reset; partial indexation γ_p. Price markup λ_p,t = λ_p + η_p,t.
- Aggregation:
  - Aggregate variables as population-weighted sums: X_t = (1−ω) X_i,t + ω X_j,t.
  - Only Ricardian households hold bonds and capital: B_t+1 = (1−ω) B_i,t+1; K_t+1 = (1−ω) K_i,t+1.
- Fiscal authority and fiscal rule:
  - Budget constraint (real per-capita): G_t + B_t/P_t = τ_d(1+τ_w) W_t/P_t N_t + τ_d R_K,t/P_t Z_t K_t − τ_d δ K_t + τ_d D_t/P_t + τ_c C_t + T_t/P_t + R_t^{−1} B_t+1/P_t.
  - Log-linear fiscal policy rule for lump-sum taxes: t_t = φ_b b_t + φ_g g_t (t_t, b_t, g_t are log-linear counterparts of lump-sum taxes, government debt and government spending).
  - Government spending process: g_t = ρ_g g_t−1 + η_g,t.
- Monetary policy:
  - Nominal interest rate rule (log-linear): r_t = φ_r r_t−1 + (1−φ_r)( ̄π_t + φ_π(π_t−1 − ̄π_t) + φ_y(y_t − y*_t)) + φ_Δπ(π_t − π_t−1) + φ_Δy(y_t − y*_t − (y_t−1 − y*_t−1)) + η_r,t.
  - ̄π_t = ρ_{̄π} ̄π_{t−1} + η_{̄π,t} (time-varying inflation objective).

### Bayesian estimation approach and data
- Methodology:
  - Bayesian inference using Metropolis-Hastings MCMC; Dynare software employed.
  - Posterior distributions combine likelihood L(Y_T|θ,m) and priors p(θ|m).
  - Marginal likelihood L(Y_T|m) used to compare models.
- Data:
  - Aggregate euro area series: real GDP, consumption, investment, employment, wage income, GDP inflation, short-term nominal interest rate.
  - Sample period: 1980Q1 through 1999Q4 (with 1970Q1–1979Q4 used to initialize unobserved variables).
  - Real variables logged and detrended by removing individual linear trends; inflation and interest rate detrended with common linear trend.
- Shocks included (ten):
  - Serially correlated: ε_b,t, ε_n,t, ε_a,t, ε_i,t.
  - Serially uncorrelated cost-push: η_p,t, η_w,t, η_q,t.
  - Government spending shock: η_g,t (serially correlated via ρ_g).
  - Monetary shocks: η_r,t and η_{̄π,t}.
- Fixed/calibrated parameter values used in estimation:
  - β = 0.99
  - α = 0.3
  - δ = 0.025
  - λ_w (steady-state wage markup) = 0.5
  - G/Y = 0.18
  - (B/P)/Y = 0.6×4
  - For specifications with distortionary taxes: τ_d = 0.14, τ_w = 0.45, τ_c = 0.20
- Priors highlighted:
  - Prior for ω: Beta with mean 0.5 and standard deviation 0.1.
  - Prior for φ_b: Inverted Gamma with mean 0.1 and degrees of freedom = 2.
  - Prior for φ_g: Normal with mean 0.1 and standard deviation 0.05.
  - Persistence parameters: Beta with uniform mean 0.85 and uniform standard deviation 0.1.
  - Shock conditional sds: Inverted Gamma with two degrees of freedom.

### Estimation results (selected)
- Share of non-Ricardian households:
  - Prior mean = 0.5 (based on Campbell and Mankiw (1989) pre-1990 US estimate).
  - Posterior mean substantially lower: equals one-fourth or roughly one-third depending on presence of distortionary taxes.
  - Interpretation: sample 1980–1999 may reflect financial deregulation and lower market participation costs.
- Consumption preference parameters:
  - Ricardian households’ estimated intertemporal elasticity of substitution 1/ς is larger than in benchmark; close to unity in specifications with non-Ricardian households (implying lower willingness to smooth consumption).
  - Degree of habit formation θ is significantly smaller in specifications with non-Ricardian households than in benchmark.
- Fiscal parameters:
  - For benchmark and specification where non-Ricardian households are exempt from taxes: imposed periodically balanced budget φ_b = 1, φ_g = 0.
  - For remaining specifications, posterior mean of φ_b equals 0.07 or 0.29 depending on distortionary taxes; posterior mean of φ_g ≈ 0.12 regardless of distortionary taxes.
- Government spending shock persistence:
  - Posterior estimate of persistence ρ_g is close to 0.95; impulse analysis uses ρ_g = 0.943.
  - High persistence implies large negative wealth effects from government spending shocks.
- Model comparison:
  - Marginal likelihoods: none of the augmented specifications with non-Ricardian households outperformed the benchmark Smets-Wouters specification.

### Assessing the role of non-Ricardian households — dynamic responses and interpretation
- Impulse-response experiment:
  - Government spending shock size: 1 percent of steady-state output.
  - Persistence used in impulse responses: ρ_g = 0.943 (posterior mean from benchmark).
- Aggregate consumption responses:
  - Benchmark (no non-Ricardian households): aggregate consumption falls noticeably on impact and then gradually returns to steady state in a hump-shaped path.
  - Augmented specifications (I–III with non-Ricardian households): aggregate consumption falls by less on impact relative to benchmark, but:
    - None of the augmented specifications generates a crowding-in of aggregate consumption.
    - Fiscal multiplier with respect to output does not exceed one in augmented specifications.
    - Any stronger short-lived impact effect is followed by a lasting period of pronounced undershooting relative to benchmark consumption.
- Behavioral decomposition:
  - Non-Ricardian households: consumption is stimulated on impact by government spending shocks (increase on impact for non-Ricardian group).
  - Ricardian households: consumption declines due to large negative wealth effect amplified by high persistence of government spending shocks.
  - Net effect: aggregate consumption falls less than in benchmark but does not rise; low posterior share of non-Ricardian households limits crowding-in probability.
- Additional model features affecting results:
  - Inclusion of non-Ricardian households alters estimated preference parameters for Ricardian households (higher intertemporal elasticity, lower habit), partially offsetting non-Ricardian positive impact on aggregate consumption.
  - Estimated model does not generate sharp increase in real wage on impact (contrast with calibrated Galí et al. model), consistent with empirical evidence of small real-wage response.
  - Sensitivity analysis (reported elsewhere in paper) finds reasonable parameter variations have no qualitative impact on main findings.

### Key quantitative values preserved from source
- β = 0.99
- α = 0.3
- δ = 0.025
- λ_w = 0.5
- G/Y = 0.18
- (B/P)/Y = 0.6×4
- τ_d = 0.14
- τ_w = 0.45
- τ_c = 0.20
- Prior mean ω = 0.5, prior sd = 0.1
- Prior for φ_b: Inverted Gamma with mean 0.1 and degrees of freedom = 2
- Posterior mean ρ_g ≈ 0.95; impulse-response used ρ_g = 0.943
- Government spending shock in impulse-response: 1 percent of steady-state output
- Estimated posterior mean of share of non-Ricardian households: one-fourth or roughly one-third (depending on tax specification)
- Fiscal rule form: t_t = φ_b b_t + φ_g g_t
- Monetary policy rule (log-linear) as specified in main text (r_t equation retained exactly in paper)

*Source: _wp05159 - References..............................................................................................................*

### 0.5 percentage points.  However, consumption starts falling below its steady-state level already

### _wp05159 - 0.5 percentage points.  However, consumption starts falling below its steady-state level already

### Key findings
- Presence of non-Ricardian households increases the impact multiplier of government spending on consumption relative to a benchmark without non-Ricardian households, but aggregate consumption still often falls below steady state due to negative wealth effects on Ricardian households.
- When non-Ricardian households are exempted from lump-sum taxes (specification II, dashed-dotted line), the impact multiplier is considerably larger and consumption never falls below its steady-state level during adjustment.
- Introducing distortionary taxes in addition to lump-sum taxes (specification III, dotted line) cuts the impact multiplier roughly in half relative to lump-sum taxation alone, because after-tax disposable income falls further (income and pay-roll tax obligations) and a consumption tax further retrenches consumption.
- Estimated share of non-Ricardian households is relatively small (about one-quarter), which explains why aggregate effects of government spending shocks remain limited and why crowding-in of consumption is unlikely under estimated parameter values.

### Dynamic responses to a government spending shock (Figure 1 and related discussion)
- Shock specification: persistent government spending shock equal to 1 percent of steady-state output with persistence parameter ρ_g = 0.943 (benchmark).
- Consumption:
  - Aggregate consumption: under some specifications falls below steady-state after a few quarters because government debt buildup raises lump-sum taxes and crowds out consumption.
  - Consumption: Ricardian households fall on impact even further than the benchmark specification, with a somewhat faster return to steady state.
  - Consumption: Non-Ricardian households increase consumption on impact under government spending shock, but small estimated share limits aggregate effect.
- Hours worked and real wage:
  - On impact, hours worked increase substantially reflecting surge in labour demand.
  - Real wage rises only very little due to high wage-setting rigidity in the estimated model (contrast with Galí et al. (2004) which implies sharp real-wage rise).
- Monetary policy reaction (Figure 2):
  - Output gap response in specifications with non-Ricardian households exceeds benchmark by almost one-tenth of a percentage point (output gap computed relative to flexible-price and wage equilibrium).
  - Inflation effect is small and roughly comparable across specifications; real marginal cost time profiles are largely similar.
  - More sizeable output gap leads to more pronounced tightening of monetary policy in specifications with non-Ricardian households, which further depresses Ricardian consumption and dampens aggregate impact.

### Responses to a monetary policy shock (Figure 3)
- Shock specification: unexpected one-quarter increase in the short-term nominal interest rate equal to 25 basis points, with monetary authority following estimated policy rule thereafter.
- Consumption:
  - Rise in short-term nominal interest rate has a comparatively large negative impact on aggregate consumption in specifications with non-Ricardian households.
  - Initial periods: disproportionate fall in Ricardian household consumption in specifications with non-Ricardian households.
- Structural reasons:
  - Estimates of both the inverse of the intertemporal elasticity of substitution and the degree of habit formation are smaller in specifications with non-Ricardian households, increasing interest-rate elasticity of consumption.
- Investment and labor:
  - Stronger decline in aggregate consumption is partially offset by a more subdued fall in investment.
  - Decrease in hours worked and the real wage is uniformly smaller in specifications with non-Ricardian households.

### Forecast-error-variance decomposition (Table 2 summary)
- Selected shocks analyzed: government spending shock (η_gt), intertemporal preference shock (η_bt), labour supply shock (η_nt), wage markup shock (η_wt), and monetary policy shock (η_rt).
- Comparison (benchmark vs. specification with non-Ricardian households):
  - Contributions of selected shocks to forecast-error variance of aggregate consumption are broadly similar across specifications.
  - Government spending shock contributions are noticeably smaller at short horizons in the specification with non-Ricardian households (consistent with more limited crowding-out on impact).
  - Wage markup shocks show a positive, albeit small, short-run effect on aggregate consumption in the specification with non-Ricardian households (virtually zero in benchmark).
- Sub-components (Panel B, specification with lump-sum taxation):
  - In the short run, government spending shocks account for about 3 percent of fluctuations in consumption of non-Ricardian households, and about 0.5 percent for Ricardian households.
  - Preference shocks explain about 15 percent of variation in non-Ricardian consumption across horizons, compared to roughly 60 percent for Ricardian consumption.
  - Labour supply shocks contribute significantly less to non-Ricardian consumption than to Ricardian consumption.
  - Wage markup shocks account for more than 25 percent of short-run fluctuations in non-Ricardian households’ consumption.
- Aggregate implication: estimated share of non-Ricardian households less than one-fourth helps explain only fairly small aggregate effects and partial cancellation of shocks affecting households differently.

### Sensitivity analysis (Figure 4 and discussion)
- Purpose: assess whether varying single parameters (holding others at estimated values) can generate crowding-in or an overall fiscal multiplier > 1.
- Parameters varied: share of non-Ricardian households ω, persistence of government spending ρ_g, fiscal policy parameters φ_b and φ_g, and unionized wage-setting parameters ξ_w and γ_w.
- Key results:
  - Share of non-Ricardian households, ω:
    - Once ω exceeds 0.35, aggregate consumption response to government spending shock becomes positive while investment response remains broadly unchanged.
  - Persistence of government spending, ρ_g:
    - To generate positive aggregate consumption response, ρ_g would need to fall below 0.87.
    - With estimated ω ≈ one-quarter, the negative wealth effect from a persistent shock outweighs positive non-Ricardian effects and crowds out investment.
  - Fiscal policy parameters:
    - Varying responsiveness of lump-sum taxes to government debt, φ_b, has almost no effect on instantaneous consumption response because government debt is predetermined and builds up slowly.
    - Lowering φ_g (share of government spending instantaneously financed by lump-sum taxes) bolsters disposable income and consumption, but even φ_g = 0 does not produce a positive impact effect.
  - Unionized wage-setting parameters:
    - Frequency of wage-reset permission (1−ξ_w) and degree of wage indexation γ_w have negligible effects on impact responses of consumption and investment.
    - Real wage and disposable income of non-Ricardian households rise only very little if nominal wages are relatively sticky.
- Overall conclusion from sensitivity analysis:
  - Only a fairly small chance that government spending shocks crowd in consumption or produce fiscal multiplier > 1 within the estimated DSGE framework; estimated parameter values lie in regions incompatible with positive aggregate consumption response.
  - Inclusion of non-Ricardian households tilts responses in desired direction but negative wealth effect on Ricardian households remains dominant.

### Policy implications and model extensions suggested
- Current model features a detailed fiscal setup (different tax types and fiscal policy rule stabilizing government debt) but treats government spending as exogenous and highly persistent.
- Potential extensions to mitigate negative wealth effects and better match evidence:
  - Allow agents limited information about the future path of exogenous government spending shocks so they must form expectations about unobserved shocks (cited mechanism: Erceg, Guerrieri, and Gust (2003)).
  - Introduce endogenous responses of the long-run government debt-to-GDP ratio to persistent government spending shocks.
  - Consider alternative fiscal policy rules where distortionary taxes (rather than lump-sum taxes) respond to government spending and debt, in light of evidence that distortionary taxes tend to rise with lasting increases in government spending.

### Selected parameter estimates (posterior means reported)
- Parameters influencing consumption choices (Table 1, specifications with non-Ricardian households):
  - ω: Benchmark 0.246; Lump-Sum Taxation 0.249; Asym. Lump-Sum Taxation 0.370
  - ς: 1.339, 1.099, 0.985, 1.101 (values across columns)
  - θ: 0.597, 0.411, 0.412, 0.412
  - ρ_b: 0.820, 0.840, 0.847, 0.825
  - σ(η_b_t): 0.414, 0.373, 0.346, 0.386
- Labour supply and wage-setting (Table 1):
  - ζ: 2.168, 2.660, 2.638, 2.343
  - ρ_n: 0.889, 0.917, 0.904, 0.894
  - σ(η_n_t): 3.706, 3.361, 3.603, 3.628
  - ξ_w: 0.731, 0.741, 0.739, 0.747
  - γ_w: 0.711, 0.712, 0.731, 0.724
  - σ(η_w_t): 0.291, 0.296, 0.295, 0.296
- Fiscal policy parameters (Table 1):
  - φ_b: periodically balanced assumption indicated by asterisk in some specifications; values include 1.000*, 0.074, 1.000*, 0.292 across columns
  - φ_g: 0.000*, 0.118, 0.000*, 0.123
  - ρ_g: 0.943, 0.947, 0.952, 0.944
  - σ(η_g_t): 0.323, 0.320, 0.318, 0.319
- Marginal likelihood (Panel D, Table 1):
  - lnL(Y_T|m): -286.10, -296.96, -295.24, -292.00
  - Note: marginal likelihood for specification with distortionary taxes but without non-Ricardian households equals 288.23 (as indicated in source).
- Additional estimation results (Table 5, selected):
  - Technology parameters φ: 0.418, 0.662, 0.629, 0.602
  - υ: 7.293, 7.302, 7.204, 7.386
  - ψ: 0.216, 0.215, 0.225, 0.219
  - ρ_a: 0.794, 0.875, 0.872, 0.849
  - σ(η_a_t): 0.658, 0.521, 0.526, 0.547
  - Monetary policy rule parameters φ_r: 0.969, 0.961, 0.967, 0.964; φ_π: 1.700, 1.684, 1.671, 1.692

*Source: _wp05159 - 0.5 percentage points.  However, consumption starts falling below its steady-state level already*

### References

### _wp05159 - References

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*Source: _wp05159 - References*

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