## _wp13141

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### Empirical evidence (SVAR: identification, sample, and main impulse responses)
- Sample and variables:
  - Quarterly US data over the period 1954q1–2007q4.
  - Baseline endogenous vector: log real per-capita government consumption expenditures; log real per-capita output; average marginal tax rate (Barro and Redlick (2011)); log real per-capita private lending; bank spread (BPLR minus quarterly Treasury bill rate).
  - Exogenous controls: constant, linear trend, lags zero to four of the Ramey-Shapiro (RS) dummy variables (RS quarters: 1965q1; 1980q1; 2001q3).
  - Choleski ordering (main): (i) government spending; (ii) output; (iii) average marginal tax rate; (iv) private lending; (v) bank spread.
- Shock normalization and horizon:
  - Shock: positive government consumption shock of size 1% of real output.
  - Horizon: 20-quarter impulse responses reported.
- Main SVAR results:
  - Real output: hump-shaped increase, peak multiplier of about 1.75 after two years and a half.
  - Private lending: statistically significant boost, peak of almost 5 percent after three years.
  - Bank spread: declines by around 50 basis points on impact; reaches a negative peak of 70 basis points after two years.
  - Private consumption: significantly crowded in by government consumption, peaking after two years.
  - Private investment: falls on impact and then experiences significant crowding-in, peaking after two years and a half.
  - Hours worked and real wage: positive responses (hours worked has an insignificant negative in quarter 2), statistically significant after a few quarters; real wage becomes significant more quickly.
  - Price mark-up: reacts negatively to the fiscal stimulus, with the drop significant at longer horizons.
- Robustness checks (Appendix A):
  - Substituting average marginal tax rate with net taxes: responses virtually indistinguishable.
  - Adding inflation and Federal Funds rate: bank spread still falls; at peak its reduction is more pronounced though initial impact is smaller.
  - Purified (unanticipated) innovations using SPF/Greenbook forecasts: slight upward shift in lending confidence band; impact multiplier for output somewhat higher; bank spread falls more at peak with wider confidence interval.
  - Using forecast errors as unanticipated shocks: government spending response more persistent; peak output multiplier bigger; lending and bank spread responses considerably amplified (wide confidence bands).

### Theoretical framework (RBC model with lending relationships and deep habits)
- Agents and key modeling features:
  - Households: save via bank deposits, supply labor; preferences include external deep habits at the level of each variety of goods.
  - Government: allocates government purchases across varieties; government consumption exhibits deep habits and the government runs a balanced budget (government spending set equal to lump-sum taxes).
  - Entrepreneurs/firms: borrow from banks to finance investment and wages; borrowing subject to deep-habit lending relationships (reduced-form hold-up representation).
  - Banks: choose deposits and loan rates to maximize expected discounted profits; loan demand exhibits deep-habit persistence.
  - Final goods firms: monopolistic competition; price/mark-up behavior interacts with deep habits.
- Core modeling devices:
  - Deep habits in private consumption, government consumption, and lending (external habit formulation).
  - Financing constraint for entrepreneurs: ∫_0^1 L_e bt db ≥ I_e t + W_t H_e t (holds with equality in equilibrium).
  - Log-linear state-space solution: ŝ_{t+1} = Φ_1 ŝ_t + Φ_2 ε_{t+1}; 𝑑̂_t = Φ_3 ŝ_t.

### Parameterization and steady-state targets (selected numeric values)
- Quarterly parameter values:
  - β = 0.99.
  - δ = 0.025.
  - σ = 1.38.
  - ω calibrated to match steady-state hours H = 0.44.
  - σ_x = 0.5.
  - ν_x set to target G/Y = 0.20.
  - α = 0.6.
  - θ = 0.86 (deep habits in consumption).
  - ρ = 0.85 (consumption habit persistence).
  - θL = 0.72 (deep habits in lending).
  - ρL = 0.85 (persistence of lending relationships).
  - ρG = 0.97 (persistence of government spending).
  - γ = 5.74 (investment adjustment cost parameter).
  - η set to target μ = 1.20 (implies η ≈ 8 given baseline θ and θL).
  - ηL set to target R_L − R_D = 0.0075 (implies ηL ≈ 425 given baseline θ and θL).
- Steady-state ratios implied:
  - Consumption-output ratio ≈ 60%.
  - Private investment-output ratio ≈ 20%.

### Model-implied responses to a 1% of output government consumption shock (selected quantitative findings)
- Fiscal multiplier and real variables:
  - Impact model-implied fiscal multiplier (response of output) ≈ 1.8.
  - Output hump and timing: investment peak delayed by a few quarters due to adjustment costs; consumption and labor responses shaped by deep habits and mark-up dynamics.
- Price mark-up and labor:
  - Deep habits generate a fall in the price mark-up (mark-up counter-cyclical) via intra-temporal and inter-temporal effects; the fall raises labor demand more than labor supply, boosting investment demand.
- Financial market responses:
  - Loan demand shifts outward (higher labor and investment financing needs); deposit supply also shifts outward due to increased saving.
  - With investment adjustment costs, supply effects dominate and loan and deposit rates fall.
  - Lending relationships lead banks to value future profits and expand lending by sacrificing current profits; loan rate falls more than deposit rate.
  - Bank spread decreases:
    - Model predicts a fall in bank spread of around 35 basis points (less than peak observed in the data).
    - Surge in lending of around 4% (in line with VAR estimates).
  - Model reproduces empirical signs and some amplitudes but not the pronounced VAR hump shape.

### Financial-accelerator mechanism and role of lending relationships
- Key comparative results:
  - θL = 0 (no lending relationships): borrower hold-up absent; bank spread remains constant by construction; financial-accelerator channel absent.
  - θL > 0: lending-relationship frictions induce a financial accelerator; higher θL increases banks’ willingness to expand lending and lower loan rates in response to fiscal stimulus.
- Numerical sensitivity:
  - Increasing θL from baseline 0.72 to 0.82 increases the impact fall of the bank spread from 35 basis points to almost 70 basis points.
  - Stronger θL → greater lending, larger increases in investment and hours, and larger expansion in output.
- Interaction with deep habits:
  - For any given positive θL, the impact response of the bank spread declines as θ increases.
  - When both θ and θL are large, combined effects produce a stronger drop in the bank spread and larger real responses.

### Sensitivity to model features and persistence parameters
- Deep habits in consumption (θ) vs. no deep habits (θc = θg = 0):
  - With θ = 0: price mark-up remains constant; negative wealth effect dominates → consumption, investment, and real wage fall; output rises less.
  - Absence of deep habits weakens supply shifts in deposit and loan markets; bank spread fall smaller.
- Investment adjustment costs (γ) vs. no costs:
  - γ = 0: immediate investment adjustment; non-hump-shaped investment; loan and deposit rates increase (loan-demand outward shift dominates).
  - γ > 0: supply-side effects can dominate; rates fall; lending-relationship mechanism still yields bank spread decline.
- Persistence of deep habits (ρ) and lending relationships (ρL):
  - ρ = 0 (one-quarter habit): negative impact responses of price mark-up substantially magnified; responses strong and short-lived; higher ρ reduces impact amplification and prolongs propagation.
  - ρL = 0 (one-quarter lending relationship): fall in bank spread substantially magnified because locking-in occurs only in first quarter; lower ρL produces higher lending response via stronger spread reduction.
  - Sign of impact responses robust to choices of ρ and ρL; magnitudes affected.
- Complementarity between private and government consumption (σx):
  - As σx → 0 (Leontief) crowding-in of private consumption stronger; as σx → 1 (Cobb–Douglas) crowding-in weaker.
  - Lower σx amplifies macro responses while preserving signs.
- “Useless” government consumption (νx = 1):
  - When public consumption does not enter utility, signs unchanged but magnitudes smaller, notably for private consumption and mark-up fall; lending and bank spread similar qualitatively.

### New Keynesian extension: price stickiness and monetary policy
- Price stickiness:
  - Rotemberg-style quadratic price adjustment cost with parameter ξ; flexible-price analog recovered when ξ = 0.
  - ξ = 41.18 corresponds approximately to a Calvo average contract duration of around 3 quarters for calibration.
- Monetary policy (Taylor rule and Fisher equation):
  - Taylor rule: log(Rn t / ̄R n) = ρr log(Rn t−1 / ̄R n) + (1−ρr)[ρπ log(Πt / ̄Π) + ρy log(Yt / ̄Y)].
  - Fisher equation: 1 + RD t+1 = Et[Rn t Πt+1].
  - Posterior Smets and Wouters (2007b) values used in scenarios: ρr = 0.81, ρπ = 2.04, ρy = 0.08.
- Quantitative outcomes under NK extension:
  - For empirically plausible deep habit formation and price stickiness, consumption and investment crowding-ins, decline in the mark-up, increase in the real wage, size of the output multiplier, and responses of private lending and bank spread are quite robust to introducing price stickiness.
  - Strong monetary reaction to the output gap (e.g., ρy = 0.5) can offset fiscal expansion: nominal interest falls less relative to inflation, possibly producing smaller fall or an increase in the real interest rate for high ξ; investment may be crowded-out and lending/spread responses attenuated though sign preserved.
  - Combination of high ξ, strong ρy, and “useless” public consumption can notably reduce fiscal effectiveness though empirical posterior estimates of ρy are typically low (around ρy = 0.08).

### Policy implications, conclusions, and suggested extensions
- Empirical-conceptual synthesis:
  - SVAR evidence indicates bank spreads respond negatively and lending increases following fiscal expansions.
  - An RBC model with a banking sector and lending relationships reproduces these patterns and generates a financial accelerator: fiscal shocks improve loan market conditions, amplifying real activity.
- Policy relevance:
  - Lending-relationship amplification matters in normal times and becomes especially relevant during tight credit conditions with lending shortages and high borrowing costs.
  - Fiscal stimulus can increase lending availability to firms, reinforcing real economic expansion.
- Suggested future research:
  - Perform a Bayesian estimation of the DSGE model to validate key features and provide DSGE-based estimates of lending-relationship parameters.
  - Extend the analysis to other advanced economies (e.g., the euro area, Japan, the UK) to identify potential country-specific effects.

*Source: _wp13141 — References, Section IV (RBC model results), Section V (disentangling model features), and Appendices (robustness and sensitivity exercises) from the provided PDF content.*

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

### References

### Major themes and research questions
- Role of fiscal policy when monetary policy faces the zero lower bound and the crisis is long-lasting.
- Empirical relevance of credit market conditions and lending relationships for business cycle dynamics.
- How a government spending expansion affects lending and the bank spread.
- Transmission of fiscal shocks within an economy featuring lending relationships.
- Modeling lending relationships via deep habits in borrowing and external deep habit formation in consumption.

### Empirical findings (SVAR estimates and related evidence)
- The estimated impulse responses from the SVAR provide evidence that:
  - "the bank spread significantly falls in response to a government spending expansion"
  - "lending increases"
- Empirical literature cited on credit spreads and downturns: evidence that credit spreads widen during downturns (references include Gertler and Lown, 1999; Aliaga-Diaz and Olivero, 2010, 2011; Villa and Yang, 2011).
- Hold-up effects and lending relationships:
  - Santos and Winton (2008) empirically show that during recessions banks raise the bank spread more for bank-dependent borrowers than for those with access to public bond markets; "the increase in the bank spread due to the informational hold up effect reaches 95 basis points in US data."
  - Petersen and Rajan (1994) estimate that in the US loan market the average duration of lending relationships is "11 years."
  - European evidence: "average lending relationship durations are in the order of 10 years" in countries such as Italy, Belgium and Norway (Angelini et al., 1998; Degryse and Van Cayseele, 2000; Kim et al., 2003).

### Theoretical contributions (RBC model with lending relationships)
- Model features and mechanisms:
  - Introduces lending relationships into an RBC framework by modeling firms' deep habits in borrowing decisions (following the device used by Ravn et al. (2006) for consumption).
  - Households and the government feature external deep habit formation.
  - Public goods enter households’ utility with a degree of complementarity with private goods.
- Main theoretical findings:
  - "a fiscal stimulus becomes more effective if increasingly stronger lending relationships are present in the loan market."
  - Government spending expansion curbs the bank spread and boosts lending, fostering better credit market conditions that generate second-round expansionary effects on economic activity.
  - The mechanism constitutes a "financial accelerator effect" in the transmission of the fiscal shock.
- Modeling justification:
  - Deep habits in lending are an effective and tractable representation of the borrower’s hold-up problem without explicitly formalizing asymmetric information.
  - Aksoy et al. (2013, Appendix) show that in the symmetric equilibrium, the bank’s profit margin under an adverse selection formulation is equivalent to the profit margin under deep habits in lending.

### Comparative and literature context
- The paper fills a gap by:
  - Estimating responses of lending and the bank spread to government spending expansions in a Structural Vector-Autoregressive (SVAR) model of the US economy.
  - Developing a Real Business Cycle (RBC) model with lending relationships that can (i) match empirical findings and (ii) provide a theoretical framework for transmission via banks with long-lasting lending relationships.
- Relation to prior DSGE literature:
  - Existing DSGE work with credit frictions (e.g., Fernández-Villaverde, 2010; Canzoneri et al., 2012; Carrillo and Poilly, 2013) studies stabilization properties of fiscal policy but does not specifically focus on lending relationships and their effect on loan market conditions.
  - Aliaga-Diaz and Olivero (2010) previously introduced lending relationships into an RBC model focusing on countercyclical bank spreads as a financial accelerator for technology shocks.
  - Aksoy et al. (2013) examine lending relationships in NK models with staggered prices and cost channels, relevant for monetary policy analysis.

### Model validation and empirical linkage
- The paper uses SVAR impulse responses to guide model calibration and to assess whether the RBC model with lending relationships can match the sign and magnitude of key responses to government spending shocks.
- Representative data/sample details and shock sizing appearing in figures and tables:
  - Figure 1: "Estimated Impulse Responses from the SVAR over Sample 1954q1–2007q4 to a Shock to Government Consumption Expenditure of Size 1% of Real Output"
  - Figures and appendices perform robustness checks and sensitivity exercises (e.g., robustness of SVAR results, sensitivity to deep habits parameters, sticky versus flexible price comparisons).

### Key statistics and exact numeric values cited in the text
- "95 basis points" — increase in the bank spread due to the informational hold up effect in US data (Santos and Winton, 2008).
- "11 years" — average duration of lending relationships in the US loan market (Petersen and Rajan, 1994).
- "in the order of 10 years" — average lending relationship durations reported for some European countries (Angelini et al., 1998; Degryse and Van Cayseele, 2000; Kim et al., 2003).
- SVAR sample and shock size explicitly referenced: "1954q1–2007q4" sample and a shock "of Size 1% of Real Output."

*Content unit: _wp13141 - References (excerpt including Introduction and contents list).*

### Section IV discusses the results in the RBC model. Section V disentangles the effects of some model

### _wp13141 - Section IV discusses the results in the RBC model. Section V disentangles the effects of some model

### Empirics (SVAR evidence and identification)
- Sample and variables:
  - Quarterly US data over the period 1954q1-2007q4.
  - Baseline vector of endogenous variables: the log of real per-capita government consumption expenditures; the log of real per-capita output; the average marginal tax rate (Barro and Redlick (2011)); the log of real per-capita private lending; the bank spread (BPLR minus quarterly Treasury bill rate).
  - Additional variables added one at a time: log real per-capita private consumption; log real per-capita private domestic investment; log per-capita hours of work; log real hourly wage; price mark-up.
- Exogenous controls and anticipation:
  - Exogenous variables: constant, linear trend, and lags zero to four of the Ramey-Shapiro (RS) dummy variables (RS quarters: 1965q1; 1980q1; 2001q3).
  - Anticipation effects addressed via inclusion of RS episodes and robustness checks; also using Auerbach and Gorodnichenko (2012) method with forecasts to purify government spending shocks.
- Identification:
  - Structural representation obtained via Choleski triangularization.
  - Main Choleski ordering used (robustness checks with alternative orderings produced negligible differences as long as government spending ordered first): (i) government spending; (ii) output; (iii) average marginal tax rate; (iv) private lending; (v) bank spread.
- SVAR impulse-response results to a positive government consumption shock of size 1% of real output (20-quarter horizon):
  - Real output: hump-shaped increase, peak multiplier of about 1.75 after two years and a half.
  - Private lending: statistically significant boost, peak of almost 5 percent after three years.
  - Bank spread: declines by around 50 basis points on impact; reaches a negative peak of 70 basis points after two years.
  - Private consumption: significantly crowded in by government consumption, peaking after two years.
  - Private investment: falls on impact and then experiences significant crowding-in, peaking after two years and a half.
  - Hours worked and real wage: positive responses (hours worked has an insignificant negative in quarter 2), statistically significant after a few quarters (real wage becomes significant more quickly).
  - Price mark-up: reacts negatively to the fiscal stimulus, with the drop significant at longer horizons.
- Estimation details and data sources (as used in this paper):
  - GDP, GDP deflator, interest rates, private consumption, investment, lending from ALFRED (Federal Reserve Bank of St. Louis).
  - Government consumption from NIPA tables (Bureau of Economic Analysis).
  - Per-capita hours of work from Francis and Ramey (2009).
  - Real hourly wage: average hourly wage of production workers in manufacturing (BLS).
  - Private lending: sum of total credit market instruments for nonfarm nonfinancial corporate business and noncorporate business (Christiano et al., 2013 approach).
  - Price mark-up computed as log ratio between national income without capital consumption adjustment in manufacturing and wage and salary disbursements in manufacturing (Monacelli and Perotti, 2008).
  - Series transformed to real per-capita and seasonally adjusted by source where appropriate.

### DSGE model: agents, key mechanisms, and motivations
- Agents and markets:
  - Households: consume, save via bank deposits, supply labor; preferences include deep habits at the level of each variety of goods.
  - Government: allocates government purchases over varieties of consumption goods; raises lump-sum taxes; government consumption exhibits deep habits.
  - Entrepreneurs (firms): borrow from banks to produce wholesale output sold in a perfectly competitive market; minimize borrowing costs and exhibit deep habits in lending; maximize discounted profits choosing factors of production and investment.
  - Final good firms: purchase wholesale good, differentiate it, and sell in monopolistically competitive market.
  - Banks: choose deposits and loan rates to maximize expected discounted lifetime profits; balance sheet with loans (assets) and deposits (liabilities).
- Central modeling features:
  - Deep habits in private consumption, government consumption, and lending (external habit formulation is used).
  - Lending relationships and borrower hold-up effects represented via deep-habit formulation in loans (reduced-form approach capturing informational asymmetries).
  - Financing constraint for entrepreneurs: total loans must finance investment and wage bill (ˆ1 0 L_e bt db ≥ I_e t + W_t H_e t), implying firms borrow to finance investment and wages (constraint holds with equality in equilibrium).
  - Resource constraint: Y_t = C_t + I_t + G_t.

### Households (formal setup and first-order conditions)
- Intertemporal utility (representative household) with deep habits:
  - U_j0 = E_0 ∑_{t=0}^∞ β^t [U(X_jt, 1−H_jt)] with β∈(0,1).
  - Consumption composite X_t j = [ (X_c t)^j , (X_g t) ] includes habit-adjusted differentiated private and public consumption goods.
- Deep-habit consumption aggregator for private varieties i∈(0,1):
  - (X_c t)^j = [ ∫_0^1 (C_jit − θ S_c it−1)^{1−1/η} di ]^{1/(1−1/η)}.
  - Habit stock S_c it evolves as S_c it = ρ S_c it−1 + (1−ρ) C_it.
- First-order conditions (representative household):
  - U_j X_c t = λ_j t.
  - E_t[Λ_j t+1 (1+R_D t+1)] = 1.
  - −U_j Ht = λ_j t W_t.
- Budget constraint (real terms) and definitions preserved as in the model text.

### Government (preferences, habits, fiscal rule)
- Government consumption aggregator with deep habits:
  - X_g t = [ ∫_0^1 (G_it − θ S_g it−1)^{1−1/η} di ]^{1/(1−1/η)}; habit stock S_g it evolves as S_g it = ρ S_g it−1 + (1−ρ) G_it.
- Aggregate real government consumption follows AR process:
  - log(G_t / ̄G) = ρ_G log(G_t−1 / ̄G) + ε_g t, with ε_g t i.i.d. mean zero, standard deviation σ_G.
- Government runs a balanced budget: government spending set equal to lump-sum taxes.

### Entrepreneurs and lending relationships
- Intratemporal loan composition problem (deep habits in lending):
  - Minimize ∫_0^1 (1+R_L bt) L_e bt db subject to loan-composite aggregator with deep habits (parameters θ_L, ρ_L, η_L).
  - Demand for loans from bank b: L_e bt = ( (1+R_L bt)/(1+R_L t) )^{−η_L} (X_L t)^e + θ_L S_L bt−1.
- Intertemporal profit maximization with financing constraint:
  - Max E_t ∑ Λ_{t,t+s} { Φ_{t+s} F(K,H) − W H − I + (X_L)^e − ∫_0^1 (1+R_L bt) L_e bt db + Ξ_e } subject to capital law of motion and ∫_0^1 L_e bt db ≥ I + W H.
- First-order conditions include:
  - Φ_t F_H,t = W_t E_t[Λ_{t,t+1} (1+R_L t)].
  - Q_t = E_t Λ_{t,t+1} [Φ_{t+1} F_K,t+1 + Q_{t+1} (1−δ)].
  - Euler-like condition equating marginal borrowing cost for investment to marginal benefit net of adjustment costs.

### Final goods firms and mark-ups
- Final good firm profit maximization over differentiated product i leads to first-order conditions tying prices, marginal cost, and habit-related multipliers:
  - P_it / P_t − MC_t + (1−ρ) λ_c t = ν_c t, etc.
- In symmetric equilibrium:
  - p_it = 1 and mark-up μ_it = p_it / MC_t = 1 / MC_t (mark-up is inverse of marginal cost).

### Banking sector (objectives and optimality)
- Bank optimization:
  - Max E_t ∑ Λ_{t,t+s} { D_bt+s+1 − L_bt+s+1 + (1+R_L bt+s) L_bt+s − (1+R_D t+s) D_bt+s } subject to L_bt = D_bt and bank-specific loan demand with deep habits.
- First-order conditions:
  - ν_bt = E_t Λ_{t,t+s} [ (R_L bt+1 − R_D t+1) + ν_bt+1 θ_L (1−ρ_L) ].
  - E_t[Λ_{t,t+s} L_bt+1] = ν_bt η_L E_t[X_L t+1].
- Interpretation: shadow value of lending equals spread benefit plus expected future profits from hold-up; optimal loan-rate sets marginal benefit equal to marginal cost.

### Equilibrium, linearization, and solution form
- Resource constraint: Y_t = C_t + I_t + G_t.
- Log-linear state-space solution (Blanchard-Kahn procedure):
  - ŝ_{t+1} = Φ_1 ŝ_t + Φ_2 ε_{t+1}.
  - 𝑑̂_t = Φ_3 ŝ_t.
  - ŝ_t includes predetermined and exogenous variables; 𝑑̂_t contains control variables; ε_t includes all random disturbances.
- Appendix provides full equilibrium conditions and deterministic steady state derivation.

### Functional forms and parameter choices (selected numerical values)
- Preference and production functional forms:
  - Utility: U(X_t, 1−H_t) = [ X_t^ω (1−H_t)^{1−ω} ]^{1−σ} / (1−σ).
  - Investment adjustment costs: S(I_t / I_{t−1}) = γ/2 (I_t / I_{t−1} − 1)^2.
  - Production: F(H_t, K_t) = H_t^α K_t^{1−α} (Cobb-Douglas).
  - Consumption composite: CES aggregate of private and public deep-habit-adjusted consumption X_t = { ν_x^{1/σ_x} (X_c t)^{(σ_x−1)/σ_x} + (1−ν_x)^{1/σ_x} (X_g t)^{(σ_x−1)/σ_x} }^{σ_x/(σ_x−1)}.
- Key parameter values (quarterly model):
  - β = 0.99.
  - δ = 0.025.
  - σ = 1.38 (coefficient of relative risk aversion).
  - ω set to match steady-state hours of work equal to 0.44.
  - σ_x = 0.5 (elasticity of substitution between private and public component).
  - ν_x set to match a government share of output of 20%.
- Notes:
  - Section V examines sensitivity to degrees of complementarity between private and public consumption and other robustness checks.
  - The appendix contains additional robustness checks, analysis disentangling effects of non-standard modeling features on the DSGE results, a New Keynesian extension with price stickiness and monetary policy, and the full set of equilibrium conditions and steady-state derivation.

*Source: _wp13141 - Section IV discusses the results in the RBC model. Section V disentangles the effects of some model*

### appendix shows also the case in which public consumption does not deliver any utility to households.

### _wp13141 - appendix shows also the case in which public consumption does not deliver any utility to households.

### Model parameterization
- Production function parameter: α = 0.6.
- Consumption deep-habit parameters: θ = 0.86 and ρ = 0.85.
- Deep-habit parameters in lending relationships: θL = 0.72 and ρL = 0.85.
- Sensitivity analysis reported for a wide range of θ, ρ, θL, and ρL.
- Persistence of government spending shocks: ρG = 0.97.
- Parameter in the investment adjustment cost function: γ = 5.74.
- Elasticity of substitution across varieties set to target steady-state gross mark-up: η set to target μ = 1.20 (implies η ≈ 8 given baseline θ and θL).
- Elasticity of substitution in the banking sector set to target bank spread: ηL set to target R_L − R_D = 0.0075 (implies ηL ≈ 425 given baseline θ and θL).
- Resulting steady-state ratios implied by parameter choices:
  - Consumption-output ratio ≈ 60%.
  - Private investment-output ratio ≈ 20%.

Table 1: Parameter choice (selected entries)
- Discount factor β = 0.99
- Capital depreciation rate δ = 0.025
- Risk aversion σ = 1.38
- Elast. of subst. in consumption composite σx = 0.5
- Production function parameter α = 0.6
- Deep habits in consumption θ = 0.86
- Consumption habit persistence ρ = 0.85
- Deep habits in lending θL = 0.72
- Pers. of lending relationships ρL = 0.85
- Persistence of government spending ρG = 0.97
- Elasticity of investment adjustment costs γ = 5.74
- Share of private component in consumption composite νx set to target G/Y = 0.20
- Preference parameter ω set to target H = 0.44
- Elasticity of substitution η set to target μ = 1.20
- Elast. of subst. in banking ηL set to target R_L − R_D = 0.0075

### Impulse responses to a government spending shock (main results)
- Shock normalized to a government consumption expenditure of size 1% of real output.
- At impact the model-implied fiscal multiplier (response of output) ≈ 1.8.
- Mechanisms driving responses:
  - Expansionary government spending generates a negative wealth effect (resources absorbed by government) that tends to reduce consumption and leisure and stimulate labor supply.
  - Deep habits in private and government consumption produce a fall in the price mark-up (mark-up is counter-cyclical) driven by:
    - An intra-temporal (price-elasticity) effect: higher habit-adjusted aggregate demand raises the weight of price-elastic demand and increases effective price elasticity.
    - An inter-temporal effect: firms lower current mark-ups to lock in consumers for higher future mark-ups.
  - The fall in the mark-up raises labor demand more than labor supply and increases demand for investment; investment adjustment costs delay the investment peak by a few quarters.
  - Increased real wage induces substitution away from leisure toward consumption, generating crowding-in of private consumption.
- Financial market responses:
  - Demand for loans by firms shifts outward due to higher labor and investment financing needs; supply of deposits also shifts outward due to increased saving from forward-looking agents.
  - With investment adjustment costs, supply effects dominate and both loan and deposit rates fall.
  - Lending relationships lead banks to factor in high future returns and expand lending by sacrificing current profits; loan rate falls more than deposit rate.
  - Bank spread decreases; model predicts:
    - Fall in bank spread of around 35 basis points (less than the peak observed in the data).
    - Surge in lending of around 4% (in line with VAR estimates).
  - The model reproduces the sign and, to some extent, the amplitude of empirical impulse responses though not the pronounced hump shape seen in the VAR.

### Financial accelerator effect (role of lending relationships)
- If θL = 0: borrower hold-up effect absent and bank spread remains constant (lending-relationship frictions removed).
- If θL > 0: model exhibits a financial accelerator effect; higher θL increases banks' willingness to expand lending and lower loan rates in response to fiscal stimulus, amplifying lending and reducing the bank spread.
- Numerical illustration:
  - Increasing θL from baseline 0.72 to 0.82 increases the impact fall of the bank spread from 35 basis points to almost 70 basis points.
- Consequence: stronger θL → greater lending, larger increases in investment and hours, and larger expansion in output. Lending relationships therefore make fiscal policy more effective by improving loan market conditions.

### Effects of some model features (comparative experiments)
- Deep habits in private and government consumption (θ ≠ 0) vs. no deep habits (θc = θg = 0):
  - With θ = 0 (no deep habits) the price mark-up remains constant; negative wealth effect dominates → consumption, investment, and real wage fall; output rises less than proportionally.
  - Absence of deep habits weakens supply shifts in deposit and loan markets; deposit and lending rates increase; bank spread still falls due to lending relationships but with much smaller amplification and at odds with empirical magnitudes.
- Investment adjustment costs (γ > 0) vs. no costs (γ = 0):
  - With γ = 0 firms adjust investment immediately; investment not hump-shaped.
  - Without adjustment costs, loan and deposit rates increase (loan-demand outward shift dominates); with adjustment costs supply-side effects prevail and rates fall.
  - In both cases the lending-relationship mechanism yields a fall in the bank spread consistent in sign with evidence.
- Complementarity between private and government consumption (σx parameter):
  - As σx → 0 (Leontief), private and public consumption are perfect complements and private consumption is more strongly crowded in by fiscal stimulus.
  - As σx → 1 (Cobb–Douglas), goods are imperfect substitutes and crowding-in is weaker.
  - Lower σx amplifies the magnitude of macroeconomic responses while preserving signs.
- Robustness and sensitivity notes from the appendix:
  - A sufficiently large degree of deep habits in consumption is needed to match empirical signs of impulse responses.
  - Positive degrees of lending relationships produce qualitatively robust results; they mainly affect magnitudes of financial variables.
  - Persistence of deep habits (in consumption and lending) affects magnitude and timing but not the sign of impulse responses.
  - A utility-enhancing government spending (as opposed to “useless” government consumption) amplifies the crowding-in effect on private consumption.
  - Main results hold under an extension to a New Keynesian framework with flexible prices assumption being harmless.

### Policy implications and conclusions
- A SVAR on US post-WWII data suggests bank spreads respond negatively and lending increases following fiscal expansions.
- An RBC model with a banking sector incorporating lending relationships reproduces these empirical patterns and exhibits a financial accelerator: fiscal shocks improve loan market conditions, which amplifies real activity.
- Policy relevance:
  - The lending-relationship amplification is important in normal times and becomes more relevant during tight credit conditions characterized by lending shortages and high borrowing costs.
  - Fiscal stimulus can increase lending availability to firms, reinforcing real economic expansion.
- Suggested avenues for future research:
  - Perform a Bayesian estimation of the DSGE model to validate key features and to provide DSGE-based estimates of lending-relationship parameters (currently estimated with single-equation methods).
  - Extend analysis to other advanced economies (e.g., the euro area, Japan, the UK) to identify potential country-specific effects.

*Source: _wp13141 - appendix shows also the case in which public consumption does not deliver any utility to households.*

### References

### _wp13141 - References

### References (bibliographic list)
- Comprehensive list of cited works across themes: fiscal policy, monetary policy, DSGE and SVAR modeling, financial intermediation, deep habits in consumption, lending relationships, fiscal multipliers, and empirical macroeconomic methods.
- Includes seminal and recent contributions such as Akerlof (1970); Barro and Redlick (2011); Blanchard and Perotti (2002); Bernanke, Gertler, and Gilchrist (1999); Caldara and Kamps (2008); Galí et al. (2007); Gertler and Kiyotaki (2010); Monacelli and Perotti (2008); Ramey (2011a, 2011b); Smets and Wouters (2007a, 2007b); Woodford (2011); and many others.
- Topics covered by references include: the market for “lemons”, measuring output responses to fiscal policy, fiscal policy in general equilibrium, the financial accelerator, availability and cost of credit for small businesses, deep habits, lending relationships, SVAR and VAR-based analyses of fiscal shocks, and estimated DSGE approaches.

### Appendix A — Robustness of SVAR results
- Objective:
  - Perform sensitivity checks on the SVAR results with focus on private lending and the bank spread responses to a government spending expansion.
  - Responses depicted to a government spending shock of size one percent of output.
- Alternative specifications analyzed (summarized findings):
  1. Substitution of the average marginal tax rate with net taxes
     - Net taxes defined as total government revenues net of transfers and interest payments.
     - Use of net taxes vs. average marginal tax rate: responses of variables of interest to a government consumption shock are "virtually indistinguishable" across specifications in both mean responses and confidence intervals (Panel (a) of Figure A.1).
  2. Introduction of the inflation rate and the Federal Funds rate (FFR)
     - Inflation computed as first difference of the log of the consumer price index (CPI). Both CPI and FFR taken from the ALFRED database of the St. Louis Fed.
     - Adding inflation and FFR to the SVAR does not materially alter government spending, real output and lending responses, but affects the dynamic response of the bank spread:
       - Bank spread still significantly falls; on impact it reacts less, but at peak its reduction is more pronounced (Panel (b) of Figure A.1).
       - Inflation and FFR initially fall and then significantly increase.
     - Section C of the Appendix extends the DSGE model to take monetary response into account explicitly.
  3. Purified (unanticipated) innovations in government spending using SPF/Greenbook forecasts
     - Uses Survey of Professional Forecasters (SPF) and Greenbook forecasts for government spending; Greenbook available 1966 to 2004, SPF for GDP since 1968 and government spending since 1982. Authors splice Greenbook and SPF to construct a continuous forecast series from 1966 to present.
     - Including the forecast growth rate of real government purchases (forecast for timet) treats an innovation orthogonal to the forecast as a purified unanticipated government spending shock.
     - Including this variable reduces the sample by 12 years (first 12 years lost).
     - Effects (Panel (c) of Figure A.1):
       - Slight upward shift in the confidence band of lending response.
       - Impact multiplier for real output somewhat higher; peak multiplier somewhat lower.
       - Bank spread falls more at peak but with wider confidence interval.
       - Overall signs and average magnitudes remain similar to baseline.
  4. SPF/Greenbook forecast errors for growth rate of government spending as unanticipated shocks
     - Forecast error computed as spliced Greenbook/SPF forecast minus first-release actual series of government spending growth rate.
     - Interpreting innovations in this forecast error as unanticipated shocks yields:
       - Signs of impulse responses preserved (Panel (d) of Figure A.1).
       - Government spending response becomes more persistent.
       - Peak output multiplier becomes bigger.
       - Responses of lending and bank spread are considerably amplified; confidence band for bank spread very wide with statistical significance only at longer horizons.
- Visualization and inference:
  - Figure A.1 shows baseline (bold lines; shaded 90% confidence bands) and alternative specifications (dashed lines; dotted-line confidence bounds). Note: shaded areas and areas within the two dotted lines represent 90% confidence intervals in the baseline and the alternative specifications, respectively.

### Appendix B — Sensitivity exercises for the DSGE model
- Objective:
  - Disentangle effects of model features and analyze robustness of main DSGE results.
  - Focus on parameters capturing degree of deep habits in consumption (θ) and degree of lending relationships (θL), their persistence, and the case when public consumption does not provide utility to households.
- Subsection 1 — Degree of deep habits (θ) and lending relationships (θL)
  - Baseline remaining parameters set as in Table 1 of the paper.
  - Results summarized from Figure B.1 (impact responses to a government spending expansion):
    - When θL = 0 (no lending relationships):
      - Impact response of the bank spread is zero at any value of θ (spread constant by construction).
    - When θ = 0 and θL > 0:
      - Bank spread falls after an expansionary government spending shock.
    - For any given positive θL:
      - The impact response of the bank spread declines as θ increases.
    - When both θ and θL become large:
      - Two effects combine to produce a stronger drop in the bank spread:
        - Stronger countercyclical movements in the price mark-up due to stronger deep habit formation in consumption, boosting demand for labor and investment and hence lending.
        - Stronger lending relationships that make banks’ future profits relatively more valuable than current profits.
    - Price mark-up behavior explains why real wage and consumption responses:
      - Are negative for low θ but turn positive for higher θ when the increase in labor demand exceeds the rise in labor supply.
    - Quantitative examples from the figure text:
      - When deep habits and lending relationships are both off, the value of the impact output multiplier is about 0.8.
      - Higher θ increases the output multiplier for any given θL due to the fall in the price mark-up.
      - Stronger θL also raises the output multiplier, via a negative effect on the bank spread that expands lending.
      - Overall, the degree of deep habits in consumption dominates the magnitude of the impact output multiplier.
- Subsections 2 and 3
  - Subsection 2: analyzes sensitivity to persistence parameters of deep habits and lending relationships (details summarized in the main text; parameter persistence examined).
  - Subsection 3: explores robustness when public consumption does not provide utility to households (details summarized in the main text).

*Source: _wp13141 - References (appendix material and bibliographic references) from the provided PDF content.*

### 2.   Persistence of deep habits in consumption and of lending relationships

### 2.   Persistence of deep habits in consumption and of lending relationships

### Sensitivity to persistence parameters (ρ and ρL)
- Analysis uses impulse responses for the first 20 quarters to assess sensitivity to:
  - persistence in deep habits in consumption, ρ;
  - persistence of lending relationships, ρL.
- Key findings on variation in ρ:
  - When ρ = 0 (deep habits last for only one quarter), the negative impact responses of the price mark-up are substantially magnified.
  - With ρ = 0 final good firms reduce the price mark-up to a greater extent to lock in customers, exploiting variety-level habits only in the first quarter; mark-up quickly returns to steady state thereafter.
  - The real wage response mirrors the price mark-up response when ρ = 0 because the stimulus on labor demand is strongest in the first quarter and quickly dies out.
  - Demand for investment, lending, and the bank spread follow the same rationale (stronger, short-lived first-quarter responses when ρ = 0).
  - Increasing ρ (higher persistence of habits) leads to:
    - lower amplification of consumption at impact;
    - greater duration of the propagation mechanism of a government spending expansion.
- Key findings on variation in ρL:
  - When ρL = 0 (lending relationships last only one quarter), banks seek to exploit lending relationships to a large extent; the fall in the bank spread is substantially magnified because locking-in new bank-to-firm customers occurs only in the first quarter.
  - Lower ρL (shorter persistence) produces a higher response of lending due to a stronger reduction in the bank spread (subfigure B.3c).
  - The price mark-up is barely affected by different degrees of persistence in lending relationships.
  - Hence changes in real variables when ρL increases are smaller than the corresponding changes when ρ increases.
- Robustness statement:
  - The sign of the impact responses of variables to a government spending shock is robust to any choice of the persistence parameters ρ and ρL, while the magnitude of responses is affected.

### Quantitative implications of a “useless” government consumption (νx = 1)
- Experiment compares baseline model (public consumption in utility) versus restricted model with public consumption delivering no utility (νx = 1).
- Shock: a government spending expansion of 1% of output.
- Findings:
  - The sign of impact responses is unchanged by whether public consumption enters the utility function, but magnitudes change, notably for private consumption.
  - When public consumption is useless to households (νx = 1):
    - the increase in public consumption does not directly affect households’ first-order conditions;
    - the effect of deep habits in both private and public consumption is reduced;
    - the price mark-up falls by less;
    - the expansion exerts a lower impact on labor demand;
    - the crowding-in effect on private consumption is weaker (though still present).
  - Private lending and the bank spread show similar qualitative behavior across the two specifications, with some quantitative differences.

### New-Keynesian (NK) extension: sticky prices and monetary policy
- Price stickiness specification:
  - Introduced as in Rotemberg (1982) with quadratic price adjustment costs ξ 2 (Pit/Pit−1 − 1)2 Yt; parameter ξ measures price stickiness.
  - Profit function and price first-order condition are adjusted accordingly; pricing equation collapses to flexible-price analog when ξ = 0.
- Monetary policy:
  - Taylor rule: log(Rn t / ̄R n) = ρr log(Rn t−1 / ̄R n) + (1−ρr)[ρπ log(Πt / ̄Π) + ρy log(Yt / ̄Y)] (equation C.4).
  - Fisher equation: 1 + RD t+1 = Et[Rn t Πt+1] (equation C.5).
  - Posterior Smets and Wouters (2007b) parameter values used in scenarios: ρr = 0.81, ρπ = 2.04, ρy = 0.08.
- Quantitative findings from NK extension:
  - Prior literature (Woodford 2011; Jacob 2010) shows sticky prices can enhance or alter fiscal effects; with deep habits, price stickiness softens fiscal expansion effects.
  - In this model, for empirically plausible deep habit formation and price stickiness:
    - consumption and investment crowding-ins, decline in the mark-up, increase in the real wage, size of the output multiplier, and responses of private lending and the bank spread are quite robust to introducing price stickiness;
    - price stickiness per se does not subvert the effects of a government spending expansion.
- Scenarios illustrated in Figure C.1 (government spending expansion = 1% of output):
  - (a) “Standard” Taylor rule (ρy = 0.08), explore ξ values:
    - ξ = 41.18 corresponds to a Calvo contract average duration of around 3 quarters for the calibration.
    - For increasing ξ the rise in demand for loans is less pronounced and the fall in the bank spread is softened; aggregate effects remain similar to flexible-price case.
  - (b) Taylor rule with strong reaction to output gap (ρy = 0.5):
    - Strong monetary response to output gap offsets fiscal expansion more; nominal interest rate falls less relative to inflation, producing a smaller fall or even an increase in the real interest rate for high ξ.
    - For high ξ and ρy = 0.5, investment can be crowded-out and the real wage can fall; rise in lending and fall in bank spread are less pronounced but sign preserved.
    - Presence of government spending in utility helps preserve private consumption response and output multiplier relative to prior literature.
  - (c) Strong reaction to output gap (ρy = 0.5) and “useless” government consumption (νx = 1):
    - Combination of reduced fiscal expansion effectiveness, high ξ, and strong monetary reaction can lead to crowding-out of consumption driven by positive reaction of the real interest rate.
    - Fall in the bank spread and rise in lending and output remain present but smaller quantitatively.
    - Empirical note: posterior estimates of ρy are typically low (around ρy = 0.08); optimal-policy literature often finds weak long-run response of interest rate to output gap (examples: ρy = 0.1, and values close to zero in Cantore et al. (2012b)).

### Model structure and steady-state relationships (summary of key equations and steady-state identities)
- Production: F(Ht, Kt) = Ht α Kt 1−α; marginal products F K,t = (1−α) Yt / Kt; F H,t = α Yt / Ht.
- Utility and deep habits:
  - U(Xt, 1−Ht) = [Xt ω (1−Ht) 1−ω] 1−σ / (1−σ).
  - Xt defined as CES aggregator of Xc t and Xg t with parameter νx and σx (equation D.5).
  - Habit stock Sc t evolves: Sc t = ρ Sc t−1 + (1−ρc) Ct; aggregate private consumption Ct = Xc t + θ Sc t−1.
  - First-order condition linking marginal utilities and real wage: −U Ht = U Xc t Wt.
- Investment and Tobin’s Q:
  - Kt+1 = (1−δ) Kt + It [1 − S(It/It−1)], with adjustment cost S((It/It−1)) = γ/2 (It/It−1 − 1)2.
  - Qt defined by expected discounted marginal value (equation D.13).
- Lending, banks, and spreads:
  - Loan demand: Lt = It + Wt Ht.
  - Lending stock and persistence: SL t = ρL SL t−1 + (1−ρL) L t; aggregate lending Lt = XL t + θL SL t−1; deposits D t = L t.
  - νt defined by expected discounted return on lending and continuation value (equation D.22).
  - Spread = RL t − RD t.
- Final good firms’ pricing conditions include marginal cost MCt, mark-up terms νc t, νg t, and multiplier λ terms (equations D.25–D.28).
- Resource constraint (sticky-price model) includes price-adjustment cost term ξ 2 (Πt − 1)2 Yt.
- Steady-state solution summary (Appendix E highlights):
  - Λ = β; RD = 1/β − 1; I = δK; Y = K 1−α H α; G = (G/Y) Y; Π = 1.
  - Expressions for Q, RL, ν, spread, wage W, and other steady-state variables provided as algebraic relationships (equations E.1–E.28).

*Source: _wp13141 - 2.   Persistence of deep habits in consumption and of lending relationships*

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