Banque Nationale De Belgique Sa · EURONEXT:BNB
Banque Nationale De Belgique Sa — Reg A Offering (November 2025)
52 slides from Banque Nationale De Belgique Sa's offering presentation, Nov 27, 2025
Slide 1: The Aggregate and Distributional Consequences of Large Monetary and Fiscal Policy Interventions
The Aggregate and Distributional Consequences of Large Monetary and Fiscal Policy Interventions in the Face of Large Shocks Greg Kaplan University of Chicago, e61 Institute and NBER Ken Miyahara University of Chicago National Bank of Belgium 27 November 2025
Slide 2: Recent Macroeconomic Dynamics
Recent Macroeconomic Dynamics Real GDP, Consumption (relative to 2010-19 trend) Primary Deficit Consolidated Federal Liabilities 1.05 .68 .2 1 1 .98 .66 .15 .95 .96 .64 .1 .9 .94 .62 .05 .85 .92 .8 .6 0 .9 2018q1 2019q1 2020q1 2021q1 2022q1 2023q1 2024q1 2018q1 2019q1 2020q1 2021q1 2022q1 2023q1 202
Slide 3: HANK Model with State-Dependent Pricing
HANK Model with State-Dependent Pricing • Quantitative model to interpret aggregate dynamics after large shocks and large policy • How would prices and output have evolved under different policy responses? • Alternative financing and design of fiscal transfers • Alternative monetary policy responses •
Slide 4: Outline
Outline 1. Model 2. Calibration 3. Simple Policy Experiments: HA vs RA, SD vs TD Large Fiscal Stimulus Non-Ricardian Effects of Fiscal Stimulus Interest Rate Hike 4. Quantitative Experiment 5. Policy Counterfactuals 6. Welfare Effects 7. Conclusions 8. Additional Slides 2 Kaplan and Miyahara (2025)
Slide 5: Households
Households • Continuum of infinitely lived households, j ∈ [0, 1] maximize: ∫ ∞ 1+ 1 −ρt Etc hjt ν max E0 e e log cjt − ψ dt subject to t=0 1 + ν1 dAjt = [it Ajt + ωjt hjt Wt + Pt djt − Pt τjt − Pt cjt ] dt Ajt ≥ 0, Aj0 , ωj0 given • Individual j variables at time t : • cjt : real consumption
Slide 6: Overview of Production Structure
Overview of Production Structure 1. Intermediate goods producers • Produce intermediate good I with labor L and materials M 2. Retailers • Differentiate intermediate goods I into varieties of retail goods yj • Set prices pj subject to adjustment costs 3. Final goods producers • Combine varieties yj
Slide 7: Final Goods Producers
Final Goods Producers • Representative firm aggregates varieties of retail goods yj , j ∈ [0, 1] into final good Y Z Z 1 ϵ−1 ϵ ϵ−1 max Pt Yt − pjt yjt dj subject to Yt = (ζjt yjt ) ϵ dj yjt ,Yt j 0 ζjt : demand shifter for variety j ϵ : elasticity of substitution between varieties • Demand for retail
Slide 8: Retail Firms
Retail Firms • Monopolistic retailer for each variety j ∈ [0, 1] • Purchase intermediate goods Ij on competitive market at price PI • Differentiate into variety j , with production function Ij,t yj,t = zj,t zj,t : idiosyncratic productivity shock • Set price pj,t subject to price-setting frictions,
Slide 9: Retailer Price Setting Problem
Retailer Price Setting Problem • Firms exert effort to increase rate of arrival λ of free opportunities to adjust κt (λ) = (γ0 λ)1+γ1 γ0 , γ 1 > 0 • Assumption: idiosyncratic demand shocks equal to productivity shocks: ζjt = zjt Geometric Brownian motions independent across firms: d log ζjt = d log z
Slide 10: Intermediate Goods Firms
Intermediate Goods Firms • Representative firm produces intermediate good I with labor L and final goods YI max PI,t It − Wt Lt − Pt Mt Lt ,Mt ,It subject to It = e Et Lαt Y Mt1−α Z ⇒ 1 − α governs strategic complementarity in price setting • Exogenous disturbance EtZ : productivity shock • Intermedia
Slide 11: Fiscal Policy
Fiscal Policy • Tax and transfer function applied to real household labor and profit income Tt (x) = ς1,t x − ς0,t ς1,t : proportional labor tax rate ς0,t : lump sum transfer • Fiscal stimulus programs: ∫ • Type-specific transfers: ετt (a, ω) ⇒ Etτ = τ j εt (aj,t , ωj,t )dj • Unvalued government consu
Slide 12: Government Debt
Government Debt • Government issues nominal long-term perpetuities: • Exponentially declining coupons at rate: δb • Qt : time t market price of bond with coupon 1 • Btδ : quantity of such bonds outstanding at time t • it : nominal interest rate on short-term (instantaneous) debt BtS • No-arbitrage c
Slide 13: Monetary Policy
Monetary Policy • Monetary authority sets short-term nominal interest rate it : 1. Baseline: exogenous path of rates and forecasts {it+τ }τ ≥0 at each t 2. Alternative: Taylor-type rules • Fisher equation relates real and nominal rates: rt = it − πt 11 Kaplan and Miyahara (2025)
Slide 14: Equilibrium Definition
Equilibrium Definition Given Such that • Initial distributions: µh0 (a, ω), µf0 (x) • Household optimize: ct (a, ω), ht (a, ω) solve household problem • Initial government bonds B0δ , B0S • Retailers optimize: λt (x), xt∗ solve retailer price-setting problem • Paths of dividend functions Dt • Aggrega
Slide 15: Outline
Outline 1. Model 2. Calibration 3. Simple Policy Experiments: HA vs RA, SD vs TD Large Fiscal Stimulus Non-Ricardian Effects of Fiscal Stimulus Interest Rate Hike 4. Quantitative Experiment 5. Policy Counterfactuals 6. Welfare Effects 7. Conclusions 8. Additional Slides 12 Kaplan and Miyahara (2025)
Slide 16: Steady State Parameters
Steady State Parameters • Households • Income process λω,ω′ : from Nikolakoudis, Kaplan and Violante (2024) • Frisch elasticity of labor supply ν = 1.0 • Discount factor ρ: match consolidated federal liablities b = 88% × annual GDP • Labor disutility ψ : match average hours = 1 in steady-state • Pro
Slide 17: Steady State: Parameters of Pricing Model
Steady State: Parameters of Pricing Model • Three parameters: 1. κ : effort cost of changing prices 2. γ : curvature of effort cost function 3. σ 2 : variance of idiosyncratic shocks • Three moments: 1. Frequency of price changes: 10% per month Nakamura, Steinsson, Sun, Villar (2018) 2. Absolute siz
Slide 18: Steady State: Household Wealth and Spending
Steady State: Household Wealth and Spending • Mean wealth: 88% × Y GDP (targeted) • Share of hand-to-mouth households: 26% • Median wealth: 20% × Y GDP (not targeted) • Average quarterly MPC out of $500: 23% 15 Kaplan and Miyahara (2025)
Slide 19: Steady State: Price Setting
Steady State: Price Setting • Optimal return point higher than static optimum: optimal return point to right mostly because of asymmetric profit function from CES not inflation drift • Asymmetric adjustment hazard for large shocks: more adjustment for inflation than deflation 16 Kaplan and Miyahara (202
Slide 20: Outline
Outline 1. Model 2. Calibration 3. Simple Policy Experiments: HA vs RA, SD vs TD Large Fiscal Stimulus Non-Ricardian Effects of Fiscal Stimulus Interest Rate Hike 4. Quantitative Experiment 5. Policy Counterfactuals 6. Welfare Effects 7. Conclusions 8. Additional Slides 16 Kaplan and Miyahara (2025)
Slide 21: Outline
Outline 1. Model 2. Calibration 3. Simple Policy Experiments: HA vs RA, SD vs TD Large Fiscal Stimulus Non-Ricardian Effects of Fiscal Stimulus Interest Rate Hike 4. Quantitative Experiment 5. Policy Counterfactuals 6. Welfare Effects 7. Conclusions 8. Additional Slides 16 Kaplan and Miyahara (2025)
Slide 22: State-Dependent Pricing Matters for Large Shocks
State-Dependent Pricing Matters for Large Shocks • Uniform increase in lump-sum transfers • Exponential decay with half-life of two quarters • Cumulative payout of 13% of steady-state debt • Unfunded: financed entirely through inflation • Non-linear Calvo model 17 Kaplan and Miyahara (2025)
Slide 23: Heterogeneous Agent Matters for Large Shocks
Heterogeneous Agent Matters for Large Shocks Inflation Annualized (%) Price Level (relative to steady-state inflation) 1.15 30 Heterogeneous agents, state-dependent pricing Heterogeneous agents, Calvo pricing Representative agent, state-dependent pricing Representative agent, Calvo pricing 1.1 20 He
Slide 24: How Big is Big?
How Big is Big? Cumulative First Year GDP Response (relative to steady-state) Average First Year Inflation Response (% p.a.) 20 .08 15 .06 10 .04 5 .02 State Dependent Pricing State Dependent Pricing Calvo Pricing Calvo Pricing 0 0 0 2 4 6 8 10 12 14 16 0 2 4 6 8 10 12 14 16 Size of Transfer (% stea
Slide 25: Outline
Outline 1. Model 2. Calibration 3. Simple Policy Experiments: HA vs RA, SD vs TD Large Fiscal Stimulus Non-Ricardian Effects of Fiscal Stimulus Interest Rate Hike 4. Quantitative Experiment 5. Policy Counterfactuals 6. Welfare Effects 7. Conclusions 8. Additional Slides 19 Kaplan and Miyahara (2025)
Slide 26: Fiscal Policy Adjustments
Fiscal Policy Adjustments • Outside steady-state: govt keeps track of two budgets: unfunded btu and funded btf bt = btu + btf 1. Unfunded btu : debt backed only by surpluses raised from steady state tax function (regular surpluses) In steady-state: b¯u = b̄ Outside steady-state: [ ( )] dbtu = rt btu
Slide 27: Fiscal Policy Adjustments
Fiscal Policy Adjustments • Outside steady-state: govt keeps track of two budgets: unfunded btu and funded btf bt = btu + btf 1. Unfunded btu : debt backed only by surpluses raised from steady state tax function (regular surpluses) In steady-state: b¯u = b̄ Outside steady-state: [ ( )] dbtu = rt btu
Slide 28: Large Failures of Ricardian Equivalence
Large Failures of Ricardian Equivalence Heterogeneous Agents: Real GDP (relative to steady-state) Heterogeneous Agents: Inflation Annualized (%) Heterogeneous Agents: Price Level (relative to steady-state inflation) 1.15 1.1 30 Unfunded Unfunded 10% funded 10% funded 90% funded 90% funded 25 1.08 Fu
Slide 29: Outline
Outline 1. Model 2. Calibration 3. Simple Policy Experiments: HA vs RA, SD vs TD Large Fiscal Stimulus Non-Ricardian Effects of Fiscal Stimulus Interest Rate Hike 4. Quantitative Experiment 5. Policy Counterfactuals 6. Welfare Effects 7. Conclusions 8. Additional Slides 21 Kaplan and Miyahara (2025)
Slide 30: Stepping on a Rake: Effects of an Interest Rate Hike
Stepping on a Rake: Effects of an Interest Rate • Unexpected 500bp increase in nominal rate with half-life of 2 quarters • Long-term debt is essential for a rate hike to lower inflation: with short-term debt inflation increases • Not due to HA vs RA or SD vs TD, rather due to assumption of no fiscal con
Slide 31: Outline
Outline 1. Model 2. Calibration 3. Simple Policy Experiments: HA vs RA, SD vs TD Large Fiscal Stimulus Non-Ricardian Effects of Fiscal Stimulus Interest Rate Hike 4. Quantitative Experiment 5. Policy Counterfactuals 6. Welfare Effects 7. Conclusions 8. Additional Slides 22 Kaplan and Miyahara (2025)
Slide 32: Our Exercise
Our Exercise • Two series of exogenous shocks, starting in 2020Q2: • Productivity in intermediate goods production EtZ : pandemic effects on supply chains • Household utility of consumption Etc : pandemic effects on spending • Two types of policy responses • Fiscal stimulus: multiple rounds of targe
Slide 33: Fiscal Stimulus Program
Fiscal Stimulus Program Government Outlays .25 .2 .15 .1 .05 0 2018q1 2019q1 2020q1 2021q1 2022q1 2023q1 2024q1 Transfers Govt Consumption Subsidies • Transfers: Uniform to bottom 60% of wealth dist • Subsidies : Treat as govt consumption • Information: Unanticipated each quarter • Financing: Baseli
Slide 34: Monetary Policy Response
Monetary Policy Response Forecasts of Federal Funds Rate 6 4 2 0 2019q1 2020q1 2021q1 2022q1 2023q1 2024q1 2025q1 2026q1 2027q1 2028q1 • Actual and forecasted paths for Fed Funds Rate per FOMC Summary of Economic Projections • Quarterly shocks to forecasted path of nominal rates • Adjust long-run so
Slide 35: Exogenous Shocks
Exogenous Shocks Real GDP (relative to 2010-19 trend) Inflation (%, Annualized) 10 1 .98 5 .96 .94 0 .92 Data Data: CPI Model Model -5 .9 2019q1 2020q1 2021q1 2022q1 2023q1 2024q1 2025q1 2026q1 2019q1 2020q1 2021q1 2022q1 2023q1 2024q1 2025q1 2026q1 • Quarterly unexpected innovations: exponential de
Slide 36: Implied Shock Series and Forecasts
Implied Shock Series and Forecasts Consumption Utility Shocks Productivity Shocks .06 0 .04 -.1 .02 -.2 0 -.3 Realization Realization Forecasts Forecasts -.02 -.4 2019q1 2020q1 2021q1 2022q1 2023q1 2024q1 2025q1 2026q1 2027q1 2028q1 2019q1 2020q1 2021q1 2022q1 2023q1 2024q1 2025q1 2026q1 2027q1 2028
Slide 37: Historical Decomposition
Historical Decomposition • Offsetting effects of shocks and policy but strong interaction: importance of non-linear model 28 Kaplan and Miyahara (2025)
Slide 38: How Well Does the Model Capture Relevant Micro Dynamics?
How Well Does the Model Capture Relevant Micro Dynamics? Monthly Probabilty of Price Change (%) Increase in Median Household Wealth (%) 16 40 Positive Changes Negative Changes 14 Total 12 30 10 20 8 6 10 4 2 0 0 2019q1 2020q1 2021q1 2022q1 2023q1 2024q1 2025q1 2026q1 2019q1 2020q1 2021q1 2022q1 2023
Slide 39: Outline
Outline 1. Model 2. Calibration 3. Simple Policy Experiments: HA vs RA, SD vs TD Large Fiscal Stimulus Non-Ricardian Effects of Fiscal Stimulus Interest Rate Hike 4. Quantitative Experiment 5. Policy Counterfactuals 6. Welfare Effects 7. Conclusions 8. Additional Slides 29 Kaplan and Miyahara (2025)
Slide 40: How Would Economy Have Evolved Without Policy Responses?
How Would Economy Have Evolved Without Policy Responses? Real GDP (relative to 2010-19 trend) Inflation (%, Annualized) Price Level (relative to trend) 1.05 15 1.15 10 1 1.1 5 .95 1.05 0 .9 1 -5 .85 -10 .95 Baseline Baseline Baseline -15 No Fiscal or Monetary No Fiscal or Monetary No Fiscal or Monet
Slide 41: How Would Economy Have Evolved Without Policy Responses?
How Would Economy Have Evolved Without Policy Responses? Real GDP (relative to 2010-19 trend) Inflation (%, Annualized) Price Level (relative to trend) 1.05 1.15 15 10 1 1.1 5 .95 1.05 0 .9 1 -5 .85 Baseline Baseline Baseline -10 .95 No Fiscal or Monetary No Fiscal or Monetary No Fiscal or Monetary
Slide 42: How Would Economy Have Evolved Under Different Fiscal Financing?
How Would Economy Have Evolved Under Different Fiscal Financing? Real GDP (relative to 2010-19 trend) Inflation (%, Annualized) Price Level (relative to trend) 1.15 15 1 10 .95 1.1 5 .9 1.05 0 .85 -5 1 Baseline (Unfunded) Baseline (Unfunded) Baseline (Unfunded) .8 -10 Funded Fiscal Stimulus (Lump Tra
Slide 43: What if Fed Had Responded Earlier to Inflation Surge?
What if Fed Had Responded Earlier to Inflation Surge? Nominal Interest Rate (%, Annualized) Real GDP (relative to 2010-19 trend) Inflation (%, Annualized) 1.05 15 6 5 10 4 1 5 3 0 2 .95 -5 1 -10 Baseline Baseline Baseline 0 Earlier Rate Hike Earlier Rate Hike Earlier Rate Hike Earlier and Longer Rate
Slide 44: Outline
Outline 1. Model 2. Calibration 3. Simple Policy Experiments: HA vs RA, SD vs TD Large Fiscal Stimulus Non-Ricardian Effects of Fiscal Stimulus Interest Rate Hike 4. Quantitative Experiment 5. Policy Counterfactuals 6. Welfare Effects 7. Conclusions 8. Additional Slides 33 Kaplan and Miyahara (2025)
Slide 45: Equivalent Variation Asset Transfers
Equivalent Variation Asset Transers • ∆(a, ω): equivalent variation associated with combined policy response, and in each in isolation V0base (a, ω) = V0nopol (a + ∆ (a, ω), ω) where "Z 1 ! # ∞ −ρt EtC hbase (at , ωt )1+ ν V0base (a, ω) = Ebase 0 e e log ctbase (at , ωt ) − ψ t dt a, ω t=0 1 + ν1 •
Slide 46: Asset Equivalent Variation Across Wealth Distribution
Asset Equivalent Variation Across Wealth Distribution Welfare Effects of Policy Intervention by Percentile (Equivalent Variation) 40 20 0 $ Thousands Fiscal Policy (with shocks) -20 Fiscal Policy (no shocks) Monetary Policy (with shocks) -40 Monetary Policy (no shocks) -60 -80 -100 0 20 40 60 80 100
Slide 47: Outline
Outline 1. Model 2. Calibration 3. Simple Policy Experiments: HA vs RA, SD vs TD Large Fiscal Stimulus Non-Ricardian Effects of Fiscal Stimulus Interest Rate Hike 4. Quantitative Experiment 5. Policy Counterfactuals 6. Welfare Effects 7. Conclusions 8. Additional Slides 35 Kaplan and Miyahara (2025)
Slide 48: HANK with State-Dependent Pricing
HANK with State-Dependent Pricing • Modern macro models offer insight into monetary and fiscal interventions in wake of Covid • Appropriate model: heterogeneous households and state-dependent pricing • Large shocks: important to study non-linear economy • Spending response to targeted fiscal stimulus
Slide 49: Outline
Outline 1. Model 2. Calibration 3. Simple Policy Experiments: HA vs RA, SD vs TD Large Fiscal Stimulus Non-Ricardian Effects of Fiscal Stimulus Interest Rate Hike 4. Quantitative Experiment 5. Policy Counterfactuals 6. Welfare Effects 7. Conclusions 8. Additional Slides 36 Kaplan and Miyahara (2025)
Slide 50: Household Spending and Wealth ⇒ Heterogeneous Agents
Household Spending and Wealth ⇒ Heterogeneous Agents • Evidence on MPCs: (i) quarterly average ≈ 25%; (ii) heterogeneity by wealth • Nature of covid stimulus: (i) direct transfers to households; (ii) targeted to low-income • Cash balances: (i) large increases particularly at low incomes; (ii) persis
Slide 51: Firm Price Setting ⇒ State Dependent Pricing
Firm Price Setting ⇒ State Dependent Pricing • Frequency of price changes: ≈ 10% • Kurtosis of price changes: ≈ 3 ⇒ cumulative price response to small money injections in simple models Alvarez and Lippi (2016) • Aggregate conditions: frequency of prices adjustment doubled during inflation surge 10 9
Slide 52: HANK Model with State-Dependent Pricing
HANK Model with State-Dependent Pricing • Heterogeneous households and incomplete markets • Consistent with micro evidence on household spending • Allows to study targeted transfers • Break Ricardian equivalence: extent and timing of financing • Allows to study a steady-state with budget deficits • Av
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