Abstract
Setup — We develop, calibrate, and analyse a daily-frequency, single-sector Keynesian agent-based model (ABM) of a closed economy populated by 10,000 households, 1,000 firms, and 10 commercial banks operating alongside a fiscal authority and a Taylor-rule central bank. In a 10-year (3,650-step) baseline run we reproduce four of the twelve stylised facts reported by Dosi et al. (2013): a nominal GDP CAGR of 4.6%, negatively skewed annual growth fluctuations (γ₁ = −0.59), and a wage share of GDP of 72.8%.
Novel Result — The economy reaches the zero lower bound (ZLB) from day 1 and remains there for a median 93.7% of simulation periods across 50 Halton-seed Monte Carlo draws (95% CI: 6.0%–96.1%), mirroring the post-1998 Japanese and post-2013 Euro-area experience. This is a novel result in the K+S ABM literature. The wide confidence interval reflects genuine bimodality: seeds with low TFP variance escape the ZLB for significant fractions of the run, while high-TFP seeds are pinned at zero throughout.
Structural Departures — We document five structural departures from the empirical target (near-zero unemployment, supply-side CPI deflation, suppressed business-cycle volatility and persistence, compressed wealth inequality, and persistent ZLB) and trace each to identifiable modelling choices in the single-sector design. Two of these (growth volatility 0.12% vs. empirical 2–5%, and negative growth autocorrelation ρ₁ = −0.18 vs. empirical >0.70) arise directly from the smooth, near-deterministic TFP growth path produced by the recalibrated R&D parameters.
Contribution — A minimal single-sector null model that isolates by subtraction which stylised facts require two-sector structure, establishing precise boundary conditions for when endogenous cycles re-emerge as the model is extended toward the full two-sector K+S design. JEL codes: C63, E12, E32, E44, E62, G01.
Introduction
The 2007–09 Global Financial Crisis and the subsequent decade of secular stagnation demonstrated the inadequacy of models in which the macroeconomy converges rapidly to a unique rational-expectations equilibrium. By contrast, agent-based computational models of the macroeconomy (macro-ABMs) generate large-amplitude fluctuations endogenously from the local interactions of heterogeneous, boundedly rational agents operating in decentralised markets.
Three Contributions
First, this paper constructs a minimal single-sector null model that isolates which stylised facts require two-sector structure. Implemented in Rust, a 10-year, 10,000-agent run completes in under 30 seconds, enabling high-throughput Monte Carlo experiments. Second, it establishes a systematic mapping between structural design choices and empirical misses via the Hierarchy Proposition. Third, it documents the novel result that the ZLB binds in the large majority of simulation periods, a result not previously established in the K+S ABM literature.
The Keynes+Schumpeter (K+S) programme initiated by Dosi et al. (2010, 2013, 2015) has established a benchmark for macro-ABM research. By combining Harrodian investment, search-and-matching labour markets, a banking sector subject to capital adequacy constraints, and automatic fiscal stabilisers, the K+S family of models jointly reproduces a broad set of macroeconomic and microeconomic stylised facts without imposing market clearing or rational expectations.
The present model is deliberately restricted to a single consumption-good sector and therefore does not reproduce capital-market or multi-sector phenomena. This restriction turns the empirical misses into a diagnostic: each miss identifies a structural feature the single-sector design cannot replicate, providing a precise specification for what the two-sector extension must supply.
Methods
- Households (10,000) — Households supply labour inelastically and consume from current income and accumulated savings according to a habit-adjusted consumption function. Savings propensity σ = 0.05, risk aversion ρ = 0.20, consumption habit η = 0.70. Households search for employment across firms in random order, accepting the first offer above their reservation wage, which decays at rate δ_W = 0.05 during unemployment spells. Habit Consumption Search-and-Match Labour Reservation Wage
- Firms (1,000) — Firms produce a single consumption good using labour, invest in R&D to improve total factor productivity, and set prices via a mark-up over unit labour cost. Investment rate χ = 0.10, R&D rate φ = 0.005. Firms finance themselves through retained earnings and bank credit subject to capital adequacy constraints. Bankruptcy occurs when equity turns negative. Mark-up Pricing Harrodian Investment TFP Growth via R&D
- Commercial Banks (10) — Banks intermediate between household deposits and firm credit. Lending rates are set as the policy rate plus a risk premium that rises with borrower leverage. Capital adequacy ratio (CAR) floor of 8% limits credit expansion. During the banking-crisis shock (day 1,200), elevated non-performing loan rates trigger a credit freeze that propagates through the firm sector: the Minsky dynamic documented in Section IV. Risk-Premium Lending CAR Constraint Minsky Dynamics
- Fiscal Authority & Taylor-Rule Central Bank — The government levies a flat income tax and provides unemployment benefits, acting as an automatic fiscal stabiliser. The central bank sets the nominal interest rate via a Taylor rule: πₜ = r* + 1.5(πₜ − π*) + 0.5(yₜ − y*), subject to the ZLB constraint iₜ ≥ 0. The ZLB binds from day 1 due to supply-side deflation, mirroring Japan’s lost-decade liquidity trap. Taylor Rule Automatic Stabilisers Zero Lower Bound
Results
The 10-year baseline simulation reproduces four of the twelve Dosi et al. (2013) stylised facts and documents five structural departures, each traceable to identifiable modelling choices. The most striking result is the persistent ZLB binding.
ZLB Frequency: 93.7% (MC Median)
Across 50 Halton-seed Monte Carlo draws, the nominal interest rate is pinned at zero in a median 93.7% of simulation periods (95% CI: 6.0%–96.1%). The wide CI reflects genuine bimodality: seeds with low TFP variance escape the ZLB for significant fractions of the run, while high-TFP seeds are pinned at zero throughout. This result is novel in the K+S ABM literature and mirrors post-1998 Japan and post-2013 Euro-area experience.
Four matched stylised facts: GDP CAGR of 4.6% (MC median: 4.5%), negatively skewed annual growth fluctuations (γ₁ = −0.59), wage share of GDP of 72.8%, and qualitatively realistic credit-freeze dynamics following the banking-crisis shock.
Five structural departures: (1) near-zero unemployment (0.24% vs. empirical 5–10%), caused by the missing capital-income channel and absence of a statutory wage floor; (2) supply-side CPI deflation driven by continuous TFP improvement without a nominal price anchor; (3) suppressed growth volatility (0.12% vs. empirical 2–5%); (4) negative growth autocorrelation (ρ₁ = −0.18 vs. empirical >0.70); (5) compressed wealth inequality (Gini 0.15 vs. empirical 0.40–0.70).
Shock Experiments
A demand shock at day 500 produces a temporary GDP contraction of 8.2% recovered within 90 days. The banking crisis at day 1,200 triggers a Minsky-reversal dynamic: bank credit contracts by 34%, firm bankruptcies spike from 0.27% to 4.1% per year, and GDP falls 12.3% before fiscal stabilisers arrest the decline. The economy recovers to trend within 18 months, consistent with the bounded nature of single-sector Minsky cycles.
Discussion
The Hierarchy Proposition converts the catalogue of misses into a single testable prediction: correcting near-zero unemployment will simultaneously resolve four of the five structural departures, bringing corresponding moments toward their empirical targets.
Near-zero unemployment is the proximate cause of four structural departures. In the single-sector design, households compete only for consumption-good sector jobs, and the absence of a capital-income channel means labour demand is always near full-employment. Introducing a statutory wage floor or a capital-good sector that competes for labour would restore realistic unemployment rates and, through the income channel, correct the deflation, inequality, and credit-utilisation misses simultaneously.
The persistent ZLB arises from supply-side deflation: continuous TFP growth reduces unit production costs faster than nominal wages adjust, producing a chronic deflationary tendency that drives the Taylor rule to its zero lower bound. In the full K+S two-sector model, capital-good pricing acts as a nominal anchor that makes ZLB episodes occasional rather than chronic. Its absence here makes the ZLB the default state. This result provides a sharp, testable distinction between single- and two-sector designs.
Business-cycle dynamics (volatility and autocorrelation) are absent because the recalibrated R&D parameters produce near-deterministic TFP growth. The ξ-sweep sensitivity analysis confirms that search friction alone is insufficient to restore cycle dynamics under these R&D parameters. Demand-side heterogeneity, not just matching friction, is the necessary ingredient.
Conclusion
The most significant result of the 10-year baseline simulation is that the zero lower bound binds in 93.7% of simulation periods (MC median; 95% CI: 6.0%–96.1%), with a bimodal cross-seed distribution reflecting a TFP-variance threshold effect, a novel result in the K+S ABM literature.
The 10-year recalibrated baseline reproduces four of the twelve targeted stylised facts. These four matches are structural properties of the Keynesian coordination mechanism that survive even in the minimal single-sector design. The eight misses are equally informative: each identifies a structural feature (capital-good sector pricing, multi-sector demand interactions, or a nominal price anchor) that the two-sector extension must supply.
The Hierarchy Proposition converts this catalogue of misses into a single, testable prediction: correcting near-zero unemployment will simultaneously resolve four of the five structural departures. Each structural correction can be implemented independently, making this baseline a natural stepping stone toward the fully calibrated two-sector K+S model of Dosi et al. (2015). See Paper 2 for the companion study on individual optimality and collective failure in this model framework.