Methodology

1. Model Overview

CrashLab implements a stock-flow consistent agent-based macroeconomic model (SFC-ABM) following the research tradition of Delli Gatti et al. (2011), Caiani et al. (2016), and the "Macroeconomics from the Bottom-up" framework.

Key Characteristics

• Heterogeneous agents: Each household and firm is a distinct entity with individual state variables
• Bounded rationality: Agents use simple adaptive rules, not rational expectations
• Disequilibrium: Markets may not clear; quantities adjust alongside prices
• Emergent dynamics: Macro patterns (business cycles, unemployment) emerge from micro interactions
• Stock-flow consistency: All financial flows are tracked; one agent's asset is another's liability

Model Architecture

┌─────────────────────────────────────────────────────────────────┐
│                        EconSim Core                             │
├─────────────────────────────────────────────────────────────────┤
│  AGENTS                                                         │
│  • Households (N=1M)    — workers, consumers, savers            │
│  • Firms (N=50K)        — producers, employers, investors       │
│  • Government (N=1)     — fiscal authority                      │
│  • Banks (N=3)          — credit intermediaries                 │
├─────────────────────────────────────────────────────────────────┤
│  MARKETS                                                        │
│  • Labor market         — decentralized matching, wage posting  │
│  • Goods market         — price competition, inventory buffers  │
│  • Credit market        — working capital, investment loans     │
├─────────────────────────────────────────────────────────────────┤
│  TIME STEP: 1 month (18 phases per step)                        │
└─────────────────────────────────────────────────────────────────┘

2. Agent Specification

2.1 Households

Each household h ∈ {1, ..., H} is characterized by:

Consumption Decision

Household consumption follows a linear rule with wealth draw:

where $Y_h$ is total income (wages + dividends + landlord profits + transfer payments). The 2% wealth draw prevents indefinite wealth accumulation.

2.2 Firms

Each firm f ∈ {1, ..., F} is characterized by:

Production Function

Output follows a Leontief (fixed proportions) technology:

where $\kappa$ is the capital-labor ratio. The Leontief form implies no factor substitution—both labor and capital are essential, reflecting short-run production constraints.

Pricing Rule

Prices are set as a markup over unit labor costs with sticky adjustment:

The 3% adjustment speed creates price stickiness, preventing deflationary spirals when productivity rises.

2.3 Government

The government sector collects taxes and provides transfers:

• Income tax: $\tau_y$ = 16% of wage income
• Corporate tax: $\tau_\pi$ = 10% of positive profits
• Base spending: $G_0$ = 16% of potential GDP
• Counter-cyclical adjustment based on output gap

2.4 Banking System

The banking system provides credit under Basel-like constraints:

• Deposit rate: 3% annual
• Lending rate: 7% annual
• Reserve ratio: 10%
• Capital requirement: 8%
• Maximum LTV: 80%

3. Market Mechanisms

3.1 Labor Market

The labor market follows a decentralized search and matching framework inspired by Mortensen-Pissarides (2010 Nobel) and Burdett-Mortensen (1998).

Job Search (Employed Workers)

For each employed worker h with tenure > 3 months:
  With probability 0.10:
    Sample 3 random firms
    best_offer = max(sampled firms' posted wages)
    if best_offer > current_wage × 1.10:
      QUIT current job
      Get hired at best-offer firm

Wage Posting (Firms)

Firms adjust posted wages based on labor market signals:

• High turnover → raise wage (max +0.5%/month)
• Few applicants → raise wage
• Many applicants → may lower wage (max -0.15%/month, sticky downward)

Hiring Decision

Target employment based on expected demand with asymmetric adjustment:

• Hiring: 85% smoothing, max +15%/period
• Firing: 60% smoothing, max -25%/period (faster cuts to prevent bleeding)

3.2 Goods Market

Consumers allocate spending across firms using a logit demand model:

where $\beta = 2.0$ is the price sensitivity parameter. This creates imperfect competition— lower prices attract more demand, but firms retain some market power.

Inventory Management

• Target coverage: 2 months of expected sales
• Markup adjustment: +2% if inventory < 1 month, -2% if > 2 months
• Depreciation: 2%/month spoilage

3.3 Credit Market

Firms borrow for working capital (wage shortfalls) and investment:

• Working capital: automatic if cash < wage bill, 7% interest
• Investment loans: if profitable and capacity-constrained, 5% interest, 5-year amortization
• Collateral: LTV ≤ 80% of capital stock

4. Dynamic Processes

4.1 Simulation Step Sequence

Each monthly step consists of 18 ordered phases:

4.2 Firm Entry and Exit

Exit Conditions

A firm exits (bankruptcy) if:

• 12 consecutive months of losses, AND
• Cash < 0 or cannot meet wage bill

Entry Conditions

New firms enter when:

• Active firms < 150
• Credit available > $1,000
• Unemployment > 3%
• AND at least one of:
  • Industry profit rate > 5% (profit signal)
  • Capacity utilization > 90% AND inventory < 1 month (supply shortage)
  • Unemployment > 10% AND firms < 80 (crisis entry)

4.3 Productivity Dynamics

Baseline total factor productivity (TFP) growth:

This 0.05%/month growth represents ~0.6% annual productivity improvement, consistent with historical averages. TFP is capped at 10× base to prevent runaway growth.

5. Automatic Stabilizers

5.1 Unemployment Insurance Fund

• Contribution: 2% payroll tax on all wages
• Benefits: 40% of average wage to unemployed
• Government backstop if fund depleted

5.2 Counter-cyclical Fiscal Policy

Government spending rises when GDP falls below potential, providing automatic demand support.

5.3 Bank Recapitalization

The government recapitalizes the banking system when:

• Bank capital < 0 (emergency)
• Lending capacity < $5,000 (proactive)
• Capital ratio < Basel minimum

This prevents credit crunch death spirals where banks can't lend → firms fail → banks lose more.

5.4 Government Employment

When unemployment exceeds 10%:

• Government hires 20% of excess unemployed per period
• Wage: 60% of market average (incentivizes private sector)
• Cap: 30% of workforce (prevents crowding out)

5.5 Debt Ceiling

Tiered fiscal brake to prevent unsustainable debt accumulation:

6. Parameter Values

Key calibrated parameters (see docs/PARAMETERS.md for complete list):

Labor Market

Fiscal Parameters

Financial Parameters

7. Comparison to DSGE Models

The dominant framework in mainstream macroeconomics is Dynamic Stochastic General Equilibrium (DSGE). CrashLab's ABM approach differs in several fundamental ways:

Limitations of This Model

• No international trade: Closed economy assumption
• Simplified finance: Single commercial bank, no asset markets
• No expectations heterogeneity: All agents use similar forecasting rules
• Calibration uncertainty: Many parameters lack empirical micro-foundations
• Scale effects: Even 1M households is 1/130th of the US economy

8. References