flowchart TB %% Nodes A["<b>Global Parameters</b><br/>α, β, r, L, volatility"] B["<b>Coffee Price</b><br/>Ornstein-Uhlenbeck Process"] C["<b>Households</b><br/>ability, wealth, trees, credit access"] D["<b>Sector Choice</b><br/>Entrepreneur vs. Farmer"] E["<b>Labor Allocation</b><br/>FOCs: marginal product equalization"] F["<b>Capital Demand</b><br/>subject to credit constraint"] G["<b>Income Calculation</b><br/>Cobb-Douglas production"] H["<b>Wealth Update</b><br/>income – consumption"] I["<b>Inequality</b><br/>Gini coefficient, histogram"] %% Connections A --> C A --> B B --> D C --> D D --> E E --> F F --> G G --> H H --> I %% Feedback Loop H -.-> C %% Styling classDef default fill:#f9f9f9,stroke:#ccc,stroke-width:0.5px,color:#000,rx:6,ry:6,font-family:Helvetica,font-size:12px; class A,B,C,D,E,F,G,H,I default;
Mitigating Inequality Under Commodity-Price Shocks
An Agent-Based Model Approach
1. Introduction
Volatility in global commodity markets has been shown to significantly impact the livelihoods of smallholder farming households in developing areas. Unpredictable fluctuations threaten household stability, alter labor decisions and prompt a variety of smoothing behaviors surrounding economic activities (Deaton (1992); Dercon (2002); Adhvaryu, Kala, and Nyshadham (2021)). Food insecurity along with negative health and educational outcomes have all been linked to to income volatility and the differing capacities households have to effectively respond to downturns (or take advantage of upturns) speaks to broader societal issues regarding fairness and equality (Akter and Basher (2014); Bania and Leete (2022) Hardy (2014)). Crafting policy that can effectively address these issues is difficult because the ways in which households decisions under risk can be hard to disentangle (Morduch (1995)). Households employ smoothing strategies to reduce fluctuations in their consumption during periods of income instability (consumption smoothing), but they also employ strategies designed to reduce fluctuations in income altogether (income smoothing) (Pandey et al. (2000)). Operating ex-ante, income smoothing is generally thought to incur costs through less efficient production allocation but reduces perceived risk by increasing diversification or increasing flexibility (Morduch (1995); Pandey et al. (2000)). Consumption smoothing usually takes place after experiencing shocks and can include migration, loans, asset liquidation charity and short-term entrepreneurship; all of which serve to stabilize incomein these circumstances (Pandey et al. (2000); Adhvaryu, Kala, and Nyshadham (2021)).
Entrepreneurship has been shown in some contexts to function strictly as a coping mechanism, helping smooth the negative impact of shocks; however, in other circumstances, it may serves to increase household resilience or act as an avenue for upward economic mobility (Adhvaryu, Kala, and Nyshadham (2021); Blattman and Dercon (2018)). The motivations behind entrepreneurial decisions, whether as temporary shock response, risk diversification or as strategic income enhancement, can be difficult to distinguish empirically, as multiple mechanisms may operate simultaneously within the same household. Furthermore, the decision to transition from farming to other entrepreneurial activities is influenced not just by heterogeneous characteristics among household members, but also on access to functioning credit markets, the cost of capital and a variety of other factors in the broader economic and policy environments (Adhvaryu, Kala, and Nyshadham (2021)). Consequently, most household micro-enterprises never transition into the formal business sector, even in environments experiencing rapid economic growth (McCaig and Pavcnik (2015)). The stickiness of informality seems odd given the potential for wealth accumulation and economic mobility entrepreneurship offers.
Realizing that entrepreneurship tends to remain a temporary coping strategy rather than a sustained pathway for economic mobility, a set of normative questions surrounding policy making begins to emerge. Why do so many households remain specialized in traditional farming. How do structural factors such as differential access to credit, heterogenous entrepreneurial abilities, and unequal asset endowments create barriers to mobility. If innate entrepreneurial ability and structural inequalities such as uneven access to credit markets and productive assets interact, policy designed to produce better outcomes may instead just serve to reinforce existing disparities. Modern theories of justice underscore the ethical imperative societies face to correct inequalities arising from factors beyond the control of individuals, including inherent differences in ability or inherited socioeconomic status (Rawls (1971); Dworkin in Atkinson and Bourguignon (2015); Sen (2006); Roemer and Trannoy (2015)). These kinds of normative frameworks suggest policy interventions should 1) address structural constraints preventing households from generating wealth and 2) Mitigate the disparities caused by inherent differences between households. Reliance strictly on market mechanisms may fail to achieve these kinds of equitable outcomes, especially in environments where price shocks are able to disproportionately harm households already disadvantaged by fewer resources or limited entrepreneurial capability (Bowles and Gintis (2001); Piketty (2014)). Consequently, understanding how economic shocks, household characteristics, and institutional environments interact becomes important in not only informing strategies aimed at stabilizing household livelihoods but also to design interventions aimed at reducing structural inequities.
2. Research Question
This study builds on the work of Adhvaryu, Kala, and Nyshadham (2021) in “Booms, Busts, and Household Enterprise,” which examines how smallholder farmers in Tanzania respond to commodity price shocks by switching between farming and entrepreneurship based on their ability. By extending this framework, the model investigates how price volatility and policy interventions shape enterprise formation and inequality.
The central question guiding this research is:
How do global commodity price fluctuations influence entrepreneurial decisions among smallholder farming households, and to what extent can policy interventions reduce inequalities associated with differences in entrepreneurial ability?
H1: Commodity price volatility amplifies wealth inequality and is driven by differences in entrepreneurial ability. Sectoral switching serves as a transmission mechanism through which ability differences translate into divergent wealth accumulation patterns.
H2: Targeted interventions, such as expanded credit access or capital grants, can reduce ability-driven wealth inequality by facilitating entrepreneurial entry among constrained households, leading to higher wealth accumulation.
Traditional empirical methods may not have trouble capturing the complex, interactions created by overlapping policy levers. This study therefore develops an agent-based model to simulate how price shocks, individual ability, and policy design interact to shape household-level outcomes and distributional dynamics.
The agent-based model/complex adaptive system framework offers several advantages:
Heterogeneity and individual decision-making: Agents differ in key attributes such as ability, wealth, and credit access, allowing the model to reflect real-world variation in household responses to changing conditions.
Emergent outcomes: Inequality, wealth and entrepreneurship rates emerge from market interactions rather, offering insight into system level patterns that traditional analysis may miss.
Nonlinear dynamics: ABMs capture feedback loops and threshold effects, revealing how small differences can lead to divergent long-term outcomes.
Policy experimentation: ABMs allow testing of counterfactual policy scenarios, supporting the evaluation of interventions aimed at mitigating structural inequality.
By generalizing Adhvaryu, Kala, and Nyshadham (2021) and extending it through simulation, this research contributes to ongoing debates about how policy can address inequality rooted in innate traits and institutional constraints.
3. Model Architecture
The model simulates a set of decisions made by households when determining how to allocate resources: observing prices, choosing a sector, and making final allocation decisions. The diagram below (Figure 1) presents a high-level concept of operations view of the model’s architecture, demonstrating how state, economic, and institutional parameters generate aggregate outcomes and feedback loops.
At each time step, households receive updated price signals and evaluate whether to remain in farming or switch to entrepreneurship. Their decision depends on individual ability and access to capital, which in turn affect income through production functions. Income then accumulates as wealth, which feeds back into future decisions by altering household state variables such as available capital and the viability of switching sectors.
4. ODD + D: Model Description
4.1 Overview
Purpose
This model explores how smallholder farming households respond to global commodity price volatility through entrepreneurship, and how differences in entrepreneurial ability, credit access, and capital constraints shape wealth inequality. Sectoral participation patterns therefore serve as the mechanism through which ability differences translate into wealth inequality. It can be used to evaluate how effective policy interventions, like credit expansion or capital grants, can be at mitigating the effects of structural inequities. It extends the framework developed by Adhvaryu, Kala, and Nyshadham (2021) into a more generic context, abstracted from Tanzania.
Entities, State Variables, and Scales
Agents: Smallholder farming households
-
State variables:
-
ability– innate entrepreneurial productivity
-
wealth– accumulated capital
-
credit_access– binary indicator of formal borrowing eligibility
-
trees– proxy for productive farm assets (heterogeneous across households) -
entrepreneur?– current occupational status (boolean) -
ever-entrepreneur?– lifetime entrepreneurship indicator -
effective-r– actual interest rate faced (formal vs informal)
-
-
Global variables:
-
coffee_price– modeled via Ornstein-Uhlenbeck process
-
pf– farm-gate price (follows coffee price) -
pe_biz– enterprise output price (affected by market saturation) -
r– formal interest rate
-
r-informal– informal interest rate (3x formal rate) -
credit-borrow-multiple– borrowing capacity multiplier for credit-constrained agents -
volatility– price shock parameter
-
α,β– Cobb-Douglas coefficients
-
L– total available labor (fixed at 1 for all households)
-
-
Scales:
- Temporal: model steps represent production cycles (seasonal)
- Spatial: no geographic layout
- Temporal: model steps represent production cycles (seasonal)
4.2 Design Concepts
| Concept | Description |
|---|---|
| Basic Principles | Enterprise choice follows constrained optimization based on ability and credit access, using Cobb-Douglas production. Based on Adhvaryu, Kala, and Nyshadham (2021). |
| Emergence | Wealth, inequality and entrepreneurship patterns emerge from household decisions and interactions with market volatility. |
| Adaptation | Agents switch to entrepreneurship when their ability exceeds an endogenously determined threshold. The threshold accounts for current prices, market saturation effects, household characteristics, and credit constraints. |
| Objectives | Maximize household income under production and financial constraints. |
| Learning | No learning is implemented; agents follow fixed decision rules. |
| Prediction | Agents estimate income using current global parameters (e.g., price) and known production functions. |
| Sensing | Agents observe global variables (coffee, or other commodity price) and their own state (wealth, ability, credit access). |
| Interaction | Indirect via shared prices and credit availability. No direct agent-to-agent communication. |
| Stochasticity | Price shocks are generated each tick. Policy variables vary across runs. |
| Collectives | Not modeled. Agents act independently. |
| Observation | The model outputs system-level metrics: Gini coefficient, mean wealth, entrepreneurship share, etc. |
4.3 Details
Initialization
At model start, households are assigned random ability and credit_access from specified distributions, and trees from a normal distribution. The coffee price begins at its long-run average. Household wealth initialized uniformly at 1.0, L (labor) is held constant at 1 for all households across all runs. Production function and other variables can also be set via slider.
Input Data
No empirical input data. Variables are set by the modeler.
Submodels
-
Price Shock Process
A soft-bounded Ornstein–Uhlenbeck (OU) process generates coffee-price dynamics:\[ p_{t+1} \;=\; p_t + \kappa\bigl(\bar{p} - p_t\bigr) + \varepsilon_t + \xi_t \]
where
-
\(\varepsilon_t \sim \mathcal{N}(0,\sigma)\) (volatility slider)
-
\(\xi_t \;=\; p_t \,\eta_t\) with probability \(1\%\),
\(\eta_t \sim \mathcal{N}(0,0.2)\) (rare symmetric boom / bust)
-
Soft bounds:
- if \(p_t > 1.5\) subtract \(0.2\bigl(p_t - 1.5\bigr)\);
- if \(p_t < 0.5\) add \(0.2\bigl(0.5 - p_t\bigr)\);
- if \(p_t > 1.5\) subtract \(0.2\bigl(p_t - 1.5\bigr)\);
- Hard floor at \(0.1\) prevents non-positive prices.
-
\(\varepsilon_t \sim \mathcal{N}(0,\sigma)\) (volatility slider)
-
Credit-Cost Function
Agents face a dual interest-rate regime:\[ r_i \;=\; \begin{cases} r & \text{if the agent has \emph{formal} credit access} \\[6pt] 3\,r & \text{otherwise (informal market)} \end{cases} \]
Sector Choice Logic: Agents switch to entrepreneurship if their ability exceeds a household-specific threshold computed iteratively based on optimal factor allocation and net income comparison
-
Market Saturation Function
Enterprise output price decreases as more agents enter entrepreneurship:\[ p_e = 0.5 + \frac{0.5}{1 + \exp(5 \times (s - 0.6))} \]
where \(s\) is the share of agents currently engaged in entrepreneurship. This creates negative externalities that naturally limit excessive entry into the enterprise sector.
Production: Cobb-Douglas output using household ability, labor, and capital
Capital Demand: Bounded by wealth and credit access
Income and Wealth Update: Income calculated and added to wealth (consumption is fixed and uniform across households)
Inequality Metrics: Gini coefficient and wealth distribution histogram
4.4 Decision-Making (+D)
Households choose between farming and entrepreneurship based on their individual ability relative to a threshold that changes with market conditions. Instead of comparing expected incomes each period, agents become entrepreneurs only when their ability exceeds this cutoff. The threshold depends on coffee prices, how many other households are already in business, production parameters, labor availability, and access to credit.
Formally, sector choice is governed by: \[
\theta_i > \theta^*
\] where: - \(\theta_i\) is the entrepreneurial ability of agent \(i\).
- \(\theta^*\) is the minimum ability level required to make entrepreneurship more profitable than farming, computed iteratively from model parameters and production constraints.
Sector Income Equations
Income in each sector is calculated using Cobb-Douglas production functions:
Farming
\[ y_f = p_f \cdot (\theta_i \cdot \phi_f) \cdot L_f^{\alpha} \cdot T_i^{1-\alpha} \] where:\(p_f\) = farm-gate price (follows coffee price)
\(\theta_i \cdot \phi_f\) = ability-adjusted farming efficiency
\(L_f\) = labor allocated to farming
\(T_i\) = household tree stock (heterogeneous farm capital)
Entrepreneurship
\[ y_e = p_e \cdot (\theta_i \cdot \phi_e) \cdot L_e^{\beta} \cdot k^{1-\beta} - r \cdot k \] where:\(p_e\) = enterprise output price (decreases with market saturation)
\(\theta_i \cdot \phi_e\) = ability-adjusted enterprise efficiency
\(L_e\) = labor allocated to enterprise
\(k\) = capital investment (subject to credit constraints)
\(r\) = interest rate (higher for credit-constrained households)
Threshold Determination
To find the threshold θ*, the model tests different ability levels to see when entrepreneurship becomes profitable. For each candidate threshold, it calculates how households would split their labor between farming and business, applies borrowing limits based on credit access, accounts for differences in farm assets, and compares net incomes after subtracting capital costs.
Agents below the threshold specialize in farming, allocating all labor to agricultural production. Those above the threshold become entrepreneurs, optimally dividing labor between farming and enterprise activities while investing capital subject to their credit constraints.
Additional Constraints
Households without formal credit access face higher borrowing costs (three times the formal interest rate) and can only borrow up to 50% of their current wealth. In contrast, households with formal credit access benefit from lower interest rates and face unlimited borrowing capacity. Market saturation also shapes entrepreneurial decisions, as enterprise output prices decrease nonlinearly with increased participation, creating competitive pressures that limit excessive entry into the business sector. The model however assumes frictionless sectoral switching with no transition costs or delays when households change occupations. Finally, households operate under static expectations, following fixed decision rules based on current conditions rather than updating their strategies or learning from experience over time.
5. Coding
This section outlines the core computational logic of the model in high-level pseudocode. The agent-based model is structured around sequential processes for price updates, sector selection, production, income, and wealth updates. Each time step represents a seasonal production cycle in which households make decisions based on updated economic conditions and individual attributes.
CREATE global parameters: α, β, r, L, volatility
CREATE households with 1) initial wealth = 1.0
2) random ability, credit access, and trees
FOR each period:
UPDATE coffee price using soft-bounded Ornstein-Uhlenbeck process
FOR each household:
COMPUTE ability threshold for entrepreneurship based on:
- Cobb-Douglas parameters
- current coffee price
- available capital (wealth + credit access)
- labor supply
IF ability ≥ threshold:
ASSIGN household to entrepreneurship sector
ALLOCATE labor and compute capital demand (bounded by wealth and credit)
CALCULATE income from enterprise production function
ELSE:
ASSIGN household to farming sector
ALLOCATE labor
CALCULATE income from farm production function
UPDATE household wealth:
wealth = wealth + income – consumption (fixed)
RECORD model outputs:
- Gini coefficient
- Mean wealth
- Entrepreneurship share
- Distribution statistics (e.g., histograms)6. The Model User Interface
6.1 The “World”
-
What you see
- 100 circles on a blank background (no geographical constraints).
- Green = farmers
- Blue = entrepreneurs
- Circle size grows with log-wealth so richer agents stand out without eclipsing the others.
- 100 circles on a blank background (no geographical constraints).
-
Why it matters
- Demonstrates the ability threshold: when coffee prices crash, a wave of blue dots appears as households cross θ*.
- Dot growth/shrinkage visualize the wealth-feedback loop that may drive long-run inequality.
- Demonstrates the ability threshold: when coffee prices crash, a wave of blue dots appears as households cross θ*.
6.2 Input & parameter sliders
| Slider group | Theory hook | Typical slider | Why you can move it |
|---|---|---|---|
| Production Function | Cobb-Douglas exponents (α, β) set marginal returns to labor. |
alpha beta L r
|
Test how labor intensity shifts sector incentives and inequality. |
| Price Dynamics | Ornstein–Uhlenbeck parameters drive shocks. |
volatility reversion-speed allow-large-shocks
|
Test of H1: higher volatility ⇒ higher inequality. |
| Sector Returns | Ability multipliers for farm vs. enterprise. |
ability-multiplier-b ability-multiplier-f
|
Explore whether modern returns widen or narrow θ*. |
| Policy & Heterogeneity | Credit access, grants, ability distribution. |
credit-access-rate credit-borrow-multiple gran-pct cap-grant? grant-pct ability-mean ability-sd tree-mean tree-sd consumption-rate
|
Test H2: can policy retard inequality growth? |
6.3 Simulation controls
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Setup – resets everything.
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Go / Go ∞ – run one tick or run continuously.
- + / – Price Shock – inject large positive or negative shocks for stress-tests.
6.4 Key monitors
| Monitor | Reporter | Theory link |
|---|---|---|
| Cum. Enterprise Share | ces |
Long-run time spent in entrepreneurship. |
| Total Wealth | total-wealth |
Aggregate welfare: is the pie growing? |
| Mean Wealth | mean [wealth] of turtles |
Baseline welfare per household. |
6.5 Plots
| Plot | Drawn from | Theory item exposed |
|---|---|---|
| Gini |
gini-wealth every tick |
Core inequality trend (H1, H2). |
| Wealth Histogram | 10-bin histogram | Shape of wealth distribution; heavy tails under big shocks. |
| Lorenz Curve | Redrawn every 10 ticks | Visual check on the Gini trajectory. |
| Total Wealth vs CES | plotxy ces total-wealth |
Interaction of sector choice and aggregate welfare. |
| Gini vs CES | plotxy ces gini-wealth |
Does high participation co-move with more or less inequality? |
| Coffee Price | OU price path | Exogenous driver for the whole chain. |
| Coffee Price × CES scatter | Tick-by-tick pairs (price, ces)
|
Non-linear or lagged response check. |
| Phase: Income Composition | Mean enterprise-income vs. farm-income | Confirms income crossover at the ability threshold. |
7 Baseline, Simulation & Scenarios
This section compares how the model behaves under a baseline realistic for an emerging economy and six policy-relevant counter-factuals.
Analysis includes:
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Quantitative summary – key outcome metrics at the final tick
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Qualitative patterns – insights from the on-screen diagnostics
- Complex-adaptive-system (CAS) insights – path dependence, feedback loops, lock-in
7.1 Baseline Scenario: Constraints in Emerging Economies
The baseline captures conditions common to emerging economies with limited financial infrastructure and uneven productive endowments.
| Feature | Justification | Parameter |
|---|---|---|
| Medium-high volatility | Global commodity dependence | volatility = 0.17 |
| Weak credit access | Informal lending dominates | credit-access-rate = 0.20 |
| Modest ability spread | Structural inequality, limited mobility |
ability-mean = 0.45, ability-sd = 0.15
|
| Traditional agriculture returns | Low productivity, labour-intensive | ability-multiplier-f = 0.8 |
| Higher enterprise returns | Entrepreneurial activity offers upside | ability-multiplier-b = 1.2 |
| No capital grants | No current subsidy programme |
cap-grant? = false, grant-pct = 0
|
| Formal / Informal rates | Dual cost of capital |
r = 0.15, r-informal = 3 × r
|
| Soft price bounds | Prevent runaway price dynamics | Floor = 0.1, Lower soft = 0.5, Upper soft = 1.5 |
Initial conditions:wealth = 1.0 for all agents; heterogeneity only through ability and assets.
Stochastic Ornstein–Uhlenbeck (OU) price shocks apply throughout the run.
7.2 Scenario Dashboard at a Glance
| Scenario | Key lever(s) | Cum. enterprise share | Total wealth | Gini† |
|---|---|---|---|---|
| Baseline | None | 0.482 | 255.4 | ~0.24 |
| Easy Credit | credit-access-rate ↑ → 0.75 |
0.597 | 279.1 | ~0.26 |
| Seed-Spark Grants |
cap-grant? = true, grant-pct = 0.20
|
0.452 | 270.2 | ~0.23 |
| Steady Prices | volatility ↓ → 0.05 |
0.430 | 266.9 | ~0.22 |
| Education & Training | ability-mean ↑ → 0.60 |
0.604 | 325.3 | ~0.28 |
| Big Push (multi-lever) |
credit-access-rate ↑ → 0.70, r ↓ → 0.05, volatility ↓ → 0.05
|
0.900 | 406.0 | ~0.34 |
| Tight-Money Crunch |
credit-access-rate ↓ → 0.10, r ↑ → 0.25
|
0.147 | 241.4 | ~0.18 |
7.3 Discussion
7.3.1 Baseline
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Inequality builds slowly. The Gini curve rises monotonically then flattens – a sign of cumulative advantage under repeated shocks plus credit rationing.
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Bimodal wealth distribution. A tall spike at ≈ 5.3 units alongside a subsistence‐level tail.
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Enterprise uptake ≈ 48 %. Entry is bounded by the 20 % formal-credit ceiling.
- CAS reading: early entrants capture compound returns and lock in advantage.
7.3.2 Single-lever Policies
| Lever | Dashboard evidence | Interpretation |
|---|---|---|
| Easy Credit | Enterprise share ↑ to 0.60; wealth +9 %; Gini ~0.26. | More households qualify for loans, boosting growth with a modest rise in inequality. Credit alone is helpful but not transformative. |
| Seed-Spark Grants | Wealth +6 %; enterprise share ↓ to 0.45; Gini ↓ slightly. | One-shot boosts help borderline entrants but fade over time; credit frictions persist. |
| Steady Prices | Wealth +4 %; share 0.43; Gini ↓. | Dampening volatility protects incumbents yet reduces incentive for new entry. |
| Education & Training | Wealth +27 %; share 0.60; Gini ~0.28. | Ability uplift raises the pie but widens gaps – skill-biased growth. |
7.3.3 Multi-lever “Big Push”
- Combines generous credit, milder volatility, and cheap formal loans.
- Enterprise share vaults to 0.90; Lorenz and Gini curves steepen.
- Positive feedback: once capital crosses a threshold, returns spiral upward, forming a high-growth, high-inequality attractor.
7.3.4 Contractionary Counterfactual
- Enterprise share collapses to 0.15; total wealth falls yet Gini improves to 0.18: equality through poverty.
- Negative feedback loop: low wealth → less credit → low income, reinforcing a low-mobility equilibrium.
7.4 CAS Behaviours Observed
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Threshold effects & tipping-points – parameter changes may trigger non-linear jumps in entrepreneurship.
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Positive feedback & lock-in – capital accumulation accelerates returns once initial hurdles are cleared.
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Path dependence – early price realizations decide who first crosses the entry threshold; later interventions cannot fully unwind this hierarchy.
- Dampening vs amplifying loops – volatility reduction removes a harmful bust spiral but also curtails opportunity-driven switching.
7.5 Policy Takeaways
-
Credit access helps but needs allies. Expanding formal credit yields modest welfare gains (+9 %) and a small rise in inequality; pairing with lower rates or skills policy may be worth examining.
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Volatility buffers are necessary but not sufficient. Price smoothing alone offers limited benefit.
-
Human-capital interventions raise averages but widen spreads. Worth testing with inclusive finance.
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One-shot grants are a weak substitute for structural reform. Their impact dissipates as shocks accumulate. Entrepreneurship stays low despite lower gini.
-
Contractionary policy yields equality through poverty. High rates suppress entrepreneurship and drag the whole distribution toward stagnation.
- System thinking is essential. Levers appear to interact non-linearly; sequencing and bundling is needed to determine both growth and its distribution.
8. Data Analysis of Behaviour-Space Results
The analysis is organised in four layers that map directly onto the evaluation criteria:
-
Robustness of stochastic replications
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Quasi-global sensitivity via penalized GAM/BAM
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Equilibrium structure inspected through phase portraits
- Lever response surfaces shown as heat-maps
8.1 Behaviour-Space Robustness
Ten seeds per parameter tuple provide adequate precision: Monte-Carlo standard errors converge to 2-4% of the mean value scale across all outcomes, indicating reasonable uncertainty levels for policy analysis.
| Table 8-1 Replication uncertainty after 10 seeds | |||
| Metric | 95% MC-SE | Mean Value | Relative MC-SE (%) |
|---|---|---|---|
| Entrepreneur Share | 0.0117 | 0.5296 | 2.20 |
| Gini | 0.0074 | 0.1648 | 4.47 |
| Total Wealth | 7.5727 | 320.0028 | 2.37 |
8.2 Quasi-Global Sensitivity — Generalized Additive Models
Three GAM models were fit to the final-tick output (n = 30,240 simulated runs, 10 replications per parameter combination) to identify the non-linear policy effects on wealth and inequality. GAMs allow flexible modeling and avoids overfitting through penalized smoothing splines. The results show which policy levers have the strongest effects and how they interact to shape final outcomes.
The models achieve good fit across all outcomes (R² > 0.80), reflecting the systematic coverage of the parameter space through the behavior-space experimental design. All policy variables show nonlinear effects, with effective degrees of freedom (EDF) mostly above 2.5. These non-linearities emerge from model dynamics rather than strictly from the experimental design, justifying the GAM specification over linear models that would miss these relationships.
| GAM Model Comparison | |||
| Effective degrees of freedom (EDF) for smooth terms, coefficients for parametric terms | |||
| Gini | Total Wealth | Entrepreneur Share | |
|---|---|---|---|
| Interest Rate (r) [S] | 4.99*** | 4.84*** | 4.98*** |
| (1326.03) | (924.38) | (21950.07) | |
| Volatility [S] | 3.81*** | 2.77*** | 4.63*** |
| (21.14) | (33.75) | (383.53) | |
| Credit Access Rate [S] | 5.98*** | 5.97*** | 5.96*** |
| (588.61) | (96.29) | (3155.23) | |
| Mean Ability [S] | 4.88*** | 4.92*** | 4.91*** |
| (381.27) | (4156.35) | (26744.43) | |
| Capital Grant [P] | -0.005*** | 18.734*** | 0 |
| (0) | (0.483) | (0) | |
| r × Credit Access [S]1 | 1 29.9*** | 1 17.83*** | 1 29.75*** |
| (746.8) | (491.95) | (397.63) | |
| r × Volatility [S]1 | 1 13.05*** | 1 8.04*** | 1 22.01*** |
| (8.91) | (1.9) | (145.64) | |
| Mean Ability × Credit Access [S]1 | 1 27.57*** | 1 29.35*** | 1 21.48*** |
| (101.4) | (130.71) | (34.4) | |
| (Intercept) [P] | 0.17*** | 315.259*** | 0.527*** |
| (0) | (0.349) | (0) | |
| R²(adj) | 0.806 | 0.793 | 0.965 |
| Dev.Expl. | 0.807 | 0.794 | 0.965 |
| n | 30240 | 30240 | 30240 |
| [S] = Smooth term (EDF shown), [P] = Parametric term (coefficient shown). F-statistics in parentheses for smooth terms, standard errors for parametric terms. Total Wealth coefficients in currency units. Significance: *** p<0.001, ** p<0.01, * p<0.05, . p<0.1 | |||
| 1 Tensor product interactions (te) show additional variance explained beyond main effects. | |||
Main Effects and Policy Leverage
Mean Ability has the largest impact on all outcomes. This finding is in line with the premise that ability-driven sectoral selection creates systematic wealth accumulation and differences compound over time. Higher-ability households enter entrepreneurship more readily and generate higher returns, creating wealth gaps that grow over time (Figure 3, Figure 4).
Interest Rate is the second-strongest effect, demonstrating the importance of capital costs in shaping economic outcomes. The smooth curves reveal threshold effects around 15 to 20 percent, suggesting potential threshold effects or tipping points.
Credit Access Rate also has strong nonlinear effects and interaction patterns. The partial effect curves show diminishing returns to credit expansion, with the steepest marginal effects occurring at moderate access levels. This may reflect the model’s dual credit logic, where formal credit access amplifies the advantages of households already well positiones.
Volatility creates a U-shaped relationship with wealth but monotonically increases inequality. Higher-ability households can exploit volatile conditions for entrepreneurial opportunities, while lower-ability households face greater downside risk.
Critical Policy Interactions
Three interaction terms prove statistically significant across models:
Interest Rate × Credit Access: The tensor surfaces reveal complementary effects: credit access becomes more effective under low interest rate environments, suggesting optimal policy coordination rather than substitution (Figure 3, Figure 4).
Interest Rate × Volatility: Interest rate policy works differently depending on how stable the environment is but the relationship is complex.
Mean Ability × Credit Access: This tests whether credit can reduce ability-driven inequality. Credit appears to help, but it helps high-ability households more.
Policy Design Implications
The GAM results reveal several critical insights for policy optimization:
Nonlinear Policy Responses: All policy levers exhibit threshold effects and diminishing returns, suggesting optimal policy ranges rather than “more is better” approaches.
Policy Complementarity: The interaction terms indicate that coordinated policy packages are more effective than isolated interventions.
Ability-Conditional Effects: The Ability × Credit Access interaction confirms that universal policies may inadvertently increase inequality by disproportionately benefiting high-ability households.
Optimal Policy Coordination: The Interest Rate × Credit Access interaction suggests that expansionary fiscal and monetary policies could be coordinated to maximize effectiveness.
These findings validate the agent-based modeling approach by revealing complex, nonlinear relationships that would be missed by traditional linear policy analysis, providing a foundation for the further analysis and policy recommendations.
8.3 Equilibrium Behavior
Phase portrait analysis reveals the dynamic pathways through which different policy regimes give way to long-term outcomes in the wealth-inequality space. Unlike static equilibrium analysis, these portraits capture the temporal evolution of system trajectories, showing where the system ends up, how it gets there and when policy effects become apparent.
The analysis examines system dynamics through temporal lenses: full 120-year patterns and first 30-year intervention windows (each tick is taken to be three months). This approach shows both the longer-term destinations of various policy trajectories as well as the early periods where differences in policies may.
Wealth-Inequality Dynamics (Figure 6) reveal a consistent pattern of trajectory divergence from common starting points, with policy differences creating distinct developmental pathways that compound over time. The portraits show clear evidence of path dependence, where early policy choices constrain long-term outcomes.
Entrepreneurship Dynamics with Wealth and Inequality (Figure 7, Figure 8) demonstrate complex, nonlinear patterns that vary significantly across policy regimes. Rather than simple monotonic relationships, the portraits reveal threshold effects and potential regime-dependent dynamics that support an emphasis on policy timing and sequencing.
Policy Gradient Effects show how different policy levers create distinct trajectory fans in the outcome space, with some policies producing tight convergent paths while others generate dispersion reflecting the underlying heterogeneity of household responses.
A set of interactive visualizations (Figure 13, Figure 14, Figure 15, Figure 16) extend the analysis into policy space, revealing how policy levels create complex surfaces that capture three-way interactions between wealth accumulation, inequality generation, and policy implementation over time. The temporal perspective continues along the lines of previous analysis by highlighting emergent system behaviors that would not be captured through static equilibrium analysis and may help to inform better policy sequencing.