How do progressive taxation, targeted transfers, and public investment interact with household-level income heterogeneity and heterogeneous marginal propensities to consume to shape aggregate demand, growth, and the size of fiscal multipliers?
Agent-based models · Model guide
How do progressive taxation, targeted transfers, and public investment interact with household-level income heterogeneity and heterogen...
How do progressive taxation, targeted transfers, and public investment interact with household-level income heterogeneity and heterogeneous marginal propensities to consume to shape aggregate demand, growth, and the size of fiscal multipliers?
Standard macro models treat fiscal multipliers as a single number: a dollar of government spending generates X dollars of GDP. But this aggregate view hides the mechanism that actually determines the multiplier's size - the distribution of the spending across households with different propensities to consume. Dosi et al. (2013) built one of the first comprehensive agent-based models with income distribution, credit, and fiscal policy operating jointly, showing that fiscal austerity in their K+S framework produced deeper recessions than representative-agent models predicted because it disproportionately hit high-MPC households. Russo et al. (2016) extended the K+S model to study fiscal multipliers directly and found that the multiplier from transfers targeted at the bottom quintile was 2 to 3 times larger than the multiplier from across-the-board tax cuts, a result that representative-agent models cannot generate by construction. Stiglitz and Gallegati (2011) provided the theoretical motivation: inequality affects macroeconomic performance through credit constraints, demand shortfalls, and financial fragility, all of which are invisible when the household sector is compressed into a single agent.
The core mechanism is the MPC gradient. Empirical evidence from Johnson, Parker, and Souleles (2006), Broda and Parker (2014), and Fagereng, Holm, and Natvik (2021) consistently shows that low-income, low-wealth households spend 60-90% of a transfer within the quarter, while high-income, high-wealth households spend 10-30%. When fiscal policy channels resources to high-MPC households - through progressive taxation, means-tested transfers, or public services that substitute for private spending - the first-round demand injection is larger, the Keynesian multiplier chain is longer, and the aggregate fiscal multiplier is higher. The ABM makes this visible by tracking each household's income, wealth, and consumption decision individually rather than averaging across the distribution.
Central banks and fiscal authorities increasingly use distributional analysis alongside aggregate forecasting. The Congressional Budget Office (CBO) publishes distributional analyses of tax and transfer proposals. The ECB's Household Finance and Consumption Survey (HFCS) provides micro data that calibrates heterogeneous-agent models. The OECD's NAEC initiative has commissioned ABM work on inequality and growth. Dosi, Fagiolo, Napoletano, and Roventini at the Sant'Anna School of Advanced Studies maintain the K+S model family, which has been used to evaluate fiscal consolidation strategies for the European Commission. Caiani et al. (2016) built a stock-flow consistent ABM with a full government sector that tracks every flow between households, firms, banks, and government, making it possible to trace the distributional consequences of any fiscal rule change through the entire circular flow.
The model family has evolved along several axes. Early versions used fixed MPC rules; newer variants let consumption propensities emerge from buffer-stock saving behavior calibrated to micro data. Tax structures have moved from flat-rate approximations to piecewise progressive schedules with multiple brackets. Transfer targeting has expanded from simple lump-sum payments to means-tested programs with phase-out ranges, UI benefits that depend on employment history, and in-kind public services. The Eurace@Unibi model (Dawid et al. 2018) adds spatial structure and labor mobility to the fiscal-inequality interaction. The active frontier includes climate fiscal policy (carbon tax incidence across the income distribution), pandemic fiscal responses (distributional effects of lockdown compensation), and fiscal-monetary interaction (how redistribution affects the transmission of interest rate changes).
The economy is assembled from five agent populations. Households are the primary agents: each carries an income level drawn from a calibrated distribution, a wealth stock, a consumption rule parameterized by the household's MPC (which depends on wealth-to-income ratio), a labor supply decision, and a tax/transfer account that records net fiscal flows. The household population is typically 1,000 to 50,000 agents in research implementations and 50 to 200 in browser-scale toy models. Firms form the second population: each produces output using labor, sets prices with a markup rule, and pays wages drawn from a calibrated wage distribution that maps into household income heterogeneity. Banks are the third population: each provides credit to firms and households subject to capital constraints, closing the saving-investment loop. The government is the fourth agent: it collects taxes according to a defined schedule (progressive, flat, or regressive), distributes transfers according to targeting rules, purchases goods and services, issues bonds, and runs a deficit or surplus. The central bank is the fifth agent: it sets the policy rate according to a Taylor-type rule and may purchase government bonds.
Interaction happens through four channels. The labor market matches firms to households, determining the wage distribution that feeds into pre-tax income inequality. The goods market aggregates household consumption and government purchases into total demand, which feeds back into firm revenue and employment decisions. The credit market connects firms to banks for investment financing and households to banks for consumer credit. The fiscal channel collects taxes from each household's income and wealth, redistributes transfers to targeted households, and purchases goods from firms - this is the channel that the model is specifically built to study, and every design choice is oriented around making the fiscal channel's distributional operation transparent and traceable.
State variables update each period in a fixed sequence: (1) the government announces the fiscal rule (tax schedule, transfer amounts, public spending), (2) firms post vacancies and wages, (3) the labor market matches workers to firms, (4) production occurs, (5) households receive income and pay taxes, (6) targeted transfers are distributed, (7) households make consumption and saving decisions based on their post-tax-and-transfer income and current wealth, (8) the goods market clears and firm revenue is realized, (9) firms make investment decisions, (10) the credit market processes loan applications, (11) banks update capital positions, (12) the government updates its budget position and adjusts the fiscal rule if automatic stabilizers or fiscal rules are active. This sequential structure means the propagation path from a fiscal policy change through the income distribution to aggregate demand is traceable step by step.
The Dosi-Roventini K+S model family has been used to evaluate fiscal consolidation strategies for the European Commission. Russo et al. (2016) showed that austerity packages concentrated on spending cuts produced deeper recessions and slower debt reduction than packages that maintained transfers to low-income households, because the spending-cut packages removed demand from the highest-MPC segment of the population. The quantitative result - a spending multiplier of 1.5 to 2.0 for targeted transfers versus 0.5 to 0.8 for across-the-board tax cuts - is consistent with the empirical range from Ramey (2019) and Chodorow-Reich (2019) when the economy has slack. The model has also been used to study the interaction between fiscal policy and financial fragility: Dosi et al. (2015) showed that fiscal austerity amplifies financial crises by reducing the income of credit-constrained households, increasing loan defaults, and tightening bank lending conditions.
Caiani et al. (2016) built a stock-flow consistent ABM with a complete government balance sheet to study how different financing modes for fiscal deficits (bond issuance versus money creation) interact with the income distribution. The model tracks every dollar from government to household to firm to bank and back, ensuring accounting consistency that many ABMs lack. This architecture has been used to evaluate modern monetary theory (MMT) proposals by simulating job guarantee programs funded by money creation, finding that the inflationary consequences depend critically on the output gap and the sectoral composition of government spending. Dawid et al. (2018) in the Eurace@Unibi framework added spatial heterogeneity and inter-regional fiscal transfers, studying how European structural funds affect convergence between rich and poor regions when households in different regions have different MPC profiles.
The model breaks down in three settings. First, when the economy is at or near full employment and capacity utilization is high, the demand-side fiscal multiplier story is less relevant and supply-side constraints dominate. The model has a rudimentary capacity constraint but does not capture the detailed supply-side response (skill bottlenecks, input shortages, sectoral reallocation) that determines the inflationary consequences of stimulus at full capacity. Second, when the question is about long-run growth rather than cyclical stabilization, the model's short-run demand focus is less useful; endogenous growth mechanisms (R&D, human capital, technology diffusion) are present in some variants but are not the model's comparative advantage. Third, when the institutional setting involves complex political economy constraints on fiscal policy (coalition dynamics, legislative bargaining, fiscal federalism), the model's exogenous policy rule cannot capture the feedback from economic outcomes to policy choices.
An individual household with state vector (income, wealth, MPC, tax bracket, transfer eligibility, consumption, labor status). Consumption decisions depend on disposable income and wealth through an MPC that varies with the household's position in the wealth distribution.
Household i's propensity to spend out of additional income. Decreasing in wealth-to-income ratio: low-wealth households have MPC near 0.8, high-wealth households near 0.2. The MPC gradient is the key micro mechanism that drives distributional fiscal multiplier differences.
The mapping from household i's gross income to tax liability. Can be progressive (marginal rates rise with income), flat (constant rate), or regressive (effective rate falls with income). The degree of progressivity is a primary policy parameter.
Government transfer to household i. Can be universal (same amount to all), means-tested (phased out above an income threshold), or targeted (limited to specific household categories such as unemployed or low-wealth).
Total government spending on goods and services purchased from firms. Enters aggregate demand directly. The composition of G across firm types affects which wages are paid and therefore which households receive the second-round income.
Emergent measure of income or wealth inequality across households. Not a parameter but a simulation output that responds to fiscal policy changes. Tracked for both pre-tax and post-tax-and-transfer distributions.
Ratio of change in aggregate output to change in government fiscal action (spending increase, tax cut, or transfer increase). Emergent from the simulation, not imposed. Varies with the composition and targeting of the fiscal action.
Cumulative government deficit as a fraction of GDP. Evolves endogenously with the fiscal stance, automatic stabilizers, and the growth rate of the economy. Subject to fiscal rule constraints when active.
Household consumption propensities vary systematically with wealth-to-income ratio: MPC_i = f(, where f is decreasing. This gradient is calibrated to micro evidence from natural experiments (tax rebates, stimulus checks).
If violated: If all households have the same MPC, the distributional channel collapses and the model reduces to a representative-agent setup where the targeting of fiscal policy is irrelevant for the aggregate multiplier.
Households use rule-of-thumb or buffer-stock heuristics for consumption rather than solving an infinite-horizon optimization problem with rational expectations about future fiscal policy.
If violated: Fully rational households with perfect foresight would internalize the government budget constraint (Ricardian equivalence), neutralizing the demand effects of deficit-financed transfers. The entire fiscal multiplier story requires some departure from full rationality.
Households do not fully offset government deficit spending by increasing saving in anticipation of future tax increases. Credit constraints, finite horizons, and myopia break the Ricardian channel.
If violated: Under full Ricardian equivalence, deficit-financed transfers have zero effect on aggregate demand because households save the entire transfer to pay the implied future tax liability. The model is designed to study a world where this does not hold.
Firms produce to meet demand up to a capacity constraint. Output in the short to medium run is demand-determined, not supply-constrained, making aggregate demand the binding margin.
If violated: In a supply-constrained economy (full employment, binding capacity), fiscal stimulus produces inflation rather than output gains. The model's fiscal multiplier results apply to economies with slack.
Labor, goods, credit, and fiscal channels clear in a fixed order each period rather than simultaneously.
If violated: Simultaneous clearing would require a general-equilibrium fixed point that compresses the sequential propagation the model is designed to trace.
No trade, no capital flows, no exchange rate channel. All fiscal spending stays within the domestic circular flow.
If violated: Open-economy leakages (import propensity varying with income) would reduce fiscal multipliers and add a distributional dimension to the trade balance. Extensions with trade exist but are not part of the baseline.
The tax schedule (brackets, rates, transfer rules) is set by the modeler as a policy experiment parameter, not endogenously determined by a political process.
If violated: Endogenous fiscal policy (e.g., median-voter tax setting) would make the fiscal rule a function of the income distribution, creating a two-way feedback between inequality and policy that the baseline model does not capture.
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