Fiscal Policy Transmission in Production Networks with Heterogeneous Households

 The theoretical model developed in the sources is a multisector New Keynesian model that integrates production networks with heterogeneous households to study the transmission of sector-specific fiscal policy. This framework moves beyond traditional aggregated models by demonstrating that fiscal transmission is governed by the interaction between sectoral production linkages and the distribution of household marginal propensities to consume (MPCs).

Core Components of the Theoretical Model

The model environment consists of several interacting parts:

• Production Network: The economy has $N$ sectors connected through complex input-output linkages. Firms use Cobb-Douglas technology with constant returns to scale, and their interconnections are summarized by an input-output matrix ($A$).
• Household Heterogeneity: In each sector, a fraction of households are hand-to-mouth (HtM), consuming all their current income, while the remainder are Ricardian (savers) who participate in asset markets to smooth consumption.
• Segmented Labor Markets: Households possess sector-specific skills and can only supply labor to their specific sector. This segmentation means fiscal policy affects household income through specific sectoral labor markets.
• Nominal Rigidities: The model incorporates nominal wage and price rigidities, which allow demand-driven shocks to have real effects on output.

Key Analytical Innovations

The sources introduce two primary analytical tools to characterize fiscal transmission:

• The Intersectoral Keynesian Cross: This captures how fiscal spending shocks propagate through the economy by combining demand-driven amplification with network propagation.
• The MPC-Augmented Network Multiplier: This sufficient statistic summarizes the propagation of sectoral demand shocks. It accounts for the feedback loop between sector-specific income and household consumption responses, alongside the propagation of shocks through the input-output structure.

Transmission Mechanisms in Multisector Economies

The model reveals that production networks do not mechanically amplify fiscal policy; instead, their effect is non-additive and depends on income redistribution. The effectiveness of a fiscal shock is governed by three forces:

1. Keynesian Spending Channel: Multipliers increase with the share of high-MPC (hand-to-mouth) households in a sector.
2. Network Propagation: Intersectoral linkages generate a "multiplier-of-the-multiplier" effect as demand in one sector transmits to upstream suppliers.
3. Income Redistribution: The interaction between these two channels depends on whether the income generated by government spending flows to high-spending households or is dissipated through intermediate input purchases and savings.

Conditions for Amplification vs. Attenuation

The model identifies a critical threshold for whether a production network amplifies or dampens fiscal transmission.

• Amplification: Occurs when fiscal policy directs income toward labor-intensive, downstream sectors that employ a large share of high-MPC households.
• Attenuation: Occurs when government spending flows to sectors where revenue primarily pays for intermediate inputs from other firms rather than wages, or where income goes to Ricardian households who tend to save it.

Ultimately, the theoretical model suggests that ignoring either household heterogeneity or the granular production structure leads to a significant mismeasurement of fiscal multipliers, as the two features jointly determine how income flows through the economy and translates into aggregate demand.

The sources introduce two primary analytical tools designed to study fiscal policy transmission in complex, multisector economies: the Intersectoral Keynesian Cross and the MPC-augmented network multiplier,,. These tools integrate two traditionally separate strands of research—production networks and household heterogeneity—to show how sector-specific shocks propagate through the economy,,.

The Intersectoral Keynesian Cross

The Intersectoral Keynesian Cross is an analytical framework that captures how fiscal spending shocks propagate through both intersectoral linkages and sector-specific spending propensities,.

• Unified Transmission: It provides a unified characterization of fiscal transmission by illustrating the feedback loop between production and demand,.
• Interaction of Channels: Graphically, it represents the economy as a system of interacting parts: production linkages (the flow of intermediate goods between sectors) and consumption spending (the flow of income back to households based on their marginal propensities to consume).
• Demand-Driven Propagation: This tool helps decompose how a demand change in one sector reallocates income across various households, which in turn feeds back into aggregate demand,,.

The MPC-Augmented Network Multiplier

This tool serves as a sufficient statistic that summarizes the propagation of sectoral demand shocks by combining demand-driven amplification with network propagation,,. It identifies two reinforcing mechanisms:

1. Keynesian Spending Multiplier: Multipliers increase with the share of hand-to-mouth (HtM) households in a sector, as these individuals spend nearly all of their labor income immediately,.
2. Network Multiplier: This captures the "multiplier-of-the-multiplier" effect, where demand in one sector transmits upstream to suppliers through the input-output structure,.

The sources highlight that fiscal multipliers are largest when spending is directed toward labor-intensive, downstream sectors that employ a large share of high-MPC households, such as wholesale and retail trade,,.

Context: Amplification vs. Attenuation

In the larger context of multisector economies, these analytical tools demonstrate that the interaction between production networks and household heterogeneity is non-additive,. These features can either reinforce or offset each other:

• Amplification: Occurs when fiscal policy directs income toward sectors where workers have high spending propensities,.
• Attenuation (Dampening): Occurs if government spending flows to sectors where revenue primarily pays for intermediate inputs rather than wages, or if the income reaches households that tend to save rather than spend,,.
• The Inflection Point: The tools identify a critical threshold (an inflection point) where stronger network linkages can actually reduce the overall fiscal multiplier because they divert income away from high-spending workers toward intermediate input purchases,,.

Ultimately, these tools show that ignoring the joint structure of production networks and household heterogeneity risks a significant mismeasurement of fiscal effects, as aggregate models fail to see how income redistribution across sectors governs the final impact on economic activity,,.

In the context of multisector economies, the transmission of fiscal policy is governed by a non-additive interaction between two primary mechanisms: the Keynesian spending channel and production network propagation. The sources argue that these channels do not operate in isolation; rather, the production network acts as a conduit that reallocates income across households with varying marginal propensities to consume (MPCs), which can either amplify or dampen the total fiscal effect.

The Primary Transmission Channels

The theoretical framework identifies three specific forces that shape fiscal transmission:

• The Keynesian Spending Channel: This channel is driven by household heterogeneity. Fiscal shocks that increase labor income in a sector generate a strong aggregate demand response if that sector employs a large share of hand-to-mouth (HtM) households. These households spend their post-tax income immediately, creating a feedback loop between income and demand.
• The Network Propagation Channel: Production linkages create a "multiplier-of-the-multiplier" effect. When the government purchases goods from a specific sector, that sector must increase its demand for intermediate inputs from upstream suppliers, transmitting the initial shock throughout the supply chain.
• The Income Redistribution Channel: Fiscal policy inherently reallocates resources. In these multisector models, spending typically redistributes income from Ricardian households (savers) to HtM households. The effectiveness of the transmission depends on whether the income generated by the policy flows to workers who will spend it or is captured by intermediate input costs and households with low MPCs.

Factors Determining Amplification vs. Attenuation

The sources emphasize that production networks do not "mechanically" amplify shocks; the direction of the transmission depends on sectoral characteristics.

• Amplification (Strong Transmission): Fiscal policy is most effective when targeted at labor-intensive, downstream sectors. Because these sectors are closer to the final consumer and spend a higher proportion of revenue on wages rather than intermediate goods, a larger share of the fiscal stimulus reaches high-MPC households. Quantitative examples include the wholesale and retail trade sector, which yields high multipliers (approx. 1.2) due to its high concentration of HtM workers.
• Attenuation (Dampening Effects): If government spending flows to sectors that rely heavily on intermediate inputs from other firms, the income is "dissipated" through the network before it can reach households directly. Furthermore, if the income reaches Ricardian households who save rather than spend, the Keynesian channel is weakened. Sectors like communication & FIRE (finance, insurance, and real estate) often display multipliers below one because they lack exposure to high-MPC households.

The Critical Threshold (Inflection Point)

A key analytical insight is the existence of a threshold condition for network amplification. When the share of HtM households in a sector is relatively low, stronger network linkages amplify the fiscal effect by spreading demand upstream. However, once the share of high-MPC households exceeds a certain point, stronger linkages can actually dampen transmission. At this inflection point, the production network begins to divert income away from high-spending local workers and toward intermediate input purchases, effectively "leaking" the stimulus into parts of the economy with lower spending responses.

Distributional and Institutional Influences

The transmission is further complicated by institutional factors:

• Labor Market Segmentation: Because households possess sector-specific skills and cannot easily move between sectors, fiscal shocks are "locked" into specific sectoral labor markets, making the initial distribution of HtM households critical.
• Financing and Taxes: The transmission is attenuated if the fiscal expansion is financed by taxes on HtM households, as this reduces their disposable income and offsets the Keynesian spending response.
• Nominal Rigidities: The presence of sector-specific wage and price rigidities ensures that demand-side shocks have real effects on output rather than being immediately absorbed by price changes.

The empirical evidence presented in the sources, primarily drawn from United States microdata, documents substantial sectoral heterogeneity in household balance sheets and production linkages. These empirical patterns are critical because they demonstrate that fiscal shocks propagate through the economy in ways that depend not only on the production network but also on the specific distribution of high-MPC households across different sectors.

Household Balance Sheet Heterogeneity (SCF Data)

Using data from the Survey of Consumer Finances (SCF) covering 1989–2019, the sources establish that household portfolios vary systematically by the sector in which the household head is employed.

• Wealth and Income Disparities: There are "pronounced and persistent" differences in liquid assets and wages across sectors. For instance, agricultural workers have a median liquid net wealth of less than $600, whereas workers in Communication & FIRE (Finance, Insurance, and Real Estate) hold more than $4,200. Similarly, median annual salaries reach approximately $72,000 in manufacturing but are only about $35,500 in agriculture.
• Hand-to-Mouth (HtM) Prevalence: These financial differences translate into varying shares of HtM households—those who consume all their current income. The fraction of HtM households ranges from roughly 28% in Communication & FIRE to over 40% in agriculture.
• Demographic Persistence: These sectoral differences are not transitory; they have remained stable across survey waves for three decades. The data also shows distinct age profiles: poor HtM households are more common at the beginning of the working life, while wealthy HtM households (those with illiquid assets but no liquid cash) peak between ages 40 and 50.

Production Network and Sectoral Bias (BEA Data)

The sources utilize Bureau of Economic Analysis (BEA) input-output tables to map the U.S. production network.

• Intersectoral Linkages: This mapping reveals a "dense system" of linkages where demand changes in one sector transmit to upstream suppliers.
• Government Procurement: Empirical evidence from U.S. procurement contracts (2001–2019) shows a significant sectoral bias in government spending, which is often concentrated in specific areas like defense-related industries or services, rather than being distributed evenly across the GDP.

Quantitative Implications for Fiscal Multipliers

When the multisector model is calibrated to this U.S. data, it reveals that the effectiveness of fiscal policy varies significantly depending on the target sector:

• High Multipliers: Spending in Wholesale & Retail Trade yields a multiplier of approximately 1.2, meaning every dollar spent generates $1.20 in economic activity. This high response occurs because the sector employs a large share of high-spending HtM households and is positioned downstream in the production network.
• Low Multipliers: Conversely, spending in Communication & FIRE yields a multiplier below unity (approximately 0.91), as it lacks exposure to high-MPC households and part of the stimulus is "dissipated" through the production structure.
• Crowding-In vs. Crowding-Out: The U.S. data suggests that only certain sectoral shocks (like those in agriculture or retail) are strong enough to crowd in private consumption; in sectors like Communication & FIRE, aggregate consumption actually declines in response to fiscal spending.

Ultimately, the sources argue that these empirical findings prove that aggregate macroeconomic models risk a significant mismeasurement of fiscal effects by ignoring how the granular U.S. production structure reallocates income between households with different spending behaviors.

The quantitative findings from the sources demonstrate that when accounting for both production networks and household heterogeneity, fiscal multipliers vary substantially across sectors, ranging from 0.91 to 1.23,. This significant dispersion is primarily driven by the interaction between a sector's position in the supply chain and the specific financial profiles of the households it employs,.

Variation in Sectoral Fiscal Multipliers

The effectiveness of fiscal policy depends heavily on which sector receives the spending:

• High Multiplier Sectors: Spending in Wholesale & Retail Trade yields one of the highest multipliers at approximately 1.2 to 1.23,,. This high response occurs because the sector employs a large share of high-spending hand-to-mouth (HtM) households and occupies a downstream position in the production network, allowing the Keynesian spending channel and network propagation to reinforce each other. Agriculture also shows a high multiplier (~1.13),.
• Low Multiplier Sectors: Conversely, spending in Communication & FIRE (Finance, Insurance, and Real Estate) results in a multiplier below unity, approximately 0.91,,. In this sector, limited exposure to high-MPC households and a production structure that does not translate easily into demand amplification cause part of the stimulus to be "dissipated",.

Household Heterogeneity vs. Representative Agent Models

The sources find that traditional representative-agent (RA) models significantly mismeasure fiscal effects:

• Increased Dispersion: Introducing household heterogeneity into a multisector model significantly increases the dispersion of fiscal multipliers compared to an RA framework, where multipliers are relatively similar and generally remain below one,,.
• Amplification Levels: In sectors like wholesale and retail trade, the heterogeneous-agent (HA) model generates multipliers that are more than 30% larger than those in a representative-agent model. Overall, using an RA framework instead of an HA benchmark reduces the median fiscal multiplier by about 8%.

Counterfactual Findings and Network Effects

Counterfactual exercises highlight that production networks do not always amplify policy effects:

• Dampening Effects: In sectors like Agriculture, the multiplier is actually larger in a counterfactual economy without network linkages. This is because the production network can redistribute income away from high-spending local workers toward intermediate input purchases, which attenuates the Keynesian channel,.
• The Inflection Point: Mining & Construction are identified as being near an "inflection point," where their fiscal multipliers (~0.98) remain largely unchanged regardless of whether production linkages or household heterogeneity are included,.
• Sectoral Composition: Equalizing employment shares across sectors would increase the median multiplier by approximately 9%, reflecting the outsized role that sectors with high HtM shares (like agriculture) play in national fiscal transmission.

Spillovers and Distributional Consequences

The quantitative analysis also tracks how shocks propagate beyond the target sector:

• Cross-Sectoral Spillovers: Sector-specific shocks generate non-negligible spillovers; for example, spending in agriculture or mining generates strong production responses in manufacturing,.
• Income Redistribution: Fiscal policy consistently redistributes income from Ricardian (saver) households to HtM households,. These distributional effects are most pronounced in the wholesale & retail trade and agriculture sectors.
• Purchases vs. Transfers: The sources find that government purchases are generally more effective at stimulating consumption than targeted transfers. In sectors like communication & FIRE, targeted transfers can actually crowd out private consumption, whereas the services sector is the only one where transfers consistently have a stimulative effect on aggregate demand.

The effectiveness of fiscal policy in a multisector economy is determined by the interaction between a sector's position in the production network and the marginal propensities to consume (MPCs) of the households it employs,. The sources highlight that fiscal policy is not a one-size-fits-all tool; its impact—measured by the fiscal multiplier—varies significantly based on several key determinants,.

1. Household Spending Behavior (The Keynesian Channel)

The most critical determinant of effectiveness is the share of hand-to-mouth (HtM) households within the sector receiving the fiscal stimulus,.

• High-MPC Households: Fiscal policy is most effective when it directs income toward sectors with a high proportion of HtM households, such as agriculture or wholesale and retail trade,. These households spend nearly all additional income immediately, creating a powerful feedback loop of demand,.
• Targeted Transfers vs. Purchases: The sources note that government purchases are generally more effective than transfers, although transfers specifically targeted at HtM households in the service sector can generate strong consumption responses,.

2. Sectoral Production Characteristics

The internal structure of a sector dictates how much of a fiscal dollar actually reaches the pockets of high-spending workers,.

• Labor Intensity: Multipliers are higher in labor-intensive sectors. If a sector spends a large portion of its revenue on wages rather than intermediate inputs, more income reaches households directly to fuel the Keynesian spending channel,.
• "Downstreamness": Sectors that are "downstream" (closer to final consumers) tend to have larger multipliers. These sectors often have higher labor shares and a more direct connection to high-MPC household demand.

3. Production Network Linkages (The Multiplier-of-the-Multiplier)

The input-output structure of the economy can either amplify or dampen fiscal transmission depending on how it redistributes income,.

• Network Amplification: In sectors with low HtM shares, stronger intersectoral linkages typically amplify the fiscal effect by generating additional demand through upstream suppliers (the "multiplier-of-the-multiplier" effect),.
• The Inflection Point: A key finding is that production networks do not mechanically amplify policy. If a sector already has a very high share of high-MPC workers, stronger network linkages can actually dampen effectiveness,. This is because the network "leaks" income away from high-spending local workers toward intermediate input purchases from other sectors that may have lower spending propensities,.

4. Institutional and Policy Factors

The broader economic environment and the way policy is implemented also serve as determinants:

• Nominal Rigidities: Fiscal stimulus is found to be more effective in sectors with higher wage rigidity. Sticky wages ensure that increased demand translates into higher output and employment rather than being immediately absorbed by price and wage increases.
• Financing and Taxes: The effectiveness of fiscal policy is attenuated if the spending is financed by taxes on HtM households. Taxes on these households reduce their disposable income, directly offsetting the stimulative effects of the Keynesian spending channel.
• Monetary Policy Response: The sources assume a "real rate rule" where the central bank offsets inflation, making the fiscal effect purely demand-driven. If monetary policy were to respond differently, the overall effectiveness would change.

Ultimately, the sources argue that ignoring these determinants—particularly the joint distribution of production linkages and household consumption responses—leads to a significant mismeasurement of fiscal effects,.