Which Government Spending Creates the Most Output?

The Question

Government spending is not monolithic. Federal defense spending on weapons systems flows into a different set of industrial sectors than state and local spending on school construction or federal nondefense spending on social services. Because each spending pattern triggers a different chain of intermediate-goods purchases through the Leontief inverse, different categories of government spending have different macroeconomic multipliers — even if their dollar totals are the same.^[1]

This study quantifies those differences for 2024 using the BEA's official twelve government final-demand columns and the 71-sector Leontief inverse.

The Method

Government Final-Demand Categories

The BEA final-demand (FD) matrix for 2024 contains twelve government columns, grouped into three agencies and four spending types:

These codes are taken directly from site_data/sectors.json (fd_cols field), which documents the BEA Use-table column scheme.^[2]

Computing the Output Multiplier

For each category $c$ with spending vector $f_c$ (sector allocations in millions of dollars), we define:

$$f_c^{\text{unit}} = \frac{f_c}{\sum_i f_{c,i}}$$

This normalizes total spending to exactly $1. The output multiplier is then:

$$m_c = \mathbf{1}' \cdot L \cdot f_c^{\text{unit}} = \sum_i (L\, f_c^{\text{unit}})_i$$

This answers: For every dollar spent by the government in category $c$, how many dollars of total gross output — across all 71 sectors — are induced, including the direct sector plus all upstream intermediate-goods chains?

Because $L$ already embeds every round of indirect effects (Sector A buys from B which buys from C…), no additional "rounds" calculation is needed. The multiplier is exact for the BEA's intermediate-goods network and is the same Type I multiplier (without income endogenization) used in the output-multiplier studies of Miller & Blair (2022, Ch. 6).

Alignment

The BEA FD table has 70 sector rows; $L$ has 71. Three sectors present in $L$ are absent from the FD table: 441 (Motor vehicle and parts dealers), 445 (Food and beverage stores), and 452 (General merchandise stores). These retail detail sectors receive $f = 0$ across all government categories — they have no row in the BEA FD table and receive no direct government final demand. Two FD rows (Other, Used) have no counterpart in $L$ and are excluded from the multiplier calculation. Net working intersection: 68 sectors. The 3 missing retail sectors are included in the $L$ matrix used for multiplication; since their $f = 0$, they contribute through $L$'s off-diagonal elements only (their upstream suppliers still count) but receive no direct government allocation.

What the Data Show

Individual Category Multipliers (2024)

Aggregate Category Multipliers

Summing across all four sub-types per agency:

Why Equipment Spending Leads

The equipment categories (F06E, F07E, F10E) achieve multipliers of 2.19–2.59 because their spending vectors are heavily concentrated in manufacturing sectors with deep intermediate-goods supply chains. The 2024 BEA defense-equipment vector (F06E) has large allocations to 3361MV (Motor vehicles — $42.3B), 3364OT (Other transportation equipment, including aircraft — $39.9B), 334 (Computer and electronic products — $21.8B), and 333 (Machinery — $2.5B). These are sectors near the top of the Rasmussen backward-linkage ranking; each dollar they receive fans out through steel, aluminum, semiconductors, chemicals, and logistics.

The consumption categories (F06C, F07C, F10C) each have a single dominant sector — GFGD (Federal general government — defense) absorbs all of defense consumption, GFGN takes all of nondefense consumption, and GSLG takes all of state-and-local consumption. These government output rows in $L$ have lower average column sums than goods-producing sectors, so their multipliers are lower.

Software/IP spending (F06S, F07S, F10S) is concentrated in construction (23) and produces identical multipliers across agency categories (1.904) because the sector allocation pattern is the same.

Clean-Input Caveat

All calculations use the square 71×71 Leontief inverse from the BEA pipeline, not the raw 70×71 A matrix. The three missing retail sectors (441, 445, 452) are explicitly set to $f = 0$ — they are not silently dropped from $L$, so their upstream-supplier effects remain active. The FD rows Other and Used (bookkeeping rows in the BEA Use table) are excluded from $f_c$ with no loss of economic content.^[1]

The Takeaway

The ranking is not politically obvious: federal defense spending on equipment produces a larger multiplier (2.19) than federal nondefense consumption (1.55) because the equipment purchase pattern is tilted toward high-multiplier manufacturing sectors. State and local spending, dominated by consumption of government services ($2.55 trillion in F10C), has a higher aggregate multiplier (1.77) than federal nondefense (1.59) primarily because of state-and-local equipment and software allocations.

The policy implication depends on what question you are asking. If the goal is maximum short-run output amplification, equipment-intensive government spending dominates. If the goal is service delivery (health care, education, social programs), the sectoral composition necessarily shifts toward lower-multiplier sectors — and comparing multipliers across categories with different social purposes is a category error. The I-O model is neutral on that normative question; it simply maps each spending pattern to its gross-output implications.^[2]

Reproduce This

Download the full replication bundle at:

/api/study/fiscal-multipliers/bundle.zip

unzip leontief_study_fiscal-multipliers.zip
cd code
pip install -r requirements.txt
python analysis.py
# Outputs: outputs/fiscal.csv, outputs/fig_fiscal_mult.json

The script reads data/L_2024.csv, data/fd_matrix_2024.csv, data/fd_cols.csv, and data/sector_names.csv. It uses only pandas and NumPy (no networkx, no scipy). The alignment of FD rows to L's index is performed explicitly and logged to stdout on every run. An analysis.ipynb notebook mirrors every step.

^[1][2]