Labor Share, Markups, and Input-Output Linkages – Evidence from the U.S. National Accounts

Layer 1: Overview

The paper asks why the U.S. labor share has declined over the postwar period, and whether rising markups or capital deepening (automation, falling capital prices) is the primary driver. The authors argue that the existing literature lacks consensus partly because micro-level studies weight producers by sales shares rather than Domar weights, which are gross-output-to-GDP ratios that correctly capture how sectoral changes propagate through the input-output structure. When intermediate inputs are themselves marked up by their producers and then re-marked-up by downstream firms (“double marginalization”), a modest sectoral markup increase is amplified into a substantially larger aggregate effect.

The empirical framework is a two-sector (goods versus services) multisector extension of the Farhi-Gourio (2018) model with Cobb-Douglas production functions and monopolistic competition in the Dixit-Stiglitz tradition. The model is calibrated to three balanced-growth-path subperiods — 1957–1973, 1984–2000, and 2001–2016 — using U.S. NIPA data covering gross output, intermediate inputs, compensation, capital stocks, investment, and sectoral price-dividend ratios from Kenneth French’s data library. The unobservable user cost of capital, which is needed to separate normal capital returns from markups (factorless income), is backed out from the model’s Euler equation via the Gordon growth formula applied to sectoral price-dividend ratios and includes a risk premium.

Main quantitative findings: The aggregate labor share fell 4.9 percentage points (pp) from 1957–1973 to 2001–2016. Aggregate markups rose 6.6 pp (from 1.072 to 1.138), more than either sector’s standalone increase, because double marginalization through input-output linkages amplifies sectoral markups into a larger aggregate effect. Sectoral gross-output markups rose approximately 3.8 pp in goods (1.039 to 1.077) and 3.3 pp in services (1.034 to 1.067). In the top-down counterfactual holding markups constant at their 1957–73 levels, the labor share falls only 0.5 pp instead of 4.9 pp — markups account for 4.4 pp of the total 4.9 pp decline. Holding labor output elasticities constant instead yields only a 2.2 pp decline; holding materials elasticities constant reduces the decline by 0.8 pp; holding structural change (sector output weights) constant causes the labor share to fall 7.7 pp — meaning structural reallocation to services offset 2.8 pp of the decline. In a bottom-up Taylor decomposition, the first-order direct effects of rising markups account for 5.0 pp and falling labor output elasticities account for 4.4 pp — together nearly twice the actual 4.9 pp decline, confirming the Grossman-Oberfield (2021) observation that individual candidate forces over-explain the total. The offsetting effects that reconcile the over-explanation are: (i) the interaction of falling goods-sector labor elasticities with structural change toward services (which have a higher and slightly rising labor elasticity) offsets 3.6 pp, and (ii) the interaction of rising markups with changing sector weights offsets a further 0.8 pp; the aggregate labor output elasticity αL barely changes (0.794 to 0.788) because capital deepening in goods (goods value-added labor elasticity fell from 0.807 to 0.700) is fully offset by reallocation to services (services value-added labor elasticity rose from 0.790 to 0.814). The final-output share of goods fell by more than half, from 0.460 to 0.194. Materials intensities rose in both sectors (goods non-intermediate factor share fell from 0.374 to 0.353; services from 0.625 to 0.572), amplifying double marginalization over time. The user cost of capital declined from roughly 13.8% to 12.3% in aggregate, driven by falling expected discount rates (from ~6.1% to ~3.4%), partially offset by rising depreciation rates. When IPP capital is excluded from NIPA measurement, the aggregate labor share declines by only 1 pp (from 0.743 to 0.732), consistent with Koh et al. (2021).

The paper’s core implication for the debate is that forces concentrated in the goods sector — capital deepening, automation, globalization, declining union power — cannot account for the aggregate labor share decline because the goods sector shrank dramatically and structural change to services largely offsets goods-specific capital deepening. A credible candidate explanation must affect both goods and services with similar strength, and rising markups do: sectoral gross-output markups increased by similar amounts in both sectors (roughly 3.3–3.8 pp each), and input-output linkages amplify their aggregate impact substantially.

Layer 2: Deep Dive

What is the model structure and why does it differ from one-sector models?

The model is a two-sector (goods, services) extension of Farhi-Gourio (2018) with Epstein-Zin preferences, Dixit-Stiglitz aggregation of varieties within each sector, Cobb-Douglas production in capital, labor, and intermediate inputs from both sectors, and sector-specific markups under monopolistic competition. The two-sector structure is essential because (i) labor shares differ substantially across sectors at any point in time, (ii) they evolve differently over time, and (iii) goods production is far more materials-intensive than services. A one-sector model cannot capture the double marginalization amplification, the input-output linkages between sectors, or the offsetting effects of structural change.

What is the identification strategy for separating output elasticities from markups?

A well-known challenge is that one must split the residual between capital’s normal return and pure profit (markup). The authors do not use micro production data. Instead they calibrate the user cost of capital from the model’s balanced-growth-path Euler equation: ρj is inferred from the Gordon growth formula applied to sectoral price-dividend ratios from Kenneth French’s data library. Given ρj, the depreciation-plus-capital-loss term δj + γQ is inferred from the sectoral investment-capital ratio. The markup then equals sectoral gross output value divided by the sum of all observed factor payments (labor compensation, materials costs) plus the imputed capital cost (user cost times capital stock). Output elasticities of each factor equal their respective cost shares in total factor payments, a standard Cobb-Douglas result.

What are the main threats to identification and how are they addressed?

Three main threats are addressed. First, the price-dividend ratio (the key input for ρj) covers only listed corporations, not all private firms; the authors note listed firms account for about 60% of business capital, and Atkeson, Heathcote, and Perri (2025) find very similar rates of return using a broader measure. Second, the shift toward share repurchases rather than cash dividends may understate payout yield and overstate the fall in ρ, inflating markups; the authors rerun the model using Boudoukh et al. (2007) repurchase-adjusted yields and find aggregate markups still increase by 5 pp (vs. 7 pp in the baseline). Third, the balanced-growth-path assumption imposes constant ratios within each subperiod, which may be violated; the robustness exercise recalibrating with 2016 end-of-sample values yields nearly identical conclusions.

How is double marginalization measured and why does it matter so much?

Double marginalization arises because approximately half of U.S. gross output value is materials costs, and those inputs are purchased from monopolistically competitive suppliers who charge a markup. When the downstream firm marks up its own price, it marks up the cost of already-marked-up inputs a second time. Formally, the aggregate markup exceeds any sectoral markup because intermediate goods get embedded in final goods through the Leontief inverse (Domar weights). The paper proves in Proposition 3 that aggregate markups are the same in gross-output and value-added models, but sectoral value-added markups are always larger than gross-output markups; this means taking simple cost- or revenue-weighted averages of sectoral value-added markups overstates the implied market power and misrepresents the channel. Materials intensities rose in both sectors over the sample, so double marginalization has itself increased over time, adding to the aggregate markup rise beyond what sectoral gross-output markups alone would imply.

What heterogeneity is documented across sectors?

Goods and services differ in three key respects that are quantified: (i) Materials intensity: goods gross-output materials share is roughly 0.60 versus 0.40 for services (2001-16 averages), making double marginalization far stronger in goods. (ii) Capital deepening: the goods value-added labor elasticity ˜αLg fell from 0.807 to 0.700 (-10.7 pp) while services ˜αLs rose from 0.790 to 0.814 (+2.3 pp). (iii) Domar weights: the goods Domar weight Φg fell from 1.018 to 0.572 while services Φs rose from 0.933 to 1.289, reflecting the shift of economic activity toward services. Despite these differences, sectoral gross-output markups increased by similar amounts in both sectors (3.8 pp goods, 3.3 pp services), which is the main reason markups can explain the aggregate decline while sector-specific capital deepening cannot.

What robustness checks are run?

Four sets of robustness exercises are presented. (1) Balanced-growth-path assumption: the model is recalibrated using only 2016 end-of-sample values for the final period; results are nearly unchanged, though markups come out slightly higher. (2) Dividend measurement: repurchase-adjusted payout yields from Boudoukh et al. (2007) are used; aggregate markups still increase by 5 pp rather than 7 pp, so the conclusion is unchanged though the magnitude is modestly smaller. (3) Missing capital — organizational capital: using Crouzet-Eberly (2021) estimates, including organizational capital reduces the markup level (from 1.138 to 1.092 in 2001-16) but barely changes the markup increase (from 4.6 pp to 3.9 pp). (4) Missing capital — land: industrial and commercial land values over 2002-16 averaged roughly $2 trillion versus a private non-real-estate capital stock of $16.6 trillion; eliminating the markup increase would require a 27% rise in the capital-output ratio, but land can provide at most a 12% increase even under extremely counterfactual assumptions. (5) Alternative user cost: using Barkai (2020)’s Aaa interest rate yields aggregate markups increasing from 1.101 to 1.151 (1984-2000 to 2001-16), similar to baseline. (6) IPP capital: excluding IPP from NIPA yields only a 1 pp labor share decline, consistent with Koh et al. (2021). (7) Intangible capital generally: including intangible capital in the NIPA does not change the importance of markups.

How do the authors reconcile their low gross-output markups with the much higher firm-level markups found by De Loecker, Eeckhout, and Unger (2020)?

The reconciliation has two parts. First, weighting: De Loecker et al. use sales-weighted markups, whereas the model-correct weighting in this context is harmonic cost-weighting (Hasenzagl and Perez, 2023); cost-weighted markups in this paper grow only 5 pp (from 1.193 to 1.246) versus 21 pp for sales-weighted markups, substantially narrowing the gap. Second, returns to scale and fixed costs: the paper assumes constant returns to scale and no fixed costs, so all markup revenue is pure profit. Firm-level studies assume fixed costs exist, meaning their markups must cover both pure profits and overhead, so markups are mechanically larger. A fixed cost share of about 15% of production costs accounts for the remaining difference between the two estimates. Importantly, both approaches produce similar economic profit rates: this paper finds sales-weighted profit rates of 4.5% (1984-2000) rising to 6.6% (2001-16), similar to De Loecker et al.’s finding of profit rates rising from 1% in 1980 to 8% in 2016.

What is the role of structural change, and why does it offset capital deepening but not markups?

Structural change — the reallocation of final-output expenditure shares away from goods toward services — acts as a natural counterweight when a factor depresses labor share only in the shrinking sector. Capital deepening (falling goods labor elasticity) is concentrated in goods; as goods’ expenditure share fell from 0.460 to 0.194, the weight placed on goods in the aggregate labor share shrank, largely undoing the direct effect of capital deepening on aggregate labor share. The second-order interaction term in the bottom-up decomposition confirms this: the interaction of falling labor elasticities with changing sector weights offsets 3.6 pp. In contrast, markups rose by similar amounts in both goods and services, so there is no equivalent shrinking-sector effect to offset the markup increase; summing the direct markup effect (−5.0 pp) with the markup-weight interaction (+0.8 pp) gives approximately the full observed decline.

How does the paper treat the possibility of labor monopsony as an explanation?

The paper acknowledges that labor monopsony (markdowns over wages) could in principle produce a gap between price and marginal cost similar to product markups. However, the authors argue the evidence does not support a role for increasing markdowns in driving the aggregate labor share trend: Yeh, Macaluso, and Hershbein (2022) find large markdowns in manufacturing but no role for them in explaining the time series of manufacturing labor share; Deb et al. (2022), allowing for both markups and markdowns, attribute changes in the price-marginal-cost gap to markups; Kirov and Traina (2023) find similar evidence in manufacturing. The authors therefore interpret their factorless-income estimates as markups rather than markdowns.

What are the policy implications and their scope conditions?

The main policy implication is that explanations for the labor share decline should focus on product market power (markups) operating across both the goods and services sectors, not primarily on capital-deepening forces such as automation or falling capital prices. The paper does not directly propose policy remedies, but the results imply that policies targeting capital deepening or trade-induced displacement alone cannot fully explain or reverse the aggregate labor share trend. The analysis is scoped to the U.S. private economy excluding real estate, 1957–2016, and the two-sector decomposition. The authors acknowledge the NIPA-based approach cannot directly speak to the firm-level sources of increasing markups (market concentration, fixed costs, intangibles), leaving the microeconomic explanation for rising sectoral markups to future research. Extension to finer industry disaggregations and other countries is flagged as a direct next step.

What is the paper’s contribution relative to Farhi-Gourio (2018) and Karabarbounis-Neiman (2014)?

Farhi-Gourio (2018) is a one-sector model calibrated at the aggregate level; this paper extends it to two sectors with explicit input-output linkages, allowing the decomposition to distinguish sector-specific from aggregate forces and to quantify double-marginalization amplification. Karabarbounis-Neiman (2014) attributed the labor share decline primarily to falling relative prices of capital (capital deepening) driven by an elasticity of substitution between capital and labor exceeding one; this paper’s calibration finds that the aggregate output elasticity of labor barely changes (0.794 to 0.788), which is inconsistent with capital deepening as the dominant aggregate force, and notes that evidence from Herrendorf et al. (2015) and Oberfield-Raval (2021) suggests the elasticity of substitution is below one in most of the goods sector. Moreira (2022) also uses an input-output model but does not allow markups by intermediate producers, which this paper shows is quantitatively crucial.

Why does the paper use NIPA data rather than firm- or establishment-level data?

NIPA data have four advantages in this context: (i) they cover all market activity rather than just publicly listed or large firms; (ii) they capture inter-sectoral input-output linkages that micro datasets lack; (iii) they include broad coverage of intangible assets (IPP) following the 1999 and 2013 revisions; and (iv) they respect standard accounting adding-up constraints, ensuring that sectoral forces aggregate consistently to the macro level. The NIPA-based calibration also has limited data requirements, making it feasible to extend the analysis back to the late 1950s and, potentially, to other countries. The main limitation is that NIPA data are available only at the two-sector level of aggregation for the full postwar period, due to the switch from SIC to NAICS classification in 1997 and the aggregated reporting of some items like proprietors’ income.

Key Concepts

Domar weight: The ratio of a sector’s gross output value to aggregate final output (GDP). Unlike expenditure weights, Domar weights exceed one when summed across sectors because they capture how a sector’s output is both a direct contributor to final demand and an indirect contributor through its use as intermediate inputs elsewhere. The paper uses Domar weights as the correct aggregation weights for sectoral labor shares, showing that properly accounting for input-output linkages through these weights is essential for connecting sectoral forces to aggregate outcomes.

Double marginalization: The amplification of sectoral markups at the aggregate level that occurs because intermediate inputs are priced above marginal cost by their producers (first markup) and then purchased and re-priced above marginal cost by downstream firms (second markup). In this paper’s model, double marginalization causes the aggregate markup to exceed either sector’s standalone gross-output markup; with roughly half of U.S. gross output being materials cost, the amplification is quantitatively large (aggregate markups of 6.6 pp increase versus sectoral increases of only 3.3–3.8 pp).

Gross-output markup: The ratio of a sector’s gross output value to the sum of all factor payments at the gross-output level (capital user costs times capital stock, plus labor compensation, plus the cost of intermediate inputs from all sectors). Under perfect competition this ratio equals one; deviations above one represent market power. This differs from value-added markups, which divide value added by only capital and labor payments, and are therefore mechanically inflated in materials-intensive sectors via double marginalization even when gross-output markups are identical across sectors.

Risky balanced growth path (RBGP): The equilibrium concept used for calibration, extending the standard balanced growth path to allow for rare disaster shocks (Farhi-Gourio). Along the RBGP, expected variables grow at constant rates, but occasional level shifts occur when the rare disaster shock materializes. This allows the model to have realistic risk premia embedded in the discount rate ρ while maintaining analytically tractable solutions; the calibration avoids modeling transitional dynamics and instead compares the RBGP parameters across sub-periods.

Output elasticity of labor (αL): The Cobb-Douglas coefficient on labor in the production function, equal under the paper’s calibration to each factor’s cost share in total factor payments. Changes in αL represent capital deepening (automation, falling capital prices) when αL falls because capital displaces labor in production. The key finding is that αL barely changes at the aggregate level (0.794 to 0.788) over the full 1957–2016 period because capital deepening in goods is offset by structural change toward services.

Factorless income: Income that remains after subtracting payments to labor (at market wages) and payments to capital (at normal user cost rates) from gross output. In this model, factorless income equals markup revenue (the portion of output value above total factor payments). Rising factorless income / markups are the mirror image of the declining labor share when the output elasticity of labor does not change.

Structural change (in this paper’s sense): The reallocation of final-output expenditure shares across goods and services sectors over time, captured by changes in the expenditure weights ϕj. The paper documents that the goods final-output share fell by more than half (from 0.460 to 0.194) over 1957–2016. Structural change acts as a counterweight to any force concentrated in the goods sector: as goods’ weight shrinks, the aggregate labor share becomes more determined by services.