Sector-Specific Substitution and the Effect of Sectoral Shocks

How a shock to an individual sector propagates to the prices of other sectors and aggregates to GDP depends on how easily sectoral goods can be substituted in production, which is determined by the intermediate input substitution elasticity. Past estimates of this parameter in the US have been restrictive: they have assumed a common elasticity across industries, and have ignored the use of imports in production. This paper uses a novel empirical strategy to produce new estimates without these restrictions, by exploiting variation in import ratios and input expenditure shares from the BEA Input-Output Accounts. I find that sectors differ meaningfully in their ability to substitute inputs in production, and that the uniform estimate of the intermediate input substitution elasticity is biased downwards relative to the median sector-specific estimate. Relative to imposing the uniform elasticity, sector-specific substitution causes domestic prices to rise more in response to oil import shocks and less in response to semiconductor import shocks. It also implies the average GDP response to a sectoral business cycle is 0.35% higher, making sectoral business cycles 17.7% less costly.

💡 Research Summary

The paper “Sector‑Specific Substitution and the Effect of Sectoral Shocks” addresses a central gap in the macro‑economic literature on production networks: the assumption that the intermediate‑input substitution elasticity is identical across all industries and that the economy is closed to imports. Both assumptions are unrealistic for the United States, where industries differ markedly in their ability to substitute inputs and where imported intermediate goods play a substantial role in production.

To overcome these limitations, the author exploits the Bureau of Economic Analysis (BEA) Input‑Output Accounts, which provide yearly industry‑input expenditure shares (Ω_ij_t) and import ratios (Φ_ij_t) for 66 major U.S. sectors. By deriving a cost‑minimization condition for a representative firm, a non‑linear relationship is obtained that links changes in expenditure shares to changes in domestic prices, import ratios, the intermediate‑input substitution elasticity (θ_i), and the Armington elasticity (ξ) that governs the substitutability between domestic and imported varieties of the same good. Because the expenditure‑share changes are observed at the industry‑input‑year level, they contain sufficient variation to identify θ_i without relying on external instruments.

The author estimates θ_i and ξ jointly using a Generalized Method of Moments (GMM) approach that matches the theoretical moment conditions implied by the cost‑minimization equation to the observed data. The resulting sector‑specific estimates reveal substantial heterogeneity: the median θ_i is roughly 0.78, while the mean is about 15 % higher, and the distribution spans from around 0.5 in oil‑and‑gas‑related sectors (low substitutability) to above 1.2 in high‑technology sectors such as semiconductors (high substitutability). The estimated Armington elasticity is consistent with the literature (ξ≈3‑4).

To assess the macroeconomic relevance of this heterogeneity, the author embeds the estimated θ_i into a multi‑sector general equilibrium (GE) model of the U.S. economy, following Horvath (2000). The model features a nested CES production function: an outer nest combines labor with an intermediate‑input bundle, while the inner nest aggregates sector‑specific intermediate composites. Imported varieties enter the inner nest under the Armington assumption, and foreign prices are taken as exogenous. The model delivers three key analytical results:

1. Theorem 1 shows how changes in sectoral sales shares (λ_i) depend on the Leontief inverse (ψ), on changes in the input‑output matrix (a), and on export revenue changes.
2. Theorem 2 derives the first‑order price response of each sector to foreign price shocks, productivity shocks, and wage adjustments, again weighted by ψ.
3. Theorem 3 extends Hulten’s theorem to second order, demonstrating that the GDP response to a sectoral productivity shock includes a term proportional to the change in λ_i, which itself is a function of θ_i.

Simulation exercises illustrate the quantitative impact of sector‑specific substitution. When a 10 % oil import price shock is imposed, the “Support activities for mining” sector experiences a 27.4 % increase in its domestic price—an order of magnitude larger than the response under a uniform elasticity. Conversely, a 10 % semiconductor import price shock leads to a 30.2 % reduction in the price response of the “Motor vehicles” sector, reflecting the high θ_i in the semiconductor industry that allows firms to substitute away from the costly imported input.

When sector‑specific θ_i are used to compute the aggregate effect of sectoral business‑cycle shocks, the average GDP response to a productivity shock is 0.35 % larger than under a common‑elasticity benchmark. This amplifies the contribution of each sector’s sales‑share adjustment and translates into a 17.7 % reduction in the overall cost of sectoral business cycles.

The paper’s contributions are threefold: (1) it provides the first industry‑level estimates of intermediate‑input substitution elasticities for a comprehensive set of U.S. sectors while explicitly accounting for imported inputs; (2) it demonstrates a GMM‑based identification strategy that avoids the need for instrumental variables, thereby exploiting richer within‑industry variation; (3) it quantifies how heterogeneity in θ_i reshapes the propagation of both price and productivity shocks through the production network, offering more accurate policy‑relevant predictions for trade‑related shocks, sector‑specific subsidies, or targeted fiscal interventions.

In sum, by moving beyond the restrictive assumption of a uniform substitution elasticity and by integrating import usage, the study delivers a more realistic depiction of shock transmission in a modern, open economy. The findings suggest that policymakers should incorporate sector‑specific substitution parameters when evaluating the macroeconomic consequences of trade disruptions or sector‑targeted policies, as the magnitude and direction of price and output effects can differ dramatically across industries.