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Sector-Specific Substitution and the Effect of Sectoral Shocks

Jacob Toner Gosselin

TL;DR

The paper relaxes two restrictive assumptions in the literature on sectoral shock propagation by allowing sector-specific intermediate-input substitution elasticities ($\theta_i$) and by incorporating imports via the Armington elasticity ($\xi$), using BEA Input-Output Accounts to identify these parameters for 66 US industries. It shows substantial heterogeneity in $\theta_i$, with the uniform elasticity biased downward relative to the median sector-specific estimate, and demonstrates that this heterogeneity materially alters how shocks to import prices and sectoral productivity translate into price movements and GDP outcomes. Using a multi-sector GE model calibrated to the US, the study finds that sector-specific substitution amplifies oil-related price responses to oil-import shocks while dampening semiconductor-related responses, and that sector-specific elasticities increase the mean GDP impact of sectoral cycles by $0.35\%$, reducing the cost of sectoral fluctuations by about $17.7\%$. Overall, accounting for sectoral heterogeneity in substitution improves macroeconomic predictions and policy relevance by more accurately capturing the non-linear propagation of shocks through production networks.

Abstract

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.

Sector-Specific Substitution and the Effect of Sectoral Shocks

TL;DR

The paper relaxes two restrictive assumptions in the literature on sectoral shock propagation by allowing sector-specific intermediate-input substitution elasticities () and by incorporating imports via the Armington elasticity (), using BEA Input-Output Accounts to identify these parameters for 66 US industries. It shows substantial heterogeneity in , with the uniform elasticity biased downward relative to the median sector-specific estimate, and demonstrates that this heterogeneity materially alters how shocks to import prices and sectoral productivity translate into price movements and GDP outcomes. Using a multi-sector GE model calibrated to the US, the study finds that sector-specific substitution amplifies oil-related price responses to oil-import shocks while dampening semiconductor-related responses, and that sector-specific elasticities increase the mean GDP impact of sectoral cycles by , reducing the cost of sectoral fluctuations by about . Overall, accounting for sectoral heterogeneity in substitution improves macroeconomic predictions and policy relevance by more accurately capturing the non-linear propagation of shocks through production networks.

Abstract

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.

Paper Structure

This paper contains 24 sections, 4 theorems, 39 equations, 6 figures, 10 tables.

Table of Contents

  1. Related Literature
  2. Theoretical Framework
  3. Model
  4. The Role of Substitution Elasticities
  5. Deriving Empirical Specification
  6. Comparison to Past Work
  7. Empirical Results
  8. Data Construction and Estimation
  9. Estimation
  10. Empirical Results
  11. Discussion
  12. Quantitative Results
  13. Shock Propagation to Prices with Sector-Specific Substitution
  14. Shock Aggregation to GDP with Sector-Specific Substitution
  15. Theoretical Appendix
  16. ...and 9 more sections

Key Result

Theorem 1

Changes in the sales share of good $i$ is Where export expenditures are $NX_{jt} = P_{jt} C^f_{jt}$. Changes in the input-output matrix are Changes in CES price indices can be written in terms of changes in sectoral prices as follows:

Figures (6)

  • Figure 1: Disentangling Supply and Demand Shifts
  • Figure 2: Identifying Variation
  • Figure 3: Uniform vs. Sector-Specific Intermediate Input Substitution Elasticities
  • Figure 4: Import Bias of Intermediate Input Substitution Elasticities
  • Figure 5: Response of GDP to Sectoral Business Cycles
  • ...and 1 more figures

Theorems & Definitions (4)

  • Theorem 1
  • Theorem 2
  • Theorem 3
  • Theorem 4