Productivity Shocks and Input Misallocation: A Decomposition
Pith reviewed 2026-05-24 07:40 UTC · model grok-4.3
The pith
Under a model of staggered productivity shocks, post-commitment shocks explain most of the dispersion in marginal revenue products for inputs in European manufacturing.
A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.
Core claim
The paper shows that, under the maintained model, shocks realized after inputs are committed are the largest contributor to marginal revenue product dispersion for every input, accounting for 75% of the variance for materials, 37% for labor, and 18% for capital. These results are consistent with input misallocation in European manufacturing reflecting post-commitment productivity shocks more than persistent heterogeneity across firms.
What carries the argument
Decomposition of marginal revenue product dispersion variance into components based on the timing of productivity shocks relative to input commitment.
If this is right
- Observed input misallocation largely captures post-commitment shocks rather than static inefficiencies.
- Dispersion shares vary by input, with materials most affected by later shocks.
- The pattern holds in European manufacturing firms over 2001-2017.
- Persistent heterogeneity across firms plays a smaller role than timing of shocks.
Where Pith is reading between the lines
- If post-commitment shocks dominate, policies improving flexibility or information after commitment could reduce measured misallocation.
- Applying the same decomposition to other industries or regions could reveal whether this timing pattern is general.
- Models assuming inputs are chosen with full knowledge of productivity may overstate the role of persistent differences.
Load-bearing premise
The model assumptions that permit separating the variance in marginal revenue product dispersion into components according to the timing of productivity shocks relative to input commitment decisions.
What would settle it
Empirical evidence that the variance contributions from post-commitment shocks are substantially smaller than the reported shares for materials, labor, and capital.
read the original abstract
This paper investigates how productivity dispersion relates to input misallocation in European manufacturing. The model features staggered productivity shocks that create wedges between anticipated and realized productivity for any production input. Using European firm-level data from 2001-2017, I show that, under the maintained model, shocks realized after inputs are committed are the largest contributor to marginal revenue product dispersion for every input, accounting for 75% of the variance for materials, 37% for labor, and 18% for capital. These results are consistent with input misallocation in European manufacturing reflecting post-commitment productivity shocks more than persistent heterogeneity across firms.
Editorial analysis
A structured set of objections, weighed in public.
Referee Report
Summary. The paper develops a structural model with staggered productivity shocks that create wedges between anticipated and realized productivity at the time each input is committed. It decomposes the observed variance in marginal revenue products (MRP) for materials, labor, and capital into components attributable to pre- versus post-commitment shocks. Using European firm-level data (2001-2017), the maintained model attributes 75% of MRP variance for materials, 37% for labor, and 18% for capital to post-commitment shocks, implying that input misallocation in European manufacturing is driven more by these timing frictions than by persistent cross-firm heterogeneity.
Significance. If the decomposition is robust to the timing assumptions, the paper supplies a quantitative attribution of MRP dispersion that links misallocation directly to the relative flexibility of inputs and the arrival of shocks. This could refine both static misallocation measures and dynamic models of adjustment costs. The European panel broadens the evidence base beyond U.S. data, and the explicit variance-share accounting is a transparent way to report model-implied contributions.
major comments (3)
- [§4 (decomposition results)] The central variance decomposition (abstract and §4) attributes shares to post-commitment shocks only under the maintained timing assumptions on information sets and commitment dates for each input. With annual data these dates are not observed, so the 75/37/18 percentages are identified via parametric restrictions on the shock process; the paper does not report sensitivity to alternative information structures or to allowing measurement error to load on the post-commitment component.
- [§3 (estimation) and §4] Parameters of the shock process are estimated on the same firm panel used to compute the MRP dispersion (abstract). This creates a circularity risk for the reported shares; the manuscript should clarify whether the decomposition is performed out-of-sample or whether the shares are purely in-sample model predictions.
- [§2 (data) and §4] No robustness checks are described for the data-construction steps (sample selection, capital-stock measurement, or output-price deflators) that enter the MRP calculation. Because the attribution percentages are the headline result, even moderate changes in these steps could alter the ranking of post- versus pre-commitment contributions.
minor comments (2)
- [§3] Notation for the timing of shocks and commitment should be made uniform across equations; the distinction between E[·|I_t] and realized productivity is not always explicit in the variance formulas.
- [§4] Table or figure presenting the variance shares should include standard errors or bootstrap intervals so readers can assess precision of the 75/37/18 point estimates.
Simulated Author's Rebuttal
We thank the referee for the constructive comments. We respond point-by-point to the major comments below.
read point-by-point responses
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Referee: [§4 (decomposition results)] The central variance decomposition (abstract and §4) attributes shares to post-commitment shocks only under the maintained timing assumptions on information sets and commitment dates for each input. With annual data these dates are not observed, so the 75/37/18 percentages are identified via parametric restrictions on the shock process; the paper does not report sensitivity to alternative information structures or to allowing measurement error to load on the post-commitment component.
Authors: We agree that the shares are identified under the maintained timing assumptions. In the revision we will add sensitivity checks to alternative information structures and specifications allowing measurement error to load on the post-commitment component, reported in an expanded Section 4. revision: yes
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Referee: [§3 (estimation) and §4] Parameters of the shock process are estimated on the same firm panel used to compute the MRP dispersion (abstract). This creates a circularity risk for the reported shares; the manuscript should clarify whether the decomposition is performed out-of-sample or whether the shares are purely in-sample model predictions.
Authors: The parameters are estimated on the full panel and the shares are in-sample model predictions. We will add explicit clarification in Sections 3 and 4 stating this and discussing the implications for interpretation. An out-of-sample split is not pursued because it would compromise panel length and precision, but the clarification addresses the circularity concern directly. revision: partial
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Referee: [§2 (data) and §4] No robustness checks are described for the data-construction steps (sample selection, capital-stock measurement, or output-price deflators) that enter the MRP calculation. Because the attribution percentages are the headline result, even moderate changes in these steps could alter the ranking of post- versus pre-commitment contributions.
Authors: We will add robustness checks on sample selection, capital-stock measurement, and output-price deflators. These will appear in a new appendix subsection referenced from Section 4, confirming that the 75/37/18 attribution is not sensitive to these construction choices. revision: yes
Circularity Check
No circularity: model-based variance decomposition is self-contained under stated assumptions
full rationale
The paper maintains a structural model with explicit timing assumptions on when productivity shocks are realized relative to input commitment decisions, then applies the model to decompose observed MRP dispersion in the European firm data. The reported shares (75% materials, 37% labor, 18% capital) are direct outputs of that decomposition rather than independent predictions or fitted quantities renamed as results. No equations reduce to self-definition, no parameters are fitted on a subset and then called predictions on the same dispersion metric, and no self-citations or imported uniqueness theorems are invoked to justify the timing structure. The derivation therefore remains non-circular: the attribution follows from the maintained model applied to the data, with the timing restrictions serving as testable maintained hypotheses rather than tautological inputs.
Axiom & Free-Parameter Ledger
free parameters (1)
- shock process parameters
axioms (2)
- domain assumption Firms commit to inputs based on anticipated productivity before shocks are realized.
- ad hoc to paper Marginal revenue product dispersion can be additively decomposed by shock timing.
discussion (0)
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