Abstract

We show that the large elasticity of substitution between capital and labor estimated in the literature on average, 0.9, can be explained by three factors: publication bias, use of aggregated data, and omission of the first-order condition for capital. The mean elasticity conditional on the absence of publication bias, disaggregated data, and inclusion of information from the first-order condition for capital is 0.3. To obtain this result, we collect 3,186 estimates of the elasticity reported in 121 studies, codify 71 variables that reflect the context in which researchers produce their estimates, and address model uncertainty by Bayesian and frequentist model averaging. We employ nonlinear techniques to correct for publication bias, which is responsible for at least half of the overall reduction in the mean elasticity from 0.9 to 0.3. Our findings also suggest that a failure to normalize the production function leads to a substantial upward bias in the estimated elasticity. The weight of evidence accumulated in the empirical literature emphatically rejects the Cobb-Douglas specification.
Funnel plot
Fig: Identification strategy drives the reported elasticities

Reference: Sebastian Gechert, Tomas Havranek, Zuzana Irsova, and Dominika Kolcunova (2022), "Measuring Capital-Labor Substitution: The Importance of Method Choices and Publication Bias." Review of Economic Dynamics 45, 55-82.

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Headline result

Elasticity of substitution between capital and labor: the meta-analytic estimate is 0.3 (best-practice specification; the mean reported estimate is 0.9), based on 3,186 estimates from 121 studies (Gechert et al. 2022, Review of Economic Dynamics).

How to cite

Sebastian Gechert, Tomas Havranek, Zuzana Irsova, and Dominika Kolcunova (2022), "Measuring Capital-Labor Substitution: The Importance of Method Choices and Publication Bias." Review of Economic Dynamics 45, 55-82.

BibTeX 
@article{gechert2022sigma,
  author  = {Sebastian Gechert and Tomas Havranek and Zuzana Irsova and Dominika Kolcunova},
  title   = {Measuring Capital-Labor Substitution: The Importance of Method Choices and Publication Bias},
  journal = {Review of Economic Dynamics},
  year    = {2022},
  doi     = {10.1016/j.red.2021.05.003},
}

Where this has been used

Tomohiro Hirano and Joseph Stiglitz cite this meta-analysis in Overlapping generations models, multiplicity of steady states and momentary equilibria, and economic fluctuations, Oxford Review of Economic Policy, where the elasticity of substitution between capital and labor decides whether the model has one steady state or several.