Thread by @SGechert

Hurray! Together with great coauthors @DomiEhrenberger, Tomas + Zuzana we finally got it published: Our #metaanalysis on the elasticity of substitution b/w capital and labor, a.k.a. the “Death to the Cobb-Douglas production function” made it to the @RevEconDyn. Thread:

First of all, here’s a 50days free access share link authors.elsevier.com/a/1d7Oo3uolWav… (which seems to work with Chrome though not with Firefox). Please feel free to share it in your networks.

The elasticity (σ) is a central parameter in macroeconomics. It determines how easy (high σ), difficult (low σ) it is to substitute capital (C) and labor (L) inputs in production. At the extreme ends, σ=0 -> no substitutability (Leontief) -> C/L always enter in fixed proportions.

If σ=infinity -> easy substitutability. (linear case) -> C/L are perfect substitutes. A special (+ often used) case is σ=1 (Cobb-Douglas) where a 1% change in relative prices of C/L (wages vs rental rate) means 1% change in relative inputs of C vs L.

A typical range of σ in macro models is [0, 1.5]. The choice of σ matters for many questions. E.g.,the effect of monetary policy on inflation (exemplified by the @federalreserve SIGMA model). With low (high) σ an increase in the policy rate has a weak (strong) effect on inflation

In the realm of public finances and fiscal policy, cuts to corporate taxes will be more (less) effective in stimulating investment if σ is high(low). If σ is >1, in neoclassical models, economic growth can continue without technological change.

T. @PikettyLeMonde theory explaining the secular fall in labor share with rising capital intensity hinges on σ>1 @gabriel_zucman. Likewise, the arguments by L. Karabarbounis and @BrentNeiman. E.Oberfield+D.Raval recently pointed out this relation: doi.org/10.3982/ECTA12…

Also, the short-run properties of the labor share after a labor augmenting technology shock hinge on σ. With σ=1 there is no effect, with σ<1 the labor share falls when labor productivity rises, which is more in line with the empirics @c_cantore.

Many macro models use the σ=1 (Cobb-Douglas) case, 1. b/c many σ-estimates support this assumption + 2. b/c it is convenient: you don’t need to care about functional income distribution (C+L will always receive a fixed share of income). Also the model is easier to solve.

What do we do in the paper? We collected lots of estimates of σ (>3000 from 121 published studies) together with 71 characteristics of the estimate or study (country coverage, econometric approach, control variables etc.). We then applied meta-analysis tools to this novel dataset

Now what do we find? 1. A naïve average of all estimates is σ=0.9, close to the Cobb-Douglas case. However, we detect considerable publication selection bias by various tests. This comes from the preference for theory-consistent or statistically significant effects.

See these so-called funnel plots (effect size vs. 1/SE): you can clearly spot that something is missing at negative σ’s. σ<0 do not match any theoretical prediction so it is plausible that authors tend to discard such estimates and search for “acceptable” values.

While this is sensible for an individual study, it can be harmful for research synthesis. Authors aren’t as selective on the upper end. We also find a tendency for statistically significant results (which is not so clearly visible). Both upward-bias the average σ.

If we correct for this publication bias, the unbiased average becomes σ=0.5. Here's a table of estimates of the mean beyond bias using non-linear methods @maxkasy A hypothetical best practice study w/ state-of-the-art methods and w/out publication bias would even result in σ=0.3.

This is so far-off a σ=1 elasticity that we called for the “Death to the Cobb-Douglas Production Function” in an earlier overly-aggressive title of the paper.Irrespectively, our results make a strong case against the Cobb-Douglas PF. So does @c_cantore ‘s:

https://twitter.com/c_cantore/status/1176618343572410370?s=20

To come full circle: what does σ=0.3 imply as compared to model predictions with σ=1? 1. More responsive monetary policy (it needs a larger change in policy rates to affect output gap and inflation). 2. Less trust in the growth effects of corporate tax cuts.

3. Searching for alternative arguments to explain the fall in the labor share that are consistent with σ<1, like business concentration, automation, directed technical change, the deterioration of union coverage etc.

CC: @pol_antras @sdullien @AchimTruger @MiriamRehm @BachmannRudi @ojblanchard1 @FazzariSteven @KrusellPer @glviolante @danieletavani @c_cantore @_LukasFreund_ Thanks for sharing.