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arxiv: 2604.13188 · v1 · submitted 2026-04-14 · 💰 econ.EM · stat.AP

Is Productivity Advantage of Cities Really Down To Mean and Variance?

Vladislav Morozov , Andrea Sy This is my paper

Pith reviewed 2026-05-10 13:31 UTC · model grok-4.3

classification 💰 econ.EM stat.AP
keywords TFP distributionsagglomerationfirm selectionproductivity decompositionsSpanish firmslocation-scale shiftsnoisy estimates
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The pith

TFP distributions in denser and less dense areas are identical up to mean and variance shifts.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper tests whether total factor productivity distributions for firms in high-density versus low-density locations are the same except for shifts in their average level and spread, plus a possible cutoff of the lowest values. This limited form of equivalence is the key assumption behind methods that split observed city productivity advantages into agglomeration effects versus selection of better firms. Using Spanish administrative records and statistical tools adjusted for measurement error in productivity estimates, the analysis confirms the distributions align once mean and variance are allowed to differ. It also finds that the variance term adds little beyond the mean for explaining patterns across sectors.

Core claim

TFP distributions are statistically identical up to mean, variance, and left-tail truncation parameters, validating the use of such productivity decompositions. Using only the mean and variance is sufficient to capture differences for all sectors. Accordingly, the productivity advantage of cities may be entirely due to agglomeration rather than stronger selection.

What carries the argument

The location-scale-truncation equivalence assumption for TFP distributions, tested with econometric methods adapted to noisy firm-level estimates.

If this is right

  • City productivity advantages can be attributed entirely to agglomeration economies rather than firm selection.
  • The standard decomposition approach separating these two channels is empirically supported.
  • Mean and variance alone describe productivity differences across all sectors without needing truncation.
  • Policy efforts should target agglomeration channels instead of selection mechanisms.
  • The same validation approach extends to differences in worker skill distributions.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • If mean and variance capture the differences, models that track only these two moments may replace full nonparametric comparisons in related settings.
  • Repeating the checks on data from other countries would test whether the pattern holds beyond the Spanish sample.
  • The framework could be used to examine productivity distributions across other dimensions such as industry type or firm age.
  • Similar tests on skill distributions might clarify whether worker quality advantages in cities also reduce to location-scale shifts.

Load-bearing premise

The adapted econometric methods for noisy TFP estimates correctly recover the underlying distributions and do not introduce artifacts that would falsely support the mean-variance-truncation restriction.

What would settle it

A finding that TFP distributions differ substantially across density levels even after allowing for mean and variance shifts and left truncation in any sector or subsample.

Figures

Figures reproduced from arXiv: 2604.13188 by Andrea Sy, Vladislav Morozov.

Figure 1
Figure 1. Figure 1: Comparison of debiased cumulative distribution functions (CDFs) of TFP in AMD [PITH_FULL_IMAGE:figures/full_fig_p008_1.png] view at source ↗
read the original abstract

Firms in denser areas are more productive, a pattern attributed to agglomeration economies and firm selection. To disentangle these two channels, the popular approach of Combes et al. (2012, ECTA) critically assumes that total factor productivity (TFP) distributions between denser and less dense areas are the same up to mean, variance, and left-tail truncation. We empirically validate this assumption using Spanish administrative firm-level data and recent econometric methods adapted to noisy TFP estimates. Our results find that TFP distributions are indeed statistically identical up to these parameters, validating the use of such productivity decompositions. Furthermore, using only the mean and variance is sufficient to capture differences for all sectors. Accordingly, the productivity advantage of cities may be entirely due to agglomeration rather than stronger selection, suggesting that policymakers should focus on policies targeting agglomeration. Finally, our approach extends to related contexts like differences in worker skill distributions.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 2 minor

Summary. The paper empirically validates the key identifying assumption in Combes et al. (2012) that firm TFP distributions in denser versus less-dense Spanish locations are identical up to location, scale, and left-tail truncation. Using administrative firm-level data and adapted econometric procedures for noisy TFP estimates, it reports that the assumption holds statistically, that mean and variance alone suffice for all sectors, and therefore that observed city productivity premia can be attributed entirely to agglomeration rather than differential selection. The approach is also positioned as extensible to other distributional comparisons such as worker skills.

Significance. If the validation survives scrutiny of the test procedures, the paper would supply useful empirical grounding for a decomposition method widely employed in urban economics, permitting cleaner separation of agglomeration and selection channels. The additional claim that higher moments add no explanatory power simplifies application of the framework, while the extension to skill distributions offers a methodological template for related questions. Reliance on administrative data rather than survey samples is a clear strength.

major comments (1)
  1. [Econometric Methods] The section describing the adapted econometric methods (likely the deconvolution or moment-based tests for distributional equivalence) contains no Monte Carlo evidence or power calculations under realistic TFP measurement-error levels. Because the central claim rests on non-rejection of the null that distributions are identical up to mean, variance, and truncation, low power against alternatives with differing skewness or kurtosis would produce false support for the Combes et al. restriction; this issue is load-bearing for the abstract's validation statement and the results in the empirical section.
minor comments (2)
  1. [Data and Descriptive Statistics] Table 1 (or the corresponding data-description table) should report the exact number of firms and observations per density quartile together with the TFP estimation procedure and any trimming rules applied before the distributional tests.
  2. [Abstract] The abstract states that 'using only the mean and variance is sufficient to capture differences for all sectors' but does not indicate whether this conclusion is based on formal tests of higher-moment restrictions or on informal comparison of fitted distributions.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their constructive comments and positive assessment of the paper's contribution to validating the key assumption in Combes et al. (2012). We address the major comment on the econometric methods below.

read point-by-point responses

  1. Referee: [Econometric Methods] The section describing the adapted econometric methods (likely the deconvolution or moment-based tests for distributional equivalence) contains no Monte Carlo evidence or power calculations under realistic TFP measurement-error levels. Because the central claim rests on non-rejection of the null that distributions are identical up to mean, variance, and truncation, low power against alternatives with differing skewness or kurtosis would produce false support for the Combes et al. restriction; this issue is load-bearing for the abstract's validation statement and the results in the empirical section.

    Authors: We acknowledge the validity of this concern. The manuscript currently does not include Monte Carlo simulations or explicit power calculations for the adapted tests under measurement error. To address this, we will incorporate a new subsection in the revised version that presents Monte Carlo evidence. The simulations will be designed to reflect the levels of TFP measurement error observed in our Spanish administrative data and will evaluate the power of the tests to detect differences in higher moments (skewness and kurtosis) when the null of equivalence up to mean, variance, and truncation holds. This addition will provide stronger support for our empirical validation and the claims in the abstract. revision: yes

Circularity Check

0 steps flagged

Empirical validation of external assumption shows no circularity

full rationale

The paper's central claim is an empirical statistical test on Spanish administrative firm-level data: TFP distributions are identical up to mean, variance, and left truncation after adapting deconvolution-style methods for noisy TFP estimates. This test is performed on external data rather than being recovered from the paper's own fitted parameters or definitions. The assumption being validated originates in Combes et al. (2012), an independent prior paper with no author overlap. No equations or procedures reduce by construction to the target result; the methods are adapted but the outcome (non-rejection) is a data-driven finding, not a renaming or self-definition. The paper is self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

The central claim rests on the validity of the 2012 distributional assumption and on the correctness of the adapted econometric procedures for noisy TFP. No new free parameters, axioms, or invented entities are introduced in the abstract.

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