Panel Data Estimation of Individual Demand in Markets with Many Consumers

Sarah Moon; Whitney K. Newey

Reviewed by Pith at T0; open to challenge.

T0 means a machine referee read the full paper against a public rubric. The mark states how deep the mechanical check went, never who wrote it. the ladder, T0–T4 →

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

T0 review · grok-4.3

The bias of individual demand estimates from panel data methods disappears as the number of consumers per market grows, provided idiosyncratic preferences are orthogonal to supply shocks.

2026-06-27 10:49 UTC pith:GNGVPQVZ

load-bearing objection The paper gives conditions under which standard panel estimators for individual demand become consistent as the number of consumers per market grows, under an orthogonality assumption between idiosyncratic preference shocks and supply shocks.

arxiv 2606.11047 v1 pith:GNGVPQVZ submitted 2026-06-09 econ.EM

Panel Data Estimation of Individual Demand in Markets with Many Consumers

Sarah Moon , Whitney K. Newey This is my paper

classification econ.EM

keywords panel data estimationindividual demandsimultaneity biasmarket sizedemand modelsrandom coefficientsorthogonality conditionsupply shocks

verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

This paper examines whether panel data can estimate individual demand rather than market aggregates while handling price endogeneity from market clearing. It shows that standard methods such as differencing produce consistent estimates in linear demand and random coefficient demand models paired with linear supply, once the number of consumers in each market grows large. The required condition is that time-varying idiosyncratic preference shocks remain uncorrelated with unobserved time-varying supply shocks. Macroeconomic influences can be handled by adding time trends, period dummies, or fixed time effects. The result supports individual-level demand estimation in settings with many buyers without fully specifying the supply side.

Core claim

In linear demand models and random coefficient demand models together with linear supply models, familiar panel data estimators such as first differencing yield individual demand estimates whose bias disappears as the number of consumers per market tends to infinity, as long as the time-varying idiosyncratic component of preferences is orthogonal to the unobserved time-varying component of supply. Macroeconomic effects are accommodated by including regressors for time effects such as trends and time period dummies or by using fixed time effects.

What carries the argument

Panel data differencing applied to individual observations across markets whose size grows, under orthogonality between idiosyncratic preference shocks and unobserved supply shocks.

Load-bearing premise

The time-varying idiosyncratic component of preferences is orthogonal to the unobserved time-varying component of supply.

What would settle it

Persistent bias remaining in differenced individual demand estimates even after the number of consumers per market becomes very large, while the orthogonality condition between idiosyncratic preferences and supply shocks holds in the data.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

Individual demand parameters can be estimated consistently without fully modeling equilibrium price determination.
The consistency result applies to both linear demand specifications and random coefficient demand specifications.
Common time effects such as trends or period dummies can be included to absorb macroeconomic shocks.
The bias reduction strengthens as the number of consumers per market increases.

Where Pith is reading between the lines

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

The approach may extend to discrete choice settings where similar orthogonality conditions are maintained.
Empirical researchers could test the orthogonality directly using supply-side instruments in large panel datasets.
The large-market asymptotics suggest applicability to scanner or transaction data with expanding coverage over time.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Desk Editor's Note

The paper gives conditions under which standard panel estimators for individual demand become consistent as the number of consumers per market grows, under an orthogonality assumption between idiosyncratic preference shocks and supply shocks.

read the letter

The main result is that bias in differenced or fixed-effects estimators for individual-level demand vanishes with large N per market, provided the time-varying preference component is orthogonal to the time-varying supply shock. This is presented for both linear and random-coefficients demand paired with linear supply. The paper also notes that time effects can be handled with trends or dummies without breaking the argument.

What is new is the explicit large-market bias-vanishing claim for these familiar estimators in a simultaneous-equations setting. The orthogonality condition is already used in many discrete-choice panel models, so the contribution is mainly showing that it delivers consistency for individual demand as market size grows. The assumption is stated plainly and described as plausible when idiosyncratic terms capture transitory preference variation.

The soft spot is that the result is conditional on that orthogonality; if the idiosyncratic preference term correlates with supply shocks in practice, the bias does not disappear. The abstract gives no proof sketch, so the derivation needs checking in the full text, but the stress-test note finds no hidden rate condition or internal inconsistency. No circularity is apparent.

This is for empirical IO researchers who want to move from market-level to individual demand estimates with panel data and are willing to maintain the stated orthogonality. It deserves a serious referee because the claim is precise, the maintained assumption is transparent, and the setting matches common data structures. I would send it to review.

Referee Report

0 major / 2 minor

Summary. The paper considers whether and how panel data can be used to estimate individual demand (as opposed to market-level demand) while accounting for simultaneity from market-clearing prices. It analyzes linear demand models and random coefficient demand models paired with linear supply, finding that the bias of standard panel estimators such as differencing vanishes as the number of consumers per market tends to infinity, conditional on the time-varying idiosyncratic preference component being orthogonal to the unobserved time-varying supply component. Macroeconomic effects can be controlled via time trends, period dummies, or fixed time effects.

Significance. If the derivations hold, the result is significant because it provides a large-market justification for applying familiar panel-data techniques to individual demand estimation without incurring simultaneity bias, under an orthogonality condition already maintained in many panel discrete-choice models. This offers a practical route for empirical work that seeks individual-level parameters while remaining consistent with market equilibrium, particularly when idiosyncratic terms represent transitory preference shocks.

minor comments (2)

[Abstract] The abstract states the main result but contains no derivation outline or key steps; while the full text presumably supplies these, a one-sentence intuition in the abstract for why the bias term vanishes with large N would improve accessibility without altering the technical contribution.
Notation for the idiosyncratic preference shock and the supply shock should be checked for consistency between the abstract and the model section to avoid any risk of reader confusion.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the careful reading and positive assessment of the paper. The referee's summary correctly identifies the core result: that standard panel estimators for individual demand remain consistent in large markets under the maintained orthogonality between idiosyncratic preference shocks and supply shocks. We are pleased with the recommendation for minor revision.

Circularity Check

0 steps flagged

No significant circularity

full rationale

The paper's central result is an asymptotic statement that bias in standard panel estimators (differencing, etc.) for individual demand vanishes as market size N grows, conditional on the explicitly maintained orthogonality between the time-varying idiosyncratic preference shock and the time-varying supply shock. This is a conventional large-N argument under a stated assumption already common in panel discrete-choice models; the abstract and description contain no fitted parameters renamed as predictions, no self-definitional loops, no load-bearing self-citations, and no imported uniqueness theorems. The derivation is therefore self-contained against the listed assumptions and does not reduce to its inputs by construction.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The paper builds on standard linear demand and supply models in econometrics, with the key additional assumption being the orthogonality condition.

axioms (1)

domain assumption the time-varying component of preferences is orthogonal to the unobserved time-varying component of supply
This is explicitly stated as the condition under which the bias disappears.

pith-pipeline@v0.9.1-grok · 5671 in / 1121 out tokens · 26805 ms · 2026-06-27T10:49:31.993096+00:00 · methodology

0 comments

read the original abstract

The purpose of this paper is to consider whether and how panel data can be used to estimate individual demand, as opposed to market-level demand, while accounting for simultaneity resulting from prices being determined in markets. We consider linear demand models and random coefficient demand models, together with linear supply models. We find that the bias of individual demand estimates obtained using familiar panel data methods, like differencing, disappears as the number of consumers in each market grows, as long as the time-varying, i.e. idiosyncratic, component of preferences is orthogonal to the unobserved, time-varying component of supply. This approximate control is assumed in many panel discrete choice models and is plausible in other models where idiosyncratic preferences represent random variation in preferences over time. Macroeconomic effects can be allowed for by including regressors characterizing time effects, such as trends and time period dummies, or fixed time effects.

discussion (0)

Reference graph

Works this paper leans on

18 extracted references

[1]

Levinsohn, and A

Berry, S., J. Levinsohn, and A. Pakes (1995). Automobile prices in market equilibrium.Economet- rica 63(4), 841–890

1995
[2]

Levinsohn, and A

Berry, S., J. Levinsohn, and A. Pakes (2004). Differentiated products demand systems from a combination of micro and macro data: The new car market.Journal of Political Economy 112(1), 68–105

2004
[3]

Berry, S. T. and P. A. Haile (2014). Identification in differentiated products markets using market level data.Econometrica 82(5), 1749–1797

2014
[4]

Berry, S. T. and P. A. Haile (2024). Nonparametric identification of differentiated products demand using micro data.Econometrica 92(4), 1135–1162

2024
[5]

Chamberlain, G. (1984). Panel data.Handbook of Econometrics 2, 1247–1318

1984
[6]

Deaner, Y

Chernozhukov, V., B. Deaner, Y. Gao, J. A. Hausman, and W. Newey (2025). Fisher-Schultz lecture: Linear estimation of structural and causal effects for nonseparable panel data. NBER Working Paper 33325

2025
[7]

Fernández-Val, J

Chernozhukov, V., I. Fernández-Val, J. Hahn, and W. Newey (2013). Average and quantile effects in nonseparable panel models.Econometrica 81(2), 535–580

2013
[8]

Chernozhukov, V., J. A. Hausman, and W. K. Newey (2019). Demand analysis with many prices. NBER Working Paper 26424

2019
[9]

Griffith, and M

Dubois, P., R. Griffith, and M. O’Connell (2020). How well targeted are soda taxes?American Economic Review 110(11), 3661–3704. 13

2020
[10]

Hausman, J. A. and W. K. Newey (2016). Individual heterogeneity and average welfare.Economet- rica 84(3), 1225–1248

2016
[11]

Hausman, J. A., W. K. Newey, and W. E. Taylor (1987). Efficient estimation and identification of simultaneous equation models with covariance restrictions.Econometrica 55(4), 849–874

1987
[12]

Hausman, J. A. and W. E. Taylor (1983). Identification in linear simultaneous equations models with covariance restrictions: An instrumental variables interpretation.Econometrica 51(5), 1527–1549

1983
[13]

Hoderlein, S. and M. Shum (2014).Nonparametric estimation of demand elasticities using panel data. Unpublished manuscript

2014
[14]

Hoderlein, S. and H. White (2012). Nonparametric identification in nonseparable panel data models with generalized fixed effects.Journal of Econometrics 168(2), 300–314

2012
[15]

Kennan, J. (1989). Simultaneous equations bias in disaggregated econometric models.The Review of Economic Studies 56(1), 151–156

1989
[16]

Large, and J

Lanier, J., J. Large, and J. Quah (2023). Estimating very large demand systems. Working Paper 2023-01, INET Oxford. MacKay,A.andN.H.Miller(2025,February). Estimatingmodelsofsupplyanddemand:Instruments and covariance restrictions.American Economic Journal: Microeconomics 17(1), 238–81

2023
[17]

McFadden, D. (1974). Conditional logit analysis of qualitative choice behavior. In P. Zarembka (Ed.),Frontiers in Econometrics. Academic Press

1974
[18]

ωi leave out

Petrin, A. (2002). Quantifying the benefits of new products: The case of the minivan.Journal of Political Economy 110(4), 705–729. A Appendix Proof of Theorem 2 Proof.Recall that qit−¯qt−¯qi + ¯q   ˜qit =β(pit−¯pt−¯pi + ¯p)   ˜pit +ηit−¯ηt−¯ηi + ¯η   ˜ηit , (pit−¯pt−¯pi + ¯p)   ˜pit = 1 β−δ ( εit−¯εt−¯εi + ¯ε   ˜εit −(¯ηm it−¯ηm t −¯ηm...

2002

[1] [1]

Levinsohn, and A

Berry, S., J. Levinsohn, and A. Pakes (1995). Automobile prices in market equilibrium.Economet- rica 63(4), 841–890

1995

[2] [2]

Levinsohn, and A

Berry, S., J. Levinsohn, and A. Pakes (2004). Differentiated products demand systems from a combination of micro and macro data: The new car market.Journal of Political Economy 112(1), 68–105

2004

[3] [3]

Berry, S. T. and P. A. Haile (2014). Identification in differentiated products markets using market level data.Econometrica 82(5), 1749–1797

2014

[4] [4]

Berry, S. T. and P. A. Haile (2024). Nonparametric identification of differentiated products demand using micro data.Econometrica 92(4), 1135–1162

2024

[5] [5]

Chamberlain, G. (1984). Panel data.Handbook of Econometrics 2, 1247–1318

1984

[6] [6]

Deaner, Y

Chernozhukov, V., B. Deaner, Y. Gao, J. A. Hausman, and W. Newey (2025). Fisher-Schultz lecture: Linear estimation of structural and causal effects for nonseparable panel data. NBER Working Paper 33325

2025

[7] [7]

Fernández-Val, J

Chernozhukov, V., I. Fernández-Val, J. Hahn, and W. Newey (2013). Average and quantile effects in nonseparable panel models.Econometrica 81(2), 535–580

2013

[8] [8]

Chernozhukov, V., J. A. Hausman, and W. K. Newey (2019). Demand analysis with many prices. NBER Working Paper 26424

2019

[9] [9]

Griffith, and M

Dubois, P., R. Griffith, and M. O’Connell (2020). How well targeted are soda taxes?American Economic Review 110(11), 3661–3704. 13

2020

[10] [10]

Hausman, J. A. and W. K. Newey (2016). Individual heterogeneity and average welfare.Economet- rica 84(3), 1225–1248

2016

[11] [11]

Hausman, J. A., W. K. Newey, and W. E. Taylor (1987). Efficient estimation and identification of simultaneous equation models with covariance restrictions.Econometrica 55(4), 849–874

1987

[12] [12]

Hausman, J. A. and W. E. Taylor (1983). Identification in linear simultaneous equations models with covariance restrictions: An instrumental variables interpretation.Econometrica 51(5), 1527–1549

1983

[13] [13]

Hoderlein, S. and M. Shum (2014).Nonparametric estimation of demand elasticities using panel data. Unpublished manuscript

2014

[14] [14]

Hoderlein, S. and H. White (2012). Nonparametric identification in nonseparable panel data models with generalized fixed effects.Journal of Econometrics 168(2), 300–314

2012

[15] [15]

Kennan, J. (1989). Simultaneous equations bias in disaggregated econometric models.The Review of Economic Studies 56(1), 151–156

1989

[16] [16]

Large, and J

Lanier, J., J. Large, and J. Quah (2023). Estimating very large demand systems. Working Paper 2023-01, INET Oxford. MacKay,A.andN.H.Miller(2025,February). Estimatingmodelsofsupplyanddemand:Instruments and covariance restrictions.American Economic Journal: Microeconomics 17(1), 238–81

2023

[17] [17]

McFadden, D. (1974). Conditional logit analysis of qualitative choice behavior. In P. Zarembka (Ed.),Frontiers in Econometrics. Academic Press

1974

[18] [18]

ωi leave out

Petrin, A. (2002). Quantifying the benefits of new products: The case of the minivan.Journal of Political Economy 110(4), 705–729. A Appendix Proof of Theorem 2 Proof.Recall that qit−¯qt−¯qi + ¯q   ˜qit =β(pit−¯pt−¯pi + ¯p)   ˜pit +ηit−¯ηt−¯ηi + ¯η   ˜ηit , (pit−¯pt−¯pi + ¯p)   ˜pit = 1 β−δ ( εit−¯εt−¯εi + ¯ε   ˜εit −(¯ηm it−¯ηm t −¯ηm...

2002