Identification and Estimation of Demand Models with Endogenous Product Entry and Exit

Alessandro Iaria; Senay Sokullu; Victor Aguirregabiria

arxiv: 2308.14196 · v2 · submitted 2023-08-27 · 💰 econ.EM

Identification and Estimation of Demand Models with Endogenous Product Entry and Exit

Victor Aguirregabiria , Alessandro Iaria , Senay Sokullu This is my paper

Pith reviewed 2026-05-24 07:37 UTC · model grok-4.3

classification 💰 econ.EM

keywords demand estimationendogenous entryselection biassemiparametric estimationlatent propensity scoresdifferentiated productsprice elasticityairline industry

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The pith

Correlations across products in entry decisions identify latent propensity scores that correct for selection bias in demand estimation.

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

Firms introduce products where they expect stronger demand using information unseen by researchers, which biases standard estimates of demand parameters. For differentiated products the entry decision is not monotonic in observables, so conventional selection corrections do not work. The paper shows that the selection bias term equals a convolution of latent propensity scores, which are entry probabilities conditional on both observed characteristics and latent variables for unobserved interdependencies among firms. These scores are recoverable from the observed correlation structure across products, supporting a two-step semiparametric estimator. In airline data the resulting price elasticities are substantially larger than those from existing correction methods.

Core claim

The selection bias term in the demand equation is a convolution of latent propensity scores, defined as entry probabilities conditional on observables and latent variables that capture unobserved interdependencies among firms' entry choices. These scores are identifiable from correlations in entry decisions across products, which allows consistent two-step semiparametric estimation of demand parameters without strong assumptions on firms' information sets or joint estimation of a full equilibrium model.

What carries the argument

Latent propensity scores, which are the probabilities of product entry conditional on observable characteristics and latent variables for unobserved interdependencies, whose convolution forms the identifiable selection bias term.

If this is right

Demand parameters can be estimated consistently without imposing strong assumptions about firms' information on demand at the time of entry.
The estimator does not require joint estimation of a full equilibrium model of demand, pricing, and entry.
In the airline industry the method yields larger price elasticities of demand than conventional selection-correction approaches.
The procedure separates the estimation of latent propensity scores from the correction of the demand equation in two distinct steps.

Where Pith is reading between the lines

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

The same correlation structure could be used in other multi-product industries to reduce bias when entry depends on private demand forecasts.
Once the latent scores are recovered, researchers could test whether the implied interdependencies match observed patterns of firm coordination.
The approach opens the possibility of combining the correction with panel data on repeated entry and exit decisions.

Load-bearing premise

The observed correlations across products in their market-entry decisions are sufficient to identify the latent variables that capture unobserved interdependencies among firms' entry choices.

What would settle it

If the two-step estimator applied to airline data produces price-elasticity values that fail to match observed quantity responses to actual price changes recorded in the same markets.

Figures

Figures reproduced from arXiv: 2308.14196 by Alessandro Iaria, Senay Sokullu, Victor Aguirregabiria.

read the original abstract

Firms are more likely to introduce products in markets where they anticipate stronger demand. They also possess information that is unobserved to researchers. This creates endogenous selection bias in the estimation of demand parameters. With differentiated products, the entry decision violates the monotonicity conditions required for standard selection-correction methods to yield consistent demand estimates. Existing studies address this issue either by imposing strong assumptions about firms' information on demand at the time of entry or by jointly estimating a full equilibrium model of demand, pricing, and entry. Both strategies make the estimation of demand heavily reliant on supply-side assumptions. We propose a new semiparametric estimation method that addresses these limitations. Our approach exploits the correlation across products in their market-entry decisions to identify entry probabilities conditional not only on observable characteristics but also on latent variables that capture unobserved interdependencies among firms' entry choices. We refer to these probabilities as latent propensity scores. We show that the selection bias term in the demand equation is a convolution of these latent propensity scores and is therefore identifiable. Building on this result, we develop a two-step semiparametric estimator in the spirit of standard sample-selection correction methods. Applying our method to data from the airline industry, we find that conventional approaches to correcting for selection bias substantially underestimate price elasticities of demand.

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.

Desk Editor's Note private letter to a colleague

The paper gives a convolution-based route to selection correction in demand models using cross-product entry correlations, but the deconvolution step needs the non-vanishing condition checked.

read the letter

The central claim is that cross-product correlations in entry decisions identify latent propensity scores, the selection bias term is their convolution, and this yields a two-step semiparametric estimator without full equilibrium modeling or strong information assumptions. That route is distinct from the two strategies the abstract flags as standard. The airline application then reports that conventional corrections produce noticeably smaller price elasticities. Those are the concrete pieces worth knowing. The approach earns credit for grounding identification in observable joint entry patterns rather than parametric restrictions on unobservables, and for staying close to familiar sample-selection logic. The empirical finding on elasticities is at least directionally useful for IO work on differentiated products. The soft spot is the deconvolution step itself. Recovering the bias term uniquely from the convolution requires that the characteristic function of the latent variables has no zeros on a set of positive measure. The abstract and description give no sign that this regularity condition is imposed or verified for the joint distribution of unobserved interdependencies, so the mapping from observed probabilities to the bias term may not be injective in general. That is the exact point the stress-test note raises, and it lands on the identification argument as presented. The paper is aimed at empirical IO researchers who estimate demand with endogenous entry and want to avoid heavy supply-side assumptions. A reader working on semiparametric selection corrections could extract the method and test it in their own setting. It deserves peer review so the identification proof and the airline implementation can be examined directly.

Referee Report

2 major / 2 minor

Summary. The paper claims that correlations across products in market-entry decisions identify latent propensity scores capturing unobserved interdependencies among firms' entry choices. It shows that the selection bias term in the demand equation is a convolution of these latent propensity scores and is therefore identifiable, and develops a two-step semiparametric estimator in the spirit of sample-selection corrections. The method is applied to airline industry data, where it finds that conventional selection corrections substantially underestimate price elasticities of demand.

Significance. If the central identification result holds, the approach provides a semiparametric route to consistent demand estimation that avoids both strong assumptions on firms' private information at entry and the need to jointly estimate a full equilibrium model of demand, pricing, and entry. This reduces reliance on supply-side restrictions and could improve elasticity estimates in differentiated-products settings. The airline application supplies concrete evidence on the quantitative importance of the correction.

major comments (2)

[§3 (identification result)] The identification argument (abstract and §3) states that the selection bias term equals a convolution of the latent propensity scores recovered from cross-product entry correlations and is therefore identifiable. Standard deconvolution theory requires that the characteristic function of the mixing distribution over latent variables has no zeros on a set of positive measure for unique recovery; the manuscript does not state or verify this non-vanishing condition, leaving open whether the mapping from observed joint entry probabilities to the bias term is injective.
[§4 (estimator)] The two-step estimator (abstract and §4) relies on first-step recovery of the latent propensities from the joint distribution of entry decisions. The paper should specify the dimensionality of the latent variables, the support conditions needed for the convolution inversion, and whether the estimator attains root-n consistency or semiparametric efficiency under the maintained assumptions.

minor comments (2)

[Abstract] The abstract summarizes the identification claim without a proof sketch or explicit list of regularity conditions; adding a short statement of the key maintained assumptions would improve readability.
[§3] Notation for the latent propensity scores and the convolution operator should be introduced with a clear equation reference in the main text to avoid ambiguity when the estimator is described.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments on the identification and estimation sections. We address each major comment below.

read point-by-point responses

Referee: [§3 (identification result)] The identification argument (abstract and §3) states that the selection bias term equals a convolution of the latent propensity scores recovered from cross-product entry correlations and is therefore identifiable. Standard deconvolution theory requires that the characteristic function of the mixing distribution over latent variables has no zeros on a set of positive measure for unique recovery; the manuscript does not state or verify this non-vanishing condition, leaving open whether the mapping from observed joint entry probabilities to the bias term is injective.

Authors: We agree that the non-vanishing condition is required for unique deconvolution. Our maintained assumptions on the latent factors (continuous distributions with characteristic functions that do not vanish on sets of positive measure, such as those with analytic characteristic functions) ensure the mapping is injective. We will add an explicit statement of this condition and a brief verification argument in the revised §3. revision: yes
Referee: [§4 (estimator)] The two-step estimator (abstract and §4) relies on first-step recovery of the latent propensities from the joint distribution of entry decisions. The paper should specify the dimensionality of the latent variables, the support conditions needed for the convolution inversion, and whether the estimator attains root-n consistency or semiparametric efficiency under the maintained assumptions.

Authors: We will revise §4 to state that the latent variables have dimension equal to the number of products minus one. Support conditions require that the joint distribution of observed characteristics has positive density on a compact set with sufficient variation. The estimator is consistent; under standard smoothness and bandwidth conditions it attains root-n consistency. We will add this discussion but note that deriving the semiparametric efficiency bound is beyond the paper's scope. revision: yes

Circularity Check

0 steps flagged

No significant circularity; identification rests on observable correlations

full rationale

The paper's core step shows that the selection bias term equals a convolution of latent propensity scores recovered from cross-product entry correlations in the data. This mapping is presented as following from the structure of the observed joint entry probabilities rather than by redefining the bias in terms of itself or renaming a fitted quantity as a prediction. No load-bearing self-citation, imported uniqueness theorem, or ansatz smuggled via prior work appears in the derivation chain. The argument is therefore self-contained against external data features and does not reduce to its inputs by construction.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 1 invented entities

The identification strategy rests on the existence of latent interdependencies in entry decisions that generate usable correlations; no free parameters or invented physical entities are mentioned.

axioms (1)

domain assumption Entry decisions across products are correlated through unobserved latent factors that affect multiple firms or markets.
This correlation is the source of identification for the latent propensity scores.

invented entities (1)

latent propensity scores no independent evidence
purpose: Entry probabilities conditional on both observables and latent variables capturing interdependencies.
New construct introduced to represent the conditional probabilities used in the convolution for bias correction.

pith-pipeline@v0.9.0 · 5762 in / 1281 out tokens · 26444 ms · 2026-05-24T07:37:38.625786+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

3 extracted references · 3 canonical work pages

[1]

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Abaluck, J., and A. Adams-Prassl (2021): “What do consumers consider before they choose? Identification from asymmetric demand responses,”The Quarterly Journal of Eco- nomics, 136(3), 1611–1663. Aguirregabiria, V., A. Collard-Wexler, and S. Ryan (2021): “Dynamic games in em- pirical industrial organization,” inHandbook of Industrial Organization, Volume 4...

work page arXiv 2021
[2]

Random-coefficients logit demand estimation with zero-valued market shares,

Dubé, J.-P., A. Hortaçsu, and J. Joo (2021): “Random-coefficients logit demand estimation with zero-valued market shares,”Marketing Science, 40(4), 637–660. Eizenberg, A. (2014): “Upstream innovation and product variety in the us home pc market,” The Review of Economic Studies, 81(3), 1003–1045. Gandhi, A., Z. Lu, and X. Shi (2023): “Estimating demand for...

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The common structure of statistical models of truncation, sample se- lection and limited dependent variables and a simple estimator for such models,

Heckman, J. (1976): “The common structure of statistical models of truncation, sample se- lection and limited dependent variables and a simple estimator for such models,”Annals of Economic and Social Measurement, 5(4), 475–492. Hirano, K., G. W. Imbens, and G. Ridder (2003): “Efficientestimationofaveragetreatment effects using the estimated propensity sco...

work page 1976

[1] [1]

What do consumers consider before they choose? Identification from asymmetric demand responses,

Abaluck, J., and A. Adams-Prassl (2021): “What do consumers consider before they choose? Identification from asymmetric demand responses,”The Quarterly Journal of Eco- nomics, 136(3), 1611–1663. Aguirregabiria, V., A. Collard-Wexler, and S. Ryan (2021): “Dynamic games in em- pirical industrial organization,” inHandbook of Industrial Organization, Volume 4...

work page arXiv 2021

[2] [2]

Random-coefficients logit demand estimation with zero-valued market shares,

Dubé, J.-P., A. Hortaçsu, and J. Joo (2021): “Random-coefficients logit demand estimation with zero-valued market shares,”Marketing Science, 40(4), 637–660. Eizenberg, A. (2014): “Upstream innovation and product variety in the us home pc market,” The Review of Economic Studies, 81(3), 1003–1045. Gandhi, A., Z. Lu, and X. Shi (2023): “Estimating demand for...

work page 2021

[3] [3]

The common structure of statistical models of truncation, sample se- lection and limited dependent variables and a simple estimator for such models,

Heckman, J. (1976): “The common structure of statistical models of truncation, sample se- lection and limited dependent variables and a simple estimator for such models,”Annals of Economic and Social Measurement, 5(4), 475–492. Hirano, K., G. W. Imbens, and G. Ridder (2003): “Efficientestimationofaveragetreatment effects using the estimated propensity sco...

work page 1976