Constrained Heterogeneity

40 Pages Posted: 23 Jan 2023

See all articles by Tetyana Kosyakova

Tetyana Kosyakova

Frankfurt School of Finance & Management

Max J. Pachali

Tilburg University - Tilburg University School of Economics and Management

Adam N. Smith

University College London - UCL School of Management

Thomas Otter

Goethe University Frankfurt - Department of Marketing

Date Written: January 20, 2023

Abstract

Distributions of preferences and other economic primitives are often key inputs in market-level counterfactual analyses. In empirical work, these distributions must be inferred from finite amounts of data where measures of statistical fit often favor simple — yet ad-hoc — parametric assumptions. In this paper, we investigate ways of imbuing preference distributions with healthy doses of economic rationality through sign and order constraints. Such constraints naturally arise whenever product attributes such as quality or price can be vertically ordered a priori. We illustrate the merits and the disadvantages of imposing such constraints using (i) truncated normal and (ii) log-normal distributions. We then develop a model that enables the analyst to flexibly structure random coefficient distributions according to basic economic arguments using a combination of log-normal, truncated normal, and unconstrained distributions. We develop feasible Bayesian inference for this model based on MCMC, and illustrate that the proposed model improves the accuracy of counterfactual price predictions after the mandatory ban of cage eggs using German household scanner panel data.

Keywords: Constrained Hierarchical Prior, Discrete Choice, Bayesian Inference, Counterfactual Simulation

Suggested Citation

Kosyakova, Tetyana and Pachali, Max J. and Smith, Adam N. and Otter, Thomas, Constrained Heterogeneity (January 20, 2023). Available at SSRN: https://ssrn.com/abstract=4331470 or http://dx.doi.org/10.2139/ssrn.4331470

Tetyana Kosyakova

Frankfurt School of Finance & Management ( email )

Adickesallee 32-34
Frankfurt am Main, 60322
Germany

Max J. Pachali

Tilburg University - Tilburg University School of Economics and Management ( email )

P.O. Box 90153
Tilburg, 5000 LE
Netherlands

HOME PAGE: http://sites.google.com/site/mjpachali/

Adam N. Smith (Contact Author)

University College London - UCL School of Management ( email )

1 Canada Square
London, E14 5AA
United Kingdom

Thomas Otter

Goethe University Frankfurt - Department of Marketing ( email )

Frankfurt
Germany
++49.69.798.34646 (Phone)

HOME PAGE: http://www.marketing.uni-frankfurt.de/index.php?id=97?&L=1

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