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Nonparametric and Machine Learning Approaches to Demand Estimation for Differentiated Products

Paper Session

Saturday, Jan. 5, 2019 10:15 AM - 12:15 PM

Atlanta Marriott Marquis, M202
Hosted By: Econometric Society
  • Chair: Vira Semenova, Massachusetts Institute of Technology

Nonparametric Demand Estimation in Differentiated Products Markets

Giovanni Compiani
,
Yale University

Abstract

I develop and apply a nonparametric approach to estimate demand in differentiated products markets. Estimating demand flexibly is key to addressing many questions in economics that hinge on the shape -- and notably the curvature -- of market demand
functions. My approach applies to standard discrete choice settings, but accommodates
a broader range of consumer behaviors and preferences, including complementarities
across goods, consumer inattention, and consumer loss aversion. Further, no distributional
assumptions are made on the unobservables and only limited functional form
restrictions are imposed. Using California grocery store data, I apply my approach to
perform two counterfactual exercises: quantifying the pass-through of a tax, and assessing
how much the multi-product nature of sellers contributes to markups. In both
cases, I find that estimating demand flexibly has a significant impact on the results
relative to a standard random coefficients discrete choice model, and I highlight how
the outcomes relate to the estimated shape of the demand functions.

Flexible Estimation of Differentiated Product Demand Models Using Aggregate Data

Amit Gandhi
,
University of Pennsylvania
Aviv Nevo
,
University of Pennsylvania
Jing Tao
,
University of Washington

Abstract

In this paper we introduce a flexible approach to estimate aggregate discrete choice models with
price endogeneity. Our approach is based on treating the inverse demand function in a dierentiated
product market, which is the object of identification in Berry and Haile (2014), as the primitive of interest that is sufficient to recover price elasticities. We then apply dimensionality reduction on the estimating equation derived from the underlying theoretical restrictions on the demand system, combined with a two-stage least squares Lasso procedure to estimate inverse demand and demand elasticities.

Identifying Distributions of Random Functions and Multidimensional Unobservables with Countable Support and Endogeneity

Zach Flynn
,
Amazon
Jeremy Fox
,
Rice University
Amit Gandhi
,
University of Pennsylvania

Abstract

We use cross sectional data to explore the identification of the distribution of unobservables in a nonlinear model with multidimensional heterogeneous unobservables possibly greater in number than the outcome variables or, more generally, heterogeneous unobservables that index random functions. For the case of statistical endogeneity, our model allows for the important case of prices generated by Bertrand-Nash pricing in an oligopoly. Given a counterexample in the literature, we explore the support condition that the heterogeneous unobservables have support on an unknown countable subset of the relevant real or function space. The countable support is learned in identification. We first show identification of the distribution of marginal effects at a particular value of the explanatory variables. For identification of the distribution of functions defined at all explanatory variable, we require that the heterogeneous unobservables index analytic functions of observable variables.

Orthogonal ML for Demand Estimation: High Dimensional Causal Inference in Dynamic Panels

Victor Chernozhukov
,
Massachusetts Institute of Technology
Matt Goldman
,
Microsoft Technology & Research
Vira Semenova
,
Massachusetts Institute of Technology
Matt Taddy
,
Microsoft & University of Chicago

Abstract

There has been growing interest in how economists can import machine learning tools designed for prediction to accelerate and automate the model selection process, while still retaining desirable inference properties for causal parameters. Focusing on partially linear models, we extend the Double ML framework to allow for (1) a number of treatments that may grow with the sample size and (2) the analysis of panel data under sequentially exogenous errors. Our low-dimensional treatment (LD) regime directly extends the work in [Chernozhukov et al., 2016], by showing that the coefficients from a second stage, ordinary least squares estimator attain root-n convergence and desired coverage even if the dimensionality of treatment is allowed to grow. In a high-dimensional sparse (HDS) regime, we show that second stage LASSO and debiased LASSO have asymptotic properties equivalent to oracle estimators with no upstream error. We argue that these advances make Double ML methods a desirable alternative for practitioners estimating short-term demand elasticities in non-contractual settings.
JEL Classifications
  • C3 - Multiple or Simultaneous Equation Models; Multiple Variables
  • L1 - Market Structure, Firm Strategy, and Market Performance