Control Function Corrections for Unobserved Factors in Differentiated Product Models

Control Function Corrections

for Unobserved Factors

in Differentiated Product Models

Kyoo il Kim

University of Minnesota

Amil Petrin

University of Minnesota and NBER

January 5, 2010

Abstract

Unobserved factors in differentiated product models can generate

bias in price elasticities. We provide a set of assumptions under which

pricing functions can be inverted to obtain controls that condition on

the problematic part of the demand error. Our approach extends the

literature by addressing endogenous prices while simultaneously allowing for non-separability between observed and unobserved factors or

complementarities in demand, cases for which the Berry (1994) correction will not work. Our approach is a simple two-step procedure of

OLS followed by Maximum Likelihood. We show how to implement

our approach on three data sets and demand specifications estimated

elsewhere that span a range of markets and levels of aggregation, including automobiles (the original Berry, Levinsohn, and Pakes (1995)

application), cable television, and margarine.

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Introduction

Models of differentiated products are widely used for estimating demand

elasticities and substitution patterns. In applications of these models it is

rare that all relevant factors are observed by the econometrician. When

some factors are unobserved, price will typically be correlated with these

unobserved factors through the equilibrating mechanism in the market. For

example, products that display desirable attributes observed by consumers

and producers but not measured by the econometrician will often have prices

that are positively correlated with the demand error. Alternatively, if advertising or other promotional activities are omitted from the specification, and

if prices are set simultaneously with these promotional levels, then price will

be correlated with the demand error. The problem has arisen in both aggregate (i.e. market-level) data and disaggregate (i.e.,...