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## Instrumental Variables Estimation of Conditional Beta Pricing
Models

**Campbell R. Harvey**

Duke University, Durham, NC 27708, USA

National Bureau of Economic Research, Cambridge, MA 02138, USA

**Chris M. Kirby**

University of Maryland, College Park, MD 20742, USA

A number of well-known asset pricing models imply that the
expected return on an asset can be written as a linear function
of one or more beta coefficients that measure the asset's
sensitivity to sources of undiversifiable risk. This paper
provides an overview of the econometric evaluation of such models
using the method of instrumental variables. We present numerous
examples that cover both single-beta and multi-beta models. These
examples are designed to illustrate the various options available
to researchers for estimating and testing beta pricing models.
We also examine the implications of a variety of different
assumptions concerning the time-series behavior of conditional
betas, covariances, reward-to-risk ratios. The techniques
discussed in this paper have applications in other areas of asset
pricing as well.