Review of Quantitative Finance and Accounting, 13 (1999): 295±313
# 1999 Kluwer Academic Publishers, Boston. Manufactured in The Netherlands.
Models with Unexpected Components: The Case for
Associate Professor of Economics, Department of Economics and Finance, University of New Orleans,
New Orleans, LA 70148, e-mail: firstname.lastname@example.org
MARK E. WOHAR
Distinguished Enron Professor, Department of Economics, University of Nebraska at Omaha, Omaha, NE 68182,
Abstract. Financial models often use unexpected explanatory variables. Conventionally, these are generated as
the residuals of auxiliary equations, which are then substituted into the model of interest in a second step. This
induces an econometric problem into the estimates, which is typically ignored. We propose a maximum
likelihood estimation method as a solution. While there may be a predisposition when using ®nancial data to
dismiss our method as dif®cult to specify correctly, Monte Carlo simulations show that our method is robust.
Further, we show that the magnitude of errors due to the generated regressor problem is somewhat larger than that
due to ignoring the effects of plausible levels of leptokurtosis. An empirical example using commercial bank
stock returns ®nds that hypothesis test conclusions from the conventional method can often be overturned.
Key words: unexpected variables, generated regressors, market models
JEL Classi®cation: G12, G22, C51
Ef®cient market theory often suggests that asset prices are caused by those portions of
factor movements that are unexpected. Unexpected variables are typically generated by
adding a step to the estimation routine to obtain residuals from an auxiliary equation. It
appears that most applied ®nancial researchers are aware that using generated regressors
presents problems for estimation and inference. However, it is equally clear that this
awareness has not always translated into the pursuit of appropriate estimation techniques.
This is evidenced by the absence of citations in ®nance journals detailing: (1) the effects of
generated regressors on inference in ®nite samples (see Hoffman et al., 1984, or Gauger,
1989), (2) incomplete but constructive improvements in estimation technique (see Murphy
and Topel, 1985; Turkington, 1985; Hoffman, 1987), (3) comprehensive explorations of
what structures in models lead to problems (see Pesaran, 1987), or (4) how estimation must
be executed to completely eliminate the problem (see McKenzie and McAleer, 1991).
This paper attempts to provide a conduit between the econometric theory related to
these issues and its application to the ®nance arena. It is not intended to be a de®nitive
study of the sensitivity of asset prices to unexpected variables. We use a simple two factor
return generating model (2FRM) for illustration. This model is simple and straightforward,