Niepełna identyfikacja w makroekonomicznym liniowym modelu czynnikowym APT 
i rola rezydualnego czynnika rynkowego 
[Underspecification in the macroeconomic APT linear factor model and the role 
of the residual market factor]

J.J. (Kuba) Szczygielski 
(Department of Financial Management, University of Pretoria, South Africa)


The linear factor model is a building block of the Arbitrage Pricing Theory 
(APT). Macroeconomic factors may be used in linear factor models to proxy for 
pervasive influences in stock returns. However, macroeconomic linear factor 
models are likely to suffer from underspecification, which may pose a challenge 
to the general validity and interpretation of linear factor models and the APT 
model. A widely applied solution to omitted factor bias in APT literature is 
the Burmeister and Wall (1986) residual market factor.

This study sets out to determine whether macroeconomic factors are adequate 
proxies for the pervasive factors that drive stock returns and whether the use 
of a conventional residual market factor derived from a domestic market 
aggregate adequately resolves underspecification. The role of a second residual 
market factor derived from a widely used global market index, the MSCI World 
Market Index, is also considered. By relating factor scores and industrial 
sector returns to macroeconomic factors and residual market factors in linear 
factor models, this study finds that macroeconomic factors are poor proxies for 
pervasive influences in stock returns and that residual market factors fail to 
account for remaining omitted factors.

Researchers of the APT and practitioners are encouraged to take note of these 
findings. The use of macroeconomic factors and the application of a widely used 
approach in APT literature to resolve factor omission may not be adequate. This 
can adversely impact the results of studies focusing on the linear factor model 
and equilibrium pricing within the APT and studies that apply macroeconomic 
linear factor models motivated by the APT in general.

(*) Based on joint work with L.M. Brummer & H. Wolmarans.