by
Minqiang Li
Department of Finance
University of Illinois at Urbana-Champaign
Neil D. Pearson
Department of Finance
University of Illinois at Urbana-Champaign
and
Allen M. Poteshman
Department of Finance
University of Illinois at Urbana-Champaign
Abstract
Most data used in finance are generated naturally rather than experimentally.
While researchers are typically interested in estimates of model parameters
that are not conditional on the particular sample, actual estimates are
necessarily conditional on the data. Recent research on survivorship bias
in equity returns and the estimation of term structure models from time-series
of interest rate data suggests that failing to account for the implicit
conditioning can seriously bias the results of empirical research. This
paper develops theoretical and numerical tools that make it possible to
account for the implicit conditioning when the underlying data are generated
by a time-homogeneous univariate diffusion, and carries out a detailed
analysis for three specific conditioning events that are of interest in
finance. The techniques are illustrated by obtaining estimates of the drift
and diffusion coefficients of a term-structure model from a standard time-series
of interest rate data both with and without conditioning on these three
events. The estimates indicate that the conditioning events have an important
impact on the estimated drift coefficient but little effect on the estimated
diffusion coefficient. A test statistic fails to reject linearity of the
drift coefficient of the short rate process regardless of which of the
conditioning events is assumed.