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Earning Estimates, Predictor Specification, and Measurement Error 223
assuming that the measurement error, U, and residual model error,
e, are independent and that measurement error is not a function of
the flash predictor.
Alternatively, one can write the preceding equation as:
I)
b
b=
l+ [variance(u)/ variance (flash predictor)]'
This suggests that the estimated coefficient, 6, has a bias toward zero
that depends upon the variance in the measurement error relative to
the variance in the flash predictor. Other things equal, the greater
the variance in the measurement error, the more biased the est
of 6. Why? Because the consensus provides a more noisy estimate of
flash earnings as measurement error increases.
For models with more than one explanatory variable, effect the
of measurement error becomes a bit more complex. It will depend
on, among other things, the number of predictors with measurement
error, the correlations between predictors, the correlations
between measurement errors, and the signs of the regression coefficients.
For the special case where predictors are not correlated and
not related to measurement errors, and measurement errors across
predictors are independent, the regression coefficients will be biased
toward zero. As predictors become more highly correlated,
however, any bias will depend on the signs of the regression coefficients
and the variance of the measurement errors relative to the
variance of the predictors, other things equal.=
ENDNOTES
The authors thank Judith Kimball for her editorial assistance.
1. One can choose from a variety of data vendors as well. For this study
we use Institutional Brokers Estimates System (IBES) data.
2. There are a variety of options regarding the estimates to include as
well as their weights. A dynamic weighting strategy, for example,
would weight more recent estimates more heavily than older
estimates. .
3. Trimmed means remove a proportion of the most extreme
observations from a data set and compute the mean of the remaining
observations. This procedure reduces the influence of outliers.