of Consumers on one-year-ahead inflation expectations,
we evaluate the CP assumptions on threshold constancy,
symmetry, homogeneity, and overall unbiasedness by
comparing the CP quantified expectations with aggregated
quantitative expectations from the same set of households
over the period 1978–2012 using monthly observations.
We then cast and generalize the CP method in an ordered
choice model that relies on less restrictive assumptions.
The performance of this generalized model is tested
by using it to quantify the same qualitative survey data
and comparing the results with both the CP estimates and
the quantitative responses from the survey. Two alternatives
to the CP unbiasedness assumption are proposed and
evaluated. The first alternative relies on a rolling-window
regression, and the second employs a time-varying parameter
model. The generalized model and the alternative calibration
schemes we advocate in this paper are applicable
to a wide array of data sets and can be implemented easily
in real time.
This study fills two gaps in the existing literature. First,
even though there is a rich body of literature on the performance
of the Carlson–Parkin method, to the best of our
knowledge, no study has modeled both the time variation
and the cross-sectional heterogeneity (in the thresholds
as well as the variances) and examined their effects
on the performance of the CP method. In a recent study,
Breitung and Schmeling (2013) report a ‘‘surprisingly weak
correlation’’ between the quantified and quantitative forecasts
of stock returns, which is attributed to the importance
of time-varying and heterogeneous thresholds. They
argue analytically that when the variance of the target variable
greatly exceeds that of the individual expectations,
cross-sectional heterogeneity plays little role in determining
the performance of the CP method. While this is likely
to be true for highly volatile targets like stock returns, the
situation could be different when the variable of interest
is consumer expectations for a closely-monitored and
tightly-controlled variable like the inflation rate or the real
GDP growth rate. Nevertheless, there is a clear need for
less restrictive assumptions about the thresholds. The generalization
we propose in this paper addresses this issue
directly by allowing for time-varying and heterogeneous
thresholds. Secondly, while quantified household inflation
expectations from the Survey of Consumers are often used
in forecasting (e.g. Ang, Bekaert, & Wei, 2007) or for testing
the REH (e.g. Souleles, 2004), no study since those of
Batchelor (1986) and Fishe and Idson (1990) has examined
the quality of these quantified expectations by comparing
them with the quantitative expectations.2 It is certainly
both important and informative to benchmark the quantified
expectations against the target variable, e.g., the official
statistic. However, as was first pointed out by Dasgupta
and Lahiri (1992), in general, a lack of fit alone should not
be considered a sign of poor performance of the quantification
method, due to the existence of unforeseen aggregate