Producer Price Index Manual: Theory and Practice ... - METAC

Producer Price Index Manual
components in the standard error of the t-statistics.
Even if multicollinearity is expected to be quite
high, large sample sizes and a well-fitting model
may reduce the standard errors on the t-statistics to
acceptable levels. If multicollinearity is expected
to be severe, the predicted value for an item’s price
may be computed using the whole regression and
an adjustment made using the predicted value, as
explained in Chapter 7, Section E.4, since there is
a sense in which it would not matter whether the
variation was wrongly attributed to either β 1 or β 2 .
If dummy variable hedonic indices are being calculated
(Section B.3 above), the time trend will be
collinear with an included variable if a new feature
appears in a new month for the vast majority of the
items, so that the data are not rich enough to allow
the separate effects of the coefficient on the time
dummy to be precisely identified. The extent of the
imprecision of the coefficient on the time dummy
will be determined by the aforementioned factors.
A similar argument holds for omitted variable bias.
Omitted variable bias
21.93 The exclusion of tastes and technology
and community characteristics has already been
discussed. The concern here is with product characteristics.
Consider again the use of a subset of
the estimated coefficients from a hedonic regression
to quality adjust a noncomparable replacement
price. It is well established that multicollinearity
of omitted variables with included variables
leads to bias in the estimates of the coefficients of
included ones. If omitted variables are independent
of the included variables, then the estimates of the
coefficients on the included variables are unbiased.
This is acceptable in this instance; the only caveat
is that it may be that the quality adjustment for the
replacement item also requires an adjustment for
these omitted variables, and this, as noted by
Triplett (2002), has to be undertaken using a separate
method and data. But what if the omitted variable
is multicollinear with a subset of included
ones, and these included ones are to be used to
quality adjust a noncomparable item In this case,
the coefficient on the subset of the included variables
may be wrongly picking up some of the
omitted variables’ effects. The coefficients will be
used to quality adjust prices for items that differ
only with regard to this subset of included variables,
and the price comparison will be biased if
the characteristics of both included and omitted
variables have different price changes. For hedonic
indices using a dummy time trend, the estimates of
quality-adjusted price changes will suffer from a
similar bias if excluded from the regression are
omitted variables multicollinear with the time
change. What are picked up as quality-adjusted
price changes over time may, in part, be changes
due to the prices of these excluded variables. This
requires that the prices on the omitted characteristics
follow a different trend. Such effects are most
likely when there are gradual improvements in the
quality of items, such as the reliability and safety
of consumer durables, 40 which are difficult to
measure, at least for the sample of items in real
time. The quality–adjusted price changes will thus,
overstate price changes in such instances.
40 There are some commodity areas, such as airline comfort,
that have been argued to have overall patterns of decreasing
quality.
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