Impute missing prices using the carry forward or shadow price method.
Usage
shadow_price(
x,
period,
product,
ea,
pias = NULL,
weights = NULL,
r1 = 0,
r2 = 1
)
carry_forward(x, period, product)
carry_backwards(x, period, product)
Arguments
- x
A numeric vector of prices, or something that can be coerced into one.
- period
A factor, or something that can be coerced into one, giving the time period associated with each price in
x
. The ordering of time periods follows of the levels ofperiod
, to agree withcut()
.- product
A factor, or something that can be coerced into one, giving the product associated with each price in
x
.- ea
A factor, or something that can be coerced into one, giving the elemental aggregate associated with each price in
x
.- pias
A price index aggregation structure, or something that can be coerced into one, as made with
aggregation_structure()
. The default imputes from elemental indexes only (i.e., not recursively).- weights
A numeric vector of weights for the prices in
x
(i.e., product weights), or something that can be coerced into one. The default is to give each price equal weight.- r1
Order of the generalized-mean price index used to calculate the elemental price indexes: 0 for a geometric index (the default), 1 for an arithmetic index, or -1 for a harmonic index. Other values are possible; see
gpindex::generalized_mean()
for details.- r2
Order of the generalized-mean price index used to aggregate the elemental price indexes: 0 for a geometric index, 1 for an arithmetic index (the default), or -1 for a harmonic index. Other values are possible; see
gpindex::generalized_mean()
for details.
Details
The carry forward method replaces a missing price for a product by the price for the same product in the previous period. It tends to push an index value towards 1, and is usually avoided; see paragraph 6.61 in the CPI manual (2020). The carry backwards method does the opposite, but this is rarely used in practice.
The shadow price method recursively imputes a missing price by the value of
the price for the same product in the previous period multiplied by the
value of the period-over-period elemental index for the elemental aggregate
to which that product belongs. This requires computing and aggregating an
index (according to pias
, unless pias
is not supplied) for
each period
, and so these imputations can take a while. The index
values used to do the imputations are not returned because the index needs
to be recalculated to get correct percent-change contributions.
Shadow price imputation is referred to as self-correcting overall mean imputation in chapter 6 of the CPI manual (2020). It is identical to simply excluding missing price relatives in the index calculation, except in the period that a missing product returns. For this reason care is needed when using this method. It is sensitive to the assumption that a product does not change over time, and in some cases it is safer to simply omit the missing price relatives instead of imputing the missing prices.
References
ILO, IMF, OECD, Eurostat, UN, and World Bank. (2020). Consumer Price Index Manual: Theory and Practice. International Monetary Fund.
See also
price_relative()
for making price relatives for the
same products over time.