Impute missing prices using the carry forward or shadow price method.
shadow_price(x, ...)# S3 method for default
shadow_price(
x,
...,
period,
product,
ea,
pias = NULL,
weights = NULL,
r1 = 0,
r2 = 1
)
# S3 method for data.frame
shadow_price(x, formula, ..., weights = NULL)
carry_forward(x, ...)
# S3 method for default
carry_forward(x, ..., period, product)
# S3 method for data.frame
carry_forward(x, formula, ...)
carry_backward(x, ...)
# S3 method for default
carry_backward(x, ..., period, product)
# S3 method for data.frame
carry_backward(x, formula, ...)
A numeric vector of prices with missing values replaced (where possible).
Either a numeric vector (or something that can be coerced into one) or data frame of prices.
Further arguments passed to or used by methods.
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 of period, to agree with
cut().
A factor, or something that can be coerced into one, giving
the product associated with each price in x.
A factor, or something that can be coerced into one, giving the
elemental aggregate associated with each price in x.
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).
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. This is evaluated in x for the data
frame method.
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.
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.
A two-sided formula with prices on the left-hand
side. For carry_forward() and carry_backward(), the right-hand side
should have time periods and products (in that order); for
shadow_price(), the right-hand side should have time period, products,
and elemental aggregates (in that order).
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.
IMF, ILO, OECD, Eurostat, UNECE, and World Bank. (2020). Consumer Price Index Manual: Concepts and Methods. International Monetary Fund.
price_relative() for making price relatives for the
same products over time.
prices <- data.frame(
price = c(1:7, NA),
period = rep(1:2, each = 4),
product = 1:4,
ea = rep(letters[1:2], 4)
)
carry_forward(prices, price ~ period + product)
shadow_price(prices, price ~ period + product + ea)
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