impute_prices {piar}

Impute missing prices

Description

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 of period, to agree with cut().

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.

Value

A copy of x with missing values replaced (where possible).

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.

Examples

prices <- data.frame(
  price = c(1:7, NA),
  period = rep(1:2, each = 4),
  product = 1:4,
  ea = rep(letters[1:2], 4)
)

with(prices, carry_forward(price, period, product))

with(prices, shadow_price(price, period, product, ea))