Impute missing prices

Impute missing prices using the carry forward or shadow price method.

Usage

shadow_price(x, ...)

# Default S3 method
shadow_price(
  x,
  ...,
  period,
  product,
  ea,
  pias = NULL,
  weights = NULL,
  r1 = 0,
  r2 = 1
)

# S3 method for class 'data.frame'
shadow_price(x, formula, ..., weights = NULL)

carry_forward(x, ...)

# Default S3 method
carry_forward(x, ..., period, product)

# S3 method for class 'data.frame'
carry_forward(x, formula, ...)

carry_backward(x, ...)

# Default S3 method
carry_backward(x, ..., period, product)

# S3 method for class 'data.frame'
carry_backward(x, formula, ...)

Arguments

x: 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.
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. This is evaluated in x for the data frame method.
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.
formula: 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).

Value

A numeric vector of prices with missing values replaced (where possible).

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

IMF, ILO, OECD, Eurostat, UNECE, and World Bank. (2020). Consumer Price Index Manual: Concepts and Methods. International Monetary Fund.

Examples