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Impute missing prices

Source: R/impute_prices.R
impute_prices.Rd

Impute missing prices using the carry forward/backward or the self-correcting overall mean method.

Usage

impute_prices(x, ...)

# Default S3 method
impute_prices(x, ...)

# S3 method for class 'matrix'
impute_prices(
  x,
  period,
  product,
  ...,
  ea = NULL,
  weights = NULL,
  pias = NULL,
  r = c(0, 1),
  method = c("overall-mean", "carry-forward")
)

# S3 method for class 'numeric'
impute_prices(
  x,
  period,
  product,
  ...,
  ea = NULL,
  weights = NULL,
  pias = NULL,
  r = c(0, 1),
  method = c("overall-mean", "carry-forward", "carry-backward")
)

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

carry_forward(x, ...)

carry_backward(x, ...)

shadow_price(x, ...)

Arguments

x

Either a numeric vector (or something that can be coerced into one), a data frame of prices, or a two-column matrix of current prices and back prices (in that order).

...

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 elementary aggregate associated with each price in x. This is evaluated in x for the data frame method. The default pools all data into one elementary aggregate.

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.

pias

A price index aggregation structure, or something that can be coerced into one, as made with aggregation_structure(). The default imputes from elementary indexes only (i.e., not recursively).

r

A pair of numeric values. The first gives the order of the generalized-mean price index used to calculate the elementary price indexes, defaulting to a geometric index. The second gives the order of the generalized-mean price index used to aggregate the elementary price indexes, defaulting to an arithmetic index. Other values are possible; see gpindex::generalized_mean() for details.

method

Name of the imputation method, one of "overall-mean", "carry-forward", or "carry-backward".

formula

A two-sided formula, or something that can be coerced into one, with prices on the left-hand side and time periods and products on the right-hand side (in that order).

Value

A numeric vector or matrix 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 self-correcting overall mean 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 elementary index for the elementary aggregate to which that product belongs. This requires computing and aggregating an index (according to pias, unless pias is not supplied) for each period. The index values used to do the imputations are not returned because the index needs to be recalculated to get correct percent-change contributions. 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.

Imputation works slightly differently depending on whether data are in a long or wide format. When x is a two-column of matrix of current and back prices (in that order), then imputation is done separately on the current price at a point in time and the back price at the next point in time. When x is a numeric vector then these two prices are necessarily the same.

References

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

impute_prices(prices, price ~ period + product, method = "carry-forward")
#> [1] 1 2 3 4 5 6 7 4

impute_prices(
  prices,
  price ~ period + product,
  ea = ea,
  method = "overall-mean"
)
#> [1]  1  2  3  4  5  6  7 12

# Can also be done with current price-back price formulation.
prices$back_price <- with(
  prices,
  price[gpindex::back_period(period, product)]
)

impute_prices(
  prices,
  cbind(price, back_price) ~ period + product,
  ea = ea,
  method = "overall-mean"
)
#>      price back_price
#> [1,]     1          1
#> [2,]     2          2
#> [3,]     3          3
#> [4,]     4          4
#> [5,]     5          1
#> [6,]     6          2
#> [7,]     7          3
#> [8,]    12          4