geks_index: GEKS index

Description

Calculate a generalized inter-temporal GEKS price index over a rolling window.

Usage

geks_index(
  price,
  quantity,
  period,
  product,
  index_formula = function(p1, p0, q1, q0) {
     nested_gmean(p1/p0, list(p0 * q0, p1 *
    q1), na.rm = TRUE)
 },
  window = nlevels(period),
  n = window - 1L,
  order = 0,
  match_method = c("all", "back-price")
)

Value

A list with a named numeric vector giving the value of the respective period-over-period GEKS index for each window.

Arguments

price: [numeric > 0] A numeric vector of prices, the same length as quantity.
quantity: [numeric >= 0] A numeric vector of quantities, the same length as price.
period: [factor] A factor, or something that can be coerced into one, that gives the corresponding time period for each element in price and quantity. The ordering of time periods follows the levels of period to agree with cut().
product: [factor] A factor, or something that can be coerced into one, that gives the corresponding product identifier for each element in price and quantity.
index_formula: [function] A function giving the index-number formula in the GEKS index. Usually a Törnqvist, Fisher (the default), or Walsh index. It must have arguments p1, p0, q1, and q0, and satisfy the time-reversal test. See vignette("index-number-formulas") for details.
window: [integer(1) > 0] A positive integer giving the length of the rolling window. The default is a window that encompasses all periods in period. Non-integers are truncated towards zero.
n: [integer(1) > 0] A positive integer giving the length of the index series for each window, starting from the end of the window. For example, if there are 13 periods in window, setting n = 1 gives the index for period 13. The default gives an index for each period in window. Non-integers are truncated towards zero.
order: [numeric(1)] A finite number giving the order of the generalized mean used to average price indexes over the rolling window. The default uses a geometric mean.
match_method: [character(1)] Either "all" to match all products against each other (the default) or "back-price" to match only back prices. The later can be faster when there is lots of product imbalanced.

References

Balk, B. M. (2008). Price and Quantity Index Numbers. Cambridge University Press.

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

Ivancic, L., Diewert, W. E., and Fox, K. J. (2011). Scanner data, time aggregation and the construction of price indexes. Journal of Econometrics, 161(1): 24--35.

Examples

Run this code

price <- 1:10
quantity <- 10:1
period <- rep(1:5, 2)
product <- rep(letters[1:2], each = 5)

cumprod(geks_index(price, quantity, period, product)[[1]])

# Calculate the index over a rolling window.
(geks <- geks_index(price, quantity, period, product, window = 3))

# Use a movement splice to combine the indexes in each window.
splice_index(geks, 2)

# ... or use a mean splice.
splice_index(geks)

# Make a Jevons GEKS index.
geks_index(
  price,
  quantity,
  period,
  product,
  index_formula = \(p1, p0, ...) gmean(p1 / p0, na.rm = TRUE, order = 0)
)