GEKS index

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

Usage

geks(f, r = 0)

tornqvist_geks(
  p,
  q,
  period,
  product,
  window = nlevels(period),
  n = window - 1L,
  na.rm = FALSE
)

fisher_geks(
  p,
  q,
  period,
  product,
  window = nlevels(period),
  n = window - 1L,
  na.rm = FALSE
)

walsh_geks(
  p,
  q,
  period,
  product,
  window = nlevels(period),
  n = window - 1L,
  na.rm = FALSE
)

Arguments

f: A price index function that uses information on both base and current-period prices and quantities, and satisfies the time-reversal test. Usually a Törnqvist, Fisher, or Walsh index.
r: 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.
p: A numeric vector of prices, the same length as q.
q: A numeric vector of quantities, the same length as p.
period: A factor, or something that can be coerced into one, that gives the corresponding time period for each element in p and q. The ordering of time periods follows the levels of period to agree with cut().
product: A factor, or something that can be coerced into one, that gives the corresponding product identifier for each element in p and q.
window: 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: 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.
na.rm: Passed to f to control if missing values are removed.

Value

geks() returns a function:

function(p, q, period, product, window = nlevels(period), n =
         window - 1, na.rm = FALSE){...}

This calculates a period-over-period GEKS index with the desired index-number formula, returning a list for each window with a named-numeric vector of index values.

tornqvist_geks(), fisher_geks(), and walsh_geks() each return a list with a named numeric vector giving the value of the respective period-over-period GEKS index for each window.

Note

Like back_period(), if multiple prices correspond to a period-product pair, then the back price at a point in time is always the first price for that product in the previous period. Unlike a bilateral index, however, duplicated period-product pairs can have more subtle implications for a multilateral index.

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

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

cumprod(tornqvist_geks(price, quantity, period, product)[[1]])
#>        2        3        4        5 
#> 1.413257 1.835676 2.284565 2.789856 

# Calculate the index over a rolling window

(tg <- tornqvist_geks(price, quantity, period, product, window = 3))
#> [[1]]
#>        2        3 
#> 1.391443 1.294442 
#> 
#> [[2]]
#>        3        4 
#> 1.292486 1.238393 
#> 
#> [[3]]
#>        4        5 
#> 1.238417 1.205921 
#> 

# Use a movement splice to combine the indexes in each window

splice_index(tg, 2)
#>        2        3        4        5 
#> 1.391443 1.801142 2.230521 2.689833 

# ... or use a mean splice

splice_index(tg)
#>        2        3        4        5 
#> 1.391443 1.801142 2.228836 2.687826 

#---- Missing data ----

quantity[2] <- NA

# Use all non-missing data

fisher_geks(price, quantity, period, product, na.rm = TRUE)
#> [[1]]
#>        2        3        4        5 
#> 1.438137 1.234230 1.234212 1.216746 
#> 

# Remove records with any missing data

fg <- geks(balanced(fisher_index))
fg(price, quantity, period, product, na.rm = TRUE)
#> [[1]]
#>        2        3        4        5 
#> 1.501481 1.148250 1.219688 1.199513 
#> 

#---- Make a Jevons GEKS index ----

jevons_geks <- geks(\(p1, p0, ..., na.rm) jevons_index(p1, p0, na.rm))
jevons_geks(price, quantity, period, product)
#> [[1]]
#>        2        3        4        5 
#> 1.527525 1.309307 1.224745 1.178511 
#>