Multiple sources of data

Price indexes are usually made from several sources of data. An important benefit of the usual two-step workflow to make price indexes is that the elemental indexes can be built piecemeal—using different sources of data and different index-number formulas—and then aggregated with a consistent structure.

Let’s extend the example in vignette("piar") by having an alternate source of data for business B5 that is always missing in the ms_prices dataset.

library(piar)

# Make an aggregation structure.
ms_weights[c("level1", "level2")] <- 
  expand_classification(ms_weights$classification)

pias <- ms_weights[c("level1", "level2", "business", "weight")] |>
  as_aggregation_structure()

# Make elemental index.
elementals <- ms_prices |>
  transform(
    relative = price_relative(price, period = period, product = product)
  ) |>
  elemental_index(relative ~ period + business, na.rm = TRUE)

elementals

## Period-over-period price index for 4 levels over 4 time periods 
##    202001    202002    202003   202004
## B1      1 0.8949097 0.3342939      NaN
## B2      1       NaN       NaN 2.770456
## B3      1 2.0200036 1.6353355 0.537996
## B4    NaN       NaN       NaN 4.576286

Instead of using survey-like data for the other businesses, B5 is made from scanner-like data with many price and quantity observations at each point in time.

set.seed(12345)

scanner_prices <- data.frame(
  period = rep(c("201904", time(elementals)), each = 200),
  product = 1:200,
  price = round(rlnorm(5 * 200) * 10, 1),
  quantity = round(runif(5 * 200, 100, 1000))
)

head(scanner_prices)

##   period product price quantity
## 1 201904       1  18.0      958
## 2 201904       2  20.3      660
## 3 201904       3   9.0      579
## 4 201904       4   6.4      903
## 5 201904       5  18.3      276
## 6 201904       6   1.6      896

These type of data often require the use of a multilateral index like the GEKS. For the sake of illustration, we’ll make a Fisher GEKS index over a 3 quarter rolling window and use a mean splice to make a single time series.

library(gpindex)

geks_elementals <- with(
  scanner_prices,
  fisher_geks(price, quantity, period, product, window = 3)
) |>
  splice_index() |>
  t() |>
  as_index(chainable = FALSE) |>
  set_levels("B5")

geks_elementals

## Fixed-base price index for 1 levels over 4 time periods 
##       202001    202002   202003   202004
## B5 0.8862618 0.8969686 1.013005 0.718693

These values can now be merged with the other elemental indexes, getting turned into a period-over-period index in the process, and then aggregated.

merge(elementals, geks_elementals) |>
  aggregate(pias, na.rm = TRUE)

## Period-over-period price index for 8 levels over 4 time periods 
##       202001    202002    202003    202004
## 1  0.9560379 1.1973001 1.0831525 2.0991849
## 11 1.0000000 1.3007239 1.0630743 1.5745154
## 12 0.8862618 1.0120809 1.1293651 3.2358970
## B1 1.0000000 0.8949097 0.3342939 1.5745154
## B2 1.0000000 1.3007239 1.0630743 2.7704563
## B3 1.0000000 2.0200036 1.6353355 0.5379960
## B4 0.8862618 1.0120809 1.1293651 4.5762862
## B5 0.8862618 1.0120809 1.1293651 0.7094664