# Spatial price indexes

It is possible to rework the functions in this package to make a spatial, rather than temporal, price index using a star model by simply replacing “time” with “space”. Although this is not a suitable approach for making a system of purchasing power parities, is it useful for making indexes that adjust pay for cost-of-living differences relative to a fixed location. These sorts of indexes are made by the United Nations International Civil Service Commission, Eurostat, and various governments and private-sector organizations for administering cost-of-living allowances.

The basic workflow is the same as with a temporal index, just treating each country as a different “time period” in a fixed-based index.

    library(piar)

    set.seed(12345)

    # Make indexes for 6 basic headings for 4 countries.
    bh_index <- matrix(
      c(rep(1, 6), runif(6 * 3, 0.8, 1.2)),
      nrow = 6,
      dimnames = list(
        paste0("BH", 1:6),
        paste("Country", 1:4)
      )
    ) |>
      as_index(chainable = FALSE)

    head(bh_index)

    #> Fixed-base price index for 6 levels over 4 time periods
    #>       time
    #> levels Country 1 Country 2 Country 3 Country 4
    #>    BH1         1 1.0883616 0.9300382 1.0942740
    #>    BH2         1 1.1503093 1.0036897 0.8004546
    #>    BH3         1 1.1043929 1.0910821 0.9564813
    #>    BH4         1 1.1544498 1.1958948 0.9849979
    #>    BH5         1 0.9825924 0.8138142 0.9552576
    #>    BH6         1 0.8665487 0.8609494 0.9609941

    # Make fixed aggregation weights.
    #            1
    #      |-----+-----|
    #      11          12
    #  |---+---|   |---+---|
    #  B1  B2  B3  B4  B5  B6

    weights <- data.frame(
      level1 = 1,
      level2 = rep(11:12, each = 3),
      bh = levels(bh_index),
      weights = runif(6, 100, 200)
    )

    head(weights)

level1 | level2 | bh | weights
--- | --- | --- | ---
1 | 11 | BH1 | 117.896
1 | 11 | BH2 | 195.166
1 | 11 | BH3 | 145.373
1 | 12 | BH4 | 132.675
1 | 12 | BH5 | 196.542
1 | 12 | BH6 | 170.748

The indexes at the basic-heading level can be aggregated as usual to get a collection of indexes that give the difference in purchasing power relative to the base country (country 1 in this example). Different choices for weights make different assumptions about how people change their spending patterns between each country and the base country.

    index <- aggregate(bh_index, weights)

As it can be costly to collect price data from various countries on a regular basis, these sorts of indexes are often updated over time by changes in exchange rates and inflation rates for each country.

    as.matrix(index[1, -1])

Country 2 | Country 3 | Country 4
--- | --- | ---
1.051 | 0.970 | 0.946

    update_factors <- runif(3, 0.8, 1.2)

    as.matrix(index[1, -1]) * update_factors

Country 2 | Country 3 | Country 4
--- | --- | ---
1.112 | 0.927 | 1.021