Skip to contents

Country Product Dummy (CPD) regression model

Source: R/estim.R
estim_cpd.Rd

estim_cpd in OECDsppps creates ...; see Details and World Bank (2013) , for more information.

Usage

estim_cpd(
  data,
  region = "region",
  product = "product",
  price = "price",
  weights = NULL,
  weights_cpd = NULL,
  base.region = NULL,
  output = "sPPP"
)

Arguments

data

Data frame, data table or tibble containing at least three columns identifying region, product and individual item-level price quotes

region

Identifier for regions (within or across countries)

product

Product identifier

price

Individual item-level price quotes; Duplicate region-product pairs are aggregated by way of averaging across region-product pairs

weights

An optional vector of weights to be used whenever duplicate regional-product pairs are found in the data. Options:

  • Default is NULL, in which case data is aggregated to region-product pairs using unweighted means.

  • If weights are provided and duplicate regional-product pairs are found, these weights are used as part of the aggregation of average regional-product pairs; see stats weighted.mean().

  • If weights = 'raw', raw data is used with no additional aggregation to region-product pairs.

weights_cpd

An optional vector of weights to be used in the fitting process of the CPD regression model; default is NULL and ordinary least squares is used. If non-NULL, weighted least squares is used, with weights \(w\) provided by weights, to minimise \(\sum(w \times e^2)\); see 'Details' of stats lm()

base.region

An optional character specifying the base to which the estimated logarithmic regional price levels are expressed When NULL, they refer to the (unweighted) regional average, similar to contr.sum()

output

Either "sPPP", which returns the estimated subnational purchasing purchasing power parities, that is, \(\hat{SPPP}_r = exp(\hat{\alpha}_r)\) or "Full", which summarises the key information of the estimate CPD model: It provides the 'Regression outputas well as the individual 'Residuals' of the CPD regression. Note that the column sPPPis derived from the factor term contrasts usingstats::dummy.coef(). The values in the column estimatecorrespond to the columnsPPPassPPP = exp(estimate)` for all factors except the 'missing' category, for which they are zero. Consequently, the regression output for this category is reported as NA, while the sPPP value is reported as described above.

Details

The CPD method is a regression-based approach for estimating price parities. It is characterised by a fixed-effects specification, in which country effects yield estimates of subnational purchasing power parities, while commodity-specific effects generate estimates of subnational price levels. The model can be written as a regression equation in which all explanatory variables take the form of dummy indicators for each region and commodity:

\[ln p_{ij} = \alpha_1 D_1 + ... + \alpha_j D_j + ... +\alpha_R D_R + \ \eta_1 \mathcal{D}_1 + ... + \eta_i \mathcal{D}_i + ... + \eta_N \mathcal{D}_N + \varepsilon_{ij}\]

where \(\alpha_j\) is the the price level of region \(j\) relative to all other regions in the comparison. \(\alpha_j\) can also be expressed relative to a reference region, for example, the national price level. Then, \(\alpha_j\) represents the subnational purchasing power parity of region \(j\) given by \(\hat{PPP}_j = exp(\hat{\alpha}_j)\).

References

World Bank (2013). Measuring the Real Size of the World Economy: The Framework, Methodology, and Results of the International Comparison Program — ICP. World Bank. doi:10.1596/978-0-8213-9728-2 .

Examples

suppressPackageStartupMessages(library(dplyr))
df <- tibble(
  region = as.factor(c(1, 2, 1, 2)),
  product = as.factor(c(1, 1, 2, 2)),
  price = c(25, 28, 23, 26)
)

estim_cpd(df, output = "sPPP")
#> # A tibble: 2 × 2
#>   region  sPPP
#>   <chr>  <dbl>
#> 1 1      0.943
#> 2 2      1.06 
estim_cpd(df, output = "Full")
#> $`Regression output`
#> # A tibble: 3 × 12
#>   region       sPPP estimate std.error statistic p.value r.squared adj.r.squared
#>   <chr>       <dbl>    <dbl>     <dbl>     <dbl>   <dbl>     <dbl>         <dbl>
#> 1 1           0.943  -0.0590   0.00232     -25.4  0.0250    NA            NA    
#> 2 2           1.06   NA       NA            NA   NA         NA            NA    
#> 3 Aggregate… NA      NA       NA            NA   NA          1.000         1.000
#> # ℹ 4 more variables: sigma <dbl>, df <dbl>, df.residual <int>,
#> #   `Number of products per region` <dbl>
#> 
#> $Residuals
#> # A tibble: 4 × 4
#>   region .fitted   .resid .std.resid
#>   <fct>    <dbl>    <dbl>      <dbl>
#> 1 1         3.22  0.00232      1.000
#> 2 2         3.33 -0.00232     -1    
#> 3 1         3.14 -0.00232     -1    
#> 4 2         3.26  0.00232      1    
#>