Example with R: Hedonics
Calculating a linear hedonic price index is very easy in R.
# Bring in some data
df <- read.csv("csv/data.csv")
df## period price chicken liver salmon
## 1 0 2 1 0 0
## 2 0 4 1 0 0
## 3 0 3 1 0 0
## 4 0 4 1 0 0
## 5 0 5 1 0 0
## 6 0 1 0 1 0
## 7 0 3 0 1 0
## 8 0 2 0 1 0
## 9 0 1 0 1 0
## 10 0 1 0 1 0
## 11 0 5 0 0 1
## 12 0 7 0 0 1
## 13 0 8 0 0 1
## 14 0 4 0 0 1
## 15 1 5 1 0 0
## 16 1 3 1 0 0
## 17 1 2 0 1 0
## 18 1 2 0 1 0
## 19 1 1 0 1 0
## 20 1 3 0 1 0
## 21 1 1 0 1 0
## 22 1 1 0 1 0
## 23 1 9 0 0 1
## 24 1 8 0 0 1
## 25 1 5 0 0 1This is a simple data set for cat food, with three characteristics—is it chicken cat food, liver cat food, or salmon cat food? To evaluate the impact of a hedonic price index, it is useful to calculate a simple transaction-price index by pooling transactions for all three types of cat food together.
# Calculate pooled price index
pooled <- lm(log(price) ~ period, df)
exp(coef(pooled)[2]) * 100## period
## 93.86748The general linear hedonic index is easy to calculate with a simple linear regression. The only trick is remembering to remove the average of each characteristic in the interaction term.
# Calculate hedonic imputation index
hedonic_imputation <- lm(log(price) ~ period + liver + salmon +
period:(I(liver - mean(liver)) + I(salmon - mean(salmon))),
df)
exp(coef(hedonic_imputation)[2]) * 100## period
## 112.2817This is the same as the two-step calculation that is normally done for a hedonic imputation index.
# Period-0 regression
hi0 <- lm(log(price) ~ liver + salmon, df, subset = period == 0)
# Period-1 regression
hi1 <- lm(log(price) ~ liver + salmon, df, subset = period == 1)
# Calculate index using predicted prices
exp(mean(predict(hi1, df) - predict(hi0, df))) * 100## [1] 112.2817It is also the same as manually calculating the stratified index.
# Bring in gpindex library
library(gpindex)
# Weight cat food by its frequency
weights <- colSums(df[-(1:2)])
# Calculate an index for each type of cat food
strata_indices <-
sapply(list(subset(df, chicken == 1),
subset(df, liver == 1),
subset(df, salmon == 1)),
function(x) with(x, geometric_mean(price[period == 1]) / geometric_mean(price[period == 0]))
)
# Aggregate
geometric_mean(strata_indices, weights) * 100## [1] 112.2817The results are very similar if a time-dummy model is used instead.
# Time-dummy index
time_dummy <- lm(log(price) ~ period + liver + salmon, df)
exp(coef(time_dummy)[2]) * 100## period
## 112.2246Adding weights for the transactions in each stratum can easily be done with a weighted regression.
# Make some weights
df$weights <- 1:25 / sum(1:25)
# Calculate weighted hedonic imputation index
hedonic_imputation <- lm(log(price) ~ period + liver + salmon +
period:(I(liver - weighted.mean(liver, weights)) +
I(salmon - weighted.mean(salmon, weights))),
df, weights = weights)
exp(coef(hedonic_imputation)[2]) * 100## period
## 111.1855This gives the same answer as the two-step calculation.
# Period-0 regression
hi0 <- lm(log(price) ~ liver + salmon, df, subset = period == 0, weights = weights)
# Period-1 regression
hi1 <- lm(log(price) ~ liver + salmon, df, subset = period == 1, weights = weights)
# Calculate index using weighted predicted prices
exp(weighted.mean(predict(hi1, df) - predict(hi0, df), df$weights)) * 100## [1] 111.1855