Diewert and Fox's Method of Value Added Growth Decomposition.

dfvad

Overview

dfvad decomposes value added growth into explanatory factors. A cost constrained value added function is defined to specify the production frontier. Industry estimates can also be aggregated using a weighted average approach.

Installation

dfvad is available from https://github.com/shipei-zeng/dfvad. To install it, install_github from the devtools package can be helpful.

devtools::install_github("shipei-zeng/dfvad")

If error messages show that the URL cannot be opened, please set the download option before installing it.

options(download.file.method = "libcurl")

If error messages show that schannel failed to receive handshake, please delete the previous package before updating it.

It has also been uploaded to the CRAN repository, which can be downloaded using:

install.packages("dfvad")

Usage

value_decom() for decomposing nominal value added growth identifies the contributions from efficiency change, growth of primary inputs, changes in output and input prices, technical progress and returns to scale.

library(dfvad)
# Use the built-in dataset "mining"
table1 <- value_decom(c("h2","x2"), c("w2","u2"), "y2", "p2", "year", mining)[[1]]
head(table1)
#>   period     value     alpha      beta     gamma efficiency   epsilon      tau
#> 1   1991 1.0869517 1.0287049 0.9944262 1.0000000  1.0000000 1.0000000 1.062544
#> 2   1992 0.9960608 0.9523963 0.9874494 1.0000000  1.0000000 1.0000000 1.059140
#> 3   1993 1.0477108 1.0373754 1.0180111 0.9997303  0.9923619 0.9923619 1.000000
#> 4   1994 0.9773035 0.9605188 1.0444275 0.9996838  0.9670585 0.9745018 1.000000
#> 5   1995 1.0545680 0.9842271 1.0168128 0.9999874  1.0000000 1.0340636 1.019052
#> 6   1996 1.1345729 1.0406754 1.0327427 1.0000000  1.0000000 1.0000000 1.055662
#>        TFPG
#> 1 1.0625440
#> 2 1.0591398
#> 3 0.9920943
#> 4 0.9741937
#> 5 1.0537516
#> 6 1.0556623
table2 <- value_decom(c("h2","x2"), c("w2","u2"), "y2", "p2", "year", mining)[[2]]
head(table2)
#>   period    value         A         B         C         E        T      TFP
#> 1   1990 1.000000 1.0000000 1.0000000 1.0000000 1.0000000 1.000000 1.000000
#> 2   1991 1.086952 1.0287049 0.9944262 1.0000000 1.0000000 1.062544 1.062544
#> 3   1992 1.082670 0.9797347 0.9819455 1.0000000 1.0000000 1.125383 1.125383
#> 4   1993 1.134325 1.0163527 0.9996314 0.9997303 0.9923619 1.125383 1.116486
#> 5   1994 1.108580 0.9762259 1.0440425 0.9994142 0.9670585 1.125383 1.087673
#> 6   1995 1.169073 0.9608280 1.0615958 0.9994016 1.0000000 1.146824 1.146138

t_weight() follows a “bottom up” approach that uses weighted averages of the sectoral decompositions to provide an approximate decomposition into explanatory components at the aggregate level.

library(dfvad)
# Use the built-in dataset "sector"
table1 <- t_weight("y", "p", "industry", "year", "alpha", "beta", "gamma", "epsilon", "tau", sector)[[1]]
head(table1)
#>   period     value    alpha      beta     gamma   epsilon      tau      TFPG
#> 1   1991 0.9951654 1.004989 0.9878890 0.9996087 0.9868727 1.016024 1.0023647
#> 2   1992 1.0145281 1.015884 0.9869371 0.9987753 0.9962747 1.016905 1.0118834
#> 3   1993 1.0656435 1.034633 1.0128698 1.0002431 1.0011899 1.015434 1.0168858
#> 4   1994 1.0649234 1.007479 1.0291213 1.0001043 1.0029142 1.024013 1.0271072
#> 5   1995 1.0565961 1.020031 1.0378505 1.0010086 0.9871089 1.010072 0.9980697
#> 6   1996 1.0703334 1.019766 1.0212297 0.9998535 1.0097033 1.018044 1.0277682
table2 <- t_weight("y", "p", "industry", "year", "alpha", "beta", "gamma", "epsilon", "tau", sector)[[2]]
head(table2)
#>   period     value        A         B         C         E        T      TFP
#> 1   1990 1.0000000 1.000000 1.0000000 1.0000000 1.0000000 1.000000 1.000000
#> 2   1991 0.9951654 1.004989 0.9878890 0.9996087 0.9868727 1.016024 1.002365
#> 3   1992 1.0096232 1.020952 0.9749843 0.9983845 0.9831963 1.033200 1.014276
#> 4   1993 1.0758984 1.056311 0.9875322 0.9986272 0.9843662 1.049147 1.031403
#> 5   1994 1.1457494 1.064211 1.0162904 0.9987313 0.9872349 1.074340 1.059361
#> 6   1995 1.2105943 1.085528 1.0547575 0.9997387 0.9745083 1.085161 1.057317

Display

Here is an example to plot the explanatory factors of productivity (logarithmic indexes). Additional packages such as ggplot2 and reshape2 are required.

library(dfvad)
library(ggplot2)
library(reshape2)
# Get the decomposition result
df <- value_decom(c("h2","x2"), c("w2","u2"), "y2", "p2", "year", mining)[[2]]
# Extract columns and rename
df_cmpt <- data.frame(df[,"period"], log(df[,c("T", "E", "C")]))
colnames(df_cmpt) <- c("year", "lnT", "lnE", "lnC")
df_tfp <- data.frame(df[,"period"], log(df[,"TFP"]))
colnames(df_tfp) <- c("year", "lnTFP")
# Set the colour scheme
palette_a <- c("goldenrod1", "seashell4", "red")
# Convert data into a tidy form
df_cmpt_tidy <- melt(df_cmpt, id.vars="year")
# Plot the components
plot_out <- ggplot(df_cmpt_tidy) + geom_bar(aes(x=year, y=value, fill=variable), stat="identity") +
        geom_line(data=df_tfp, aes(x=year,y=lnTFP,color='black'), lwd=0.5) +
        ylab('Log Index') + xlab('Year') + 
        scale_fill_manual("", values=palette_a) + 
        scale_colour_manual("", values=c('black'='black'), labels = c('lnTFP')) + 
        scale_x_continuous(breaks = seq(min(df$period), max(df$period), by = 3)) + 
        theme_classic()
print(plot_out)