In ianksalter/uktax: Functions for Calculating UK Tax and Benefits for Economic Analysis

knitr::opts_chunk$set(
  collapse = TRUE,
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This document describes the methodology used for deriving a tax and benefit function based upon GINI and related data. The primary source of data is the OECD Income Distribution Database. Deriving the tax and benefit function requires the follw requires the following data items:

• Gini (gross income before taxes)
• Gini (market income before taxes and transfers) NOTE determine which one of these we should use.
• Gini (disposable income, post taxes and transfers)
• Mean Disposable Income (current prices)
• Mean Income (before taxes and transfers) note this needs to be calculated from the following
• Total Earnings (current prices)
• Capital Income (current prices)
• Income from self-employment and goods produced for own consumption (current prices)
• Capital and private transfers(current prices)
• Total Number of Housholds

Given a $mean$ and a $gini$ we can calculate the parameters for some income distributions:

For the Log Normal Distribution

Mean: $\mu = mean$

Standard deviation: $\sigma = erf^{-1}(gini)/2$

Since we know that $gini = erf(\sigma/2)$
Therefore $erf^{-1}(gini) = \sigma/2$
and $\sigma/2 = erf^{-1}(gini)$
so $\sigma = 2erf^{-1}(gini)$

For the (type 1) pareto distribution:

Scale: $x_{m} = ?$

Shape: $\alpha = ?$

Since we know from wikipedia that

x_{m} we need an idea of minimum income this can be obtained from the following data and using minimul income. Might need to take a weighted mean. https://data.oecd.org/benwage/adequacy-of-minimum-income-benefits.htm

TODO: Similar for pareto distribution but need a greater understanding of the pareto distribution.

Vignettes are long form documentation commonly included in packages. Because they are part of the distribution of the package, they need to be as compact as possible. The html_vignette output type provides a custom style sheet (and tweaks some options) to ensure that the resulting html is as small as possible. The html_vignette format:

• Never uses retina figures
• Has a smaller default figure size
• Uses a custom CSS stylesheet instead of the default Twitter Bootstrap style

Vignette Info

Note the various macros within the vignette section of the metadata block above. These are required in order to instruct R how to build the vignette. Note that you should change the title field and the \VignetteIndexEntry to match the title of your vignette.

Styles

The html_vignette template includes a basic CSS theme. To override this theme you can specify your own CSS in the document metadata as follows:

output: 
  rmarkdown::html_vignette:
    css: mystyles.css

Figures

The figure sizes have been customised so that you can easily put two images side-by-side.

plot(1:10)
plot(10:1)

You can enable figure captions by fig_caption: yes in YAML:

output:
  rmarkdown::html_vignette:
    fig_caption: yes

Then you can use the chunk option fig.cap = "Your figure caption." in knitr.

More Examples

You can write math expressions, e.g. $Y = X\beta + \epsilon$, footnotes^[A footnote here.], and tables, e.g. using knitr::kable().

knitr::kable(head(mtcars, 10))

Also a quote using >:

"He who gives up [code] safety for [code] speed deserves neither." (via)

ianksalter/uktax documentation built on March 19, 2020, 5:45 a.m.