Quantiles

  • cut points that divide our data into equal chunks with equal probability of being selected (equal number of observations in each chunk).

  • Quantiles: Quartiles (4), Deciles (10), Percentiles (100)…

  • Range

  • IQR - Interquartile range

Quartiles: every 25% of observations

Quartiles: non-normal distribution

Deciles: every 10% of observations (Normal)

Deciles: Gamma distribution

See more on the Gamma distribution

Example (1): income deciles

Deciles (1) of Income Distribution

Deciles (2) of Income Distribution

Let us draw a histogram with frequency by deciles!

  • Note: the total population in 1998 was 6 billion
  • Is it useful?

Deciles (3). New insights

Let us plot % share of total income on Y axis.

Deciles (4). New insights

What does it show?

Where is the global income generated and distributed?

Deciles (5). Change over time

What had changed between 1998 and 2011?

Deciles (6). By country

Deciles (7). By country

Example (2): inequality, taxes and subsidies (1)

Fiscal policy can redistribute income

  • Taxes could be ‘collected’ from the ‘rich’:

    • Direct taxed: income tax
    • Indirect taxed: VAT, and excises

  • Subsidies could ‘distribute’ wealth to the ‘poor’:

    • Direct subsidies: unemployment benefits, child support
    • In-kind subsidies: health and education

  • See: https://commitmentoequity.org/

See Fiscal Incidence in Armenia and FISCAL POLICY IN INDONESIA

The Data

Data below is produced based on the representative HH surveys.

  • For each individual income by sources and expenditure by cause are calculated.

  • Then individuals are aggregated into the deciles of income.

  • Each individual earns market income, while taxes and subsidies subtract or add to it.

Progressive taxation

Regressive taxation

Home work

Robust vs non robust variance

  • Would the mean or the median best represent the central tendency?

  • What does this say about the robustness of the two measures?

  • Would the standard deviation or the IQR best represent the amount of variability in the incomes?

Source: (Diez et al. 2022)

At home: Match distribution with the box plot

  • Describe the distribution in the histograms below and match them to the box plots.

Source: (Diez et al. 2022)

Diez, David, Mine Cetinkaya-Rundel, and Christopher D Barr. 2022. OpenIntro Statistics: Fourth Edition. OpenIntro. https://www.openintro.org/book/os/.