*Some calculations I did for my own satisfaction*

**Keywords**: Regulation & Taxation;

Forgive my statistical pedantry, but John Key recently stated something like ‘the average earner would getting tax cuts of $25 a week’. What he meant was that ‘on average earners were getting tax cuts of $25 a week’.

This led me to wonder what the average earner would receive. ‘Average’ is a tricky concept here. The only sensible meaning in the Key formulation is the earner in the middle of the earnings distribution.

I have the 2001 Census returns for full time workers, adjusted for average earnings increases since then to the 2006 (March ending – the one we are in) year. It is not perfect, because there has been a lot more employment since 2001, which would tend to be at the lower end of the distribution, skewing it down. (Which means the following is generous to Key’s claim.) Moreover, there has probably been an increase in wage dispersion – that is skill rates rising relative to unskilled rates – which does not affect the results very much, providing we are mainly concerned about the middle of the distribution. Additionally, the Census responses are subject to error. I checked it – for these purposes – and found this data base gave an average tax reduction to full -time workers of $26.70, close enough to the Key figure given the upward skewness of the distribution I am using relative, to the actual distribution, and confirming these results are going to be mildly favourable to National.

According to the data base, the median earner is going to earn $38,600 this year (742 p.w.) . Such an earner is going to get a tax cuts of $15.20 a week, less than two-thirds of the figure that Key accidentally stated.

Or to put it the other way around, in order to get a tax cut of $25.00 p.w., the worker has to be earning at least $42,350 p.a. ($814 p.w.).

Having done these calculations, it occurred to me that it might be useful to prepare the following table. The first column shows the tax cut; the second column shows the income required to attain that tax cut (in the March 2008 year); the third column shows the proportion of full-time earners who would receive the cut; the fourth column shows the proportion of all adults (over 15 years old) who would receive the tax cut. I dont think anyone would be surprised at the figures, but they give a quantitative estimate of what will be intuitively understood.

**Proportion in Receipt of Tax Cut**

Tax Cut ( p.w.)Income Required (p.a.)Full-time EarnersAll adults (>15)

More than $10At least $29,50068.2%36.5%

More than $15At least $38,65049.8%28.9%

More than $20At least $40,50046.3%25.7%

More than $25At least $42,35043.7%24.1%

More than $30At least $43,20042.0%23.3%

More than $40At least $47,93034.4%18.9%

More than $50At least $63,94021.1%11.6%

More than $70At least $81,15015.3%8.4%

More than $90At least $98,5006.3%3.5%

Then I realised I could manage the data al little differently to calculate who got a share of the total tax cut. The results are as follows:

**Share of Total Tax Cuts**

Decile | All adults (>15) |

Top | 45.5% |

2nd | 23.4% |

3rd | 11.2% |

4th | 7.0% |

5th | 5.3% |

6th | 3.9% |

7th | 2.7% |

8th | 1.0% |

9th | 0.0% |

Bottom | 0.0% |

TOTAL | 100% |

No one will be surprised to observe that the top 20 percent of the population get over two thirds of the value of the total cuts (and so the bottom four fifths get the remaining third).

Note.: The data base was constructed by Anita, who used it to discuss gender differences in **Tax Cuts and Social (In)equality**