# Distributional Characteristics in more detail

A few days ago I gave a ranking of broad aggregates of goods by their distributional characteristic.  As promised here is a link to a more detailed discussion of this issue with an explanation of the methodology etc http://www.ucd.ie/t4cms/wp09.10.pdf

## 7 replies on “Distributional Characteristics in more detail”

would the general assumption be that price deflation in (for instance) food/fuel will help lower income households

if that is the case does deflation ultimately make the less well off more well off – assuming they can keep their current income (even if it is less than average?) – this is a question not a statement btw.

@Karl
The implications for real incomes per decile are discussed in the Jennings et al. paper that David refers. This paper is discussed elsewhere on this blog.

David’s paper helps to understand the pattern of change in the real income distribution, and provides a short cut when contemplating a single price change (e.g., excise on tobacco).

Karl, if nominal incomes are fixed, then price deflation will help all households. What the distributional characteristic shows is which specific goods (in terms of their price falling) will have the most impact on less well-off households. Falls in food, say, will help both rich and poor households but will have a relatively greater effect on poor households. But I stress that the calculations in this paper are for broad aggregates and there may well be individual food items (for example) which are disproportionately consumed by richer households. However the methodology to calculate the distributional characteristic for any individual good is quite straightforward and explained in the paper.

Maria Johnsays:

I want to calculate distributional characteristics of goods. my only available data is the expenditures and income in the HBS. Your article is very useful but still I am not sure about the distributional weights. Could i just take total expenditures of each decile to be the betas? Is it a must to use e? I know you said its choice of the analysts. but can you give me a hint on how to choose e?

Maria John, tried to send this to your email but it bounced back – here is a reply

There is no hard and fast rule as to how to choose e.

If you set e=1, then a household with an income of say 10000 will have only half the social weighting of a household with 5000 i.e. a half=5000/10000. Higher values of e give a higher relative weighting to poorer households. A value of e=0 gives an equal weight to all households (and the distributional characteristics collapse into one). So in terms of choosing e, most people give a range of values and see how the results are sensitive to the choice of e. I would say that values of 1, 2 and 5 constitute a reasonable range.

Maria Johnsays:

Please, clarify. Given the formula for the distributional characteristics there are two important things that are confusing me. How the calculate Beta and how to calculate the xji(proportion of j consumed by household i). I have data on exependitures and income. What I think so far is: Betas are the percentage consumption of each good for each household or in other words fraction of total budget for the household). xji shows how much xj is consumed by household i as a fraction of total consumtion of xj in the economy.

This would imply different betas for different goods, different betas for different income groups(or households)