Ten fundamental problems in the theory of welfare economics


and fifteen technical reasons why the United Nations should use life-length statistics in place of economic data to assess the progress of poor people


Matt Berkley

17 June 2003



1.  All existing measures of income inequality
-  for example income ratios between rich and poor, and Gini indices  -
fail to take into account the following fact:
rich people who began the period or were born during it are disproportionately represented in the data, due to higher survival rates.

In all countries, richer people survive each period at a higher rate than poor people. 


In that respect, all existing measures of income inequality underestimate

a) lifetime income inequality, and

b) inequality of distribution to people during a period.  



This point is concerned with one-time measurements, and comparisons of these measurements between countries.   In a country where poor people live longer, the measured “inequality” is more.    But the outcome, in terms of distribution of income to real people, is more equal.  

As with all the points below, we might ask ourselves “but does it matter in practice  -  are the effects small or large?”  

The short answer is that we do not know the size of the effects for any country at any time.   Where there are increases or decreases in life expectancy, this does not tell us whether this was due to changes in life length among rich or poor.   There are various sources of information which might lead us to come to some kind of conclusion.  

The longer answer is in several parts:  

i) it matters for the interpretation of current statistics: 
ii) it matters for the clarity of the structure of economic thought;  
iii) it matters for the interpretation of economic history, where large demographic changes are known to have taken place (think of the plague);  
iv) it matters for the future, where aiming for the same economic indicators may be the wrong thing to do in a scientific sense (think of AIDS).  


2.  All statements by economists as to the economic progress of poor people,
based on changes in traditional measures of income inequality,
have failed to take account of the following fact: 

Changes in inequality of life length during a period partially determine

the inequality of annual income among living people at its end – but in the “wrong” direction.   

This point is concerned not with the level of income differentials among living people but the change.  

Economists have mistakenly treated income gains and losses to people as the sole determinant of the ratio or index.   That is not the case. The mathematical value of a Gini index, or the ratio of rich to poor people’s incomes, is not only determined by income gains and losses to individuals.   It is also determined by demographic change. 

Economists claim to have measured the change in inequality of distribution to people during a period.    But that is not what they have measured.    Changes in income differentials are merely one kind of determinant of the level of “inequality” recorded at the end of a period by an economist using an income ratio or a Gini index. 

If poor people begin to live longer, the Gini index will look “worse” to an economist who makes the usual but erroneous assumption.   The assumption is this:  “a trend towards less equality in annual income at the end of a period shows, other things being equal, more losses to poor people”.    That is the common belief among economists, and it is not true.   We might call this a second “distribution fallacy” or “inequality fallacy”.  

There is a meaningful and important distinction between

a) trends in inequality of distribution when comparing people alive at different times and
b) inequality of distribution of income to people during a period. 

Without information on life length, you cannot calculate from (b) from (a)  You cannot calculate the change in distribution to people from comparing populations whose composition may have changed. 


For a social scientist to ask “what happens if the poor live longer?” is one question.  


Another question, more relevant to the current situation, is “what can I say about gains or losses if I don’t know the trends in life length at different levels of income?”.    The right answer is “nothing”.   A scientist might infer from some knowledge of the country what the trends in life length were.   In other words, they might think they know the rough trend or lack of trend, and thus infer the level of income gains or losses to poor people from economic statistics.    That would be an inference, dependent on the reliability of the information about life length.   


Inferences are a part of using information wisely  -  where they have some basis.    There is a difference between an estimate, a guesstimate and a guess. 



3. All statements by economists as to average income gains in a population,
based on income per capita in different years,
suffer from a related flaw.   

The traditional assumption in economics is that “the people must have had income gains if the average rose and income inequality was unchanged.”.   

That is not true.  If poor people live longer, the average will be lower. 
The fall in the average is caused by a better average outcome to real people. 

A fall in the average is consistent with income rises for every single person in a population during the period.  
A rise the average is consistent with income falls for every single person in a population during a period. 
World economic growth would fall if the hungry were kept alive longer.  

There is a general fallacy of inference by economists in respect of what population averages measure. 
We might call this the “economic fallacy”  -  the fallacy that what is good for the economic statistics is good for the people.   

But then that is a fallacy for several additional reasons also  – see below.   Perhaps we should call this the average-income fallacy, or the “growth” fallacy.

4. All economists’ statements as to average gains or losses to people in poorest fifths
or other abstract segments of the economy suffer from a related flaw.   

The demographic factors in relation to “fractiles”  -  a jargon word for these abstract segments -  are more complex than in the case of averages for the whole economy.   For example, here are two variables  which influence average income in the poorest fifth. 

If people in other fifths live longer,
the average for the poorest fifth will rise.  

If people in the poorest fifth live longer,
the average for the poorest fifth will fall.  

If you do not know the trends in life length, you do not know the average gain or loss to people in the poorest fifth during the period. 

It is quite hard for me, as a non-economist, to see how data on poorest fifths, on their own, could be used to infer aggregate costs or benefits to real people. 
It is also hard to see why anyone would use such data, whose meaning in terms of gains and losses is unknown, to form policies to help poor people.

Suppose you want to use data on poorest fifths to find out whether the incomes of people in them went up or down, or by how much.    You need to know quite a few things about demographic trends.  

If you want to find out about economic gains or losses, you need to know quite a lot more as well (see below on prices, assets, children and so on).  

Some kinds of statements about specific matters which may be relevant to assessment of economic gains and losses  -  such as statements about income rises and falls, or statements about purchasing power  -  have no philosophical import whatsoever.  


They are not matters of opinion, but of science.    For example, if I want to know if people were able to consume more or less with their income (or consumption expenditure) that is a scientific matter with a clear answer.   The facts in the real world which could answer the question are facts about physical consumption of goods;   consumption of services of a particular quality;   and in the case of people who can afford to save, the purchasing power of their savings.   Such questions are not in themselves answerable using cross-sectional statistics.    

5. All economists’ statements as to “better” or “worse” outcomes to poor people,
based on the proportion of people below a per-day consumption poverty line,
or the poverty gap ratio
or any such static measures of the depth of poverty among living people,
any combination of these with other cross-sectional statistics of living poor persons,
suffer from a related flaw.  

If very poor people die earlier,

all of those measures look “better” to an economist unaware of the flaw.  


They look “worse” to that economist if very poor people live longer.   
They look “better” if the non-poor live longer.

Unfortunately economists do not generally have consumption lines in any case.   If a “poverty” line is defined by income level, then it is subject to the expenditure fallacy, the extra-items fallacy and the children fallacy (for all of which see below). 

6.  All economists’ statements about aggregate welfare gains or losses

using all the above kinds of statistics
– population averages, measures of inequality, quintile averages, proportions of people below a certain level of income, poverty gaps and so on  -
suffer from an additional flaw which is more serious than the other mortality flaw: 

they have not taken into account the welfare benefit of living longer

or the welfare cost of dying early.   

If you die early, it is not only in failing to take account of the effect of your absence on the cross-sectional statistics that an economist inferring welfare gains or losses has made a mistake.   It is also in failing to count the welfare cost to you of dying early.     

Could a measure of lifetime welfare (welfare x years) solve this problem?    No.  


Why not?   Because the cost of losing your life a year early is not quantifiable in any objective sense.    The “cost” of dying early or the “benefit” of living longer is not objectively comparable to welfare levels for you while you are alive, or for other people while they are alive.   Either of these involves an entirely subjective judgement  -  a moral choice.   The value of a year of life is a matter of taste. 

That is so both in relation to a) statements about the outcome for one individual and b) statements about aggregate outcomes among many people. 


Supposing a social scientist says that the following was a “better” outcome:   x number of people died and y number of living people had on average z amount of welfare gains which outweighed the deaths”.  

That judgement would not be objective in any way:   it would be based on a personal opinion.   

Nor is it possible for someone to make such a comparison in relation to welfare outcome for even one person, without basing their judgement on a personal opinion as to the value of life.   Think of your own life.  


Suppose you have the choice of a higher welfare level every year, but a shorter life.   Is that better or worse than having a lower welfare level in a long life?    Well, that depends on what you choose to give up.     

Suppose there were an objective measure of welfare level of living persons  -  so that you could look around you and say “my friend John has a rating of 67, and my friend Mary has a rating of 33, and I have a rating of 96”.  

What loss in the annual rating would outweigh an extra year of life for John, Mary or you?


For every rating, and every length of life, the answer would be a matter of personal preference.    And that would be if we had a static measure of welfare, or well-being, or happiness, or fulfilment, or whatever we want to call it.    This is one problem which utilitarian philosophers have not faced.    The duration of happiness is according to Bentham one factor in the “felicific calculus”.    Well, it’s obviously important to people.   But how important compared to its intensity at the time?   

The point is that even if you could measure well-being, you couldn’t measure the satisfactoriness of a whole life.   Some people want to live shorter but more fulfilling lives.   Others may not.    People differ in their approach to risk.   And people differ on what they count as a satisfactory life.  



Let’s get back to social scientists’ statements about aggregate “welfare” outcomes for people during a period.  


For a doctor to say that “there was a better aggregate outcome” if some patients died but many got slightly better would be an expression of a personal opinion.    The same would apply to economists who made similar claims on the basis of measures of lifetime economic welfare.    Any claimed measure of poverty, or wealth, or welfare, which combined life length and a static or annual measure would necessarily be based on personal values of the social scientist.    It would not be social science, but science plus opinion.  


There is a second major problem with using lifetime welfare as an indicator of welfare outcomes (or a third, if we count the fact that welfare, and deprivation, are not possible to capture with statistics without introducing value judgements anyway!).  

Measuring lifetime welfare would value the life of a poor person as less than the life of a rich person.   How?    Well, if we aggregate the lifetime welfare measures into average outcome, we would find that if a “poor” person dies early, the index is affected less than if a “rich” person dies early.   

That also would be the result of a value judgement by the social scientist.    Suppose we talk about the inverse of welfare, which is deprivation.   Is a country less poor if the poorest person dies early than if a richer person dies early?    If anything, to me the reverse seems to be true.   If the poorest people begin to die earlier, then the problem of poverty is worse.  


If richer people begin to die early, then the problem is probably not poverty, but disease or perhaps obesity.    There is a U-shaped relationship between food consumption and life length.    It is a commonplace of medical knowledge that most people in rich countries would live longer if they ate less.    The problem then would not be deprivation, but it would be a welfare problem.    Incidentally, Picasso said “God save me from getting what I want”.    The satisfaction of wants is not necessarily the way to happiness  -  depending on a number of factors, among them luck and what we mean by happiness.    The satisfaction of wants is not the same thing as the satisfaction of needs.    


Another problem if lifetime economic welfare were used is that the relationship between a measure such as economic statistics and welfare is not linear.   Let’s think about hungry people.   It is fairly obvious that the economic welfare of people who don’t have enough to eat is measurable by how adequate their food intake is.   

At some levels of consumption, a lower level of consumption per day may be far more preferable to a person if it means longer life.  The non-linearity of the relationship between daily food consumption and daily welfare level among hungry and malnourished people is a complex matter to think about.  

Suppose lifetime income were the measure of welfare.   The implication would be that a poor person had gained less by surviving than a richer person.   And for that income would have to be a reliable static indicator of welfare, with a linear relationship to welfare.   If we think about it (see below on extra items of expenditure, and prices, and perhaps think about people you know) we realise that it is not.    It would be dangerous to have social scientists using a method which assumed that people on lower incomes had less to gain by living longer.    

7.  All economists’ statements about income gains and losses,

based on all the kinds of statistics above,
where these were derived from per capita data,

fail to take account of the facts that
a) adults need more food than children and
b) the ratio of adults to children varies across countries and times

Where, for instance, birth rates fall,

the [average gain]    (the average people have for their age now compared to what they would have had on average at that age in the past)

is less than

the [increase in income per capita].  


Related considerations apply to traditional measures of income inequality, the proportion of people in poverty, and so on.   

Economists already know that the “economic growth” rates of countries for example in the “East Asian economic miracle” were significantly influenced by demographic shifts.  



To take another example:  The change in the proportion of people below a consistent poverty line is not knowable from per capita statistics, without knowledge of changes in the age structure among poor people. 

There are theoretical discussions among economists about adjusting for children, and studies have been done using various methods.  

But all statements by economists on the basis of large-scale studies of income or consumption fail to make any such adjustments.  

Those statements include those by the World Bank and the United Nations on trends in poverty (which is not measurable by a fixed consumption line if the proportion of adults is rising, as in the real world at present);   those by all economists on world income inequality;   those by all economists claiming to have studied the relationship between average incomes and poverty, and the effects of policies on poor people.  

There is no theoretical requirement on professional economists to take into account the fact that adults need more food.
There should be.  

8. All economists’ statements about the progress of poor people,
based on statistics using the proportion of people below what is termed a poverty line,

fail to take into account that the proportion of poor people is affected by not only
a) economic gains and losses to poor people and
b) demographic changes among poor people,
but also
c) demographic changes among people above the line.  

Suppose we had a reliable static (daily or yearly) measure of poverty. 

If a government helps people above the line to live longer,
the proportion in poverty will fall.  

If people above the line have more babies,
the proportion in poverty will fall.  

If richer people reduce fertility rates more slowly than poor people,
the observed “income inequality” will change. 

None of these means that poor people did better or worse.  

The influence of these factors on economists’ measures of poverty is unknown.  

9.  All economists’ statements as to income gains or losses to poor people during a period,
based on existing measures of income inequality,
suffer from the flaw that
the inflation rate for poor people’s goods was not taken into account.


An income rise is consistent with a rise in prices which outweighs the benefit of that rise.   
Without any specific data on price trends in poor people’s goods, any conclusions as to economic gains or losses are therefore invalid.  

For instance, if there is

a) a 1% increase in income per capita,


b) zero change in annual income inequality
   (measured by Gini index, income ratios or anything else)


c) zero consumer price inflation in the economy

that cannot possibly tell us that

d) “poor people had 1% gains in purchasing power”.  

A 1% increase in poor people’s incomes
(which is in any case not calculable without taking changes in differential mortality and differential age structure into account)
does not tell you that they were able to buy more.  

That is because there is an inflation rate for poor people’s goods. 
If the price of bread triples, the impact on the overall inflation rate will be far less. 
The fact that the overall inflation rate is zero, or –1%, or 10%, tells you nothing about the inflation rate for the poor.  

Without knowing how the price of wheat or rice and other basic goods changed,
you cannot tell whether poor people had gains or losses in real (inflation-adjusted for the goods they can afford) income.   

For people who can only afford a very limited range of the items whose price changes influence the overall consumer price index:

a change in income,
adjusted by the overall inflation rate,
is not rationally described as a change in real income.  

It is merely the nominal, numerical value of income adjusted by a rate which is of unknown relationship to the inflation rate for poor people. 

It is hard to see how a description of income statistics among poor people which have not been adjusted by the inflation rate for poor people’s goods could be accurately described as showing economic gains or losses.  
The statistics cannot tell us about economic gains or losses to poor people.  


The above means that all past work on, for example, the relationship between GDP per capita and economic gains to poor people using poorest fifths has included a failure to take this logical step into account.  

The work could not have told us the level of economic gains to poor people even if demographic factors had been taken into account.    Additional reasons why the last sentence is true are found in point 10 below:  changes in assets and items of necessary expenditure were not taken into account.   An assumption that these were of zero importance (or alternatively that changes in these are always proportional to income or expenditure changes) has no theoretical or empirical support, but is crucial to any argument that income or expenditure statistics show the level of economic gain or loss.  

An additional reason why welfare gains and losses could not have been assessed using such a method is found in point 6 above:  it places zero value on the welfare value of even a very short life being extended.   In different countries, poor people live for different lengths of time;  and life length changes over time.  

There are data on past prices for basic goods in the United States, but not for countries where most of the world’s population live.  

Income only provides half the equation for statements about consumption levels. 
The other half is expenditure need.  
Part of expenditure need is determined by need for extra items of expenditure in particular places or at different times.  

Part of expenditure need is determined by prices.   



There is no theoretical requirement for economists to take prices into account when claiming annual consumption rises or falls among poor people, or implying changes in purchasing power, or claiming economic gains, or claiming welfare gains. 

There should be.   



10.  All economists’ statements as to economic benefits to people during a period,

based on statistics for declared income, suffer from this flaw:

Income, even where adjusted by


a) age structure,

b) death rates, and

c) trends in prices paid by the people being studied,

is only one of several key aspects of economic welfare.   

A lower declared income is consistent with a higher degree of economic power, capabilities, status or welfare:

i) If you have a large house, you are, most people would agree, richer than someone with no house and slightly more income.    Assets often decrease the need for expenditure:   if you have a house you don’t pay rent.   If you have a car you can buy in bulk.   

ii) If you want to become more prosperous, there are at least two ways you can achieve this:  increase your income or decrease your expenditure.   But the minimum cost of living in a place is not a matter of choice.  That is not only because of prices.  The cost of living includes relative need for extra items of expenditure.   


For instance, if more items of expenditure are needed in cities and a higher proportion of people, as time goes by, live in cities, then the cost of living has gone up more than the consumer price index. 


The cost of each of the extra items (which may include water, rent, transport, fuel and so on) may even fall  -  which would bring the inflation rate down.   Then the cost of living according the consumer price index would have fallen.   But in reality it has risen.    The cost of living is the cost of living, not the cost of items irrespective of which items are necessary.    For an economist to say that they have measured the changing cost of living because they have measured price changes is a false statement. 

iii) People don’t always declare their real income!   The informal sector in countries where most people live is large.    In all countries, it is not unknown for people to gain non-declarable benefits from employment, both legal and illegal.    This can range from company cars to subsidised lunches to bribes.    It may be hard for a social scientist to admit such facts, but they are features of the real world.   


To make credible and reasonably scientific statements as to economic gains and losses  -  rather than gains and losses in purchasing power of income, which is what the adjusted statistics would refer to  -  an economist would have to take into account all the key aspects of economic welfare.  

Many people might think that for an economist to claim that

“assets have no importance in economic welfare”
“changes in necessary items of expenditure have no importance in economic welfare”

would not correspond to reality. 

And yet economists’ use of income statistics to infer the direction and level of changes in economic welfare depends logically on both those claims.  


The underlying assumption is this:   “Changes in declared income show a proportional benefit or loss to people, in the same direction”.    

Many people might think that is not rational.  




Six questions for theorists of welfare economics and fifteen reasons for using life length as the indicator for hungry and extremely poor people


1.  Given the omission of data on key aspects of economic welfare above, in what way would it be accurate to say that income statistics measure

a) welfare outcomes or
b) economic-welfare outcomes in the aggregate to real people?

2.  Is omitting changes in any of the following not a serious omission?

a) assets, including gifts and inheritance;
b) debts
c) undeclared income including employment perks and monetary gifts
d) inflation to the poor
e) extra items of expenditure
f)  age structure
g) life length

3.  What, if any, would be a practical and cost-effective way, in the real world, of measuring enough of the key variables that a reasonable person would say that economic welfare had been measured? 


4.  Is it more sensible to base our opinions about what is good or bad for people (and they can after all only be opinions) by:

a) ignoring life length as a variable or
b) counting an extra year for a rich person as better and/or
c) valuing a year of life in money terms?  

5.  Is it more sensible to measure the progress of hungry people by

a) measuring income, then adjusting for life length, prices paid by hungry people, extra items, and age structure


b) using statistics on how long people live?  

Note 1:   If you are chronically hungry and you eat more, you will probably live longer.    
Note 2:   Whoever you are, the value of more life length to you is a matter of opinion.   

Putting it the other way round, the value of other things relative to an extra year of life is a matter of opinion.   

6.  In the real world in the year 2003, a number of facts are known which may be relevant to answering question 5 in practice.  

i) The main set of economic data on poor countries produced by the World Bank (Deininger and Squire) is not reliable.  

Anthony Atkinson of Nuffield College, Oxford is one of the most respected authorities on income inequality in the world.   Both he and James Galbraith of Texas have carried out studies which indicate that the data are not reliable.   

ii) The dataset suffers from a number of fundamental problems.   

The data are not comparable across countries or times due to the variation in survey methods.  
The implication is that no-one really knows what a higher or lower statistic in a country is telling us.   It might mean that the people were asked different questions about their consumption.    It might mean that their food intake was valued at a national price rather than at the local market price.    It might mean the people consumed more.  We don’t know.  

iii) To gather reliable data on income would involve a large and expensive project.  

But we still don’t know what that would achieve.  Martin Ravallion, who is co-designer of the methodology for the World Bank poverty counts, is on record as stating that rich people and very poor people do not cooperate with surveys;   destitute people are unreachable.   The same problem could apply to survival-rate data, but is one of the few flaws which may apply to that method.   


Income and expenditure surveys may involve two hundred questions for each household.   Survival-rate data involve a handful of questions.   Cooperation may be far easier to achieve with such surveys;   and even if not, the coverage can be vastly extended so that the results are on a more sound statistical basis.  

iv) Prices paid by poor people, and trends in these, are unavailable for countries where most poor people live.  

And yet prices are clearly essential for measuring poverty using income.   


An income rise is not the same thing as an income gain.  

If economists adjusted for life length, they would know about income rises and falls, but not gains or losses.   Income statistics measure the values on the faces of the coins, not how much those coins can buy.    We cannot know from income statistics whether poor people did better or worse.    To know that, we need to know the price of the cheapest food.    Currently, economists do not know from their studies of income how much more or less food poor people could buy with their money.  

v) To gather reliable price data for poor people would be a large, complex and expensive project.   

This is clear to anyone familiar with the International Comparison Programme (hosted by the World Bank), which sets purchasing-power parity rates for countries.    


vi) Data on extra items of necessary expenditure in different places or at different times are unavailable.     

And yet these are essential also for assessing poverty using income.   It is not realistic to assess poverty in the year 1990 using the same income level as in 2015 if people in cities have to pay for more essential items and there is progressive urbanisation, as in the world at present. 

vii) To gather data on extra items would be a large, complex and expensive project.  


viii) No-one knows how far economic statistics have been or will be influenced by changes in life length.   


ix) For an economist to combine all the factors necessary to assess economic poverty would not be transparent except to people familiar with the technical aspects.

Necessary factors include income, prices, the proportion of children, extra items, life length, assets and debts.    Currently large-scale studies of income measure that.   They do not measure poverty.    Economists would like to make the process more complex.    That is not perhaps a healthy option.   

x) Where a method of social science is less transparent to non-specialists, it is more open to abuse  -  intentional or otherwise  -   by politicians, bureaucrats or social scientists afraid for their careers. 

Examples of abuse include the World Bank’s monitoring of the Millennium Goal on poverty.   This monitoring which has suffered from unreliable data, the mortality flaw, the inflation flaw, the children flaw, and the extra-items flaw.   The cause of the inclusion of these flaws in the method is not publicly known.   

The mortality flaw was mentioned by Martin Ravallion, co-designer of the methodology, in a World Bank document in 1996.   He ignored it in the methodology.    Professor Angus Deaton warned the Chief Economist of the World Bank, Nicholas Stern, of the mortality flaw in 2000.    I warned Eric Swanson, the head of the World Development Indicators project at the World Bank of the flaw in a 40-minute telephone conversation in 2001 whose sole subject was that flaw.  

Martin Ravallion wrote an article in 1995 in the Economic Journal stating that the precise method of adjusting for children was important for measuring poverty.   He used no such method in his own claims on global poverty trends, despite the fact that the proportion of adults has been rising.    If the World Bank had accurate prices, the “dollar-a-day” line would not tell us about daily consumption adequacy.   That would need information on increases or decreases in extra items of expenditure, including an adjustment of the line upwards to keep in line with the rising proportion of adults.   Adults need more food than children.   Other things being equal, the World Bank has, by failing to adjust for adults’ needs, must have progressively underestimated the proportion of poor people as time has gone by.  

xi) Most people’s idea  -  and most academics’ idea  -  of poverty or deprivation includes a large element of vulnerability to early death.   

To escape from poverty, in the minds of most people, has as an important element being better able to survive under various conditions.  

xii) Data on child survival in a whole country may tell us about survival rates among poor people

(but not necessarily, since the advances in child survival may occur first among rich people).   

xiii) Data on child survival can be cross-checked using demographic measures.

The principle here is that it is easy to count how many four-year-olds there are and compare this with the number of one-year-olds three years earlier.  

xiv) Data on child survival are comparable internationally, while income statistics present a whole host of technical problems in this respect

-  such as comparing the price of beans and wheat in country A with the price of fish and rice in country B, and working out the nutritional value of each;  accounting for extra items of expenditure;   taking into account how big the people are and so on. 

xv) Measuring life length is cheap, easy, humane and transparent.