Thursday, September 19, 2013

Skewness in lifecycle income

Well, I thought I would try to estimate the amount of income inequality that is due to life-cycle effects.  I made the assumption that within each age group, all incomes were equal (at the age group mean), and then estimated the median income of the total population.  I was surprised to find that the age-egalitarian median income was higher than the mean income:

I had assumed that income distribution was always positively skewed.  But, what this shows is that typical lifecycle income is negatively skewed.  In other words, there are many years in a typical lifetime where income is a little bit higher than the lifetime average, and there are few years where income is significantly below the average.  In fact, it is a two-humped distribution, with a large hump of years from about 25 to 65 with above average income, and another smaller hump with very little income during the other years.

As schooling extends farther into the 20's, long retirement becomes more common, and the number of older Americans grows, the negative lifecycle skew should become less pronounced, so this will cause the statistical aggregate mean income to look excessively stagnant compared to past median income.  But, there are at least two other interesting factors here:

1) Since lifecycle income skews negative, this actually normally makes the median income appear higher than it would without the effect of lifecycle income changes.  This factor probably inflated statistical median income growth in the 1990's.  One way to think about this is that, at any given time, the median income household for that period of time is probably making an income higher than their lifetime average income.  So, for instance, when the baby boomers were middle aged in the 1990's, at their peak earning years, this factor was especially causing the median income to be elevated, because more households were near their peak lifetime income level.

In this graph, the green line is a measure of how much the negative skew of lifecycle earnings inflates the median income.  This has flattened, and should start decreasing as baby boomers age into retirement, which will cause the measured median to decline.  The red line is the ratio of the mean income to the median income, which is a rough measure of the positive skew of incomes.  The blue line is the ratio of the mean income to the median income adjusted for the negative lifecycle skew.  After adjusting for the increasing negative lifecycle skew, this shows past income inequality increasing even more, once changes in the lifecycle adjustment are included.

2) The non-normal distribution of incomes over a typical household's lifetime might create a false picture of a two-tiered economy.  Middle class households would register many years at roughly half their lifetime average incomes, and even more years with incomes higher than average.  But, they would not register very many years with incomes between 50% and 100% of their lifetime average income.  In order to create a clear picture of lower income families, adjustments would have to be made to account for middle or upper class households with lumpy income and consumption smoothing.  Unadjusted measures of the bottom 2 quartiles of household income will tell us very little about the true state of households with low lifetime incomes.

We can get a sense of this error by viewing the income range of a single age group:

This is from 2007 detailed census data.  The data for the total population appears to have a large mass of very low income households.  But, we can see by isolating the 35-44 year old age group that this is mostly a product of households at other age levels who will mostly be earning above average incomes when they are 35-44, and are taking advantage of the extra wealth to extend schooling or retirement during other years.  In fact, we should expect that households with lower lifetime incomes will be more likely to be working in their 20's and 60's, so they will not be populating that low income hump in the blue line.  They will have less lumpy lifetime income and will probably be earning incomes much closer to their average lifetime incomes during those years.

Wealth, ironically, causes a statistical anomaly that shows phantom poverty.

I propose that the distribution of 35-44 year olds here is much closer to the distribution we should be referencing when considering the number of households in poverty relative to the whole population.

PS.  I saw a paper somewhere recently, I think, that discussed the negative skew of lifecycle income, but I can't remember where I saw it.  Please let me know in the comments, if anyone knows of it.  Also, please comment if any of the statistical inferences here seem way off base.

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