Per Capita versus Per Household Personal Income III

In my previous blog, I showed how per capita and per household income varied between Maine and New Hampshire.  However, some folks may dismiss this as one special case where per household income makes a difference to the analysis that a larger private sector share of personal income means greater economic prosperity in the long-run.

So, the charts below show a scatter-plot of the relationship between the private sector and income under the per capita metric (chart 1) and per household metric (chart 2) for the lower 48 states.  In both charts, Alaska and Hawaii are excluded from the observations.

The first thing to note is that the r-squared is higher under the per household metric (0.52) versus (0.46). The r-squared measures how closely the observations conform to the predicted line as measured in the equation shown.  Even just eye-balling the chart you can see that in chart 2 the observations are more tightly clustered.  And Utah, the state that started this saga, has clearly moved from an outlier in chart 1 to middle-of-the-pack in chart 2.

Secondly, the correlation is steeper under the per household metric which means an even greater increase/decrease in income with a bigger/smaller private sector.  On average, a 1 percentage point increase/decrease in the size of the private sector yields an increase/decrease in household income of $2,617.  That’s a nice chunk of change.

Per Capita versus Per Household Personal Income II

This is the follow-up blog to my previous post on Per Capita versus Per Household Personal Income to illustrate how per household income is a better metric than per capita income when comparing states.  As shown in the first chart, there has been a significant decline in average household size of 35 percent to 2.7 people from 4.13 people in the United States.

Maine and New Hampshire have mirrored the overall trend, but to varying degrees.  Maine’s household size was generally larger than the national average and New Hampshire from 1929 to the 1970s.  By the late 1970s/early 1980s, Maine’s household size had fallen below the national average and below New Hampshire.  After the 1980s, New Hampshire’s household size stabilized just below the national average while Maine’s continued to slide lower.

The next two charts then compares the growth in real, per capita income with that of real, per household income for both Maine and New Hampshire.  With the two charts next to each other, it is easy to see that a larger gap begins to develop in per household income, relative to per capita income, between Maine in New Hampshire beginning in the 1980s–the same time that New Hampshire’s household size overtook Maine’s.

Overall, Maine’s relative economic performance relative to New Hampshire has been boosted, in the short-term, by a falling household size.  However, when adjusting for this effect Maine’s economic performance worsens substantially.  On per capita terms, New Hampshire’s income is 17 percent higher than Maine’s in 2009; while on per household terms it is 26 percent higher.

I will post another blog in the next few days showing how this relationship changes among all 50 states.

Note: The historical data from the Census Bureau on households was only available every ten years during the decennial census.  Intervening years were interpolated.  Since 2000, household size has been reported on a more frequent basis under the new American Community Survey (ACS).  However, for technical reasons, this analysis only uses the 2009 ACS data with the intervening years being interpolated.  This will be replaced by data from the 2010 decennial census when it becomes available.

Per Capita versus Per Household Personal Income

For state-to-state comparisons, per capita personal income is the standard-bearer.  Its simple to calculate and simple to understand; however, it’s also simply misleading.

Why?  States where the average household is larger are penalized under a per capita ranking  because children don’t earn anything.  I discovered this problem when I noticed what an outlier Utah was in the per capita personal income rankings where Utah ranks as the 49th highest in 2009 at $31,612.  However, Utah also has the largest average household size at 3.23 people.  And there is a large variance among states with the lowest household size belonging to North Dakota at 2.32 people.

As such, failing to hold constant the difference in the size of households rewards states with small households and penalizes states with large household using a per capita personal income metric.  To illustrate, let’s look at Maine versus New Hampshire.

In 2009 per capita terms, Maine ranks as the 30th highest at $36,479 while New Hampshire ranks as the 10th highest at $42,585.  New Hampshire’s per capita personal income is 16.7 percent higher or $6,107 dollars for every man, woman and child.

However, the average household in New Hampshire is larger than it is in Maine.  New Hampshire’s households average 2.62 people (the 24th highest in the country) while Maine’s households average 2.42 people (the 49th highest in the country).

After adjusting personal income by household, New Hampshire ranks as the 14th highest per household personal income at $111,402 while Maine ranks as the 41st highest per household personal income at $88,261.  New Hampshire’s per household personal income is 26 percent higher, or $23,141, than Maine’s . . . adjusting for household size makes a big difference.  Also note that Maine’s relative economic performance falls from 30th under per capita to 41st under per household . . . another big difference.

My take away from this is that per capita personal income is a seriously flawed metric.  A state can, in the short-term, enjoy a bonus to its per capita income by simply having fewer children which shrinks the average household size.  However, as Maine is now discovering there is a long-term price to be paid called Demographic Winter.  Last year the U.S. Census Bureau reported that Maine’s population in 2009 fell for the first time since at least the 1960’s.  Think economic development in Maine is already tough . . . try doing it with a shrinking population base!

Another blog will be posted soon to further illustrates why per household personal income is the better metric.