The Mean and the Median Tell Two Different Stories

Averages, if you’re not careful, can as easily mislead as enlighten.  It matters a lot which statistical measure of the “average-ness” that’s used.  A good example comes in the case of the U.S. long-term trend of economic growth.  What we’re interested in is to what degree the amount of GDP the average household has available has increased over time.  It’s the prime way economists measure whether not living standards are improving.  GDP, of course, is the measure we use to count output in the economy.  GDP is the total market value of all goods and services produced for final demand in a year.   Real GDP is the inflation-adjusted version of it so we can compare GDP from different years.   But of course, just because total GDP, or even real GDP, is going up from year to year is no assurance that living standards are generally increasing.  After all, if real GDP grows by 1% per year but the population grows by 2% per year, there’s less per mouth each year.

So we need to adjust the real GDP measure to account for population growth. We want a measure of average GDP per person or average GDP per household.  Those readers who didn’t fall asleep in statistics class might recall that technically “average” isn’t a statistical measure.  Instead there are several different ways of calculating what statisticians prefer to call “central tendency” instead of “average”.  The two most common calculations in economics are the mean and median.  And there’s a huge difference between them.  The mean is  what you probably learned in primary school as the “average”.  To calculate it we take the total and divide by the number of people in the population.  When economists cite GDP per capita, we are, in fact, calculating the mean Real GDP per person.  The mean, the real GDP per capita for the U.S. over the last 34 years has grown at around a 1.9% annual rate.  That might not sound like much, but remember the power of compounding means that at 1.9%, mean real GDP per person will double in less than 40 years – one working lifetime.  Sounds good, right?  Sounds like the American dream in action, right? Wrong.

Real GDP per capita when looking at the U.S. is highly misleading because most of the growth only goes to the top 1% income folks.  The vast majority of Americans, the other 99% of us, haven’t experienced anything like that growth.  To see the difference let’s consider real income of the median household.  Remember Gross Domestic Income is the same as Gross Domestic Product.  It’s just counted differently by counting income available to spend instead of actual spending.  Long run, they are the same.  Now let’s quick review what the median is. The median is the middle observation. It means that there’s as many observations with a lesser value as there are with a greater value.  In this context it means that there are exactly as many households with a smaller income as there are households with a larger income.  It’s another way of looking at the average.  In this case we’re looking for the most typical household.  Statistics note:  mean will equal median if both sides of the distribution are identical, but in income this isn’t true – millionaires, billionaires, and rich households are a lot richer than the $49,700 median income but the poorest households can only $49,700 poorer at most.

In the U.S. over the last 34 years, the median household income has only grown at less than 0.5% per year despite increases in education.  So real GDP per person grows at 1.9% per year, but real median income only grows less than 0.5% per year.  At 0.5%, it will take 150 years for income to double.  End of the American dream of doing a lot better than your parents. What accounts for the difference?  It’s the upper 1% of the income distribution, the rich folks, millionaires and billionaires, that have skimmed off the 65% of all of the GDP gains for 34 years.

Princeton economics professor Uwe Reinhardt explains in the NYTimes Economix blog:

So if an American macroeconomist — a specialist who tends to think of nations as people — or high-level government officials or politicians mimicking a macroeconomist boasted on a television talk show that “average family income grew by 3 percent during 2002-7, more than in most European economies,” about 99 percent of American viewers, reflecting on their own experience, would probably scratch their heads and wonder, “What is this guy talking about?”

The third chart, below, exhibits the growth path of real G.D.P. per capita in the United States over the period 1975-2009 and the corresponding path of real median household income. The data show that over the 34-year period, real G.D.P. per capita rose by an annual compound rate of 1.9 percent. Those data come from the Economic Report of the President to the Congress (Tables B-2 and B-34).

Sources: Economic Report of the President to Congress (G.D.P.); Census Bureau (income)

According to the Census Bureau data (see Table H-6), however, median household income in the United States rose by less than 0.5 percent a year. Other than national pride in league tables, that 1.9 percent average economic growth does not mean much for the experience of the median household in the United States.

GDP and GDI: Two Sides of the Same Coin (Theoretically)

One of the starting points for understanding macroeconomics is to understand basic measures of the economy and what we call the “circular flow” of goods and services.  The “circular flow” refers to the idea that firms are the economic “agents” who produce and sell all our goods and services for sale, and that households are the folks who consume those goods.  Of course in reality, both groups are made up of the same people, but we divide up the activities into firms and household consumption.  Given this division of activities into two groups, the circular flow is the idea that the groups both buy and sell to each other.  Households buy the products sold by firms, but households also sell their labor to the firms.  This is all good and it shows how interdependent firms and households are.  Firms can’t hire and pay if they don’t sell products, but households can’t buy those products unless they are able to sell their labor to the firms.

We generally measure the size of an economy by adding up the total value of all the goods and services that are produced and then sold.  This is what we call GDP – Gross Domestic Product.  GDP is the accepted way to measure the size of an economy.  The GDP number as observed and estimated each period is what should technically be called Nominal GDP.  It’s the starting point for estimating Real GDP.  Real GDP is GDP adjusted for changes in the overall level of prices – it takes the inflation/deflation out of the GDP numbers so we can compare GDP from different time periods.

The GDP numbers as reported by the government agencies is generally computed by observing and at times estimating how much spending happened.  In other words, it’s an attempt to add up the value of all final sales by firms of the products they produced.  A “final” sale means the product has been sold to someone who intends to use it up or consume it as opposed to reselling it or making it into an even better product.

There is however another way to estimate GDP.  Since the total value of what firms produce is the money the firms receive, then we could look at how that money is disposed of by those firms.  Put in other words, instead of looking at what households spend to buy goods and services, we can look at the income households received.  We could look at the other side of the circular flow.  When calculated this way, we give it a slightly different name: Gross Domestic Income or GDI.  Because of the circular flow, the two sides shoudl be the same.  In other words, in theory GDP should equal GDI.  In general and over the long haul they do.

Of course theory and practice sometimes differ.  On a quarter-by-quarter basis, GDI and GDP differ slightly because of difficulties in measuring precisely – what we call statistical discrepancy.  Occasionally the discrepancy is bigger than other times for reasons economists don’t fully understand.  The first half of 2011 was one of those periods.  So was 2007.  But as you can see from this graph (thanks to James Hamilton at Econbrowser), in general GDP does equal GDI.



One of the most fundamental identities in macro economics is that income = spending.  Since this is a macro-level national income accounting identity, that means two things: First, it must be true after-the-fact as an accounting factoid. In other words, when the BEA adds up the numbers each quarter, the money spent in the economy had to be equal to the income (really sources of funds).  Another way of stating this is that we say the size of the economy is the market value of everything we produced for final use.  There’s two ways we could count this.  We could count how much was spent to buy all of the goods/services we produced – that’s called GDP, gross domestic product. We count GDP by counting what was spent by whom, consumers (C), businesses for investment (I), government (G), and rest-of-world (eXports – iMports).  Hence the equation GDP = C + I + G + (X – M) which I’m forever repeating in class.

But there’s a second way to count how much we produced and that’s to count the money flow through the Resources or Factor markets.  We call this the GDI, or Gross Domestic Income.  It’s what we got paid to produce the GDP. We break-up GDI according to the type of income being paid and to whom. Roughly it’s wages, profits, interest, and taxes.

Like I said, income = spending. So, GDI = GDP. It’s an after-the-fact necessity of the accounting framework by definition.  But it’s also a useful concept for analysis of disequilibrium and dynamics.  After all, think of what happens in the following scenario.  Suppose every month we spend $1000 and we get paid $1000. Income = spending. But suppose some month, income declines unexpectedly to $900. In the month the income declines, we either cut our spending short to adjust to the new lower income, or we borrow (or spend from accumulated financial assets) to make up for the shortfall and adjust our spending the following month.  In this scenario, we can identify that when income from productive sources = spending we have an equilibrium in the economy and no changes are expected.  But if income is less, then we are at a disequilibrium and can expect changes. For the economy as whole then, we have:

C + I + G + X – M = GDP = GDI = Wages + Profits + Interest + Taxes.

So with that in mind, let’s look at what’s been happening.  I turn to Rebecca Wilder at Angry Bear:

There are two measures of income: the spending side (Gross Domestic Product, or GDP) and the income side (Gross Domestic Income, GDI). I’d like to see what GDI is telling us about the Y/Y recovery, since it’s a better predictor of turning points, according to FRB economist Jeremy J. Nalewaik.

The chart illustrates the contribution to Y/Y GDI growth coming from each of the main income components. (Click to enlarge.)The series is deflated using the GDP deflator, since the BEA only releases the nominal numbers. All references to GDP and GDI below refer to the real series.

What conclusions can we draw?  Well it’s largely a confirmation of conclusions about GDP – the “recovery” is unbalanced. It isn’t being shared with 80-90% of the population that works for a living.  Wages are not growing, but corporate profits have recovered in record time near record levels. Productivity has improved but the benefit goes to capital owners, not labor.  A very interesting comment was provided by Mark Sadowski:

We only have five quarters of data for the current recovery. However, how does it compare so far? So far 76.7% of the growth in RGDI has gone to corporate profits. Needless to say this recovery is setting a totally new precedent.

What can we conclude? This seems to be an increasing pattern with recent recoveries. I speculate that much of it has to do with the combination of sticky wages, an increasing degree of labor flexibility and a trend towards lower inflation rates. Such a combination means adverse shocks to AD result in larger increases in unemployment. Recoveries in a low inflation environment are notably slower due to the limitations of conventional monetary stimulus against the zero lower bound. Thus the labor surpluses are increasingly persistent and compensation growth becomes slower and slower in each subsequent recovery.

Is this bad? Only if you work for a living.