When the Economic Numbers Don’t Add Up

Bias Disclaimer: Please refer to the post on my biases if you wish to read this post without having to guess where I am coming from.

There has been some unease about the accuracy of the Economic Data that has been thrown at us the last few months – perhaps years.  Barry Ritholtz over at TBP has been talking about it for quite some time now in relation to payroll data, home prices, and just about everything else.  He also mentioned it this week in discussing CPI.

Some people automatically pull out the "C" –card – with "C" standing for full-blown government conspiracy.  I don't buy that so much.  I believe it is the confluence of a few factors – but most importantly our inability to understand two main ideas – demographics and statistics. 

First, let's speak briefly on demographics.  You know how I feel on this topic and I am preparing a slew of pieces on demographics and Economics and will bring it to you very soon – after I get the chance to really dig through the numbers.   But I will touch on the main idea upon our biases in population.  Basically, population growth or decline is a Long Tail process that is relatively stable in the short term.  Since GDP growth per capita is not a figure that will vary wildly from actual GDP growth on a quarterly or even annual basis, it is relatively ignored.  The same is true with income per capita and any other "average" value based on the number of people.  With a huge demographic bubble as the Baby Boomers – the margins all of a sudden become much more important.  The housing data is a prime example.  People in their 80's usually are not out buying and selling homes neither are 20 year olds.  It is a certain 35 – 60 year old demographic buying and selling.  Prices rise due to many buyers than there are sellers.  As the spread narrows and diverges, this causes great ramifications.  Home prices is not a number defined by population statistics but is grounded in them.  The same can be seen with most economic numbers such as payroll, employment, consumption, inflation, GDP, etc. 

In general, I think demographics explains most of why things seem so strange as a whole, but it is in the statistical (mis)interpretation of data that the bias is revealed.  Statistics, by definition are a measure of an overall population.  Sample statistics are performed on a sample large enough to make inferences to a degree of confidence about an overall population.    The measures that are most popular and most susceptible to (mis)interpretation are measures of central tendency – such as mean and standard deviation.  Mean, or average is thrown at us by the media outlets all day long. In a normal distribution the population mean is approximated through the Expected Value

µ ≈ E(x) = ∑(Pi*Xi), 0 < i < ∞. 

Xi's are the realizations and Pi's are the probability of realizations or frequencies.  Thus, the sumproduct of the value of an event by the chance that this event will occur.  Most people think of a normal distribution and immediately picture the bell curve.  When we average things in our head or on paper we usually sum up the values and divide by how many values there were.  Assumptions of the normal distribution cause this to be an accurate measure at times.   Implicitly, we assign 1/n probabilities to each value and under according to the law of large numbers any population approaches the normal population thus making observations at the margins very meaningless – as long as the expected value you are estimating actually follows the normal distribution. This is because the measure of distance from the mean – standard deviation is well, standard and deviations to the left and right cancel each other out.  .   See the bell curve below:

In this case, the mean is the same thing as the median, which is the n/2 observation in a list of n. As long as the two are equal then there is a 50%/50% chance that an observation is either greater than or below the mean.  Therefore the Expected Value for X is not the same as the 50% percentile.  When this is not the case however things deteriorate quickly.  This is known as skewness.

In, Fooled by Randomness and The Black Swan, Taleb discusses how the normal distribution is largely a theoretical fantasy and most random processes do not follow such a distribution.  His major philosophy is based on the idea of "fat tails" which is called kurtosis – the prevalence of relatively likely extreme observations.  He believes that the normal distribution underestimates events that deviate wildly from the mean.  The belief that normal distribution is the "norm" affects the way people form their expectations.   The differences are shown below:

 

One way we fail to understand this is our interpretation of Income Data.  Income in the US is not normally distributed.  Besides being a hot topic of political debate, it seems to really mess with many economic variables we interpret. 

Source:http://www.visualizingeconomics.com

 

I have posted the US income distribution above.  Income per capita – a quick and dirty calculation would greatly overstate median income.  This is the mean income and is $46,326.  The Median is $63,326.   That is more than a $20,000/ year difference which is enormous especially for the 20% of the population who aren't making that much as it is. 

Although income is an important determinant in GDP, as well as our economy and markets as a whole– it is consumption that gets people on CNBC all hot and bothered.   If you pay attention to the releases,  real consumption has been rising and rising , but MEDIAN income has been stagnant to falling when looked at based on inflation.   How can this be so?

This can be explained both statistically and psychologically. All five percentiles of people have a much different consumption elasticity of income for members in a "typical basket of goods".   As typical baskets of goods become more narrowly focused inflation becomes more personal and complex to analyze.  A $1.00 rise in income for someone in the 98^th percentile as compared with someone in the 20^th percentile will yield different figures for their contribution to consumption and even greater differences as you start looking at what is consumed.  The 98^th percentile will likely remain stable or purchase a few more goods.   The people below the 20^th percentile - those working paycheck to paycheck - will probably increase consumption by 100% or more.  Even a slight increase in income for the top 2% would cause a huge increase relative to the economy and corporate earnings while for the 20%'s it may not make a difference if any, and differences made are nominal since these people make much less than the top 2%.   The battle for consumption is then fought at the 40%– 98% Americans.  These people feel the effects of a decrease in income much more than those on the tails.  They also make up a significantly large group of income earners and hence spenders.  Thus in an economy where income disparity exists , small increases in consumption of the top 2% will offset any decreases that the other 30%, since the skewness and kurtosis of the distribution implies that they make almost two times as much money but not nearly enough to cause that increase to be insignificant.  By assuming a normal distribution, a very different inference would be made – as any income gain or loss would hit everyone equally and the change in consumption would be directly proportional to the change of income. Therefore Consumption /Income is a much more relevant variable in analysis as it eliminates much of this bias and follows a more easily approachable number.  One would argue however that price inflation without wage inflation could inflate this number as well, so (PCE/CPI)/Real Disposable Income would be more appropriate. 

 

This brings us to my piece on inflation earlier this week.  I contended that the effects of inflation of energy and food are very important when compared to income since its income elasticity of demand is so high. What does inelastic income elasticity of demand imply in statistical terms?  It is defined as change in consumption/change in income.  Since both consumption and income are stable values in real terms the nominal volatility is represented by the underlying inflation.  When comparing the graphs of CPI (Food and Energy) and CPI (ex Food and Energy) this volatility difference is evident – Food and Energy prices are more volatile.  Yet, in reality this is a meaningless value because all it does is smooth out volatile inflation, and we should only be concerned with the existence of inflation not its components or origination.  Smoothing out data creates a distribution that is much more normal as you eliminate the trend and try to capture the variation in the noise.  People looking at risk and inferring return and return and inferring risk will cause high returns with low perceived risks – causing a market with tons of biases that is very far out of touch with reality.   

 

-β

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