Last week the Federal Reserve and NORC released its triennial, consumer finance survey of American families. The take-aways that many received from this detailed 2013 report, full of descriptive statistics, is that mostly all well-off American families have received a disproportionate share of the economic recovery, and that this has been a tremendous recovery and off the backs of all other American families. It's a little dismal that the Federal Reserve analysts have done little to adjust these isolated and fractional interpretations from the overall survey report.
With much of descriptive statistics, the summarization of information into statistics (such as with the reliance on making too much between just differences between "averages" and "medians" without any underlying probability to effectively argue which end of the distribution is changing), implies that we will lose an important range of information that is helpful in better understanding what has happened since 2007 (i.e., 2 survey reports ago). Yet this elementary knowledge gap is on display, even by leading academics and media quick to introduce inequality into these discussions (here, here, here). This article is not about the righteousness -if at all- of how much better the well-off are versus everyone else. This article primarily serves two functions: (A) it shows principal probability techniques based on summary statistics, and (B) it shows that the well-off were disproportionately hurt during the financial crisis and have partially rebounded but are still in a weaker position versus pre-crisis. Contrasting 2013 with 2007, the whole pie size is smaller, and so too is the slice size for everyone including the most well-off American families. There is a large swath of Americans, in every economic indicator (we'll define this later below) category, whose fortunes are basically middling, along with the broader net economic stagnation (between 2007, and 2013). Only by the time future survey reports comes around, will these analytical conclusions be more robust. Since by then, the pie size would have significantly eclipsed what it was in 2007.
Before we pore over illustrations and analysis, we show the underlying descriptive data for public and internal statistics. Because they are in Excel, they are quite accessible for our purposes. The files shown are also 2013 inflation-adjusted values that we look at throughout this web log article. This was done so we can more succinctly focus on the underlying trend, in the net worth versus income relationship, after accounting for the impact of inflation. The survey data here is something we analyzed in 2011, so it is good to continue looking at it with this refreshed survey update.
First we create a probability distribution of the 2007 net worth and income for American families. See this below, and as one goes through the charts they should pay close attention to the range of net worths and of incomes (together we term these "economic indicators"). Using an advanced simulation we created a sampling distribution of 1,000, where the variance of expectation, expectation of variance, and total variance for these economic indicator samples all align with the summary report statistics. In probability theory, the total variance equates to the expectation of variance plus (in this case significant) variance of expectation.
Next we show the same chart for 2010, except here we color label the data based on the economic indictor for changes along the economic distribution, since 2007. Have families, relative to their peers, gotten better, worse, or half-and-half. For our probability distribution, nearly a fifth of all American families saw both their net worth and their income become worse off versus for the same group in 2007. Most of the remaining may have had -in 2010- either their net worth or their income (though not both) worsen. This last point should be key in our thinking concerning the strength of the Federal Reserve's survey report conclusions, which focus mostly on just summary statistics. Also note that the underlying data are not serially connected. So we simply contrast groups of families, but we do not follow non-existent transition matrices for families who migrate into better or worse economic tranches. There are other government reports that attempt to get at a narrow set of these quintiles, but in any case that is not the focus here.
Yet on net from 2007, to 2013, a third of the most well-off group of families still have both their net worth and incomes worse off. The chart below shows this randomness of outcomes, in a way the Federal Reserve summary statistics completely fails to illustrate. Arguably they are targeting perhaps a different audience, with a different appetite in information.
With much of descriptive statistics, the summarization of information into statistics (such as with the reliance on making too much between just differences between "averages" and "medians" without any underlying probability to effectively argue which end of the distribution is changing), implies that we will lose an important range of information that is helpful in better understanding what has happened since 2007 (i.e., 2 survey reports ago). Yet this elementary knowledge gap is on display, even by leading academics and media quick to introduce inequality into these discussions (here, here, here). This article is not about the righteousness -if at all- of how much better the well-off are versus everyone else. This article primarily serves two functions: (A) it shows principal probability techniques based on summary statistics, and (B) it shows that the well-off were disproportionately hurt during the financial crisis and have partially rebounded but are still in a weaker position versus pre-crisis. Contrasting 2013 with 2007, the whole pie size is smaller, and so too is the slice size for everyone including the most well-off American families. There is a large swath of Americans, in every economic indicator (we'll define this later below) category, whose fortunes are basically middling, along with the broader net economic stagnation (between 2007, and 2013). Only by the time future survey reports comes around, will these analytical conclusions be more robust. Since by then, the pie size would have significantly eclipsed what it was in 2007.
Before we pore over illustrations and analysis, we show the underlying descriptive data for public and internal statistics. Because they are in Excel, they are quite accessible for our purposes. The files shown are also 2013 inflation-adjusted values that we look at throughout this web log article. This was done so we can more succinctly focus on the underlying trend, in the net worth versus income relationship, after accounting for the impact of inflation. The survey data here is something we analyzed in 2011, so it is good to continue looking at it with this refreshed survey update.
First we create a probability distribution of the 2007 net worth and income for American families. See this below, and as one goes through the charts they should pay close attention to the range of net worths and of incomes (together we term these "economic indicators"). Using an advanced simulation we created a sampling distribution of 1,000, where the variance of expectation, expectation of variance, and total variance for these economic indicator samples all align with the summary report statistics. In probability theory, the total variance equates to the expectation of variance plus (in this case significant) variance of expectation.
Next we show the same chart for 2010, except here we color label the data based on the economic indictor for changes along the economic distribution, since 2007. Have families, relative to their peers, gotten better, worse, or half-and-half. For our probability distribution, nearly a fifth of all American families saw both their net worth and their income become worse off versus for the same group in 2007. Most of the remaining may have had -in 2010- either their net worth or their income (though not both) worsen. This last point should be key in our thinking concerning the strength of the Federal Reserve's survey report conclusions, which focus mostly on just summary statistics. Also note that the underlying data are not serially connected. So we simply contrast groups of families, but we do not follow non-existent transition matrices for families who migrate into better or worse economic tranches. There are other government reports that attempt to get at a narrow set of these quintiles, but in any case that is not the focus here.
Now let's look at the 2013 illustration instead. Here we see that nearly a tenth of American families saw a rebound in their fortunes from 2010, to 2013. So both their net worth and income gained.
We follow this with a second 2013 chart, except here we show the net change versus the 2007 peak, instead of just versus the 2010 trough. Here again we see that despite the recent recovery for some American families, nearly a fifth of families are still worse off (on both economic indicators) versus 2007.
What the above charts don't make clear enough is that the recent rebound that occurred was generally concentrated in those American families who were the most well-off, and that this group still carries much of the concentration of economic destruction since the financial crisis. Now this latter statement is only meant relative to 2007 levels, for the same peer group. It is of course not a statement about their still clearly high, absolute-wealth versus everyone else.
We will now recast the same four simulations above, except below we will transform both chart axis to a logarithmic scale. The academic literature often does this for economic data even though here the distributed data seems to follow one of perhaps the exponential family instead of lognormal. Note the distribution about zero, as well as the tail weights (and see here, and here). Yet the transformations shown below are visually effective. To read these charts below, take families earning 1m dollars (or 1000k dollars). This is shown on the axis at 1000 (000s), similar to the charts above. But the difference is that while in the visuals above 1000 is located 1/2 way between 0 and 2000, on the visuals below 1000 is located 1/2 way between 100 and 10000.
So we start with our 2007 "baseline".
We see from the underlying survey report that all American family incomes greater than $80k are considered top-quartile. Similarly so are all net worths greater than $560k. As a consequence, much of the real estate -seen in the top four charts of this article- is just giving us an acute sense of where the top-quartile (the "well-off" group who were by a greater share worse off during the financial crisis, through 2010). The chart below gives us a clearer sense of where the basic concentration of relative economic pain, where nearly half of the well-off American families saw a drop in both their net worth fall and income. We also can not show negative net worths on a logarithmic chart [i.e., log(y)>0, so y-data truncated below 0], though it is a social trap for many families who are earning a meager income and still have financial debt, which exceeds their assets. We see those families have not been had their balance sheets sufficiently equitized and are in no path to build their way out of severe poverty.
In 2013, the rebound we see was also mostly concentrated in those families most well-off. By the numbers as well as shown in the chart below, the majority of the American families seeing a rebound between 2010 and 2013 (in both economic indicators) were in those families we'd consider most well-off (e.g., top-quartile, though we will note later this also applies if we cut the data more finely to the top-decile.)
Yet on net from 2007, to 2013, a third of the most well-off group of families still have both their net worth and incomes worse off. The chart below shows this randomness of outcomes, in a way the Federal Reserve summary statistics completely fails to illustrate. Arguably they are targeting perhaps a different audience, with a different appetite in information.
Now this story line, of weaker economic indictors still being concentrated among those well-off, stays identical in each of these charts above. Even if we compress the upper partition, from the top-quartile, to the top-decile of American families. Note that that we would lose statistical significance in the results, based on the large expectations of variance about the wide economic range of American families we see in the illustrations above (from those in the middle, to those at the top). From a probability perspective, we also just saw in a recent NBER working paper, leading economic researchers using this reason to choose equal tertile partitions, instead of deciles or percentiles.
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