Worthometer Methodology

2632673143_367e15d278_bWelcome fellow number geeks!

On this page I describe how I created the Worthometer in eight labor intensive steps. I write all this down for several reasons. First, I want the process to be transparent so that you can judge for yourself whether the resulting data has any real value (I believe it does). Second, I want to open the methodology to reasonable critique by other number geeks so that I can improve the quality of any future Worthometers. Third, I want to fully describe the process I followed so that it’s easier for me to retrace my steps whenever it’s time to update the data.

To save time and space, I’ll limit my description to the work I performed on the US Census Bureau’s 2011 SIPP. I followed an almost identical process with respect to the Federal Reserve Board’s 2013 SCF and University of Michigan’s 2013 PSID. I see no reason to prepare duplicative methodologies.

Step 1: Collect Published Net Worth Percentiles
My sources for 2011 SIPP net worth data are Excel formatted spreadsheets available for download at http://www.census.gov/people/wealth/data/dtables.html. I use the data reported in Table 4 to create the following spreadsheet:

Net Worth Percentile
$0 18.10
$5,000 27.20
$10,000 32.00
$25,000 38.60
$50,000 45.50
$100,000 55.90
$250,000 73.80
$500,000 86.40

This gives me eight data points of net worth survey results, but many gaps remain, so I proceed to Step 2.

Step 2: Derive Additional Percentiles From Published Data
Table 1 of the of Census Bureau’s spreadsheet states that the median, or 50th Percentile, for all surveyed households is $68,828. This gives me a ninth data point that I can add to the spreadsheet in Step 1 above.

Table 1 also presents the following additional data regarding the net worth of surveyed households:

Net Worth Range Median
Negative or zero -$8,610
$1 to $4,999 $1,679
$5,000 to $9,999 $7,113
$10,000 to $24,999 $16,039
$25,000 to $49,999 $36,524
$50,000 to $99,999 $71,982
$100,000 to $249,999 $159,226
$250,000 to $499,999 $341,848
$500,000 and over $836,033

I use this data to tease out additional net worth percentile figures. Since, for example, the reported midpoint of the net worth range $25k-$49,999 is $36,524, and I know from Step 1 that $25,000 is at the 38.60th Percentile and $49,999 is within $1 of the 45.50th Percentile, I can conclude that the $36,524 net worth figure reflects a midpoint percentile of 42.05 ((45.5-38.6)/2=42.05). When I perform the same calculations for all of the other Table 1 data and add it to the percentile data I collected from Table 4 (see Step 1 above) I can produce an expanded spreadsheet with eighteen data points for surveyed net worth percentiles:

Net Worth Percentile
-$8,610 9.05
$0 18.10
$1,679 22.65
$5,000 27.20
$7,113 29.60
$10,000 32.00
$16,039 35.30
$25,000 38.60
$36,524 42.05
$50,000 45.50
$68,828 50.00
$71,982 50.70
$100,000 55.90
$159,226 64.85
$250,000 73.80
$341,848 80.10
$500,000 86.40
$836,033 93.15

As you can see, this collection of published and derived net worth percentile data appears in increments of 0.05. This aspect of the data leads me into Step 3.

Step 3: Enter Published and Derived Percentiles into Spreadsheet of .05 Percentile Increments
The spreadsheet I created in Step 2 above starts at the 9.05th Percentile and ends at the 93.15th Percentile. I create a spreadsheet with those outlying limits that is 1683 lines long and graduated into .05 increments. I populate eighteen of those lines with my eighteen published and derived percentile/net worth data points (see Step 2 above). That leaves me with 1665 lines to fill up with interpolated data, so I’m on to Step 4.

Step 4: Fill all Gaps With Linear Interpolation
Whenever gaps appear in a table of data, those gaps can be filled through a variety of interpolative methods (including linear, cubic spline, and others). I choose to use a process of linear interpolation. Why? Because it’s easy and based upon what I’ve read, I don’t think more complicated approaches would necessarily produce better interpolated data. Basically, I split the data between two known data points into equal 0.05 slices and use the results to populate the gaps in the table. For example, as reflected in the last spreadsheet from Step 2 above, a gap exists between the known net worth/percentile figures of $7,113/20.60 and $10,000/32.00. As divided into .05 percentile increments, this gap consists of 48 lines in my massive 1683 line spreadsheet. Applying the process of linear interpolation, the incremental gain for each .05 increase in percentile on these 48 lines is $60 ($10,000-$7,113=$2,287 and $2,887/48 lines=$60.00). I follow a similar process to fill out all the other data gaps between known points on my 1683 line Excel spreadsheet. Excel formulas help ease this process, but it’s still time consuming.

Step 5: Repeat Steps 1-4 for 2013 SCF and 2013 PSID Data
This takes a massive amount of time, but when I’m finished I have an interpolated database for all three surveys sliced into very fine increments of 0.05 net worth percentiles. The cool thing about this data is that it’s all apples-to-apples because it’s all been sliced into the same .05 percentile pieces. But this is far too large a spreadsheet—1801 lines!—to publish at FrugalFringe.com. When I try to do it WordPress crashes, so I proceed to Step 6 below.

Step 6: Strip out all Data Except for 0.50 Percentile Increments
This reduces the 1801 lines of overwhelming spreadsheet down to a mere 181 lines. Thus is the unmanageable made manageable.

Step 7: Prepare Chart Reporting Averages from all Three Surveys, a/k/a the “Worthometer”
The three surveys don’t all report the same ranges of net worth, but they all provide percentile data for net worths that fall between $8,300 to $836,033. Therefore, if anyone’s net worth falls within this range, the Worthometer provides a percentile ranking that reflects an equally weighted average of all three surveys. If a given person’s net worth falls outside of the range of -$6,529 to $1,388,542, then the reported percentile ranking reflects an averaging of two surveys or, in the case of negative net worths between -$27,416 to -$21,293, the results of the 2013 PSID only. Here’s a chart that summarizes the range of net worth/percentiles reported by each survey:

Survey Net Worth Range Reported Percentiles
2013 SCF $85 to $1,871,800 12.50 to 95
2011 SIPP ($8,610) to $836,033 9.05 to 93.15
2013 PSID ($27,416) to $1,364,834 5 to 95

Step 8: Test Linear Interpolation of Net Worth Percentile Data Against Actual Data
The Canadian federal government’s study of household net worth is entitled the Survey of Financial Security (SFS). The 2005 SFS data was published in two parts: (1) an early summary release which reported figures for the mid-point medians of five quintiles of net worth ranging from CDN$1,000 to CDN$862,900; and (2) a later detailed release, known as the Public Use Microdata File (PUMF), which reported net worth percentiles along twenty-seven additional data points in the same net worth range ($1,000-$862,900).

The 2005 SFS data allows me to test whether the technique of linear interpolation for a small subset of data points provides a useable prediction of actual net worth data. The short answer is encouraging: linear interpolation of just five percentile data points predicts actual 2005 SFS PUMF data points closely, particularly for data points located above the 30th percentile.

So here’s my long answer to the short answer above. First, I collect the five 2005 SFS percentile data points:

Net Worth Percentile
$1,000 10
$37,300 30
$148,400 50
$361,200 70
$862,900 90

Next, I collect the 27 data points from the 2005 SFS PUMF:

No. Net Worth Percentile
1 $1,000 9.85
2 $2,000 12.58
3 $3,000 13.67
4 $4,000 15.21
5 $5,000 15.92
6 $6,000 17.16
7 $7,000 17.76
8 $8,000 18.22
9 $9,000 18.86
10 $10,000 19.33
11 $15,000 22.11
12 $20,000 24.43
13 $25,000 26.72
14 $30,000 27.98
15 $40,000 30.13
16 $50,000 32.23
17 $60,000 34.47
18 $80,000 38.63
19 $100,000 42.10
20 $150,000 49.83
21 $200,000 55.28
22 $250,000 60.91
23 $300,000 65.28
24 $400,000 72.50
25 $500,000 78.14
26 $600,000 82.61
27 $800,000 88.87

When I interpolate the 5 data points from the summary 2005 SFS and match up those results with the net worth-percentile figures from the 27 listed data points, I produce the following table:

No. Net Worth Percentile Interpolated Variance
1 $1,000 9.85 10.00 -0.15
2 $2,000 12.58 10.56 2.02
3 $3,000 13.67 11.11 2.56
4 $4,000 15.21 11.67 3.54
5 $5,000 15.92 12.22 3.70
6 $6,000 17.16 12.78 4.38
7 $7,000 17.76 13.33 4.43
8 $8,000 18.22 13.89 4.33
9 $9,000 18.86 14.44 4.42
10 $10,000 19.33 15.00 4.33
11 $15,000 22.11 17.78 4.33
12 $20,000 24.43 20.56 3.87
13 $25,000 26.72 23.33 3.39
14 $30,000 27.98 26.11 1.87
15 $40,000 30.13 30.54 -0.41
16 $50,000 32.23 32.34 -0.11
17 $60,000 34.47 34.14 0.33
18 $80,000 38.63 37.75 0.88
19 $100,000 42.10 41.35 0.75
20 $150,000 49.83 50.19 -0.36
21 $200,000 55.28 54.88 0.40
22 $250,000 60.91 59.58 1.33
23 $300,000 65.28 64.27 1.01
24 $400,000 72.50 71.55 0.95
25 $500,000 78.14 75.54 2.60
26 $600,000 82.61 79.52 3.09
27 $800,000 88.87 87.49 1.38

As the Variance column reports, linear interpolation provides approximate predictions of the actual PUMF data for points below the 30th percentile. But the technique’s predictive accuracy improves greatly above the 30th percentile. Here’s a graph that plots the PUMF on a blue line and the interpolated data on a red line.

2005 SFS Canadian Chart

As you can see, the red interpolated line tracks closely with the blue PUMF line that contains actual data. Therefore, in the context of net worth surveys, linear interpolation provides a close approximation of actual percentiles from a much fuller data set. In fact, I can run a calculation that determines the extent to which the interpolated red line predicts the actual percentile values that make up the PUMF blue line. This calculation is know as a “coefficient of determination” or “R Squared.” When I perform the calculation, the resulting R2 value is 0.9861, a very high score (the top possible score is 1.0) which suggests that linear interpolation provides a very solid predictor of the percentile scores contained in the actual data. Here’s the spreadsheet I created to perform the R2 calculation.

No. x y predicted SStot SSres
1 $1,000 9.85 10.00 720.683853 0.022500
2 $2,000 12.58 10.56 581.560020 4.098375
3 $3,000 13.67 11.11 530.176209 6.547912
4 $4,000 15.21 11.67 461.629098 12.555211
5 $5,000 15.92 12.22 431.623709 13.673560
6 $6,000 17.16 12.78 381.637931 19.203872
7 $7,000 17.76 13.33 358.555264 19.595378
8 $8,000 18.22 13.89 341.346153 18.758523
9 $9,000 18.86 14.44 318.107042 19.497131
10 $10,000 19.33 15.00 301.562520 18.748900
11 $15,000 22.11 17.78 212.738431 18.768149
12 $20,000 24.43 20.56 150.443853 15.011320
13 $25,000 26.72 23.33 99.511709 11.469511
14 $30,000 27.98 26.11 75.960909 3.492746
15 $40,000 30.13 30.54 43.106520 0.168544
16 $50,000 32.23 32.34 19.941186 0.012621
17 $60,000 34.47 34.14 4.953098 0.106182
18 $80,000 38.63 37.75 3.742075 0.778369
19 $100,000 42.10 41.35 29.208020 0.560475
20 $150,000 49.83 50.19 172.513631 0.128016
21 $200,000 55.28 54.88 345.381575 0.157904
22 $250,000 60.91 59.58 586.339320 1.775650
23 $300,000 65.28 64.27 817.070464 1.015458
24 $400,000 72.50 71.55 1281.958242 0.895323
25 $500,000 78.14 75.54 1717.641975 6.771192
26 $600,000 82.61 79.52 2108.136209 9.536285
27 $800,000 88.87 87.49 2722.172653 1.904290
990.78 14817.701667 205.253398
27 R Squared = 0.986148095
36.69556

Here’s the bottom line: if you seek a “fair approximation” of where your household ranks in the nationwide surveys of net worth, the Worthometer is more than worth its while.

So that’s it for my description of methodology. If you have any comments about any of this, please leave them below.

Photo Credit: Hollerith Census Machine by Marcin Wichary. To see original at Flickr, click here.

3 Responses to Worthometer Methodology

  1. David February 26, 2016 at 9:18 AM #

    Do you really average the various data sets to arrive at your table?
    How do you adjust for inflation from one year to the next?
    Thanks.

    • A Noonan Moose February 26, 2016 at 9:57 AM #

      David:

      As to question 1: Yes. For net worths that fall between $8,300 to $836,033 (see description of step 7 in the above text), the Worthometer provides a percentile ranking that reflects an equally weighted average of all three surveys, i.e. each of the three surveys contributes an equal share (33.3333%) to the Worthometer. For example, for the 25th percentile the Worthometer reports a net worth of $5,131. This figure reflects an average of the interpolated 25th percentile figures for the three surveys: $3,200 (2013 PSID) $3,394 (2011 SIPP) and $8,800 (2013 SCF).

      As to question 2: I adjust the Worthometer for inflation by updating it as each new PSID, SIPP, or SCF survey is released. For example, see this post.

      Thanks for the question!

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