A Mathematical Model, Adopted as Econophysics, to 

Detect Tax Noncompliance

John Angle

ORCID #: 0000-0002-6603-3695

inequalityprocess@gmail.com

Tresoria, LLC

Post Office Box 215

Lafayette Hill, Pennsylvania, 19444 JEL Code: C67, G10, G12, G17 

PACS Code 89.65Gh 

MSC : 60k35, 82C22 
Tresoria LLC

Take-aways from this talk:

There is more information in money income data than is 

recognized in academic economics.

Fr’instance, a math model of income exposes simulated 

stealthy tampering with labor income data to promote the 

popularity of a wannabe dictator. The model was developed 

independently of academic economics.
A Potential Real-Life Application of the Model: Closing the 

Tax Gap 

 The tax gap is estimated by the Taxpayer Compliance 

Measurement Program (TCMP), an SRS survey. This talk’s model 

might uncover useful information in TCMP data that makes the 

survey more focused on noncompliance.

 The model’s credibility: 

 The model has been adopted as econophysics, the branch of physics remaking academic economics into a science. See the 2020 Cambridge 

University Press textbook, 

“Income Distribution Dynamics 

of Economic Systems: an Econophysics

Approach”:
The Model as Econophysics: 

First paragraph under the section heading “The Angle Process”, (page 154): 

“Before the term econophysics was even 

created, Angle (1983) advanced the 

fundamental concepts of an agent-based 

model of wealth formation based on particle-like 

microscopic interactions of agents. The Angle 

process, was elaborated in a long sequence of 

papers spanning decades [citations to 29 of 

Angle papers].” 
The Model as Econophysics:

Last paragraph of “The Angle Process” section (page 158): 

“...John Angle has in fact pioneered the 

statistical econophysics approach to the income 

and wealth distribution problem, [an] approach 

which was, often independently, followed later 

by other econophysicists ....” 

(Marcelo Byrro Ribeiro. 2020. “Income Distribution Dynamics of Economic Systems: an 

Econophysics Approach. Cambridge, U.K.: Cambridge University Press).
The model is abstracted from two ideas: 

1) Pervasive competition among people for wealth in flow or 

stock form, the human version of population biology’s view 

of competitive exclusion allocating niche to individuals, and,

2) the speculation that that human workers more productive 

of wealth are more sheltered in this pervasive competition 

for wealth.
The model:

1) All particles in a population are randomly paired.

2) Each pair flips and calls a fair coin. 

3) If Particle A wins the toss, it receives a share of 

Particle B’s wealth. That share is B’s parameter. 

4) If Particle B wins the toss, it receives a share of 

Particle A’s wealth. That share is A’s parameter. 

5) Particle parameters are fractions of 1.0, 

excluding1.0 and 0.0.

This model is simple, testable, and the empirical process it mimics 

apparently ubiquitous, i.e., the model is a candidate for a law of 

nature. Physicists like it. 
Confirmations of the Model:

 Many dozens of empirical confirmations grouped 

under 15 headings in the handout. See Handout, 

also example on next slide (dotted curves are 

model fits).

 Seven maxims of mainstream economics never 

suspected in academic economics of being the 

joint consequence of such a simple stochastic 

model. See Handout.

 Hundreds of citations in the econophysics literature.

Simulation of Model Exposing Stealthy Tampering 

with Labor Income Data to Help Wannabe Dictator 

Get Past the Last Free Election1

Cast of Characters (the story is fiction, the data set U.S. because it is 

clean, the time is now, the setting is in a land far, far away): 

1) Wannabe Dictator needs enthusiastic support from blue collar 

authoritarians to be re-elected despite falling incomes of the less skilled;

2) Administrator of the national statistics agency promises Wannabe “GREAT 

STATS!!” before election day;

3) A crew of ethically compromised statisticians is promised “leapfrog” 

promotion if the crew’s “statistical adjustment“ of the data helps Wannabe

win.

1Angle, J. 2017. “Detecting Politically Motivated Tampering With Workers’ Labor Income In Survey Data”.

Proceedings of the 2017 Joint Statistical Meetings, (American Statistical Association, Social Statistics Section, 

Joint Statistical Meetings). Pp.1681-1686. CD-ROM. Alexandria, VA: American Statistical Association. Data to be 

tampered with are from public use samples of the March Current Population Survey, labor income 1961-2010.
First meeting of the “GREAT STATS!!” Committee:

 Agency Administrator tells the “leapfroggers” to add a random 

increase to the reported labor incomes of respondents without a 

post-secondary education in a just completed national survey; 

 Leapfrogger A says that “adjustment” will obliterate frequency 

spikes over round numbers, a feature of respondent answers, 

something that hostile academics will seize on. 
Then bumptious Leapfrogger B unveils a plan:

“Journalists haven’t a clue about raking. That’s where we’ll get away with data 

tampering.”, says B.

Agency Administrator sternly admonishes B to never say ‘tamper’. B stands 

corrected, and is permitted to continue to describe the plan for an adjustment:

”During raking, we’ll increase the weight of records in the target group with labor 

incomes above the target group’s median, and decrease the weights of those 

with labor incomes below their median, ....”. [More details about B’s plan in Angle, 

2017].
While frequency spiking after stealthy “adjustment” has only changed 

imperceptibly, as intended in B’s plan, median labor incomes of workers without 

post-secondary education are substantially up. [dotted white lines]
 But.... the parameters of this talk’s model are violated, exposing tampering that 

substantially changed estimates for workers without a post-secondary education: 

white dotted curves. Upshot: now wannabe dictators can’t get away with keeping 

two sets of income data, one set for the media, another for oligarch pals and 

economic and military planning.
I offer this model and its findings to the Federal 

Committee on Statistical Methodology in hopes 

that the U.S. Government can benefit from 

them.

I’d be happy to do short term consulting on 

applications of the model, gratis.
Photo credit: National Park Service

Photo Credit: National Park Service

All ears? 

What about synthetic income data for privacy 

protection? Generated by the model?

Other questions?
A Mathematical Model, Adopted as Econophysics, to 

Detect Tax Noncompliance

John Angle

ORCID #: 0000-0002-6603-3695

inequalityprocess@gmail.com

Tresoria, LLC

Post Office Box 215

Lafayette Hill, Pennsylvania, 19444 JEL Code: C67, G10, G12, G17 

PACS Code 89.65Gh 

MSC : 60k35, 82C22