Blair Fix

I've spent a lot of time on this blog debunking economists' claims about
productivity. Usually, I come at the problem from a fairly technical
angle, meaning I break down the contradictions involved in economists'
methods. Today, I want to try a more philosophical approach. I'm going
to talk about dualism --- the idea that something can be two things at
once.

### Dualism in science

Science is filled with dualist statements --- claims that a substance is
two things at once. Of course, scientists don't use this terminology.
They call their dualist statements 'mathematical equations'. Here's a
famous one from Albert Einstein:

::: {style="text-align:center"}
[ \displaystyle E = mc\^2 ]{.katex-eq katex-display="false"}
:::

In this equation, Einstein claims that matter and energy are two sides
of the same coin. In other words, there is some mysterious force that
can convert matter into energy and vice versa.

Because mass-energy equivalence sounds pretty wild, Einstein's equation
gets a lot of attention. But science is rife with conceptually identical
statements. For example, Newton claimed that there is something called a
'force' that can be converted into 'acceleration':

::: {style="text-align:center"}
[ \displaystyle F = ma]{.katex-eq katex-display="false"}
:::

When you reflect on these equations, you realize that they are making
rather profound metaphysical claims about the world --- much like
claiming that the Father, the Son and the Holy Ghost are the same thing.
So were Einstein and Newton just doing theology?

No. They were doing science.

Unfortunately, most introductory science textbooks don't explain the
distinction. Instead, they take a rather theological approach to
pedagogy. Textbooks often present formulae as received wisdom, and then
tell students to explore the consequences. Similarly, many science
popularizers know that the public is hungry for metaphysics, and so they
discuss the 'profound' implications of various theories. But what
popularizers rarely do is explain why scientists trust the formulas they
use.

Part of the problem comes down to mathematical notation itself. On its
own, a mathematical equation is not science. It is a *definition*. For
example, I can define a quantity *F* that is the product of mass times
acceleration:

::: {style="text-align:center"}
[ \displaystyle F = ma ]{.katex-eq katex-display="false"}
:::

Until I test this equivalence, however, I haven't done science. To do
science, we must treat our mathematical definition as a mathematical
*question*. Unfortunately, there is no accepted notation for this way of
thinking. But perhaps it might look like this:

::: {style="text-align:center"}
[ \displaystyle F =? \~ ma ]{.katex-eq katex-display="false"}
:::

To test this equation/question, we devise ways of independently
measuring both sides of it. Now, by 'independently', I don't mean
measurement that is 'theory free', since that's impossible. All
measurement depends on preconceptions about the world. (To measure the
length of different objects, for example, you assume that the length of
your ruler remains constant.) In science, 'independent' measurement
simply means we use methods that don't depend on the theory we are
testing.

So if we are testing Newton's equation, we can't measure force in terms
of acceleration. Instead, an independent measurement might be something
like this:

1. measure force with a spring gauge,
2. measure mass with a balance scale
3. measure acceleration using the change in velocity over time.

These measurements all depend on preconceptions about the world. But
they do not logically imply Newton's equation. And so if we find that
force is the product of mass times acceleration, we've shown that
Newton's equation is not merely a human definition. It is a truth
statement about the natural world.

We can do the same thing with Einstein's equation --- albeit using tools
that are more complicated. For example, in 2005, [Simon
Rainville](https://www.nature.com/articles/4381096a){target="_blank"
rel="noopener"} and colleagues used atomic-mass differences to test the
equivalence of matter and energy. They found that Einstein's equation
was accurate to seven decimal places.[^1^](#fn1){#fnref1 .footnote-ref
target="_blank" role="doc-noteref" rel="noopener"}

Again, it is the experimental confirmation that renders an equation
meaningful. Without the observational component, we are left with
nothing but a human definition. And that brings us to theology.

### Dualism in theology

If science is the combination of logical definitions with empirical
observations, theology is science without the observation. It is a web
of human definitions, and nothing more.

As an example, take the Catholic concept of the
[Trinity](https://en.wikipedia.org/wiki/Trinity){target="_blank"
rel="noopener"}, which is notorious for its bizarre logic. According to
church dogma, God exists simultaneously as 'The Father', 'The Son' and
'The Holy Spirit'. But while these three entities are all God, they are
somehow distinct from each other. Thus the Holy Spirit is God. And the
Son is God. But the Holy Spirit is not the Son. Confused? That's because
the Trinity is logically incoherent. But don't worry, the church says
it's be true.

[]{#fig-trinity}

<figure class="wp-block-image size-large">
<img
src="https://i0.wp.com/economicsfromthetopdown.com/wp-content/uploads/2022/08/trinity.png?w=723&amp;ssl=1"
decoding="async" data-recalc-dims="1" />
<figcaption>Figure 1: The Shield of the Trinity. <a
href="https://commons.wikimedia.org/wiki/File:Shield-Trinity-Scutum-Fidei-English.svg"
target="_blank" rel="noopener">Wikimedia Commons</a></figcaption>
</figure>

The Trinity is a prime example of theological dualism. We have a set of
definitions, and nothing else. Sure, you can argue about the
definitions. But there's no objective way to settle the score. Quarrels
over the Trinity are the medieval equivalent of debates in modern
fandom. It's like when Star Wars fans argue about whether Anakin
Skywalker 'died' when he became Darth Vader. The correct answer is that
there is no correct answer. The 'truth' is however you define it.

Although it makes for abysmal science, the theological stance is a great
way to sound authoritative while you spout bullshit. The self-styled
libertarian 'philosopher' Ayn Rand was a master of this technique. Here
she is [laying
out](http://aynrandlexicon.com/lexicon/existence.html){target="_blank"
rel="noopener"} her philosophy of objectivism:

> The formula defining the concept of existence and the rule of all
> knowledge: A is A. A thing is itself. You have never grasped the
> meaning of \[this\] statement. I am here to complete it: Existence is
> Identity, Consciousness is Identification.

Rand's writing is a tour-de-force in theological nonsense. Start with a
tautology (A = A). Follow it up with some weighty definitions (existence
= identity). Claim you have a 'rule for all knowledge'. Marvelous
bullshit.

### Dualism in economics

Perhaps the best definition of economics is that it is 'secular
theology'. Economics adopts the veneer of science, but, like theology,
is based on untestable definitions.

In economics, the most pervasive dualism is the equivalence between
income and productivity:

::: {style="text-align:center"}
[ \displaystyle \text{income} = \text{productivity} ]{.katex-eq
katex-display="false"}
:::

Unlike Ayn Rand's poetic bullshit, the dualism between income and
productivity is meant to be quantitative and literal. In neoclassical
economics, a person's income indicates their contribution to society.

Like all good theology, the theory starts with a definition. If Alice
has some output *Q* that is sold at some price *P*, her gross income is
defined as:

::: {style="text-align:center"}
[ \displaystyle I = Q \cdot P ]{.katex-eq katex-display="false"}
:::

For example, if Alice grows 10 apples and sells them for \$1 each, her
gross income would be \$10:

::: {style="text-align:center"}
[ \displaystyle I = (10 \text{ apples }) \cdot ( \\1 \text{ per apple} )
= \\10 ]{.katex-eq katex-display="false"}
:::

If Alice grew half as many apples, her income would be cut in half:

::: {style="text-align:center"}
[ \displaystyle I = (5 \text{ apples }) \cdot ( \\1 \text{ per apple} )
= \\5 ]{.katex-eq katex-display="false"}
:::

From this angle, it seems like the duality between income and
productivity is sound. The problem is that it is actually *unnecessary*.
If we can count what Alice produces (apples), we can measure her
productivity directly. So we don't need income.

Worse still, if the price of apples changes, not only is the
income-productivity duality unnecessary, it is also *false*. For
example, if Alice grows the same number of apples each year, the reality
is that her productivity is constant. And yet if the price of apples
changes, we infer from her income that her productivity has *changed*.
That's just wrong.

So right off the bat, we have a logical problem with the
productivity-income duality. Either it is correct but unnecessary, or it
is both unnecessary and incorrect. Either way, the duality is unsound.

Of course, there is nothing wrong with having a hypothesis that is
logically unsound. It just means that when you notice the problem, you
should abandon the hypothesis. But that's not what happened in
economics. Instead, the income-productivity duality became the basis for
the entire system of national accounts.

Along the way, economists invented various fairy tales to justify their
theology. For example, in the late 19th century, the economist John
Bates Clark [tried to
'prove'](https://archive.org/details/distributionwea02clargoog){target="_blank"
rel="noopener"} that in a competitive market, each agent earned what
they produced. To his credit, Clark realized that the only way this
proof worked is if everyone produced the same commodity. The problem is
that this assumption renders Clark's hypothesis moot. If everyone
produces the same commodity, we can measure their productivity directly,
meaning we don't need income.

It gets worse. In the real world, where people produce many different
commodities, we cannot measure productivity directly. (We cannot compare
apples and oranges.) And so economists infer productivity by measuring
income. But in this situation, Clark's proof breaks down.

To address this logical problem, economists have invented more theology.
Prices, they claim, are themselves a duality. Prices are both a monetary
quantity and a measure of *utility*:

::: {style="text-align:center"}
[ \displaystyle \text{price} = \text{utility} ]{.katex-eq
katex-display="false"}
:::

So yes, prices may change, but that's because the underlying utility of
a commodity has changed. Or maybe it hasn't. The problem is that
economists never measure utility. They *infer* it from prices. And so
the whole operation becomes circular --- a theological definition, and
nothing more. Joan Robinson nicely
[summarized](https://archive.org/details/EconomicPhilosophy){target="_blank"
rel="noopener"} the situation:

> Utility is a metaphysical concept of impregnable circularity; utility
> is the quality in commodities that makes individuals want to buy them,
> and the fact that individuals want to buy commodities shows that they
> have utility.

In other words, economists propose a definition, and these use this
definition to justify itself. That's theology, folks.

### The dualism smell test

Since both science and theology appeal to dualism, it can be difficult
to distinguish the two forms of thought. With that in mind, here's a
dualism smell test.

Dualism always starts with a definition. Force is mass times
acceleration. The Son is God. Income is productivity. To distinguish
between science and theology, you should look at what follows the
definition. In the case of science, the definition should be followed by
an empirical test. Thus, scientists didn't just take Newton at his word.
They tested his laws of motion and found them to be correct (at
non-relativistic speeds).

Now, the wonder of mathematics is that by manipulating algebraic
definitions, you can derive predictions that follow from the starting
assumptions. It's important to test these predictions. But if they hold,
that doesn't mean that the assumptions are correct. That's why
scientists always test both the predictions of a theory and its
assumptions. The classic example is Newton's theory of gravity. When
combined with his theory of dynamics, you get a rich set of predictions
--- enough to send people to the moon.

These correct predictions, however, didn't stop scientists from testing
the core assumption --- the claim that inertial mass is equivalent to
gravitational mass (a dualist statement). Indeed, this 'weak equivalence
principle' has been [tested
continuously](https://en.wikipedia.org/wiki/Equivalence_principle#Tests_of_the_weak_equivalence_principle){target="_blank"
rel="noopener"} for more than four centuries. No one has found a
violation.

When people like Milton Friedman spout theological nonsense, they'll try
to convince you that assumptions don't matter. Friedman notoriously
claimed that if a theory gives 'correct predictions', that's [good
enough](http://digamo.free.fr/hausman82.pdf#page=76){target="_blank"
rel="noopener"}. Don't believe him. Assumptions are the most basic part
of science. If they are wrong, the whole theory is garbage.

Speaking of Uncle Milton, that brings me to theological dualism. When
you do theology, the goal is to use a definition to (seemingly) prove
your point and to avoid the fact that you are not testing your
definition. One of the more amusing applications of this technique is in
supposed logical 'proofs' of God's existence. My favorite proof comes
from [Rene
Descartes](https://plato.stanford.edu/entries/descartes-ontological/){target="_blank"
rel="noopener"} and goes something like this:

1. God is perfect.
2. It is more perfect to exist than to not exist.
3. Therefore, God exists.

Do you see what Descartes did here? He used two definitions to make his
point. He defined God as perfect. He defined existence as more perfect
than non-existence. Presto, God exists.

Sorry, Rene, that's not how it works. You've got to test your
assumptions.

Is God 'perfect'? Hard to say, since God is unobservable and
'perfection' is a subjective aesthetic. And is it 'more perfect' to
exist than to not exist? Again, there's not much to test here since
we're talking about aesthetics. But mathematicians might disagree. Only
imperfect circles exist (in the real world). Yet mathematicians can
imagine perfect ones. So maybe it is 'more perfect' to not exist.

In short, dualism fails the smell test if it is not followed by an
empirical test. If there is no such test, what you have is not science
... it is theological rot --- a web of interlocking definitions that
tell us nothing about the natural world.[^2^](#fn2){#fnref2
.footnote-ref target="_blank" role="doc-noteref" rel="noopener"}

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\[Cover image: [Wikimedia
Commons](https://commons.wikimedia.org/wiki/File:Yin-yang-pond.jpg){target="_blank"
rel="noopener"}\]

Want to know more about how economists equate income with productivity?
Here are five pieces on the topic:

1. [No, Productivity Does Not Explain
 Income](https://economicsfromthetopdown.com/2019/07/08/no-productivity-does-not-explain-income/){target="_blank"
 rel="noopener"}
2. [Productivity Does Not Explain
 Wages](https://economicsfromthetopdown.com/2019/11/14/productivity-does-not-explain-wages/){target="_blank"
 rel="noopener"}
3. [Productivity and Income ...
 Again](https://economicsfromthetopdown.com/2020/05/23/productivity-and-income-again/){target="_blank"
 rel="noopener"}
4. [Debunking the 'Productivity-Pay
 Gap'](https://economicsfromthetopdown.com/2020/01/17/debunking-the-productivity-pay-gap/){target="_blank"
 rel="noopener"}
5. [Real GDP: The Flawed Metric at the Heart of
 Macroeconomics](https://economicsfromthetopdown.com/2019/04/29/real-gdp-the-flawed-metric-at-the-heart-of-macroeconomics/){target="_blank"
 rel="noopener"}

### Notes

::: {.footnotes .footnotes-end-of-document role="doc-endnotes"}
1. [Rainville and colleague's experiment worked as follows. They let an
 atomic nucleus capture a neutron, after which the nucleus emits a
 gamma ray. To test Einstein's equation, Rainville compared the mass
 change between the reactants and product to the energy of the gamma
 ray.]{#fn1}

 The experiment is an interesting case-study in how measurement
 depends on theory. To measure the energy of the gamma ray, Rainville
 used the [Planck
 relation](https://en.wikipedia.org/wiki/Planck_relation){target="_blank"
 rel="noopener"}, which describes how the energy of a photon relates
 to its wavelength. The measurement of wavelength, in turn, depended
 on [Bragg's
 Law](https://en.wikipedia.org/wiki/Bragg's_law){target="_blank"
 rel="noopener"} of diffraction. And to measure mass, Rainville used
 [cyclotron
 resonance](https://en.wikipedia.org/wiki/Cyclotron_resonance){target="_blank"
 rel="noopener"}. Converting the resonance frequency to mass depends
 on both Newtonian mechanics and the theory of the electromagnetic
 [Lorenz
 force](https://en.wikipedia.org/wiki/Lorentz_force){target="_blank"
 rel="noopener"}.[↩︎](#fnref1){.footnote-back target="_blank"
 role="doc-backlink" rel="noopener"}

2. [Okay, theology does tell us something about the natural world. It
 demonstrates that the human species is adept at fooling
 itself.[↩︎](#fnref2){.footnote-back target="_blank"
 role="doc-backlink" rel="noopener"}]{#fn2}
:::

I’ve spent a lot of time on this blog debunking economists’ claims about productivity. Usually, I come at the problem from a fairly technical angle, meaning I break down the contradictions involved in economists’ methods. Today, I want to try a more philosophical approach. I’m going to talk about dualism — the idea that something can be two things at once.

Dualism in Science, Theology, and Economics

In science, being wrong is call for a celebration.

Now that you think I'm crazy, let me explain. Science is about the
search for *truth*. Logically, this means we should celebrate when we
are *right*. But here's the catch. How do we know when we are right? We
can't.

Science is about *conditional* truth. We have ideas that we *think* are
right because they have not yet been proven wrong.

Science is a bit like evolution. Of all the species that have ever
existed, the vast majority went extinct. The best we can say of living
species is that they are not *yet* extinct. The same goes for scientific
theories. Of all the hypotheses ever proposed, the vast majority are
wrong. The ones that have survived are not *yet* wrong. (The bad ones
are not *even* wrong. More on this in a bit.)

So when we have an idea that turns out to be wrong, we should celebrate.
It means we know we are on the wrong path. Time to ditch our idea and
try another one. This is how science should work.

The problem is that this is *uncomfortable*. Being wrong is not
something we like to admit. Even the best scientists can have trouble
admitting their failures. Take Albert Einstein. His theory of general
relativity predicted something called gravitational waves. These are
waves in the fabric of space and time that are caused by the motion of
massive objects. One of the recent triumphs of empirical science is that
we have
[detected](https://en.wikipedia.org/wiki/First_observation_of_gravitational_waves)
these waves. So we're quite sure they exist.

But in 1936, Einstein wrote a paper in which he argued that
gravitational waves do *not* exist. The paper was rejected during peer
review. Einstein was furious. He would later admit that the peer
reviewer was correct and that his own arguments were wrong. But it took
some time for emotions to subside. Read the story
[here](https://physicstoday.scitation.org/doi/10.1063/1.2117822). It's a
fascinating case study of science at work.

If a scientist like *Einstein* was unaware of his own mistakes (at least
at first), it means the rest of us (with far lesser minds) must be extra
skeptical of our ideas. As a species, we're prone to self delusion about
our own competence. This may be an evolutionary adaptation. When you are
running from a lion or battling an enemy, it's best not to wallow in
your mistakes. That's a surefire way to die. It's far better to be
overconfident in the moment and make decisions with gusto. Reflection
can come later.

This adaptation may explain a curious part of our psychology. We're
attracted to people who are *confident*. The number one trick of the con
artist is to exude a calm, easy confidence while boldly lying to your
face. This confidence puts you at ease --- it makes you trust them. The
con artist is the polar opposite of a good scientist. A good scientist
should be racked with doubt. But a con artist must be supremely
confident. (If you are interested in the psychology of the con, I highly
recommend Maria Konnikova's book [*The Confidence
Game*](https://www.goodreads.com/book/show/25387895-the-confidence-game)).

On the spectrum between extreme confidence and extreme doubt,
politicians come somewhere in between the con artist and the scientist.
OK, most politicians are pretty close to con artists (the angry orange
man in the Oval Office comes to mind). Think of political debates where
the moderator asks, "Describe a time when you were wrong." Has a
politician ever given a straight answer to this question? Doubtful. They
usually find a way to avoid the question and emphasize their strengths.
Confidence, not skepticism (or self doubt), is what we seem to look for
in leaders.

### The secret to supreme confidence

Let me tell you the secret to supreme confidence. It's simple. Your
ideas must be *immune to evidence*. When your ideas have this property,
they can *never be wrong*. By extension, *you* can never be wrong! This
means you can act with confidence. There is no need for self-doubt or
skepticism. You have the answers! The world needs to listen to you!

It's no accident that this type of thinking is the hallmark of political
ideologies. *They cannot be wrong*. This property is what makes
ideologies so attractive to us. We can be supremely confident in our
ideology because there is no conceivable way that it could be proven
wrong. So if you are a scientist and you find that you're rarely wrong,
you have a problem. It probably means you're not doing science. You're
doing *politics*.

But be in good spirits. You're not alone. Many (if not most) economists
have deluded themselves in the same way. Most of their ideas can never
be wrong. That's why economists are so confident.

Let's look at an example. *Utility maximization* is probably the most
important example of ideology masquerading as science. Neoclassical
economists propose that humans are rational actors. When confronted with
any decision, humans choose the path that maximizes their utility.

Economists who buy into this idea find it immensely seductive. It
explains everything about human behaviour! What a stunning achievement
of science. Except it's not.

The catch is that utility maximization is completely immune to evidence.
It cannot be wrong. Since utility is unobservable, there is no
conceivable way to show that humans do *not* maximize utility. So
neoclassical microeconomics is an ideology masquerading as science. You
can use utility maximization to justify any claim you like. That's a
nice property to have in an ideology. You can preach the miracles of the
free market with confidence.

Not convinced by this critique? Let's use the same reasoning and apply
it to thermodynamics. Suppose we have a theory that explains the
internal combustion engine in terms of invisible, little green people.
Inside every engine is an invisible person that ignites the fuel at the
correct time. This theory is a towering achievement because it explains
how all internal combustion engines work.

But it is conveniently immune to evidence. Since the little green people
are invisible, we can never observe them. We can never show that the
green people are *not* the cause of the fuel ignition. What a shame.

If we look closely at our ideologies (neoclassical economics, Marxism,
all religions) we find invisible green people everywhere. Ideology and
superstition preserve these green people for future generations. We fool
ourselves over and over. *Science* should be about killing invisible
green people. Science needs to purge ideas that cannot be wrong.

### Other people are wrong a lot ... but not me {#other-people-are-wrong-a-lot-but-not-me}

It's easy to find problems in other people's ideas. It's far harder to
find problems in our own theories. I think we need to train ourselves to
do it. This should be a basic part of science education.

I feel fortunate to have had [Jonathan
Nitzan](https://en.wikipedia.org/wiki/Jonathan_Nitzan) as a teacher.
Jonathan fondly tells stories of interviewing prospective candidates in
the department of Political Science at York University. His favourite
question: "Give an example of when you were wrong." The candidate's
response, according to Jonathan, is usually complete surprise. Few give
concrete examples.

I'm probably lucky that I have never had Jonathan Nitzan as an
interviewer. But his story stays with me. Every now and then I ask
myself "name a time when you were wrong". I admit it's deceptively hard
to do. But it's an essential exercise for maintaining skepticism about
your own work. As Richard Feynman famously
[said](http://calteches.library.caltech.edu/51/2/CargoCult.htm), "The
first principle is that you must not fool yourself---and you are the
easiest person to fool".

So let me practice what I preach. *Here is a time when I was wrong*.

Some years ago, I was studying the firms owned by members of the Forbes
400. These are the 400 richest individuals in the United States. The
Forbes 400 list provides the companies from which these individuals
earned their wealth.

As a little research project, I tracked down the employment size of
these companies. I was interested in how the size of these Forbes 400
firms related to the size of firms associated with the general
population. Here was my initial result, posted on the capitalaspower.com
[forum](http://www.capitalaspower.com/forum/viewtopic.php?f=6&t=426) in
2015:

<figure id="attachment_152" class="wp-caption alignnone"
aria-describedby="caption-attachment-152" style="width: 2597px">
<img
src="https://i0.wp.com/economicsfromthetopdown.com/wp-content/uploads/2019/04/billionaire.png?resize=723%2C570&amp;ssl=1"
class="alignnone size-full wp-image-152" loading="lazy" decoding="async"
data-attachment-id="152"
data-permalink="https://economicsfromthetopdown.com/2019/04/16/lets-celebrate-being-wrong/billionaire/"
data-orig-file="https://i0.wp.com/economicsfromthetopdown.com/wp-content/uploads/2019/04/billionaire.png?fit=2597%2C2047&amp;ssl=1"
data-orig-size="2597,2047" data-comments-opened="1"
data-image-meta="{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;0&quot;}"
data-image-title="Billionaire" data-image-description=""
data-image-caption="&lt;p&gt;The size distribution of firms owned by Forbes 400 individuals. I compare this to the US firm size distribution. In hindsight, this comparison is wrong.&lt;/p&gt;
"
data-medium-file="https://i0.wp.com/economicsfromthetopdown.com/wp-content/uploads/2019/04/billionaire.png?fit=300%2C236&amp;ssl=1"
data-large-file="https://i0.wp.com/economicsfromthetopdown.com/wp-content/uploads/2019/04/billionaire.png?fit=723%2C570&amp;ssl=1"
data-recalc-dims="1" width="723" height="570" alt="Billionaire" />
<figcaption>The size distribution of firms owned by Forbes 400
individuals. I compare this to the US firm size distribution. In
hindsight, this comparison is wrong.</figcaption>
</figure>

In this figure, I compare the size distribution of firms owned by Forbes
400 members to the size distribution of all US firms. My conclusion was
that Forbes 400 members owned firms that are far larger than the firms
associated with the general US public.

But in hindsight, I made an embarrassing error. Can you spot it? If you
can't, it makes me feel better. Because it took me years to figure out
my mistake.

Let's begin with the Forbes 400 firms. These are firms that come from
sampling *individuals*. We track down the 400 richest people, then we go
and look at the firms they own. We plot the size distribution of these
Forbes 400 firms.

My intention was to compare these firms to the ones associated with the
*average person*. The correct way to do this is to sample *individuals*
from the general US public. We then record the size of firm associated
with each individual. We compare this firm size distribution to the
Forbes 400 distribution.

But this is *not* what I did in the figure above. Instead I sampled from
the *firm* population. I reported the size distribution of all US firms.
I then compared this to the firm size distribution associated with
Forbes 400 members. But this was a mistake. Sampling *firms* is
completely different than sampling *individuals* and recording the firm
size associated with each person. The analysis in the figure above is
just *wrong*.

Years later I realized my mistake. To make the correct comparison, we
need to find the size distribution of firms associated with the general
US public. As far as I know, there is no raw data on this distribution.
But we can estimate it from the firm size distribution. I won't go into
the details here. The derivation is in the [supplementary
materials](https://static-content.springer.com/esm/art%3A10.1007%2Fs42001-018-0019-8/MediaObjects/42001_2018_19_MOESM1_ESM.pdf)
of a [recent
paper](https://link.springer.com/article/10.1007/s42001-018-0019-8).

Here is the correct comparison. The figure below again shows the size
distribution of firms associated with Forbes 400 individuals. It also
shows the 'Execucomp 500'. These are the firms associated with the 500
highest paid executives in the United States (according to the Execucomp
database). I compare these firm size distributions to a model. I won't
go into the model here, but it's about hierarchy.

<figure id="attachment_153" class="wp-caption alignnone"
aria-describedby="caption-attachment-153" style="width: 1012px">
<img
src="https://i0.wp.com/economicsfromthetopdown.com/wp-content/uploads/2019/04/forbes.png?resize=723%2C632&amp;ssl=1"
class="alignnone size-full wp-image-153" loading="lazy" decoding="async"
data-attachment-id="153"
data-permalink="https://economicsfromthetopdown.com/2019/04/16/lets-celebrate-being-wrong/forbes/"
data-orig-file="https://i0.wp.com/economicsfromthetopdown.com/wp-content/uploads/2019/04/forbes.png?fit=1012%2C884&amp;ssl=1"
data-orig-size="1012,884" data-comments-opened="1"
data-image-meta="{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;0&quot;}"
data-image-title="forbes" data-image-description=""
data-image-caption="&lt;p&gt;Size distribution of firms associated with the Forbes 400 and Execucomp 400. The null effect is what we expect if we sampled the general population. (Source)&lt;/p&gt;
"
data-medium-file="https://i0.wp.com/economicsfromthetopdown.com/wp-content/uploads/2019/04/forbes.png?fit=300%2C262&amp;ssl=1"
data-large-file="https://i0.wp.com/economicsfromthetopdown.com/wp-content/uploads/2019/04/forbes.png?fit=723%2C632&amp;ssl=1"
data-recalc-dims="1" width="723" height="632" alt="forbes" />
<figcaption>Size distribution of firms associated with the Forbes 400
and Execucomp 500. The null effect is what we expect if we sampled
individuals from the general population. <a
href="https://link.springer.com/article/10.1007/s42001-018-0019-8">(Source)</a></figcaption>
</figure>

What is important here is the 'null-effect' --- the dotted line. This is
the size distribution of firms that we expect if we sampled individuals
from the US public and recorded the size of firms that they are
associated with. This distribution is uniform when plotted on a log
scale. Compare this to my original analysis on the capitalaspower.com
forum. It's very different, isn't it.

Fortunately (for me) the original conclusion still stands. Forbes 400
members own firms that are larger than those associated with the general
population. But this difference is far less spectacular than my original
analysis suggested. The original results were plain wrong. It's
embarrassing, but also cause for celebration. It meant I was doing
science.

Of course, I'm assuming that my new results are correct. But if I heed
the advice I just gave above, I should admit that they are *not yet
wrong*.

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In science, being wrong is call for a celebration. Now that you think I’m crazy, let me explain. Science is about the search for

 truth

. Logically, this means we should celebrate when we are

 right

. But here’s the catch. How do we know when we are right? We can’t. Science is about

 conditional

truth. We have ideas that we

 think

are right because they have not yet been proven wrong. Science is a bit like evolution.

Rogue Scholar Beiträge

Dualism in Science, Theology, and Economics

Let’s Celebrate Being Wrong