Henrique Costa

When it comes to job titles, data scientist is one of the biggest buzzwords in recent years. It is also one of the fastest growing fields of professional activity. Can an economist really be a data scientist? What skills are needed?

Can Economists Become Data Scientists?

[![](https://hcostax.com/blog/maths_economics/feature.jpg){.img-fluid}](feature.jpg){.lightbox
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In today's post, I want to start a discussion about the use of
mathematics and statistics in economics, and with this shocking
sentence:

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When a person studies economics for the first time, it is likely that
they will not encounter "crazy" equations that go beyond basic
mathematics. There is a lot of content to learn the various conceptual
definitions such as price, supply, demand, costs, profit, etc., in
addition to the various market structures.

As you delve deeper into the subject, you realize there is more to it
than just simplistic theories and newspaper chatter. So, what would be
the best way to explain the concepts of price, quantity of product sold
and production cost without referring to a single example without using
mathematics?

This *paper*:

> *KATZNER, Donald W. [Why mathematics in
> economics?](https://www.jstor.org/stable/4538849?seq=1). Journal of
> Post Keynesian Economics, v. 25, n. 4, p. 561-574, 2003.*

makes a very convincing defense of the use of mathematics in economic
science.

Although economics is technically recognized as a social science,
students who embark on a "nebulous" adventure (undergraduate course) in
this field receive (or should receive) a solid foundation in
mathematics. Because determining how scarce resources can be reallocated
requires a minimum understanding of mathematics, to calculate what the
distribution cost will be and evaluate (quantitatively) among other
measures. Thus, the field of economics is full of mathematical equations
and applications.

What is learned in teaching economics are mainly linear algebra,
calculus and statistics. These are the basis for achieving the infamous
econometrics. In algebra it is taught about total cost and total
revenue. In calculus the objective is to find the derivatives of
indifference and utility curves, profit maximization curves, cost
minimization and growth models.

In statistics, economists learn about predictive models and how to
determine how likely a certain event is to occur. Econometrics, for some
peculiar reasons, is called *"economentira"* for the use of models in
which the final objective is to estimate and predict a certain variable.

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As you progress through related topics, you will find examples such as
market demand curves (sum of several individual demand curves) or
changes in the supply and price of a *commodity* or calculating the
price elasticity of a commodity. consumption, each concept is validated
using mathematics. Definitely, a mathematical and statistical approach
is needed to have clarity when we arrive at the long-awaited "solution"
to the problems proposed to professionals in this area.

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data-gallery="quarto-lightbox-gallery-2"
data-glightbox="description: .lightbox-desc-2"
title="A typical review for the basic econometrics final exam"><img
src="https://hcostax.com/blog/maths_economics/img/econometria.jpg"
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alt="A typical review for the basic econometrics final exam" /></a></p>
<figcaption>A typical review for the basic econometrics final
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It has been noted that in the 19th century mathematics was considered as
a means of achieving truth; (rational) logic made it imperative to use
mathematics to prove any theorems. Many problems posed in economics are
therefore motivated to be solved by mathematics. Have these problems
really been solved?

Analyzes and studies carried out in the field of applied economics help
to explain the interdependent relationship between different variables.
An example is trying to explain what causes an increase in the price of
a product, such as the price of beef, or an increase in the unemployment
rate, or even a drop in inflation and a reduction in the basic interest
rate. Mathematical functions are used as a logical tool through
**models** from which these phenomena of everyday life can become more
understandable.

In fact, there is an exhaustive discussion about the importance of
relevant applied work and the uses of these metrics in economic science.
It is interesting to know that several economists have been awarded the
[Nobel
Prize](https://pt.wikipedia.org/wiki/Pr%C3%A9mio_de_Ci%C3%AAncias_Econ%C3%B3micas_em_Mem%C3%B3ria_de_Alfred_Nobel)
for applying mathematics/statistics to economics, including the first
awarded in 1969 to [Ragnar Frisch and
JanTinbergen](https://www.jstor.org/stable/1402316?seq=1). The most
interesting thing is that [Leonid
Kantorovich](https://pt.wikipedia.org/wiki/Leonid_Kantorovich) he won a
Nobel Prize in 1975 in economics for his contribution to the theory of
optimal resource utilization and he was a mathematician!

Many students who are looking to pursue a career in economics are
advised to take a Mathematics course, as applied studies are covered in
mathematics. The use of mathematical models and applications in this
area has been notable in the last two decades.

[Economics --- the science that stopped being
dark](https://valor.globo.com/eu-e/noticia/2012/10/23/como-a-teoria-economica-deixou-de-ser-uma-ciencia-sombria.ghtml)(In
Brazilian Portuguese) , with advances in [Alfred
Marshall](https://pt.wikipedia.org/wiki/Alfred_Marshall), with the
well-known marginalist revolt that embraced the use of mathematics as an
integral part of the economy, now more intensive than ever. Mathematics
plays the main role in many sciences like physics, chemistry, etc. And
it's really the backbone of the modern economy.

Mathematics in economics is an important tool in decision making.
Economists are hired by companies or governments to investigate and
estimate the risk or likely outcomes of an event. Economists who work
for companies in the financial market make mathematical calculations
(models) to assess whether the risk of investing in a certain asset
outweighs its potential benefits.

Economists use their mathematical "skills" to find ways to reallocate
money, even in counterintuitive ways. Using a profit-maximization chart,
economists can advise a venue to sell only 75% of available tickets,
rather than 100%, a strategy to maximize its profit. If the company
lowers ticket prices to attract new concert-goers and fill the stadium
to capacity, it could make less money than selling just 75% of the
tickets at a much higher price.

Economists also use mathematics to determine the long-term success of a
business, even when some factors are unpredictable. For example, an
economist working for an airline uses forecasting based on econometric
models to determine the price of fuel for two months ahead. The company
uses this data to block fuel prices or to protect the fuel, the famous
*"hedge"*. Bijan Vasigh, author of the book ["Introduction to Air
Transport
Economics"](https://www.amazon.com/Introduction-Air-Transport-Economics-Applications/dp/1409454878),
explains that the [Southwest Airlines](https://www.southwest.com) gained
a financial advantage over other operators due to its fuel hedging
strategy.

However, not everything is rosy, much less a bed of roses, there are
limitations to what can be done using econometric models in the economy.
Economists perform mathematical calculations with imperfect information.
Their economic models are useless in times of natural disasters, union
strikes or any other catastrophic event. Furthermore, mathematics rarely
helps economists predict irrational human behavior. A fundamental
assumption of economics is that humans act rationally. However, humans
often make irrational decisions based on choices and preferences, or
even pure fear or love. These two factors cannot be accounted for in an
economic model.

But there are already some techniques, including in the field of
*Machine Learning* that try to solve such problems. But that is the
subject of another post that I will make soon.

But the potential of these methods is recognized and therefore extremely
useful, and economists are reviewing the way calculations are carried
out to account for intangible effects, such as pollution. Mathematical
models are necessarily based on simplifying assumptions, so they are not
likely to be perfectly realistic. Mathematical models also lack the
nuances that can be found in narrative models. The point is that
mathematics is a tool, but it is not the only tool or even the best tool
that economists should use.

So, what is your opinion regarding the use of mathematics and statistics
in economic science? Is it possible to think about economics without at
least mathematizing it?

Adapted from
[original](https://medium.com/the-empirical-mode/o-uso-da-matem%C3%A1tica-na-economia-6d6de2e39dab).

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## Citation {#citation .anchored .quarto-appendix-heading}

<div>

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For attribution, please cite this work as:
:::

::: {#ref-costa2018 .csl-entry .quarto-appendix-citeas}
Costa, Henrique. 2018. "The Mathematization of Economics." September 21,
2018. <https://doi.org/10.59350/tvp77-8gp37>.
:::

</div>
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In today’s post, I want to start a discussion about the use of mathematics and statistics in economics, and with this shocking sentence:  When a person studies economics for the first time, it is likely that they will not encounter “crazy” equations that go beyond basic mathematics.

The mathematization of Economics

[![](https://hcostax.com/blog/ceteris_paribus/feature.jpg){.img-fluid}](feature.jpg){.lightbox
gallery="quarto-lightbox-gallery-1"}

I will present here some personal reflections on a concept that is
considered very simple and perhaps common in economics, but which is
labeled as the height of ignorance for making an assumption that cannot
be observed in reality, but which in my view is a mistake. mistake. The
concept: *ceteris paribus*, or better said "the *ceteris paribus*
condition".

Well, have you ever tried to imagine the meaning of *ceteris paribus?*
The idea is somewhat simplistic, and means **"everything else is
constant"** or **"all other things remaining unchanged"**. Nothing new
on earth, because economists, students and enthusiasts know this
condition well, and learn in the academic world that in economic
analysis there is always this *ceteris paribus* thing.

Examining a fact under the condition that an effect **X**, *ceteris
paribus* had a cause **Y**, or better said, that a specific effect
occurs from an isolated cause without other potential causes interfering
or not have no involvement.

If you think about this statement in depth, this condition seems a bit
absurd, as in reality a specific effect never has an isolated cause, as
it is a static look at dynamic events. There are many criticisms about
this assumption, but most are based on a misinterpretation of the
*ceteris paribus* condition.

Understanding the literal meaning of the term does not make you an
expert user of it. It is a fact that observing or studying something and
having to say that if everything else is constant, it goes beyond the
idea that the results may be unrealistic. However, you need to abstract
to understand. Is it possible for this condition to happen? As? And when
does it occur?

If you want to carry out a methodologically in-depth study to understand
scientific applications, please consume **Chapter 2** of this
masterpiece:

> *Schlicht, E. (1985). [Isolation and Aggregation in
> Economics](https://epub.ub.uni-muenchen.de/3/1/schlicht_isolation.pdf).
> \[S.l.\]: Springer Verlag. ISBN 0-387-15254-7*.

To illustrate, I will simulate a situation and use an example where I
prepare my morning coffee, and so by assumption, I will sweeten it (as
sugar is not welcome in my coffee). So I have the following ingredients:
water, sugar, and 100% Arabica coffee powder (my favorite). We know that
to prepare coffee, roughly speaking, you just need to mix all the
ingredients. Of course, as long as certain ingredients are suitable for
this, as in the case of water, which must reach a preparation
temperature (considered ideal) close to 90°C, but there is always that
classic doubt: how much sugar would be ideal for sweetening? My coffee?

In econometric models there is a similar methodology: to estimate a
variable **Y** it is necessary to mix the "effects" of variables **X**,
as long as some variables **X** meet certain conditions, as there will
be moments in which it will be necessary to apply transformations to the
variables, changing from level to logarithmic, applying differences,
among others. As is the process of changing the water temperature.

To solve this problem, a common economist will say:

> Hmm, Depends!

But a Scientist will say:

> For an *ex-ante* analysis, it will be necessary to test hypotheses!

Firstly, we outline two hypotheses that 1 liter of coffee will be
prepared, and so 1 liter of water (at a temperature of 90°C), 4 spoons
of coffee powder (as I like strong coffee) are used, so we can say the
following :

- As an **alternative hypothesis**, the sugar value is zero, supposedly
  the presence of sugar in the drink is practically zero, so the drink
  "needs to be sweetened".

- As a **null hypothesis**, the sugar value is non-zero, where at least
  one spoon (or cube) of sugar is supposedly added, as we are curious
  about the positive marginal effects, so the drink is being sweetened.

We are interested in inferring about the **null hypothesis**, as it is
from there that we consider sweetening the drink, once the alternative
hypothesis occurs, simply apply the variable **sugar** (for a better fit
of the model ) until the drink is sweetened.

Now we can identify the marginal effects that the increase in sugar can
have on the drink, and a very curious irony is that we are here looking
for an optimization solution. Testing the sugar variation in order to
seek an optimal point of balance, that is, where the addition of sugar
can lead to a point of balance between sucrose and the acidity of the
coffee, making the drink sweetened to the consumer's taste.

Theoretically, you add a spoonful of sugar and try it; If it's not at
the desired point, you can add a little more and try again; and so on
until you reach the flavor you like most. In other words, after mixing
the ingredients, only the amount of sugar will be adjusted, keeping the
proportions or quantities of the other ingredients fixed. It is in this
"keeping fixed" that the *Ceteris Paribus* condition occurs, that is,
**"keeping all other things unchanged"**.

This is exactly what the *ceteris paribus* condition means: keeping some
variables fixed in their proportions and quantities or constants (in
this case, the water and coffee powder after mixing and infusing) and
changing only the sugar, to understand the effect that sugar has on the
variable **Y** (the coffee itself).

One of the first appearances of the use of this term in economics is
contained in the work of the 17th century economist Richard Cantillon,
with the title:

> *Cantillon, Richard. [Essays on the Nature of Commerce in
> General](https://books.google.com.br/books?id=J1ZPAWiGRucC&lpg=PP1&pg=PP1#v=onepage&q&f=false).
> Routledge, 2017*.

In economic science, this concept is widely used in models, mainly in
neoclassical theory, as it allows the interpretation of cause and effect
events in the real world in a representative way.

Imagine having to deal with the enormous and growing flow of information
that is generated every day, at all times? Everyone would go crazy!!!
So, economic theory simplifies the analysis so that it is possible to
find solutions to problems: it is like disregarding some information (or
considering that they are constant, that they do not change or do not
alter your analysis) and then analyze the effects of other information.

Do not think that this is absurd, or that it is unrealistic, if for any
moment this thought crossed your mind, please review it immediately, as
economic theory is made up of many, many observations, deductions and
tests of the events of cause and effect of the real world, and that is
why it is recognized as science today.

Another very interesting example in which I was able to observe the
effect of this condition is in the financial market, the theory of
portfolio diversification guarantees the reduction of the investor's
exposure to non-systemic risk, that is, disregarding non-systemic risk
and keeping it fixed close to null may be an effect of the *ceteris
paribus* condition, as the investor diversifies his investments to
protect himself from the fluctuation of such assets, trying to keep
non-systemic risk to the minimum possible, and when a correlation closer
to zero is achieved, he assumes that it is free of non-systemic risk and
thus alters its market positions based on systemic risks. There are so
many real examples that use this condition that it goes beyond
sweetening my coffee.

The condition *ceteris paribus* is present in our daily lives, in almost
everything it is possible to find it, but there will be skeptics who
will say: *"but in reality nothing remains fixed or constant"*, or even
*"that is part of the idea of general balance, and in general it is
unreal, because balance is not empirical"*, well, the real world is
dynamic, but in my humble opinion, the world has always been in a
natural balance, the dynamism of the real world is nothing more is than
equilibria interacting simultaneously, so therefore, the *ceteris
paribus* condition can make some real and palpable sense.

Finally, the *ceteris paribus* condition means that we can keep some
variables fixed or constant to analyze only what matters; This condition
is very useful for creating econometric models used to better calculate
and interpret real-world phenomena.

I hope I have fulfilled my mission of exploring the *ceteris paribus*
condition in a similar way for a better understanding. In the next
publications I will deal with models in economic science, to explain why
this science is so full of mathematical and statistical applications.

Adapted from
[original](https://medium.com/the-empirical-mode/a-condi%C3%A7%C3%A3o-ceteris-paribus-para-ado%C3%A7ar-meu-caf%C3%%20A9-7da9b9326604).

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Hey! 👋, did you find my work useful? Consider buying me a coffee ☕, by
clicking here 👇🏻
:::
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[![](https://img.buymeacoffee.com/button-api/?text=Buy%20me%20a%20coffee&emoji=&slug=hcostax&button_colour=5F7FFF&font_colour%20=ffffff&font_family=Cookie&outline_colour=000000&coffee_colour=FFDD00)](https://www.buymeacoffee.com/hcostax)
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:::::: {#quarto-citation .section .quarto-appendix-contents}
## Citation {#citation .anchored .quarto-appendix-heading}

<div>

::: {.quarto-appendix-secondary-label}
For attribution, please cite this work as:
:::

::: {#ref-costa2018 .csl-entry .quarto-appendix-citeas}
Costa, Henrique. 2018. "The Ceteris Paribus Condition." September 16,
2018. <https://doi.org/10.59350/jxf43-hc691>.
:::

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I will present here some personal reflections on a concept that is considered very simple and perhaps common in economics, but which is labeled as the height of ignorance for making an assumption that cannot be observed in reality, but which in my view is a mistake. mistake.

Postagens de Rogue Scholar

Can Economists Become Data Scientists?

The mathematization of Economics

The Ceteris Paribus Condition