Finance – Parts Per Billion

Logarithmic Harmony in Natural Chaos

Mathematics is one powerful tool to make sense out of randomness but bear in mind that not every randomness could be handled effectively with the mathematical tools we have at our disposal today. One of such tools called Benford’s Law proves that nature works in logarithmic growth and not in linear growth. The Benford’s law helps us to make sense of the natural randomness generated around us all the time. This is also one of the first-hand tools used by forensic accountants to detect possible financial frauds. It is one phenomenal part of mathematics which finds patterns in sheer chaos of the randomness of our existence.

Benford’s Law for natural datasets and financial fraud detection

People can find patterns in all kinds of random events. It is called apophenia. It is the tendency we humans have to find meaning in disconnected information.
Dan Chaon, American Novelist

Is There Any Meaning in Randomness?

We all understand that life without numbers is meaningless. Every single moment gazillions and gazillions of numbers are getting generated. Even when I am typing this and when you are reading this – some mathematical processing is happening in bits of the computer to make it happen. If we try to grasp/understand the quantity of numbers that are getting generated continuously, even the lifetime equivalent to the age of our Universe (13.7 billion) will fall short.

Mathematics can be attributed to an art of finding patterns based on certain set of reasoning. You have certain observations which are always true and you use these truths to establish the bigger truths. Psychologically we humans are tuned to pattern recognition, patterns bring in that predictability, predictability brings in safety because one has knowledge of future to certain extent which guarantees the higher chances of survival. So, larger understanding of mathematics in a way ensures better chances of survival per say. This is oversimplification, but you get the point.

Right from understanding the patterns in the cycles of days and nights, summers, and winters till the patterns in movements of the celestial bodies, the vibration of atoms, we have had many breakthroughs in the “pattern recognition”. If one is successful enough to develop a structured and objective reasoning behind such patterns, then predicting the fate of any process happening (and would be happening) which follows that pattern is a piece of cake. Thus, the power to see the patterns in the randomness is kind of a superpower that we humans possess. It’s like a crude version of mini-time machine.

Randomness inherently means that it is difficult to make any sense of the given condition, we cannot predict it effectively. Mathematics is one powerful tool to make sense out of randomness but bear in mind that not every randomness could be handled effectively with the mathematical tools we have at our disposal today. Mathematics is still evolving and will continue to evolve and there is not end to this evolution – we will never know everything that is there to know. (it’s not a feeling rather it is proved by Gödel’s incompleteness theorem.)

You must also appreciate that to see the patterns in any given randomness, one needs to create a totally different perspective. Once this perspective is developed then it no longer remains random. So, every randomness is random until we don’t have a different perspective about it.

So, is there any way to have a perspective on the gazillions of the numbers getting generated around us during transactions, interactions, transformations?

The answer is Yes! Definitely, there is a pattern in this randomness!!

Today we will be seeing that pattern in detail.

Natural Series – Real Life Data

Take your account statement for an example. You will see all your transactions, debit amount, credit amount, current balance in the account. There is no way to make sense out of how the numbers that are generated, the only logic behind those numbers in account statement is that you paid someone certain amount and someone paid you certain amount. It is just net balance of those transactions. You had certain urgency someday that is why you spent certain amount on that day, you once had craving for that cake hence you bought that cake, you were rooting for that concert ticket hence you paid for that ticket, on one bad day you faced certain emergency and had to pay the bills to sort things out. Similarly, you did your job/ work hence you got compensated for those tasks – someone paid you for that, you saved some funds in deposits and hence that interest was paid to you, you sold some stocks hence that value was paid to you.

The reason to explain this example to such details is to clarify that even though you have control over your funds, you actually cannot control every penny in your account to that exact number that you desire. This is an example of natural data series. Even though you have full control over your transactions, how you account will turn out is driven by certain fundamental rules of debit/ credit and interest. The interactions of these accounting phenomenon are so intertwined that ultimately it becomes difficult to predict down to every last penny.

Rainfall all around the Earth is very difficult to predict to its highest precision due to many intermingling and unpredictable events in nature. So, by default finding trend in the average rainfall happened in given set of places is difficult. But we deep down know that if we know certain things about rainfall in given regions we can make better predictions about other regions in a better way, because there are certain fundamental predictable laws which govern the rainfall.

The GDP of the nations (if reported transparently) is also very difficult to pin down to exact number, we always have an estimate, because there are many factors which affect that final number, same goes for the population, we can only predict how it would grow but it is difficult to pin point the number.

These are all examples of real life data points which are generated randomly during natural activities, natural transactions. We know the reason for these numbers but as the factors involved are so many it is very difficult to find the pattern in this randomness.

I Lied – There is A Pattern in The Natural Randomness!

What if I told you that there is certain trend and reference to the randomness of the numbers generated “naturally”? Be cautious – I am not saying that I can predict the market trend of certain stocks; I am saying that the numbers generated in any natural processes have preference – the pattern is not predictive rather it only reveals when you have certain bunch of data already at hand – it is retrospective.

Even though it is retrospective, it can help us to identify what was manipulated, whether someone tried to tamper with the natural flow of the process, whether there was a mechanical/ instrument bias in data generation, whether there was any human bias in the data generation?

Logarithm and Newcomb

Simon Newcomb (1835-1909) a Canadian-American astronomer once realized that his colleagues are using the initial pages of log table more than the other pages. The starting pages of log tables were more soiled, used than the later pages.

Log tables were instrumental in number crunching before the invention of any type of calculators. The log tables start with 10 and end in 99.

Newcomb felt that the people using log tables for their calculations have more 1’s in their datasets repetitively in early digits that is why the initial pages where the numbers start with 1 are used more. He also knew that the numbers used in such astronomical calculations are the numbers available naturally. These numbers are not generated out randomly, they signify certain quantities attributed to the things available in nature (like diameter of a planet, distance between stars, intensity of light, radius of curvature of certain planet’s orbit). These were not some “cooked up” numbers, even though they were random but they had natural reason to exist in a way.

He published an article about this but it went unnoticed as there was no way to justify this in a mathematical way. His publication lacked that mathematical rigor to justify his intuition.

Newcomb wrote:

“That the ten digits do not occur with equal frequency must be evident to anyone making much use of logarithmic tables, and noticing how much faster the first one wears out than the last ones.”

On superficial inquiry, anyone would feel that this observation is biased. It seemed counterintuitive, also Newcomb just reported the observation and did not explain in detail why it would happen. So, this observation went underground with the flow of time.

Frank Benford and The Law of Anomalous Numbers

Question – for a big enough dataset, how frequently any number would appear in first place? What is the probability of numbers from 1 to 9 to be the leading digit in given dataset?

Intuitively, one would think that any number can happen to be in the leading place for given dataset. If the dataset becomes large enough, all nine numbers will have equal chance to be in first place.

Frank Benford during his tenure in General Electric as a physicist made same observation about the log table as did Newcomb before him. But this time Frank traced back the experiments and hence the datasets from these experiments for which the log table was used and also some other data sets from magazines. He compiled some 20,000 data points from completely unrelated experiments and found one unique pattern!

He realized that even though our intuition says that any number from 1 to 9 could appear as the leading digit with equal chance, “natural data” does not accept that equal chance. The term “Natural data” refers to the data representing any quantifiable attribution of real phenomenon, object around us, it is not a random number created purposefully or mechanically; it has some origin in nature however random it may seem.

Frank Benford thus discovered an anomaly in natural datasets that their leading digit is more 1 or two than the remaining ones (3,4,5,6,7,8,9). In simple words, you will see 1 as leading digit more often in the natural datasets than the rest of the numbers. As we go on with other numbers the chances that other numbers will be frequent in leading position are very less.

In simple words, any naturally occurring entity will have more frequent 1’s in its leading digits that the rest numbers.

Here is the sample of the datasets Frank Benford used to find this pattern:

Dataset used by Frank Benford in his 1938 paper “The Law of Anomalous Numbers”

So, according to Benford’s observations for any given “natural dataset” the chance of 1 being the leading digit (the first digit of the number) is almost 30%. 30% of the digits in given natural dataset will start with 1 and as we go on the chances of other numbers to appear frequent drop drastically. Meaning that very few number in given natural data set will start with 7,8,9.

Thus, the statement of Benford’s law is given as:

The frequency of the first digit in a populations’ numbers decreases with the increasing value of the number in the first digit.

Simply explained, as we go on from 1 to 9 as first digit in given dataset, the possibility of their reappearance goes on reducing.

1 will be the most repeated as the first number then 2 will be frequent but not more than 1 and the frequency of reappearance will reduce and flatten out till 9. 9 will rarely be seen as the leading digit.

The reason why this behavior is called as Benford’s Law (and not Newcomb’s Law) is due to the mathematical equation that Benford established.

Where, P(d) is the probability that a number starts with digit d. Digit d could be anything 1,2,3,4,5,6,8 or 9.

If we see the real-life examples, you will instantly realize how counterintuitive this law is and still nature chooses to follow it.

Here are some examples:

I have also attached an excel sheet for complete datasets and to demonstrate how simply one can calculate and verify Benford’s law.

Population of countries in the world –

The dataset contains population of 234 regions in the world. And you will see that 1 appears the most as first digit in this dataset. Most of the population numbers start with 1 (70 times out of 234) and rarely with 9 (9 times out of 234)

Country-wise average precipitation –

The dataset contains average rainfall from 146 countries in the world. Again, same pattern emerges.

Country wise Gross Domestic Product –

The dataset contains 177 countries’ GDP in USD. See the probability yourself:

Country-wise CO₂emissions:

The data contains 177 entries

Country wise Covid cases:

Here is one more interesting example:

The quarterly revenue of Microsoft since its listing also shows pattern of Benford’s Law!

To generalize we can find the trend of all these data points by averaging as follows:

This is exactly how Benford avearaged his data points to establish a generalized equation.

Theoretical Benford fit is calculated using the Benford equation expressed earlier.

So here is the relationship graphically:

Now, you will appreciate the beauty of Benford’s law and despite seeming counterintuitive, it proves how seemingly random natural dataset has preferences.

Benford’s Law in Fraud Detection

In his 1938 paper “The Law of Anomalous Numbers” Frank Benford beautifully showed the pattern that natural datasets prefer but he did not identify any uses of this phenomena.

1970 – Hal Varian, a Professor in University of California Berkely School of Information explained that this law could be used to detect possible fraud in any presented socioeconomic information.

1988 – Ted Hill, an American mathematician found out that people cannot cook up some numbers and still stick to the Benford’s Law.

When people try to cook up some numbers in big data sets, they reflect certain biases to certain numbers, however random number they may put in the entries there is a reflection of their preference to certain numbers. Forensic accountants are well aware of this fact.

The scene where Christian pinpoints the finance fraud [Warner Bros. – The Accountant (2016)]

1992 – Mark Nigrini, a South African chartered accountant published how Benford’s law could be used for fraud detection in his thesis.

Benford’s Law is allowed as a proof to demonstrate accounts fraud in US courts at all levels and is also used internationally to prove finance frauds.

It is very important to point the human factor, psychological factor of a person who is committing such numbers fraud. People do not naturally assume that some digits occur more frequently while cooking up numbers. Even when we would start generating random numbers in our mind, our subconscious preference to certain numbers gives a pattern. Larger the data size more it will lean to Benford’s behavior and easier will be the fraud detection.

Now, I pose one question here!

If the fraudster understands that there is such thing like Benford’s Law, then wouldn’t he cook up numbers which seem to follow the Benford’s Law? (Don’t doubt my intentions, I am just like a cop thinking like thieves to anticipate their next move!!!)

So, the answer to this doubt is hopeful!

The data generated in account statements is so huge and has multiple magnitudes that it is very difficult for a human mind to cook up numbers artificially and evade from detection.

Also, forensic accountants have showed that Benford’s Law is a partially negative rule; this means that if the law is not followed then it is possible that the dataset was tampered/ manipulated but conversely if the data set fits exactly / snuggly with the Benford’s law then also there is a chance that the data was tampered. Someone made sure that the cooked-up data would fit the Benford’s Law to avoid doubts!

Limitations of Benford’s Law

You must appreciate that nature has its ways to prefer certain digits in its creations. Random numbers generated by computer do not follow Benford’s Law thereby showing their artificiality.

Wherever there is natural dataset, the Benford’ Law will hold true.

1961 – Roger Pinkham established one important observation for any natural dataset thereby Benford’s Law. Pinkham said that for any law to demonstrate the behavior of natural dataset, it must be independent of scale. Meaning that any law showing nature’s pattern must be scale invariant.

In really simple words, if I change the units of given natural dataset, the Benford law will still hold true. If given account transactions in US Dollars for which Benford’s Law is holding true, the same money expressed in Indian Rupees will still abide to the Benford’s Law. Converting Dollars to Rupees is scaling the dataset. That is exactly why Benford’s Law is really robust!

After understanding all these features of Benford’s Law, one must think it like a weapon which holds enormous power! So, let us have some clarity on where it fails.

Benford’s Law is reflected in large datasets. Few entries in a data series will rarely show Benford’s Law. Not just large dataset but the bigger order of magnitude must also be there to be able to apply Benford’s Law effectively.
The data must describe same object. Meaning that the dataset should be of one feature like debit only dataset, credit only dataset, number of unemployed people per 1000 people in population. Mixture of datapoints will not reflect fit to Benford’s Law.
There should not be inherently defined upper and lower bound to the dataset. For example, 1 million datapoints of height of people will not follow Benford’s Law, because human heights do not vary drastically, very few people are exceptionally tall or short. This, also means that any dataset which follows Normal Distribution (Bell Curve behavior) will not follow Benford’s Law.
The numbers should not be defined with certain conscious rules like mobile numbers which compulsorily start with 7,8, or 9; like number plates restricted 4, 8,12 digits only.
Benford’s Law will never pinpoint where exactly fraud has happened. There will always be need for in depth investigation to locate the event and location of the fraud. Benford’s Law only ensures that the big picture is holding true.

Hence, the examples I presented earlier to show the beauty of Benford’s Law are purposefully selected to not have these limitations. These datasets have not bounds, the order of magnitude of data is big, range is really wide compared to the number of observations.

Now, if I try to implement the Benford’s Law to the yearly revenue of Microsoft it reflects something like this:

Don’t freak out as the data does not fully stick to the Benford’s Law, rather notice that for the same time window if my number of datapoints are reduced, the dataset tends to deviate from Benford’ Law theoretically. Please also note that 1 is still appearing as the leading digit very frequently, so good news for MICROSOFT stock holders!!!

In same way, if you see the data points for global average temperatures (in Kelvin) country-wise it will not fit the Benford’s Law; because there is no drastic variation in average temperatures in any given region.

See there are 205 datapoints – big enough, but the temperatures are bound to a narrow range. Order of magnitude is small. Notice that it doesn’t matter if I express temperature in degree Celsius of in Kelvins as Benford’s Law is independent of scale.

Nature Builds Through Compounded Growth, Not Through Linear Growth!

Once you get the hold of Benford’s law, you will appreciate how nature decides its ways of working and creating. The Logarithmic law given by Frank Benford is a special case of compounded growth (formula of compound interest). Even though we are taught growth of numbers in a periodic and linear ways we are masked from the logarithmic nature of the reality. Frank Benford in the conclusion of his 1937 paper mentions that our perception of light, sound is always in logarithmic scale. (any sound engineer or any lighting engineer know this by default) The growth of human population, growth of bacteria, spread of Covid follow this exponential growth. The Fibonacci sequence is an exponential growth series which is observed to be at the heart of nature’s creation. That is why any artificial data set won’t fully stick to logarithmic growth behavior. (You can use this against machine warfare in future!) This also strengthens the belief that nature thinks in mathematics. Despite seemingly random chaos, it holds certain predictive pattern in its heart. Benford’s Law thus is an epitome of nature’s artistic ability to hold harmony in chaos!

You can download this excel file to understand how Benford’s law can be validated in simple excel sheet:

benford-partsperbillion Download

References and further reading:

Cover image – Wassily Kandinsky’s Yellow Point 1924
The Law of Anomalous Numbers, Frank Benford, (1938), Proceedings of the American Philosophical Society
On the Distribution of First Significant Digits, RS Pinkham (1961), The Annals of Mathematical Statistics
What Is Benford’s Law? Why This Unexpected Pattern of Numbers Is Everywhere, Jack Murtagh, Scientific American
Using Excel and Benford’s Law to detect fraud, J. Carlton Collins, CPA, Journal of Accountancy
Benford’s Law, Adrian Jamain, DJ Hand, Maryse Bйeguin, (2001), Imperial College London
data source – Microsoft revenue – stockanalysis.com
data source – Population – worldometers.info
data source – Covid cases – tradingeconomics.com
data source – GDP- worldometers.info
data source – CO2 emissions – worldometers.info
data source – unemployment – tradingeconomics.com
data source – temperature – tradingeconomics.com
data source – precipitation – tradingeconomics.com

Entrepreneurship and Poverty

We are surrounded by many entrepreneurs which go unnoticed and have nothing to do with the keywords like technology, unicorn, angel investors. A high chunk of these unnoticed entrepreneurs are poor entrepreneurs, almost a billion around the world. Nobel laureate economists Abhijit Banerjee and Esther Duflo studied such poor entrepreneurs which has created deep insights and answered many questions. Providing supporting capital – microcredit to such poor entrepreneurs is not the final answer to this riddle.

Paying close attention to the larger fraction of the poor entrepreneurs

Monthly Revenue of a ‘Chai-wala’

It is very common discussion among group of youngsters to roughly estimate revenue of their “Snacks n’ Tea” seller while enjoying that short break. The discussion ends when the earnings estimate from that seller’s business reaches to a figure which is far bigger than what these “highly qualified” youngsters actually earn thereby inspiring them to think about pursuing their own business, start-up. What actually happens after such short surge of inspiration is also a common knowledge. Very few of such people actually work on entrepreneurship, their business idea and again very few of these truly taste the success. Social media, mainstream media have also positively affected and boosted the startup mentality, entrepreneur mentality among the youngsters through TV-series, reality shows, success stories, popular talk shows, podcasts and nonetheless video platforms like YouTube. The “F.I.R.E. culture” (Financially independent, Retire early) is also one wave of thought which inspires such entrepreneurs to create something of value, turn it into a business and sell it at higher valuation to gain financial independence early in life. (Although, FIRE is not limited to financial freedom through entrepreneurship only). Following their passion and working over it to create a start-up and then becoming a wealthy person is also one famous new career route for today’s youngsters.

In short, for our generation, entrepreneurship holds the key to financial independence thereby key to the freedom (materialistic freedom to be more specific) – life living on their own terms, without any terms and conditions.

When looked through “the pop-cultural” lens towards entrepreneurship one will see all the glamour, money, popularity, angel investors, “unicorn startup” funds and success stories. In reality there are very few practical examples in these enterprises which successfully fit to all such criterion, which really have created value in the society; most of them are actually just publicized bubbles rather black holes sucking in the attention, time and money of the investors.

The Reality of Entrepreneurship Around the World

Start-ups represent only the early developmental part of an entrepreneurship. Even though they represent such an early and small part of the concept of entrepreneurship, start-up stands as the biggest lamp, biggest fire attracting the youth like moths.

Here are some interesting facts:

9 out of 10 startups fail

7.5 out of 10 venture-backed startups fail

2 out of 10 new businesses fail in the first year of operations

Only 1% of startups become unicorn firms like Uber, Airbnb, Slack, Stripe, and Docker

The success percentage for first-time founders is 18%

20% start-ups fail before the end of their 1^st year, and almost 70% start-ups end by their 10^th year.

These facts are not presented to demean the value of stat-ups or to negatively criticize start-ups thereby idea of entrepreneurship (although there are some people who also try to capitalize their failure in both the good and bad ways). When you will look at the complementary positive data on start-ups you will realize that the successful start-ups even being low in numbers created value to the society in totally different ways, they changed the ways of working and doing things through the exploitation of technology.

The glamour while portraying the concept of entrepreneurship is actually overshadowing the key idea behind it which is “ingenuity”.

Poor Entrepreneurs

What is the definition of an entrepreneur? The dictionary definition goes like this- “a person who sets up a business or businesses, taking on financial risks in the hope of profit.” Literally, a person who runs an enterprise. Now look at the pictures above, can you tell which one of these is an entrepreneur?

This will make us realize that how the glamour built around the word entrepreneur is actually a mirage. The basic idea in entrepreneurship is the risk taking for the gaining profit. We are surrounded by such small entrepreneurs in our day-to-day life, most of these are poor entrepreneurs. World renowned Nobel laureate economists Abhijit Banerjee and Esther Duflo have contributed to uncover the reality of such poor entrepreneurs and many questions associated with such poverty.

Why should one be interested in poor entrepreneurs?

According to the data collected by Abhijit Banerjee and his team roughly 12% of the population in rich countries calls themselves as self-employed i.e., entrepreneurs. The interesting thing is that the poor countries have far higher percentage of self-employed people. Nearly 70% people call themselves entrepreneurs – self-employed in poor countries. These are the people who are mostly single person entrepreneurs like tailors, bricklayers, auto-drivers, street-vendors, shopkeepers.

“…most income groups in poor countries seem to be more entrepreneurial than their counterparts in the developed world-the poor no less so than others… ”
Abhijit Banerjee and Esther Duflo, Poor Economics – rethinking poverty and the ways to end it

Looks like bigger chunk of the entrepreneurial population of the world is not really glamorous and full of revenues, capital and resources. The intention to focus on this information is not to degrade entrepreneurship, rather it is to understand why the percentage of entrepreneurship is huge in poor countries where availability of resources and capital is already hitting rock bottom low? How do they manage such ventures in low margins? Do these entrepreneurial ventures bring them out of the poverty? If yes then, how? If not then why?

If entrepreneurship is supposed to give people freedom to operate on their own conditions, freedom to be their own boss, freedom to take control over their own lives, bring their ideas into the society then why poor countries where the entrepreneurial fraction is huge are not coming out of poverty? Why most of such poor entrepreneurs remain poor even after embarking on the journey of self-employment?

Trust me the answer is not related to ‘lower rates of returns’ only!

Ingenuity of the Poor Entrepreneurs

Let us understand the challenges faced by the poor entrepreneurs listed as below:

Being poor, they are inherently low on capital (obviously)
They have low or no access to formal financing institutions like banks, insurance companies
As they have no access to formal finance, they approach local moneylenders and borrow with high rates of interest
They have very low risk-taking capacity because any investment other than that for sustenance is a survival challenge
They have very crude social support in terms of materialistic and emotional levels. They are surrounded by people having same difficult lives. They rarely have good connections with people who will trust them, people who will have access to better conditions capital-wise or relation-wise

Even after having these challenges, the fraction of entrepreneurs in poor countries is surprisingly high. How is this possible?

As Abhijit Banerjee explains, the poor entrepreneurs have clever ideas to run their businesses even at low capital. The unavailability of resources, material/ capital means forces them to find out new creative ways to make living. You will see many such innovative entrepreneurs around who try to make living by using some really interesting ideas e.g., the human hair collectors roaming around town to exchange with utensils/toys, the scrap collectors who collect specific types of waste only and sell them to bigger scrap dealers in bulk, there are some dust collectors in the gold markets of many cities in India where poor people collect road dust around the gold shops and try to extract tiny amount of gold from such collected dust to sell it.

But how many of these innovative, creative and ventures with true ingenuity actually turn into a unicorn or a big company? In simple words, one knows how costly are the hair extensions/ wigs are then why the hair collectors are not getting rich with their business? If gold is that precious then why these dust collectors are not getting rich with this gold dust collection ventures?

This is where the insights created by Abhijit Banerjee play a very vital role. In his book “Poor Economics – rethinking poverty and ways to end it” co-authored by Esther Duflo, he has given very important insights into the world of poor people, the challenges they face and ways to uplift them.

Let us deep dive into the key concepts to understand the economics of such entrepreneurs.

Representation of the Poverty

Figure 1 The S-shaped curve and the poverty trap
Source: Poor Economics – rethinking poverty and the ways to end it by Abhijit Banerjee and Esther Duflo

Economists use the diagram shown above to indicate the relation between income of today and the income a person will earn in the future. You will see an S -shaped curve forming. The red zone indicates the poverty trap zone where a poor person starts from A1 earns a meager amount which is not enough to sustain making the net income negative thereby proceeding to A2 which is backward directed/ decline in income. This reduced income restricts his/her freedom to choose (as the words go “beggars cannot be choosers”), risk-taking ability, reduction in available capital thereby scarcity of capital disposable to meet the daily basic requirements. So, the ventures in which poor people are engaged are down-valuing ventures according to this representation – which is used to represent “The Poverty Trap”. For those who think that the ventures of poor people always end up in losses thereby degrading their existing states, this curve in red zone represents that vicious cycle.

Most of the economists think that poverty is not a vicious cycle. By providing minimum enough capital/ resources to the lowermost group, their lives can be kick-started where the ventures will give net positive incomes, thereby gradually increasing their income over the time. That is why the world around us is explained by blue shaded part of the diagram, known as inverted L-shaped curve.

Figure 2 The inverted L-shaped curve
Source: Poor Economics – rethinking poverty and the ways to end it by Abhijit Banerjee and Esther Duflo

Please note one interesting detail in this diagram which we will bring further in our discussion. The initial slope of the curve is steep indicating substantial valuation increase in income but as the curve proceeds slope of the curve ends into flat thereby indicating less or no increase in valuation of the income over the longer period.

In very simple words, a venture can only sustain over the time if there is some net gain over the time (always remaining net positive, even if it becomes smaller and stagnant over time). Very few people and actually no one would engage in a venture where they see their future valuation, future earnings dropping over the long-time horizon. That why most of the economist accept Figure 2 to represent the incomes of today and tomorrow for anyone.

Asking the Right Questions

Now that we have realized that it will take very small amount of effort and capital to uplift the poor entrepreneurs why doesn’t that help them immediately? Abhijit Banerjee in his studies asked some important questions which reveal why just giving poor enough money won’t solve the complete problem. Abhijit Banerjee clarifies that it is the inherent nature of the enterprises/ businesses, societal conditions and even the mindset of the poor entrepreneurs that makes them stagnant in their ventures. Even if they are running their small businesses successfully, they will always make just enough to sustain in long time horizon, very few will be the outliers which come out of this stagnancy.

Abhijit Banerjee pointed out that most of the poor entrepreneurs repay their loans on high interest rates. The high returns rates are attributed to the lending from informal financiers like local money lenders, relatives. If poor entrepreneurs are successfully repaying such high interest loans while sustaining through the business, then that means that their overall rate/ fraction of earning for the capital invested is also very high.

So, why don’t they become relatively wealthy even after running business with high rate of overall returns?

Here we can take support of the inverted L-shaped curve for poor entrepreneurs and build on that further.

Figure 3 Diminishing marginal returns in poor enterprises
Figure created from the explanation in the book Poor Economics – rethinking poverty and the ways to end it by Abhijit Banerjee and Esther Duflo

Abhijit Banerjee explained the reasons for the stagnancy in poor enterprises in practical ways based on his field research. He explains the important behavior of marginal returns in terms of the poor enterprises. Marginal returns are the what left after an entrepreneur pays off everything – like payment on tools, payment of the wages to the workers, payment of the things bought to sell. Marginal return is take-home money after the business is done.

Now let us see the inverted L-shaped curve in figure 3 for poor enterprises. At the start of the business the marginal returns (shown as the height of the vertical blue arrow) are very high for the extra capital invested (shown as the length of the black horizontal arrow). The early investments in the business yields higher returns – higher marginal returns.

But, as the curve proceeds, due to the inherent nature of the businesses poor entrepreneurs are involved in as the capital investment goes on increasing, for every unit increase in such investment the marginal returns go on reducing and diminish further.

You can see in the figure 3, there are four different instances of extra capital investment in the poor enterprises. The L-shaped curve increases rapidly at early investment stage but as the capital investment goes on increasing the curve quickly flattens out, indicating the stagnancy.

In poor enterprises any new unit capital investment will give diminished marginal returns over the time

This behavior can be explained by the example of local fruits and vegetable vendors. First a person starts out with very few 2 or 3 vegetables (potato, tomato, onions for example). Being the commodity vegetables, they are sold very easily, fast and margins are also pretty good for the amount invested to buy them in wholesale. So, with those good returns he/she now buys different vegetables and now provide more options to his/ her customers. Now you will realize that not everyone buys every vegetable he/she has to offer, the sell of potato, tomato, onions may still remain good. But in order to expand he/she cannot depend on selling those only, and as he/ she expands into new varieties there comes the uncertainty of not everyone buying it. Perishable nature of these products is also one problem over which he/she has no control. The overall return may increase by incorporating more variety of items or by buying a cart to access many customers but for every new investment further done to grow this business, the guarantee of higher returns is very low.

So, the vegetable/ fruit vendor realizes this at a stage in his/her business that buying only those items which would sell, items which will not perish immediately with limited customer accessibility through cart is the only option to survive. You have to understand the limitations created by the nature of the businesses poor entrepreneurs are invested in.

That is exactly why only giving money to poor entrepreneurs won’t bring them out of the poverty. The businesses they can perform stagnate very rapidly.

Now, someone should ask the question for the case of the vegetable/ fruit vendor.

The questions could be asked as follows,

The vendor should buy a vehicle so that he will contact more customers, why doesn’t he / she do so?
The vendor should go to the wholesale market to buy the vegetables and fruits even at low rates to increase his margins, what stops him/ her?
The vendor should rent a place in cold storage to maintain his items fresh till they are sold to the end customer, what is the hurdle?

Now, let us assume ourselves as this vendor and try to answer these questions.

If the sell is stagnant even with a cart, why should one put exceedingly high amount in a vehicle purchase. This will be a big capital step. As the accessibility to formal lending is difficult, it brings capital in but the returns will be very low due to the borrowing at higher rates of interest.
In order to buy at wholesale low rates connections with the wholesale tycoons are vital. Such connections are based on mutual benefits which the poor entrepreneurs hardly have access to.
Cold storage rentals are significantly high for the amounts they earn so that goes there.

You must understand that these are not some contrived examples created to prove certain points. These are real life challenges and questions faced by poor entrepreneurs. It is only because of such challenges the poor entrepreneurs have that creative mindset, low cost, less capital-intensive problem-solving mindset. This also the reason economists found that poor entrepreneurs have very low number of people involved per business, they cannot afford to employ others due to the stagnancy.

As the study done by Abhijit Banerjee indicates, even if you provide some extra marginal income to the poor entrepreneurs so that they can access such options where extra capital is required, they will still choose to not invest that extra amount in the business because they know that for that extra investment the returns will not be that high over the longer period. (Abhijit Banerjee experimented with such extra capital provisions to poor entrepreneurs in Sri Lanka through lottery system, these entrepreneurs chose to invest that extra money in their livelihoods instead of businesses)

The Big Gap to Fill

Now you should understand that even when extra capital is provided, that extra capital definitely won’t go into the growth of the poor enterprises. The question now comes that why poor entrepreneurs don’t have wide mindset? Why can’t they think big? Looks like the horizons and the mindset of poor entrepreneurs are so narrow that they are scared of risk taking. For the exact reasons the micro-financing institutions have tried to disseminate finance education, entrepreneurial education to the poor entrepreneur they lent money. But economists found that it is the inherent nature of the enterprises that poor can and are involved in, which makes them to think so.

Abhijit Banerjee here clarifies what exactly is the difference between the poor entrepreneurs and the rich entrepreneurs. For that let us look at the figure 4

Figure 4 Combining technologies and S-shaped curve of entrepreneurship
Source: Poor Economics – rethinking poverty and the ways to end it by Abhijit Banerjee and Esther Duflo

You must appreciate the beauty with which Abhijit Banerjee has explained the difference between poor and rich entrepreneurs. Any incorporation of production technology in an enterprise will improve the productivity. Buying machinery, tools, infrastructures can largely boost the business performance. This boost due to production technology is shown as curve QR.

What does the curve OP represent?

As you have already seen, curve OP starts with no to less capital investment and flatten out immediately. It is the curve of poor entrepreneurship.

Now you must understand that in order to gain marginally/ exceptionally high returns one needs to start with high up-front capital in hand (Indicated as capital OQ). The big tech startups, the big supermarket chains start exactly from here where there are high chances of success (This is also why rich start-ups or any non-poor start-ups demand high funding).

In the case of high marginal returns in poor enterprises in their early stages of development we can easily think that high marginal returns should create the foundation of a successful long-term business. These high margins will allow the person to invest more in the same business, to employ more people to expand the workforce, to purchase new machinery, new tools. But these high marginal returns could never fill that capital gap for poor. This is what majorly differentiates between poor and rich entrepreneurs.

So, one has to really appreciate the gap lying between poor and rich entrepreneurs. This gap of capital to create production technology is too large for poor entrepreneurs and for the business they run. It is not just their narrow mindset, rather they are so close to the harsh reality that they prefer not to follow such seemingly “imaginary” paths.

Conclusion

Entrepreneurship for our young generation seems like a glamorous venture with big money, new technologies, new ideas, new technologies, “angel” investors and “unicorn” start-ups but we always forget that we are surrounded by many entrepreneurs which go unnoticed and have less to nothing to do with the keywords explained here.

A high chunk of these unnoticed entrepreneurs are poor entrepreneurs. They are part of our lives in a big way – you can think of the vendors of every small thing you use in your whole day.

Most of the people in poor countries are self-employed or entrepreneurs. This proportion is far less in developed nations.

Poor entrepreneurs seem to make high returns in their business but most of those high returns go to the repayment of the loans at high interest rates due to the inaccessibility to formal financial institutes which can lend at relatively lesser rates of interest. These businesses are very small and unprofitable over the time even though the rates of returns are exceptionally high.

Providing capital and opportunities to poor to start their business is not the solution to their improvement. Even after such provisions they will engage in the enterprises which rapidly stagnate over the time.

In order to come out of such stagnation they will need to fill that huge gap capital to incorporate production technologies which is impossible without the involvement of anti-poverty policies which will create opportunities and involvement of big formal institutes to provide no risk capital.

“The idea of the entrepreneurial poor is helping to secure a place within the overall anti-poverty policy disclosure where big business and high finance feel comfortable getting involved.”
C. K Prahlad, taken from the book Poor Economics by Abhijit Banerjee and Esther Dulfo

Poor entrepreneurs have less risk-taking ability, no to less business connections, no credit/ loan capability when compared to their rich entrepreneur counterparts. They have to fill that huge gap of up-front capital which could have brought new production technology, employed more skilled labor. Filling this high capital gap is impossible for poor entrepreneurs. That is exactly why a smart, ingenuous street vendor even while having the best and the original ideas cannot expand his/ her business into big industries, companies and malls.

When we are understanding that poor enterprises rarely promote multiple employment/ connected employments, we should understand that supporting the poor entrepreneurship won’t drastically improve the employment rates of the nation, especially the poor nations. This is also why creation of good jobs is very important.

References:

Poor Economics – rethinking poverty and the ways to end it by Abhijit Banerjee and Esther Duflo
MIT OpenCourseWare – 22. Entrepreneurs and workers – Lecture by Abhijit Banerjee
106 Must-Know Startup Statistics for 2023
90% Of Startups Fail: Here’s What You Need To Know About The 10%
News reference – Sifting through sludge for a sprinkle of gold – The Times of India