The purpose of this document is to reflect on my experience taking real analysis as an undergraduate economics major (not a math double major.) It could perhaps provide some insight into what went well, what didn't go well, and my expectation versus reality on the difficulty and the content.

Preparation

I took real analysis (RA) when I was a senior, it was the first upper division math class I had taken, as I was not majoring or minoring in math. The class had reached a sort of mythical level in the undergraduate economics student's ethos who is interested in graduate school. A prohibitively difficult hurdle. That was certainly the case for me, but after the course actually started, it became clear that this course is like any other, preparing for it will pay dividends.

Taking Discrete Mathematics First

The best preparation for me was to take what's called "Discrete Mathematics" at my university. It's essentially an introduction to logic and proofs (with some probability sprinkled at the end, though it was of no use to RA specifically.) It teaches you fundamental proof writing techniques (Direct proofs, Contradiction, Contrapositive, Induction) which build off of an understanding of logical operators and rules (e.g. DeMorgan's Law.) With this, you are also taught some essential set theory knowledge, in fact, I think about 90% of what I know about set theory now comes from Discrete Math, as RA applies set theory constantly, but the vast majority of it was covered in my case in Discrete Math.

Discrete Math gives you tools and understanding so you can actually focus on the content of RA without getting caught up in how certain rules of logic work, how to write a proof, and getting mixed up with set operations. I can confidently say that I would have struggled much more without having prior exposure to these concepts.

Additional Materials

If you are unable to take such a course before you take RA, there are many books that serve the same purpose. One that helped me immensely was "How to Prove it: A Structured Approach". For the course itself, we used: "Discrete Mathematics and its Applications", which was also fantastic. Additionally, you can also just pick up a RA book before the course starts. In the book "Understanding Analysis", by Abbot, the first chapter goes over these preliminaries (in less detail than you would otherwise get in a different book, but still.)

For any additional preparation, MIT has a full course online which includes recorded lectures, HW, and exams. I didn't fully make use of this, but It was useful in doing some review to see a different perspective on how to approach the same problems.

Purpose: Not an "IQ Test"

Something that I heard often before taking the class is that it's just an "IQ Test." Implying that the material in the course has nothing to do with what you would be learning in an econ PhD program, and that you generally don't get much out of the class other than as a signaling tool.

However, I feel like this is not the case. RA is not some mysterious or particularly niche topic. It's calculus, which people tend to accept ubiquitously as necessary for studying economics or doing economics research. RA is nothing more than what you learned in calculus I-III, at a more rigorous level. If you already believe a solid foundation in calculus is necessary for econ, but view RA as just a signaling litmus test, RA is nothing but calculus.

My limited knowledge of PhD level courses in economics suggest that calculus and knowing how to write proofs are necessary for performing well. Regardless of if you want to be a theorist or not, you have to take the core theory classes.

Mathematical Familiarity

But beyond just understanding calculus at a better level and learning how to write proofs, there is a lot of utility in RA.

During the semester I took the course, I was also taking a class in probability, a class in advanced econometrics (Econ 143 at UC Berkeley), and writing an honors thesis. Each of these, I found useful applications of what I learned in RA for.

More than the fact that both of the classes I was taking uses calculus, I was also just much more comfortable with reading and understanding math. This came from having more exposure to notation, with reading and writing proofs, and set theory. This is also likely because RA was my first upper-division math class, if I had taken abstract algebra or a proof based linear algebra class first, I likely would have received the same benefits from those courses.

This same comfortability was useful in reading econ papers, and not being put-off by notation (or, intimidated, honestly.)

Taking RA with these classes was also useful for perspective on each of them. RA is all about proving calculus, probability has many applications of calculus, and econometrics has applications of probability. A rough, but helpful landscape in my mind of the gradient from pure to applied math.

Notes on Typesetting and GitHub

For my courses that semester, I committed to typing my homework and problem sets in LaTeX. Before, I just took pictures of my work and uploaded them. It's a rather uncomfortable transition, but I'm glad I chose to do so. It was a good excuse to become more comfortable with LaTeX, and it acted as a final review of everything before submitting it, as I had to essentially rewrite all of my work again. I used overleaf, which I highly recommend. I has git integration, which I'm currently using to create a solutions document for the 4th edition linear algebra done right. It's good practice to get comfortable with working on multiple remote repositories with git, which of course is also an essential skill.

Conclusion

I hope this short note was helpful to someone preparing to take the class, and/or wondering what the actual material is like and how it could be useful in potential applications to econ research from my limited perspective.

There are many eye-catching ways to open a piece on the South Korean housing system of Jeonse. I could tell you that a huge portion of Korean renters do not have monthly expenses on properties; I could tell you that it takes hundreds of thousands of dollars to simply rent an apartment—and at the same time, it’s free.

So, what is it?

Jeonse(전세) is a housing arrangement whereby the tenant pays a large sum of money to the landlord for a lease of one to two years, and at the end of the lease, the entirety of the money is returned to the tenant. But, why would any landlord agree to this arrangement? To understand the dynamics of the Jeonse system, it would be helpful to take a look at the reason why it began.

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Background

The Jeonse system became established in mid to late 20th-century Korea. The booming housing market was in dire need of a vehicle to develop since traditional mortgages were not very feasible, with extremely high interest rates.

Therefore, it was difficult and very expensive for investors to borrow and spend in more traditional ways. This was an issue since investment incentives were needed for the rapidly industrializing country. Jeonse was a solution to this problem.

Instead of thinking of Jeonse as we would typical housing payments, think of it as a loan from the renter’s side. The tenant loans out money to the landlord, at a 0% interest rate for the 2-year lease, during which the landlord reinvests the loan money into other capital. This would often include buying more properties, taking Jeonse from new tenants, and repeating. Of course, since the loan is cheap, it’s extremely easy to make a profit on other investments. Landlords used the system as a way to get cheap money for capital investments, while tenants used the system to build up savings in hopes of being a homeowner themselves.

While the system worked as a huge boon to Korean growth in its earliest stages, it’s evolved a great deal up to the current day. Issues with falling interest rates, price hikes, and government regulations have all stood as obstacles to Jeonse.

Obstacles and Evolution

Price hikes in the deposits of Jeonse have become a huge issue or even a crisis, as labeled by some media outlets. Perhaps that label is a justified one.

“Over just a two-month period in 1990, 17 people were driven to suicide by increases in jeonse. For financially disadvantaged people, jeonse prices were a matter of life and death.”

Korea JoongAng Daily, 2020

What caused these price hikes? Why are Jeonse prices a question of mortality in Korea? Let’s answer the former first.

Price Hikes

Price increases don’t occur for just one reason. Of course, there’s the natural expansion of an industrializing economy, with housing prices inflating in urban areas, but a big part of increases in Jeonse deposits are due to falling interest rates.

Low interest rates heat up the market through increases in investment, and since Jeonse is a percentage of the value of the property, when property increases in value there is a proportional increase in the sum required.

Overall increases in demand are also a culprit, causing the normal proportion needed for a deposit (40-60%) to increase up to 80-90% of the property value.

How was this issue tackled in the 1990s? Simply put, more homes were built.

“Is there any other choice than building more homes when tenants killed themselves after housing prices rose by 20 to 30 million won?”

Moon Hee-gap

More than 2 million units were built in response, cooling the market and slowing the rapid price increases. However, the high proportion of property value requested is still prevalent today.

Low interest rates have also made a stark difference in how Jeonse is paid. In times of higher interest rates, families paid the sum outright. However, especially during the Covid era of extremely low rates, many tenants simply take out a loan for Jeonse, provided they have the necessary credit. The interest they have to pay on the loan is often less than what they would have to pay monthly for rent.

In addition to tenants taking out loans, there have been a few other changes in how Jeonse is paid.

Quasi Jeonse

There is another solution for increases in lump sum payments, known as Quasi-Jeonse. This is a mix of traditional Jeonse with monthly rent, whereby the tenant pays the deposit, and any increases in said deposit are instead paid monthly rather than a simple increase in the lump payment.

In a paper by Ki-Hyun Ryu and Jin-Ah Kim, from the Journal of Housing and the Built Environment, they predict that Jeonse will continue to evolve towards this state of Quasi-Jeonse as traditional leases become less affordable.

Ownership Culture

Now, to tackle the second question, why has Jeonse worked, and how has that played into extreme responses, such as suicide, when it doesn’t?

“Reliance on nonfinancial assets by Koreans stood at 64.4 percent, followed by Australians with 57 percent. Americans and Japanese held 28.1 percent and 37.9 percent, respectively, of their assets in nonfinancial properties, the data showed.”

Jie Ye-eun, The Korea Herald, 2021

As an American, I often imagine the United States to have a large number of people tying up their investments into housing. However, as seen above, this is not as true as we think it is. Well over half of Korean wealth is in nonfinancial assets (physical capital, such as housing), while the proportion of wealth in financial assets is only around 35%.

This concentration into housing assets has been one factor of how Jeonse has worked, there is less money tied into financial assets and more available for deposits. However, this also means that there is a much larger reliance on housing markets as a wealth-building vehicle for most Koreans.

Shifting Away

As interest rates fall, it makes less and less sense on the landlord side to use Jeonse, many are shifting away towards monthly rent, an avenue that the South Korean government supports.

In 2014, the South Korean government announced new tax benefits to tenants and property owners for renting instead of Jeonse. On the property owner side, this also includes a tax break for those who own more than two residential properties in an attempt to encourage them to rent out more, and rental income under a certain limit will be exempt from taxation. On the renter’s side, replacing deductions with income tax credits, increasing the benefit limit, and raising the ceiling for annual salary by 20 million won.

Is it working?

While data on Jeonse has only been collected since 2011, this year marks the first time that Jeonse has fallen below 50% of the market share, with renting becoming the majority. Largely due to increasing rates making it harder for people to borrow for Jeonse payments.

Korean outlets predict that Jeonse may disappear completely if hikes persist over the next few decades. If that’s the case, then the Jeonse system will be ended by its own original raison d’etre.

Closing Thoughts

The Jeonse system is something very far outside of the normal tenant experience in America or the West generally, and therefore it’s extremely interesting to dive into.

No matter if it’s waxing or waning in prevalence, it’s clear that it has had a huge impact on the development of South Korea, the culture of ownership among Koreans, and its ability to adapt seems to suggest that it won’t completely disappear anytime soon.

The following years will be critical as we see the consequences of government regulation on the housing market unfold, as well as increasing rates as we depart from the Covid era.

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