Random thoughts of an economist

A thought on how to evaluate whether education expansion helps improve mobility.

Posted in Econometrics, Economics, Hong Kong, Statistics/Econometrics, teaching by kafuwong on September 11, 2015

We often see reports comparing the median income of university graduates over time. The sad news is that the median income of university graduates are often found declining over time. One common conclusion is that the expansion of university education has not helped improve social mobility. And, university graduates seem to be doing worse than before.

While median income is easier to compute, I do not think it is the right measure to address the question of social mobility, or how university graduates nowadays fare when compared to the previous cohorts. A correct measure is some form of median income with an control of the expansion of university education.

Imagine the following hypothetical situations. Suppose that we have a stable population structure. Suppose 20 percent of high school graduates can attend university ten years ago. Imagine we end up with 20 persons achieving high school level and 5 persons achieving university level. The median income of high school graduates was X1 and that of university graduates is Y1. Y1 is usually higher than X1, reflecting the difference in ability of the two groups and added value of education.

For the sake of illustration below, let’s assume that the 5 university graduates have incomes of 12100, 12200, 12300, 12400, 12500. Obviously the median income is 12300. That is, Y1=12300. Let’s further assume that the top 5 earners of high school graduates earn 8100, 8200, 8300, 8400, and 8500 respectively.

Today, due to the expansion of higher education, 40 percent of high school graduates can attend university. Following from the example above, we end up with 15 persons achieving high school level and 10 persons achieving university level. Suppose then the 10 university graduates have incomes of 11100, 11200, 11300, 11400, 11500, 12100, 12200, 12300, 12400, 12500. Let’s denote the median income of high school graduates as X2 and that of university graduates as Y2. Note that the median income X2 is based on a smaller group size while that of Y2 is based on a larger group size. We can easily imagine that X2 will be lower than X1 because we can imagine that the top five earners (“more able”?) were removed from the original high school group and put into the university group. And Y2 will be lower than Y1 because the university group includes the “less able” ones.

Thus, if we compare the change of median income by education groups, we are bound to see a deterioration in income in BOTH GROUPS. Some would conclude that education expansion is bad.

Wait a minute. Obviously, the five persons who achieved university level because of the education expansion achieve a higher income. (11100, 11200, 11300, 11400, 11500) versus (8100 8200 8300 8400 8500). A substantial improvement in social mobility (as measured by income) due to the education expansion, isn’t it?

That is, we are evaluating whether education expansion is useful, we should focus on these 5 persons who had not the chance to study university but now have the chance to do so.

If we still insist on using measures similar to median income of the university graduates across time to conclude whether university graduates are doing worse than better, we need to make an adjustment. From the example above, we probably should compare the top 25 percentile income level today to the median income 10 years ago!

Generalization based on the sample size of one

Posted in Hong Kong, Statistics/Econometrics, teaching, Water by kafuwong on July 21, 2015

Recently, lead in water has occupied headlines of major newspapers in Hong Kong. Experts are consulted. Some experts appeared to mis-speak carelessly. The most laughable statement was made by a medical doctor, who is a consultant of the “Hong Kong Poison Control Network”. He remarked that lead poisoning can be caused by chewing on a pencil, among many other causes. It was so laughable that it is widely circulated on the internet.

Admit it, most of us do not know why this statement is laughable. OK. It is laughable because pencils (called “lead” pen in Chinese) do not contain any lead in the writing core nowadays. Although the writing core of some early pencils were made of lead, it has since replaced by the non-toxic grahpite. (http://pencils.com/pencil-history/) And, the statement came from a consultant of the “Hong Kong Poison Control Network”.

In fact, at least supposedly so, nowadays even the paint cover of pencils should not contain lead so that most pencils are safe for chewing (not encouraged).


Internet is a powerful tool. A friend appeared excited about the lead poisoning from pencil chewing story that he added a catchy title to his sharing of the news report about the doctor’s statement: “If you cannot trust doctors, who can you trust?”

It is this catchy and exaggerated statement that caught my attention. I have to admit, I like it.

Nevertheless, the statement is clearly too much a generalization based on the sample size of one. That “specific doctor” may not be trustworthy on this specific issue, but it does not mean that “specific doctor” is not trustworthy on other issues. Certainly, it does not mean that other doctors are not trustworthy.

Beware of similar generalization from a small sample of observations.

The redemption rate of cake coupons

Posted in Economics, Hong Kong, Information, teaching by kafuwong on February 16, 2015

A friend was trying to redeem his cake coupon from a chain bakery. His coupon was two days from expiry. If he had not done it in time, the chain bakery will gain.

Hm… What is the redemption rate of cake coupons? That is, how much do the chain bakery gain per year due to people’s failure to redeem their coupons?

I do not have the numbers. Nonetheless, here is a thought experiment.

Imagine that 40% of the cake coupons are not redeemed. Shop A is willing to sell the coupons at 60% of the nominal value. Of course, shop A will try to sell the coupons at the nominal as much as it can. Selling at full nominal value will ensure a gain of 40 dollar gain per 100 value of coupon. This is good money.

The problem is that shop A is not alone. Likely, shop B also sells similar coupons. If shop A is selling at full nominal value, shop B can steal shop A’s customers by selling the coupons at a small discount, say 5%. If information is perfect, all customers will buy the coupons from B. But, A is not stupid. Seeing the loss of customers, it will try to steal shop A’s customers by selling the coupons at a bigger discount, say 10%. …. We can easily see that this competition game will continue until both shops will be selling near at 40% discount. We see the power of competition.

Now, how do we get an estimate of the redemption rate? Easy. We go to shop A, tell them that we are going to get marry and are planning to buy a lot of cake coupons, and ask them the discount we can get. Do the same to shop B, just to double check. That “1-discount” will be close to the redemption rate.

Does it look suspicious to you? Check please!

Posted in Economics, Information, Leisure, teaching by kafuwong on October 9, 2014

A friend sent me a striking table of “actuarial study of life span vs. age at retirement”. The table shows a person who retires at age 49.9 will die at 86 on average, and a person who retires at age 65.2 will live to 66.8 on average. The data suggests that I should consider retiring early.

Wait a minute! A person who retires at age 65.2 will live to 66.8 on average? It is absolutely not consistent with my casual observations.

I could not help doing a quick search of “actuarial study of life span vs. age at retirement” (without the quotation marks, of course). Surprisingly, I found that the table was founded based on a real study –- a Boeing study done almost 30 years ago. The study has been circulated in the internet for many years and finally reached me. Lucky me!

Interestingly, Boeing has tried to tell the public that the chart or table was wrong. According to Boeing, there is simply no correlation between age at retirement and life expectancy of Boeing retirees.

Why are such rumors still around? I think it is because most users in the internet are not willing to spend much time questioning and verifying the accuracy of the information. Spreading some seemingly striking news/information attracts attention. Most of us feel happier with more attention from our friends. There is a cost of verifying the accuracy of the information, though. Such comparison of COST and BENEFIT dictates our decision whether to spread the rumors, though implicitly.

Spreading news/information is understandably more costly to people with good reputation of providing accurate information. Thus, one would expect reputable reporters less likely to spread news/information without careful verification. That tells us where to turn if we want accurate information and where to turn if we want some rumors to enjoy.

I do not like this kind of rumors. I try not to spread suspicious items. At the same time, though, I do like to test my ability in catching such problematic information and verifying them. It has become one of my major pastime. LOL.

Additional readings:

Are you sure what you saw was black?

Posted in Economics, Hong Kong, Information, teaching by kafuwong on October 6, 2014

Beside the extreme of white and black, there is a spectrum of grey. Given a color of grey, some might conclude it as black and some white.

It depends on the referenced color. When grey is put next to white, it looks like black. When grey is put next to black, it looks like white.

I feel that I saw black. Then, I am sure that what I saw was not white. Because, if the color were in fact white, I would not conclude black — even if the reference were white.

How can I know that the color I was is likely grey? The color was in fact grey if some of my friends and I saw black and many others saw white.

The views of others are so important! Their views provide important information for me to correct my view of black. Those who are willing to tell me their different views deserve my best respect. Thank you.

Who would rush to claim that he/she is one hundred percent sure what he/she saw was black? Those who do not know the existence of grey. Those who fail to deduce the color of grey from the conflicting views. If these two groups of people insist what they saw as the only truth, clashes may follow.

One solution is education! Education helps broaden our horizon (seeing the existence of grey) and train our critical thinking (concluding grey)!

[Fine print: Assume that all of us are telling the truth.]

Historic preservation is other people’s job

Posted in Economics, Environment, Historic Preservation, Hong Kong, teaching by kafuwong on May 17, 2014

A historic building near my workplace was being demolished to make room for a residential high rise. Some of my friends were annoyed by such development. They wanted the century old building to be preserved.

Obviously, there is a conflict in opinion of the owner and the public (my friends included) on such historic preservation issues. Lured by the hefty offer, the owner wants to sell the property to the developers. The public want the preservation. The owner would have no objection on the preservation if someone is willing to compensate him for the opportunity (of cashing in). The preservation should be done only if the total willingness to pay (from the public) for the preservation is larger than the best alternative (the value of the property. development). The big question is how much the public are willing to pay to the owner, in total.

Due to the public good nature, such decision and the finance of historic preservation often falls into the hands of the government. And, naturally, the government has to weight the conflicts.

People’s behavior is predictably rational!! If it is my property, I would like to be able to sell to the developers and pocket the money. If it is other people’s property, I would vote to force the owner to keep it as a heritage building. When we do not have to pay a cent, a lot of us will cry “preservation”. Yes! Let the government buy out the property! We tend to say we are willing to pay a lot to see the preservation.

This is a typical example of public good provision. When we do not have to pay for the public good out of our own pocket, we tend to claim we are willing to pay a lot for the public good. That is, an exaggeration of our willingness to pay in order to influence the decision of the government. If we rely on this process, we will have an “over-supply” of historic preservation. Imagine, we create a voting site for every historic preservation in question. Can you guess how many historic preservation projects will be done? In fact, almost all the time, no voting sites are created, no opinion polls are done. Often, we use the media to create a feeling that the public is willing to pay a lot for the reservation.

In the contrary, if we have to pay whatever we claim we are willing to pay, we tend to report less because one person’s understatement will unlikely change the decision of the government (that is approximately based on the total willingness to pay for the preservation and the value of development) and yet an understatement of our willingness to pay can help reduce our payment. When everyone is thinking in the same way, we will have an “under-supply” of historic preservation. Imagine, for every historic preservation in question, we can set up a donation account. Can you guess how many historic preservation projects will be done?

Like many public goods, the optimal supply of historic preservation is non-trivial. The key is to find out how much the public is willing to pay for the preservation. While it is possible to adopt some mechanism (e.g., Clarke-Groves mechanism) to induce people to truly reveal their willingness to pay, the decision of historic preservation often relies on a group of experts, and sometimes political debates.

Why do we rely on a group of experts? Because what the public say may not be as trustworthy as the impartial expert group.

[Additional reading: Handbook on the Economics of Cultural Heritage edited by Ilde Rizzo, Anna Mignosa.]

Be careful with your “title”!

Posted in China, Information, Life, Parenting, teaching by kafuwong on May 9, 2014

Saw a link in the Facebook about a page of supposedly prestigious “XYZ” university. But the title was shown as “XXX” university. If you had once been a student of the “XYZ” university, you should feel annoyed. One of my Facebook friends felt annoyed.

I joked: “Will they give a scholarship or Starbucks coupon to the first person who will write to point out the typo in “XXX University”? They should!”

After writing the joke, I couldn’t help visiting the link. I found no obvious errors on the page. In fact, I search for “XXX”, I could not find any trace of “XXX” in that page. Then, why would Facebook showed the page title as “XXX”? It turned out that the error was more fundamental than I thought. I found that Facebook used the “title” of the html page (hidden unless we pay special attention to it) as the title of the link. That is, when I viewed page source, I saw:

“XXX University” inside the html code of “title”.

If I were the administrator of the XYZ university, I would feel very embarrassed to see this error. So, I decided to send the administrator an email.

This is a laughable “hidden” error in your page of view-source: http://abcde.org/#news-students. The error shows on your facebook link. It should be “XYZ” instead of “XXX” in the “title”. Please check!

Several hours later, I got a reply from the administrator:


In English, “Thank you $#%. We will make correction immediately.

Although I am proficient in Chinese, that “$#% (之处)” is something I cannot make sense of. It is an obvious typo.

They made a mistake. I alerted them of the mistake. They returned with another mistake in their “thank you” email. So, it looks like “to them, making mistake is a rule rather than exception”.

Just for fun, I have just sent the administrator another email asking what he meant by “$#% (之处)”. What would you feel and say upon receiving my email — if you were the administrator?

It is education! STUPID!

Posted in China, Economic growth, Economics, Parenting, teaching by kafuwong on March 24, 2014

Nobody said it better about the Taiwanese protest about a trade pact with mainland China than one of my friends who teaches Economics in Taiwan.

Rule no. 1 of free trade: comparative advantage.

All students who have taken Economics should know this principle. The major source of gains from trade is from the specialization in the tasks that we are relatively good at – at least in the short run.

Under free trade, refusing to specialize in tasks that we have comparative in will result in lower income and living conditions. In a sense, the competition that comes with free trade will crush us.

So, how can I survive the wave of free trade? The key is in understanding our own comparative advantage.

What determines our comparative advantage in performing different tasks? At the individual level, comparative advantage is determined by our inborn talent and temper (genes?), education, training and experience. Inborn talent and temper cannot be changed. However, education, training and experience can be adjusted to change our comparative advantage. For instance, an exchange experience at a German university might improve our comparative advantage in the trading business between Hong Kong and Germany. A bachelor degree in Economics will give us a comparative advantage in working in banks.

That is, we still can choose things we like to do but we have to invest enough so that we will have comparative advantage in the things we like to do!

In the longer run, competition will force us to invest in tasks that we want to have comparative in. You invest. I invest. Then, the productivity will eventually improve. We have a better world with higher productivity and more goods to consume.
What if you are the laid-back type who has no intention to invest and improve, or change career to specialize in things you have comparative advantage in? Then, you are doom to suffer once the competition (due to free trade) arrives.

In short, if you can ride on the wave of free trade, you win. If not, you will lose.

One way or the other, Taiwan has to open itself to the rest of the world. Keeping Taiwan close is not an option. Mainland China is the best example. Much of its growth has been due to the openness to the rest of world since 1978. Ride the wave earlier, you gain more. Ride the wave later, you lose (or gain less).

Students, go back to your classrooms. Study very very hard! Make sure you will have comparative advantage in the things you like to do.

P.S.: I am more sympathetic with those older people who would have difficulty in making their adjustment. To them, government should give a helping hand.

How much do you value my friendship?

Posted in Economics, Parenting, teaching by kafuwong on March 20, 2014

A Facebook friends put some used stuff for auction (some e-auction platform). To advertise, he announced it via his Facebook status. And, he added “Will give discount for friends!”

Immediately, I wanted to call him up and see how much discount I could get from him. The discount I got, when compared with the discount he gave to other friends, would tell me how much he valued my friendship.

It would be interesting to do a similar thought experiment: Suppose you have an item for sale. And, you are willing to give discount to friends. Suppose all your Facebook friends send you a private message and ask for a discount. What discount will you give to each of them?

Can iPhone be regarded as money? An internationally accepted one?

Posted in Economics, Exchange rate, teaching by kafuwong on March 11, 2014

With the development of Bitcoin, people have shown interest in what we mean by currency or, simply, money. To be called money, an object should serve three functions: (1) unit of account, (2) medium of exchange, (3) store of value.

Many objects can serve these three functions to different degrees and thus can be called money — to certain degree. Seashells were once used as money. That is, in the market, the prices of goods were quoted in terms of seashells (unit of account). Goods were exchanged for seashells and seashells for other goods (medium of exchange). The owner of seashells could save them for use later without substantial loss of its value (store of value) or, possibly, a gain in value. As money in ancient times, seashells were widely used units of account, mediums of exchange and served as a store of value.

In prisoner of war camps, and prisons, cigarettes were and are used as money. (http://en.wikipedia.org/wiki/Prisoner-of-war_camp#Cigarettes_as_currency)

Some objects are used as money in Territory A but not in Territory B. The Yuan/Renminbi is legal tender in China, but not in the United States. Yen is money in Japan, but not legal tender in China. That is, money is often territory-specific; where the territory can be a country, province or club. In fact, in Ithaca, New York of the United States, “hours” are used as money among a specific group of individuals, but does not go beyond Ithaca. (http://en.wikipedia.org/wiki/Ithaca_Hours)

Bitcoin caught widespread attention and use as money across territories. Some merchants quoted prices in bitcoins (unit of account), used them for exchange (medium of exchange) and stored for later use (store of value). Unlike the Yuan/Reminbi, Yen, Dollar and other currencies, Bitcoin was not backed by any government; it’s value based primarily on trust.

Then, can Apple’s iPhone be used as currency internationally? It is easy to check. How often do we see prices quoted in terms of iPhones? How often do people buy and sell goods using iPhones as units of exchange? Do people use iPhones as a store of value?