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.

Repairmen needed to give electrical pencil sharpeners a second life

Posted in Economics, Environment, Hong Kong, Parenting by kafuwong on July 16, 2015

A year ago, the ten-year-old electric pencil sharpener in our office began to fail. It was one of those better electric pencil sharpeners and could stopped automatically on sharpened pencils. Our office had no choice but to dispose the old one and to buy a new one of the same model. I took the old one home to let my son play with it.

The new one malfunctioned within days. As it was under warranty, the office then got a replacement. The newly replaced one worked but lacked the function of automatically stopping on sharpened pencils. My colleagues called the company for a repair. The salesperson said the new one did not have this function of automatic stopping and refused to send anyone to repair it. (Bad salesmanship, and lies as well!) After a year, it failed. Now, as it was no longer under warranty, the office decided to discard it. Again, I took it home to let my son play with it.

Were we successful in resurrecting the two pencil sharpeners? To my colleague’s surprise, we did. (I said “we” because I made substantial contribution.) On the ten-year-old pencil sharpener, we discovered that it just needed some oil — it took us a long time to discover. After applying some oil, it worked like new.

One the one-year-old, the major problem was a mis-alignment of a switch. Not only that we brought it back to life successfully, we also fixed the function of automatically stopping on sharpened pencils.

No, I am not trying to brag about how good we are in repairing the machine.

Here is my observation: Many years ago (when I was younger), a lot of broken electrical appliances were repaired and used for a long period of time. Now, most broken electrical appliances are thrown away. The natural question is WHY!

I think the answer lies in the cost of purchasing new electrical appliances and the labor cost of repairment. The labor cost has gone up substantially in Hong Kong. The cost of buying new electrical appliances is low. When the cost of repairment is higher than the cost of buying new electrical appliances, the decision is not to repair. As more people make similar decisions of not to repair their broken electrical appliances, more broken electrical appliances will end up at landfills.

How to reduce the amount of broken electrical appliances in landfills? We need more rag-and-bone men and repairmen.

Anyone interested in joining me to collect and repair broken electrical pencil sharpeners?

Can you believe that?

Posted in Hong Kong, Information by kafuwong on July 2, 2015

Saw an article a couple days ago about a comparison of prices of beer across the globe.  Hong Kong is the second most expensive city to consumer beer at the pub.  (http://www.scmp.com/news/hong-kong/economy/article/1830376/hong-kong-second-most-expensive-city-world-beer-drinkers)  Should we be surprised to see the catchy DISTORTED titles such as “Hong Kong second most expensive city in the world for beer drinkers”?  

I could not help sharing it with a beer buddy who knows a thing or two about beer and has been in Hong Kong a couple of times.  I added my observation:  “Much cheaper to buy from supermarkets.”

I am not surprised that he had already seen the study because beer is always on his radar.  Here is his comments:

This study has been well publicized but has a fundamental distortion in its methodology. I read the longer version in the Wall Street Journal. It picked the bar prices from only three hotel chains..Hilton, Best Western, and Holiday Inn..to create its pricing index. As most travelers know, hotel bar prices are likely to be inflated over the regular market offerings. This is well illustrated by the bar prices published for Prague with an average price of $4.32 for a 1/3 liter. Even very good microbrews in a normal Prague pub sell for around $1.80 for a 1/2 liter.

So while the study may be generally correct in a comparative analysis of bar prices for cities, it gives a distorted pricing level. It’s pretty much like most of those ever-present annoying “best or most expensive cities” lists in which the originator (usually in the travel or relocation business) of the “study” uses an expedient methodology that addresses the tourist or ex-pat with company/institutional financial subsidy audience instead of the traveler or resident of those cities.

I think we have a lot to learn from him.  In reading any report, mind the details.  The title “Hong Kong second most expensive city in the world for beer drinkers” is biased/distorted and is meant to catch our attention. I wonder how many of us would question the information contained in the title?  How many of us would read the news content for additional information.    How many of us would try to read the report to find out what is really in it? How many of us would read the “fine print” and “research methodology” in the report for additional information?

The problem is: when we have so much information floating around, how can we read the details of every report and be able to tell which is trustworthy and which is not?  Difficult!

At least, now, we know not to trust the newspaper title “Hong Kong second most expensive city in the world for beer drinkers” and anything similar.

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.

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.]

True or False: The increase of tourists has cost Hong Kong 3.5% GDP.

Posted in Econometrics, Economics, Hong Kong, Population, Research, Statistics/Econometrics, teaching by kafuwong on March 4, 2014

First, there is an i-Cable story which uses the statistical analysis of a colleague. Second, there is a column written by a friend. They are both about the extra waiting time due to the influx of tourists.

In the i-Cable story, the reporter took the MTR trains from Tai Wai Station to Wan Chai Station. It showed the amount of waiting to get on a train at every interchange. Then, the reporter interviewed a colleague of mine. He showed that the number of MTR passengers was highly positively related to the number of tourists. Therefore, an increase in the number of tourists would cause an increase in the number of MTR passengers, and consequently the amount of waiting to get on trains, and the amount of time one has to spend on commuting. My colleague’s analysis was not about how the number of tourists would impact on the commuting time. But, audience will get the impression.

In her article, my friend estimated the amount of loss of GDP due to waiting. She used the extra 10-minute commuting time by LegCo member’s experiment during rush hour and deduce a loss of 3.5% of GDP. Suppose all employees has to work 47 hours per week on average and suppose each of them wastes 10 minutes commuting. The extra 20 minutes round trip (10 minutes x 2) is equivalent to a loss of 3.5% of GDP. Striking! The story certainly catches eyes of a lot of people, including me. Unfortunately, striking stories are often wrong — if you are willing to check their calculation or deduction.

I would like to raise two questions:
(1) Is the “extra” waiting time of 10 minutes an upper bound, lower bound or median? I took MTR today and did not have to wait for the next train to get in. Imposing the upper bound on all employees will yield a very unreasonable exaggerated number. I think it is actually much less than 3.5% of Hong Kong’s GDP.
(2) Given it is indeed extra 10-minute waiting, how much of it is due to the tourist or our increase in population and government policy to divert the flow of traffic from buses to MTR (for cleaner air, perhaps)? I do not think most tourists would take the MTR during rush hour. Of course, there are exceptions.
I am waiting for some serious researchers to provide good answer to my questions. Yes, data could be a big problem.

If you are interested in seeing the i-Cable story, here is the link to the video:
If you are interested in the column, here is the link to the article:

The cost of regulation

Posted in Economics, Hong Kong, Regulation, teaching by kafuwong on February 6, 2014

Several ferry lines have been closed or about to close. You know why? It is an aftershock of a ferry tragedy off Lamma Island in 2012 (39 persons died).

The scale of the casualty in 2012 was mainly due to the mistakes in shipbuilding and inspection. In part, Marine Department gave the operation permit to the ship without doing a thorough inspection according to the safety rules. That was why the ship sunk so fast, causing so many casualty.

Safety is a function of capital and labor. Safety can be improved by a better inspection of the ships before they are allowed to operate, the provision of enough life-jackets in case of accidents, more stringent training and test requirement on the caption, and more crew members on the ship. Marine Department was right that such additional measures would reduce the chance of ferry accidents and the scale of casualty.

Additional safety regulations can kill some of the ferry business. The additional safety measures add to the cost of operation. A ferry line that was making break-even profit would begin to incur a loss with the requirement of additional crew members on board.

That is exactly what we are seeing on the ferry services between Mui Wo and Discovery Bay. A single journey from Mui Wo to Discovery Bay will take about 25 minutes by ferry but 75 minutes by bus. The ferry has been doing a great service to the 40 Mui Wo children who attend school in Discovery Bay, at the very least. Of course, the ferry operator has been earning a reasonable profit. With the requirement of additional crew member on board, the ferry operator had planned to stop its services because the operation would induce a loss and such loss situation could not be resolved by charging a different fare.

Glad to know. Finally, the Marine Department approved the exemption to this specific operator. The specific operator will not need to meet the requirement of adding an additional crew member on board. I am sure this is the result of the lobbying effort of the Mui Wo and Discovery Bay residents. The Mui Wo and Discovery Bay ferry services have been a safe one before the Lamma tragedy. Why do we need additional safety measure after an “unrelated” tragedy? The across-the-board increase in safety requirement was unreasonable!

Life is full of tradeoffs. There is a cost to everything. We want to improve the safety of ferry services, we will have to commit real resources on it. The two parties involved will determine jointly the optimal level of safety, based on their preference and financial constraints (and many other things, such as technology). They engage in trade only because both parties find the trade beneficial. An additional requirement imposed by a third party (say, the government) can disrupt the mutually beneficial trade; the benefits to the original involved parties will likely be reduced. That is, improper regulations can hurt the economy.

Regulators, be mindful about such tradeoffs. The ferry services between Mui Wo and Discovery Bay would be a good case to keep in mind.

[Additional reading: “Reprieve for Discovery Bay Ferry”, South China Morning Post, February 6, 2014.]

Who stole my Chinese New Year?

Posted in Economics, Hong Kong, Life, Parenting, teaching by kafuwong on January 29, 2014

I still remember the great time people had during Chinese New Year in Hong Kong. At the end of the year, we would be busy preparing for the New Year. We always had a big house cleaning several days before the New Year. We always bought some new clothes to be worn during the New Year. We stocked up food (vegetables, live chickens, etc.) for the New Year. We had feasts during the first couple of days of the New Year. We visited relatives whom we have not seen for the whole year during the New Year. Yes, lucky money in red envelopes was something kids (myself included, back then) looked forward to eagerly, too.

Time has changed. The New Year day is no longer that different from an ordinary day – if not for the additional streak of public holidays. I could not help pondering the reasons behind such change.

Why are the days before New Year no longer a special clothes-shopping season. When I was kids, most families in Hong Kong were poor. We could hardly afford to buy any new clothes. So, a family may be able to buy one or two sets of new clothes for each family member per year. Since we wanted to celebrate the New Year and were going to meet relatives during the New Year, we wanted to dress the best then. Thus, the best time to buy new clothes was before the New Year. Now, families are richer. Most family can afford to buy clothes year round. Therefore, the days around New Year are no longer special shopping days for a typical family in Hong Kong.

Why don’t we stock up vegetables and live chickens at home anymore? Refrigerators allow us to store food, not just at home, but also in supermarkets. The supermarkets can stock up food and keep them fresh using refrigerators even if supply is short during the New Year. And, improvement of transportation technology allows us to procure supply from other countries who do not celebrate Chinese New Year. The need of stocking up food at home has greatly diminished.

Visiting relatives? Yes, we still do, but not just during the Chinese New Year. Imagine in the old days when transportation was costly (in terms of both time and money), we could not afford to visit our relatives any time we wanted to. Transportation has become faster and cheaper. We do not need to wait until the New Year to see them. In addition, the improvement of telecommunication allows us to communicate with our relatives any time. New Year is no longer a special time for such communication.

Yes, when we meet relatives during the first couple of days of the New Year, we may have feast. In the old days, we would cook at home. But, now, a great percentage of us will do it in restaurants. The chores are now left to the restaurant workers.

Even lucky money in red envelopes may not mean much to kids today. In the old days, when kids were so poor, any lucky money was good money. Kids are rich these days (their parents give them large amount of pocket money weekly). A ten-dollar bill in a red envelope? Are you kidding me?

Yes. We still celebrate Chinese New Year. Yes. I can always use a few days off work and get to see some friends and relatives.