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!


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:

When will you publish your book?

Posted in Econometrics, Forecasting, teaching by kafuwong on April 24, 2010

Today is the last teaching day of a postgraduate level course of Economic Forecasting. After the lecture, a student quietly waited for me.  Usually, right after lecture, I would be busy saving my video lecture, packing up my laptop and the external sound card connected to the AV system. etc.    It turned out that he was waiting for my signature on the printed copy of my textbook draft for the course.  I no longer use any published text for the course.  I have written one.  It still needs polishing but it is a readable draft. 

I signed on the cover of his copy.  I feel so honored.  He also pointed out some mistakes in the book.  I am glad.  At least one student has been reading my book seriously. 

“When will you publish the book?”  He is not the first one to ask this question.  Some of my colleagues did before him.  Honestly, I have no plan to do so.  You know what: A typical printed copy of a textbook will be priced at two hundred Hong Kong dollars, out of which the author will get less than 40 dollars as royalty.  Counting the trouble of publishing I have to go through, the 40 dollars of royalty is not worth the effort.  Why do I write the book then?  I started writing the book because I was not satisfied with the books available.  I wanted to use a customised book to improve teaching and learning of the course materials.  My effort of writing the book will be worthwhile if my students learn better with it. 

When I feel the draft is ready, I intend to make the book available to all soon — free of charge.  I am not the only one with such intention.  If you search the internet, you will easily find a lot of free textbooks.  The extreme is http://pareto.uab.es/mcreel/Econometrics/.  Michael Creel has made his graduate econometrics text an “open source”, specifically, licensed as GNU GPL. In his words, “anyone can access the document in editable form, and can modify it, as long as they make their modifications available. This allows for personalization, as well as a simple way to make contributions and error corrections. The hope is that people preparing to teach econometrics for the first time might find it useful, and eventually be motivated to contribute back to the project.”  If more authors contribute in similar manner, we will likely have a faster progress in knowledge advancement.

Impact of an revaluation of Reminbi on the Chinese economy

Posted in China, Econometrics, Economics, Exchange rate, Forecasting, Research, Trade balance by kafuwong on April 17, 2010

Recently (early 2010), the United States has been pushing China to revalue its currency (Reminbi).   Central to the debate of revaluation of Reminbi (RMB) is the impact of such revaluation on the Chinese economy.  I have seen people giving a qualitative analysis (for instance, http://mpettis.com/2010/03/how-will-an-rmb-revaluation-affect-china-the-us-and-the-world/).  How do we obtain a quantitative estimate of the impact? 

Building a structural model?  Building a structural model of the Chinese economy can take enormous time and resources — not something you and I can afford.  An alternative but cheaper approach is to assume that a small set of macroeconomic variables (employment, real exchange rate, trade balance, consumer price index, etc.) approximately evolves over time as a close system.  This set of macroeconomic variables is known as a vector of variables.  This vector is assumed to evolve over time as an autoregressive process (i.e., y_t=a_0+a_1 y_{t-1} +... +a_p y_{t-p}+e_t, or in other words, current values of the vector depends on the past values of the vector and a shock).   We can then apply Ordinary Least Squares (OLS) to estimate the parameters equation by equation.  An impulse response function can be calculated.  The impulse can be a change in the real exchange rate (which is a ratio of domestic and foreign prices adjusted for exchange rate).  The response can be the trade balance, or the unemployment rate.

This modelling technique is called the Vector AutoRegressions, or VAR in short.  It is often taught in courses like Economic Forecasting.