Junior College or polytechnic? A simple game theoretic model. (Now playing Champagne Supernova by Oasis)
Introduction
This article is inspired by the Straits Times reports on Saturday, 13/11/1999. I was pleasantly surprised, upon reading the two articles, 1 and 2, that they brought up the theme that I was pushing for in my educational voucher article; that anyone who qualify for a university should get a voucher subsidy.
It is a tough decision to make, after the 'O' levels, whether to apply to Junior College (henceforth JC) or the polytechnic (henceforth poly). The main complication, in my opinion, is the uncertainty over our chances of qualifying for the University. I remember reading this bulletin issued by the Singapore Polytechnic in 1989, the year I did my 'O' levels, stating that the chances of someone getting into NUS/NTU with the best 6 'O' levels aggregate of between 13-20 points are something like only 10-20%. I had 20 points in my preliminary examinations and you can imagine my dilemma then!
Recently, in the Straits Times, there have been some discussions on the need to relax the strict entrance criteria on universities' admissions. The concept that is constantly being mentioned is that of 'equal opportunities', between diploma-holders and 'A' level holders; the focus seems to be on refining what exactly does the term 'equal opportunities' means. It appears that NUS/NTU came under some heavy criticisms, from Singaporeans, who claimed that overseas universities are more willing to consider other gauges of an applicant's ability, such as interviews, reference letters, personal statement etc.
I am all for the proposal of a more holistic method of assessing applicants. I believe that allowances should be made for late developers. However, I begin to think, "Is the issue so simplistic? Will the problem be solved once we managed to define exactly what does 'equal opportunity' means?" I will argue here that it will not. The main problem here is that a JC graduate and a poly graduate have unequal prospects when they finish their respective courses. A JC graduate needs university training more crucially than a poly graduate. Having 'equal opportunities' for university admissions will only worsen the 'unequal prospects' that both of them already face.
Since we are all 'lovers of economic reasoning' here J, I have decided to take a stab at forming an economic model to think about this issue. Of course, I am not proficient enough at this moment to use the concepts of set theory, such as quasi-concavity, open/closed balls and all that hard-core stuff, and I think it will put a lot of my readers off even if I could J. What I am proposing here is a simple game-theoretic model, using the basic concepts that all of us have learned in microeconomics, that might shed some light in how we make those decisions in enrolling in JC or poly. The key element, as I have mentioned earlier, is our expectations of success in qualifying for the university. I also hope to use this model to explain whether the following statement by the university's representative makes sense, that
"When contacted, the spokesmen for the two universities here said that those who take the polytechnic route have chances equal to any A-level holder."
It is so typical of bureaucrats to make such vague statements J. My model will show that the above statement cannot be true. If it is, nobody would enroll in junior colleges.
Some institutional and literature background
Being a product of the Singapore's educational system as well as researching into this area, I have concluded that Singapore's educational system is mainly based on the eugenics principle, most of a person's intelligence is nature rather than nurture, in the light of 80/20. Thus the main objective of students seeking an education can be assumed to be signaling to the employers what 'quality' they are.
Those who have taken labor economics should be familiar with this theory of education as a signal. Michael Spence (1974) was credited with this theory, but the heart of the problem was recognized earlier by George Akerlof (1970) with his classic lemons market article. The basic concept here is that, all students are born with different intelligence levels which are unobservable. Assuming here that intelligence corresponds to productivity, employers would like to hire the high productivity worker by paying him/her a higher wage and hire the low productive worker by paying him a lower wage. The problem facing employers here is asymmetric information, more precisely, its the problem of adverse selection. The workers know what quality they are but the employers do not. Thus, what happens is that employers will only pay a market wage for low productivity workers irregardless of the worker's actual quality, and all the high productivity workers will leave the market.
Thus, education comes into the picture to solve this problem. Putting it simply, those higher productivity workers can now seek an education to signal to the employers that they are of a higher quality. One important contribution by Michael Spence showed that, for education to serve as an effective signal, high productive workers must be able to acquire it at a lower cost than low productive workers. Now we all realize why examinations are set at such a difficult level here or why smart Singaporeans undergraduates in Australia are worried when the examinations there are so easy that even their friends who are party animals can score As J. There is a very detailed account of this particular issue by a former overseas graduate here.
Once the signal is in place, employers will thus pay a higher wage for those with education and a lower wage for those without and will be confident that he is getting the right quality worker for whoever he is paying for. The strategies and beliefs of both the worker and the employer would be a perfect Bayesian equilibrium.
Michael Spence won the American John Bates Clark medal for this and other important research. When I first studied this model, it totally revolutionized my perspective of education. Notice the significance of this model: that even if education does nothing to enhance our productivity, it is still beneficial for ourselves and society in demanding education, to separate the productive and the unproductive ones in Singapore.
Perhaps one example on how path-breaking Michael Spence's work is that he has provided an answer to Sandra Davie, an ST journalist, who ask whether a degree would have helped Sim Wong Hoo here. Spence's model explains why those people of 'high productivity' but without a degree, for example Sim Wong Hoo before he made it big with Creative Technologies, are usually self-employed. Even though these people may be very productive, they will find it very difficult to find an employer who is willing to pay them a wage consummating with their productivity, because of their lack of a signaling device.
Of course, once Creative Technologies became 'big', there is no need for him to have a degree for he already has a better signaling device. But I can imagine that, for every one Sim Wong Hoo, we must have many other productive people who are underemployed due to their lack of qualifications. Spence's model is admittedly a very simplistic model that has many 'unrealistic' assumptions, but I shall use the basic framework, with some modifications, to explain a student's choice after 'O' levels, whether to go to JC or poly.
The model
The following are the assumptions of my model:
Students are classified in strictly 2 categories of intelligence: Smart and Average. The students only have a vague idea which category they are in and must form an expectation on their intelligence.
A university degree holder is automatically guaranteed a better future than a diploma holder. However, a diploma holder would have a better future than a person with only 'A' levels.
A student can make it to NUS if and only if 2 conditions are fulfilled: He is a smart student and he enrolls into a JC, i.e. smartness and enrollment in a JC are both necessary and sufficient conditions to enter NUS. The educational bureaucrats at MOE and NUS would set the examinations and cut-off point in such a way to ensure this, in line with the crucial finding by Michael Spence that I explained earlier.
Any student, whether smart or average, can get a diploma after enrolling in the polytechnic
A poly route will end with a diploma, with no chance of making it to NUS. Similarly, a student can get a diploma only if he enrolls in the poly; a JC student cannot enroll in the poly after 'A' levels.
The cost of going into JC and polytechnic is the same.
There is a normal distribution of optimistic and pessimistic students among the 'O' level holders.
I model this situation as a simplified 'game' played between the student and the government. The student maximizes his payoff by enrolling in the JC if he is a smart student and the poly if he is an average student. The government maximizes its payoff when the student does that too. Obviously, if we are talking about Spencer's type of asymmetric information, where the student knows his quality whereas the government do not, we can show that there will be a trivial solution of two Nash equilibrium, which results in both the individual and the society maximizing their benefits.
Thus, to make the analysis non-trivial, I am making a modification to Spencer's model; that there is uncertainty in both sides, the student and the government, about the quality of each student. With this uncertainty, the government is assumed to behave like assumption 3, setting the cut-off points strictly, to ensure that only the 'smart' students enroll in NUS. Alternatively, assumption 3 states that the government is more willing to tolerate a type one error with regards to university admissions, i.e. rejecting a smart student, then a type two error, accepting an average student.
Assumptions 5 and 6 are clearly wrong in the context of the current system but the objective for their existence is to get the basic result of the model first. Later, I will relax these two assumptions to deal with the above statement from the university spokesperson. The rest of the assumptions are merely simplifying assumptions that assures us of a sharp result.
The analysis of the model
In such a model, the student is taking a gamble by enrolling in the junior college. He is gambling that he will do well enough in the 'A' level examinations to secure a place in the university, which will give him the highest payoff, given by assumption 2. Let me first define the terms, 'optimistic' and 'pessimistic', to be used in this model:
Definition 1:An optimistic person will always view himself as of 'high intelligence'.
Definition 2:A pessimistic person will always view himself as of 'average intelligence'
From these two definitions and assumption 7, we have the following proposition:
Proposition 1: In equilibrium, there would be people of both levels in intelligence enrolled in both JCs and polys.
The proof of this proposition is fairly trivial: By definition 1 and 2, the following 2 scenarios described what a student, who is of high intelligence, would do:
S1) If he is optimistic about his intelligence, he would enroll in the JC.
S2) If he is pessimistic, he would enroll in the polytechnic.
Similarly, the scenarios possible, under a student with average intelligence, are:
A1) If he is optimistic about his intelligence, he would enroll in the JC.
A2) If he is pessimistic, he would enroll in the polytechnic.
Based on the eugenic principle, intelligence is a given factor. Similarly, by assumption 7, the number of optimistic and pessimistic 'O' level holders are also exogenously given.
Now, let us examine the properties of this equilibrium. Looking at what happens when the student turns out to be of high intelligence, It is clearly seen that, under scenario S2, he made the wrong choice. This smart person should have enrolled in JC instead of the polytechnic, because he would make it to NUS, by assumption 3, thus enjoying a higher payoff by assumption 2.
Looking at what might happen when the student is of average intelligence, we can see that, while he maximizes his payoff under the second scenario, he made the wrong choice under the first one. Under the first scenario, he will fail to enter NUS under assumption 3. This person should have enrolled in the poly instead of JC, for he will get his diploma, by assumption 4 and similarly enjoy a higher payoff, by assumption 2.
Thus, society wants the average student to enroll in the poly and the smart students to enroll in the JC. The problem is, neither society nor the students know exactly who are these students. Assuming that there is a normal distribution of optimists and pessimists among the student population, which is assumption 7 in my model, this brings a 'market failure', in the sense that some smart students enroll in the poly due to a mistaken pessimism while some average student enrolls in the JC due to mistaken optimism. Students in both these categories are worse off and so is society.
Of course, my above analysis has been fairly trivial at this point. This reminds me of the long-standing joke among non-economists that economists are like parrots that are trained to say "supply and demand"; meaning that their models merely analyzing the obvious.
However, I hope you can all see the value of 'analyzing the obvious' in this issue. By doing so, we are force to state our assumptions explicitly, thus making us aware of the sensitivity of our conclusion to the many assumptions that we have. Let me state at this point that, because I only limit myself to literary words in this analysis, many of the statements I make are still very imprecise. Until I am comfortable enough in mathematics, it will have to remain as it is.
Nevertheless, my model will not be useful if it stops at this point. By the principle of comparative statics, my model should provide some information concerning how our equilibrium result will change as certain parameters changes (Samuelson 1947, p.257). Thus, armed with the above primitive model, we can now ask the question: What happens to enrollment in both JCs and polys if we alter the entry requirements?
Extensions of the model (The main theorem and its corollary)
Thus, society attempts to corrects some of these market failures by enabling poly students to have a chance in entering NUS, after getting a diploma, as well as enabling JC students to enter poly after getting their 'A' levels. Thus, I now relax assumption 5. What happens to the basic result?
The crucial variable here is the entrance requirement for diploma holders to qualify for NUS. The complaints of those diploma holders, who are smart but enroll in the poly due to mistaken pessimism, are the lack of transparency in the requirements. This leads to a perception that it is much more difficult for a 'smart' student, once having mistakenly enrolling in the poly, to get into NUS.
The statement by the University's spokesperson can be interpreted in several ways. Firstly, he could mean that the criteria for polytechnic students will allow any student who is good enough for NUS to get in. In our above model, let's model it as a smart student enrolling in the poly due to mistaken pessimism. As he goes through the poly educational system, he received confirmation that he is of the smart category. Thus, by providing 'equal chances', it could mean that these smart students will be able to enroll into NUS after poly with no additional cost. Thus I make two more assumptions in my model:
8. A person at the end of the JC/poly term, will receive confirmation of his intelligence.9. There is no additional cost in entering NUS through the poly route rather than through a JC route
From the model, you can see how this change in policy affects the results. If all the other seven assumptions, other than assumption 5, hold, the model predicts that everybody, whether smart or average, would choose to enroll in the poly. The proof is simple: If the student is of average intelligence, from assumption 4, he will always get a diploma by entering the poly and, from assumption 2, he will be better off with a diploma then merely an 'A' level certificate.
If he turns out to be a smart student, he will be able to confirm it at the poly, by assumption 8, and enroll in NUS after receiving that confirmation, by assumption 9. Combining assumptions 6 and 9, there is no benefit for the smart student to enroll in the JC at all. I can now state the main theorem of my model:
Theorem 1: Once 'equal opportunities' are implemented, everybody, whether smart or average, would enter the poly.
Of course, you may argue that the simplifying assumptions of my model do not hold exactly in the real world. However, looking at the 'realistic' picture, the road to NUS from a JC path is fraught with risks; risks of the General Paper, the second language, as well as risks of getting bad results from the principal subjects. An 'A' level certificate holder, unlike a diploma holder, is clearly worse off in the job market, an opinion expressed here. The benefits of having a diploma, as a fail-safe measure if we fail to qualify for NUS, will significantly outweigh the additional costs involved in enrolling in the poly.
Thus, if theorem 1 is true, it means that MOE should not implement equal opportunities if they want to see a demand for JC education. Thus, there will be a number of smart students, who are pessimistic about their intelligence and enroll into the polytechnic, will not be able to enroll in NUS/NTU. Overseas universities, on the other hand, can accept these smart students since they do not face the constraints that MOE faces, such as the subsidy as well as the equity issues. Theorem 1 thus points towards the following corollary:
Corollary 1: A smart poly student, although denied a place in NUS, end up being accepted and even doing well in an overseas institution.
Therefore, NUS cannot give these students equal opportunities; some incentives must be given to students of high intelligence, to ensure they will continue to demand a JC education. In this case, it is preferential treatment for NUS entry. This preferential treatment would hold even if our economy does not require a fixed number of diploma holders.
I have made many other unspecified assumptions in this model, for example, assuming that JC and poly education is homogenous throughout all the JCs and polys. Furthermore, I am unable to provide any proof for corollary 1 at this moment (But I have to admit it is a nice feeling in finally being able to use terms that appear in journal articles J). This is the tradeoff that I must make in order to make this article free of mathematical jargon. If I ever make it to graduate school in the US, I hope to be able to turn this into a proper working paper.
Further extensions: Relaxing assumption 6
Relaxing assumption 6, making it more realistic by stating that the costs of an education is lower at a JC than at poly, also brings forth some interesting insights. When diploma holders complain about the unfairness of JC students having priority in entering NUS/NTU, I feel that it is a red herring (A 'politically correct' reason that actually concedes the real reason).
The real reason I hypothesize on why these diploma holders have such a high demand for university education in Singapore, is not because they feel that our institutions are better than overseas, it is because tertiary education here are heavily subsidized by the government. We have learned in microeconomics that subsidies tend to lead to distortions in economic efficiency. Thus, when undergraduates do not confront the true cost of education, for example, if they face a lower private cost, the resulting demand would be higher that what is economically efficient.
That set me thinking, polytechnic education was designed to be a tertiary education. In that light, JC and poly are not directly comparable since JC is more of a post-secondary education. That explains why JC students can continue to use the student Transitlink card while poly students could not J. By enrolling in the poly instead of the JC, poly students has taken the first slice of the tertiary subsidy pie. Thus, it can be argued that poly students should have lower chances of enrolling in NUS since, by qualifying for NUS/NTU, they get to enjoy the subsidy another time.
In the context of our model, the effects of relaxing assumption 6, along with assumption 5 earlier, will not result in the same sharp result of every student enrolling in the poly, as stated in the theorem. We would expect some smart students preferring to take the risk of enrolling in JC. In equilibrium, I would expect those who enrolled in JC are only those that are very confident of making into the University. Even if there are 'equal opportunities', the higher cost of a polytechnic education, both in terms of fees and the additional year, would make these students enroll in a JC. However, we should still see enrollment in JCs drop because of the 'equal opportunities' given to both diploma holders and 'A' level holders.
Thus, from the previous two paragraphs, an interesting policy implication arises: If diploma holders want to have 'equal opportunities' to enter NUS/NTU, we can give it to them, provided that they confront either the true cost of education in NUS, or they enjoy a lower subsidy once they get into NUS to take into account the tertiary subsidy that they have already enjoyed in the poly. The principle here is that you are only subsidized once for tertiary education. If you see an eventual goal of getting a degree from our local universities, you should not enroll in the poly.
In this way, I believe the high demand from our poly students for NUS/NTU would taper off. If I am in their shoes, having to confront the true cost of university education, I might as well head overseas anyway J. Thus poly students should be aware that, for all the complaints that they are making about fairness (In Hokkien, I will tell these people, "Mai Kao Bei", translated as Don't cry Father J), their demand for a chance at university education here is more of a demand arising from the high subsidy in university education, i.e. their demand is distorted, rather than any real enthusiasm for NUS/NTU per se. From the newspaper report given here, it appears that the poly graduates are aware of the subsidy, but what they apparently did not mention is that they have already enjoyed a subsidy for tertiary education in the poly.
Conclusion
In summary, the two main insights of my model are:
In economics, models should have testable propositions for them to be scientific. Let me just suggest one based on my above theorem: It seems likely that, with the emergence of SMU as well as the broadening of the university entrance criteria to include SATs, we are indeed heading towards a more 'holistic' system to assess potential applicants to our universities. If my model above is correct, I would predict that enrollment for JC education would decrease significantly, at a 5% to 15% level of significance J from now on, as those 'O' level holders are realizing that JC education is too big a risk. Maybe in 15-30 years time, the data would show it to be such.
With this model in mind, I have sent a letter to the Straits Times Forum page, mentioning the above two insights. I am glad to announce that they have actually published it, my first published letter to the Forum! Here is the published version. Such a pity I could not send them my above model to let them know the beauty of economic reasoning J.
The main aim of the above letter to the ST Forum is to balance up the perspective on the need to relax NUS/NTU's entrance criteria. One cannot help but feel that the emphasis, best summarized by the Straits Times poll here, have been overwhelmingly in favor of giving poly graduates more opportunities in entering local universities. Furthermore, I am personally quite embarrassed that the only defense on the present system is given by an undergraduate who said this:
"It is not fair to those like me who toiled hard through my A levels to make it to the local universities only to have the standards diluted to admit more poly graduates."
In fact, it was this sentence that made me finally decide to write in to the Straits Times. I felt that a stronger defense could be made using my above model. Under this model, the group of Singaporeans who are the worst off, under the current system, are not poly graduates but those JC graduates who only have an 'A' level certificate, listed as assumption 2 in my model. They have neither taken any tertiary subsidy nor are they prepared for the job-market. Hence, if the polytechnic 'lobby groups' succeed in pushing for 'equal opportunities', the effect would be to make these JC graduates even worse off than what they already are.
Critics might say, "That is why we allow these people an opportunity to enroll in the polytechnics." That is the other consequence of relaxing assumption 5, allowing those JC students to enroll into poly if they fail to qualify for NUS. Putting it bluntly, these students gambled unsuccessfully in their decision to enter the JC instead of the poly after 'O' levels and allowing them to enter the poly is like a consolation prize. If going to JC is indeed a gamble, yes, I agree that is that risk JC students must face, for the sake of being given preferences in entering the universities. At least I have established that there should not be equal opportunities for now.
Predictably, the official government reply to this issue totally avoided the question on the lack of transparency in the criteria for poly graduates, as well as the question on whether poly graduates and 'A' level holders should or should not have equal opportunities. I was chuckling when I saw that he avoided the first question by stating:
"The fact that many overseas universities are prepared to admit our polytechnic graduates directly into the second or even third year of their degree programmes is clear indication of the standards of our polytechnics and the qualifications they award."
The pressing question that poly graduates are asking is, "Why is it that NUS/NTU can reject those poly students who are later accepted into these overseas universities?" While my model explains it using corollary 1, the MOE spokesperson ignored it completely by quoting the above point. Interestingly, he made no mention of my letter. If I want to be optimistic, I would regard the points there as something he would like to say too but he could not since he is speaking on behalf of MOE J.
Policy implications
I am sympathetic to late developers, being one of them myself. I was in a single science class when I took my 'O' levels and frankly, I never thought I could make it to the university nor cope with the curriculum there when I already have so much problems with the secondary school syllabus. Let us now examine what policies may be introduced to help late developers.
My above model, since it is based on education as a signal, did not endogenize a student's intellectual development, but it does offers an insight on how 'equal opportunities' might be provided. Since the main problem is that of uncertainty in entering universities, one possible policy implication might be to grant a direct route to the local university for all JC students. That means, based on 'O' level results, anyone who makes a certain aggregate would be automatically given places in NUS/NTU. They then take perhaps a 1-2 year matriculation period, similar to the present JC system, where they prepare themselves to enter university. There might still be 'A' level examinations but it will no longer count as a criteria for university admission.
Those who do not make that aggregate for their 'O' levels will enroll in the polytechnic. At the end of their course, they are given another opportunity to qualify for NUS/NTU. Since there is no longer any competition from JC students, who already secured their place in NUS/NTU after 'O' levels, any suitable criteria based on polytechnic grades or interviews can be given. Thus, this ensures that late developers are given a second chance without lowering the welfare of the JC students.
If the above proposal is unfeasible, I would then go back to my original voucher proposal that I have mentioned here. This time, let us make it a 'tertiary voucher' instead of just a voucher for university education. The idea is that, all Singaporeans be given an educational voucher for tertiary education. I can envision three different scenarios:
Of course, we should decide exactly how much value the voucher should have. Under scenario 3, which might be the most costly scenario if he decides to pursue further education, the student should be prepared to fork out more on his own if he wishes to pursue that. Alternatively, for equity purposes, the student should not have to fork out any amount on his own, for a poly education, should he decides to be content with a diploma.
I would suggest that JC education should not take any value from the voucher since it is still, after all, a secondary education. Thus, in scenarios 1 and 2, the student is only incurring an opportunity cost, which may be more significant, in pursuing JC education first.
Again, the beauty of this voucher scheme is that of equity. All Singaporeans get the same subsidy for tertiary education, for them to pursue their own ideal dreams. In this way, NUS/NTU/SMU, as well as overseas universities, would charge Singaporeans the full cost of education, which the students can use their voucher to offset the cost. Thus, whether there are equal or unequal opportunities, there should not be any complains from either JC students or poly graduates.
References
Akerlof, George A (1970), "The Market for 'Lemons': Qualitative Uncertainty and the Market Mechanism." Quarterly Journal of Economics, Vol. 84.
Samuelson, Paul Anthony (1947), Foundations of Economic Analysis. Cambridge :Harvard University Press.
Spence, Michael A (1974), Market Signaling. London: Harvard University Press.
The Straits Times. Various issues.