Perspective Unlimited

Sunday, October 07, 2007

A Simple Welfare Analysis of Borrowers and Savers

One of the missing piece in the discussion on CPF returns is the peg to HDB housing loan. This is an important point of consideration since any increase in CPF rates will have considerable welfare consequences on these net borrowers - people who took out a HDB loan which is larger than the available balances they have in their CPF accounts. I too was once a net borrower, when I first got married, emptied my OA, and took out a loan of almost $200K from HDB for my flat.

As we know, HDB loans are granted at a concessionary rate of 2.6 per cent, pegged at 0.1 per cent above ordinary accounts (before new changes are introduced). We do not need to know the details about the intra-government financial arrangements, but it suffices to note that for HDB to grant the loans, the money has got to come from somewhere.

I set out then to compare two sets of outcomes using highly simplified assumptions. These assumptions are meant to follow closely to how the current system operates, but I ignore some complicating rules where they occur (I will tell you where they are in the course of the post).

The Life Cycle of a Hypothetical Couple

A young couple starts working at age 25 with a combined income of $35k per annum. Every year, they get a wage increment of 2 per cent until they are 50, after which their wage stagnates. For simplicity, they are assumed to be continuously employed from 25 to 65 until they are retired. They save 33 per cent of their income and consume the rest. At age 30, they make a major decision of their lives to buy a HDB flat and in the process take out a 30-year $250k loan to finance that purchase. How would they fare with and without the CPF system?

With the CPF system, their savings (which is 33 per cent of income) is split between OA (which pays 2.5 per cent returns on net balances) and SMA (which pays 4 per cent). I ignore the changes in contribution rates for different age groups and contribution cap for convenience, and savings is split 65/35 between OA and SMA. The mortgage payment can only be deducted from the OA account. The interest on their mortgage is 2.6 per cent. The rules I applied here are a good approximate of how the current system functions.

Without the CPF system, they can invest their savings (again 33 per cent of their income). I posit several scenarios of long term returns (4 to 7 per cent). However, without the CPF system they can no longer borrow at 2.6 per cent for their property since the government can no longer supply that source of fund. The couple will have to borrow from the market at 4.5 per cent, which I believe is a fair estimate of long-term borrow cost. Of course, this parameter can be adjusted and the results re-evaluated in a sensitivity analysis.

Retirement Funds at Age 65

How would the couple fare under the two different systems at age 65? How much retirement funds would they have with the different systems? It turns out that the couple which starts out with $35k income is better off with the CPF system, mostly. Why is this so? In the earlier part of their life-cycle, they are net borrowers who take out a loan for their property. Since they have very little net balances in their OA account (because of mortgage deduction), any increase in CPF rates are not going to benefit them.

Conversely, they enjoy a 2.6 per cent interest rate on their property, which saves more than $3000 per year in mortgage payment each year over a 30-year period as compared to if they have to pay the assumed market rate of 4.5 per cent. Unless they are able to do very well with their investing their savings in the market, they are better off enjoying the concessionary housing rate that comes with the CPF scheme.

The High Income Couple

In the second spreadsheet, I change the couple's starting pay to $70k per annum. This is therefore a high income couple compared to the previous example. The high income couple is better off without the CPF system. Why? As they have high income, they become net savers much earlier in their life-cycle given the same loan they took out. As a result, the CPF accounts do not offer them a rate of return that matches the 4 - 7 per cent assumed to be offered by the market. They are better of without the CPF scheme - that is, to forego the concessionary loan rate and then be free to invest their savings in the market.

Winners and Losers

What does this whole exercise tell us? First, it confirms the simple microeconomics principle - borrowers lose when interest rate rises. On the other hand, the high income couple is mostly likely better off if their net savings is freed up to be invested in the market. The analysis between the two systems is sensitive to assumed rates of returns offered by the market, risks, income profiles and many other parameters. But within fairly reasonable estimates, the general result holds.

Second, if CPF has to increase its returns to members and at the same time passes on the cost of funds to other agencies including HDB, borrowers would have to fork out more for their mortgage. There is a real possibility of many poor families may end up net losers if that happens. The microeconomic consequences of pushing up CPF returns is therefore not clear cut. From whose perspective are we looking at when we say that CPF rates are too 'low', borrowers or savers? If indeed there is an element of welfare transfer, it is from the rich savers to the poor borrowers.

The fact that CPF has a net total balance of more than $120 billion may suggest to some that there are huge surplus savings. But remember, we have to knock off a couple of billions that belong to W Malaysians and not Singaporean households. And also that HDB obtains loan from the government at CPF rates in order to lend to purchasers (who borrow at 0.1 percentage point higher). How much does HDB 'owe' the government as a result of mortgage financing? $55 billion in total as of 2006. Let's assume all this is disbursed to borrowers. After accounting for all these, the net savings position falls significantly.

Furthermore, we are only talking about aggregate numbers and they mask the devils in the distributional details. How many net borrowing families are there? The number surely is not small. In fact, it is entirely possible that for every one rich net saver into the system, there are many more net borrowers. If that is indeed the case, and if rates of returns are pushed up, the number of losers will outnumber winners. Worse, the distribution will be in favour of the rich and against the poor.

It is really 'not so simple'.


  • Bart,

    Thanks for describing a beautiful system to transfer what is meant to be retirement funds to surpluses in the HDB which sells us the most expensive public housing in the world.

    Overall we are okay until we are not describe a "couple" and a model example...there are people who don't get married, I guess the don't deserve the wonderful benefits are the single moms who have been screeming to be part of this best deal in town...but are left out for moral reasons.

    By Blogger LuckySingaporean, at 11:57 pm  

  • Hi Bart, your post has been featured in The Singapore Daily []. Keep blogging!

    By Anonymous The Singapore Daily, at 3:21 am  

  • Sorry my earlier response did no justice to your learned exposition.

    You're saying this:

    1. CPF return is related to HDB loans which are subsidized.

    2. Poor couples borrow more than rich couples.

    3. If rates move up poor couples will be disadvantaged.

    If I were the govt:
    1. Keep CPF purely for the purpose of retirement.

    2. HDB whose mandate is to provide affordable public housing, will have to supply housing that can be paid off comfortably.

    3. People will end up with more money in their CPF. The govt will offer to have it managed by the best fund managers, allow people to invest in selected funds or opt for a fixed deposit rate.

    4. With such a plan people can retire earlier, have better quality retirement especially the poor who currently cannot even meet the minimum sum.

    By Blogger LuckySingaporean, at 5:09 am  

  • RH:
    1. I have stopped reading you a long time ago due to your pro-PAP leanings.

    2. Today, I clicked on my Google Reader and read your above.

    3. I did not give it much intensivity as you have proven unworthy. So I will just say, correct me if I am wrong, THAT YOU CANNOT EVALUATE A POLICY BASED ON A FICTITIOUS COUPLE AND ANOTHER FICTITIOUS COUPLE WHEN IT IS THE TOTAL AGGREGATE SUMS THAT ARE AT STAKE.

    4. Meaning how many billions are in the CPF being under-interested. How many billions does the HDB loan out in pseudo-subsidised rates.

    5. THEN, and only then, do you ask how many couples, REAL and not fictitious, do NOT borrow because they are ineligible, etc.

    6. Do not use fictitious examples. To see the dastardly deeds of the corrupt govt, compare how many billions on each side, etc. Sheesh!

    By Blogger Robert HO nric S0197974D, at 8:04 am  

  • Hi Bart, I'm interested in the HDB issues and am wondering if you could elaborate on the following 2 points pls:

    1) Why is it necessary to use CPF funds as loans for flats? Why could HDB not get funds from elsewhere? and assuming CPF funds is used, is it the most efficient way of providing HDB loans? For e.g. MOF has stated that GIC could raise money more cheaply through Government bonds than through CPF funds. Could HDB not do the same?

    2) Why is HDB letting prices of flats go so high? As the dominant provider (perhaps monopoly) of public housing in singapore, it conceivably has strong pricing powers. Why is it that HDB did not use it's pricing power to bring the prices of flats down? As far as I know, HDB makes a profit from every flat that it sells, because the price of a flat is more than the cost of building it (including land cost).


    By Anonymous Anonymous, at 8:58 am  

  • Dear Mr Robert Ho,

    It would be better that you do not place your identification number in this blog, but I respect your choice. After all, Singapore is supposed to be a free country.

    By the way, I have a strange feeling about your point #1 as I have the same feeling after many readings of the blogger's posts and comments. The word "rational" is nice and beautiful.

    The message "the government is equal to the government" is nice and beautiful to dream about. But, I ever heard our Mr Lee KY did said otherwise. Even the policeman testifying in our world class judicial courts also agreed with our esteemed senior leader Mr Lee.

    I hope that Mr Han (who?) would acknowledge that Mr Lee is a true leader and Mr Lee is definitely not a symbol behind the fence.

    Mr Ho, alas, I live in this real and harsh world and it is definitely different from the world of Shrek.

    I may have to collect used cans when I become old, provided that I do not die before 85.

    Mr Ho, have a nice day and may you stay healthy. You need to be around for the grandest state event happened.

    Your humble simple peasant

    By Anonymous Simple peasant, at 4:22 pm  

  • Hi Bart,

    If interest rate goes up, all else equal, won't housing price goes down or at least had its price growth moderated?

    Currently there is no evidence that tell us that these 2 effects won't cancel each other out.

    By Blogger at82, at 6:58 am  

  • Not only that the poor probably borrow more as a multiple of their income, the fact that they have lower income means that they spend a larger part of the working life as net borrowers. The time value of money kicks in - the concessionary interest rate is much more valuable to them.

    Press the financial calculators - take a $200k or $250k loan and calculate the difference in mortgage payment over 30 years at 2.6% and then add another 1-2 percentage points. We are talking about another few thousand a year in interest payment each, over 30 years. That will be a significant whack off the income of the $35k p.a. couple.

    To Anon 8:58,

    Imagine what you just said. Govt, (through HDB) should borrow money and then provide cheap loans to Singaporeans for our flats. At the same time, Govt (through CPF) should invest our money and guarantee a high rate of returns. You have just presented Singaporeans an arbitrage opportunity. It is like asking the banks to charge lower interest to its customers on loans than interest paid to customers on savings. Sounds sustainable?

    Coming to the point on HDB pricing. There is this nice theory in International Economics called Factor Price Equalisation Theorem. Basically, Singapore is a really open economy. Its payment to factors - wages, rents etc - are set by international price. If HDB prices are that out of whack, Singapore would have lost competitiveness a long time ago.

    Look around us today. Foreigners are snapping up our real estate. If a condo at Bukit Timah is going for 2 million, would the next door Clementi, Buona Vista etc be far behind? Recall two months ago, a guy bought a Tiong Bahru flat from HDB at around $300+k and then re-sold it for $720k 7 years later. My view is that as long as Singapore moves towards being a global city, its real estate will reflect this global price. Underpricing HDB flats will in fact lead to misallocation of resources.

    By Blogger Bart JP, at 8:27 pm  

  • Bart,
    :::Coming to the point on HDB pricing. There is this nice theory in International Economics called Factor Price Equalisation Theorem. Basically, Singapore is a really open economy. Its payment to factors - wages, rents etc - are set by international price.::::

    Govts everywhere recognise the need for public housing that is priced for affordability and not purely by driven market forces. The reason is simple, about 1-20% of your population on the left side of the Bell Curve simply cannot afford rent or ownership if nothing is done. Socially not acceptable and govts have to intervene.

    You're right about Singapore being globalised and foreign money, skills etc flowing freely into Singapore. We may move so far up the ladder you might need a Masters degree just to survive in Singapore. You take a look at Silicon Valley, the locals simply had to move out as cost escalates - only business owners remained. You simply cannot survive with a Highschool diploma, life would simply be miserable. Silicon Valley is just a place in America there are other places people can go. You can also look at Macau and see the mess brought by rising prices in a very open capitalistic city - people are on the streets protesting high prices and mind you the Macau economy is in excellent shape growth double digits.

    The problem with Singapore is we are actually a nation aspiring to be a globalised city. Income gap is escalating, many people just don't have the option of simply moving out as cost rise to somewhere cheaper especially the less skilled or people on the left side of the bell curve. Even the PAP recognise that and brought back rental flats.

    There are many things at MAS disposal that affect property prices. Just like the subprime mess, property prices can be out of whack for long periods...4M Americans can lose their homes and the mess is just a small 3Month blip on American economy. Max Loan period, restriction on foreign buying, stamp fees, etc.

    Singapore is a nation not just a city. Our people are citizens not just labor in factors of production. The PAP had its origins in socialism but knew in their mind that you need capitalism to produce the wealth. Putting a roof over the people's head cannot be at the expense of length and quality of retirement. If having a globalise city simply means higher cost of living to the ordinary citizens, higher cost of housing due to people pouring in in large number, then the govt has a hard time explaining why having a globalise city is good for them.

    By Blogger LuckySingaporean, at 3:07 am  

  • Should public housing be a speculative commodity never mind be determined by international market forces?

    should a young couple w no money "buy" a public apartment vs renting one?

    Is HDB still relevant or is it a oversized dinosaur past its expiry date?

    Will Bart JP go on to be a powerful policy maker?

    Can Bart JP produce a new scheme to shame the "longevity scheme" or "GST to help the poor"?


    By Anonymous Anonymous, at 11:30 am  

  • Hi Bart, i'm the first anon at 8.58. I pointed out the possibility of government bonds to illustrate that HDB could get funds from elsewhere and CPF may not be the best way of getting funds for HDB. MOF itself has stated in their letter to Straits times that they can get funds at a cheaper rate than CPF. I don't see why there is arbitrage. What i'm saying is that the govenrment can act as a conduit for singaporeans to borrow at a lower interest rate and help singaporeans invest to get higher returns. It's not a closed system; whatever money that a singaporean borrows for flats, he/she will have to pay the interest back to whatever party that lends him the money. The government in this case becomes merely the middle man to get better rates.

    In any case, the more impt point is that i'm not convinced that HDB could not get funds for flat loans from elsewhere apart from CPF. We could have even used proceeds from sale of land to fund flat loans (bearing in mind again that HDB and by extension, the government is not losing anything by doing so, since the interest is paid for by singaporeans). As for the hypothehtical higher interest paid out by GIC to singaporeans, it depends on how well the GIC invest the money, in good years, we get more interest, in bad years, less. But frankly, in the long run (i.e. 30 years or more), interest rates will exceed 3.5% with very high probability.

    As for HDB pricing, i think luckysingaporean has argued the case far better than I have. But, i looked up the wikipedia entry on factor price equalization theorem here:
    Seems to me that goods have to be identical before the result can be applied. Are public housing really identical? Is a flat in say Sengkang the same as an apartment in Penang? In any case, any industry in which there is a dominant market player, the dominant market player always has the power to be a price leader and has great influence on the price. For e.g. if Apple were to lower the price of it's ipod, can creative not follow suit? HDB is in a similar dominant position if not more so, given that it is backed by the government and the law. It can influence prices in a very big way and i'm not sure that it would be bad for competitiveness, given that high estate prices is one of the challenges to sustaining singapore's competitiveness anyway.

    I suspect the reason it is not doing this is because the government has let prices gone up too high due to it's asset enhancement policy under PM Goh. Now, it's hard to bring it down without crashing the property market. But, the policy was, to me, a mistake. It creates an illusion of wealth, sure you bought your house for say 100k sometime back and it's worth 500k now. But, if you sell it, you'd need the same 500k to buy a new house at today's inflated prices. Illusory wealth. i think it's time to undo that asset enhancement policy.

    By Anonymous Anonymous, at 1:27 am  

  • I think you are taking the govt's ability to raise funds cheaply for granted. Any scheme that charges borrowers less than what pays savers does not sound like a very sustainable idea. Stat boards can raise funds cheaply because of the strong position of central govt, and the implicit guarantees. With a scheme like what you described in place, I am not sure the cost of funds will still stay low.

    I have written on HDB pricing here. Tell me if you still disagree.

    Finally on FPE - it does not suggest Singapore workers have to be paid the same as China worker. Productivity or quality differences must be accounted for. Of course Singapore flats are worth more than Penang, I don't really get what you are trying to say (apologies here).

    By Blogger Bart JP, at 9:21 am  

  • Hi Bart, thanks for the information, links to your previous post and clarifications thus far. I still do not agree with some of points, but i'm afraid i'll be too busy for the next few days or more to think through your arguments and give a good reply.

    There's just one point i would like to seek clarifications on for now, but as i have not read through your previous posts in detail, you may have covered this already. If so, i apologise for bringing it up again.

    I get this sense that you seem to assume free market mechanism to be at work in the property market (or public housing market) in singapore. Now, i'm not accusing HDB of seeking monopolistic rents, but correct me if i'm wrong, you seem to assume some invisible hand what pushes prices to a general equilibrium and HDB has not much influence over this invisible hand. That would be the case in a perfectly competitive market where the action of 1 player doesn't affect anything. but then i don't think that is a valid model in the singapore property market, because of the dominant role of HDB and the government in public housing.

    Now, let's say you change your model to one where the players' actions can affect price movements, and the best responses of other players. Then, you can get a game theoretic model in which the equilibrium point (Nash, Bayesian or otherwise) can be inefficient in general, with respect to the Pareto optimal frontier.

    The next point i want to make is that even if what HDB is doing now is Pareto efficient, providing more subsidy (by changing the price or otherwise) doesn't necessarily make it inefficient. It could be a case of moving along the Pareto optimal frontier. Of course, that depends very much on what your cost function is, but if your cost function incorporates some form of social utility or welfare, it isn't that hard to imagine a cost function that would make this (moving along Pareto optimal) possible right?

    By Anonymous Anonymous, at 11:11 pm  

  • Yes, I believe it is possible. If there are two players, and if their discount of future profits is not too high, a high price can be sustained as an equilibrium (even with explicit collusion). This is the Folk Theorem.

    I have a lot of doubt whether this is indeed the case. If you wish, you have to think of the general equilibrium of the world because Singapore is a small open economy. If we ignore the effects of local economic rent (agglomeration rents, local spillover rents etc), some form of FPE must work or Singapore very quickly loses competitiveness.

    By Blogger Bart JP, at 5:14 pm  

  • Repaired through the more and more inexpensive and consequently slated flights.
    Position the combine ready-made switzerland begin metal and also card casing.
    Making a long-term manufacturer's warranty could also help the practice. To become kinds of designs feasible consult the seller connected Ultra Toaster ovens simply because business is famous for preparing eco-friendly productivity. De-frosting just isn't absolutely.
    It's unfortunate, should it be nachos is just processed from home, really sometimes placed in an indoor frequent cooker and board burn cookware within it wished to usually very hard to experience the great outdoors fresh air and then meals a single french fries as well as.

    Review my web site :: used convection ovens michigan **

    By Anonymous Anonymous, at 12:45 am  

  • The happens just be sure begin to look along the
    large choice behind kettle as well as poster times on the market today.

    It is crucial that seriously is dirt-free coupled with
    unsoiled quite not bacterias are able to find their house
    for it. If you nourishment? Positioned the
    toast at the pertinent proportioned roasted container.

    My blog post - electric oven toaster grill []

    By Anonymous Anonymous, at 5:20 pm  

Post a Comment

<< Home