The simplest example is if A = B and B = C then by definition A must equal C. Taking a simple example, letâ€™s assume that my friend tells me all cars are blue and that he has a car. By extension I can know that my friends car is blue because my friend has a car and all cars are blue. The transitive property provides us a way to reconcile truths against other things we know to be true.

Before proceeding to explain how this relates to Singaporean public finances, let me frame the transitive property in financial terms. Letâ€™s assume that my friend tells me on January 1st that he has $10,000 in an investment account. I see my friend one year later and he tells me his investments made 10% last year. I can safely assume that my friend has around $11,000 in his investment account.

There are two important points about the transitive property as it relates to finance. First, if my friend tells me he starts off with $10,000 in an investment fund returns 10% in one year but then tells me he has $5,000 in his investment account, I know that my friend is leaving out important information. Maybe my friend is only counting the gains on investments that did not lose money or maybe my friend went and bought a new car, but a 10% return on $10,000 with no other changes should leave $11,000 in the bank. Second, while perfect information is always better, the transitive property allows us to work very logically with imperfect information. For instance, if my friend tells me that he started the year with $10,000 in an investment fund and finished the year with $9,000, unless he spent money, I can safely assume his investments lost 10%. I do not need perfect information to be able to figure out a lot about the finances of Singapore.

The Singapore government is trying its best to avoid the transitive property in defending its investment and public finance record. Let me give you three examples of how we can use the transitive property to study Singaporean public finances. First, Temasek claims that it has earned an annualized 17% since inception which gives us the ability to take the amount of money they currently have and calculate (estimate) backwards to how much they started with in 1974 or conversely calculate (estimate) how much they should have now based upon how much they claim to have started with. We donâ€™t need the government to provide us every piece of data and every number.

Second, we can estimate how Singapore is allocating investment funds between GIC and Temasek. The reasoning is simple: if virtually any of the government surpluses and CPF funds after 1974 went to Temasek, it would have trillions of dollars given their claimed 17% return. That would imply that either Singapore is sitting on * trillions* of undisclosed dollars or virtually all surpluses and CPF funds went to GIC.

Third, despite the popular belief that Singapore has not disclosed the size of their reserves, we can use the transitive property to calculate the size of GIC. On the Singapore balance sheet published by the government they list their total assets. We know how their total assets, Temasek assets, and government assets. If the total amount of assets is the sum of the government , Temasek, and GIC, we can easily calculate the size of GIC. Put another way if 50 = 10 + 20 + x, we can calculate the value of x.

Letâ€™s put this into practice. From 1974 through 2012, the sum of Singaporean debt and operational surpluses equaled $708 billion SGD. According to their 2012 public balance sheet, the government of Singapore list $765 billion SGD in assets. Please explain to me how Singapore saved and borrowed for investment purposes a total of $708 billion SGD between 1974 and 2012, claims to earn 17% and 7% over more than 30 years in Temasek and GIC, but only declares $765 billion SGD in assets. Either investments are not earning what is claimed or money is being spent that is not being accurately reported. There is * no* other explanation.

By definition Singapore cannot: a) invest $708 billion SGD b) claim a 17% and 7% return on investments over more than 30 years and c) only have $765 billion SGD. One of these * must* be false. We can see clearly that only two of these three assertions can be true.

This is not a cultural problem, debt cost, currency loss, accounting issue, or government secrecy that is causing this discrepancy. One of these claims has to be false.

If anyone wants to empirically point out where the error lies I will gladly listen. However, I will not be intimidated by anyone. Anyone.