Tuesday, June 5, 2012

Does economics justify high ministerial salaries?

Singapore ministers are known for drawing the largest salaries amongst politicians around the world - its Prime Minister earns US$1.7m a year, more than four times higher than Barack Obama's relatively paltry US$400,000. One reason, amongst others, is that without high pay, “corruption will set in, and we will become like many other countries, and face the problems that many other countries face,” then Defense Minister Teo Chee Hean told the press in 2007.

This is a contentious issue in Singapore. Opposition member of parliament Low Thia Kiang, in the same year, argued that Finland, Denmark and Switzerland managed to have less corruption with lower pay. Other opinions on the net range from outright disagreement - "you don’t need a ridiculous pay to prevent corruption" - to contemplative acceptance: "the only empirical study of the issue [...] concluded that higher pay was associated with less corruption".

Can economics contribute anything of value to this debate?


We should establish some notions about economics first. Many associate economics with money (and economists with evil-capitalist-scums-of-the-world), but the truth is that economics is really concerned about happiness. Pour through the maths and you'll find that it is about people finding the best way to be as happy as they can. For example, basic undergraduate models demonstrate that although having more money increases happiness, this happiness plateaus after some level and people would rather have their free time to do other things. Yes, you can have too much money in economics.

It may sound strange, but happiness can be represented mathematically. Here's how it looks like graphically. In the diagram below, the level of happiness is shown in the y-axis. The units don't matter; what matters is that there is "more" happiness, and "less" happiness. On the x-axis we have income, which represents, well, income.


Now look at the blue line. The blue line shows the relationship between happiness and money - having more income increases happiness, but happiness increases by smaller amounts as income grows more and more. I could buy lots of things with $10,000, but the next $10,000 buys me more things that I don't really need, and my purchases with the next $10,000 start to get frivolous.

Lastly, our minister's salary is also depicted by the red dot.

We model corruption next. Corruption is not just about accepting a bribe and getting away with it. There is some chance you will get caught, and you are faced with two possible futures - one in jail, and one where you get away scot-free. In fact, you should think of it as a lottery. Buying the corruption ticket gives you a high level of happiness if you win, and low level of happiness if you lose. These are shown by the green dots below, on the same blue line as the earlier graph.


Like a lottery, there is a probability of getting caught and not getting caught. This probability is used to find our minister's expected happiness. Expected happiness is simply the average happiness from both outcomes, but weighted by these probabilities. If the expected happiness from this lottery exceeds that from not taking the lottery, the minister will take the bribe.

The expected happiness is depicted by the dotted green line which connects the two green dots. Let's assume that our minister only has a 20% of getting caught. As a result, his expected happiness which is shown by the white dot is closer to the "not caught" scenario.

This is worth some elaboration. Simply put, deciding whether to take a bribe or not is like deciding whether to buy a lottery ticket. If the ticket costs $10 and there's a 90% chance you will win $1,000 you will probably take the gamble. This is because your expected returns are high, at 0.9 X 1,000 = $900 which far exceed the cost of the ticket. If however, there's only a 2% of winning you might prefer to keep your $10 since the expected returns of 0.02 X 1,000 = $20 won't be worth the risk even though $20 is more than $10.

With these basics in place, we can now combine the two graphs:


Recall that the red dot shows the amount of happiness our minister gets if he is not corrupt, and the white dot is the expected level of happiness he gets if he enters the corruption lottery. Because the probability of getting caught is set at only 20%, the white dot is pretty near the "not caught for corruption" outcome. Subsequently, it ends up above the red dot. Hence, our minister is gets a higher level of happiness from taking the bribe. We have ourselves a corrupt minister.

Sensing this, the Prime Minister increases ministerial salaries to deter corruption. Will this work?

With the pay increase, the red and green dots shift around abit. This can be a little tricky, so follow closely:
  • The "caught for corruption" dot stays in place since jail is equally bad whether you are rich or richer.
  • The minister gets a higher salary, so the red dot moves to the right. 
  • The level of the bribe stays the same, so the horizontal gap between the green "not caught" dot and the red dot is unchanged. 
  • The chance of getting caught is still the same at 20%, so the white dot is still near the "not caught" dot.


Putting these together, we see that the white dot is now below the red dot. The minister is happier not taking the bribe, and the Prime Minister's policy has worked. Note that I didn't resize the curves or do any graphical gimmick - everything was done on Excel with simulated numbers so it is really possible, although not guaranteed, that higher salaries deter corruption.

If you've made it this far, well done! Give yourself a pat on the back.

On the other hand, many Singaporeans feel that ministerial salaries are too high, and this has become quite an important election issue. However, economics shows that lower salaries might encourage corruption. Can we have our cake and eat it?

Economics to the rescue again. In fact, the problem is not about finding a balance, but that we have one arrow (pay), but at least two targets (win votes and prevent corruption). According to the something called the Tinbergen Rule, you need at least two arrows for two targets. For example, I like fries but I want to keep fit, so I need two arrows - a trip to the gym and a trip to McDonalds - to have both. Can economics find other arrows to prevent corruption?

One such arrow is to make it harder to take a bribe and get away with it. This reduces the probability of winning the corruption lottery.

Return to the graph without the salary increase, as shown below. Recall that the expected happiness from the lottery is the average of the happiness levels from the "caught" and "not caught" outcomes, but weighted by their probabilities. Since the likelihood of getting caught is higher, the weight shifts towards the left, and the white dot is closer to the "not caught for corruption" dot.

This white dot is now below the red dot, and our minister is happier not taking the bribe.


There's more than one arrow in the economist's quiver. Alternatively, we can make penalties for corruption more severe. When this happens, the "caught for corruption" dot shifts to the left. What this does to the white dot is to shift it down. It is now below the red dot. Again we have prevented our minister from taking the bribe.


In fact, this might explain why hell has to be a place of eternal suffering. 

I digress. The last, but by no means the least, arrow is to have ministers of strong moral fiber. Ministers might be inculcated with a strong code of ethics and selected on the basis of remarkable personal integrity. They might be elected because of their great empathy, and think about those they harm should they accept a bribe.

You don't need behavioural economics to model this, just regular economics. All that happens, using our now-all-too-familiar graph, is that the entire blue line shifts down when our minister violates his moral beliefs. The same income now gives our minister is less happiness than before.

This occurs because without the (spiritual?) peace that comes when he is aligned with his moral code of conduct, he is unhappier even if his income increases. Or maybe living a lie is just too difficult. Whatever the case, the incentive to take a bribe then disappears. In fact, one study found that reading the Ten Commandments before doing a test reduces the chance of a person cheating!

In conclusion (finally!), economics does support having high ministerial salaries to deter corruption. But economics also adds that this is not the only way to deter corruption. Better detection of corrupt activities, harsh penalties, and strong ethics also work.

No comments:

Post a Comment