Thursday, July 12, 2007

Kaldor Hicks Preview

Gabriel says that I should post my ideas no matter how nascent because lets get real, whose gonna want my ideas.

So here is one that I have been kicking around promising myself that I would finish the write up on but haven’t gotten around to it.


Kaldor-Hicks tends to overestimate the net benefits of a policy whose distribution is uncertain.

That is, when we think about whether a policy is a good idea we do a cost-benefit analysis. We add up all the costs to whomever they occur and all of the benefits to whomever they accrue. If the benefits are greater than the costs we declare the policy to be efficient.

Perhaps, the policy is not equitable but it is efficient. The winners could compensate the losers and be better off.


Now the problem is that the winners don’t compensate the losers. And, that’s not just a problem for the reason you think it is. We all admit that the distribution of the gains may be such that the winners don’t personally value their gains as much as the losers personally value their losses. However, without the ability to do interpersonal comparisons we are stuck.

Yet, there is another problem. If the distribution of the gains is not certain then the individual agents will value them at less than their face value. Likewise if the distribution of the losses is not certain than the individual agents will value them at more than there face value.

This means that even if the total benefits outweigh the total losses with certainty, uncertain distribution can lead to individual agents perfering not to make the trade.

To drive the point home I create the following example:

There is a policy were the gains to the winners outweigh the losses to the losers with certainty but NO AGENT wants to see the policy enacted. That is, there is a policy which passes cost-benefit analysis but is uniformly rejected by each person affected by it.


The simplest example is easy. Suppose that the benevolent government is offered the following deal. One million of your residents will be selected and given $100,000. Another one million of your residents will be selected and charged $99,999.

To make matters simple only residents who have at least $99,999 will participate in this program. However, whether the resident is a winner or loser is chosen at random.

This program seems like an economic free lunch. The gains are guaranteed to outweigh the losses by $1 million. The selection process is completely random, so there are no economic distortions. In fact, there is no a priori reason to expect that the winners will have lower marginal utilities of income than the losers.

Yet, we could expect that every single agent will reject this program. Why? They reject it because the program exposes them to risk. The cost of that risk outweighs the expected benefit of program.

Perhaps, the agents could insure against the risk. Since the expected gains are positive they should be able to write a contract that splits the expected gains with an insurer so that everyone winds with more than what they started with.

However, what if I said that I am not going to announce the winners and the losers? I am simply going to subtract the losses from the losers net worth and add the gains to the winners net worth with no record of the transaction. How could one insure that?

If this seems a little far fetched and unrelated to real world issues, allow me to change the offer again. Rather than simply adding $100,000 or subtracting $99,999 I am going to do this.

The winners will receive an increase in the demand for their services and a pay raise. The losers will see their jobs outsourced to Asia. The winners won’t know for sure why they lost they received a raise. The losers won’t know for sure why they lost their job.

To add another layer of realism lets change the terms a little. I won’t change any of the expected values but this time instead of selecting 1 million winners and giving them each raises worth $100,000, I will select 100 million winners and give them each raises worth $1000.

The expected gains from this deal are still $1 million. Does anyone want to go for it?


There are two insights that I draw from this thought experiment.

1) That distributional risk is a real concern in policy. If the winners don’t know they will be winners and the losers don’t know if they will be losers the policy will seem better than it really is.

This was the idea that I started with. Workers I talked to disliked outsourcing not just because some people did loose there jobs but because they felt like any of them could loose their jobs. The difference is subtle but important. The first is just about direct costs; the second includes a notion of risk.

2) The second insight I take away is that just as Von Neumann / Morgenstern risk comparisons allow us to define cardinal rather than simply ordinal utility. Who-will-gain risk comparisons allow us to define a sort of interpersonal utility comparison. If you had an equal shot of being on any end of this policy would you still support it? Its not exactly interpersonal comparisons but it carries much of the intuition we want to gain from it.

Comments? Suggestions?

39 comments:

Anonymous said...

If you had an equal shot of being on any end of this policy would you still support it?

It sounds like the Rawlsian original position. I don't agree with his minimax idea, but you could use some other decision making function instead. If you had an equal probability of ending up in the position of any other person post-policy, would you support it?

Dallas Weaver said...

Looking at this problem from an individual decision makers viewpoint, the concept of risk becomes relative to the assets of the individual. A risk of a $99,999 loss for an expected gain of $1 is much too high of risk relative to the small expectation value of the gain. However, if the risk is $1 for an expectation value of the gain is 0.000001$ and it was just a trivial transaction cost -- putting coins in a slot machine while waiting at LV airport -- people would take the risk.

dWj said...

Given the world you've constructed -- i.e., leaving out some results from prospect theory -- you can still do cost-benefit analysis here, you just have to be a bit more careful. The expected utility after taking a 50/50 +100000/-99999 risk will (presumably) be equal to the expected utility of a definite loss. A concept of cost/benefit constructed around the definite dollar equivalent of the expected utility change will work a bit better than one constructed around expected dollar gains and losses.

Of course, the straight "add up the dollars" mechanism is simpler, and therefore more likely to be employed, and your caveat that it can overstate (or understate) total benefits from a "how much would you be willing to pay / have to be paid to support this proposal?" standpoint is a good one to keep in mind.

Gabriel said...

I agree with the previous commentators. Your social choice criterion need to have some risk aversion built in.

On another note, not knowing who the winners and losers are going to be is a feature, not a bug. It means that things can be fairer. Actually, once upon a time, it was required of justice to be blind to such thing as income, wealth, etc. All citizens are citizens and nothing more. That's a bit out of fashion these days.

I'm glad to see that someone is thinking about these things. The use of c&b analysis in government (in Western nations) has been pretty much taken up also because it helps bureaucrats get out of providing reasons for their actions. "I just did c&b a."

dWj said...

Gabriel -- cf. "Average reciprocity of benefits", a delightful phrase used by Oliver Wendel Holmes in justifying a regulation on coal mining companies that he held was not a regulatory taking because, based on ex ante knowledge, the rule benefited all such companies, even though ex post it might not.

Karl Smith said...

If you guys have time, look at the paper draft.

Putting risk aversion into the social choice criterion is what I am all about.

They key message, however, is that individual risk not just aggregate risk counts.

Furthermore, our basic intuition is gathered from models that do not count individual level risk. Once, you do that some of the intuition dries up - namely that increases in voluntary exchange always produce net benefits.

Laurent GUERBY said...

I wrote in April 2006 a blog entry about Ricardo (in french) where I mentionned about the "gains from trade":

"""Un des aspects non abordés sur wikipédia ou dans l'article Krugman est qu'un système totalement spécialisé est nécessairement moins tolérant aux risques, et les risques pris ont bien sur un prix, ce qui est une autre limite à prendre en compte."""

Translation: "One of the point not touched upon on wikipedia or in Krugman article is that a specialized system (where all countries produce according their optimal comparative advantage) is less tolerant to risk, and risk of course have a price: this is another limit to take into account".

This is not exactly the same as your a priori distributional risks based on uncertainty, but it's certainly another kind of risk that should be studied and I couldn't find any publication about it.

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