Keynes famously wrote about the problems with expected utility analysis:
"By "uncertain" knowledge, let me explain, I do not mean merely to distinguish what is known for certain from what is only probable. The game of roulette is not subject, in this sense, to uncertainty… Even the weather is only moderately uncertain. The sense in which I am using the term is that in which the prospect of a European war is uncertain, or the price of copper and the rate of interest twenty years hence, or the obsolescence of a new invention, or the position of private wealthowners in the social system in 1970. About these matters there is no scientific basis on which to form any calculable probability whatever. We simply do not know."
but then rather glumly concluded:
"Nevertheless, the necessity for action and for decision compels us as practical men to do our best to overlook this awkward fact and to behave exactly as we should if we had behind us a good Benthamite calculation of a series of prospective advantages and disadvantages, each multiplied by its appropriate probability, waiting to be summed."
He does not seem, to me, to be completely at ease with this conclusion. But he does say it!
I didn't include this gem from Oskar Morgenstern, which also reluctantly concurs with Keynes, but highlights the practical constraints:
“Finally, we mention a serious organizational difficulty in discussing and criticizing statistics. These are virtually always produced by large organizations, government or private; and these organizations are frequently mutually dependent upon each other in order to function normally. Often one office cannot publicly raise questions about the work of another, even when it suspects the quality of the work, since this might adversely affect bureaucratic-diplomatic relations between the two and the flow of information from one office to another might be hampered. A marked esprit de corps prevails. All offices must try to impress the public with the quality of their work. Should too many doubts be raised, financial support from Congress or other sources may not be forthcoming. More than once has it happened that Congressional appropriations were endangered when it was suspected that government statistics might not be 100% accurate. It is natural, therefore, that various offices will defend the quality of their work even to an unreasonable degree.”
I'm wondering how you choose what surgery to have or whether to force your child to take violin lessons. Surely you weigh up the pros and cons for that decision, which is a type of cost benefit analysis.
Other problems with cost-benefit analyses and econometrics in general:
1. Dollars are not just rubber rulers, or costantly shrinking rulers, considering that the price-of-everything-valued-in-everything-else matrix constantly varies in its entries, dollars are like n-D rubber cubes vibrating in all those dimensions while shrinking in most of them over time.
2. The utility of money, even with a constant and unidimensional measure, must be approximately logarithmic and different for people with different amounts of money, that is, a given percent increase in wealth is equally useful to the prince and the pauper, though the absolute amounts of money differ by orders of magnitude, as Daniel Bernoulli's solution to the St. Petersburg paradox showed about 300 years ago. This also implies that the objective for an entity over time for investments is maximizing rate of return, not absolute returns, and that future benefits have to be discounted not just by inflation, or the "risk-free" rate of return, but by the rate one could reasonably anticipate getting from instead investing in alternative opportunities. (And that rate isn't the same for everybody, nor are their time horizons, nor how much volatility and risk they should rationally accept, still less their actual revealed preferences for risk/reward, so aggregate statistics would have a very hard time approximating utility, even if they tried, which they don't.) Further, aggregate utility is not the sum of amounts of money, (even assuming a perfect measure, which the dollar isn't), as with GDP, but rather the sum of individual log-utilities, so that, e.g., the worth of $100 each to 10 people, each of whom had $1 before, easily outweighs the worth of $10,000 (10x) to 1 person who had any amount of money ($1 or more) before. (20 zeroes of utility vs. 4, if all had $1).
Both of those problems are on top of the people doing cost-benefit analyses just making the numbers up to get the answers they want.
I like the positive part of the post, but must say that after reading Applebaum's book (The economist's hour) and glancing through "thinking like an economist," I feel that both authors took to heart the old saying of never letting the truth get in the way of a good story.
The Kaldor-Hicks criteria on which CBA is based tried very hard to get away from interpersonal comparisons of utility, and they did so (i) by moving everything to $-equivalents, so we went from SUM(Utility) to SUM($) and (ii) by moving to hypothetical, rather than actual reallocations (IF in situation X, Person 1 could compensate Person 2 for their loss and still be better off....).
But the rejoinders were swift. Scitovsky showed that the Kaldor-Hicks criteria was not transitive (X kaldor-hicks dominates Y, but Y kaldor-hicks dominates X). Samuelson showed that you can't come up with rankings of national income and then Arrow came along with his impossibility theorem.
The fundamental issue, that moving from welfare to $ requires a societal judgment on an an extra $ to person i, was theoretically impossible to avoid, and the project to microfound CBA fails. Atkinson then got us out of Arrow's impossibility result by imposing a minimal societal judgment: the Pigou-Dalton transfer (taking a $ from someone rich and giving it to someone poor axiomatically worsens our social welfare function). Under that axiom, he showed that you get the Gini coefficient.
So, a who's who of some of the greatest economists basically said that you cannot escape societal judgments in adjudicating between different projects. This is completely in addition to the problems of certitude in Manski, and in my view, foundational, since more data can never solve this.
Yet, here we are. At the end of the day, we are back to justifying the projects we want by using CBA and his terrible friend, CEA.
This isn't new. Peter Self was making the same points in Econocrats and the Policy Process decades ago (1977 on a quick check).
The other side of this coin, similar to the Keynes quote below, is that a decision has to be made, and some kind of number is going to go into it. CBA at least gets you part of the way/
It says a lot that we have made a cost-benefit analysis in financial terms. If the costs and benefits included "human flourishing/happines/some-other-factor that might not even be amenable to financial estimation, it might make for better decisions.
I'm reminded that Anglo countries have taken as a core principle that financial analysis is teh best way to make decisions from the individual all teh way to the national. But since not all nations ascribe to that way of thinking, it fails at the international level. If we think of the need to control GHG emissions, it is always couched in financial terms, and since we cannot price the future, it inevitably seems to cost more than the financial benefit. Horrible outcomes for people can result on that basis. This is the cost of accepting economists as the "highest authority", or these days the messages that the securities markets return to governments. National borrowing is now controlled by the bond market, preventing any effective spending to alleviate the effects of a poor economy on the lives of the population.
This made me think about operations research. People often talk about how to find the “optimal”, but the math only works after someone decides what the objective should be. So maybe the real issue isn’t optimization itself, but forgetting that the objective function already contains judgments lol
Keynes famously wrote about the problems with expected utility analysis:
"By "uncertain" knowledge, let me explain, I do not mean merely to distinguish what is known for certain from what is only probable. The game of roulette is not subject, in this sense, to uncertainty… Even the weather is only moderately uncertain. The sense in which I am using the term is that in which the prospect of a European war is uncertain, or the price of copper and the rate of interest twenty years hence, or the obsolescence of a new invention, or the position of private wealthowners in the social system in 1970. About these matters there is no scientific basis on which to form any calculable probability whatever. We simply do not know."
but then rather glumly concluded:
"Nevertheless, the necessity for action and for decision compels us as practical men to do our best to overlook this awkward fact and to behave exactly as we should if we had behind us a good Benthamite calculation of a series of prospective advantages and disadvantages, each multiplied by its appropriate probability, waiting to be summed."
He does not seem, to me, to be completely at ease with this conclusion. But he does say it!
I didn't include this gem from Oskar Morgenstern, which also reluctantly concurs with Keynes, but highlights the practical constraints:
“Finally, we mention a serious organizational difficulty in discussing and criticizing statistics. These are virtually always produced by large organizations, government or private; and these organizations are frequently mutually dependent upon each other in order to function normally. Often one office cannot publicly raise questions about the work of another, even when it suspects the quality of the work, since this might adversely affect bureaucratic-diplomatic relations between the two and the flow of information from one office to another might be hampered. A marked esprit de corps prevails. All offices must try to impress the public with the quality of their work. Should too many doubts be raised, financial support from Congress or other sources may not be forthcoming. More than once has it happened that Congressional appropriations were endangered when it was suspected that government statistics might not be 100% accurate. It is natural, therefore, that various offices will defend the quality of their work even to an unreasonable degree.”
I'm wondering how you choose what surgery to have or whether to force your child to take violin lessons. Surely you weigh up the pros and cons for that decision, which is a type of cost benefit analysis.
Other problems with cost-benefit analyses and econometrics in general:
1. Dollars are not just rubber rulers, or costantly shrinking rulers, considering that the price-of-everything-valued-in-everything-else matrix constantly varies in its entries, dollars are like n-D rubber cubes vibrating in all those dimensions while shrinking in most of them over time.
2. The utility of money, even with a constant and unidimensional measure, must be approximately logarithmic and different for people with different amounts of money, that is, a given percent increase in wealth is equally useful to the prince and the pauper, though the absolute amounts of money differ by orders of magnitude, as Daniel Bernoulli's solution to the St. Petersburg paradox showed about 300 years ago. This also implies that the objective for an entity over time for investments is maximizing rate of return, not absolute returns, and that future benefits have to be discounted not just by inflation, or the "risk-free" rate of return, but by the rate one could reasonably anticipate getting from instead investing in alternative opportunities. (And that rate isn't the same for everybody, nor are their time horizons, nor how much volatility and risk they should rationally accept, still less their actual revealed preferences for risk/reward, so aggregate statistics would have a very hard time approximating utility, even if they tried, which they don't.) Further, aggregate utility is not the sum of amounts of money, (even assuming a perfect measure, which the dollar isn't), as with GDP, but rather the sum of individual log-utilities, so that, e.g., the worth of $100 each to 10 people, each of whom had $1 before, easily outweighs the worth of $10,000 (10x) to 1 person who had any amount of money ($1 or more) before. (20 zeroes of utility vs. 4, if all had $1).
Both of those problems are on top of the people doing cost-benefit analyses just making the numbers up to get the answers they want.
I like the positive part of the post, but must say that after reading Applebaum's book (The economist's hour) and glancing through "thinking like an economist," I feel that both authors took to heart the old saying of never letting the truth get in the way of a good story.
The Kaldor-Hicks criteria on which CBA is based tried very hard to get away from interpersonal comparisons of utility, and they did so (i) by moving everything to $-equivalents, so we went from SUM(Utility) to SUM($) and (ii) by moving to hypothetical, rather than actual reallocations (IF in situation X, Person 1 could compensate Person 2 for their loss and still be better off....).
But the rejoinders were swift. Scitovsky showed that the Kaldor-Hicks criteria was not transitive (X kaldor-hicks dominates Y, but Y kaldor-hicks dominates X). Samuelson showed that you can't come up with rankings of national income and then Arrow came along with his impossibility theorem.
The fundamental issue, that moving from welfare to $ requires a societal judgment on an an extra $ to person i, was theoretically impossible to avoid, and the project to microfound CBA fails. Atkinson then got us out of Arrow's impossibility result by imposing a minimal societal judgment: the Pigou-Dalton transfer (taking a $ from someone rich and giving it to someone poor axiomatically worsens our social welfare function). Under that axiom, he showed that you get the Gini coefficient.
So, a who's who of some of the greatest economists basically said that you cannot escape societal judgments in adjudicating between different projects. This is completely in addition to the problems of certitude in Manski, and in my view, foundational, since more data can never solve this.
Yet, here we are. At the end of the day, we are back to justifying the projects we want by using CBA and his terrible friend, CEA.
Actuarial computations beat economic theory!
This isn't new. Peter Self was making the same points in Econocrats and the Policy Process decades ago (1977 on a quick check).
The other side of this coin, similar to the Keynes quote below, is that a decision has to be made, and some kind of number is going to go into it. CBA at least gets you part of the way/
It says a lot that we have made a cost-benefit analysis in financial terms. If the costs and benefits included "human flourishing/happines/some-other-factor that might not even be amenable to financial estimation, it might make for better decisions.
I'm reminded that Anglo countries have taken as a core principle that financial analysis is teh best way to make decisions from the individual all teh way to the national. But since not all nations ascribe to that way of thinking, it fails at the international level. If we think of the need to control GHG emissions, it is always couched in financial terms, and since we cannot price the future, it inevitably seems to cost more than the financial benefit. Horrible outcomes for people can result on that basis. This is the cost of accepting economists as the "highest authority", or these days the messages that the securities markets return to governments. National borrowing is now controlled by the bond market, preventing any effective spending to alleviate the effects of a poor economy on the lives of the population.
This made me think about operations research. People often talk about how to find the “optimal”, but the math only works after someone decides what the objective should be. So maybe the real issue isn’t optimization itself, but forgetting that the objective function already contains judgments lol