Monthly Archives: May 2012

216 – Diminishing marginal benefits of economics

One of the foundational concepts of economics is the idea of diminishing marginal benefits. In this post I argue that it applies to economics itself.

A classic example of diminishing marginal benefits is the application of fertilizer to a wheat crop. As you add more fertilizer, the wheat yield increases, but it does so at a diminishing rate. The yield curve gets flatter and flatter as the fertilizer rate increases.

This flattening off of benefits has been found to be extremely common as the level of an input to a production process increases (even those related to the environment – see PD183). In economic text books, it is assumed to be the default case. It underpins almost all of the field of production economics. It is built into the thinking of economists about anything to do with production.

Ironically, however, we possibly don’t often stop to think that it applies to our own discipline. If the X axis of the graph represents the level of resources and effort put into analysing an economic decision problem, and the Y axis represents the benefits generated from the resulting decision, we would expect to see just the same sort of shape to the graph.

To illustrate, imagine that we have a limited budget to spend on new projects and we are trying to select from a list of potential projects the ones that will deliver the best value for money – the greatest benefits per dollar of costs.

One option for us would be to choose to do no economic analysis at all and just use our judgement about which projects are best. The projects we chose would generate some benefits. The benefits may or may not be sufficient to outweigh the costs and, unless we are freakishly lucky or clever, the benefits would be less than we could make if we did do some economic analysis.

Next, suppose we do a simple ‘quick-and-dirty’ economic analysis of each of the potential projects and calculate a benefit: cost ratio for each. The analysis wouldn’t be very sophisticated, and the numbers we used would be somewhat uncertain (because we would not be devoting much effort to getting the best possible numbers) but, nevertheless, decision theory shows that the information produced will probably help us make significantly better decisions.

You can see where this is going. There are many ways that we could add accuracy, detail and sophistication to the analysis we do of each project. For example, we could:

  • explicitly represent the risks and uncertainties involved
  • represent the risk attitudes of the decision makers
  • represent the benefits and costs over a series of years, rather than a single year
  • include ‘option values’ representing the value of deferring a decision
  • conduct sophisticated statistical analysis to estimate the relationships and parameters to include in the analysis
  • if relevant, conduct non-market valuation studies to estimate the intangible values expected to result from the projects

and so on.

The more sophisticated, detailed and comprehensive we make the analysis, the greater would be the expected benefits from the resulting decisions, but evidence shows that the benefits increase at a diminishing rate.

One reason is that more sophisticated modelling and better data is expensive. We can do our quick-and-dirty modelling at very low cost and get some benefits, but doing a better analysis is likely to involve a lot more effort and cost. Thus, even if we are able to double the benefits, we would probably more than double the costs, resulting in some flattening out of the curve.

Another reason is that perfect decision making imposes an upper bound on how many benefits we can generate from the decision. Once our analysis is sophisticated enough to support good decision making, the additional benefits that can be delivered through better decision making are limited to the difference between good and perfect decision making. Usually, the level of sophistication required to get to reasonably good decision making is a long way short of the frontiers of economics research.

So, where should applied economists aiming to support real decision makers strike the balance between simplicity and sophistication? There is no easy answer to that. It depends on the importance of the decision problem, the quality of existing information that their analysis will be built on, the time frame for the decision, and so on. But the existence of diminishing marginal benefits from economics means that the optimal balance will be pushed to some degree towards the simple end of the spectrum, more so, no doubt, than people who like building complex economic models would prefer!

Just to be clear, I am not arguing that any simplistic analysis is good enough. In the field I work in, environmental economics, I am constantly seeing decisions for which the supporting analysis is clearly not nearly sufficient (Pannell and Roberts 2010). But improving the quality and sophistication of the analysis doesn’t mean that we have to go to the other extreme. I believe that the analysis needs to consider all of the key factors explicitly (PD159), and to do so in a logical and theoretically sound way (PD158), but the treatment of each of those key factors can be relatively simple.

This difficult balance is something we’ve considered carefully in our development of the Investment Framework for Environmental Resources (INFFER) (Pannell et al. 2012).

Further reading

Pannell, D.J. and Roberts, A.M. (2010). The National Action Plan for Salinity and Water Quality: A retrospective assessment, Australian Journal of Agricultural and Resource Economics54(4): 437-456. Journal web site here ♦ IDEAS page for this paper

Pannell, D.J., Roberts, A.M., Park, G., Alexander, J., Curatolo, A. and Marsh, S. (2012). Integrated assessment of public investment in land-use change to protect environmental assets in Australia, Land Use Policy 29(2): 377-387. Journal web site ♦ IDEAS page for this paper

215 – However

A big part of my job as an academic is reading unpolished writing of other people: research students’ theses, colleagues’ draft research papers, journal papers I am asked to review, draft funding proposals, and so on. Of the many writing mistakes that I see, one of the most common, even amongst people who otherwise write well, is mis-use of the word however. It’s not at all difficult to get it right, but it’s remarkable how many people don’t.

The key point is that you should not use however to combine two contrasting sentences into one sentence. If you want to do that, use but. Or else keep using However but punctuate for two sentences.

Wrong: I don’t know why so many people get this wrong, however, I know from experience that they do.

Correct: I don’t know why so many people get this wrong but I know from experience that they do.

Correct: I don’t know why so many people get this wrong. However, I know from experience that they do.

An acceptable alternative version of the last example is to use a semicolon in place of the full stop: ‘… get this wrong; however, …’. Used in this way, the semicolon is a lot like a full stop but it emphasises that the two sentences are related (as they always are when you use however in this way).

On occasions, I’ve had trouble convincing people about all this. These are often people who write quite well, but have somehow fallen into misusing however and have been doing it for years without being pulled up for it.

In such cases, I pull out the big guns: “Fowler’s Modern English Usage”, the world’s ‘acknowledged authority’ on usage, as they say themselves on the cover! Here’s what they say:

“Avoid at all cost the illiteracy of using however as a simple substitute for but, or of allowing a sentence to run on when However should have had a capital H at the start of a new sentence.”

How delightfully blunt!

Just to confuse matters, there is a way in which it is possible to use however in the middle of a sentence without upsetting me (or Fowler). The usage that’s acceptable is to move However from the start of a sentence to the middle:

Correct: I don’t know why so many people get this wrong. I know from experience, however, that they do.

Notice that the however is not linking together what could otherwise be two separate sentences. If you take the however out of the second sentence, it doesn’t become two sentences. But that is what happens if you delete however from the Wrong example above.

Further reading

Burchfield, R.W. (ed.) (1996). The New Fowler’s Modern English Usage, 3rd Edition, Clarendon Press, Oxford.

214 – The perils of asking people

Most of us answer survey questionnaires now and then. If we take a survey seriously, we probably feel that the responses we provide capture how we really feel. Most of us are unaware of how sensitive our answers can be to the way a question is asked.

There are various reasons why it can be a good idea to ask the public about their beliefs, their preferences, their likely behaviour, and so on. Social scientists, including economists, do it regularly. Reasons include to help evaluate policies or projects, or just to understand people. Governments also do it, to help decide which policies to adopt, and how to implement them.

Most people who are not social scientists have no idea how tricky this task of asking people can be. Here is an illustration.

Suppose that the government wishes to foster water conservation by encouraging the adoption of a package of water saving technologies in the home. People who adopt these measures will have lower water bills because of lower water consumption, but the government wants to provide an additional push, and provides a one-off discount on the water bill for households that install them.

Proposal 1: Would you support a proposal that rich households (e.g. with family income over $300,000 per year) should receive a higher discount than poor households (e.g. with family income below $50,000 per year)? Assume that the level of water saving is the same with or without this proposal.

If you are like most people, you would not support that proposal. To most of us, it seems unreasonable to favour rich people. They are already better off, so why should they get an additional benefit?

Now suppose instead that the government takes a different approach to the scheme. In that first scheme, the default position was that the household did not adopt the technologies, and a discount was provided if they did. In the alternative scheme, the view is that everybody should install the technologies, so the default position is that every household does. Everybody receives a one-off reduction in their water bill (the same reduction for everybody, consistent with your preference under the first proposal) to help offset the installation costs. Those households that cannot demonstrate that they have installed the technologies will be hit with a surcharge on their bill.

Proposal 2: Would you support a proposal that poor households should pay just as large a surcharge as rich households? Assume that the level of water saving is the same with or without this proposal.

You probably reject that proposal too. It feels unreasonable, doesn’t it?

If you are one of the majority who answers ‘no’ to both proposals, the bad news is that this is completely illogical. Saying ‘no’ to the first proposal is exactly equivalent to saying ‘yes’ to the second, and answering ‘no’ to the second proposal is equivalent to answering ‘yes’ to the first proporal.

To illustrate: if you say ‘no’ to the first proposal, you are saying that the savings on the water bills of poor people from installing the technology should be just as large as for rich people.

If you say ‘no’ to the second proposal, you are saying that the savings on the water bills of poor people from installing the technology should be less than for rich people. (They would get charged less for not installing, so the cost avoided if they do install would be less.)

(If you are finding it hard to get your head around that, there is a numerical example at the end that should make it clear.)

Why did you answer so illogically? Most people can’t answer this question. They just feel confused.

If you were in the illogical majority and answered ‘no’ to both proposals, go back and look again at both proposals and decide which one do you want to change to ‘yes’.

The amazing thing is that you probably don’t want to change either answer. They both still feel absolutely right, even though you now know that one gives the opposite result to the other.

If we did a public survey on this, we would get completely different results depending on how we described the system – as based on discounts or surcharges.

So which result would be the true representation of how people feel about these issues? My proposed answer to this question is neither/both. The worrying thing for a researcher is that the two contradictory outcomes can both be an accurate reflection of how people feel, depending on the wording and context of the question. It’s as if the real world changes depending on how you ask the question.

This dependence of people’s answers on the wording and context of questions is called a ‘framing effect’. Skilled survey developers who wish to get reasonably accurate results are well aware of the risk of framing effects (although sometimes it is hard to decide which frame is preferred, as in the above example). Less skilled/experienced survey developers – perhaps people who are not social scientists and are just having a go at a survey – often make awful mistakes.

Where does that leave us? Amongst other things, I think it means that we need to be cautious and humble in interpreting the results of surveys and other forms of public consultation. Remember that the way that people express their preferences and beliefs can sometimes be highly sensitive to how the question is asked, and be prepared to take any particular survey result with at least a pinch of salt. I always like to see the exact wording of a survey before I put too much weight on its findings.

It also highlights the importance of not taking the task of developing a survey lightly. If you are responsible for a survey, make sure you use an expert or get expert help and become well-informed about the pitfalls.

Numerical example

Water bills before policy change: Poor people $300; Rich people $500

Scheme 1 (subsidy)

Water bills if we answer ‘no’ to proposal 1, and the subsidy to both groups is $100.

  • If they don’t adopt: Poor $300; Rich $500
  • If they do adopt: Poor $200; Rich $400

Scheme 2 (surcharge)

The discount given to everyone, on the assumption that everyone adopts, is $100. If we answer ‘yes’ to proposal 2, the surcharge to both groups for not adopting is $100.

  • If they don’t adopt: Poor $300; Rich $500
  • If they do adopt: Poor $200; Rich $400

Notice that all the bills are the same as before, whether they adopt or not. So answering ‘no’ to proposal 1 is identical to answering ‘yes’ to proposal 2. If we answer ‘no’ to proposal 2, the bills for people who don’t adopt might be, say, $250 and $500, so rich people get a larger benefit from adopting. That corresponds to answering ‘yes’ to proposal 1.

Further reading

Bütler, M. and Maréchal, M.A. (2007). Framing effects in political decision making: evidence from a natural voting experiment, University of St. Gallen Department of Economics working paper, number 2007-04. IDEAS page for this paper

Kahneman, D. (2011). Thinking, Fast and Slow, Farrar, Straus and Giroux, New York.

Kragt, M. & Bennett, J. W. (2012). Attribute framing in choice experiments: How do attribute level descriptions affect value estimates? Environmental and Resource Economics, 51, 43-59. IDEAS page for this paper

Pannell, P.B.W. and Pannell, D.J. (1999). Introduction to Social Surveying: Pitfalls, Potential Problems and Preferred Practices, SEA Working Paper 99/04.