Monthly Archives: January 2012

204 – Describing changes in percentages

Describing changes or differences in percentages can be perilous, particularly if the thing that is changing is itself a percentage. If you aren’t careful, you can easily do it in a way that is interpreted differently than you intend.

People often describe percentage changes in percentages poorly. It’s a pet peeve of mine. Even in scientific research articles, in which the writing should be clear and unambiguous, it is not too hard to find something like the following.

In 1945, 26% of Australian women smoked. Over the next 30 years, this figure increased by 27%.

This has two possible meanings. It might mean that the percentage of Australian women who smoked increased by a factor of 27%. In other words, the initial percentage was multiplied by 1.27 (or 127%). In that case, the later percentage of women smokers would be 26% x 127% = 33%. The increase is 27% of 26% = 7%.

Alternatively, it might mean that the percentage of women who smoked increased by 27 percentage points. The later percentage would then be 26% + 27% = 53%.

The two interpretations can have very different results, as they do in that case. Here’s another similar example.

In 2004, smoking accounted for 18% of deaths from all causes among men. The equivalent figure for women was 8% lower.

Does this mean that smoking accounted for 16.5% of deaths among women (= 92% of 18%) or 10% (= 18% – 8%)?

The correct answers are 33% and 10% respectively, but there is no way that you could be sure of this from the way they were written above.

The issue is that a percentage change in a percentage can be expressed in relative terms (relative to the original number) or in absolute terms (the number of percentage points). If you don’t indicate which of these two you mean, then other people have no option but to guess, and they might guess wrong.

It is easy to avoid this ambiguity. If the percentage change you are referring to is measured in absolute terms, just insert “percentage points” in the sentence appropriately: “this figure increased by 27 percentage points” or “the equivalent figure for women was 8 percentage points lower”.

If the percentage change is relative, insert “a factor of” instead: “this figure increased by a factor of 27 percent” or “the equivalent figure for women was a factor of 8 percent lower”.

Or if you feel that these make the text a bit cumbersome, just tell us the second percentage, rather than saying how different it is from the first percentage: “this figure increased to 33 percent” or “the equivalent figure for women was 10 percent”.

203 – Predicting adoption of new farming practices

Predicting adoption of new practices by farmers is important for researchers, extension agents and policy makers. A new tool to assist with this difficult task has been released.

My most successful published paper, in some respects, is a review of the published research literature on landholder adoption of conservation practices (Pannell et al., 2006). It was a really enjoyable paper to write, partly because it was done with an outstanding team of collaborators. The level of interest in the paper has been remarkable, and this has led me and the co-authors to deliver a range of other activities and outputs on the topic, including a couple of national workshops ( and a book (Pannell and Vanclay, 2011).

One thing you couldn’t do based on the review paper alone is predict the level and speed of adoption for a particular farming practice that hadn’t already been studied in detail. In fact, there doesn’t seem to be any tool or framework anywhere that will predict adoption of agricultural practices (not just conservation practices) in a quick and easy way.

The only real option has been to undertake detailed surveys of potential users of the practice, but that’s a big job.

It struck me that this was an important information gap. There are lots of situations where people do need to predict adoption of new farming practices.

Examples include:

  • agricultural scientists wondering whether to research a particular agricultural technology
  • agricultural extension agents wondering whether a new agricultural practice is worth promoting
  • policy officers developing a program to encourage uptake of new practices

In each case, there is a lot of value in knowing whether or not the technology or practice is potentially adoptable by farmers. If not, it would be better to save the resources involved in researching or promoting something that will never be taken up. In part because of the lack of a suitable tool, there are many examples of research or extension or policy programs that have wasted resources on proposed farming practices that were never going to be adopted.

Recognising the need, and the existing knowledge gap, a team of researchers from the Future Farm Industries CRC (all of whom had been involved in the book, the workshops and/or the review paper) decided to try to develop a simple tool to predict adoption of agricultural practices. The team, consisting of Rick Llewellyn (CSIRO), Perry Dolling (Department of Agriculture and Food WA), Roger Wilkinson (Department of Primary Industries Victoria), Mike Ewing (CRC FFI) and me, obtained funding from the CRC to employ a research fellow, Geoff Kuehne (CSIRO).

We started by developing a framework that specified how all the different bits of information would fit together. Then we quantified the model and tested it against available real-world data, where we could find it. It performed pretty well!

We’re calling the tool ADOPT (Adoption and Diffusion Outcome Prediction Tool). It provides a step-by-step approach to evaluating and predicting the likely level of adoption of specific agricultural innovations. Predictions are made in response to the answers to a series of 22 questions, which the user responds to with a particular innovation and a particular target population of potential adopters in mind.

The 22 questions cover issues relating to the innovation and the target population. In each case, the questions explore the relative advantage of the innovation and its trialability.

After a couple of years work, we have decided to release a test version of the tool to anybody who wants to have a go with it. If you’re interested, download the tool from, and let us know what you think.

Further reading



Also see for a set of videos on this topic.

202 – The cost of umbrellas

Tom Waits has an excellent new album out called “Bad As Me”. It’s classic Tom, with rough, growly vocals delivering stories of wit, wisdom and humanity, in an eclectic array of musical styles. In one song he observes that, “everybody knows umbrellas cost more in the rain”. Economics on a Tom Waits album! But is it true? And if so, why?

It appears that Tom has an excellent grasp of the basics of micro-economics. His observation is exactly what you’d expect from a simple economic model of the market for umbrellas.

This sort of market model has a demand curve (showing the number of umbrellas that people would want to buy at different prices) and a supply curve (showing the number of umbrellas that umbrella producers would be willing to sell at different prices). If the market price is too high, producers find that they can’t sell all the umbrellas they would like to, so they are prompted to drop the price and reduce production. If the price is too low, producers find that its not worthwhile producing as many umbrellas as people want at that price, so they are prompted to raise the price and increase production.

The end result is that the market price eventually settles where the supply and demand curves intersect, because that is the only situation where there is no shortage or excess of umbrellas. This occurs at price P0 in Figure 1.

Figure 1.

Then in comes Tom Waits, singing “everybody knows umbrellas cost more in the rain”. On a rainy day, what changes? For one thing, people who didn’t remember to take their umbrellas with them when they went out have a particularly strong desire for an umbrella. As a result, the price they are willing to pay is probably higher than usual. The demand curve rises from DemandDry to DemandWet (Figure 2).

Figure 2.

At the same time, the supply of umbrellas on a particular wet day is likely to be more or less fixed. The upward sloping supply curve in Figure 1 is probably relevant to a long-ish time frame, like a year, but on a single wet day, producers are unlikely to increase their production and get the extra umbrellas into the shops in time to meet the increased demand. This means that the supply curve is more-or-less vertical on that day, meaning that the number of umbrellas available for sale that day would be the same, almost regardless of the price people were willing to pay for them.

Figure 2 shows the result of rising demand and fixed supply – the price goes up (from P0 to P1). The Tom Waits theory of umbrella pricing is looking good.

That’s all very well, but it strikes me that, at least in some environments, the Tom Waits theory of umbrella pricing is unlikely to hold.

If you went to your local shopping mall and found a store that sold umbrellas, do you really think that the price would be higher on a rainy day than on a dry day? I doubt it.

For one thing, I don’t think that stores would find it worthwhile to go through their umbrella stock replacing their price tags day after day depending on the weather.

For another, at least some stores care about their reputations with shoppers, and being caught jacking up their umbrella prices on wet days and putting them back down on dry days could be a recipe for bad publicity if they got caught.

So in that sort of retail environment, I reckon Tom is just wrong.

He’s more likely to be right in a situation where the umbrellas don’t have individual price tags, and where sellers are not concerned about maintaining customer relations – perhaps in a public market where prices are determined by haggling. I’ve just had a week’s holiday in Istanbul, which has many such markets. I’d be pretty confident that, in that environment, umbrellas really would cost more in the rain.

The contrast between a shopping mall and a Turkish market illustrates that the simplest economic supply and demand model is too simple in some cases, as it ignores factors like transaction costs (including such things as the cost of changing price tags) and the value of maintaining a seller’s reputation. The simple market model is a good tool to start thinking about these issues, but it needs additional complexities to be included to be relevant more generally. Many academic economists are interested in what those additional complexities are and how they affect things.