How CO2 will inflate the price of beer

The New Zealand Herald reported this week:

A lack of CO2 supply nation-wide has brewers fearful of a beer shortage this summer.

The closure of the Marsden Point refinery at the end of March means the only remaining domestic source of liquid and other food-grade CO2 is Todd Energy's Kapuni gas field in Taranaki.

Garage Project co-founder Jos Ruffell said the CO2 shortage was crippling the beverage industry.

The brewery is currently operating at 50 per cent capacity and often goes weeks at a time without being able to package beer.

What happens when there is a shortage of CO2? We'd expect the price of CO2 to rise. This is demonstrated in the diagram below, of the market for food-grade CO2. At the current market price of P0, the quantity of CO2 demanded is QD, while the quantity supplied is QS. Since QD is greater than QS, there is a shortage. When there is a shortage, some buyers are missing out. If you are a buyer in this market, how do you avoid being one of the buyers who misses out? You find yourself a seller, and you make a deal - you pay them a little bit above the market price, and they make sure that you don't miss out. In other words, when there is a shortage, buyers tend to bid the price up. This will continue until the price is bid up to P1, where the quantity demanded and the quantity supplied are both equal to Q1. At that point, the market is in equilibrium.

What does that mean for the beer market? A higher price of food-grade CO2 means that the cost of producing beer will rise. The effect of this is shown in the diagram below. The increasing cost of production decreases the supply of beer from S0 to S1. Now, if the price of beer remained at the original equilibrium price of P0, the quantity of beer demanded would remain at the original equilibrium quantity of Q0, but the quantity of beer supplied would fall to QS, creating a shortage (that is what the quote from the article above suggests). However, it seems to me that it is more likely that the price of beer will rise, to the new equilibrium price of P1.

So, you can probably expect your beer to cost a bit more this summer, thanks to the shortage of food-grade CO2.

How academic writing has changed over time

Many years ago, in a bout of enthusiasm, I read several classic novels. I coped all right with Mary Shelley's Frankenstein, and Bram Stoker's Dracula (both written in the 19th Century), but I found both James Fenimore Cooper's Last of the Mohicans and Jonathan Swift's Gulliver's Travels (both written in the 17th Century) to be heavy going. It was the language, and adjusting to the unusual turn of phrase was a challenge. In more recent times, I have had occasion to read parts of some of the classics in economics, including bits of Adam Smith's Wealth of Nations. I found that when I stray from the parts of the book that are already well known to me, it is quite taxing to read.

The challenge in these cases is the language. It is a truism that language has changed over time, and those brought up on contemporary writing can find it challenging (as I do) to read things that were written well before their time. Is that because more recent writing is easier to read in terms of word use, or because the structure, turns of phrase, and writing styles are more familiar? Based on my experiences, I suspect the latter (although I'm not convinced that they are genuinely separable, and of course there could be many other factors at play). Some mild support of my suspicions is available in this recent article by Ju Wen (Chongqing University) and Lei Lei (Shanghai International Studies University), published in the journal Scientometrics (sorry, I don't see an ungated version online). Wen and Lei look at the rate of use of adjectives and adverbs in the abstracts of journal articles published in general, biomedical and life sciences over the period from 1969 to 2019 (over 775,000 abstracts are included). They reason that, based on past research:

...adjectives and adverbs cluttered scientific writing and made scientific papers less readable...

So, greater use of adjectives and adverbs would suggest that abstracts have become less readable over time. Wen and Lei find:

...an upward trend in the use of adjectives and adverbs in scientific writing, that is, researchers used an increasing number of adjectives and adverbs in reporting their scientific findings.

And interestingly:

...the use of emotion adjectives and adverbs demonstrated a similar upward trajectory while those of the nonemotion adjectives and adverbs did not.

Of course, their analysis is mostly descriptive and doesn't actually demonstrate reduced readability, and neither does it identify why it is that the language used in abstracts has changed over time. Wen and Lei offer a couple of speculations:

To get their works published in academic journals, scientific writers may resort to linguistic devices such as emotion words (adjectives and adverbs in our case) to make their articles more positive and seemingly more appealing to editors and reviewers...

The structured abstracts usually follow an Introduction-Method-Results-Discussion format which requires the writers to summarize precisely the core information of their manuscript within a limited number of words. In such conditions, writers may become increasingly dependent on the use of adjectives and adverbs to highlight their stance and evaluation... in the study. Hence, the use of adjectives and adverbs helps writers make compelling arguments and helps readers remember key points in the full text of an article.

It would take some more detailed work, perhaps making use of exogenous changes in abstract structure or changes in editorial teams, to tease out whether either of those mechanisms explains the underlying changes. Nevertheless, if we take these results at face value, they do suggest that academic writing (at least in the sciences) is not becoming easier to read over time. So, perhaps I should persevere with the economics classics, for some time yet.

[HT: Marginal Revolution]

Book review: Spending Time

Lesson one of economics tells us that resources are scarce. For every resource, there isn't enough to do all of the things that we might want to do with it. So, we have to make choices about how best to use our scarce resources to achieve our goals. It is tempting to focus any discussion of resources on tangible resources like money (financial capital). However, doing so potentially misses the most fundamental of all resources available to us: time.

Daniel Hamermesh's 2019 book Spending Time is devoted to helping us to better understand this key resource. The book is mostly devoted to describing our current uses of time, based mainly on data from the American Time Use Survey, with occasional data from other countries including the UK, France, Germany, and Australia. The limited selection of data sources demonstrates a need for much more attention to be paid to time use. For example, New Zealand's most recent national time use survey was in 2009-10, and I believe there was only one other survey before that, in 1998-99. In one of the few times New Zealand appears in the book, Hamermesh uses data from the earlier time use survey, showing that total work (including both paid work and household production) is equal for men and women. This is a somewhat surprising fact, when set alongside other OECD countries where total work is mostly higher for women than for men. The book reveals many other surprising facts, including that:

People who are married or cohabiting state that they sleep fourteen minutes less per night than singles of the same age. 

Hamermesh focuses on four categories of time use: (1) work for pay; (2) home production ("activities that we could pay others to do for us", like cooking or cleaning); (3) personal care ("activities that are human biological necessities, such as sleeping eating or having sex"); and (4) leisure ("anything that we typically do not have to do, that we enjoy, and that we cannot outsource"). Hamermesh works through each of those categories of time use, and then presents a number of comparisons, between women and men, between young and old, between richer and poorer, and between different US regions.

I found most of the book to be somewhat unsurprising, although not always (as the quote above highlights). I also learned a number of interesting new facts (new to me, at least), including that the US has no legal mandate for paid vacations (which explains why Americans spend more hours annually in paid work than people in other countries).

The reliance mostly on a single data source, and the general nature of the topic, could easily lead to a relatively dry and lifeless book. However, Hamermesh manages to keep it interesting with anecdotes from his own experience, and the occasional humorous quip, such as:

While most vegetables are not gendered, the American couch potato is male.

I felt that the one thing that was missing from the book was a good discussion of the implications of time use. Hamermesh devotes the final chapter to this topic, but it felt a bit too much like a late tack-on to an otherwise interesting book. Given the topic, I really wanted to know how we should be spending our time better. If time is becoming more scarce (an argument Hamermesh puts forward early in the book), then what is to be done about it? The solutions seemed quite banal to me (such as spreading work time more evenly across people and across people's lifetimes).

Nevertheless, I enjoy Hamermesh's research (and have referred to it several times on this blog, including his earlier book, Beauty Pays (which I reviewed here)). If you want to know more about how people spend time, the most valuable resource, this is a useful reference book to start with.

Good reason to avoid mediation analysis

Following on from yesterday's post on the problems with instrumental variables analysis, I read this post by Uri Simonsohn on the Datacolada blog about mediation analysis. Mediation analysis has always struck me as somewhat odd, and it isn't an approach that is common in economics. And fortunately so, as Simonsohn points out that the problems with mediation analysis are actually quite serious:

In mediation analysis one asks by what channel did a randomly assigned manipulation work. For example, suppose that an experiment finds that randomly assigning Calculus 101 students to have quizzes every week (X) increased their final exam grade (Y).  Mediation analysis is used to test whether this happened because quizzes led students to study more hours through the semester (M). Mediation is present if the estimated effect of X gets smaller when controlling for M...

The problem of interest to this post is that if there is any variable, besides X, that correlates with M and Y (a very likely scenario), mediation is invalid.

Notice the similarity to yesterday's post about instrumental variables analysis. However, instrumental variables analysis might still be valid in many cases, but it requires a strong theoretical basis for the exogeneity of the instrument. For mediation analysis, this problem is probably fatal for almost all applications. Simonsohn provides a very clear explanation of why, and concludes:

In general, if we do mediation analysis, it means we expect X to lead M and Y to be correlated in our experiment. If we expect that, we should expect that other factors, confounds, cause M and Y to be correlated outside our experiment.

This post explains why such correlation invalidates mediation. In other words, this post explains why, in general, we should expect mediation to be invalid.

Simonsohn also provides some good references that provide further support for the problems with mediation analysis (along with an interesting reading that strongly critiques path analysis more generally, which I will certainly follow up on in a future post). It is certainly clear (if it wasn't already) that mediation analysis should be left out of the regular statistical toolbox.

[HT: David McKenzie on the Development Impact blog]