On Translating Earnings From The Past

A few days ago, John Avery Jones published a great piece on the Bank of England blog (“Bank Underground”), investigating how much Jane Austen earned from her novels in the early 1800s. By using the Bank’s own archives and tracking down Austen’s purchases of “Navy Fives” (Bank of England annuities, earning 5%), Avery Jones backed out that Austen’s lifetime earnings as a writer was probably something like £631 – assuming, of course, that the funds for this investment came straight from the profits of her novels.

Being a great fan of using literature to illustrate and investigate financial markets of the past, I obviously jumped on this. I also recently looked at the American novelist Edith Wharton’s financial affairs and got very frustrated with the way commentators, museums, and scholars try to express incomes of the past in “today’s terms”, ostensibly vivifying their meaning.

For the Austen case, both Avery Jones and the Financial Times article that followed it, felt the need to “translate” those earnings via a price index, describing them as “equivalent to just over £45,000 at today’s prices”.

Hang on a minute. Only “£45,000”? For the lifetime earnings of one of the most cherished writers in the English language? That sounds bizarrely small. That figure wouldn’t even pay for the bathroom in most London apartments – and barely get you a town-house in Newcastle. The FT specifically makes a comparison with contemporary fiction writers:

“[Austen’s] finances compare badly even with those of impoverished novelists today: research last year by the Authors’ Licensing and Collecting Society found that writers whose main earnings came from adult fiction earned around £37,000 a year on average”

Running £631 through MeasuringWorth’s calculator yields real-price estimates of £45,910 (using 1815 as a starting year) – pretty close. But what I think Avery Jones did was adjusting £631 with the Bank’s CPI index in Millenium of Macroeconomic Data dataset (A.47:D), which returns a modern-day price of £45,047 – but that series ends in 2016 and so should ideally be another 7% or so from 2016 until May 2019.

 “This may not be the best answer”

Where did Avery Jones go wrong in his translation? After all, updating prices through standard price indices (CPI/RPI/PCE etc) is standard practice in economics. Here’s where:

untitled-1

The third line on MeasuringWorth’s result page literally tells researchers that the pure price number may not reflect the question one is asking. The preface to the main site includes a nuanced discussion about prices in the past:

“There is no single ‘correct’ measure, and economic historians use one or more different indices depending on the context of the question.”

When I first estimated Mr. Darcy’s income, this was precisely the problem I grappled with; simply translating wealth or incomes from the past to the present using a price index severely understates the meaning we’re trying to convey – i.e., how unfathomably rich this guy was. There is no doubt that Mr. Darcy was among the richest people in England at the time (his annual income some 400 times a normal worker’s salary), a well-respected and wealthy man of elevated rank. However, translating his wealth using a price index doesn’t even put him on the Times’ Rich List over the thousand wealthiest Britons today. Clearly, that won’t do.

Because we are much richer today in real terms, price indices alone do not capture the meaning we’re trying to communicate here. Higher real income – by definition – is a growth in incomes above the rise in prices. We therefore ought to use a more tangible comparison, for instance with contemporary prices of food or mansions or trips abroad; or else, using real income adjustments, such as GDP/capita or average earnings.

MeasuringWorth provides us with three other metrics over and above the misleading price-index adjustment:

Labour Earnings = £487,000
using growth in wages for the average worker, it reports how large your wage would have to be today to afford what Austen could afford on £631 in 1815. Obviously, quality adjustments and technological improvements make these comparisons somewhat silly (how many smartphones, air fares and microwaves could Austen buy?), but the figure at least takes real earnings into account.

Relative Income = £591,300
Like ‘Labour Earnings’, this adjustment builds on the insight above, but uses growth in real GDP/capita rather than wages. It more closely captures the “relative ‘prestige value’” that we’re getting at.

Both these attempt are what I tried to do for Mr. Darcy (Attempt #2 and #3) a few years ago.

Relative Output = £2,767,000
This one is more exciting because it captures the relationship to the overall economy. If I understand MeasuringWorth’s explanation correctly, this is the number that equates the share of British GDP today with what Austen’s wealth – £631 – would have represented in 1815.

Another metric I have been experimenting with is reporting the wealth number that would put somebody in the same position in the wealth distribution of our time. For example, it takes about £2,5m to qualify for the top-1% of British wealth (~$10m in the United States) distribution today. What amount of wealth did somebody need to join the top 1% in, say, 1815? If we could find out where Austen’s wealth of £631 (provided her annuities were her only assets) rank in the distribution of 1815, we can back out a modern-day equivalent. This measure avoids many of the technical problems above for how to properly adjust for a growing economy, and how to capture inventions in a price index – and it gets to what we’re really trying to convey: how wealthy was Austen in her time?

Alas, we really don’t have those numbers. We have to dive deep into the wealth inequality rabbit hole to even get estimates (through imputed earnings, capital stocks or probate records) – and even then the assumptions we need to make are as tricky and inexact as the ones we employ for wage series or prices above.

The bottom line is pretty boring: we don’t have a panacea. There is no “single correct measure”, and the right figure depends on the question you’re asking. A reasonable approach is to provide ranges, such as MeasuringWorth does.

But it’s hard to imagine the Financial Times writing “equivalent of between £45,000 and £2,767,000 at today’s prices”…

Nightcap

  1. Working in President Trump’s Council of Economic Advisers Casey Mulligan, Supply and Demand (in that order)
  2. How not to use percentages in a news story Joakim Book, Power & Market
  3. Climate change denialism Jacques Delacroix, Liberty Unbound
  4. The Mahabharata in South Asia, Europe, and East Asia Michael Kinadeter, JHIBlog

Let’s Find Out – or: the Power of Reference

The core message of a number of books I’ve recently had the great pleasure to read has been fairly simple. Have a look. Check it out. Put your numbers in perspective. In a world awash with statistics and cognitive biases imploring us to cheer mindlessly for our own team, having the skill and wherewithal to step back and carefully ask: “can this really be so?” is golden.

One of recently passed celebrity professor and YouTube phenomenon Hans Rosling’s most profound advice for countering misinformation about the state of the world is precisely this: put all numbers in perspective. Never accept unaccompanied numbers – never believe the numerator without checking the denominator. What matters, as Bryan Caplan never ceases to emphasize as the GMU Economics creed, “are statistics, not emotions – and arguments, not stories.”

But, a statistic may never be left alone, Rosling maintains, but always compared to other relevant numbers. What share of its total category does this statistic represent? What was it last year, 5 or 10 or 20 years ago? Is there some self-evident change in associated behavior that is relevant or ought to explain it? A century ago street cars used to kill and injure hundreds of people every year, but since very few American cities make use of street cars today, the casualty is fortunately much lower. If we keep in mind that miles travelled by cars far outnumber miles travelled by street cars, reporting the number of street car deaths – while probably correct – entirely miss the point when discussing traffic safety. In How Not To Be Wrong, Mathematics professor Jordan Ellenberg quipped

Dividing one number by another is mere computation ; knowing what to divide by what is mathematics.

Here’s another example. If I told you about 23 000 individual deaths and spent a brief 10 second on each of them, going through the list would take me almost three days. On a personal level like that, 23 000 deaths is an absurd, insane, catastrophe-style event that few people are emotionally equipped to handle – essentially the size of my hometown, wiped out in a single year. If I told you those 23 000 deaths were due to antibiotic resistant diseases in the U.S. last year, the pandemic scenarios working through your mind quickly escalate. That many! Let’s find the nearest bunker!

If I then told you that cancer and heart diseases (each!) claim the lives of about 20x that, the fear of lethal apocalyptic germs consuming the world ought to quickly recede. Oh.

Here’s another example. It is entirely correct to point out that the number of people killed in worldwide airplane accidents in 2018 (556 people) was much higher than the year before (44 people) and the year before that (325 people). Would one be excused for believing that air travel is getting more risky and dangerous? Forbes, for instance, ran a roughly accurate story claiming that airline fatalities increased by 900%.

Not in the slightest. The number of fatalities from air travel has been falling for decades, all while the number of flights and miles travelled have increased exponentially, meaning that the per-flight, per-mile or per-passenger risk of death has kept dropping. Not to mention that alternative modes of travelling like driving is magnitudes more dangerous.

While Rosling teaches us to figure out what the base rate is, i.e. putting our statistic into appropriate perspective, one of Philip Tetlock’s tricks for becoming a ‘Superforecaster’ is to use Bayesian updating of one’s beliefs. This picks up precisely where Rosling’s idea left off. Once we know where to start, we have to amass more information, numbers and observations from other points of view – Bayesian updating is a popular method to incorporate and synthesize new information with the old.

In short “Calculation, like logic, is your friend” (Landsburg 2018: 44). Statistics matter and numbers can deceive. In order to better understand our realities and see through mistakes that others make – either intentionally to deceive or persuade, or unintentionally through ignorance – we must embrace the core message of people like Ellenberg, Tetlock, Duffy, Rosling or Pinker.

Always Be Comparing Thy Numbers. Never accept an unaccompanied statistic. Never trust numerators without denominators.

Nightcap

  1. Bringing natural law to international relations Samuel Gregg, Law & Liberty
  2. How to face down the Secret Service Irfan Khawaja, Policy of Truth
  3. Affirmative Action at Harvard and statistics Gelman, Goel, & Ho, Boston Review
  4. The right’s triumph; the Left’s complicity Chris Dillow, Stumbling & Mumbling

Twelve Things Worth Knowing According to Jacques Delacroix, PhD, Plus a Very Few Brain Food Items.

Note: I wish you all a prosperous, healthy, and writerly year 2019. (No wishes for happiness, it will come from all the above.)

I have a French nephew who is super-smart. Not long after graduating from the best school in France, he moved to Morocco where he married a super-smart Moroccan woman. He is so smart that he asked me for my intellectual will before I depart for another planet. It’s below.

Here are my qualifications: I taught in universities for thirty years, including twenty-five years in a business school in Silicon Valley. My doctorate is in sociology. (Please, don’t judge me.) My fields of specialization are Organizational Theory and the Sociology of Economic Development. My degree is from a very good university although I am a French high school dropout. My vita is linked here (pdf). Its academic part is respectable from a scholarly standpoint, no more. There is much additional info in my book: I Used to Be French: an Immature Autobiography, available from me, and on Amazon Kindle, and in my electronic book of memoirs in French: “Les Pumas de grande-banlieue: histoires d’émigration”, also on Amazon Kindle.

1. When the facts don’t fit your perspective you should change …. ? (Complete sentence.)

2. One basic complex idea worth knowing that resists learning: natural selection.

Note: the effective mechanism involved is multi-generational differential reproduction. You don’t understand natural selection until you can put a meaning on all three words.

3. Another basic idea worth knowing, a counter-intuitive one, that also resists learning: the principle of Comparative Advantage: If you are not working at what you do the very best, you are impoverishing me. There is a ten-lesson quick course on my blog to explain this. Look for short essays with the word “protectionism” in the title. A longform version can also be found, here.

4. Taking from the poor is a stupid way to try to become rich when you can invent a new world – like Steve Jobs – and be immensely rewarded for it. Or open a decent restaurant and be well rewarded, or learn welding. There isn’t much you can take from the poor anyway because they are poor. Plus, the bastards often resist!

5. Culture is in the heads (plural). Everything else isn’t “culture.”

6. How a body of people act is not simply the addition of the thinking of its individual human members. (There is a sociology!)

7. Beware those pesky fractions. Quick test: Five years ago, my income was 40% of yours. Now, my income is only 20% of yours. Am I earning less than I did five years ago?

8. Correlation is not causation but there is no causation without some sort of correlation.

9. Statistical significance is significant even if you don’t quite know what it signifies. Find out. It’s not hard.

10. Use statistical estimation methods even if you don’t understand them well. It will improve your reasoning rigor by confronting you brutally with the wrongness of your guesses. And you can only become better at it with practice.

11. There is not text that’s not improved by extirpating from it half of all adjectives and adverbs.

12. Reading is still the most efficient way to improve your comprehension of the world.

It seems to me that if you understand these twelve points inside out, you are well above average in general culture; that’s even true on a global scale.

Below are some intellectual anchoring points of my life. They are subjectively chosen, of course. Don’t lend them too much credence.

My favorite singer-composers: Jacques Brel; the Argentinean Communist Atahualpa Yupanqui. (I can’t help it.)

My favorite instrumental musics: baroque music, the blues.

My favorite painters: Caravaggio (link); Delacroix (Eugene); Delacroix (Krishna).

I don’t have a favorite book because I read all the time without trying to rank books. These three books have made a lasting impression, changed my brain pathways forever, I suspect: Daniel Defoe, Robinson Crusoe; George R. Stewart, Earth Abides; Eric Hoffer, The True Believer: Thoughts on the Nature of Mass Movements.

The only two intelligent things I have said in my life:

“Once you know a woman well vertically, you know nothing about her horizontally.”

“There is not bad book.”

On the point of quantifying in general and quantifying for policy purposes

Recently, I stumbled on this piece in Chronicle by Jerry Muller. It made my blood boil. In the piece, the author basically argues that, in the world of education, we are fixated with quantitative indicators of performance. This fixation has led to miss (or forget) some important truths about education and the transmission of knowledge. I wholeheartedly disagree because the author of the piece is confounding two things.

We need to measure things! Measurements are crucial to our understandings of causal relations and outcomes.  Like Diane Coyle, I am a big fan of the “dashboard” of indicators to get an idea of what is broadly happening.  However, I agree with the authors that very often the statistics lose their entire meaning. And that’s when we start targeting them!

Once we know that this variable becomes the object of target, we act in ways that increase this variable. As soon as it is selected, we modify our behavior to achieve fixed targets and the variable loses some of its meaning. This is also known as Goodhart’s law whereby “when a measure becomes a target, it ceases to be a good measure” (note: it also looks a lot like the Lucas critique).

Although Goodhart made this point in the context of monetary policy, it applies to any sphere of policy – including education. When an education department decides that this is the metric they care about (e.g. completion rates, minority admission, average grade point, completion times, balanced curriculum, ratio of professors to pupils, etc.), they are inducing a change in behavior which alters the significance carried by this variable.  This is not an original point. Just go to google scholar and type “Goodhart’s law and education” and you end up with papers such as these two (here and here) that make exactly the point I am making here.

In his Chronicle piece, Muller actually makes note of this without realizing how important it is. He notes that “what the advocates of greater accountability metrics overlook is how the increasing cost of college is due in part to the expanding cadres of administrators, many of whom are required to comply with government mandates(emphasis mine).

The problem he is complaining about is not metrics per se, but rather the effects of having policy-makers decide a metric of relevance. This is a problem about selection bias, not measurement. If statistics are collected without an intent to be a benchmark for the attribution of funds or special privileges (i.e. that there are no incentives to change behavior that affects the reporting of a particular statistics), then there is no problem.

I understand that complaining about a “tyranny of metrics” is fashionable, but in that case the fashion looks like crocs (and I really hate crocs) with white socks.

The Cost of ‘Free’ – or why I don’t like freeware

This is a partial response to Fabio Rojas recent post on the fate of Stata, a statistics package, given the rise of a free alternative, R. Rojas and others have many reasons for why R is a good package, but for now I wish to deal with the argument that it being ‘free’ is a virtue.

R is free, but I see it as a fault because it reveals that it doesn’t have a devoted support system and because it isn’t free at all. It’s actually very costly!

If you’ve spent any time with an economist you should know that there is no such thing as a free lunch. If R is free we should not simply assume it is better. To the contrary we should ask why it is free. As I have tried to argue elsewhere, it is because when you purchase software you aren’t just purchasing a few lines of code. You’re purchasing the support system that comes with it. When a company purchases Stata, or any commercial software, they do so with the expectation that they can call a dedicated hotline for troubleshooting. As software has evolved you’ve seen companies experiment with pricing to acknowledge the fact that we don’t purchase a one time software but a continuous support system.

Consider Xbox or Playstation’s online services. Their use is charged on a per time basis because it costs money to run servers and provide customer support. Even ‘freemium’ games, which nominally don’t require any money to play, survive off micro transactions which enable companies to earn steady revenues in exchange for continuing support and new content. I would not be surprised if freemium statistical software is tried in the future – access to basic regressions is free but more advanced models cost money to run. I half joke.

But let’s assume you’re good at coding and don’t need much support outside of a few days reading an R book. Should you praise R for being ‘free’? No, because you still paid the time value of your time. Every hour spent learning how to code in R is an hour you could have spent doing any number of things.

Now to be clear, you may still want to learn R if it frees up your time in the future by automating X process. This post isn’t to argue against adopting R. My point is only to say that it isn’t free in a meaningful sense. Adopting R costs in the sense that you’re giving up a devoted support system and value of time equal to how long it takes you to become proficient in it.

It’s possible that once you account for those things R is still ‘cheaper’ than commercial software like Stata or SPSS. That is an empirical question beyond the scope of this post.