Wednesday, 21 December 2016

How Rich Is Mr. Darcy?

Pre-Christmas chill has meant picking up my lovely edition of Pride & Prejudice. There's something about the language and the beautiful words that capture me  Jane Austen was onto something. Anyways, I started to think about the numbers and the incomes she reports throughout the book (and remembered how Piketty used them to portray how capital simply "earns its return r"). One of the first things we learn in the book is that insanely rich Mr. Bingley has let Netherfield, and he has "four or five thousand a year" (chapter 1). In chapter 7 we're told that Mr. Bennet (Lizzy's, the protagonist's, father) earns £2000/year and that his father-in-law left them £4000. In chapter 16 we also learn that Mr. Darcy, the rich proud and unpleasant fellow we initially loath, has £10k/year. It is never really explained or described how they earn this, and Piketty infamously argues that it was normal for capital to simply reproduce at some percent every year  so normal, in fact, that it's superflous for Austen to even describe it. 

Before numbers will start flying at your face, there are three things I want to point out: 
  1. Income is not wealth, ok? (here’s a good explanation if it confuses you).
  2. Many of the figures below are very simple comparisons or two-variable adjustments from two hundred years back. Insofar as the historical data is accurate (which is a problem in itself), the comparisons are slightly misleading since institutional settings have changed behaviour between late-Georgian Britain, where working hours and taxation are two brilliant examples; for instance, heavy taxation of income today changes the extent to which individuals take out remuneration as income, which means that somebody as rich as Mr. Darcy living today would spend considerable effort at moving his income around for tax purposes (abroad, taking it out as dividends, re-investing in company etc). This means that whatever present-day person we compare with have every incentive to reduce his/her reported income, a constraint hardly applying for the real Mr. Darcy. This means the comparison overshoots Mr. Darcy's wealth in relation to rich people today.
  3. To get some perspective, I figured some reference point is needed. To qualify for the Krugman-style 'charmed circle of the 1%' in the UK wealth distribution, you need a total wealth (stocks and bonds and properties) or around £2.9m; to enter the top 1% in the UK income distribution, one needs to earn around 150k/year. 
Enough. How rich is Mr. Darcy? I'm hardly the first person to ask this question, but the other ones I found were either too out-dated or too wrong ("purchasing power" = prestige value?!). There are various ways of trying to translate money-income-prices-wealth from two centuries back into our age, and I'm gonna attempt three different ones here:
1) estimating wealth by yields, and deflating by a price index (in this case, Bank of England Three Centuries of Macroeconomic Data, 'TCMD');
2) compare their incomes to real GDP/capita, and translate the relationship into modern-day terms;
3) compare to "a normal" income.

Attempt 1: Wealth by Yields 

Here I simply find their total wealth by inverting the yields. Skipping the econo-speak, I compare Mr. Darcy's 10k/year with the current interest rate as given by consols (18th and 19th century government debt). That is, as elementary finance would give us, we can find the total wealth of an income stream from either consols or vast land-holdings (which is probably more likely in Mr. Darcy's case) if we know the interest rate. Here comes the first problem  from when are we comparing? Consols in 1813 (when Pride & Prejudice was published) yielded around 5% (TCMD A19:P but Austen started writing the book in 1796, when consols yielded much lower. And if one held the consols to maturity, they paid 3%, a strategy not unlikely for the large-scale gentry of the 1800s. To get around the problem I'll do both, despite the fact that it doubles the amount of numbers: 
10k/year @ 3% would be worth £333.3k. [A]
10k/year @ 5%  would be worth £200k [B]
(Mr. Bingley's and Mr. Bennet's assets would be somewhat lower than that, at £40-66k and £100-166k respectively)
Then we have to deflate them by the price index, to "translate" them into present-day pounds. Again we're faced with the problem of when. It matters a lot a) which data set and which historian’s price indices I use, and b) what year I use. The problem is that this period coincided with the Napoleonic wars, and wars seriously screw up money, prices and long-time indices – mostly because they distort production and consumption patterns, but also from massive price inflation, often from money-printing. Since not all sources have a complete index over the full period we need (1796-2015), we use the Bank of England index above, some of the best indices historians have, spliced together into one.

That gives us the following: If we use 1796 as a starting year, Mr. Darcy's wealth would have a purchasing power of £28m for [A], and £16.8m for [B]. If we use 1813 as a starting year, Mr. Darcy's wealth would have a purchasing power of £15.6m for [A] and £9.4m for [B]. The difference between the first and the second sets of numbers is the large price inflation during the Napoleonic wars; Ten thousand pounds could simply buy you much more in 1796 than in 1813  and since we don't know which one Austen refers to, we'll have to assume both. 

Mr. Darcy is rich, in other words, but not obscenely so; he wouldn't even be among the richest thousand Britons today, even if he does qualify for the top 1% (for the lowest estimate, Mr. Bennet doesn't even qualify for that). These figures also undershoot what we are really getting at since it only shows how much Mr. Darcy would be able to buy today with the price-adjusted income he had back then. Of course, we’ve also have massive increases in incomes and real GDP, over and beyond changes in prices and so we have to use some real measure.

Attempt 2: in relation to real GDP/capita

To correct for the problem above, we should add some relation to GDP/capita. Real GDP per capita has increased by 15.1x (1510%) from 1813, or 15.5x (1550%) since 1796. Again, the numbers are from spliced series in Bank of England's TCMD (A4:N)

Using the increases since 1796 (15.5x), those rough increases would give us the following: 
£434m for [A]
£260m for [B]
Using the increases since 1813 (15.1x), those rough increases would give us the following:
£235.5m for [A]
£142m for [B]
That would actually put Mr. Darcy in the list for the richest 500 Britons today, almost regardless of what figures we use (except for the 1813 [B] which would put him some 50m outside it, but still well in the top 1000 richest Britons  Mr. Bingley is safely inside the top 1000 richest, except for the lowest figure, and Mr. Bennet doesn't make the list at all, but is still within the top-1%). This method, very much derivative of the first attempt, in addition to all the other shortcomings, ignores changes in income inequality since then. That is, we would want some measure that bases itself on what normal people earned in 1813 or 1796.

Attempt 3: Compared to a normal income

This is one of the most hotly debated issues in economic history; how much did various groups in society earn at various points in time, and at what time during the industrial revolution did "normal" wages start to rise? GDP/capita is obviously not a "normal" wage, especially not in societies with as widely disbursed income distributions as 19th century Britain. The best data we have suggests that real wages started trending up somewhere in the first half of the 19th century, but the range is quite wide where the "pessimist" case says 1850 and the "optimist" case and the "super-optimist" case much earlier in the 1810s-1820s. 

Here are some of the data over annual wages (daily wages multiplied by 300) that historians have found, ranging from agricultural labourers (BOWLEY) to "Normal workers" (FEINSTEIN) and skilled/unskilled construction workers (CLARK):
Annual Income. 300 working days.
CLARK Craftsman
CLARK Helper

As shown in the table, there is quite a range for us to compare, and again the time-period that we pick matters a lot for the comparison (the unweighted average between these four professions increase from £26/year to £36/year and then £45/year)

What I do below is to divide Mr. Darcy's income (10k/year) with the lowest and highest observation for the 1790 and 1810 data, to get an estimate of how many times "a normal" wage his "ten thousand a year" is. What I then do is multiply this by the 'median equivalised disposable income' (fancy way of saying a rather normal household) as given by the UK Office for National Statistics; in 2014/15 they reported this income as £25 746/year for an hourly wage of around £15. That is, a bit above what your average student part-time job would be, but a fair estimate of what a "normal wage" is: 
1790: the income figure ranges from £7.4m/year to £14.7m/year depending on which 1790 worker I use for comparison.
1810: the income figure ranges from £4.6m/year to £7.6m/year depending on which 1810 worker I use for comparison.
Remember, these figures are incomes, and translated like this would put Mr. Darcy among the absolute highest earners in the U.K. Allegedly, Adele earned ~£60m last year, and Wayne Rooney earns something like 13.5m quid a year playing football; the Queen's sovereign grant is something like £45m and the CEO of the largest FTSE100 company is paid around £20m yearly. Indeed, even Mr. Bennet's mere 2000/year would in put him into the upper half of the top 0.1% in the U.K.

A few caveats are required. This last attempt obviously overstates incomes by assuming that income distributions were the same in 2015 as in 1813 (or 1796), and so Mr. Darcy probably earned a little bit less than these insane figures. Also, as mentioned above, tax-avoiding behaviour was probably little attempted in the early 1800s, whereas minimizing income as salary has many tax-related benefits today  that would understate our reference point (and by implication overstate Mr. Darcy's incomes). Moreoever, all the attempts above ignore the massive increase in quality and technology and knowledge that we've seen over the last two centuries. Trying to quantify that is a black hole; how much better is electricity, tomatoes or typing machines now than in 1813? Or more broadly, "lighting services" (sun + wax candles vs cheap electricity) or "writing services" (irksome feather-pens vs my brilliant computer)?

For whatever number we came up with here, one must remember that in many ways the poorest Britons today live better than did Mr. Darcy regardless of which method for calculating income or wealth I used. For all his wealth, he still froze in winter, constantly stank of horse or pig or mud, had to travel very very slowly to town, died at 50 and likely saw several of his sisters, nephews or cousins die in childbirth or before they turned one, drank awful drinking water even when avoiding the many outbreaks of Cholera or the constant smog from the coal-burning fires in urban households (the Channel Four series The 1900 House is a good indication for how, then remove another hundred year of development).

All in all, in modern language Elizabeth Bennet should check her privilege. Pride & Prejudice, as literary critics have long argued, is a story of wealthy daughters marrying even wealthier men. 

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