Good Math, Bad Math

I’ve been getting a ton of questions about an article from the Independent about a guy named Bertie Smalls. Bertie was a british thief who died quite recently, who was famous for
testifying against his organized crime employers back in the 1970s. The question concerns one
claim in the article. Bertie was paid £10,000 for his part in a robbery in 1972. The article alleges that £10,000 in 1972 is equivalent to £200,000 today.

Lots of people think that that looks fishy, and have been sending me mail asking
if that makes any sense.

Full disclosure. I’m not an economist – I’ve never studied it, and I’m not particularly interested in it. So my methods of trying to figure this out may be completely nonsensical from an economist’s point of view.

I tried two ways of figuring out some kind of conversion factor between 1972-£ and 2008-£: one based on wage comparisons, and one based on gold prices. Neither is necessarily a good measure, but they’re both arguably basic measures of the value of a currency, and they’re both fairly things where it’s easy to get historic statistics. Then I tried looking up some other ways of computing the conversion, which are commonly used by economists.

For wages, I’ve used average minimum wages for agricultural work in the UK. In
1972, the average minumum wage was £58 for 40 hours work. Today, the statutory minimum wage in the UK is £214 for 40 hours. By that comparison, the
a 1972 pound is worth about 3.7 2008 pounds, so by this measure, 10,000 1972 pounds are worth about 37,000 2008 pounds.

Another way of computing it is to look at the price of a valuable commodity. Using gold, you get a different ratio. Using historical gold prices, you find that 10,000 pounds in 1972 is worth about 140,000 pounds today.

For what economists consider to be valid comparisons, I found a nice site that does
computations of these figures
using consumer price indices, gross domestic product, and per-capita GDP. It’s only updated with data through the end of 2006, so it’s off slightly, but it’s good enough for this discussion. The price index comparison says 10,000 1972 pounds are equivalent to about 90,000 2006 pounds; per-capita GDP says it’s worth about 180,000 2006 pounds; by average wage, it’s worth about 150,000 2006 pounds; by raw GDP, it’s worth
about 200,000 2006 pounds.

So – the article is clearly using the GDP measure. I don’t think that’s a particularly good one; comparing raw GDP doesn’t adjust for changes in population, which definitely has a skewing effect to increase the ratio. My choice would be price index comparison, which
is basically the cumulative effect of inflation. But GDP is a reasonable choice. So the
article isn’t completely unreasonable. They chose the method of computing the figure which produced the largest ratio of current value with 1972 value – clearly they wanted to make the figure look as impressive as they reasonably could – but they did use a figure that is,
arguable, a valid measure of relative values.

Comments

  1. #1 Eric Lund
    February 12, 2008

    I’m not an economist either, but I think you’re being too kind here. First, as you point out, raw GDP does not include adjustments for population changes. If GDP increase does not keep up with population increase, the people of that country become poorer overall (see numerous examples in Africa). Second, GDP can also rise because the country as a whole is getting richer.

    The adjustment I would have made would be the UK’s CPI (or equivalent statistic), assuming it was available over the entire period. The question for most people (including, I assume, Mr. Smalls) would be how much money would you need today to buy things that would have cost UKP10k in 1972. Minimum wage only measures what the poorest people can buy, which is not the same thing. Things like GDP only become relevant if you’re upper class.

  2. #2 Steve
    February 12, 2008

    The problem with price indexes is that they are based on the average price of a representative basket of goods in that year – however, the quality and characteristics of those goods changes over time. In 1972 it would be impossible to buy, for example, a modern computer or flat screen TV. More generally, price changes between goods (e.g. chicken gets cheaper relative to beef) will change both production and consumption patterns, which the GDP measure will capture, but the CPI won’t.

    Using GDP as a price index allows for changing the basket of goods over time, since GDP is the value of all goods and services produced in that year. The argument is, if I have an amount of money to buy X% of the goods made in 1972, how much money do I need to have to buy X% of the goods made in 2008.

    None of the individual measures are perfect – it largely depends on what you are trying to compare. For this article, since the author is trying to say something about individual wealth, I probably would have gone with the average wage index or the per capita GDP effect. But the GDP deflator is a very standard measure in economics. (BTW, I am an economics graduate student).

  3. #3 Tom
    February 12, 2008

    Once factor you do leave out, is that british currency was decimalised in (i’m fairly sure, date might be off, before i was born) 1971, so the actual value of the pound was artificially changed anyway. Whether or not this affects this particular case i dont know, it seems probably not as we are talking 1972, but any talk of british currency values around this time period does potentially need to take this into account.

  4. #4 Luna_the_cat
    February 12, 2008

    One thought is that the “amount it’s worth” might also be skewed by housing prices here in the UK, which have risen so astronomically as to be unbelievable, and are probably factored into computing the inflation somehow.

    To give you an idea — my husband bought his first flat, in 1980, for £6,500. When we sold that flat in 1996 it was ~£39,000. Just had a quick look at the local property register — that same flat today would be around £65,000.

  5. #5 David
    February 12, 2008

    Gold is problematic. In 1971 Nixon ended the U.S. dollar convertability to gold and by 1980 gold was trading at $850 an ounce. Last year gold reached a 25+ year high of $845.50

    I took a look at wheat prices as a commodity and they were $1.61 in 1972 and $3.64 in 2007. Another commodity was cattle and it had prices of $34.58 and $86.50 respectively. One more commodity is crude oil, with prices of $3.6 – $64.2

    This pegs $10,000 at a value of
    wheat – $ 22,609
    cattle – $ 25,014
    crude oil – $178,333

    I also did steel but could only find historical charts from 1972 to 1998, and it had prices of $7.13 and $18.75 So based on this $10,000 in 1972 would have been worth $26,297 in 1998

    I think you would have to take into account a lot of factors to get a really meaningful number. Certainly you would need to take into account Housing, Transportation, Food, Medical, and taxes.

    I am also not an economist, so I have no idea if things like money supply and credit affect the value of the $ or £.

  6. #6 Mark C. Chu-Carroll
    February 12, 2008

    David:

    I agree that gold isn’t a particularly good comparison. From what I read about this stuff today, it seems to me that the per capita GDP is probably the most informative measure; but the overarching message seems to be much more that saying “X dollars in 1972 == Y dollars in 2008″ is pretty much meaningless.

  7. #7 Eric Pedersen
    February 12, 2008

    Either GDP or per-capita GDP would seem to be usable measures… GDP if you want to find out how much of the total national output that money would buy, and per-capita GDP if you wanted to find out how much it would raise the mean person’s wages. CPI isn’t really a good measure at all, for the reasons that Steven mentioned; it’s based off a bundle of goods, and it’s nearly impossible to find a bundle where the relative prices of the goods in the bundle, and the prices of items in the bundle relative to other goods in the economy doesn’t vary. I suspect that CPI is only really useful for short time series (ie: 5-10 years) and gets progressively and rapidly less useful as time goes on.

  8. #8 Randy
    February 13, 2008

    GDP is not a good measure because real GDP should be rising each year while the price of a “theoretical good basket” should stay about the same in real terms. A theoretical good basket could be concocted by looking at the price of several items in 1972 dollars and looking at the price of the same items now. Of course to have an accurate good basket you have to pick goods that aren’t subject to vast improvements in technology (like computer chips) or changes in government dealings (like petroleum). A paper was written a few years back about how the Big Mac is a very good currency value indicator. You could use it as a theoretical good basket.

  9. #9 randy
    February 13, 2008

    …sorry, no such data on Big Mac prices. Suffice it to say it is doubtful that a good basket price went up by a scale of 20. While technological and competitive improvements should be inducing a DROP in real prices.

  10. #10 Michael Ralston
    February 13, 2008

    Randy: Except … if there’s inflation.
    Which there WAS a lot of in the 1970s, at least in the US.

    Which is sort of the point here.

  11. #11 Chris Long
    February 13, 2008

    Re: the decimalisation of the pound, I don’t think that’s relevant. The value of a pound didn’t change during decimalisation – all that changed was that the old pound had 240 pence and the new one had 100 pence (so the value of a penny changed a lot).

    I believe there was a slight inflationary effect in that many shops changed their prices to be round decimal figures instead of round shillings-and-pence figures… and of course, they made sure the new price was always slightly higher :-)

  12. #12 Eric Pedersen
    February 13, 2008

    Randy:
    Well, that’s the case only if “x dollars is equivilent to y dollars today” is only talking about adjusting for inflation. I’d argue that you should take into account growth, at least in per-capita GDP. If the average person is making more today in real terms, then (theoretically) it should take significantly higher gains to entice them to risky behaviour, like crime. Adjusting only for inflation ignores the incentives issue.
    (Also: there is a measure of inflation based only on the GDP: the GDP deflator. It’s calculated by dividing nominal GDP by real GDP, but don’t ask me how they calculate either of those values… its a little outside my areas of interest.)

  13. #13 John D.
    February 13, 2008

    Some people don’t *want* the dollar to change value. Ever.

    This article was highlighted on a conservative site. Ever since I’ve been trying to figure out if it’s good logic, bad logic, or undecidable so no one’s going to win the argument:

    “An Engineer Measures the Falling Dollar”
    http://article.nationalreview.com/?q=ODI1YzNkMjBmOWFhNDFkMGFiOTk3MjkyNWU1MTM5NTE=

    He feels that a dollar changing value is as ridiculous as “the measurement of the foot fell 10% against the meter today.”

  14. #14 GreatZamfir
    February 13, 2008

    John D., I’m pretty sure the guy has no idea what he is talking about. In his last piece, he states that his purposed system would not be a gold standard, because in such a system gold IS the currency, while in his system the government would ‘perform operations’ to keep the dollar pegged to gold.

    But suppose the government guarantees that they will keep the dollar fixed to gold. In that case, I could use my dollars to buy gold on the market, making the gold price go up (or the dollar go down vs. gld), after which the government will sell gold to make it go down again. That’s pretty much the same as the government guaranteeing to give me gold in exchange for dollars, which is of course the gold standard.

    An important thing to keep in mind when thinking about gold-standard like schemes, is that they only work when the value of gold, or whatever you use, is mainly determined by its use as currency, not by other uses. Otherwise a rise in its use as jewelry would mean that prices and wages everywhere have to redefined to the new level. So in a gold-standard system most of the gold would be used as currency, or more likely be stored in vaults as guarantee for paper money.

    But then the artificially high value of gold would only exist because people expect that in the future, their gold would still have value as currency, and therefore still be artificially high priced. This is not extremely different from the current system where dollars only have value because people expect them to have value tomorrow.

  15. #15 David
    February 13, 2008

    John D.,

    That was an interesting article. I like the authors sentiment, but I think his arguement runs into the same issues as this blog topic.

    If the dollar is fixed then what exactly does it measure? The author of the article mentioned gold, but that has problems too. I believe the main problem is that the value of goods change, not just the value of the dollar (or pound for you Brits). The value of the goods themself change.

    The value of a dollar in terms of buying an ounce of gold in 1980, 1993, and 2008 may vary considerably, and at the same time have no relationship to the value wheat, sugar, and television in 1980, 1993, and 2008. Is anyone in the market for some top dollar Beanie-Babies circa 1994?

    Maybe the dollar should be based (pegged) on per-capita GDP.

  16. #16 Crœsos
    February 13, 2008

    Brad DeLong (who is an economist) had an interesting entry at his old blog entitled “How Rich Is Fitzwilliam Darcy?” that approaches the same problem over a longer stretch of time, attempting to determine what the £10,000 annual income attributed to Pride & Prejudice’s main romantic interest would be in contemporary American dollars.

    http://www.j-bradford-delong.net/movable_type/2003_archives/002730.html

  17. #17 bwv
    February 13, 2008

    The DeLong article is excellent and addresses the two issues – the CPI attempts to price in terms of comparable goods and services without taking into account the general increase in relative wealth over the period.

    Just backing into the 20X increase in the OP that translates into a 8.9% annual rate of inflation which seems much to high to me.

  18. #18 bwv
    February 13, 2008

    Actually you can get UK CPI here:
    http://www.statistics.gov.uk/statbase/tsdataset.asp?vlnk=229

    I get a 6.37% annualized CPI over the period or about a 10x (not 20x like in the article)

    England had even nastier inflation than the US in the 1970s – years of 20+ CPI increases

  19. #19 IanD
    February 13, 2008

    Tom, The UK ₤ did not change value simply because of decimalization. One day a ₤ consisted of 20 shillings, or 240 (old) pennies; the next day it consisted of 100 (new) pennies. 100NP bought exactly the same as what 240p or 20/- had bought the day before (other than the few unscrupulous people that used D-day to hike their prices on the basis that most people wouldn’t be able to tell).

  20. #20 Brett Dunbar
    February 13, 2008

    At decimalisation a pound went from the smallest coin being 1/240th of a pound (1d) to 1/200th of a pound (1/2p). The new lowest value coin was worth 20% more than the old.

  21. #21 Tim Lin
    February 14, 2008

    Remember that in this particular case (when we’re refering to money wich was actually acquired at the time), the author may deem it appropriate to factor in present value of the money, meaning that interest will come into play. Assuming a fairly constant 8.5% return on investment over the past 36 years (which is a close approximation of the growth of FTSE during that time), that money would indeed generate close to 200,000₤ by present time.

  22. #22 IanD
    February 14, 2008

    Brett, Tom’s point was that decimalization caused the actual value of the pound to be artificially changed. I’m saying it didn’t. 5p bought exactly the same as 1/- had done.

    The ½p coin was only issued to allow the old 6d coin (“tanner”) to remain in circulation for a while (6d = 2½p). It was dropped in 1984.

  23. #23 Randy
    February 14, 2008

    Michael: I really think you’ve under appreciated how much my comments were aimed at adjusting for inflation (and only inflation as per Eric).

    Eric: I think what you said was a very fair comment, but my read on this whole thing was equivalent was only taking into account inflation since all other notions of equivalence are too subjective.

  24. #24 Kaleberg
    February 21, 2008

    Using the Google, I get:

    http://research.stlouisfed.org/fred2/data/EXUSUK.txt
    (The St. Louis Federal Reserve historical series)

    1972-01-01 2.5705
    1972-02-01 2.6037
    1972-03-01 2.6181
    1972-04-01 2.6102
    1972-05-01 2.6124
    1972-06-01 2.5691
    1972-07-01 2.4447
    1972-08-01 2.4502
    1972-09-01 2.4410
    1972-10-01 2.3948
    1972-11-01 2.3515
    1972-12-01 2.3449

    In 1972, 10,000 GBP was worth about $25,000.

    http://data.bls.gov/PDQ/outside.jsp?survey=nc
    (The BLS Inflation Calculator)

    $25,000
    in 1972
    has the same buying power as
    $126,244.02
    in 2008

    I’ll round that to about $125,000 which is a fair chunk of change.