How Much Should Bale Cost Real?

It looks increasingly likely that Gareth Bale will transfer from Tottenham to Real Madrid for a world record transfer fee. Negotiations are ongoing, with both parties keen to get the best deal possible deal with the transfer fee. Reports speculate that this transfer fee will be anywhere in the very wide range of £80m to £120m.

Given the topical nature of this transfer saga, I decided to explore the world record breaking transfer fee data, and see if these data can help predict what the Gareth Bale transfer fee should be. According to this Wikipedia article, there have been 41 record breaking transfers, from Willie Groves going from West Brom to Aston Villa in 1893 for £100, to Cristiano Ronaldo’s £80m 2009 transfer to Real Madrid from Manchester United.

When comparing any historical price data it is very important that we are comparing like with like. Clearly, a fee of £100 in 1893 is not the same as £100 in 2009. Therefore, the world record transfer fees need to be adjusted for inflation. To do this, I used the excellent measuringworth website, and converted all of the transfer fees into 2011 pounds sterling.

bale

The plot above demonstrates a very strong linear relationship between logged real world record transfer fees and time. The R-squared indicates that the year of the transfer fee explains roughly 97% of the variation in price.

So, if Real Madrid are to pay a world transfer fee for Bale, how much does this model predict the fee will be? The above plot demonstrates what happens when the simple log-linear model is extrapolated to predict the world record transfer fee in 2013. The outcome here is 18.37, so around £96m, in 2011 prices. We can update this value to 2013 prices. Assuming a modest inflation rate of 2% we get £96m[exp(0.02*2)]=£99.4m. No small potatoes.

rm(list=ls())

bale = read.csv("bale.csv")
# data from:
# http://en.wikipedia.org/wiki/World_football_transfer_record
# http://www.measuringworth.com/ukcompare/

ols1 = lm(log(real2011)~year, bale)

# price
exp(predict(ols1,data.frame(year=2013)))
# inflate lets say 2% inflation
exp(predict(ols1,data.frame(year=2013)))*exp(0.02*2)

# nice ggplot
library(ggplot2)
bale$lnprice2011 = log(bale$real2011)
addon = data.frame(year=2013,nominal=0,real2011=0,name="Bale?",
                   lnprice2011=predict(ols1,data.frame(year=2013)))

ggplot(bale, aes(x=year, y=lnprice2011, label=name)) + 
  geom_text(hjust=0.4, vjust=0.4) +
  stat_smooth(method = "lm",fullrange = TRUE, level = 0.975) +
  theme_bw(base_size = 12, base_family = "") +
  xlim(1885, 2020) + ylim(8, 20) +
  xlab("Year") + ylab("ln(Price)") +
  ggtitle("World Transfer Records, Real 2011 Prices (£)")+
  geom_point(aes(col="red"),size=4,data=addon) + 
  geom_text(aes(col="red", fontface=3),hjust=-0.1, vjust=0,size=7,data=addon) + 
  theme(legend.position="none")
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Malthus in 21st Century Europe

Reverend Thomas Malthus is well known for his pessimistic views on population growth and economic welfare. The ubiquitous ‘Malthusian model’ is simple and lucid tool which offers an explanation as to why living standards showed no substantive improvement between the Neolithic revolution and the 19th century.

A consequence of the Malthusian model’s popularity is that many people have overlooked the motivation and core point of Malthus’ analysis. Malthus’ aim, outlined in various editions of An Essay on the Principle of Population (notably the second), was to encourage social reforms which promoted later marriage, particularly amongst the poorest in society.

His argument was simple. Sex outside marriage was socially unacceptable, so marriage marked the beginning of sexual relations. Malthus, a clergyman, did not consider fertility control within marriage as an option. Therefore, the earlier couples married, the higher their fertility would be. If early marriage was common across society, this would (exponentially) increase the next generation and thereby reduce income per person because population has increased more than income. Ultimately, Malthus promoted later/delayed marriage as a tool for economic growth and encouraged the foundations of social institutions capable of enforcing this.

While Malthus is one of the most studied and remarked upon character in the history of economic thought, the consensus is that he got it wrong. The purpose of this blog post is to ask: Can any of Malthus’ ideas help us understand economic and demographic trends in the modern Europe?

In the 200 plus years since Malthus wrote the first essay fertility, the institution of marriage and economic conditions have changed immensely in Europe. We might expect economic conditions and marriage to be unrelated, since marriage is no longer a prerequisite for childbirth. Similarly, the economic cost of marriage is (or at least can be) lower than in preindustrial societies where dowries are involved. In addition, modern welfare systems offer child support which helps the poorest in society, something which Malthus, as an opponent of the English Poor Laws, may have disagreed with (although his opposition to poor relief softened somewhat over time).

The above graphic is consistent with Malthus’ hopes. When economic conditions (measured by unemployment change) decline people delay or postpone marital unions. Assuming that there is a delay in the proposition of marriage, it is better to use the lagged unemployment rate. However, this does not matter as there appears to also be a strong relationship between contemporaneous unemployment rate and the marriage rate.

While Malthus might have found the first plot somewhat comforting, we also know that it is socially acceptable for couples to have births outside of wedlock. The figure above demonstrates that despite the social acceptance of out of wedlock births, crude birth and marriage rates are still highly correlated modern Europe. With this in mind, the link between unemployment and fertility is illustrated in the below. Once again the link is clear.

One of the most striking aspects of these graphics is the Crisis. Since 2008, most European nations have experienced a collapse in economic conditions, and inevitable rise in unemployment. Despite this, the demographic trends still obey what would seem to be ‘Malthusian’ logic.