Correlation between Olympic Medals and GDP

I have been hit by the Olympic bug, stuck to the tv watching competitive events not normally televised. The Olympics seems to be a strange event where every 4 years we get behind our athletes to support them in events we rarely care about (how many times have you watched an IAAF meeting or a weightlifting competition outside of Olympic screening?)

As we see the USA and China in their familiar competitive environment, I looked at the medals tables over the previous 4 Olympics and began to wonder if I was just trying to reason random data, or if there is scientific proof regarding the economic prowess of a nation and its ability to achieve Olympic success. Stumbling on some academic work, I thought I should share... 

A June 2008 economic paper published by consultants PricewaterhouseCoopers found a strong historic link between money and medals: Countries with the bigger GDPs tend to be represented most often on Olympic podiums. It’s logical — nations with more resources can, if they choose, devote more money to investing in their athletes.

Similarly higher GDP per capita may also be associated with higher average nutrition and health levels could also boost performance in some sports.

Now for the stats...

In an article written by Xun Bian (2005) in The Park Place Economist, Volume XIII, the author attempted to quantify the relationship I mentioned above. The paper follows two studies on modeling national Olympic performance and using both a multiple linear regression model  and the ever popular Cobb-Douglas production function to estimate the influence of population size, economic resources, political and economic structure, and hosting advantage on nations’ Olympic performance.   

For the linear regression: Mt = C + α1 Nt + α2 (Yt / Nt) +α3 P +α4 Ht + ε. 

Mt denotes the medal number for a country at a particular Olympic Game.

Yt/Nt is therefore the per capita GDP of the country at the Olympic year. P and Ht are dummy variables for political and economic structure and hosting. P takes the value 1 if the country

has socialist background, which means the country is or was a socialist country, and it takes 0 if otherwise. Similarly, if the country is hosting the Olympics in that year, Ht takes the value of 1,

and 0 if otherwise. 

From the model we can note GDP per capita, population, socialism and hosting have positive coefficients noting the positive correlation between these variables, however we must not read too much into this model, with maximum adjusted R^2 of 50%, we would say that at least 50% of the variation in medal counts is unexplained by this model. Note however how statistically significant the variables are! 

Lets take a look at the second model, the Cobb Douglas Production Function: 

 As we have learnt in multivariable calculus, this is a function of 2 variables namely population (N), economic resources (Y):      Mt = At (Nt)^γ (Yt)^θ 

By taking natural log of both sides of the equation to make it linear in log form,  yields the following specification for Olympic medal counts: lnMt = lnAt + γ lnNt +θ lnYt + e. 

Since At captures other aspects that are influential on a country’s Olympic performance, we can

replace lnAt with the constant C, the communist dummy variable P, and the hosting dummy variable Ht. Therefore, the actual equation I used takes the

following form, in which α1 = γ and α2 = θ.

lnMt = C + α1 lnNt + α2 lnYt +α3 P +α4 Ht + e

The results are as follows: 

Notice we have not improved the adjusted R^2 and the coefficient ln Nt variable for population is now negative (but not statistically significant in this model), indicating a negative correlation between population size and Olympic performance. 

The author however says the above results are consistent with previous studies on national

Olympic performance (Johnson and Ali , 2000  & Bernard and Busse , 2000), this paper finds that socioeconomic variables, including population size, economic

resources, hosting advantage, and political structure have a significant impact on a country’s Olympic performance. 

In general, population size and economic resources are positively correlated with medal

counts. The larger the population size, the more likely a country is going to do better in the Olympics; the richer a country is, the more Olympic medals it will likely win. Being a hosting nation and having a communist background both have a favorable influence on a country’s Olympic performance.

The Young Economist