2. Inequality, future outcomes and the Olympics

Many arguments regarding the negative relationship between inequality and outcomes speak to relative capabilities. Robert Fogel (Reference Fogel1994) pointed out that food production in 18th century France was so low that those at the bottom of the income distribution were so undernourished that they could not provide more than 6 hours of light work every day. Chronic malnutrition limited the ability to increase incomes. Elsewhere, Angus Deaton (Reference Deaton2003: 130–131) rephrased the argument by stating that guaranteeing ‘basic needs’ by redistribution enables those at the bottom ‘to participate gainfully in the labor market’. As such, ‘destitution is (…) seen as a problem that can be dealt with by a more equitable distribution’. Channels that emphasize heavier credit constraints at the bottom of the income distribution or limit the ability to make investments in human capital amount to the same: more inequality entails greater constraints at the bottom of the income distribution.

The link between inequality and the ability to win medals is similar. Innate athletic skills are distributed independently of income. However, the training of an athlete is a costly endeavor – a cost which is also independent of income. Athletes from richer households have an easier time clearing that hurdle. Thus, the pool of the best athletes in a country is limited by this ability to leap over the cost hurdle. All else being equal, high inequality limits the ability of the poorest to participate in international competitions such as the quadrennial Olympic Games (Krishna and Haglund, Reference Krishna and Haglund2008). Most studies of Olympic outcomes rarely consider inequality (Bernard and Busse, Reference Bernard and Busse2004; Johnson and Ali, Reference Johnson and Ali2004; Trivedi and Zimmer, Reference Trivedi and Zimmer2014). However, the few studies that do find a negative effect of inequality on Olympic performance (Bai et al., Reference Bai, Uhlmann and Berdahl2015; Berdahl et al., Reference Berdahl, Uhlmann and Bai2015).

On the other hand, we ought to consider the gains of winning a medal as well. There are important rewards from Olympic participation (e.g. prizes, prestige, advertisement contracts, etc.). Thus, inequality can also act as a motivator. In fact, if the rewards are roughly equal in monetary terms, it stands to reason that they are subjectively more valuable for those at the bottom of the income distribution. Thus, the issue becomes one of the appropriability of the benefits from training efforts (Alchian, Reference Alchian1965; Campbell et al., Reference Campbell, Mixon and Sawyer2005; Shughart and Tollison, Reference Shughart and Tollison1993) which brings in the role of property rights regimes. Secure property rights animate individuals to allocate productive resources to the most valued ends.Footnote ² Using the Olympic performance of former communist countries during their transition to market economies, Shughart and Tollison (Reference Shughart and Tollison1993) argued that private property rights were ‘not sufficiently well established to permit these athletes to capitalize the returns from Olympic victory in ways available to their Western counterparts’. The result was that athletes ‘tended to supply less medal winning effort’ in the 1992 Olympic Games which they used as their example (as these Olympics occurred during a transition).Footnote ³

Campbell et al. (Reference Campbell, Mixon and Sawyer2005) extended on Shughart and Tollison's insights by testing whether or not economic freedom affected medal counts. Although they found that economic freedom had a strong positive effect on medal counts, it is their choice of economic freedom as a measure institutional quality that matters to us. For our purposes, it is the ‘legal system and property rights’ component of the economic freedom index that matters most. That component of the index attributes values based on the protection of property rights, the legal enforcement of contracts, the reliability of police forces and the regulatory costs of the sale of property (Fraser Institute, 2018).Footnote ⁴ All of these elements speak to whether or not athletes can appropriate the returns from their efforts. A weak property rights regime (i.e. a regime with low economic freedom) creates fewer incentives to invest efforts in athletic performance. There is already corollary support in the form of the finding that corruption reduces medal counts (Pierdzioch and Emrich, Reference Pierdzioch and Emrich2013). As corruption undermines the quality of property rights, it reduces the ability to appropriate returns from winning a medal and, consequently, deters effort. In other words, just as they are expected to increase productivity-enhancing capital investments (Hall and Lawson, Reference Hall and Lawson2014; Hall et al., Reference Hall, Sobel and Crowley2010), property rights can increase investments in enhancing Olympic productivity.

In other words, bad institutions amplify the effect of inequality on medal numbers and good institutions mitigate that effect. At the same level of inequality, countries with better institutions provide stronger incentives for those at the bottom to invest resources toward winning medals. The countries with bad institutions are unable to generate the same efforts. Thus, we can expect that, if grouped by level of inequality, countries with better institutions win more medals (all else being equal). Conversely, if grouped by quality of institutions, we can expect that countries with less inequality win more medals. Finally, there is the possibility that one channel dominates the other. We consider all these possibilities in this paper.

3. Methods and data

Our empirical strategy has to reflect our underlying assumption of the heterogeneous impact of inequality on Olympic performance assumption. In terms of estimation strategy the heterogeneous impact of inequality can be captured using multiple equilibria analysis. We start with an assumption that there are at least two institutional regimes, under which inequality can either be detrimental to performance of athletes (regime of low level of economic freedom), or irrelevant for the performance of athletes (regime of high level of economic freedom). Under the regime of low economic freedom, athletes cannot easily appropriate the gains from winning a medal and thus there are fewer incentives to invest in improving Olympic performance. Under the regime of high economic freedom, these incentives are stronger and more numerous. In both regimes, the cost that inequality imposes is the same so that only the benefits that athletes can capture (i.e. those which stem from institutional quality) generate differences in performance. To do so we apply a threshold model to estimate the threshold between two regimes, rather than making an arbitrary decision (Hansen, Reference Hansen2000). The model takes the following form:

(1)$$\eqalign{y_i = & \theta _1x_i + \beta _1c_i + u_i, \;\quad q_i \le \gamma , \;\cr y_i = & \theta _2x_i + \beta _2c_i + u_i, \;\quad q_i > \gamma , \;} $$

where y _i is the outcome variable, namely medals per million persons; x _i is the level of inequality; c _i are controls for income, saving, expenditures on health and military, life expectancy, age, weight and number of athletes; u _i is the error term; θ and β are coefficients for the related regimes. It follows that q _i represents the threshold variable, namely the index of economic freedom, whereas γ is the threshold separating the two regimes.

Institutions enter the estimation indirectly as a regime identifier. Comparing θ ₁ and θ ₂ would provide information on the impact of institutional regimes on the interplay between inequality and the outcome variable. However, we might be interested in the direct impact of institutions on the outcome variable. In addition, multiple equilibria analysis is applied to the outcome variable as well as countries with zero medals should be considered in a separate equation resembling hurdle model. We reformulate model (1) with respect to a natural threshold of zero in the outcome variables and define two equations: the first equation explains the non-zero part, whereas the second equation explains the probability of winning at least one medal (zero against non-zero outcome). However, the given hurdle model does not imply a threshold. Countries not scoring any medals would most likely have a different set of slopes for the same variables. The hurdle model can be specified in the following way, where the first equation is estimated using a gamma regressionFootnote ⁵ and the second equation is estimated using a logit model:

(2)$$\eqalign{& y_i = \pi _xx_i + \pi _cc_i + e_i, \;\quad \quad \quad \,\,\,y_i > 0 \cr & nonzero_i = \phi _xx_i + \phi _cc_i + v_i, \;\quad nonzero_i = \left\{{\matrix{ {1, \;} & {{\rm if}\,y_i{\rm \;} > 0{\rm \;}} \cr {0, \;} & {{\rm if}\,y_i{\rm \;} = 0{\rm \;}} \cr } } \right.} $$

where y _i would be the number of medals per one million population, excluding zeros, and nonzero _i would be the binary outcome for zero and nonzero cases. π and ϕ are the coefficients, whereas e and v are the errors. Due to the nonlinear nature of the gamma and logit models, average marginal effects (AMEs) are calculated and reported.

We combined multiple datasets to obtain estimates of inequality and relevant controls (see Table 1). The data on medals and population were taken from IOC (2012, 2016) and The World Bank (2018). We calculate the number of medals per million inhabitants to capture a country's effectiveness in winning medals. We used the EFW index produced by the Fraser Institute (2018) and averaged the values over the period of 2000–2014.Footnote ⁶ The EFW is particularly well-suited for our purposes because of the property rights component (which carry an important weight in the index) which speaks to athletes' ability to appropriate the rents from Olympic participation. Thus, it is an efficient tool to test our argument that inequality's effects are offset by institutional quality. Averaging of the EFW values is an important feature of the present paper as the decision to invest efforts is based on property rights before the Olympics which is why we average the values of EFW before the Olympics.

Table 1. Descriptive statistics

The proxies for inequality (Gini index and the income share of the top 10%) were taken from The World Bank (2018). Following the same logic as for the EFW, we averaged them for the period of 2000–2014 or 2000–2015, where applicable. As for control variables, we included GDP per capita, savings rate, state expenditures on health and the military, life expectancyFootnote ⁷ and the characteristics of athletes who participated.Footnote ⁸ The variables for GDP per capita and the savings rate are used because they capture the stock of resources available in any given country (with the expectation that richer countries can more easily afford Olympic participation). The variables for state expenditures on health and the military are used as proxies for state support to sports aimed at reducing the portion of training costs that are shouldered by athletes themselves. Only a handful of countries report data on state support to sports (International Monetary Fund, 2020). However, we expect a correlation between state expenditures on health and the military and state support for sports.Footnote ⁹ Thus, these variables are included as proxies to avoid a potential bias from omitting a variable measuring the degree to which training costs are being socialized through government funding to sports. Life expectancy is included to capture the overall health of the population. We also included country-averaged statistics of individual athletes as well as controls for broader regions (e.g. sub-Saharan Africa, East Asia, Latin America, Europe, etc.).Footnote ¹⁰ We also included a control variable for the medals won in previous Olympic Games. This is done to reflect the finding that investments for one Olympics increased significantly the chance of winning medals in subsequent Olympics (Bernard and Busse, Reference Bernard and Busse2004).Footnote ¹¹ In other words, we account for a persistence effect of previous Olympics.

We also need to discuss our main variable of interest, medals won relative to population, in order to explain additional steps that we took. We selected that variable because it relates to the efficiency of countries in winning medals. Because the number of medals is expressed relative to population, including an independent variable for population size would create collinearity. However, population is a relevant indicator because it speaks to the availability of resources for competitions (Bernard and Busse, Reference Bernard and Busse2004; Rathke and Woitek, Reference Rathke and Woitek2008; Tcha and Pershin, Reference Tcha and Pershin2003). Thus, we could be biasing our results by omitting a population variable. We provide two solutions. First, we include the number of athletes per country as a share of all participating athletes. This indirectly captures some of the effect of population size as larger countries have more athletes. However, this is far from ideal because it is a measure of relative size and will not capture the absolute effect of population. As such, we took the second step of including a robustness check where we alter our econometric strategy. Rather than using medals to population, we use the medal count. This allows us to include population polynomials. Because of the large number of zeroes, we apply zero-inflated negative binomial regressions. Our main results are found to hold (see footnote 16 for the online appendix).

Before we proceed, we must highlight one limitation of our approach that we were unable to circumvent. Not all Olympic disciplines are the same in terms of costs: training an athlete for cycling is costlier than training for the 100 m dash. These costs, in turn, may affect the choice of disciplines in which athletes specialize especially in countries with high levels of inequality. To resolve this problem, we attempted to create a ranking of the costs of the different disciplines but the sources we found were of low quality and disagreed heavily on the actual ranking (in part because the costs of training also vary by country).Footnote ¹² As such, we were unable to resolve this issue. However, we indirectly and partially control for this problem. First, our variable for income per capita controls for athletes' foregone incomes. Second, the costs of Olympic training include expensive facilities that exceed the private cost to athletes are often covered by government funding or by private sponsorship. Our inclusion of state expenditures on health and the military helps capture the part of training costs that are funded through taxpayers (see footnote 10). Essentially, these entail that we capture the training costs that are borne by athletes and governments but we do not capture costs borne by private sponsors. Thus, these are imperfect remedies that nevertheless minimize the problem of the lack of reliable cost estimates by discipline.