# Success at the Summer Olympics: How Much Do Economic Factors Explain?

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## Abstract

**:**

## 1. Introduction

## 2. Data

Participated in from 1988–2012 | Number of Countries |
---|---|

1 | 4 |

2 | 4 |

3 | 2 |

4 | 5 |

5 | 27 |

6 | 22 |

7 | 144 |

#### 2.1. Distribution of Medal Winnings

Number of Medals Won | 1988 | 1992 | 1996 | 2000 | 2004 | 2008 | 2012 |
---|---|---|---|---|---|---|---|

0 | 66.2 (98) | 62.3 (99) | 58.8 (110) | 59.6 (112) | 61.6 (117) | 55.7 (108) | 56.0 (108) |

1–5 | 18.9 (28) | 22.6 (36) | 23.0 (43) | 22.9 (43) | 18.9 (36) | 25.8 (50) | 24.9 (48) |

6–10 | 2.7 (4) | 3.8 (6) | 5.9 (11) | 5.3 (10) | 8.9 (17) | 8.2 (16) | 7.3 (14) |

11–15 | 4.1 (6) | 1.3 (2) | 3.7 (7) | 3.7 (7) | 1.6 (3) | 2.1 (4) | 3.6 (7) |

16–20 | 1.4 (2) | 3.8 (6) | 2.1 (4) | 1.6 (3) | 2.1 (4) | 2.1 (4) | 3.1 (6) |

21–25 | 2.0 (3) | 1.3 (2) | 2.1 (4) | 1.6 (3) | 1.1 (2) | 1.0 (2) | 0.0 (0) |

> 25 | 4.7 (7) | 5.0 (8) | 4.8 (9) | 5.3 (10) | 5.8 (11) | 5.2 (10) | 5.2 (10) |

**Figure 1.**Characteristics of Olympic winnings and participation. (

**a**) Share of zero-medal winners; (

**b**) Share of countries with no female participation; (

**c**) Changes in the share of female athletes; (

**d**) Female participation in 1988 and 2008.

1988 | 1992 | 1996 | 2000 | 2004 | 2008 | 2012 |
---|---|---|---|---|---|---|

Persistent zero winners | ||||||

– | 90% | 88% | 88% | 91% | 85% | 89% |

Persistent > 25 winners | ||||||

– | 75% | 64% | 89% | 91% | 82% | 90% |

Observed Frequencies of Medal Winnings | ||||||
---|---|---|---|---|---|---|

Medals Won at Subsequent Olympiad | ||||||

0 | 1–5 | 6–15 | 16–25 | >25 | ||

Medals Won at Previous Olympiad | 0 | 0.88 | 0.12 | 0.00 | 0.00 | 0.00 |

1–5 | 0.26 | 0.60 | 0.14 | 0.00 | 0.00 | |

6–15 | 0.01 | 0.26 | 0.58 | 0.13 | 0.02 | |

16–25 | 0.00 | 0.03 | 0.28 | 0.51 | 0.18 | |

>25 | 0.00 | 0.00 | 0.00 | 0.12 | 0.88 |

#### 2.2. Female Participation

Number of Females | 1988 | 1992 | 1996 | 2000 | 2004 | 2008 | 2012 |
---|---|---|---|---|---|---|---|

0 | 24.3 (36) | 21.4 (34) | 15.0 (28) | 5.3 (10) | 4.7 (9) | 4.7 (9) | 1.0 (2) |

1–5 | 45.9 (68) | 46.5 (74) | 49.2 (92) | 51.6 (97) | 54.2 (103) | 53.1 (103) | 55.7 (113) |

6–10 | 7.4 (11) | 8.8 (14) | 9.6 (18) | 11.2 (21) | 8.9 (17) | 7.2 (14) | 7.4 (15) |

11–15 | 2.0 (3) | 2.5 (4) | 3.7 (7) | 5.3 (10) | 4.2 (8) | 6.2 (12) | 4.4 (9) |

16–20 | 2.7 (4) | 0.6 (1) | 4.3 (8) | 3.7 (7) | 7.9 (15) | 4.6 (9) | 4.9 (10) |

21–25 | 2.7 (4) | 3.1 (5) | 1.6 (3) | 2.7 (5) | 3.2 (6) | 3.6 (7) | 3.4 (7) |

>25 | 15.5 (23) | 17.0 (27) | 16.6 (31) | 20.2 (38) | 16.8 (32) | 20.6 (40) | 23.2 (47) |

#### 2.3. Other Variables

Variable | Definition | Mean | Between Country Standard. Dev. | Within Country Standard. Dev. |
---|---|---|---|---|

Number of medals | Number of medals won | 4.59 | 16.62 | 3.22 |

Athlete share | $ln\left(\frac{\text{country\u2019s}\phantom{\rule{4.pt}{0ex}}\text{athletes}}{\text{total}\phantom{\rule{4.pt}{0ex}}\text{athletes}}\right)$ | −6.38 | 1.49 | 0.40 |

Female share | $\frac{\text{country\u2019s}\phantom{\rule{4.pt}{0ex}}\text{females}}{\text{total}\phantom{\rule{4.pt}{0ex}}\text{athletes}}$ | 0.31 | 0.12 | 0.15 |

Per capita GDP | $ln\left(\frac{\text{GDP}}{\text{10,000}*\text{population}}\right)$ | −1.15 | 1.61 | 0.61 |

Population | $ln\left(\frac{\text{population}}{\text{10,000,000}}\right)$ | −0.84 | 2.33 | 0.16 |

Islamic | =1 if Islamic, 0 otherwise | 0.11 | 0.31 | 0 |

Host | =1 if host, 0 otherwise | 0.01 | 0.03 | 0.07 |

Olympiad before Hosting | Olympiad of Hosting | Olympiad after Hosting | |
---|---|---|---|

South Korea | − | 401 | 226 |

Spain | 229 | 422 | 289 |

USA | 545 | 646 | 586 |

Australia | 417 | 617 | 470 |

Greece | 140 | 426 | 152 |

China | 383 | 600 | 386 |

Great Britain | 304 | 559 | − |

## 3. Selection Model

## 4. Structural Treatment of Athletic Participation

## 5. Explanatory Variables and Estimation

`xtprobit`command for the selection equation, and using

`xtreg`for the shares equation. The dynamic specifications are estimated using regular probit for the selection equation, and using regular OLS for the shares equation. The main additional complication of this approach is the computation of the asymptotic variance due to the use of generated regressor; see [27] for details. We are unaware of the precise modification required for the computing the asymptotic variance matrix of the second stage estimates, but the literature offers many examples in which this is done using the bootstrap method. Standard errors reported below adjust for clustering at the country level.

## 6. Results

#### 6.1. Selection: The Probability of Winning Any Medal

**Table 8.**Probit estimates of the probability of winning any medal (average marginal effects in brackets).

Static Model | Dynamic Model | Static Model | Dynamic Model | |||||
---|---|---|---|---|---|---|---|---|

(1) | (2) | (3) | (4) | |||||

Coeff. | St. Err. | Coeff. | St. Err. | Coeff. | St. Err | Coeff. | St. Err | |

Athlete share | 1.134 ${}^{*}$ | 0.091 | 0.886 ${}^{*}$ | 0.084 | • | • | • | • |

[0.16] | [0.13] | |||||||

Female share | 0.923 ${}^{*}$ | 0.382 | 0.280 | 0.362 | −0.395 | 0.398 | −0.559 ${}^{\u2020}$ | 0.319 |

[0.13] | [0.04] | [−0.08] | [−0.10] | |||||

Per capita GDP | 0.129 ${}^{*}$ | 0.058 | 0.066 | 0.049 | 0.520 ${}^{*}$ | 0.065 | 0.323 ${}^{*}$ | 0.038 |

[0.02] | [0.01] | [0.10] | [0.06] | |||||

Population | 0.158 ${}^{*}$ | 0.057 | 0.070 | 0.044 | 0.761 ${}^{*}$ | 0.073 | 0.342 ${}^{*}$ | 0.036 |

[0.02] | [0.01] | [0.15] | [0.06] | |||||

Islamic | −0.161 | 0.254 | −0.005 | 0.191 | −1.434 ${}^{*}$ | 0.395 | −0.499 ${}^{*}$ | 0.170 |

[−0.02] | [<−0.01] | [−0.27] | [−0.09] | |||||

Constant | 6.815 ${}^{*}$ | 0.523 | 5.030 ${}^{*}$ | 0.520 | 0.977 ${}^{*}$ | 0.225 | −0.133 | 0.157 |

Any medal${}_{t-1}$ | − | − | 0.865 ${}^{*}$ | 0.138 | − | − | 1.611 ${}^{*}$ | 0.115 |

[0.12] | [0.29] | |||||||

Random effects? | Yes | No | Yes | No | ||||

Random effect variance | 0.636 | − | 1.359 | − | ||||

Log likelihood | −366.57 | −286.65 | −443.91 | −353.32 | ||||

Sample size | 1313 | 1098 | 1,313 | 1,098 |

Predicted | ||||
---|---|---|---|---|

>0 Medals | 0 Medals | |||

Actual | >0 medals | 360 | 79 | |

0 medals | 54 | 605 |

Country | Year | Country | Year | Country | Year |
---|---|---|---|---|---|

Afghanistan | 2008 | Iceland | 2000 | Qatar | 2000 |

Algeria | 1992 | Iceland | 2008 | Qatar | 2012 |

Algeria | 2008 | Ireland | 1992 | Saudi Arabia | 2000 |

Armenia | 2008 | Israel | 1992 | Saudi Arabia | 2012 |

Bahamas | 1992 | Kuwait | 2000 | Singapore | 2008 |

Bahrain | 2008 | Kuwait | 2012 | Sri Lanka | 2000 |

Barbados | 2000 | Kyrgyz Republic | 2000 | Sudan | 2008 |

Cameroon | 2000 | Kyrgyz Republic | 2008 | Suriname | 1992 |

Chile | 2000 | Macedonia | 2000 | Syria | 1996 |

Chinese Taipei | 1992 | Malaysia | 1992 | Syria | 2004 |

Colombia | 2000 | Malaysia | 2008 | Tajikistan | 2008 |

Costa Rica | 1996 | Mauritius | 2008 | Togo | 2008 |

Cyprus | 2012 | Moldova | 2008 | Tonga | 1996 |

Dominican Republic | 2004 | Mongolia | 1992 | Trinidad and Tobago | 1996 |

Ecuador | 1996 | Mongolia | 1996 | Tunisia | 1996 |

Ecuador | 2008 | Mongolia | 2004 | Tunisia | 2008 |

Egypt | 2004 | Montenegro | 2012 | Uganda | 1996 |

Eritrea | 2004 | Mozambique | 1996 | Uganda | 2012 |

Estonia | 2000 | Nigeria | 1992 | United Arab Emirates | 2004 |

Gabon | 2012 | Norway | 2004 | U.S. Virgin Islands | 2008 |

Ghana | 1992 | Panama | 2008 | Uruguay | 2000 |

Grenada | 2012 | Paraguay | 2004 | Venezuela | 2004 |

Guatemala | 2012 | Portugal | 1996 | Vietnam | 2000 |

Hong Kong | 1996 | Puerto Rico | 1992 | Vietnam | 2008 |

Hong Kong | 2004 | Puerto Rico | 2012 | Zambia | 1996 |

Hong Kong | 2012 | Qatar | 1992 | Zimbabwe | 2004 |

Argentina | France | South Korea |

Australia | France | Morocco |

Austria | Great Britain | Mexico |

Belgium | Greece | Netherlands |

Bulgaria | Hungary | New Zealand |

Brazil | Indonesia | Poland |

Canada | India | Romania |

Switzerland | Iran | Sweden |

China | Italy | Thailand |

Denmark | Jamaica | Turkey |

Spain | Japan | United States |

Finland | Kenya |

Angola | Dominica | Madagascar | St. Lucia |

Albania | Eritrea | Maldives | Sao Tome and Principe |

Antigua and Barbuda | Fiji | Marshall Islands | Suriname |

Aruba | Micronesia | Mali | Swaziland |

Burundi | Gabon | Malta | Seychelles |

Benin | Gambia | Montenegro | Chad |

Bermuda | Guinea-Bissau | Monaco | Turkmenistan |

Burkina and Faso | Equatorial Guinea | Mauritania | Timor-Leste |

Bangladesh | Grenada | Malawi | Tonga |

Belize | Guatemala | Burma | Tuvalu |

Bolivia | Guyana | Nauru | Tanzania |

Bosnia Herzegovina | Honduras | Niger | St. Vincent and the Grenadines |

Brunei | Haiti | Nicaragua | Vanuatu |

Bhutan | Iraq | Netherlands Antilles | Samoa |

British Virgin Islands | Jordan | Nepal | Yemen |

Botswana | Kiribati | Oman | Congo |

Central African Republic | St. Kitts and Nevis | Palau | American Samoa |

Cote d’Ivoire | Laos | Papau New Guinea | Andorra |

Cook Islands | Lebanon | Rwanda | Guinea |

Comoros | Libya | Solomon Islands | Palestine |

Cape Verde | Liberia | Sierra Leone | U.S. Virgin Islands |

Cayman Islands | Liechtenstein | El Salvador | Cambodia |

Cyprus | Lesotho | San Marino | Guam |

Djibouti | Luxembourg | Somalia |

#### 6.1.1. Why the Model May Provide an Inadequate Fit for Small Countries

#### 6.2. Outcome: Conditional Model of the Level of Success

Coeff. | St. Err. | |
---|---|---|

Female share | −1.224 ${}^{*}$ | 0.123 |

Host | 0.611 ${}^{*}$ | 0.294 |

Per capita GDP | 0.306 ${}^{*}$ | 0.015 |

Population | 0.329 ${}^{*}$ | 0.012 |

Islamic | −0.638 ${}^{*}$ | 0.073 |

medal share${}_{t-1}$ <75th pct | omitted | |

medal share${}_{t-1}$ 75–90th pct | 1.181 ${}^{*}$ | 0.067 |

medal share${}_{t-1}$ 90–95th pct | 1.985 ${}^{*}$ | 0.107 |

medal share${}_{t-1}$ 95–99th pct | 2.062 ${}^{*}$ | 0.123 |

medal share${}_{t-1}$ ≥99th pct | 1.924 ${}^{*}$ | 0.238 |

Constant | −5.730 ${}^{*}$ | 0.061 |

R-square | 0.78 |

**Table 14.**Alternative estimates of the medal share equation: Without and with control for endogeneity.

(1) Static Model without ${K(z}_{\mathrm{it}})$ | (2) Dynamic Model without ${K(z}_{\mathrm{it}})$ | (3) Static Model with ${K(z}_{\mathrm{it}})$ | (4) Dynamic Model with ${K(z}_{\mathrm{it}})$ | (5) Fixed Effects Model | ||||||
---|---|---|---|---|---|---|---|---|---|---|

Coeff. | St. Err. | Coeff. | St. Err. | Coeff. | St. Err | Coeff. | St. Err | Coeff. | St. Err. | |

Athlete share | 1.403 ${}^{*}$ | 0.082 | 0.454 ${}^{*}$ | 0.072 | 0.771 ${}^{*}$ | 0.070 | 0.410 ${}^{*}$ | 0.044 | 0.490 ${}^{*}$ | 0.133 |

Female share | 1.094 ${}^{*}$ | 0.235 | 0.307 | 0.222 | 0.662 ${}^{*}$ | 0.248 | 0.209 | 0.213 | 0.346 | 0.270 |

Host | −0.163 | 0.106 | 0.331 ${}^{*}$ | 0.185 | −0.167 | 0.187 | 0.463 ${}^{*}$ | 0.201 | 0.360 ${}^{*}$ | 0.125 |

${Mills}_{it}$ | 1.113 ${}^{*}$ | 0.129 | 0.118 | 0.115 | 0.351 ${}^{*}$ | 0.166 | −0.114 | 0.086 | − | − |

${K(z}_{it})$ | − | − | − | − | 0.295 ${}^{*}$ | 0.125 | −0.126 ${}^{\u2020}$ | 0.075 | − | − |

Constant | 0.961 ${}^{*}$ | 0.371 | −3.817 ${}^{*}$ | 0.347 | −0.179 | 0.571 | −4.678 ${}^{*}$ | 0.467 | −2.852 ${}^{*}$ | 0.657 |

share${}_{t-1}$ < 75 pct | − | − | omitted | − | − | omitted | − | − | ||

share${}_{t-1}$ 75–90th pct | − | − | 0.724 ${}^{*}$ | 0.087 | − | − | 0.815 ${}^{*}$ | 0.131 | − | − |

share${}_{t-1}$ 90–95th pct | − | − | 1.516 ${}^{*}$ | 0.119 | − | − | 1.769 ${}^{*}$ | 0.184 | − | − |

share${}_{t-1}$ 95–99th pct | − | − | 2.085 ${}^{*}$ | 0.141 | − | − | 2.398 ${}^{*}$ | 0.222 | − | − |

share${}_{t-1}$ ≥ 99th pct | − | − | 2.856 ${}^{*}$ | 0.157 | − | − | 3.241 ${}^{*}$ | 0.248 | − | − |

Random effects? | Yes | No | Yes | No | No | |||||

Random effect variance | 0.366 | − | 0.567 | − | − | |||||

Sample size | 514 | 439 | 514 | 439 | 439 |

#### 6.2.1. Why the Structural Assumptions May Fail for Large Countries

**Figure 3.**Locally-weighted nonparameteric regressions of Model 4 residuals on the exclusion restrictions.

#### 6.3. Fitted Medal Winnings

## 7. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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^{1}In estimations not reported in this paper, we included as additional covariates county-specific time averages of all explanatory variables to allow correlation between the covariates and the random effect [20]. That modification did not contribute any additional explanatory power in explaining medal winnings, nor did it alter the main qualitative findings regarding the explanatory variables.^{2}One could also argue that female participation is endogenous. However, because almost all Olympic sports separate events by gender, it seem plausible that, after conditioning on a country’s athlete share, the gender composition of its contingent is largely exogenous.^{4}The purpose of this first-stage regression is not to interpret estimates from the regression, but rather to calculate a control function from it. Consequently, although athlete shares are bounded between 0 and 1, it is not necessary to perform a logit-type transformation, as we do for medal shares.^{5}In exploratory work we also considered the number of events in which a country enters its competitors as a measure of the breadth of its participation and its overall sporting prowess. However, there is a very high linear dependence between the number of athletes and the number of events in which they participate. Given our relatively small sample size, this collinearity makes the interpretation of individual coefficients unreliable and hence the reported equations exclude this regressor.^{6}We present the nonparametric regressions separately for each of the three exclusions restrictions to ease visual interpretation, and also because our relatively small sample size precludes nonparametric regression with multiple regressors.

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## Share and Cite

**MDPI and ACS Style**

Trivedi, P.K.; Zimmer, D.M. Success at the Summer Olympics: How Much Do Economic Factors Explain? *Econometrics* **2014**, *2*, 169-202.
https://doi.org/10.3390/econometrics2040169

**AMA Style**

Trivedi PK, Zimmer DM. Success at the Summer Olympics: How Much Do Economic Factors Explain? *Econometrics*. 2014; 2(4):169-202.
https://doi.org/10.3390/econometrics2040169

**Chicago/Turabian Style**

Trivedi, Pravin K., and David M. Zimmer. 2014. "Success at the Summer Olympics: How Much Do Economic Factors Explain?" *Econometrics* 2, no. 4: 169-202.
https://doi.org/10.3390/econometrics2040169