Comparative efficiency of national health systems: cross national econometric analysis
BMJ 2001; 323 doi: https://doi.org/10.1136/bmj.323.7308.307 (Published 11 August 2001) Cite this as: BMJ 2001;323:307Data supplement
Annex: Efficiency or Performance Index and Uncertainty Intervals, 191 countries, 1993-97.
Measurement of efficiency (performance)
Yit is the level of population health observed for country i in time t.Assuming there are two inputs, say health expenditure per capita (X1) and educational attainment (X2), efficiency can be derived from the following regression model (variables in logs):
Yit=α +β1X1it+β2X2it+β3(X1it)2+β4(X2it)2+β5(X1it)(X2it)+vit-ui,
where vit is the random error term with mean zero, and ui³ 0 measures country specific inefficiency. Rewriting this as:
Yit=αi+β1X1it+β2X2it+β3(X1it)2+β4(X2it)2+β5(X1it)(X2it)+vit,
where the new intercept αi=(α-ui) is now country specific, parameters can be estimated with a standard fixed-effects panel-data model. To ensure all ui are positive, the country with maximum estimated αi is the reference, or α =max(αi), and the estimated ui = (ααi).
We define efficiency (performance) (Ei) as the time average of
E(Yit½ui, Xit)- Healthitmin
E(Yit½ui=0, Xit)- Healthitmin
or:
Healthit-Healthit min
Healthit max-Healthit min
In terms of table 1, αis the constant term, β1 is the coefficient on health expenditure, β2is the coefficient on average years schooling, and β3is the coefficient on square of average years of schooling. The terms β4 and β5 were dropped from the final estimated model.
Annex: Efficiency or Performance Index and Uncertainty Intervals, 191 countries, 1993-97.
Rank Uncertainty Interval (80%)
Country Performance Index
Uncertainty interval (80%)
1 1 - 5 Oman 0.992 0.975 - 1.000 2 1 - 4 Malta 0.989 0.968 - 1.000 3 2 - 7 Italy 0.976 0.957 - 0.994 4 2 - 7 France 0.974 0.953 - 0.994 5 2 - 7 San Marino 0.971 0.949 - 0.988 6 3 - 8 Spain 0.968 0.948 - 0.989 7 4 - 9 Andorra 0.964 0.942 - 0.980 8 3 - 12 Jamaica 0.956 0.928 - 0.986 9 7 - 11 Japan 0.945 0.926 - 0.963 10 8 - 15 Saudi Arabia 0.936 0.915 - 0.959 11 9 - 13 Greece 0.936 0.920 - 0.951 12 9 - 16 Monaco 0.930 0.908 - 0.948 13 10 - 15 Portugal 0.929 0.911 - 0.945 14 10 - 15 Singapore 0.929 0.909 - 0.942 15 13 - 17 Austria 0.914 0.896 - 0.931 16 13 - 23 United Arab Emirates 0.907 0.883 - 0.932 17 14 - 22 Morocco 0.906 0.886 - 0.925 18 16 - 23 Norway 0.897 0.878 - 0.914 19 17 - 24 Netherlands 0.893 0.875 - 0.911 20 15 - 31 Solomon Islands 0.892 0.863 - 0.920 21 18 - 26 Sweden 0.890 0.870 - 0.907 22 19 - 28 Cyprus 0.885 0.865 - 0.898 23 19 - 30 Chile 0.884 0.864 - 0.903 24 21 - 28 United Kingdom 0.883 0.866 - 0.900 25 18 - 32 Costa Rica 0.882 0.859 - 0.898 26 21 - 31 Switzerland 0.879 0.860 - 0.891 27 21 - 31 Iceland 0.879 0.861 - 0.897 28 23 - 30 Belgium 0.878 0.860 - 0.894 29 23 - 33 Venezuela, Bolivarian Republic of 0.873 0.853 - 0.891 30 23 - 37 Bahrain 0.867 0.843 - 0.890 31 28 - 35 Luxembourg 0.864 0.847 - 0.881 32 29 - 38 Ireland 0.859 0.840 - 0.870 33 27 - 40 Turkey 0.858 0.835 - 0.878 34 25 - 48 Belize 0.853 0.821 - 0.884 35 33 - 40 Canada 0.849 0.832 - 0.864 36 32 - 42 Cuba 0.849 0.830 - 0.866 37 30 - 49 El Salvador 0.846 0.817 - 0.873 38 28 - 52 Saint Vincent and the Grenadines 0.845 0.812 - 0.876 39 35 - 43 Australia 0.844 0.826 - 0.861 40 36 - 44 Israel 0.841 0.825 - 0.858 41 39 - 47 Germany 0.836 0.819 - 0.852 42 33 - 54 Dominican Republic 0.834 0.806 - 0.863 43 37 - 53 Egypt 0.829 0.811 - 0.849 44 41 - 50 Finland 0.829 0.812 - 0.844 45 38 - 55 Algeria 0.829 0.808 - 0.850 46 41 - 55 Tunisia 0.824 0.803 - 0.844 47 38 - 58 Yugoslavia 0.824 0.798 - 0.848 48 40 - 61 Honduras 0.820 0.793 - 0.844 49 37 - 63 Grenada 0.819 0.789 - 0.850 50 42 - 59 Uruguay 0.819 0.794 - 0.842 51 41 - 64 Colombia 0.814 0.787 - 0.843 52 42 - 65 Paraguay 0.813 0.785 - 0.842 53 43 - 64 Qatar 0.813 0.786 - 0.839 54 43 - 69 Saint Lucia 0.809 0.781 - 0.837 55 41 - 70 Cape Verde 0.808 0.776 - 0.842 56 47 - 64 Armenia 0.806 0.785 - 0.823 57 51 - 61 Croatia 0.805 0.789 - 0.821 58 48 - 65 Iran, Islamic Republic of 0.805 0.783 - 0.827 59 45 - 73 Dominica 0.804 0.774 - 0.833 60 49 - 67 Azerbaijan 0.803 0.781 - 0.820 61 52 - 65 China 0.800 0.782 - 0.813 62 55 - 66 Slovenia 0.797 0.781 - 0.813 63 56 - 73 Mexico 0.789 0.771 - 0.808 64 55 - 76 Albania 0.789 0.766 - 0.808 65 61 - 72 Denmark 0.785 0.769 - 0.801 66 57 - 80 Sri Lanka 0.783 0.761 - 0.807 67 57 - 80 Panama 0.783 0.759 - 0.807 68 56 - 83 Kuwait 0.782 0.753 - 0.808 69 61 - 78 The former Yugoslav Republic of Macedonia 0.781 0.761 - 0.796 70 59 - 83 Bosnia and Herzegovina 0.780 0.754 - 0.803 71 65 - 76 Argentina 0.779 0.762 - 0.794 72 67 - 78 United States of America 0.774 0.758 - 0.789 73 61 - 86 Bhutan 0.773 0.748 - 0.797 74 63 - 84 Nicaragua 0.772 0.750 - 0.793 75 65 - 84 Iraq 0.770 0.752 - 0.791 76 67 - 85 Brunei Darussalam 0.768 0.749 - 0.787 77 61 - 88 Suriname 0.768 0.740 - 0.798 78 66 - 88 Brazil 0.767 0.745 - 0.787 79 70 - 84 Trinidad and Tobago 0.767 0.750 - 0.780 80 72 - 83 New Zealand 0.766 0.750 - 0.780 81 73 - 83 Czech Republic 0.765 0.749 - 0.779 82 66 - 91 Yemen 0.761 0.733 - 0.789 83 72 - 88 Seychelles 0.759 0.739 - 0.778 84 73 - 91 Georgia 0.758 0.736 - 0.776 85 73 - 89 Pakistan 0.757 0.738 - 0.777 86 75 - 92 Malaysia 0.751 0.731 - 0.771 87 77 - 92 Barbados 0.749 0.730 - 0.770 88 85 - 92 Slovakia 0.742 0.729 - 0.757 89 84 - 94 Poland 0.742 0.723 - 0.758 90 79 - 98 Indonesia 0.741 0.715 - 0.766 91 85 - 99 Syrian Arab Republic 0.733 0.712 - 0.755 92 89 - 96 Bulgaria 0.733 0.717 - 0.747 93 89 - 103 Lithuania 0.724 0.705 - 0.742 94 89 - 104 Libyan Arab Jamahiriya 0.723 0.699 - 0.746 95 89 - 105 Cook Islands 0.722 0.696 - 0.746 96 89 - 104 Ecuador 0.721 0.700 - 0.742 97 91 - 105 Lebanon 0.719 0.697 - 0.740 98 93 - 107 Nepal 0.714 0.691 - 0.736 99 93 - 107 Guatemala 0.714 0.691 - 0.735 100 94 - 107 Jordan 0.711 0.689 - 0.732 101 97 - 104 Ukraine 0.711 0.695 - 0.726 102 93 - 111 Thailand 0.710 0.682 - 0.736 103 93 - 109 Bangladesh 0.709 0.684 - 0.735 104 92 - 115 Guyana 0.704 0.672 - 0.738 105 101 - 111 Hungary 0.698 0.682 - 0.714 106 102 - 111 Republic of Moldova 0.696 0.680 - 0.710 107 100 - 113 Republic of Korea 0.694 0.674 - 0.711 108 93 - 121 Niue 0.693 0.650 - 0.731 109 103 - 116 Gambia 0.687 0.671 - 0.704 110 100 - 121 Micronesia, Federated States of 0.684 0.656 - 0.717 111 107 - 117 Romania 0.682 0.668 - 0.696 112 107 - 119 Uzbekistan 0.681 0.662 - 0.700 113 105 - 120 Mauritius 0.679 0.657 - 0.702 114 105 - 121 Tonga 0.677 0.651 - 0.704 115 107 - 119 Estonia 0.677 0.657 - 0.694 116 109 - 119 Belarus 0.676 0.657 - 0.692 117 109 - 121 Sao Tome and Principe 0.671 0.651 - 0.691 118 112 - 120 India 0.670 0.654 - 0.683 119 111 - 123 Peru 0.665 0.643 - 0.686 120 108 - 123 Vanuatu 0.665 0.639 - 0.689 121 115 - 125 Latvia 0.655 0.631 - 0.677 122 114 - 127 Saint Kitts and Nevis 0.650 0.621 - 0.679 123 115 - 131 Antigua and Barbuda 0.641 0.606 - 0.678 124 120 - 133 Fiji 0.632 0.600 - 0.662 125 121 - 131 Palau 0.632 0.606 - 0.656 126 122 - 131 Philippines 0.630 0.608 - 0.653 127 124 - 131 Russian Federation 0.623 0.606 - 0.638 128 123 - 134 Tuvalu 0.618 0.594 - 0.644 129 124 - 137 Myanmar 0.612 0.584 - 0.641 130 125 - 136 Viet Nam 0.611 0.587 - 0.634 131 127 - 139 Samoa 0.602 0.579 - 0.626 132 128 - 138 Senegal 0.601 0.584 - 0.620 133 129 - 139 Côte d'Ivoire 0.598 0.580 - 0.617 134 128 - 140 Kyrgyzstan 0.598 0.575 - 0.620 135 129 - 138 Kazakhstan 0.598 0.581 - 0.615 136 129 - 139 Benin 0.596 0.576 - 0.616 137 127 - 142 Bahamas 0.593 0.564 - 0.624 138 132 - 144 Mongolia 0.581 0.555 - 0.607 139 134 - 143 Haiti 0.580 0.561 - 0.599 140 131 - 144 Marshall Islands 0.579 0.549 - 0.609 141 137 - 145 Comoros 0.570 0.550 - 0.590 142 137 - 145 Bolivia 0.567 0.544 - 0.590 143 139 - 146 Gabon 0.559 0.538 - 0.579 144 138 - 148 Kiribati 0.554 0.525 - 0.581 145 140 - 148 Tajikistan 0.551 0.523 - 0.580 146 141 - 149 Papua New Guinea 0.546 0.520 - 0.572 147 144 - 154 Maldives 0.524 0.496 - 0.555 148 146 - 153 Eritrea 0.521 0.504 - 0.538 149 146 - 154 Sudan 0.519 0.496 - 0.543 150 146 - 155 Afghanistan 0.517 0.488 - 0.547 151 147 - 153 Mauritania 0.517 0.501 - 0.533 152 145 - 158 Turkmenistan 0.513 0.479 - 0.546 153 147 - 156 Democratic People's Republic of Korea 0.510 0.485 - 0.536 154 148 - 157 Somalia 0.506 0.480 - 0.530 155 152 - 160 Lao People's Democratic Republic 0.489 0.466 - 0.510 156 154 - 162 Guinea-Bissau 0.481 0.462 - 0.499 157 153 - 162 Cambodia 0.481 0.460 - 0.501 158 153 - 162 Ghana 0.479 0.457 - 0.500 159 155 - 164 Togo 0.472 0.452 - 0.492 160 157 - 164 Guinea 0.469 0.455 - 0.483 161 156 - 165 Chad 0.465 0.444 - 0.487 162 157 - 166 Burkina Faso 0.463 0.441 - 0.483 163 158 - 167 Djibouti 0.457 0.434 - 0.479 164 160 - 166 Central African Republic 0.454 0.436 - 0.470 165 159 - 167 Angola 0.453 0.433 - 0.473 166 162 - 168 Nauru 0.444 0.424 - 0.464 167 164 - 170 Congo 0.433 0.411 - 0.454 168 164 - 172 Mozambique 0.424 0.399 - 0.450 169 167 - 171 Ethiopia 0.418 0.400 - 0.435 170 168 - 172 Mali 0.410 0.393 - 0.426 171 168 - 174 Burundi 0.403 0.374 - 0.435 172 169 - 174 Cameroon 0.399 0.375 - 0.421 173 170 - 174 Madagascar 0.394 0.378 - 0.410 174 172 - 175 Equatorial Guinea 0.377 0.355 - 0.400 175 174 - 176 Nigeria 0.353 0.331 - 0.375 176 175 - 178 Liberia 0.337 0.318 - 0.355 177 176 - 178 Niger 0.323 0.306 - 0.340 178 176 - 178 Kenya 0.320 0.298 - 0.343 179 179 - 180 Uganda 0.280 0.264 - 0.295 180 179 - 180 United Republic of Tanzania 0.279 0.260 - 0.298 181 181 - 185 Rwanda 0.240 0.214 - 0.265 182 181 - 185 South Africa 0.232 0.209 - 0.251 183 181 - 185 Sierra Leone 0.230 0.213 - 0.247 184 181 - 186 Swaziland 0.229 0.205 - 0.255 185 182 - 187 Democratic Republic of the Congo 0.217 0.198 - 0.235 186 183 - 188 Lesotho 0.211 0.187 - 0.236 187 186 - 188 Malawi 0.196 0.181 - 0.211 188 187 - 189 Botswana 0.183 0.172 - 0.194 189 185 - 189 Namibia 0.183 0.152 - 0.214 190 190 - 190 Zambia 0.112 0.095 - 0.129 191 191 - 191 Zimbabwe 0.080 0.057 - 0.103
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