Yes, such an index indeed exists:
The Regional Authority Index (RAI) tracks regional authority on an annual basis from 1950 to 2010 in 81 countries. The sample consists of all EU member states, all OECD member states, all Latin American countries, ten countries in Europe beyond the EU and eleven in the Pacific and South-East Asia.
I've selected the country scores as of the year 2010 into the table below. You can find a detailed calculation of how they arrived to each score on the author's website. If you're wondering why there's only 80 countries instead of 81, it's because Serbia and Montenegro split back in 2006.
| Country | Regional authority index |
|------------------------|--------------------------|
| Germany | 37,0 |
| Spain | 33,6 |
| Belgium | 33,1 |
| United States | 29,6 |
| Italy | 27,3 |
| Bosnia and Herzegovina | 27,1 |
| Switzerland | 26,5 |
| Canada | 26,0 |
| Australia | 25,4 |
| Argentina | 23,5 |
| Austria | 23,0 |
| Malaysia | 21,5 |
| Indonesia | 20,8 |
| Russian Federation | 20,1 |
| Mexico | 20,0 |
| France | 20,0 |
| Brazil | 19,5 |
| Peru | 18,1 |
| Netherlands | 17,5 |
| Bolivia | 13,5 |
| South Korea | 13,0 |
| Japan | 13,0 |
| Colombia | 12,3 |
| Sweden | 12,0 |
| Uruguay | 12,0 |
| Norway | 12,0 |
| Philippines | 11,5 |
| United Kingdom | 11,2 |
| Greece | 11,0 |
| New Zealand | 11,0 |
| Hungary | 10,9 |
| Thailand | 10,3 |
| Romania | 10,0 |
| Croatia | 9,0 |
| Czech Republic | 9,0 |
| Paraguay | 8,2 |
| Poland | 8,0 |
| Slovakia | 8,0 |
| Turkey | 8,0 |
| Ecuador | 8,0 |
| Denmark | 7,3 |
| Finland | 7,1 |
| Venezuela | 7,0 |
| Serbia | 6,4 |
| Haiti | 5,5 |
| Panama | 5,4 |
| Cuba | 5,0 |
| Nicaragua | 4,5 |
| Portugal | 3,8 |
| Dominican Republic | 3,7 |
| Ireland | 3,0 |
| Latvia | 3,0 |
| Lithuania | 3,0 |
| Chile | 3,0 |
| Albania | 2,0 |
| Bulgaria | 2,0 |
| Macedonia | 2,0 |
| Israel | 2,0 |
| Slovenia | 1,0 |
| El Salvador | 1,0 |
| Guatemala | 1,0 |
| Honduras | 1,0 |
| Trinidad and Tobago | 0,5 |
| Cyprus | 0,0 |
| Estonia | 0,0 |
| Iceland | 0,0 |
| Luxemburg | 0,0 |
| Malta | 0,0 |
| Montenegro | 0,0 |
| Kosovo | 0,0 |
| Singapore | 0,0 |
| Brunei | 0,0 |
| East Timor | 0,0 |
| Bahamas | 0,0 |
| Barbados | 0,0 |
| Belize | 0,0 |
| Costa Rica | 0,0 |
| Guyana | 0,0 |
| Jamaica | 0,0 |
| Suriname | 0,0 |