transition probabilities as in Kremer et al., we focus on ten-year intervals.<sup>16</sup> The longer time span seems more appropriate to analyze the so-called MIC trap since transitions (or lack of them) from middle income to high income status do not occur overnight. Moreover, our focus is mainly on the transitions from middle-income to other status and less on the long-run distribution of world income. Nevertheless, we do compute the ergodic distribution and the half-life implied by the respective matrices of transition probabilities.

We exclude from our analysis oil-exporting as well as resource rich countries since these countries are outliers as resource discoveries are a very special form of “catch-up.”<sup>17</sup> We include many East European and Central Asian countries in the analysis, although for many of them GDP per capita series were only available since 1990 in our sample.<sup>18</sup> We use PPP income per capita from Maddison (2010) to compute the transition matrices for 125 countries from 1950 to 2008.

Suppose that a country's relative income per capita follows a first-order Markov chain with time-invariant transition probabilities denoted by , with _i_ = 1,..., _N_ and _j_ = 1,..., _N_ . Each describes the likelihood that state _i_ will be followed by state _j_ . We denote the set of states as . The probability that equals some particular value _j_ depends only on the most recent value and not on other past realizations of : In other words, a country's relative income today depends solely on yesterday's relative income and not on any other past realizations. We can represent the transition probabilities in matrix form as:

> 16 This also reduces the effect of business cycle fluctuations on countries that are near the relative income thresholds. We recalculate the transition matrices detrending the GDP per capita series using the Hodrick-Prescott filter. Our main results change very little.

> 17 The following countries are included in the analysis: Afghanistan, Albania, Argentina, Armenia, Australia, Austria, Bangladesh, Belarus, Belgium, Benin, Bolivia, Bosnia, Brazil, Bulgaria, Burkina Faso, Burma, Burundi, Cambodia, Canada, Cape Verde, Central African Republic, Chile, China, Comoro Islands, Costa Rica, Côte d'Ivoire, Croatia, Cuba, Czech Republic, Denmark, Djibouti, Dominican Republic, Egypt, El Salvador, Eritrea and Ethiopia, Estonia, Finland, France, Gambia, Georgia, Germany, Ghana, Greece, Guatemala, Guinea, Guinea Bissau, Haïti, Honduras, Hong Kong SAR, China, Hungary, India, Ireland, Israel, Italy, Jamaica, Japan, Jordan, Kenya, Kyrgyzstan, Laos, Latvia, Lebanon, Lesotho, Liberia, Lithuania, Macedonia, Madagascar, Malawi, Malaysia, Mali, Mauritania, Mauritius, Moldova, Mongolia, Morocco, Mozambique, Namibia, Nepal, Netherlands, New Zealand, Nicaragua, Niger, North Korea, Pakistan, Panama, Paraguay, Peru, Philippines, Poland, Portugal, Puerto Rico, Romania, Rwanda, Sao Tomé & Principe, Senegal, Seychelles, Sierra Leone, Singapore, Slovakia, Slovenia, Somalia, South Africa, South Korea, Spain, Sri Lanka, Swaziland, Sweden, Switzerland, Taiwan, China, Tajikistan, Tanzania, Thailand, Togo, Tunisia, Turkey, Uganda, United Kingdom, Ukraine, Uruguay, United States, Uzbekistan, West Bank and Gaza, Zaire (Congo-Kinshasa), Zambia, and Zimbabwe.

> 18 Our main messages do not change even if we exclude these countries (see Appendix 3).

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