According to the convergence hypotheses, countries with low per capita incomes should grow at a faster rate than countries with high per capita income and eventually converge. The neoclassical model predicts two types of convergence: absolute and conditional.
Absolute convergence implies that developing countries, regardless of their particular characteristics, will eventually catch up with the developed countries and match them in per capita output.
Conditional convergence implies that convergence is conditional on the countries having the same saving rate, population growth rate and production function. If these conditions hold the model implies convergence to the same level of per capita output as well as the same steady state growth rate.
However, empirical evidence suggests that some poor countries are converging while others are not. This explained by the club convergence hypothesis.
Club convergence implies that only rich and middle-income countries that are members of the club (Countries which develop appropriate legal, political and economic systems; open trade and capital flow)are converging to the income level of the richest countries of the world. Countries with the lowest per capita income in the club grow at the fastest rate.
Countries outside the club without appropriate institutional structures may fall into a non-convergence trap.