convergence or divergence

When looking at data that plot average growth rate of GDP to log GDP per worker/capital, evidence of convergence can never been found. Unless we restrict the countries to OECD countries, introducing once again sampling bias. There are might be three reasons behind this lack of backing from data.
1. true lack of convergence. This may imply the standard growth model that economists have been so happy with are incomplete at least or wrong.
2. The fundamentals (I mean fundamentals in a narrow sense--institutions mainly, not including education, which I would want to be modeled endogenously) are different. It is very reasonable to expect that rich countries tend to have good fundamentals while poor countries might not.
3. Poor countries tend to have reversals in fundamentals due to political instability brought by poverty. this point is similar to point 2, but there is a subtle difference in that, point 2 takes a static view of poor countries, on average, have bad institutions. While this take a more dynamic view. If I take a Markov Matrix to represent the chance of countries staying on or changing into different state of institutions (effective, mediocre, and bad), the function of going from good to bad (relatively) should be a decreasing function in the wealth of the country. This can be partially confirmed by the shape of the distribution. The band of growth rate is often narrow at the wealthy end, and VERY broad at the poor end. ( there is some outlier at the wealthy end and I will talk about these in "A New Way of calculating GDP and Its Implications for Theories"). If we clean out periods of regression resulting from institutions reversals, we might get good evidence for convergence.