It has a simple stochastic model and some statistics for verifying if the real world agrees with it. You are deluding yourself if you think one can study economics without advanced statistics.
Are these study's preregistered? It seems like there is so many degrees of freedom the researcher could easily take a stroll through the garden of forking paths.
No idea. I like this study, it doesn't have as many degrees of freedom as is usual, the theory is kept to a minimum, and the data is kept to the maximum available. But you are right, there is still a lot to go wrong.
Anyway, I haven't seen many empiric studies of poverty traps. The real test is, given many of those if they will agree with the theory, not what any single one says.
so how does one account for early economics writing being light on math. Were economists Adam Smith, Hayek, and Ricardo deluded because they did not know advanced stats?
It has a simple stochastic model and some statistics for verifying if the real world agrees with it. You are deluding yourself if you think one can study economics without advanced statistics.