Convergence

Abstract

We clarify the concept of convergence. This concept has been defined in many ways in growth theory and empirics. Recently, a rise in the poorer country income as a proportion of the richer country's income has been called relative convergence, a decrease in the poorer country's income short fall from the richer country's income absolute convergence, and equality of the initially poorer country's income to the richer country's income that depends on the initial conditions full convergence We prove for continuous income changes the following: Relative convergence is a necessary but not a sufficient condition for absolute convergence and relative divergence is a sufficient but not a necessary condition for absolute divergence. We emphasize that faster growth is not sufficient for income gap reduction-it may take even 800/900 years of faster growth before income gaps start decreasing. Neo-classical growth theory has not used the phrases "relative convergence" or "full convergence" in describing convergence. Some seminal papers have used the phrase "absolute convergence" but given it the meaning that all countries' incomes eventually become equal irrespective of initial conditions. We relate convergence concepts as defined above to the meaning other authors have given to "convergence" in growth theory since 1956.

Keywords: O40, O41, O47 Relative convergence, Absolute convergence, Full convergence, Growth theory

JEL Classification: O40, O41, O47