Leapfrogging, Growth Reversals and Welfare

We show that leapfrogging and growth reversals entail sizeable welfare gains and losses, respectively, in an AK economy that cannot credibly commit to investment when borrowing from international financial markets. Small no-commitment delays originate a trade-off that has an ambiguous effect on welfare: they reduce the long-run consumption growth rate but increase the initial level of consumption that is optimally chosen. Essentially, the larger the delay, the tighter the borrowing constraint and the weaker the incentives to accumulate capital, so that smaller growth and larger initial consumption follow. We show under logarithmic utility and small delays that the short-run effect dominates the long-run effect and that welfare improves, provided that the economy has historically been growing fast enough, and numerical examples suggest that this benchmark result extends to CRRA utility. When relative risk aversion is larger than one, it follows that there exists a positive welfare-maximizing delay associated with slower growth relative to the no-delay case. We then apply our results to show that leapfrogging in consumption level typically imply large welfare gains. In contrast, growth reversals occur for large delays and lead to significant welfare losses. Finally, financial integration, as measured by the credit multiplier given the no-commitment delay, is welfare-improving only for economies that have historically been growing fast enough.