Recent empirical work by Barro and Sala-i-Martin and by Mankiw, Romer and Weil has found that economies across the world are converging towards their steady state at a `universal' speed of convergence of about 2% per year; this apparently holds for data from US states, European regions and nations elsewhere. This `steady state' is best characterized by Mankiw, Romer and Weil, who take account of both physical and human capital accumulation, with the latter roughly equal to secondary school enrolments. By taking the observed values of the rate of investment in human and physical capital to proxy their steady-state values, they determine explicitly the steady state towards which the economy is converging.

In Discussion Paper No. 691, Programme Director Daniel Cohen argues that this calculated steady state need not proxy the true steady state towards which the economy converges. He demonstrates that differentiating the production function around the economy's starting-point delivers a pattern of growth that always `looks like' the convergence towards the `pseudo steady state' that would prevail if the savings rates remained fixed indefinitely at their initial values. These authors may have discovered an indirect means of estimating the production function, but their results tell us neither the speed of convergence towards the actual steady state nor indeed whether such a steady state exists.

Cohen maintains that if enrolment in secondary school is not an exogenous parameter, perhaps reflecting a country's `taste' in education, but rather an endogenous function of its stage of development, the `true' steady state will differ from the `pseudo steady state' that prevails when all savings rates are equal. Further, even though these models exhibit decreasing returns to both human and physical capital, there may be no steady state towards which the economy is moving. If human capital can grow without bound, there is no such steady state, but controlling for the current savings rate exhibits a negative correlation between growth and initial income the `universal' coefficient found by Barro and Sala-i-Martin. This depends on the parameter of the production function alone, and it represents the speed of convergence towards the true steady state only if savings in both physical and human capital have already reached their steady- state values. Cohen reports calculations on a two-dimensional dynamic system (in physical and human capital) to test whether it is stable in other cases. His results reject the hypothesis that the system is convergent.

Tests of the `Convergence Hypothesis': A Critical Note
Daniel Cohen

Discussion Paper No. 691, August 1992 (IM)