Estimations of US debt dynamics: Growth cum debt and the savings glut in Kouri’s model

We derive the central differential equation of the neoclassical growth model for the case of a CES (constant elasticity of substitution) production function with perfect capital movement in terms of the debt/GDP ratio and estimate it in several ways for the United States and in a later step the whole model. Debt data are derived from the accumulation of differences between investment and savings. The result is that at least since 1960 the US debt/GDP ratio follows the pattern of a stable differential equation, which will lead to a long-run debtor position. The debt/GDP ratio will approach a value between 50% and 60% (depending on the specification used) unless a structural break increases the world interest rates or, similarly, US spreads reduce the US demand for foreign debt. A value of 50% will be achieved around 2040. We also find short-run deviations from this long-run path, which are characterized by non-sustainable explosive debt growth. These phases are characterized by high interest rates and followed by devaluations of the dollar. Our simple method allows detecting such phases early on by way of testing a stability condition rather than working with arbitrary threshold levels. The estimation of the whole model yields an elasticity of substitution for capital and labour of .155 with autocorrelation correction (and 1/3 without), a growth rate of labour-augmenting technical change of 1.65% (1.5%) and a corresponding initial level of labour productivity as of 1959 of about 350 (320). As a complement to the growth model we estimate the Kouri model using time-varying coefficients obtaining a forecast of the debt/GDP ratio of about 57% for 2050 as for the growth model. As the rest of the world is catching up with the USA in terms of wealth this is a long-run version of Bernanke's savings glut idea.