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.
JEL code: F21, F43, O 19, 40, 51.
Keywords: Growth, long run capital movements, productivity, time-varying coefficients, non-linear GMM growth model estimation, asset markets.
UNU-MERIT Working Papers ISSN 1871-9872