TY  - GEN
AB  - This paper establishes conditions for the asymptotic stability of balanced growth
paths in dynamic economic models as typical cases of homogeneous dynamical systems.
Results for common two-dimensional deterministic and stochastic models are
presented and further applications are discussed.
According to Solow & Samuelson (1953) balanced growth paths for deterministic
economies are induced by so-called Perron-Frobenius solutions defined by an eigenvalue
λ > 0 (the growth factor) and by an eigenvector $\bar{x}$ , a fixed point of the system
in intensive form. Contraction Lemma A.1 states for continuous deterministic systems
that convergence to a balanced path occurs whenever the product λ · M($\bar{x}$)
of the eigenvalue λ multiplied with the contractivity 0 < M($\bar{x}$) < 1 of the stable
eigenvector $\bar{x}$  of the intensive form is less than one. For λ·M($\bar{x}$) > 1 all unbalanced
orbits in the neighborhood of the balanced path diverge in spite of convergence
in intensive form. This confirms that convergence to a stable eigenvector of the
intensive form is only a necessary condition for convergence in state space.
In the stochastic case, the condition for asymptotic stability of balanced growth
paths (Theorem B.2) uses results from a stochastic analogue of the Perron-Frobenius
Theorem on eigenvalues and eigenvectors. Convergence (divergence) occurs if the
expectation of the product λ(ω) · M(ω) is less than (greater than) one, i.e. if the
product is mean contractive. This is equivalent to the condition that the sum of
the expectations of the logarithmic values of the stochastic growth rate and of the
contractivity factor of the intensive form are less than (greater than) zero.
DA  - 2020
KW  - balanced growth
KW  - stability
KW  - stochastic balanced growth
KW  - random fixed points
KW  - Perron-Frobenius solution
LA  - eng
PY  - 2020
SN  - 0931-6558
SP  - 39-
TI  - Stable Balanced Expansion in Homogeneous Dynamic Models
UR  - https://nbn-resolving.org/urn:nbn:de:0070-pub-29433443
Y2  - 2024-11-22T10:47:07
ER  -