TY - JOUR
T1 - Tensor Spline Approximation in Economic Dynamics with Uncertainties
AU - Chu, Moody T.
AU - Kuo, Chun Hung
AU - Lin, Matthew M.
N1 - Funding Information:
Acknowlegments Moody T. Chu was supported in part by the National Science Foundation under Grants DMS-0732299 and DMS-1014666. Matthew M. Lin was supported in part by the National Science Council of Taiwan under Grant 99-2115-M-194-010-MY2.
PY - 2013/8
Y1 - 2013/8
N2 - Modern economic theory views the economy as a dynamical system in which rational decisions are made in the face of uncertainties. Optimizing decisions over time on market behavior such as consumption, investment, labor supply, and technology innovation is of practical importance. Interpreting all market behavior in a broad sense, the problem finds further applications in many areas other than economics. Finding the policy function inherent in the associated Euler equation has been an important but challenging task. This note proposes using composite 1-dimensional cubic splines in tensor form to process the Newton iterative scheme on approximating the unknown policy functions. This tensor spline approach has the advantages of freedom in the node collocation, simplicity in the derivative calculation, fast convergence, and high precision over the conventional projection methods. Applications to the neoclassical growth model with leisure choice are used to demonstrate the working of the idea. In particular, tensor products are employed throughout to simplify and effectuate the operations.
AB - Modern economic theory views the economy as a dynamical system in which rational decisions are made in the face of uncertainties. Optimizing decisions over time on market behavior such as consumption, investment, labor supply, and technology innovation is of practical importance. Interpreting all market behavior in a broad sense, the problem finds further applications in many areas other than economics. Finding the policy function inherent in the associated Euler equation has been an important but challenging task. This note proposes using composite 1-dimensional cubic splines in tensor form to process the Newton iterative scheme on approximating the unknown policy functions. This tensor spline approach has the advantages of freedom in the node collocation, simplicity in the derivative calculation, fast convergence, and high precision over the conventional projection methods. Applications to the neoclassical growth model with leisure choice are used to demonstrate the working of the idea. In particular, tensor products are employed throughout to simplify and effectuate the operations.
UR - http://www.scopus.com/inward/record.url?scp=84879954290&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84879954290&partnerID=8YFLogxK
U2 - 10.1007/s10614-012-9331-1
DO - 10.1007/s10614-012-9331-1
M3 - Article
AN - SCOPUS:84879954290
SN - 0927-7099
VL - 42
SP - 175
EP - 198
JO - Computational Economics
JF - Computational Economics
IS - 2
ER -