Summary.
We formulate an optimal estimation process in a stochastic growth model with an unknown true probability model. We consider a general reduced model of capital accumulation with an infinite horizon and introduce a learning process in the stochastic dynamic programming. When the only available information is a sample realization generated by a stationary and ergodic stochastic process, we prove that the optimal estimation process based on likelihood-increasing behavior converges to the true probability measure and the likelihood-increasing estimator defines a transition function on the sample space.
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Received: 24 January 2004, Revised: 18 February 2005,
JEL Classification Numbers:
C13, C44, C61, O41.
An earlier version of this paper was presented at the annual Meeting of the Japanese Economic Association at the University of Tokyo, at the annual Conference of the Japan Society for Industrial and Applied Mathematics at Keio University, and at the 7th Czech-Japan Seminar on Data Analysis and Decision Making under Uncertainty in Awaji Island. I have benefited from useful comments from Hidetoshi Komiya, Andrew McLennan, Toru Maruyama, Nancy Stokey, Shinichi Suda, Shin-Ichi Takekuma, Akira Yamazaki, and an anonymous referee. I would also like to thank Fumihiro Kaneko for invaluable technical discussions. This research was partly supported by Grant-in-Aid for Scientific Research (No. 14730021) from the Japan Society for the Promotion of Science.
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Sagara, N. Stochastic growth with a likelihood-increasing estimation process. Economic Theory 28, 51–72 (2006). https://doi.org/10.1007/s00199-005-0619-4
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DOI: https://doi.org/10.1007/s00199-005-0619-4