Chapter 13 Numerical methods for linear-quadratic models

Amman, Hans M.

doi:10.1016/s1574-0021(96)01015-5

Cited by 11 publications

(16 citation statements)

References 75 publications

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“…11 The representative cost-to-go helps to sort out the basic characteristics of the different parameter sets. The Monte-Carlo results are useful in reconciling the theoretical results in Mizrach (1991) and Amman andKendrick (1994a, 1995) with the computational findings in Tucci (1998Tucci ( , 2004 and to shed some light on the outlier problem' discussed in Amman et al (2008).…”

Section: Non-convexitiesmentioning

confidence: 69%

“…Such is the case of the analytical results that were originally derived to track down the sources of nonconvexities in small models. These results in Mizrach (1991) and Amman andKendrick (1994b, 1995) allow one to fully characterize the three components of the cost-to-go function for the simplest one-state, one-control, one unknown parameter, quadratic linear adaptive control problem with a time horizon of two periods. Therefore, in Tucci et al (2010) we have used these results as a starting point to compare the average or representative cost-to-go with different parameter sets and thus to analyze the effects of these different parameter sets on individual runs of a Monte Carlo experiment.…”

Section: Non-convexitiesmentioning

confidence: 96%

“…Research on passive and active learning stochastic control of economic models has been underway for more than thirty years dating back to the early work of Prescott (1972), MacRae (1972) and Taylor (1974) and including work by Norman (1976), Kendrick (1976Kendrick ( , 1980Kendrick ( , 1981, Easley and Kiefer (1988), Kiefer (1989), Kiefer and Nyarko (1989), Tucci (1989), Mizrach (1991), Aghion et al (1991), Amman (1996), Amman andKendrick (1995, 1997), Wieland (2000aWieland ( , 2000b, Beck and Wieland (2002), Tucci (2004), Cosimano andGapen (2005b, 2005a), Cosimano (2008), Tesfaselassie, Schaling and Eijffinger (2007) and others. What have we learned about learning from this research?…”

Section: What We Have Learnedmentioning

confidence: 99%

“…In contrast, in time periods where the cost-to-go function is apparently convex, 9 See Amman andKendrick (1997, 1999c). then efficient gradient methods can be used.…”

Section: Non-convexitiesmentioning

confidence: 99%

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Learning About Learning in Dynamic Economic Models

Kendrick

Amman

Tucci

2014

Handbook of Computational Economics Vol. 3

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This chapter of the Handbook of Computational Economics is mostly about research on active learning and is confined to discussion of learning in dynamic models in which the systems equations are linear, the criterion function is quadratic and the additive noise terms are Gaussian. Though there is much work on learning in more general systems, it is useful here to focus on models with these specifications since more general systems can be approximated in this way and since much of the early work on learning has been done with these quadratic-linear-gaussian systems.We begin with what has been learned about learning in dynamic economic models in the last few decades. Then we progress to a discussion of what we hope to learn in the future from a new project that is just getting underway. However before doing either of these it is useful to provide a short description of the mathematical framework that will be used in the chapter.Key words: Active learning, dual control, optimal experimentation, stochastic optimization, time-varying parameters, forward looking variables, numerical experiments.JEL Classification: C63, E61.Email addresses: kendrick@austin.utexas.edu (David A. Kendrick), h.m.amman@uu.nl (Hans M. Amman), tucci@unisi.it (Marco P. Tucci). 1 Corresponding author David A. Kendrick. We are indebted to a referee for many helpful comments and suggestions.

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Section: Non-convexitiesmentioning

confidence: 69%

Section: Non-convexitiesmentioning

confidence: 96%

Section: What We Have Learnedmentioning

confidence: 99%

“…In contrast, in time periods where the cost-to-go function is apparently convex, 9 See Amman andKendrick (1997, 1999c). then efficient gradient methods can be used.…”

Section: Non-convexitiesmentioning

confidence: 99%

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Learning About Learning in Dynamic Economic Models

Kendrick

Amman

Tucci

2014

Handbook of Computational Economics Vol. 3

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“…The adaptive or dual control approach, see Kendrick (1981, Amman (1996) and Tucci (2004), uses methods that draw on earlier work in the engineering literature by Tse and Bar-Shalom (1973). The optimal learning approach uses numerical approximation of the optimal decision rule, see Wieland (2000aWieland ( , 2000b, in methods that are related to earlier work by Prescott (1972), Taylor (1974) and Kiefer (1989).…”

Section: Introductionmentioning

confidence: 99%

Comparison of policy functions from the optimal learning and adaptive control frameworks

Amman

Kendrick²

2014

Comput Manag Sci

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How Active is Active Learning: Value Function Method Versus an Approximation Method

Amman

Tucci

2020

Comput Econ

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In a previous paper Amman et al. (Macroecon Dyn, 2018) compare the two dominant approaches for solving models with optimal experimentation (also called active learning), i.e. the value function and the approximation method. By using the same model and dataset as in Beck and Wieland (J Econ Dyn Control 26:1359-1377, 2002), they find that the approximation method produces solutions close to those generated by the value function approach and identify some elements of the model specifications which affect the difference between the two solutions. They conclude that differences are small when the effects of learning are limited. However the dataset used in the experiment describes a situation where the controller is dealing with a nonstationary process and there is no penalty on the control. The goal of this paper is to see if their conclusions hold in the more commonly studied case of a controller facing a stationary process and a positive penalty on the control.

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Chapter 13 Numerical methods for linear-quadratic models

Cited by 11 publications

References 75 publications

Learning About Learning in Dynamic Economic Models

Learning About Learning in Dynamic Economic Models

Comparison of policy functions from the optimal learning and adaptive control frameworks

How Active is Active Learning: Value Function Method Versus an Approximation Method

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