Economists’ Mathematical Manual

Sydsæter, Knut; Strøm, Arne; Berck, Peter

doi:10.1007/978-3-662-03995-3

Cited by 20 publications

(19 citation statements)

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“…2). Since there is a unique solution, the local analysis implies that u * is also the global maximum (Sydsaeter et al, 2008) C-4 for the standard deviations around the mean traits, and the S.I. for the Mathematica code of the simulations).…”

Section: Uninvadable and Convergence Stable Strategiesmentioning

confidence: 99%

Life history and deleterious mutation rate coevolution

Avila

Lehmann

2022

Preprint

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The cost of germline maintenance and repair gives rise to a trade-off between lowering the deleterious mutation rate and investing into life-history functions. Life-history and the mutation rate therefore coevolve, but this joint evolutionary process is not well understood. Here, we develop a mathematical model to analyse the long-term evolution of traits affecting life-history and the deleterious mutation rate. First, we show that under certain biologically feasible conditions, the evolutionary stable life-history and mutation rate can be characterised using the basic reproductive number of the least-loaded class. This is the expected lifetime production of offspring without deleterious mutations born to individuals with no deleterious mutations. Second, we analyse two specific biological scenarios: (i) coevolution between reproductive effort and mutation rate and (ii) coevolution between age-at-maturity and mutation rate. These two scenarios suggest two broad results. First, the trade-off between lowering mutation rate vs investing into life-history functions depends strongly on environmental conditions and baseline mutation rate. Second, the trade-offs between different life-history functions can be strongly affected by mutation rate coevolution and higher baseline mutation rates select for faster life histories: (i) higher investment into fecundity at the expense of survival and (ii) earlier age of maturation at smaller sizes.

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Section: Uninvadable and Convergence Stable Strategiesmentioning

confidence: 99%

Life history and deleterious mutation rate coevolution

Avila

Lehmann

2022

Preprint

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“…For a general statement of this theorem, see, e.g.,Sydsaeter, Strøm and Berck (1999), p.28. For a general statement of this theorem, see, e.g.,Sydsaeter, Strøm and Berck (1999), p.28.…”

mentioning

confidence: 99%

Dynamic General Equilibrium Modeling

Heer

Maußner

2009

130

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PrefaceGiven the huge number of responses and comments to the first edition of our book, we felt obliged to come up with the second edition within such a short period of time. Stochastic Dynamic General Equilibrium modeling is certainly among the most rapidly changing fields in economics and we try to cover the most recent developments.In this edition, we reorganize and extend the presentation of solution methods in the former Chapters 1 through 4 and add major new material. Different from the first edition Chapter 1 serves as introduction, but does not present any solution techniques. It covers deterministic and stochastic representative agent models, elaborates on their calibration and evaluation, and ends with a characterization of the solution methods presented in Chapters 2 through 6. Chapter 2 now includes a section on the secondorder approximation of policy functions, the extended deterministic path algorithm in Chapter 3 is applied to an open economy model with a unit root, and we consider various techniques to speed up value function iteration in Chapter 4. In the second part of the book on heterogenous agent economies we split the former Chapter 7 on overlapping generations (OLG) models. The solution of OLG models with perfect foresight is now covered in Chapter 9, where we also consider different ways to compute the transitional dynamics of these models. A new application deals with a model of the demographic transition. OLG models with aggregate and individual uncertainty are solved in Chapter 10.Computer Code. As one of our main ambition, we keep the essential feature of this book to make all our programs that we used for the computations available on our website www.wiwi.uni-VIII Preface augsburg.de/vwl/maussner/. Therefore, the reader does not need to download any program code from other websites in order to replicate any of our findings, for example, on the statistics and characteristics of business cycle models or the dynamics of the distribution function in heterogeneous-agent economies. In the email correspondence with our readers this very feature of our book has often been pointed out as a crucial one by the graduate students in order to get started with his or her own research. If you are endowed with the programs for all the basic models of the business cycle, growth, and the distribution that we cover in this book, it is easy to start modifying them and work on your own projects.Numerical methods are introduced one after the other and every new method is illustrated with the help of an example. This book and its accompanying web page is particularly designed for those students with little or no prior computing experience. We start from the scratch and deliberately concentrate on models that are formulated in discrete time so that we are able to bypass the technical complexities that arise when stochastic elements are introduced into continuous time optimizing models. The computer code is available either in Gauss or Fortran or both. The former computer language is almost identical to Matla...

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“…By Schur's theorem (e.g. Sydsaeter et al, 1999), this is the case if the following set of necessary and sufficient conditions hold:…”

Section: A1 Log-linearized Equilibrium Conditionsmentioning

confidence: 98%