By Jerome Adda, Russell W. Cooper
This e-book is an efficient, concise textual content for college kids and researchers that mixes the instruments of dynamic programming with numerical thoughts and simulation-based econometric equipment. Doing so, it bridges the normal hole among theoretical and empirical learn and provides an built-in framework for learning utilized difficulties in macroeconomics and microeconomics. partly I the authors first overview the formal concept of dynamic optimization; they then current the numerical instruments and econometric innovations essential to evaluation the theoretical types. In language obtainable to a reader with a restricted historical past in econometrics, they clarify lots of the tools utilized in utilized dynamic learn this day, from the estimation of likelihood in a coin turn to a sophisticated nonlinear stochastic structural version. those econometric thoughts give you the ultimate hyperlink among the dynamic programming challenge and knowledge. half II is dedicated to the applying of dynamic programming to precise parts of utilized economics, together with the examine of industrial cycles, intake, and funding habit. In each one example the authors current the categorical optimization challenge as a dynamic programming challenge, represent the optimum coverage capabilities, estimate the parameters, and use types for coverage evaluate. the unique contribution of Dynamic Economics: Quantitative equipment and purposes lies within the built-in method of the empirical program of dynamic optimization programming types. This integration exhibits that empirical functions truly supplement the underlying thought of optimization, whereas dynamic programming difficulties offer wanted constitution for estimation and coverage review.
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Extra resources for Dynamic Economics: Quantitative Methods and Applications
Does the size of r matter in this discussion? Explain. 7 For the cake-eating problem, the natural source of uncertainty has to do with the agent’s appetite. In other settings we will focus on other sources of uncertainty having to do with the productivity of labor or the endowments of households. To allow for variations of appetite, suppose that utility over consumption is given by euðcÞ; where e is a random variable whose properties we will describe below. The function uðcÞ is again assumed to be strictly increasing 7.
Hence the method requires that Fð^ cðX; CÞÞ is zero at some particular points Xi and not over the whole range ½XL ; XH . The method is more efﬁcient if these points are chosen to be the zeros of the base elements pi ðXÞ, here Xi ¼ cosðp=2iÞ. This method is referred to as an orthogonal collocation method. 5 Basis functions, ﬁnite element method the solution to a system of nonlinear equations: Fð^ cðXi ; CÞÞ ¼ 0; i ¼ 1; . . ; n: This method is good at approximating policy functions that are relatively smooth.
Whether the cake is of this size because we initially have a large cake and can eat a lot of it or a small cake and are frugal eaters is not relevant. All that matters is that we have a cake of a given size. This property partly reﬂects the fact that the preferences of the agent do not depend on past consumption. If this were the case, we could amend the problem to allow this possibility. 7). For now we assume that a solution exists so that we can explore its properties. 7) can be written as u 0 ðcÞ ¼ bV 0 ðW 0 Þ: 6.