By Jerome Adda, Russell W. Cooper
This ebook is a good, concise textual content for college kids and researchers that mixes the instruments of dynamic programming with numerical recommendations and simulation-based econometric tools. Doing so, it bridges the conventional hole among theoretical and empirical learn and gives an built-in framework for learning utilized difficulties in macroeconomics and microeconomics. partly I the authors first evaluation the formal conception of dynamic optimization; they then current the numerical instruments and econometric options essential to evaluation the theoretical versions. In language obtainable to a reader with a restricted history in econometrics, they clarify lots of the tools utilized in utilized dynamic examine this present day, from the estimation of likelihood in a coin turn to a classy nonlinear stochastic structural version. those econometric options give you the ultimate hyperlink among the dynamic programming challenge and knowledge. half II is dedicated to the applying of dynamic programming to express parts of utilized economics, together with the learn of commercial cycles, intake, and funding habit. In each one example the authors current the explicit optimization challenge as a dynamic programming challenge, signify the optimum coverage services, estimate the parameters, and use versions for coverage evaluate. the unique contribution of Dynamic Economics: Quantitative tools and functions lies within the built-in method of the empirical software of dynamic optimization programming versions. This integration exhibits that empirical functions truly supplement the underlying concept of optimization, whereas dynamic programming difficulties offer wanted constitution for estimation and coverage review.
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Example text
8 in Stokey and Lucas (1989). The proof of the theorem relies on showing that strict concavity is preserved by TðVÞ: namely, if VðsÞ is strictly concave, then so is TðVðsÞÞ. Given that sðs; cÞ is concave, then we can let our initial guess of the value function be the solution to the one-period problem: V0 ðsÞ 1 max sðs; s 0 Þ: s 0 A GðsÞ V0 ðsÞ is strictly concave. 12) will be strictly concave. As noted earlier, our interest is in the policy function. Note that by this theorem, there is a stationary policy function that depends only on the state vector.
Hence techniques must be used to approximate the solutions of these problems. We present a variety of techniques in this chapter that are subsequently used in the macroeconomic applications studied in part II of this book. The presentation starts by solving a stochastic cake-eating problem using a procedure called value function iteration. The same example is then used to illustrate alternative methods that operate on the policy function rather than the value function. Finally, a version of this problem is studied to illustrate the solution to dynamic discrete choice problems.
The function uðcÞ is again assumed to be strictly increasing 7. To be careful, here we are adding shocks that take values in a finite and thus countable set. See the discussion in Bertsekas (1976, sec. 1) for an introduction to the complexities of the problem with more general statements of uncertainty. Theory of Dynamic Programming 21 and strictly concave. Otherwise, the problem is the original cakeeating problem with an initial cake of size W. In problems with stochastic elements, it is critical to be precise about the timing of events.