By David A. Kendrick
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Extra resources for Stochastic Control for Econometric Models
Dynam. Control, ¾(1): 133–4 (1980). 9 CHAPTER 3. 3 Inequality Constraints on State Variables The method described in the previous section is adequate if there are constraints on control variables but not on state variables since the linear search can be halted when a constraint is reached. However, when there are constraints on state variables or on combinations of state and control variables, that method is not adequate. 10 Fortunately they are embodied in a number of computer codes, including the three mentioned above.
Chapter 6 Multiplicative Uncertainty If all uncertainty in economic problems could be treated as additive uncertainty, the method of the previous chapter could be applied; however, many economic problems of interest include multiplicative uncertainty. Consider, for example, agricultural problems. The total output is represented as the yield of the crop per acre times the number of acres planted. But since the yield is a random variable, multiplicative uncertainty occurs because the acreage is a state or control variable and the yield multiplies the acreage.
In contrast, Garbade used the quadratic linear approximation method discussed in Chap. 3. 3) are made along the nominal path, as described in Sec. 2. Finally, the resulting quadratic linear control problem is solved. 6) One merit of this procedure is that the quadratic approximation in the criterion functions works like a tracking problem in the sense that the problem is solved to minimize some weighted sum of terms in Ü ÜÓ and Ù ÙÓ for all . Thus the quality of the approximation is enhanced by the fact that the criterion works to keep the optimal path for both the controls and states close to the nominal paths about which the approximation is made.
Stochastic Control for Econometric Models by David A. Kendrick