Analytic Derivatives for Estimation of Discrete-Time, Linear-Quadratic, Dynamic, Optimization Models
推导了离散时间线性二次无限期动态优化模型中最优策略矩阵对参数的解析导数，解决了梯度算法中缺乏解析导数的问题，使参数估计更可靠、准确、快速。
ESTIMATION OF PARAMETERS in discrete-time, linear-quadratic, infinite-horizon, dynamic, optimization models (Hansen and Sargent, 1980, 1981) is a nonlinear estimation problem. An impediment to effectively computing parameter estimates and their covariances in these models with gradient algorithms (Kennedy and Gentle, 1980, pp. 425-512) has been the absence of expressions for computing analytic VoP, the gradient matrix of first-partial derivatives of the optimal policy matrix P with respect to parameters of the optimization problem collected in vector 0. Derivatives can always be approximated numerically, but gradient algorithms perform more reliably, accurately, and quickly when analytic derivatives are used. In this paper we derive linear systems whose solution yields analytic V P. We also express Vo P in a closed form, which, while not computationally recommended because it involves sparse, Kronecker-product, matrices, may be analytically useful. We consider a higher-order problem put into first-order, state-space, form. Present results can be used with Euler-equation solution methods after making the appropriate translation (Hansen and Sargent, 1981, pp. 134-135).