Analysis and Control of Dynamic Economic Systems

a₁ absolute value analysis applied assumed autocovariance function autocovariance matrix b₁ calculations canonical variables certainty equivalence Chapter characteristic roots characteristic vectors complex roots compute consumption function control problem control variables covariance matrix cross-spectral density cycles defined denoted density matrix derived deviations diagonal dynamic economics dynamic programming dynamic properties econometric model elements endogenous equal estimate evaluate exogenous variables expected welfare loss expenditures feedback control equation first-order frequency G₁ given identity income Kalman filter lagged Lagrange multipliers linear combination linear stochastic difference linear systems loss function macroeconomic mean minimize multiperiod multiplier nonlinear nonstochastic observations obtained optimal control equations optimal policy parameters path periodic components pseudospectrum quadratic quadratic function random disturbances random variable residuals result s₁ solution solving specified spectral density function stationary stochastic difference equations stochastic dynamic stochastic system target variables tion u₁ variance weighted sum welfare function x₁ y₁