Sankhya: The Indian Journal of Statistics

2000, Volume 62, Series B, Pt. 3, pp. 433--447

ESTIMATING TIME-VARYING PARAMETERS IN LINEAR REGRESSION MODELS USING A TWO-PART DECOMPOSITION OF THE OPTIMAL CONTROL FORMULATION

By

M.J. MANOHAR RAO, University of Bombay, Mumbai

SUMMARY. This paper discusses an econometric technique based on optimal control theory which, by employing a variation of the near-neighbourhood search problem, is seen to be suitable for the type of research that requires estimating time-varying parameters for linear regression models. The methodology is based on the characterization of the time-varying parameter (TVP) problem as an optimal control problem, with an explicit allowance for welfare loss considerations, which leads to an algorithm capable of updating the values of the time-varying parameters as well as their covariance matrices. The technique adopts an instruments-targets approach, with the initial condition and the emphasis on parameter flexibility being the instruments; and the total welfare loss and the norm of the error vector being the targets. The methodology is a blend of the flexible least squares and Kalman filter techniques. By determining all the required priors endogenously, it is seen to overcome some of the drawbacks associated with these two earlier approaches to the TVP problem. The method works on the premise that the dynamics of the system are determined by the system itself without being specified by the user in an arbitrary~fashion.

AMS (1991) subject classification. 62F03.

Key words and phrases. TVP models, near-neighbourhood search problem, parameter flexibility, tracking error, smoothing vector, welfare loss, norm function, updating algorithm, instruments-targets approach.

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