Hisashi Tanizaki

Overview

Hisashi Tanizaki (Kobe-Gakuin University) extended the Kalman filter to accommodate binary (qualitative) dependent variables by replacing the continuous observation equation with a binary choice model whose CDF is linearized via a first-order Taylor expansion. The resulting pseudo-linear measurement equation allows the standard Kalman filter recursions to proceed with iteration at each time step.

Key Contributions

• Extended the standard Kalman filter to handle binary $y_t$ via CDF linearization around the current filtered state estimate (Tanizaki 1993).
• Developed a distribution-free EM-like procedure for estimating observation noise variance $R$ and state transition matrix $\Phi$ without assuming a parametric distribution for the discrete latent state.
• Applied to money excess demand estimation (Jan 1959–May 1989, $n=364$), showing strong dominance of time-varying models over fixed-parameter probit/logit ($\log L \approx -222$–$-234$ vs. $-248$; $\rho \approx 0.33$–$0.48$ vs. $0.11$).

Related

• State-Space Representation
• Random Coefficient Model
• Tanizaki (1993) Kalman Filter Model with Qualitative Dependent Variables