On Parameter Estimation in Unobserved Components Models subject to Linear Inequality Constraints
This work addresses parameter estimation challenges in econometric models with constraints, offering incremental improvements in computational efficiency for researchers in time-series analysis.
The authors tackled the problem of approximating nonstandard densities in unobserved components models with linear inequality constraints by proposing a quadratic programming-based method using a multivariate Gaussian density, achieving comparable trend estimates to existing methods with improved sample efficiency.
We propose a new \textit{quadratic programming-based} method of approximating a nonstandard density using a multivariate Gaussian density. Such nonstandard densities usually arise while developing posterior samplers for unobserved components models involving inequality constraints on the parameters. For instance, Chan et al. (2016) provided a new model of trend inflation with linear inequality constraints on the stochastic trend. We implemented the proposed quadratic programming-based method for this model and compared it to the existing approximation. We observed that the proposed method works as well as the existing approximation in terms of the final trend estimates while achieving gains in terms of sample efficiency.