Estimation and Inference in a Non-Linear State Space Model: Durable Consumption

Several ways of modelling non-linear state space models have been suggested. The extended Kalman Filter is a tractable way of doing so. One application is to consumer durable demand. Models explaining this flow are normally conditioned on the stock. For the UK, measures of the stock are unavailable. However, it might be estimated from a non-linear state space model. The model is estimated using a linear approximation of the first order conditions for the household's consumption problem and the stock accumulation identity. The results suggest there is very little time variation in depreciation rates over our sample, and that households are close to risk neutrality. Diagnostics suggest further refinement of the model is called for.