Abstract: Based on Barro's endogenous growth theory and expanded Cobb-Douglas production function， this paper constructs the time-varying parameter state space model， calculates the dynamically optimal fiscal social security expenditure of Jilin province from 1998 to 2018 by using Kalman filter iteration algorithm， and discusses how to achieve the optimal scale. The results show that the optimal ratio of fiscal social security expenditure to total financial expenditure in Jilin province presents a nonlinear dynamic characteristic， fluctuating between 18.23% and 18.57%. The dynamic change of optimal scale of fiscal social security expenditure shows a nonlinear increasing trend year by year， from 3.466 billion yuan to 69.707 billion yuan. The actual scale of fiscal social security expenditure only exceeded the optimal scale in 2002-2006， but did not reach the optimal scale in other years. There are rigid constraints on fiscal social security expenditure， and the realization of its optimal scale should be a dynamic and gradual process. Therefore， a dynamic optimal orientation model is constructed， and a feasible scheme is proposed for dynamically adjusting the growth of fiscal social security expenditure to the optimal scale during the 14th Five-Year Plan period (2021-2025) in Jilin province.

Key words: fiscal social security expenditure;dynamic optimal scale;time-varying parameter state space model, Kalman filter