Policy Formulation for an Optimal Level of Savings in a Dynamic Setting
Authors:   Directorate General of Revenue Analysis, Federal Board of Revenue, Islamabad, Pakistan, Ahmed Muhammad Ashfaq , Nawaz Nasreen ,   Directorate General of Revenue Analysis, Federal Board of Revenue, Islamabad, Pakistan
Published: April 2024

Objective: Previous literature on optimal savings relies on specific utility and production technology functional forms which might not be able to produce robust results as different utility / production functions may lead to dramatically different or opposing results. This paper derives an optimal savings policy based on parameters (such as slopes of demand and supply curves) which can be empirically estimated and provides a unique and robust result irrespective of shape and form of individual utilities / production functions. Furthermore, existing literature does not consider welfare loss when savings market is adjusting to final equilibrium after a shock while deriving an optimal savings policy. In addition to that, number of savers (all public and private saving entities, including households, firms, etc.) and saving rate are vital parameters for savings in an economy, and while deriving an optimal savings policy, it is necessary to take into consideration these parameters to ensure that quantum of savings due to interest rate movement gets adjusted in target time duration, without which there may be additional efficiency loss than that envisioned while deriving an optimal savings policy for an economy. Methods: This research project designs a dynamical model for savings market and extends that to a three-dimensional savings system in an economy by taking into consideration number of savers, saving rate, and interest rate; and based on that derives an optimal comprehensive savings policy while accounting for efficiency losses when savings market, saving rate, and number of savers are adjusting to final equilibrium, in addition to the welfare loss on account of equilibrium shift. Results: Without consideration of welfare loss / gain while savings market is adjusting after implementation of a savings policy, welfare picture remains incomplete, and the optimal savings policy based on partial welfare cannot be considered as optimal in true sense. Traditionally, welfare of only producer and consumer is taken into consideration without accounting for welfare of production factors. An expression of efficiency loss / gain as a result of savings policy based on welfare including those of production factors has been presented and optimal savings policies have been derived by minimizing efficiency losses and presented as a final result in the form of mathematical expressions. This paper demonstrates that both supply and demand shocks operate through a common channel, i.e., inventory of funds in savings market as both kinds of shock affect inventory of funds and hence can be categorized just as an inventory shock. Conclusion: For optimal welfare gains, practitioners / policy makers must estimate theoretically derived optimal savings policies based on the dynamic model developed in this paper and presented in the form of mathematical expressions from real world relevant data for implementation.