Impact of fiscal policy delays on the system dynamics of IS-LM model: A mathematical model approach

Delays in fiscal policy reside either in taxation or in government expenditure. The former delay refers to the time lag between when taxes are accrued and when they are paid. And the latter delay refers to the amount of time that passes between making a purchasing decision and making a purchase. This work combines both these delays into a business cycle model, namely the IS -LM model. Firstly, two mathematical models, Model A and Model B, based on delayed differential equations, are constructed with non-linear and linear functional forms respectively, for investment and liquidity preference. After that, a steady-state solution is computed, which is unique in both instances. Linear stability analysis is performed around the equilibrium point in both the models. Also, when the delay reaches a critical point, Hopf bifurcation occurs. The switch in the stability of equilibrium point for both the models is also discussed. Lastly, numerical simulations are performed to validate our analysis. In both the models, adding a correct mix of time delays aids in maintaining or regaining the stability of equilibria. Also, the effect of relationship between the parameters like tax rate and share of delayed tax revenue is closely scrutinized to assess the stability of the system, which is not cogitated before.