Fiscal policy and the business cycle: An argument for non-linear policy rules

In this paper, I explore how fiscal policy decisions relate to the business cycle and, building on that, how the effects of policy interventions may vary depending on when policy is conducted in the business cycle. To assess this, I estimate a small to medium-sized DSGE model with expressive non-linear fiscal and monetary rules using a higher-order approximation. The estimation procedure employed in this paper combines several existing approaches developed by Herbst and Schorfheide (2016), Jasra et al. (2010), Buchholz, Chopin and Jacob (2021) and Amisano and Tristani (2010) to trade off computation time and inference quality. The model is estimated using Sequential Monte Carlo techniques to estimate the posterior parameter distribution and particle filter techniques to estimate the likelihood. Together, the estimation procedure reduces the estimation from weeks to days by up to 94%, depending on the comparison basis. To assess the behaviour of the effects of fiscal policy interventions, I sample impulse responses conducted along the historical data. The results present time-varying policy rules in which the effects of fiscal shocks go through deep cycles depending on the initial conditions of the economy. Among the set of fiscal instruments, government consumption goes through the most persistent cycles in its effectiveness in stimulating output. In particular, the effects of government consumption stimulus are estimated to be more effective during the financial crisis and, later, the Covid crisis, while being less effective in periods of above steady state output like the early 2000s. Relating the effects of specific stimulating shocks to the initial conditions using regression techniques, I show that fiscal policy is more effective at stimulating output if the interest rate and debt are low. Furthermore, the effects of government consumption are estimated to be increasing in output while tax cuts are decreasing. As a last contribution, I explore how the behaviour of the central bank and government varies depending on the business cycle by analysing sampled policy rule gradients constructed on historical data. For the central bank, the results show that in phases of high output growth, the central bank puts more emphasis on controlling inflation and less on output. As the economy shifts into crisis, the central bank reduces its focus on inflation and shifts towards bringing output growth back to target. For the fiscal side, the behaviour is heavily governed by the current debt level, and, for example, during the high debt periods of the 1990s, labour taxation became increasingly responsive to debt to stabilize the budget.