Essays on Fiscal Rule Design and its implications

The three chapters of this thesis examine different aspects of the design of fiscal rules and their implications on the effects of policy interventions and how policy reacts to the economy.

Chapter 1 focuses on the design of fiscal rules in DSGE models, which has been shown to matter crucially in identifying the effects of policy interventions and analyses two mechanically distinct components of fiscal policy rules: fiscal rule interactions and multimodality.

In a first exercise, a set of alternative fiscal rules is considered for the benchmark Leeper, Plante and Traum (2010) model, with the main design feature being across budget block (expenditure vs taxation) interactions. The models are compared using the Bayesian data density. The results show that the Leeper, Plante and Traum (2010) model is competitive in the set but may be improved by including across-budget component interaction with taxes ordered first. Mechanically, the budget component interactions trickle down to how policy interventions are financed, showing increased coordination across blocks. In the benchmark, a government consumption shock raises the federal government's expenditures, and along the path, taxation increases to bring the debt level back to the steady state. In the recursive block models, budget impacts can be temporarily purely expansionary in that expenditure increases and taxation is reduced. Combining both aspects, it seems to reflect a temporary but coordinated approach to raise output across the expenditure and taxation categories.

Secondly, I explore the role of multimodality in fiscal rules. Herbst and Schorfheide (2016) showed that fiscal parameters in the aforementioned model can become multimodal, leading to multimodal impulse responses. In essence, what that means is that fiscal policy may have varied impacts depending on the exact posterior parameter draw. For the Leeper, Plante and Traum (2010) model, I argue using graphs and demonstrate that the source of multimodality in the model is likely the structural design of the rules. Furthermore, building on the analysis in Herbst and Schorfheide (2016), I apply bi-modal regions to the highest posterior density regions as intervals tend to overestimate uncertainty of bi-modal distributions. The results show that the effects of consumption taxation shocks not only predict different scenarios depending on the mode but also disjointed impact scenarios. In particular, for consumption taxation shocks, the average effect of a structural shock is not a particularly likely event by itself.

In Chapter 2, 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 chapter 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 of Chapter 2, 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.

Chapter 3 applies the model developed in Chapter 2 to a forecasting exercise using the DSGE-VAR framework. The analysis confirms previous results of the literature that the DSGE-VAR framework and, by extension, DSGE models are frequently useful in aiding forecasting performance for output compared to standard models. Furthermore, I show that DSGE-VAR models can help aid forecasting performance of governmental variables like government consumption and debt quite significantly. However, there seems to be no single best methodology across all data series and forecasting settings considered, similar to the results in Gürkaynak, Kısacıkoğlu and Rossi (2014). Rather, the best-performing methodology may depend on factors like sample selection, modelling framework and potentially others.

In a novel exercise, I explore the utility of a variation of the Chapter 2 model with a Zero Lower Bound constraint for forecasting. Overall, the model performs well but is not necessarily competitive with the much simpler DSGE-VAR. However, the ZLB model does show some strength in forecasting fiscal variables.