There is a large debate surrounding the effects of fiscal policy and the size of fiscal policy multipliers. Estimates of ﬁscal policy multipliers differ widely in the literature (Ramey 2011). Why are fiscal multipliers changing over time and what determines their magnitude? Such questions are even more important now that governments worldwide are investing in large fiscal support programmes to mitigate the effects of the recent COVID crisis (Soyres et al. 2022, Deb et al. 2022, Kalemli-Ozcan 2022).

A possible explanation for the wide range of estimates found in the literature is that the effects of ﬁscal shocks and the government spending multipliers vary over time. On the one hand, Auerbach and Gorodnichenko (2012), Caggiano et al. (2015), and Fazzari et al. (2015, 2021) ﬁnd that ﬁscal multipliers are higher than normal during recessions; on the other hand, Owyang et al. (2013) and Ramey and Zubairy (2018) ﬁnd that the amount of slack in the economy does not substantially affect their size, while the presence of a zero lower bound might. These studies, however, rely on threshold models, which imply a very speciﬁc form of time variation that depends on a state variable (e.g. the unemployment rate in Ramey and Zubairy 2018, or capacity utilisation in Fazzari et al. 2015). A similar result, emphasising that the effects of ﬁscal policy may depend on the interaction between ﬁscal and monetary policy has been suggested by Cloyne et al. (2021) and Rossi and Zubairy (2011). More recently, Barnichon et al. (2021) ﬁnd that the multiplier depends on the sign of the shock, i.e. whether the shock is contractionary or expansionary.

In a recent paper (Inoue et al. 2022), we shed new light on the determinants of fiscal multipliers by using a novel time-varying parameter local projection with instrumental variables (TVP-LP-IV) methodology. Unlike the existing literature, where local projection estimates of fiscal multipliers only vary depending on the value of an observable state variable (as in Ramey and Zubairy 2018 or Auerbach and Gorodnichenko 2012), we avoid imposing restrictive assumptions on the type of instability in the data. Using our methodology, we let the data ‘speak’ and uncover periods in which multipliers are exceptionally high or low.

We find that the existing literature on the size of ﬁscal multipliers and the effects of ﬁscal policy shocks has overlooked potentially important instabilities.

Figure 1 plots our estimates of the fiscal multiplier over time (dashed green line) together with the estimates based on a state-dependent threshold model (continuous red line) where the multiplier depends on whether there is slack in economy or not (that is, whether unemployment is above a certain threshold). Times in which there is slack in the economy are highlighted by shaded areas. Clearly, the state dependent model cannot adequately explain the evolution of the multiplier over time.

Similarly, Figure 2 plots our estimates of the fiscal multiplier over time (dashed green line) together with the estimates based on a state-dependent threshold model (continuous red line) where the multiplier depends on whether the economy is at the zero lower bound. Times in which the economy is at the zero lower bound are highlighted by shaded areas. The zero lower bound-state dependent model cannot fully explain the evolution of the multiplier over time as well.

**Figure 1** TVP-LP-IV estimates of the fiscal multiplier (4-year integral) together with estimates of a state-dependent model based on unemployment as the state variable

**Figure 2** TVP-LP-IV estimates of the fiscal multiplier (4-year integral) together with estimates of a state-dependent model based on the zero lower bound as the state variable

Our estimated responses of government spending and output to ﬁscal policy shocks as well as the cumulative spending multipliers are heterogeneous across time: their evolution over time cannot be adequately characterised by traditional state variables, such as unemployment or whether the economy is at the zero lower bound, thus featuring richer information than state-dependent models.

We also ﬁnd that the sign of the ﬁscal policy shock does not entirely explain the ﬂuctuations of the multipliers either; the size of public debt, instead, emerges as an important explanatory variable. In fact, by comparing the time evolution of the fiscal multiplier with that of several macroeconomic variables, the correlation is the highest with public debt. Once our TVP-LP model has suggested the driving variable, we can then fit a state-dependent model to compare our results with those in the literature. Figure 3 shows our estimates of the fiscal multiplier over time (dashed green line) together with the estimates based on a state-dependent threshold model (continuous red line) where the multiplier depends on the value of public debt (that is, whether the debt is above a certain threshold). Clearly, the state dependent model that uses public debt as the state variable describes the evolution of the multiplier over time better than the state variables used in the existing literature.

**Figure 3** TVP-LP-IV estimates of the fiscal multiplier (4-year integral) together with estimates of a state-dependent model based on public debt as the state variable

These results also highlight the potential advantages of using the TVP-LP-IV estimator in guiding researchers in identifying potentially important instabilities and their determinants, and, at the same time, contribute to the methodological literature on local projections (Jordà 2005, Montiel Olea and Plagborg-Møller 2021, among others) by extending them to unstable environments.

## References

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Barnichon, R, D Debortoli and C Matthes (2021), “Understanding the size of the government spending multiplier: it’s in the sign”, *Review of Economic Studies*, forthcoming.

Caggiano, G, E Castelnuovo, V Colombo and G Nodari (2015), “Estimating ﬁscal multipliers: EWS from a non-linear world”, *The Economic Journal* 125(584): 746–776.

Cloyne, J S, Ò Jordà and A M Taylor (2021), “Decomposing the fiscal multiplier”.

de Soyres, F, A M Santacreu and H Young (2022), “Demand–supply imbalance during the Covid-19 pandemic: The role of fiscal policy”, VoxEU.org, 1 March.

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