RDP 2022-09: Estimating the Effects of Monetary Policy in Australia Using Sign-restricted Structural Vector Autoregressions 1. Introduction

For a central bank to set monetary policy effectively, it is important to understand the macroeconomic effects of changes in its policy rate. However, estimating these effects is difficult. Doing so requires disentangling the effects of changes in the policy rate from the effects of other forces that drive macroeconomic fluctuations and to which monetary policy itself responds. A common way to disentangle these effects is to use a structural vector autoregression (SVAR) with zero restrictions imposed on some of the structural parameters; these zero restrictions correspond to particular assumptions about the structure of the economy. However, these restrictions are sometimes only loosely based on economic theory and may be controversial. Moreover, when applied in the Australian context, such restrictions often yield estimates that imply a so-called ‘price puzzle’, where prices rise in response to a positive monetary policy shock (e.g. Bishop and Tulip 2017).

An alternative approach is to replace the zero restrictions with an arguably weaker set of sign restrictions that are consistent with economic theory or other prior information. For example, rather than assuming that inflation does not respond within the quarter to a change in the policy rate (a zero restriction), we might assume that inflation does not increase in response to an increase in the policy rate (a sign restriction). The cost of using these weaker restrictions is that they only determine a set of possible values for the effects of monetary policy (i.e. they are ‘set identifying’ rather than ‘point identifying’). In this work, I explore the extent to which different sign restrictions are informative about the effects of changes in the cash rate.^[1] In doing so, I use a ‘prior robust’ approach to Bayesian inference (Giacomini and Kitagawa 2021). This is important, because there are well-known problems with conducting Bayesian inference in set-identified models; in particular, a component of the prior is never updated and results may be sensitive to the choice of prior (e.g. Poirier 1998; Baumeister and Hamilton 2015).

I initially consider a minimal set of sign restrictions on impulse responses to a monetary policy shock that should, in principle, be sufficient to disentangle this shock from shocks to aggregate demand and supply (Section 3).^[2] This involves restricting the cash rate and prices to move in opposite directions following a monetary policy shock, as in Uhlig (2005). When using a standard approach to conducting Bayesian inference under sign restrictions, I find that output falls with reasonably high posterior probability following a positive monetary policy shock. However, the robust approach indicates that the results obtained using the standard Bayesian approach are largely driven by the choice of prior, and the identifying restrictions appear to be uninformative about the responses of macroeconomic variables; for example, the results are consistent with both decreases and increases in output following a positive monetary policy shock. This highlights the importance of using the robust Bayesian approach to inference in this setting.

One explanation for the ambiguous output response obtained using sign restrictions on impulse responses is that combinations of expansionary supply and demand shocks may ‘masquerade’ as positive monetary policy shocks (Wolf 2020). The intuition is that, although the monetary policy shock is the only ‘pure’ shock that satisfies the sign restrictions, linear combinations of other shocks also satisfy the restrictions and have expansionary effects. Consequently, estimates obtained under these sign restrictions may imply that positive monetary policy shocks have expansionary effects even when this is a not a feature of the data-generating process. In an attempt to overcome the problem of masquerading shocks, I consider two types of additional sign restrictions.

First, I impose sign restrictions on the monetary policy reaction function, as in Arias, Caldara and Rubio-Ramírez (2019). More specifically, I impose that – all else equal – the cash rate is not increased in response to lower output and/or prices. These restrictions are consistent with the types of monetary policy rules that are typically used in macroeconomic models. When imposed on their own, these restrictions on the reaction function are more informative about the effects of monetary policy on output than the previous restrictions imposed on impulse responses; under the robust approach to inference, there is reasonably strong evidence that output falls following a positive monetary policy shock. However, there is also evidence of a price puzzle following the shock. Combining the restrictions on the reaction function with restrictions on the impulse responses yields even stronger evidence that output falls following a positive monetary policy shock. Moreover, under the combined restrictions, there is little evidence of a price puzzle at any horizon.

Second, I consider imposing additional sign restrictions based on an existing ‘proxy’ for the monetary policy shock. The proxy is taken from Beckers (2020), who applies a variant of the approach in Romer and Romer (2004) to purge the cash rate of its systematic response to macroeconomic and financial conditions. This proxy has been constructed with the purpose of measuring monetary policy shocks, so it should be positively correlated with the ‘true’ monetary policy shock. Assuming that the proxy is uncorrelated with all other structural shocks (i.e. exogenous), the proxy can be used to point identify the impulse responses to the monetary policy shock in a proxy SVAR (e.g. Gertler and Karadi 2015; Stock and Watson 2018). However, exogeneity of the proxy with respect to other shocks is a strong assumption.

Accordingly, I explore whether the proxy is still informative about the effects of monetary policy when the exogeneity assumption is relaxed and replaced with a set of less-restrictive sign restrictions. Specifically, I impose that the proxy is positively correlated with the monetary policy shock and that the contribution of the monetary policy shock to the variance of the proxy is greater than the contribution of any other shock. These restrictions maintain that the proxy primarily contains information about the monetary policy shock while allowing for the possibility that it is contaminated by other shocks. Augmenting the sign restrictions discussed above with the proxy-based sign restrictions appreciably tightens the set of estimates, which suggests that the proxy contains useful identifying information even without assuming exogeneity. Under the full set of restrictions, there is strong evidence that output and prices fall following a positive monetary policy shock at horizons beyond a year or so.

The results described above are based on the responses of variables to a ‘standard deviation’ monetary policy shock. These are useful for understanding the sign of the response to a change in the cash rate, but are less useful for understanding the magnitude of the response. For instance, understanding the effect of increasing the cash rate by 100 basis points requires knowing the effect of a monetary policy shock that results in the cash rate increasing by 100 basis points; the effects of a standard deviation shock do not provide this information. However, as discussed in Read (2022b), interval estimates obtained under the robust approach to inference may be unbounded (i.e. infinite in length) when the parameter of interest is the impulse response to a 100 basis point shock. This occurs because the identifying restrictions may admit the possibility that the cash rate does not respond on to a monetary policy shock on impact. Sign restrictions may therefore be extremely uninformative about the effects of a 100 basis point shock. Accordingly, I explore the informativeness of the sign restrictions when trying to assess the effects of a 100 basis point shock to the cash rate (Section 4).

Most of the restrictions described above are uninformative about the effects of a 100 basis point shock. However, the full set of restrictions (i.e. including the proxy-based restrictions) allows us to draw some useful inferences about the effects of changes in the cash rate. Following a 100 basis point monetary policy shock, there is fairly strong evidence that output declines by at least half of a per cent after two years, which is consistent with the peak response of output lying towards the upper end of the range of existing estimates. More specifically, I find that there is a reasonably high posterior probability assigned to output responses that exceed the peak responses in the RBA's multi-sector and MARTIN models (Gibbs, Hambur and Nodari 2018; Ballantyne et al 2019). A version of my model that includes the unemployment rate also assigns fairly high posterior probability to unemployment responses larger than the peak response in the MARTIN model.

Overall, this work suggests that some sign restrictions are not very informative about the effects of Australian monetary policy. However, imposing a rich set of restrictions allows us to draw some useful inferences. More generally, a takeaway from this work is that it is important that we continue to search for credible identifying restrictions and question the assumptions underlying existing estimates of the effects of monetary policy.

Before describing the formal framework of the paper (Section 2), I will briefly describe the relationship between this work and the existing literature. Previous work has used sign restrictions in SVAR analyses of the Australian economy, including Liu (2008), Jääskelä and Jennings (2010) and Jääskelä and Smith (2011). These papers impose restrictions on impulse responses to multiple shocks, which requires taking a stand on the nature of the non-monetary policy shocks. In contrast, the restrictions I consider relate (primarily) to the monetary policy shock, and I remain agnostic about the effects of other shocks; this approach is in the same spirit as Uhlig (2005) and Arias et al (2019). Another key difference is that I consider sign restrictions on parameters other than impulse responses. Fisher and Huh (2022) impose sign restrictions on the monetary policy reaction function in an SVAR of the Australian economy, although they do not consider combining these restrictions with other types of identifying restrictions. The aforementioned papers do not address the problem of posterior sensitivity to the choice of prior that arises when using sign restrictions.

More broadly, this paper complements previous attempts to estimate the effects of monetary policy in Australia. Recent examples include Bishop and Tulip (2017) and Beckers (2020), who apply variations of the approach in Romer and Romer (2004) to purge the cash rate of anticipated changes. Earlier work tended to impose a system of zero restrictions sufficient to achieve point identification of impulse responses in an SVAR; examples include Brischetto and Voss (1999), Suzuki (2004), Berkelmans (2005) and Lawson and Rees (2008).

Footnotes

I make no distinction between the effects of anticipated (or ‘systematic’) changes in the cash rate and unanticipated changes (i.e. monetary policy shocks), since the effects are the same given an appropriately defined counterfactual path for the cash rate. In defining the causal effect of an anticipated change in the cash rate, one needs to specify a counterfactual path for the cash rate against which the anticipated response can be compared; the difference between these paths can be represented by a monetary policy shock (or sequence of shocks). [1]

I talk about ‘identifying a monetary policy shock’ as shorthand for ‘identifying the effects of a monetary policy shock’, since the two are equivalent; the effects of the shock are identified if the shock itself is identified and vice versa. [2]