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Growth-at-risk and macroprudential policy design
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Growth-at-risk and macroprudential policy design

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This paper explores a potential application of the empirical growth-at-risk (GaR) approach to the assessment and design of macroprudential policies. In parallel to the concept of value-at-risk, the GaR of an economy over a given horizon is a low quantile of the distribution of the (projected) GDP growth rate over the same horizon. In contrast to the standard macroeconomic focus on the expected value (and, perhaps, the variance) of aggregate output growth, looking at low quantiles of such growth implies, as in risk management, a focus on the severity of potential adverse outcomes. The recent impulse to use the concepts of GDP-at-risk (Cecchetti, 2008) and GaR (Adrian et al., 2018) is mainly empirical. It is related to the availability of econometric techniques that extend regression analysis (single dependent variable models, panel data models and vector auto-regressive models) to quantiles and their use in macroprudential applications by a growing number of authors. Conceptually, relative to other indicators of financial stability, GaR features the advantage of having an explicit and intuitive statistical interpretation and being measured in the same units as GDP growth, the most universal summary indicator of an economy’s overall performance. However, existing empirical efforts still lack a clear fit with an explicit policy design problem of the type considered for other macroeconomic policies. This paper aims to fill this gap. The analysis relies on a simple linear representation of the empirical GaR approach in combination with a linear-quadratic social welfare criterion that rewards expected GDP growth and penalises the gap between expected GDP growth and GaR. Akin to the mean-variance approach in portfolio theory, it is shown that, if the growth rate follows a normal distribution, this welfare criterion is consistent with expected-utility maximisation under preferences for GDP levels exhibiting constant absolute risk aversion. The baseline formulation – which abstracts from the time dimension by considering cumulative growth over the relevant policy horizon – focuses on the case in which macroprudential policy design is facing a trade-off: the available policy instrument can linearly increase GaR but at the expense of reducing expected GDP growth. Under the baseline specification, the optimal policy rule is linear in a variable named the “risk indicator” which represents the exogenous drivers of systemic risk. The sensitivity of the optimal policy to changes in this risk indicator is independent of the risk preferences embedded in the welfare criterion. This sensitivity depends directly on the impact of risk on the gap between expected growth and GaR, and inversely on the effectiveness of policy in reducing this gap. Optimal macroprudential policy targets a gap between expected growth and GaR which does not depend on the level of the risk indicator but on the cost-effectiveness of macroprudential policy and the risk preference parameter.
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ISSN 2467-0669
ISBN 978-92-9472-231-7
DOI 10.2849/27197
Luettelonumero DT-AC-21-002-EN-N
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ISSN 2467-0669 ISBN 978-92-9472-231-7 DOI 10.2849/27197 Luettelonumero DT-AC-21-002-EN-N
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