Working papers

Optimal quantitative easing and tightening

Published:

This paper studies optimal use of the central bank balance sheet in a simple New Keynesian model with portfolio frictions. Optimal quantitative easing (QE) entails large and rapid purchases of government debt when the short-term policy rate hits the lower bound. Optimal balance sheet reduction (quantitative tightening, QT) is more gradual. QT strategies similar to those pursued by the Federal Reserve and Bank of England can achieve similar welfare to optimal policy as long as the pace of QT is appropriately calibrated.

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Global R*

Published:

(with Ambrogio Cesa-Bianchi and Rana Sajedi - October 2023 update)

We use a structural overlapping-generations model to quantify the effects of five exogenous forces that drive the global trend equilibrium real interest rate, Global R*. We find that Global R* rises from the mid-1950s to the mid-1970s, declining steadily thereafter. The decline is driven predominantly by slowing productivity growth and increasing longevity.

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Structural change, global R* and the missing-investment puzzle

Published:

(with Andrew Bailey, Ambrogio Cesa-Bianchi, Marco Garofalo, Nick McLaren, Sophie Piton and Rana Sajedi)

This paper focuses on two key trends: the secular decline in risk-free interest rates; and the recorded weakness in investment, despite an increasing wedge between the return on capital and the risk-free rate. The first trend suggests a fall in the long-run global equilibrium interest rate, Global R* and analysis using a structural model finds that rising longevity and falling productivity growth were the main drivers of this decline. We use industry-level data for the United Kingdom to investigate the second trend and find a strong role for intangible capital.

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Flexible inflation targeting with active fiscal policy

Published:

This paper studies optimal time-consistent monetary policy in a simple New Keynesian model with long-term nominal government debt. Fiscal policy is ‘active’, so that stabilisation of the government debt stock is a binding constraint on monetary policy. Away from the lower bound on the monetary policy rate, optimal monetary policy cannot fully offset the effects of shocks to the natural rate of interest, reducing welfare. At the lower bound, active fiscal policy mitigates the effects of recessionary shocks by inducing a rise in inflation expectations, increasing welfare. If debt duration is long enough, improved performance at the lower bound may outweigh higher welfare losses in normal times.

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Optimal policy with occasionally binding constraints: piecewise linear solution methods

Published:

(with Matt Waldron)

This paper develops a piecewise linear toolkit for optimal policy analysis of linear rational expectations models, subject to occasionally binding constraints on (multiple) policy instruments and other variables. The flexibility and applicability of the toolkit to very large models is demonstrated in a variety of applications.

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Monetary financing with interest-bearing money

Published:

(with Ryland Thomas)

Recent results suggesting that monetary financing is more expansionary than bond financing in standard New Keynesian models rely on a duality between policy rules for the rate of money growth and the short-term bond rate, rather than a special role for money. We incorporate two features into a simple sticky-price model to generalize these results. First, that money may earn a strictly positive rate of return, allowing money-financed transfers to be used as a policy instrument at the effective lower bound, without giving up the ability to use the short-term bond rate to stabilize the economy in normal times. Second, a simple financial friction generates a wealth effect on household spending from government liabilities. Though temporary money-financed transfers to households can stimulate spending and inflation when the short-term bond rate is constrained by a lower bound, similar effects could be achieved by bond-financed tax cuts.

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Concerted efforts? Monetary policy and macro-prudential tools

Published:

(with Andrea Ferrero and Benjamin Nelson)

We study the coordination of monetary and macro-prudential policies in a model with nominal rigidities, housing, incomplete risk-sharing between borrowers and savers, and macro-prudential tools in the form of loan-to-value limits and bank capital requirements. A welfare-based loss function suggests a role for active macro-prudential policy to enhance risk sharing, though complete macro-prudential stabilization is not generally possible. Nonetheless, simulations of a house price boom and subsequent correction suggest that macro-prudential tools could alleviate debt-deleveraging and help avoid zero lower bound episodes, even when macro-prudential tools themselves impose only occasionally binding constraints on debt dynamics in the economy.

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Optimal quantitative easing

Published:

This paper studies optimal monetary policy in a simple New Keynesian model with portfolio adjustment costs. Purchases of long-term debt by the central bank (quantitative easing; ‘QE’) alter the average portfolio return and hence influence aggregate demand and inflation. The central bank chooses the short-term policy rate and QE to minimise a welfare-based loss function under discretion. Adoption of QE is rapid, with large-scale asset purchases triggered when the policy rate hits the zero bound, consistent with observed policy responses to the Global Financial Crisis. Optimal exit is gradual. Despite the presence of portfolio adjustment costs, a policy of ‘permanent QE’ in which the central bank holds a constant stock of long-term bonds does not improve welfare.

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The Bank of England’s forecasting platform: COMPASS, MAPS, EASE and the suite of models

Published:

(with Stephen Burgess, Emilio Fernandez-Corugedo, Charlotta Groth, Francesca Monti, Konstantinos Theodoridis and Matt Waldron)

This paper describes the Bank of England’s forecasting platform and provides examples of its application to practical forecasting problems. The platform consists of four components: COMPASS, a structural central organising model; a suite of models, used to fill in the gaps in the economics of COMPASS and provide cross-checks on the forecast; MAPS, a macroeconomic modelling and projection toolkit; and EASE, a user interface.

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Non-rational expectations and the transmission mechanism

Published:

(with Tim Taylor)

This paper compares two approaches to modelling behaviour under non-rational expectations in a benchmark New Keynesian model. The ‘Euler equation’ approach modifies the equations derived under the assumption of rational expectations by replacing the rational expectations operator with an alternative assumption about expectations formation. The ‘long-horizon’ expectations approach solves the decision rules of households and firms conditional on their expectations for future events that are outside of their control, so that spending and price-setting decisions depend on expectations extending into the distant future. We show that both approaches have very similar implications for macroeconomic dynamics when departures from rational expectations are relatively small, but as expectations depart further from rationality the two approaches can generate significantly different macroeconomic implications.

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Misperceptions, heterogeneous expectations and macroeconomic dynamics

Published:

(with Tim Taylor)

We investigate the extent to which misperceptions about the economy can become self-reinforcing and thereby contribute to time-varying macroeconomic dynamics using a New Keynesian model with long-horizon expectations and dynamic predictor selection. Agents have access to a set of alternative predictors to form expectations and choose among them based on noisy measures of their recent performance. This dynamic predictor selection generates endogenous fluctuations in the proportions of agents using each predictor, contributing to macroeconomic dynamics. The presence of a ‘persistent predictor’ can lead to changes in beliefs which are self-reinforcing, giving rise to endogenous fluctuations in the time-series properties of the economy. Such fluctuations arise even if we replace the ‘persistent predictor’ with learning under constant gain.

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Asset purchase policy at the effective lower bound for interest rates

Published:

This paper studies optimal policy in a stylised New Keynesian model that is extended to incorporate imperfect substitutability between short-term and long-term bonds, providing a channel through which central bank asset purchases can affect aggregate demand. However, the imperfect substitutability between bonds that gives asset purchases their traction also reduces the potency of conventional monetary policy. Nevertheless, a policy in which the central bank uses asset purchases as an additional policy instrument can improve outcomes in the face of a negative demand shock that drives the short-term policy rate to its lower bound.

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The impact of permanent energy price shocks on the UK economy

Published:

(with Ryland Thomas and Iain de Weymarn)

This paper builds a dynamic general equilibrium model that includes a variety of channels through which energy prices affect demand and supply. On the demand side we model household consumption of final energy goods (petrol and utilities) separately from other goods and services. On the supply side, we model the production of final energy goods and the way that they enter the production process of other goods and services. We calibrate the model using UK data and examine how the various channels in the model contribute to the responses to permanent energy price shocks of a similar magnitude to those observed in the recent data. We show the effects of such shocks have important implications for monetary policy.

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Evaluating and estimating a DSGE model for the United Kingdom

Published:

(with Ozlem Öomen)

We build a small open economy dynamic stochastic general equilibrium model, featuring many types of nominal and real frictions that have become standard in the literature. In recent years it has become possible to estimate such models using Bayesian methods. These exercises typically involve augmenting a stochastically singular model with a number of shocks to structural equations to make estimation feasible, even though the motivation for the choice of these shocks is often unspecified. In an attempt to put this approach on a more formal basis, we estimate the model in two stages. First, we evaluate a calibrated version of the stochastically singular model. Then, we augment the model with structural shocks motivated by the results of the evaluation stage and estimate the resulting model using UK data using a Bayesian approach. Finally, we reassess the adequacy of this augmented and estimated model in reconciling the dynamics of the model with the data. Our findings suggest that the shock processes play a crucial role in helping to match the data.

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