The views expressed on this website are the private views of Tom D. Holden and do not represent the views of the Deutsche Bundesbank, the Eurosystem or its staff.


Tom works on:

  • theoretical and applied macroeconomics,
  • monetary economics,
  • dynamic stochastic general equilibrium (DSGE) modelling,
  • and other fields.


Robust Real Rate Rules

Econometrica, Forthcoming

Latest working paper, 2024

Central banks wish to avoid self-fulfilling fluctuations. Interest rate rules with a unit response to real rates achieve this under the weakest possible assumptions about the behaviour of households and firms. They are robust to household heterogeneity, hand-to-mouth consumers, non-rational household or firm expectations, active fiscal policy and to any form of intertemporal or nominal-real links. They are easy to employ in practice, using inflation-protected bonds to infer real rates. With a time-varying short-term inflation target, they can implement an arbitrary inflation path, including optimal policy. This provides a way to translate policy makers’ desired path for inflation into one for nominal rates. US Federal Reserve behaviour is remarkably close to that predicted by a real rate rule, given the desired inflation path of US monetary policy makers. Real rate rules work thanks to the key role played by the Fisher equation in monetary transmission.

Working paper PDF Working paper online appendices PDF Working paper supplemental appendices PDF Replication materials Slides Shorter slides Non-technical slides Much older video presentation

Existence and uniqueness of solutions to dynamic models with occasionally binding constraints

The Review of Economics and Statistics, 2023

Occasionally binding constraints (OBCs) like the zero lower bound (ZLB) can lead to multiple equilibria, and so to belief-driven recessions. To aid in finding policies that avoid this, we derive existence and uniqueness conditions for otherwise linear models with OBCs. Our main result gives necessary and sufficient conditions for such models to have a unique (“determinate”) perfect foresight solution returning to a given steady state, for any initial condition. While standard New Keynesian models have multiple perfect-foresight paths eventually escaping the ZLB, price level targeting restores uniqueness. We also derive equilibrium existence conditions under rational expectations for arbitrary non-linear models.

Publisher’s version Working paper PDF Working paper appendices PDF Working paper on RePEc

Credit crunches from occasionally binding bank borrowing constraints

Journal of Money, Credit and Banking, 2020

We present a model in which banks and other financial intermediaries face both occasionally binding borrowing constraints, and costs of equity issuance. Near the steady state, these intermediaries can raise equity finance at no cost through retained earnings. However, even moderately large shocks cause their borrowing constraints to bind, leading to contractions in credit offered to firms, and requiring the intermediaries to raise further funds by paying the cost to issue equity. This leads to the occasional sharp increases in interest spreads and the countercyclical, positively skewed equity issuance that are characteristics of the credit crunches observed in the data.

Co-author: Paul Levine Co-author: Jonathan Swarbrick

Publisher’s version Published version on RePEc Working paper PDF Working paper on RePEc

Reconciling Jaimovich-Rebello preferences, habit in consumption and labor supply

Economics Letters, 2018

This note studies a form of a utility function of consumption with habit and leisure that (a) is compatible with long-run balanced growth, (b) hits a steady state observed target for hours worked and (c) is consistent with micro-econometric evidence for the inter-temporal elasticity of substitution and the Frisch elasticity of labor supply. Employing Jaimovich–Rebello preferences our results highlight a constraint on the preference parameter needed to target the steady-state Frisch elasticity. This leads to a lower bound for the latter that cannot be reconciled empirically with external habit, but the introduction of a labor wedge solves the problem. We also propose a dynamic Frisch inverse elasticity measure and examine its business cycle properties.

Co-author: Paul Levine Co-author: Jonathan Swarbrick

Publisher’s version Published version on RePEc Working paper PDF Working paper on RePEc

Current Working Papers

Rationing under sticky prices

Latest working paper, 2024

Consumer demand places an upper bound on sales, not a lower bound. And yet, when we solve sticky price models (Calvo or menu-cost), we assume firms sell the entire quantity demanded at their price. This produces completely unreasonable behaviour, as firms with old prices end up selling at a price below their marginal cost. Instead, firms should ration demand to keep their marginal costs no greater than their price. We show in a continuous time New Keynesian (NK) model with idiosyncratic demand shocks that this produces drastically different results to the standard NK model. Whereas a standard sticky price model can never generate the jump in the price level we see following cleanly identified monetary shocks, the model with rationing can. Whereas a standard sticky price cannot match the flattening of the Phillips curve when output & inflation are low, the model with rationing does, and when output & inflation are high, the Phillips curve can become so steep it bends backwards. Whereas in standard sticky price models, the optimal inflation rate is always very close to zero, in models with rationing the optimal inflation rate can be really quite high. The model with rationing also fixes many of the counter-intuitive properties of the standard NK model, such as the upper bound on inflation.

Slides Shorter slides

Computation of solutions to dynamic models with occasionally binding constraints

Reject & resubmit, Quantitative Economics

Latest working paper, 2016

We construct the first algorithm for the perfect foresight solution of otherwise linear models with occasionally binding constraints, with fixed terminal conditions, that is guaranteed to return a solution in finite time, if one exists. We also provide a proof of the inescapability of the “curse of dimensionality” for this problem when nothing is known a priori about the model. We go on to extend our algorithm to deal with stochastic simulation, other non-linearities, and future uncertainty. We show that the resulting algorithm produces fast and accurate simulations of a range of models with occasionally binding constraints.

Working paper PDF Working paper on RePEc

Capital heterogeneity and investment prices: How much are investment prices declining?

Latest working paper, 2022

Not as much as you may think. Investment-specific technological change (ISTC), reflected in the declining price of new investment goods, has been recognized as an important potential driver of economic growth, business cycles, the labor share, and the equilibrium real rate. However, the declines in investment prices are heavily concentrated in a few asset types, most notably computers, while most asset types exhibit little change. How one aggregates these price changes is hence critical to evaluating the aggregate importance of ISTC. We demonstrate theoretically the correct aggregation approach using a standard neoclassical model with multiple capital goods. The correct aggregation depends on the question studied. Second, empirically, we evaluate the quantitative impact of using the correct aggregation procedure. We find that the contribution of ISTC to any of these questions is smaller than if one ignores aggregation issues.

Co-author: Francois Gourio Co-author: Matthew Rognlie


Exact inflation targeting with inflation swaps

Latest working paper, 2023

Central banks can remove all uncertainty from future inflation by simultaneously intervening in two different inflation swap markets, leaving nominal rates to float freely. The first swap type returns gross inflation minus the contract rate. The second, returns gross inflation times gross inflation minus the contract rate. If the central bank sets both contract rates equal to the inflation target, then a Jensen’s inequality argument implies that inflation is at target with probability one. The central bank is able to fix two prices simultaneously as fixing just one would produce indeterminacy. Fixing both pins down inflation without invoking any dubious terminal conditions on inflation. With a time-varying target, this enables the central bank to robustly implement near-optimal policy.

Extended abstract PDF Slides

Business cycles in space

Latest working paper, 2020

Many important shocks in the real world are correlated not only in time, but also across some notion of space. This may be physical space, or the space of product, firm or household types. As a result of this spatial correlation, aggregate volatility emerges naturally from idiosyncratic shocks. In this paper, we introduce a tractable framework that allows for such shocks without necessitating the discretisation of space, or a departure from perturbation approximation. As a lead example, we construct a dynamic, stochastic, general equilibrium model of economic geography (DSGEEG). This model features population movement, firm dynamics and semi-endogenous growth. Using it, we show how transitory, spatially located productivity shocks can lead to persistent movements in population, helping to explain internal migration patterns in the U.S., and regional wage and investment dynamics. As an additional theoretical contribution, we derive conditions for the existence of continuous-in-space shock processes on a range of spaces of economic interest.

Co-author: Jonathan Swarbrick

Working paper PDF

Quantifying the transmission of European sovereign default risk

Latest working paper, 2018

We build a non-stationary Hawkes model of sovereign credit risk for seven European countries, and estimate it on CDS data from the run-up to the Greek default. We model a country’s credit risk as partly driven by a weighted combination of risks across countries. We find Spain and Portugal are the chief drivers of this component, with Greece’s contribution also significant. Greece and Portugal are found to be particularly sensitive to external risk, with a Greek default 35% less likely in our period without shocks elsewhere. Our novel maximum-likelihood procedure permits tractable estimation of high-dimensional Hawkes models with unobserved events.

Co-author: Ana-Maria Dumitru

Working paper PDF Working paper on RePEc with earlier title

Catch-up cycles

Latest working paper, 2018

We build a DSGE model of technological catch-up in countries behind the global frontier. We go on to estimate it on Spanish and U.S. data, with the U.S. acting as the technological leader, and Spain as the follower. The model generates highly persistent movements in productivity in the emerging economy from un-persistent shocks to the technological leader, helping to explain Spanish data. Unlike the prior literature, our model would generate permanent productivity gaps between the global technological leader and other economies even were the leader’s technological progress to halt, helping to explain why the great recession has not been accompanied by convergence in productivity. This is due to the diminishing returns to technological transfer in our model. It is further exacerbated by competition between firms in the following economy, which reduce each firm’s share of production profits. We draw tentative conclusions on policies to enhance productivity in countries behind the global frontier.

Co-author for next version: G. Kemal Ozhan

Working paper PDF

Medium-frequency cycles in a stationary world

Latest working paper, 2016

Existing models of endogenous growth generate implausibly large trend breaks in output when augmented with standard business cycle shocks. This paper presents a model without this deficiency, yet still capable of generating large medium-frequency fluctuations around the trend. Ensuring the robustness of the trend requires that we eliminate the strong scale effects and knife edge assumptions that plague most growth models. In our model, medium-frequency fluctuations arise from changes in the proportion of industries producing patent protected products. However, variations in the number of firms within each industry ensure that process improvement incentives remain roughly constant. An estimated version of the model matches well the observed pattern of medium frequency cycles.

Working paper PDF Slides with additional material

Other Papers

Various older papers are listed here.

Other old papers are on SSRN here.