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.
Fields
Tom works on:
- theoretical and applied macroeconomics,
- monetary economics,
- dynamic stochastic general equilibrium (DSGE) modelling,
- and other fields.
Publications
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
Robust Real Rate Rules
Revise(d) & resubmit(ted), Econometrica
Latest working paper, 2023
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 Much older video presentation
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.
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.
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.
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
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
Replaced Papers
The papers below have been replaced by newer papers taking different approaches to the same topic. There may still be something of interest in them.
Aggregation bias in investment and capital
Latest working paper, 2020
In the US BEA Fixed Asset tables, the relative price of capital is increasing (in units of consumption), while the relative price of investment (in the same units) is falling. We build a vintage capital model to explain these surprising facts. The model predicts that the BEA will mismeasure the true growth rates of both relative prices, with a bias driving a wedge between the two. The calibrated model implies that real growth in US GDP per capita is overstated by about 0.1 percentage points per year.
Reconciling near trend-stationary growth with medium-frequency cycles
Latest working paper, 2013
Existing models of dynamic 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 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.
Data consistent modelling of medium-frequency cycles and their origins
Latest working paper, 2013
This paper presents four stylized facts on medium-frequency cycles, then builds and estimates a model capable of replicating both these facts and standard business-cycle ones. We show that GDP returns to trend at long lags, that aggregate mark-ups always lead output, and are only counter-cyclical at low frequencies, and that medium-frequency cycles are larger in countries with longer patent protection. Since traditional dynamic endogenous growth models generate large trend-breaks following business-cycle shocks, our model is based on that of Holden (2013a). After estimation, a financial-type shock to the stock of ideas emerges as the key driver of the medium-frequency cycle.
Online appendices to “Reconciling near trend-stationary growth with medium-frequency cycles” and “Data consistent modelling of medium-frequency cycles and their origins”
Latest working paper, 2013
This paper presents the online appendices to Holden (2013a) and Holden (2013b). We discuss the derivation of the first order and free-entry conditions, the steady state level of relative productivity of non-protected industries, and the nature of the inventor-firm bargaining procedure. We go on to present the full equations of both models considered, details of the data used for estimation, and the results of this estimation procedure.
Efficient simulation of DSGE models with inequality constraints
Revise & resubmit, Journal of Economic Dynamics and Control, lapsed
Latest working paper, 2012
This paper presents a fast, simple and intuitive algorithm for simulation of linear dynamic stochastic general equilibrium models with inequality constraints. The algorithm handles both the computation of impulse responses, and stochastic simulation, and can deal with arbitrarily many bounded variables. Furthermore, the algorithm is able to capture the precautionary motive associated with the risk of hitting such a bound. To illustrate the usefulness and efficiency of this algorithm we provide a variety of applications including to models incorporating a zero lower bound (ZLB) on nominal interest rates. Our procedure is much faster than comparable methods and can readily handle large models. We therefore expect this algorithm to be useful in a wide variety of applications.
Working paper PDF Working paper on RePEc
Rough or Dormant Papers
The papers below are either extremely rough, or are dormant (for now). There may still be something of interest in them.
Tractable estimation and smoothing of highly non-linear dynamic state-space models
Latest working paper, 2017
We present an algorithm for tractably estimating non-linear dynamic models, such as DSGE models with occasionally binding constraints, or stochastic volatility models. The algorithm presents an extended skew-t, augmented-state, version of the Cubature Kalman Filter of Arasaratnam and Haykin (2009) with dynamic state space reduction, to give adequate speed, and to ensure that it can handle the large state spaces generated, for example, by pruned perturbation solutions to medium-scale DSGE models. The use of an extended skew-t approximation to the state’s distribution allows the filter to also track the distribution’s third and fourth moments. We extend the base algorithm to allow for alternative cubature procedures to further improve the tracking of non-linearities. We illustrate that the method can solve some of the identification problems that plague linearized DSGE models, and show that the method can readily handle the estimation of stochastic volatility models with time varying correlation between level and volatility innovations. We go on to extend the algorithm to produce smoothed estimates of states, and we use this to assess which shocks caused the great recession in the model of Christiano, Motto, and Rostagno (2014).
Learning from learners
Latest working paper, 2013
Traditional macroeconomic learning algorithms are misspecified when all agents are learning simultaneously. In this paper, we produce a number of learning algorithms that do not share this failing, and show that this enables them to learn almost any solution, for any parameters, implying learning cannot be used for equilibrium selection. As a by-product, we are able to show that when all agents are learning by traditional methods, all deep structural parameters of standard new-Keynesian models are identified, overturning a key result of Cochrane (2009; 2011). This holds irrespective of whether the central bank is following the Taylor principle, irrespective of whether the implied path is or is not explosive, and irrespective of whether agents’ beliefs converge. If shocks are observed then this result is trivial, so following Cochrane (2009) our analysis is carried out in the more plausible case in which agents do not observe shocks.
Working paper PDF Working paper on RePEc
Others
Further (sometimes rough!) papers can be seen in the following links:
My thesis My SSRN page My Google Scholar page My RePEc page
Policy / Non-academic Papers
Universal basic income as a tool for tax and benefit reform
Social Liberal Forum Publication Number 8 (2017)
“Also published in: “Four go in search of big ideas”, Edited by Helen Flynn (2018)
Universal basic income (UBI) is often presented as a way of supporting an increase in the fraction of population not in full time employment. Here, I wish to outline an alternative vision based upon using UBI to simplify the tax and benefit system and enhance work incentives. Rather than funding an increase in the number of people without jobs, my proposed system is designed to produce higher levels of employment. By replacing many existing benefits with a UBI, families will no longer need to worry about their benefits being withdrawn as they start earning more, giving them stronger incentives to work, and pulling thousands out of the poverty trap created by the existing benefits system. Furthermore, while the poorest will obtain the largest direct benefit from the proposed system, its wider benefits will be shared by people of all incomes due to reduced economic distortions.