Tim Worrall • Professor of Economics • The University of Edinburgh

II Research

Research Interests My principal research interests (with corresponding JEL classification) are: Game Theory and Bargaining Theory (C7) • Market Structure and Pricing (D4) • Information and Uncertainty (D8) • Intertemporal Choice and Growth (D9) • Consumption, Saving, Production, Employment and Investment (E2) • Financial Markets (G1) • Corporate Finance and Governance (G3) • Regulation and Industrial Policy (L5). My main areas of current research are in limited commitment, principal-agent problems and contract theory, risk and uncertainty and network design.
Research Grants Economic and Social Research Council, one of several Co-Investigators on Large Grant "Credit and Labour Market Foundations of the Macroeconomy" with John Hardman-Moore (Principal Investigator), £6 million, June 2015 - June 2020 • Royal Economic Society award on "Evaluating the Research Performance of UK Economics" with Gauthier Lanot, 12k, September 2006 - December 2006 • Economic and Social Research Council award on "Dynamic Relational and Self-Enforcing Contracts" with Jonathan Thomas (Principal Investigator), 151k, January 2005 - December 2006 • Department for International Development award on "The effects of macro-financial liberalisation policies on micro-household savings and credit behaviour in developing countries" with Peter Lawrence (Principal Investigator), Robin Bladen-Hovell, and Gauthier Lanot, 145k, April 2001 - March 2003 • Leverhulme Trust Fellowship, "Quasi-credit in less developed countries", 15k, 1998-9 • Keele Research Incentive Scheme, "Quasi-credit and LDCs", 5k, 1989.
Research Collaborators Spiros Bougheas (Nottingham University)
Martin Diedrich (University of Bath)
Sergey Foss (Heriot-Watt University)
Francesco Lancia (Ca' Foscari University of Venice)
Gauthier Lanot (Umeå University)
Ethan Ligon (University of California at Berkeley)
Costas Milas (University of Liverpool)
Pierre Picard (University of Luxembourg and CORE, Louvain-la-Neuve)
Alessia Russo (University of Padua)
Seva Shneer (Heriot-Watt University)
Jonathan Thomas (Edinburgh University)
Nicholas Vasilakos (University of East Anglia)
Current Students Sikandar Soin (Edinburgh), submitted November 2021.
Former Students Pongpalin Yingchoncharoen (Lecturer, Thammasat University, Thailand), graduated with MRes in Economics, Edinburgh University 2018.
Aodi Tang (Economic Model Analyst, Risk Stratergy, HSBC Bank, Edinburgh), graduated Edinburgh University 2018.
Rongyu Wang (Lecturer, Shandong University of Arts, China), graduated Edinburgh University 2016.
Sareh Vosooghi (Career Development Fellow in Economics, St Edmund Hall, University of Oxford), graduated Edinburgh University, 2016.
Vasco Filipe de Figueiredo Alves (Lecturer in Economics, University of Birmingham), graduated Edinburgh University, 2016.
Michael King, graduated University of Manchester, 2011.
Ioannis Lazopoulos (Lecturer in Economics, University of Surrey), graduated Keele University, 2006.
Alex Dickson (Senior Lecturer in Economics, University of Strathclyde), graduated Keele University, 2005.
Svetlana Andrianova (Reader in Economics, University of Leicester), graduated London South Bank University, 2001.
Research Overview Much of my work has been on limited commitment. Limited commitment occurs when contracts or agreements cannot be perfectly enforced. Most economic contracts have limited commitment. Examples, in particular, are to be found between countries, where there is no supranational legal framework, and in less developed countries, where there is a weaker legal framework. A key result of this work is to show that in order to provide incentives for the parties to provide information or comply with the contract, the temporal structure of the contract will be non-stationary even when the underlying environment itself is not changing over time. The literature in this area has focussed on two motivations for contracting: either risk-sharing or joint production. Together with Jonathan Thomas, I have made contributions to both areas of this literature. In a recent paper, we bring both motivations together to consider a single unified framework
Current Projects A major theoretical paper on "Dynamic Relational Contracts under Complete Information" with Jonathan P. Thomas (Edinburgh) is written. In it we consider a long-term relationship between two agents who undertake costly actions or investments that produce a joint benefit. Agents have an opportunity to expropriate some of the joint benefit for their own use. The question asked is how to structure the investments and division of the surplus over time so as to avoid expropriation. Two cases are considered: (i) where agents are risk neutral and are subject to limited liability constraints and (ii) where agents are risk averse, have quasi-linear preferences in consumption and actions but where limited liability constraints do not bind. In the risk-neutral case, there may be an initial phase in which one agent overinvests and the other underinvests. However, both actions and surplus converge monotonically to a stationary state in which there is no overinvestment and surplus is at its maximum subject to the constraints. In the risk-averse case, there is no overinvestment. For this case, we establish that dynamics may or may not be monotonic depending on whether or not it is possible to sustain a first-best allocation. If the first-best allocation is not sustainable, then there is a trade-off between risk sharing and surplus maximization. In general, surplus will not be at its constrained maximum even in the long run.

Work with Pierre Picard (Luxembourg), examines "Currency Areas and Inter-regional Assistance" and the implications of limited commitment of fiscal transfers between countries for the optimality of a currency union. We use a new international macroeconomic model to show that when fiscal transfers between countries are subject to limited commitment, a currency union can be optimal, even in a model that would typically favour flexible exchange rates. The reason is that a currency union will provide a hard landing if a country reneges on its fiscal transfers and this can be enough to induce greater risk-sharing and enhanced welfare. In a similar vein in a paper on ``Is a Policy of Free Movement of Workers Sustainable?" we examine country migration policies. Allowing free migration can enhance labour market flexibility and generate some extra income-smoothing benefits. However, immigration may also lead to increased congestion of local factors. When governments cannot fully commit to their migration policies, they therefore may be tempted to close borders to reduce short-term losses. We examine circumstances under which stable migration policies may be sustainable and address the issue of citizenship as well as residency.

Whilst working on the dynamic relational contracts paper it became apparent that existing results in the literature on convergence of stochastic recursive sequences were quite restrictive. In particular, existing theorems prove convergence to a unique invariant distribution when policy functions are monotone, a mixing condition is satisfied and when the underlying driving process is stochastically monotone. It is the last of these three assumptions that is restrictive. Experiments with examples showed that there was convergence (in those examples) even when the underlying process was not stochastically monotone. Joint work with Sergey Foss (Heriot-Watt), Seva Shneer (Heriot-Watt), and Jonathan P. Thomas shows that there is convergence to a unique invariant distribution when policy functions are monotone and continuous, a mixing condition is satisfied and when the underlying driving process is regenerative. Regenerative processes are those that can be split into independent and identically distributed (i.i.d.) cycles. For example any finite-state time-homogenous Markov chain with a single closed class of communicating states has this property. This result gives an off-the-shelf convergence theorem for many dynamic economic models.

Most models of risk sharing with limited commitment assume that agents are infinitely lived. Joint work with Alessia Russo (Oslo) and Francesco Lancia (Vienna) considers an overlapping generations model where agents live for two periods. We consider a simple model with random endowments. In this setting it is sometimes efficient for the young to transfer to the old and sometimes visa-versa. With limited commitment, the old will not transfer to the young, because they have no future benefit, whilst the young may transfer to the old (a pension) if they expect the future young to do likewise. We are able to characterise a steady-state solution, and when it exists, and characterise a stable saddle path solution that converges to the steady state and involves steadily rising consumption for the old along the transition.

Although the risk sharing model with limited commitment is well understood when there are just two agents, or when there is a continuum of agents, less is known about how to characterise the solution with a finite set of agents. It is important to know about the case with a finite set of agents because many applications, for example, risk sharing in village communities, fall into this category. Joint work with Ethan Ligon (Berkeley) examines this case. To make progress we assume an extra symmetry that there is just one winner from among the n agents and consider only stationary solutions. We consider two variants: one where the winner follows a deterministic order and a second where the winner is stochastically determined. The first case is solved for any n and any discount factor. What can be shown is that consumption of losers will tend to fall the more time it is since he/she last won. In the second case we have results for low discount factors when n-1 agents are constrained and numerical solutions for larger discount factors.

In joint work with Spiros Bougheas (Nottingham), I consider the issue of the homogeneity of securitised loan pools. This is important because in practice banks usually tranche loans into single types rather than portfolios. Consider a bank that has different types of loans on its books that it would like to sell. There is adverse selection as buyers don't know the quality of the loans. Banks may use a retention strategy to signal the quality of loan, that is, retain a "skin in the game". The question we ask is whether banks prefer to sell loans separately of as a portfolio. We show how the answer depends on parameter values. In particular, we show that banks prefer to sell loans separately if the fees from new loans are relatively small but may prefer to sell loans as a portfolio if the fees are larger. The intuition is that it is costly to signal loan type and even more costly to signal a portfolio type: therefore, the fees from loan sales need to be larger to justify portfolio sales.
Future Projects Jonathan Thomas and I plan to develop a number of applications of our general dynamic relational contracts paper. One possible application of our model is to the dynamics of household bargaining. There is a growing literature of family decision making that models the family, not as a single aligned entity as if it were an individual agent, but as group of agents whose preferences are not completely aligned. This line of inquiry goes back to Becker (1973), but there has been recent renewed interest in Nash bargaining models of family and with implications for labour supply and public good provision within the household. It is important therefore to consider the implications of limited commitment for decisions within the household. Furthermore, the empirical evidence strongly suggests that lack of commitment is an important feature of household consumption patterns (see Mazocco, 2007). We plan therefore to develop a model of household behaviour with limited commitment which addresses the implications for household production, labour supply and public good provision over time. Another extension to generalise the model to make the breakdown payoffs endogenous is also planned.

As part of the ESRC large grant on Credit and Labour Market Foundations of the Macroeconomy, I, together with Jonathan Thomas and others, will be examining the evolution of wages throughout the course of an employment relationship and in particular the effects of macroeconomic changes. The evolution of wages is dependent on risk sharing and commitment, fairness considerations, (for example, a constraint that ensures firms do not have an incentive to replace current workers in a downturn), and firm-worker match quality. This market is however, only one aspect of general labour markets. Bewley emphasises that there is also a secondary sector that operates more like a spot market. A complete account of what happens in the labour market over the business cycle therefore would encompass the secondary sector too. From a theoretical perspective, this suggests that the presence of unemployment requires an articulation of why workers laid off from the primary sector and waiting/searching for new primary sector jobs do not take stopgap jobs in the secondary sector in the meantime. The aim of this work will be to develop models of long-term worker-firm relationships based on market incompleteness and heterogeneous match quality that are consistent with the micro-data. This theoretical work will be carried out alongside a parallel empirical investigation of the cyclical behaviour of real and nominal wages. It is anticipated that this work will shed light on some puzzling labour market experience during the great recession, including the growing pro-cyclicality of real wages in the U.K. and the contrasting experience of the U.S.
Talks and Presentations
  • Universidad Carlos III Madrid, Spain, May 2018
  • National Bureau of Economic Research Summer Institute (Macro Public Finance Research Group), Boston, July 2017
  • Society for the Advancement of Economic Theory, Faro, June 2017
  • Society for Economic Dynamics, Edinburgh, June 2017
  • UmeŚ University, Sweden, February 2017
  • Theoretical Research in Development Economics conference, Duke University, April 2016
  • Heriot-Watt University, November 2015
  • Society for the Advancement of Economic Theory, Cambridge, July 2015
  • Hull University, February 2015
  • Durham University, September 2014
  • Manchester University, September 2014
  • Liverpool University, November 2013
  • University of Oslo, Oslo, Norway, September 2013
  • Yonsei University, Seoul, Korea, June 2013
  • York Game Theory Symposium, June 2013
  • Workshop on macroeconomic applications of dynamic games and contracts, Stony Brook, New York, July 2012
  • Journées d'Economie Publique Louis-André Gérard-Varet, Marseilles, June 2012
  • Keele University, February 2012
  • Strathcylde University, February 2012
  • City University, January 2012
  • Durham University, October 2011
  • European Trade Study Group, Copenhagen, September 2011
  • Society for Economic Dynamics, Ghent, July 2011
  • Society for the Advancement of Economic Theory, Faro, June 2011
  • Econometric Society Winter Meetings, Denver, January 2011
  • TOM Workshop on Frontiers of Migration Research, Bamberg, July 2010
  • University of Dundee, March 2010
  • University of Surrey, November 2009
  • Workshop on the Theory and Empirics of Risk Sharing, Gremaq, Toulouse School of Economics, October 2009
  • Society for Economic Dynamics, Istanbul, July 2009
  • Canadian Economic Association, Toronto, May 2009
  • Workshop of the Regional Studies Research Network on Geographical Localisation, Intersectoral Reallocation of Labour and Unemployment Differentials, Rimini, May 2009
  • Warwick University, November 2008
  • 2nd St Andrews Workshop in Applied Microeconomics, September 2008
  • Society for Economic Dynamics, Massachusetts Institute of Technology, July 2008
  • Canadian Macroeconomic Study Group, Ottawa, November 2007
  • University of Durham, November 2007
  • Workshop on Risk Sharing, Gremaq, Toulouse School of Economics, September 2007
  • Bristol University, May 2007
  • Sheffield University, May, 2007
  • Econometric Society European Meetings, Vienna, August 2006
  • European Economic Association, Vienna, August 2006
  • Canadian Economic Association, Montreal, May 2006
  • Royal Economic Society, Nottingham, April 2006
  • University of California at Berkeley, March 2006
  • Manchester University, February 2006
  • Workshop on Limited Commitment, Edinburgh University, November 2005
  • Society for Economic Dynamics, Budapest, June 2005
  • European Economic Association, Madrid, August 2004
  • Queen's University Belfast, May 2004
  • Birmingham University, May 2004
  • Durham University, November 2003
  • Econometric Society European Meetings, Stockholm, August 2003
  • Game Theory Workshop, University of Nottingham, April 2003
  • University of Newcastle, April 2003
  • Birkbeck College London, March 2002
  • University of Surrey, February 2002
  • Econometric Society European Meetings, Lausanne, August 2001
  • South Bank University, May 2000
  • Nottingham University, May 2000
  • Birmingham University, November 1999
  • European Congress of the Econometric Society, Santiago de Compostela, Spain, 1999
  • Department of Agricultural Resource Economics, University of California at Berkeley, April 1999
  • Durham University, 1997
  • University of Liverpool, June 1996
  • University of Loughborough, May 1996
  • Institute for Empirical Macroeconomics at the Federal Reserve Bank of Minneapolis, Minnesota, April 1996
  • 7th World Congress of the Econometric Society, Tokyo, 1995
  • University of Manchester, 1995
  • Summer Research Workshop on New Macroeconomics, July 1994
  • University of Sheffield, 1994
  • University of Keele, 1994
  • University of Aberystwyth, 1993
  • University of Exeter, 1993
  • University of Salford, 1993
  • 1st Summer School in Economic Theory at La Sorbonne, Paris, April 1993
  • Centre for Operations Research and Economics at the University of Louvain-la-Neuve, Belgium, April 1993
  • 6th World Congress of the Econometric Society in Barcelona, August 1990
  • European Congress of the Econometric Society, Budapest, August 1986
  • European Congress of the Econometric Society, Madrid, August 1984