Tim Worrall • Hallsworth Research Fellow • The University of Manchester

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 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), 157k, 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)
Ethan Ligon (University of California at Berkeley)
Pierre Picard (University of Luxembourg and CORE, Louvain-la-Neuve)
Jonathan Thomas (Edinburgh University)
Martin Diedrich (Imperial College London)
Current Projects Strand I: When contracts or agreements cannot be perfectly enforced, there is said to be limited commitment. Most economic contracts have limited commitment. Examples in particular are to be found between countries 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 either 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 P. Thomas, I have made contributions to both areas of this literature. The agenda for the next two years is to develop and generalise the joint production model and over the next two-five years to develop applications of the general model and provide an integration with the risk-sharing literature.

A major theoretical paper on "Dynamic Relational Contracts with Credit Constraints" (with Jonathan P. Thomas) is written. In it we consider a long-term relationship between two risk- neutral agents who undertake costly actions or investments which 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. It is shown that investments may be either above or below the efficient level and that actions and the division of the surplus converges to a stationary solution at which either both investment levels are efficient or both are below the efficient level. This paper represents an important advance on the current literature in considering two-sided investment and two-sided limited commitment. Preliminary versions of this paper have been presented at several international conferences. We have recently extended the results of the paper, allowing for agents to save.

Three further papers on dynamic relational contracts which build upon the general paper are in process. In the first we will examine special cases in which the Pareto- frontier is concave. One such special case is where the production function is additive in the actions of the two agents. In these special cases we are able to show some monotonicity properties of convergence to the steady-state. In addition, unlike the general paper, results can be proved using standard dynamic programming techniques. In a second paper we show that in the two-sided action case the value function (Pareto-frontier) is differentiable even though it is known that is in general non-differentiable in the one-sided case. In a third paper we extend the model to examine the case with risk-averse agents. There is only a weaker characterisation of the optimum contracts in this case, but we are able to show convergence under some circumstances. The results for the first two papers are already established, although for the third paper further work on developing the results is still necessary. Another paper to generalise the model to allow to make the breakdown payoffs endogenous is also planned.

We intend to develop a number of applications of the model. 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. This would build upon our existing general model but would require a more detailed specification of production inside and outside the household.

In work (with Pierre M. Picard) I examine "Currency Areas and Inter-regional Assistance" and the implications of self-enforcement of fiscal transfers between countries for the optimality of a currency union. It is shown that when fiscal transfers between countries are subject to self-enforcement, 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 work in progress 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. Both papers have been presented at international conferences.

Strand II: Although the principal-agent model has been analysed very thoroughly, there are still a number of aspects that are relatively neglected. One is the falsification of the state by the agent; another is endogenous screening where the agent type is determined endogenously by a decision of the agent prior to the contracting process. Both are important practical issues.

A current paper with Spiros Bougheas addresses the issue of cost padding by regulated firms. Cost padding is one of the key concerns of regulatory practice. In the model the firm can, at some cost, hide its true cost from the regulator and thus engage in costly-state falsification. This model is extended to allow endogenous type selection as the firm can choose its level of capital investment and thus the level of its cost function. It is shown how a modified cost-plus contract is optimal despite the fact that the firm pads costs.

Bank finance and credit contracts remain an important issue in monetary economics. In a paper with Spiros Bougheas we are examining credit contracts where there can be costly state falsification and costly state verification of returns. We show that the optimum contract has both debt and convertible features whereby the contract can be converted to equity under certain circumstances. Work is in progress to develop the endogenous screening aspect of the cost padding model to consider a general mechanism design problem. This will provide a technical analysis of the continuity properties of endogenous distribution of types in a standard screening model.

Strand III: A key concept in economics is that of the market. But the market should not be regarded as an amorphous object. Rather it is a nexus of interconnections between buyers and sellers. The aim of this research is to better understand the structure of these interconnections.

Kranton-Minehart (2001) have identified the number of links required for a complete network, where all goods are sure to be given to the top-valuing buyers. By way of extension, Martin Diedrich and I have made progress towards identifying the number of links that are needed for certain types of incomplete networks, where some goods can only go to less-than-top valuation buyers. In particular, we conjecture that adding an extra link to the network is most effective if the network is only moderately dense, suggesting that efficient networks will exhibit a fair degree of incompleteness. Our recent investigations have opened up a very promising new approach to this problem, based on an explicit order-theoretical investigation of the overlap structure of the sets of non-connected buyers and sellers. We conjecture that efficient incomplete networks are "regular" (in a formally defined sense) and we hope to find an explicit formula for the maximum number of feasible allocations for a given number of links. Based on these new results we would then be able to investigate an explicit condition on the optimal density of the network, weighing the costs of the required links against the benefits of greater degrees of completeness.
Talks and Presentations
  • 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