Numerical Maximisation of Likelihood: A Neglected Alternative to EM?

There is by now a long tradition of using the EM algorithm to find maximum‐likelihood estimates (MLEs) when the data are incomplete in any of a wide range of ways, even when the observed‐data likelihood can easily be evaluated and numerical maximisation of that likelihood is available as a conceptually simple route to the MLEs. It is rare in the literature to see numerical maximisation employed if EM is possible. But with excellent general‐purpose numerical optimisers now available free, there is no longer any reason, as a matter of course, to avoid direct numerical maximisation of likelihood. In this tutorial, I present seven examples of models in which numerical maximisation of likelihood appears to have some advantages over the use of EM as a route to MLEs. The mathematical and coding effort is minimal, as there is no need to derive and code the E and M steps, only a likelihood evaluator. In all the examples, the unconstrained optimiser nlm available in R is used, and transformations are used to impose constraints on parameters. I suggest therefore that the following question be asked of proposed new applications of EM: Can the MLEs be found more simply and directly by using a general‐purpose numerical optimiser?     

Between Neo-Liberalism and the Social Market: Approaches to Debt Adjustment and Consumer Insolvency in the EU

Many EU countries introduced debt adjustment systems as a response to the growth of over-indebtedness since the 1980s. These systems, originally introduced in many countries as crisis measures, have now become normalized, metamorphosing through a continuing learning process into a combination of debt adjustment and insolvency relief through a discharge of debt, sometimes after only 1?year, but often after a debt repayment plan over a period of 3–7?years. Since the early 2000s, new Member States of the EU have also introduced insolvency systems, often based on models from the old states. This paper examines experience in European consumer insolvency systems, based on the modest empirical studies of existing systems, primarily England, France and Germany. It discusses the reasons for the use of consumer insolvency, and the limited data on the characteristics of users, charts distinct national approaches and outlines common themes and objectives for consumer insolvency in the context of EU measures to create an integrated credit market in a “competitive social market. To economy”. It concludes by underlining the absence of systematic social science knowledge on existing systems and outlines areas for further research.     

The economics of household waste management: a review

In recent years reducing the amount of waste generated by households has become an important policy issue in industrialised economies. It is no longer acceptable to discard waste without concern for environmental and natural resource issues. In an effort to reduce household waste various policy instruments such as kerbside charges, deposit-refund schemes, integrated sales tax exemptions and virgin material taxes, have been proposed and/or implemented. This article reviews the economics literature that has addressed household waste management. It is argued that a comprehensive modelling framework is necessary if the complex policy environment is to be accurately described.     

AN ANALYSIS OF MANAGEMENT AGREEMENT BARGAINING UNDER ASYMMETRIC INFORMATION

This paper provides a game theoretic analysis of Management Agreements under asymmetric information. A simple two-period game is employed to represent the Coasian bargaining process which takes place between the farmer and English Nature over the introduction of a Management Agreement. The analysis shows that if the farmer possesses an information advantage and wishes to exploit it to gain an economic rent from the bargaining process, inefficient outcomes are possible. The implications of the analysis for the continued reliance upon voluntarism and Management Agreements for the protection of Sites of Special Scientific Interest are considered.