Parameter constancy in cointegrating regressions

This paper proposes an approach to testing for coefficient stability in cointegrating regressions in time series models. The test statistic considered is the one-sided version of the Lagrange Multiplier (LM) test. Its limit distribution is non-standard but is nuisance parameter free and can be represented in terms of a stochastic bridge process which is tied down like a Brownian bridge but relies on a random rather than a deterministic fraction to do so. The approach provides a test of the null hypothesis of cointegration against specific directions of departure from the null; subset coefficient stability tests are also available. A small simulation studies the size and power properties of these tests and an empirical illustration to Australian data on consumption, disposable income, inflation and money is provided.     

Structural Change Tests in Tail Behaviour and the Asian Crisis

This paper explores tests of the hypothesis that the tail thickness of a distribution is constant over time. Using Hill's conditional maximum likelihood estimator for the tail index of a distribution, tests of tail shape constancy are constructed that allow for an unknown breakpoint. The recursive test is shown to be inconsistent in one direction, and only a one-sided test is recommended. Specifically, the test can be used when the alternative hypothesis is that the tail index decreases over time. A rolling and sequential version of the test is consistent in both directions. The methods are illustrated on recent stock price data for Thailand, Malaysia and Indonesia. The period covers the recent Asian financial crisis and enables us to assess whether breakpoints in domestic asset return distributions are related to known changes in institutional arrangements in the foreign currency markets of these countries.     

Optimal group size in microlending

Microlending, where a bank lends to a small group of people without credit histories, began with the Grameen Bank in Bangladesh, and is widely seen as the creation of Muhammad Yunus, who received the Nobel Peace Prize in recognition of his largely successful efforts. Since that time the modeling of microlending has received a fair amount of academic attention. One of the issues not yet addressed in full detail, however, is the issue of the size of the group. Some attention has nevertheless been paid using an experimental and game theory approach. We, instead, take a mathematical approach to the issue of an optimal group size, where the goal is to minimize the probability of default of the group. To do this, one has to create a model with interacting forces, and to make precise the hypotheses of the model. We show that the original choice of Muhammad Yunus, of a group size of five people, is, under the right, and, we believe, reasonable hypotheses, either close to optimal, or even at times exactly optimal, i.e., the optimal group size is indeed five people.