Decomposing and Testing Long‐term Returns: an Application on Danish IPOs

An improved method for measuring and testing long‐run returns is proposed. The method adjusts for the right‐skewed distribution of long‐run buy‐and‐hold by decomposing average cross‐sectional buy‐and‐hold returns into mean components and volatility components. The method is applied to initial public offerings in Denmark. The mean‐component under performance of initial public offering stocks compared to the market is 30% and significant after 5 years. Compared to matching firms the under performance of IPO stocks is 13% after 5 years but insignificant.     

Equilibrium price and advertisement distributions

We consider an economy where many sellers sell identical goods to many buyers. Each seller has a unit supply and each buyer has a unit demand. The only possible information flow about prices is through costly advertising. We show that in equilibrium the sellers use mixed strategies in pricing which leads to price and advertisement distributions. With convex advertising costs each seller sends only one advertisement in the market. We also delineate a class of advertising costs which ensures that sellers may send multiple advertisements in equilibrium. Higher prices are advertised more than lower prices.     

A strategic predictive distribution for tests of probabilistic calibration

Forecasts of probability distributions are needed to support decision making in many applications. The accuracy of predictive distributions should be evaluated by maximising sharpness subject to calibration. Sharpness relates to the concentration of the predictive distributions, while calibration concerns their statistical consistency with the data. This paper focuses on calibration testing. It is important that a calibration test cannot be gamed by forecasts that have been strategically designed to pass the test. The widely used tests of probabilistic calibration for predictive distributions are based on the probability integral transform. Drawing on previous results for quantile prediction, we show that strategic distributional forecasting is a concern for these tests. To address this, we provide a simple extension of one of the tests. We illustrate ideas using simulated data.     

On probability models in voting theory

This paper illustrates the use of probability models to study properties of voting rules. In particular, a simple occupancy distribution and its limiting Dlrichlet form are introduced, corresponding to simplifying assumptions about voters' preferences. We use as illustrations the occurrence probability of the Condorcet Paradox, a vintage problem in social choice theory, along with the related concept of Condorcet efficiency, a measure of goodness for voting rules. Further examples include properties of a lottery rule and the vulnerability of certain voting rules to strategic manipulation. Prospects for future work are indicated.     

An identity for the product moments of order statistics

A general identity for the product moments of successive order statistics is given, which is valid in a class of probability distributions including Weibull, Pareto, exponential and Burr distributions.     

A new approach to maximum likelihood estimation of sum-constrained linear models in case of undersized samples

Maximum likelihood procedures for estimating sum-constrained models like demand systems, brand choice models and so on, break down or produce very unstable estimates when the number of categories ( n ) is large as compared with the number of observations ( T ). In applied research, this problem is usually resolved by postulating the contemporaneous covariance matrix of the dependent variables to be known apart from a constant of proportionality. In this paper we develop a maximum likelihood procedure for sum-constrained models with large numbers of categories, which does not require too many observations, but nevertheless allows for n covariance parameters to be estimated freely.     

Testing joint hypotheses when one of the alternatives is one-sided

We propose a class of statistics where the direction of one of the alternatives is incorporated. It is obtained by modifying a class of multivariate tests with elliptical confidence regions, not necessarily arising from normal-based distribution theory. The resulting statistics are easy to compute, they do not require the re-estimation of models subject to one-sided inequality restrictions, and their distributions do not require bounds-based inference. We derive explicit distribution and power functions, using them to prove some desirable properties of our class of modified tests. We then illustrate the relevance of the method by applying it to devising an improved test of random walks in autoregressive models with deterministic components. In this example, the usual alternative to a unit root is one-sided in the direction of stable roots, while deterministic components are allowed to go either way, and we show that it is beneficial to take the partially one-sided nature of the alternative into account.     

Concomitants of Record Values Arising from Morgenstern Type Bivariate Logistic Distribution and Some of their Applications in Parameter Estimation

In this paper we have obtained the joint probability density function of concomitants of two record values and hence obtained an explicit expression for the product moment of concomitants of two record values arising from Morgenstern family of distributions. Appling this expression for the product moments of concomitants of record values we have derived the best linear unbiased estimators based on concomitants of record values of some parameters involved in Morgenstern type bivariate logistic distribution which is a subfamily of the Morgenstern family of distributions. The efficiencies of these estimators based on the first n concomitants of record values for n≤10 are also obtained.     

Quasi ex-ante inflation forecast uncertainty

We propose a measure of the effects of monetary policy based on an analysis of the distribution of the ex-post inflation forecast uncertainty. We argue that the difference between the distributions of the ex-ante and ex-post uncertainties reflects the impact of monetary policy decisions. Using the theoretical background of the New Keynesian model with imperfect information and a monetary policy rule, we derive a proxy for ex-ante inflation uncertainty called quasi ex-ante forecast uncertainty, which is free to a certain extent of the effects of monetary policy decisions. Furthermore, we introduce the compound strength measure of monetary policy, as well as the uncertainty ratio, which approximates the impact of monetary policy on the reduction of the inflation forecast uncertainty. Our empirical results show that the greatest policy effect in reducing the inflation forecast uncertainty occurs for countries which conduct either a well-established or a relatively pure inflation targeting policy.