Adaptive confidence intervals of desired length and power for normal means

In all empirical or experimental sciences, it is a standard approach to present results, additionally to point estimates, in form of confidence intervals on the parameters of interest. The length of a confidence interval characterizes the accuracy of the whole findings. Consequently, confidence intervals should be constructed to hold a desired length. Basic ideas go back to Stein (1945) and Seelbinder (1953) who proposed a two-stage procedure for hypothesis testing about a normal mean. Tukey (1953) additionally considered the probability or power a confidence interval should possess to hold its length within a desired boundary. In this paper, an adaptive multi-stage approach is presented that can be considered as an extension of Stein's concept. Concrete rules for sample size updating are provided. Following an adaptive two-stage design of O’Brien and Fleming (1979) type, a real data example is worked out in detail.     

Decentralized Trading With Private Information

The paper studies how asset prices are determined in a decentralized market with asymmetric information about asset values. We consider an economy in which a large number of agents trade two assets in bilateral meetings. A fraction of the agents has private information about the asset values. We show that, over time, uninformed agents can elicit information from their trading partners by making small offers. This form of experimentation allows the uninformed agents to acquire information as long as there are potential gains from trade in the economy. As a consequence, the economy converges to a Pareto efficient allocation.     

Trade Union Action and Collective Bargaining in Europe: Trends and Problems

This paper deals with the transformations that have taken place in European countries over the last ten years— the decade of the 80s— in union action and collective bargaining. For the latter in particular the trend towards greater convergence, or to maintain the traditional differences found between the industrial relations systems of one country and another, emerges clearly. The conclusions, moreover, underline the persistence (and the rise during the past years) of safeguards and negotiational contractual mediation, the greater (at least as compared to the previous decade) adhesion of bargaining action to the economic situation, and the determining influence that the various national economies have had on this action, with a rising importance played by the industrial relations of the major firms.     

On the Failure of the Bootstrap for Matching Estimators

Matching estimators are widely used in empirical economics for the evaluation of programs or treatments. Researchers using matching methods often apply the bootstrap to calculate the standard errors. However, no formal justification has been provided for the use of the bootstrap in this setting. In this article, we show that the standard bootstrap is, in general, not valid for matching estimators, even in the simple case with a single continuous covariate where the estimator is root‐N consistent and asymptotically normally distributed with zero asymptotic bias. Valid inferential methods in this setting are the analytic asymptotic variance estimator of Abadie and Imbens (2006a) as well as certain modifications of the standard bootstrap, like the subsampling methods in Politis and Romano (1994).