Alternative methods of computing estimates of inequality measures from grouped data are critically examined in terms of their theoretical and empirical properties. The use of a simple “split-histogram” technique of interpolation is explained and supported. Theoretical and empirical support is also provided for the “⅓/⅔ rule”—a simple computational procedure for a point estimate of an inequality measure derived from its standard grouping bounds.

It is often desirable to know whether or not a risky asset's beta coefficient has changed and, if so, at what point in time the change occurred. For example, this knowledge is of obvious importance to beta-using security analysts and portfolio managers. As another example, a given theory may imply that a particular firm's beta should have changed at different points in time. Investigators may want to test such a hypothesis. Furthermore, tests are frequently performed on the effects of events on residuals of the market model, tests requiring the assumption of beta stability. For these, and possibly other reasons, it is useful to be able to detect that a change in beta did, in fact, take place as well as, in some instances, identifying the point in time at which the change took place.

We develop and estimate an equilibrium model of ability tracking in which schools decide how to allocate students into ability tracks and choose track-specific teacher effort; parents choose effort in response. The model is estimated using Early Childhood Longitudinal Study data. Our model suggests that a counterfactual ban on tracking would benefit low-ability students but hurt high-ability students. Ignoring effort adjustments would significantly overstate the impacts. We then illustrate the trade-offs involved when considering policies that affect schools’ tracking decisions. Setting proficiency standards to maximize average achievement would lead schools to redistribute their inputs from low- to high-ability students.

We document that corporate financial misconduct has significant consequences for politicians' election outcomes and, in particular, those politicians that serve on U.S. congressional committees with SEC-relevant oversight responsibilities (“SEC-relevant politicians”). These politicians display a 31% greater likelihood of losing a reelection campaign after a local firm faces SEC enforcement for financial misconduct. We also document that SEC-relevant politicians appear to influence the SEC to limit career effects due to the potential consequences from enforcement against local firms. First, the timing of enforcement action announcements around SEC-relevant politicians' elections appears opportunistic. Second, firms in the districts of SEC-relevant politicians are less likely to receive SEC enforcement actions relative to other firms and, when faced with enforcement, receive smaller penalties. Collectively, these results suggest that politicians' career concerns impede the SEC's enforcement efforts.

When estimating a single equation with an error generated by an autoregressive process of higher order than one using a sequence of likelihood ratio tests to determine the correct order, the asymptotic size of the tests will be biased because of multiple optima of the likelihood function. A new type is suggested similar to the Durbin test [2] which is not biased in this way. IN HIS ARTICLE on testing for serial correlation in the presence of lagged endogenous variables [2] Durbin proved a general theorem which gives a significance test shown to be generally asymptotically equivalent to a likelihood ratio test. This paper proposes a generalization which gives a test criterion that may be preferred to the existing test criteria insofar as it can be set up using a less arbitrary choice of the parameters to be re-estimated, and also has the advantage of being relatively simple to compute. It seems more appropriate than the general Durbin form of test for application to the dynamic specification problem discussed in the third section of this article.