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In this chapter we demonstrate the construction of inverse test confidence intervals for the turning-points in estimated nonlinear relationships by the use of the marginal or first derivative function. First, we outline the inverse test confidence interval approach. Then we examine the relationship between the traditional confidence intervals based on the Wald test for the turning-points for a cubic, a quartic, and fractional polynomials estimated via regression analysis and the inverse test intervals. We show that the confidence interval plots of the marginal function can be used to estimate confidence intervals for the turning-points that are equivalent to the inverse test. We also provide a method for the interpretation of the confidence intervals for the second derivative function to draw inferences for the characteristics of the turning-point.

This method is applied to the examination of the turning-points found when estimating a quartic and a fractional polynomial from data used for the estimation of an Environmental Kuznets Curve. The Stata do files used to generate these examples are listed in Appendix A along with the data.

The estimation of regression models subject to linear restrictions is a widely applied technique; however, aside from simple examples, the equivalence between the linear restricted case to the reparameterization and the substitution case is rarely employed. We believe this is due to the lack of a general transformation method for changing from the definition of restrictions in terms of the unrestricted parameters to the equivalent reparameterized model and conversely from the reparameterized model to the equivalent linear restrictions for the unrestricted model. In many cases, the reparameterization method is computationally more efficient especially when estimation involves an iterative method. But the linear restriction case allows a simple method for adding and removal of restrictions.

In this chapter, we derive a general relationship that allows the conversion between the two forms of the restricted models. Examples emphasizing systems of demand equations, polynomial lagged equations, and splines are given in which the transformation from one form to the other are demonstrated as well as the combination of both forms of restrictions. In addition, we demonstrate how an alternative Wald test of the restrictions can be constructed using an augmented version of the reparameterized model.

Recent changes in smoking laws have influenced gambling behaviour at electronic gaming machine (EGM) venues. In this chapter, we review the literature that examines the interrelationship between gambling, problem gambling, and smoking in order to gauge the indirect effects of smoking bans in gaming venues. We then perform an analysis on the consequences of a smoking ban in Victoria, Australia, that was instituted on 1st September 2002. This analysis investigates the nature of the pattern of drops in local EGM revenue and the impact on the state tax revenue.

The Blinder Oaxaca decomposition method for defining wage differentials (generally referred to as discrimination) from the wage equations of two groups has had a wide degree of application. However, the decomposition measures can very dramatically depending on the definition of the non-discriminatory wage chosen for comparison. This paper uses a form of extreme bounds analysis to define the limits on the measure of discrimination that can be obtained from these decompositions. A simple application is presented to demonstrate the use of the bootstrap to define the distributions of the discrimination measure.

The collection of chapters in this 30th volume of Advances in Econometrics provides a well-deserved tribute to Thomas B. Fomby and R. Carter Hill, who have served as editors of the Advances in Econometrics series for 25 and 21 years, respectively. Volume 30 contains a more varied collection of chapters than previous volumes, in essence mirroring the wide variety of econometric topics covered by the series over 30 years. Volume 30 starts with a chapter discussing the history of this series over the last 30 years. The next five chapters can be broadly categorized as focusing on model specification and testing. Following this section are three contributions that examine instrumental variables models in quite different settings. The next four chapters focus on applied macroeconomics topics. The final chapter offers a practical guide to conducting Monte Carlo simulations.