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This chapter develops an asymptotic theory for a general transformation model with a time trend, stationary regressors, and unit root nonstationary regressors. This model extends that of Han (1987) to incorporate time trend and nonstationary regressors. When the transformation is specified as an identity function, the model reduces to the conventional cointegrating regression, possibly with a time trend and other stationary regressors, which has been studied in Phillips and Durlauf (1986) and Park and Phillips (1988, 1989). The limiting distributions of the extremum estimator of the transformation parameter and the plug-in estimators of other model parameters are found to critically depend upon the transformation function and the order of the time trend. Simulations demonstrate that the estimators perform well in finite samples.

‘A MAP OF THE WORLD that does not include Utopia is not worth glancing at’ wrote Oscar Wilde. ‘It leaves out the one country at which humanity is always landing. And when it lands there it looks out and, seeing a better country, sets sail again. Progress is the realization of Utopias’.

IN the two years since the last Farnborough Air Show was held by the Society of British Aerospace Companies the aircraft industry has achieved an almost complete metamorphosis from the body blows in the form of major programme cancellations that almost felled it in 1965 to the very healthy position that it holds today.

The author develops and extends the asymptotic F- and t-test theory in linear regression models where the regressors could be deterministic trends, unit-root processes, near-unit-root processes, among others. The author considers both the exogenous case where the regressors and the regression error are independent and the endogenous case where they are correlated. In the former case, the author designs a new set of basis functions that are invariant to the parameter estimation uncertainty and uses them to construct a new series long-run variance estimator. The author shows that the F-test version of the Wald statistic and the t-statistic are asymptotically F and t distributed, respectively. In the latter case, the author shows that the asymptotic F and t theory is still possible, but one has to develop it in a pseudo-frequency domain. The F and t approximations are more accurate than the more commonly used chi-squared and normal approximations. The resulting F and t tests are also easy to implement – they can be implemented in exactly the same way as the F and t tests in a classical normal linear regression.

Measurement of diminishing or divergent cross section dispersion in a panel plays an important role in the assessment of convergence or divergence over time in key economic indicators. Econometric methods, known as weak σ-convergence tests, have recently been developed (Kong, Phillips, & Sul, 2019) to evaluate such trends in dispersion in panel data using simple linear trend regressions. To achieve generality in applications, these tests rely on heteroskedastic and autocorrelation consistent (HAC) variance estimates. The present chapter examines the behavior of these convergence tests when heteroskedastic and autocorrelation robust (HAR) variance estimates using fixed-b methods are employed instead of HAC estimates. Asymptotic theory for both HAC and HAR convergence tests is derived and numerical simulations are used to assess performance in null (no convergence) and alternative (convergence) cases. While the use of HAR statistics tends to reduce size distortion, as has been found in earlier analytic and numerical research, use of HAR estimates in nonparametric standardization leads to significant power differences asymptotically, which are reflected in finite sample performance in numerical exercises. The explanation is that weak σ-convergence tests rely on intentionally misspecified linear trend regression formulations of unknown trend decay functions that model convergence behavior rather than regressions with correctly specified trend decay functions. Some new results on the use of HAR inference with trending regressors are derived and an empirical application to assess diminishing variation in US State unemployment rates is included.

Whereas investments in new attractions continue to rise within the theme park industry, knowledge regarding the effects of new attractions on theme park performance and attendance remains scarce. In order to isolate these effects, the purpose of this paper is to present the results of an econometric study explaining the variance in theme park visitor numbers and quantifying the effects of new attractions on theme park attendance.

The paper is based on an econometric study, in which models were produced for four European theme parks. No pooled modelling was used, meaning that four different models were created; one for each participating theme park. Various variables affecting theme park attendance were identified and quantified, and subsequently the effects of new attractions on visitor numbers were isolated.

Findings indicate that all new attractions opened at Park D during the research period have had a positive long‐term influence on attendance. This positive influence lasted for no more than two years. No significant short‐term influence was found. There were significant differences in effect between new attractions which could not yet be explained.

The research by design only takes into account the economic effects of new attractions and disregards all environmental and socio‐cultural effects. Even though the research provides an accurate approximation of the effects of new attractions on attendance, this effect should, according to the author, not be perceived as a stand‐alone effect yet as a part of a complex system. A situational approach taking into account several other situational as well as qualitative factors would do the complex reality more justice than a, even though effective, simplified and general approach.

Industry operators can now use the econometric model presented in this paper to determine the effects of new attractions on their theme park's attendance and use this knowledge to further fine‐tune their investment policy.

The paper presents the first econometric model successful at isolating and quantifying a new attraction's effect on theme park attendance and can thus be a valuable tool in perfecting one's investment policy. The paper furthermore includes a brief introduction to a situational approach of determining a new attraction's effects on theme park performance.

A semiparametric stochastic frontier model is proposed for panel data, incorporating several flexible features. First, a constant elasticity of substitution (CES) production frontier is considered without log-transformation to prevent induced non-negligible estimation bias. Second, the model flexibility is improved via semiparameterization, where the technology is an unknown function of a set of environment variables. The technology function accounts for latent heterogeneity across individual units, which can be freely correlated with inputs, environment variables, and/or inefficiency determinants. Furthermore, the technology function incorporates a single-index structure to circumvent the curse of dimensionality. Third, distributional assumptions are eschewed on both stochastic noise and inefficiency for model identification. Instead, only the conditional mean of the inefficiency is assumed, which depends on related determinants with a wide range of choice, via a positive parametric function. As a result, technical efficiency is constructed without relying on an assumed distribution on composite error. The model provides flexible structures on both the production frontier and inefficiency, thereby alleviating the risk of model misspecification in production and efficiency analysis. The estimator involves a series based nonlinear least squares estimation for the unknown parameters and a kernel based local estimation for the technology function. Promising finite-sample performance is demonstrated through simulations, and the model is applied to investigate productive efficiency among OECD countries from 1970–2019.

We provide a new characterization of the equality of two positive-definite matrices A and B, and we use this to propose several new computationally convenient statistical tests for the equality of two unknown positive-definite matrices. Our primary focus is on testing the information matrix equality (e.g. White, 1982, 1994). We characterize the asymptotic behavior of our new trace-determinant information matrix test statistics under the null and the alternative and investigate their finite-sample performance for a variety of models: linear regression, exponential duration, probit, and Tobit. The parametric bootstrap suggested by Horowitz (1994) delivers critical values that provide admirable level behavior, even in samples as small as n = 50. Our new tests often have better power than the parametric-bootstrap version of the traditional IMT; when they do not, they nevertheless perform respectably.