Root n consistent and optimal density estimators for moving average processes

Abstract.  The marginal density of a first order moving average process can be written as a convolution of two innovation densities. Saavedra & Cao [Can. J. Statist. (2000), 28, 799] propose to estimate the marginal density by plugging in kernel density estimators for the innovation densities, based on estimated innovations. They obtain that for an appropriate choice of bandwidth the variance of their estimator decreases at the rate 1/ n . Their estimator can be interpreted as a specific U -statistic. We suggest a slightly simplified U -statistic as estimator of the marginal density, prove that it is asymptotically normal at the same rate, and describe the asymptotic variance explicitly. We show that the estimator is asymptotically efficient if no structural assumptions are made on the innovation density. For innovation densities known to have mean zero or to be symmetric, we describe improvements of our estimator which are again asymptotically efficient.     

Survey nonresponse and the distribution of income

The paper examines the distributional implications of selective compliance in sample surveys, whereby households with different incomes are not equally likely to participate. Poverty and inequality measurement implications are discussed for monotonically decreasing and inverted-U compliance-income relationships. We demonstrate that the latent income effect on the probability of compliance can be estimated from information on response rates across geographic areas. On implementing the method on the Current Population Survey for the U.S. we find that the compliance probability falls monotonically as income rises. Correcting for nonresponse appreciably increases mean income and inequality, but has only a small impact on poverty incidence up to poverty lines common in the U.S. Martin Ravallion: Corresponding author.     

Will oil markets tighten again? A survey of policies to manage possible oil supply disruptions

The effects of an oil supply disruption on the U.S. economy are analyzed along with the various policy options. Part of the analysis is based on a computerized model of the U.S. economy and the world oil market. Micro as well as macroeconomic issues are considered. The paper argues against the use of price controls and allocations and also against a disruption tariff used as a stand-alone measure. It advocates the use of some stabilizing macroeconomic measures and a temporary producer tax similar to the windfall profits tax.     

The use of canonical analysis

The first part of this non-technical review of canonical analysis is concerned with the principle, the data requirements, the interpretation, the evaluation and the application in consumer research of canonical analysis. In this context, concepts as canonical correlation, weights, loadings and scores are explained. Their interrelationships are discussed. Then the characteristics of specific forms of canonical analysis: canonical correlation, canonical regression, redundancy analysis and partial canonical analysis are discussed. Their different application properties are emphasized. The last part consists of an application of canonical correlation analysis for brand positioning. Here the relationship with discriminant analysis is illustrated. Furthermore the usage of canonical analysis for optimal scaling purposes is illustrated for the same example.     

Abstractions on steroids: A critical realist approach to computer simulations

Computer simulations are increasingly used within various fields of the social sciences, including analytical sociology and computational social science. However, the method has yet to fully find its place within critical realism, generally regarded as reductionist and methodological individualist and thus inadequate to the task of grasping the full and enigmatic complexity of social life. This article contributes to the discussion by suggesting an alternative approach to computer simulations in the social realm. Instead of representing reality, simulations are seen as a way of boosting abstraction by enabling us to isolate and study the effects of emergent mechanisms. The need for such tools is growing more urgent in an age characterized by rapid change and global networks of causal interrelation. Hence there is a need not only for new tools to deal with causal complexity within critical realism, but also for a critical realist perspective to fill the meta‐theoretical vacuum on which the simulation approach is largely based. The approach developed here provides a challenge to the predominant ways in which simulations are utilized today, with increasingly sophisticated models aiming towards realistic representation on the basis of empirical data.     

The Great Recession and Welfare State Reform: Is Retrenchment Really the Only Game Left in Town?

By 2010, when the Greek sovereign debt crisis changed into an existential crisis of the euro, all developed democracies entered a phase in which they had to consolidate their budgets, typically implying a politics of austerity. The scholarly literature, as well as the popular press, suggests that – consequently – welfare retrenchment and cost containment became the only games left in town. In this article, we study the welfare state reform measures taken between 2010 and 2012 in four countries characteristic of mature welfare state regimes (liberal, UK; conservative, Germany; social democratic, Denmark; and hybrid, the Netherlands) to examine empirically whether austerity has indeed become the only item left on the policy menu. Our analysis reveals that retrenchment features prominently on the agenda everywhere, but nowhere by itself. While compensation for income loss is rare since 2010, this still happens. More unexpectedly, reforms in line with a social investment agenda (like expansion of child care or active labour market policies) are still being pursued in all our four cases.     

Estimating the error distribution function in semiparametric additive regression models

We consider semiparametric additive regression models with a linear parametric part and a nonparametric part, both involving multivariate covariates. For the nonparametric part we assume two models. In the first, the regression function is unspecified and smooth; in the second, the regression function is additive with smooth components. Depending on the model, the regression curve is estimated by suitable least squares methods. The resulting residual-based empirical distribution function is shown to differ from the error-based empirical distribution function by an additive expression, up to a uniformly negligible remainder term. This result implies a functional central limit theorem for the residual-based empirical distribution function. It is used to test for normal errors.     

Revenue Management with End‐of‐Period Discounts in the Presence of Customer Learning

Consider a firm that sells identical products over a series of selling periods (e.g., weekly all‐inclusive vacations at the same resort). To stimulate demand and enhance revenue, in some periods, the firm may choose to offer a part of its available inventory at a discount. As customers learn to expect such discounts, a fraction may wait rather than purchase at a regular price. A problem the firm faces is how to incorporate this waiting and learning into its revenue management decisions. To address this problem we summarize two types of learning behaviors and propose a general model that allows for both stochastic consumer demand and stochastic waiting. For the case with two customer classes, we develop a novel solution approach to the resulting dynamic program. We then examine two simplified models, where either the demand or the waiting behavior are deterministic, and present the solution in a closed form. We extend the model to incorporate three customer classes and discuss the effects of overselling the capacity and bumping customers. Through numerical simulations we study the value of offering end‐of‐period deals optimally and analyze how this value changes under different consumer behavior and demand scenarios.     

Prediction in moving average processes

For the stationary invertible moving average process of order one with unknown innovation distribution F, we construct root-n   consistent plug-in estimators of conditional expectations E(h(_Xn+1)|_X1,…,_Xn)$E(h(X_{n+1})|X_1,\dots ,X_n)$. More specifically, we give weak conditions under which such estimators admit Bahadur-type representations, assuming some smoothness of h or of F. For fixed h it suffices that h   is locally of bounded variation and locally Lipschitz in _L2(F)$L_2(F)$, and that the convolution of h and F   is continuously differentiable. A uniform representation for the plug-in estimator of the conditional distribution function P(_Xn+1?·|_X1,…,_Xn)$P(X_{n+1}?·|X_1,\dots ,X_n)$ holds if F has a uniformly continuous density. For a smoothed version of our estimator, the Bahadur representation holds uniformly over each class of functions h that have an appropriate envelope and whose shifts are F-Donsker, assuming some smoothness of F. The proofs use empirical process arguments.