W.F. Sheppard's Smoothing Method: A Precursor to Local Polynomial Regression

W.F. Sheppard has been much overlooked in the history of statistics although his work produced significant contributions. He developed a polynomial smoothing method and corrections of moment estimates for grouped data as well as extensive normal probability tables that have been widely used since the 20th century. Sheppard presented his smoothing method for actuaries in a series of publications during the early 20th century. Population data consist of irregularities, and some adjustment or smoothing of the data is often necessary. Simple techniques, such as Spencer's summation formulae involving arithmetic operations and moving averages, were commonly practised by actuaries to smooth out equally spaced data. Sheppard's method, however, is a polynomial smoothing method based on central differences. We will show how Sheppard's smoothing method was a significant milestone in the development of smoothing techniques and a precursor to local polynomial regression.     

Union security rights at the polls: A call for modeling right-to-work voting

From 1944 to 1986, 19 states held 27 referendums on right-to-work legislation, with 22.5 million people voting on the proposals. Despite its prominence as a public issue, most research on right-to-work laws focuses on their industrial relations impacts, and not on employees’ individual rights to refrain from joining unions or those same employees’ responsibilities to support their bargaining unit representative. Nor has there been any research on what citizen groups determine those rights and responsibilities in a right-to-work referendum. This study explores a potential operational model of anti-right-to-work voting with a multiple regression analysis of Missouri’s 1978 right-to-work election results, and hopes to serve as a stimulus to additional research on these particular dimensions of the right-to-work issue.     

Homevoters vs. leasevoters: A spatial analysis of airport effects

We use a public referendum on a new aviation concept in Berlin, Germany, as a natural experiment to analyze how the interaction of tenure and capitalization effects influences the outcome of direct democracy processes. We distinguish between homevoters, i.e., voters who are homeowners, and leasevoters, i.e., voters who lease their homes. We expect that homevoters would be more likely to support initiatives that positively affect the amenity value of a neighborhood because some of the related benefits of leasevoters are neutralized by adjustments in market rents. Likewise, homevoters would be more likely to oppose initiatives that negatively affect the amenity value of a neighborhood. Our empirical results are consistent with these expectations, implying that public votes on local public goods do not necessarily reflect the spatial distribution of welfare effects in mixed-tenure environments.     

信息不对称条件下有效的公共决策模式探析

根据信息经济学的不对称理论和博弈论,公共决策实质上就是非同质性决策参与者的多重利益博弈过程。公共决策模式包括精英决断型、冲突斡旋型、专家建议型、代表协商型和全民公决型五种类型。公共决策产出实质上就是通过这五种模式做出的关系调整与利益平衡。     

Forecasting correlated time series with exponential smoothing models

This paper presents the Bayesian analysis of a general multivariate exponential smoothing model that allows us to forecast time series jointly, subject to correlated random disturbances. The general multivariate model, which can be formulated as a seemingly unrelated regression model, includes the previously studied homogeneous multivariate Holt-Winters’ model as a special case when all of the univariate series share a common structure. MCMC simulation techniques are required in order to approach the non-analytically tractable posterior distribution of the model parameters. The predictive distribution is then estimated using Monte Carlo integration. A Bayesian model selection criterion is introduced into the forecasting scheme for selecting the most adequate multivariate model for describing the behaviour of the time series under study. The forecasting performance of this procedure is tested using some real examples.     

Edgeworth approximations for semiparametric instrumental variable estimators and test statistics

We establish the validity of higher order asymptotic expansions to the distribution of a version of the nonlinear semiparametric instrumental variable estimator considered in Newey (Econometrica 58 (1990) 809) as well as to the distribution of a Wald statistic derived from it. We employ local polynomial smoothing with variable bandwidth, which includes local linear, kernel, and (a version of) nearest neighbor estimates as special cases. Our expansions are valid to order n^−2ε for some 0<ε<1/2, where ε depends on the smoothness and dimensionality of the data distribution and on the order of the polynomial chosen by the practitioner. We use the expansions to define optimal bandwidth selection methods for both estimation and testing problems and apply our methods to simulated data.     

Functional coefficient regression models with time trend

We consider the problem of estimating a varying coefficient regression model when regressors include a time trend. We show that the commonly used local constant kernel estimation method leads to an inconsistent estimation result, while a local polynomial estimator yields a consistent estimation result. We establish the asymptotic normality result for the proposed estimator. We also provide asymptotic analysis of the data-driven (least squares cross validation) method of selecting the smoothing parameters. In addition, we consider a partially linear time trend model and establish the asymptotic distribution of our proposed estimator. Two test statistics are proposed to test the null hypotheses of a linear and of a partially linear time trend models. Simulations are reported to examine the finite sample performances of the proposed estimators and the test statistics.     

More than just a special case: The value of double bind theory for bringing light into the dark side of organizational paradoxes

In their recently published article, Berti and Simpson introduced a comprehensive framework for the systematic analysis of the dark side of organizational paradoxes. While I follow the authors in connecting the analysis of this dark side to types of organizational power, I am concerned with the narrow view on double binds as an expression of coercions only. This narrow view not only runs counter to the basic idea of double bind theory, but also neglects or even denies transition dynamics between different types of organizational double binds. To address these issues, I develop an alternative framework for the analysis of the dark side of organizational power that considers double binds in a broader and more fruitful way. This framework not only facilitates the analysis of transition dynamics between types of double binds, but also reveals practical strategies for mitigating paradoxes and disentangling them from implicit structures that are in the blind spot of Berti and Simpson's framework.     

STATED PREFERENCES FOR PUBLIC SERVICES: A CLASSIFICATION AND SURVEY OF APPROACHES

The wider range of stated preference approaches to value public goods has not been systematically reviewed in recent years. The objective of this paper is to provide an overview of this literature and to evaluate the strengths and limitations of alternative approaches. Since the public referendum has served as a ‘blueprint’ for survey design, two key dimensions by which many surveys differ from the public referendum are used for a simple classification of approaches. This yields eleven approaches, including different variants of micro-based demand surveys, referendum surveys, budget allocation surveys and contingent valuation surveys. Their evaluation in terms of the preference information they produce and the assumptions they require suggests there is no single preferred approach. Instead, each approach has its characteristic profile of strengths and limitations which follow from how it strikes the balance between the conflicting goals of measuring entire willingness-to-pay distributions and presenting manageable, credible and incentive compatible questions. Ultimately, judgments about the suitability of alternative approaches for specific objectives should rely on empirical evidence. Progress in the field could greatly benefit from a routine implementation of powerful experimental validity tests in applied work.     

Three Sides of Smoothing: Categorical Data Smoothing, Nonparametric Regression, and Density Estimation

The past forty years have seen a great deal of research into the construction and properties of nonparametric estimates of smooth functions. This research has focused primarily on two sides of the smoothing problem: nonparametric regression and density estimation. Theoretical results for these two situations are similar, and multivariate density estimation was an early justification for the Nadaraya-Watson kernel regression estimator.
A third, less well-explored, strand of applications of smoothing is to the estimation of probabilities in categorical data. In this paper the position of categorical data smoothing as a bridge between nonparametric regression and density estimation is explored. Nonparametric regression provides a paradigm for the construction of effective categorical smoothing estimates, and use of an appropriate likelihood function yields cell probability estimates with many desirable properties. Such estimates can be used to construct regression estimates when one or more of the categorical variables are viewed as response variables. They also lead naturally to the construction of well-behaved density estimates using local or penalized likelihood estimation, which can then be used in a regression context. Several real data sets are used to illustrate these points.     

Near unit root small open economies

The marginal utility of wealth in incomplete markets small open economy models follows a unit root process. I study the nonlinear properties of devices often used to remove the unit root and I find that they generate different dynamics when matching emerging markets. Models with endogenous discount factors reinforce consumption response to shocks and increase the countercyclicality of the trade balance to output ratio. Conversely, models with debt frictions ameliorate the responses of consumption and trade balance. Hence, to generate dynamics similar to those in emerging economies, the debt frictions need to be small, inducing a near unit root behavior in their Euler equations. This difference across models is hidden when matching developed economies because of consumption smoothing and the mild countercyclicality of the trade balance.     

Polynomial approximations in cross-sectional models

The time-series distributed lag techniques of econometrics can be usefully applied to cross-sectional, spatial and cross-section time-series situations. The application is perfectly natural in cross-section, time-series models when regression coefficients evolve systematically as the cross-section grouping variable changes. The evolution of such coefficients lends itself to polynomial approximation or more general smoothing restrictions. These ideas are not new, Gersovitz and McKinnon (1978) and Trivedi and Lee (1981) providing two of the earliest applications of cross-equation smoothing techniques. However, their applications were in the context of coefficient variation due to seasonal changes and this may account for the non-diffusion of these techniques. The approach here is illustrated in the context of age-specific household formation equations based on census data, using Almon polynomials when the regression coefficients vary systematically by age group. A second application is provided, using spatial data, explaining the incidence of crime, by region; using polynomial and geometric smoothing to model distance declining regional effects.     

人力资本与基础设施投资的动力学分析

本文将公共支出引入一个两部门城市化和内生增长模型,由模型导出的人力资本跨时转移条件方便我们分析经济的过渡动力学行为。数值解结果表明,在物质资本报酬递减的情形下,公共支出的部门间配置由经济过渡动力内在地确定和稳定;如果物质资本表现出某种程度的报酬递增,公共支出的部门间配置将表现出内在不稳定。动力学分析表明,公共支出与经济增长之间存在非线性关系,换言之,存在促进经济增长的最优税率或最优公共支出比例。     

Economic dynamics of reservoir sedimentation management: Optimal control with singularly perturbed equations of motion

We analyze the economic dynamics of reservoir sedimentation management using the hydrosuction-dredging sediment-removal system. System dynamics depend on two interdependent hydraulic processes evolving at different rates. The accumulation of water impounded in the reservoir evolves on a ‘fast’ time scale, while the loss of water storage capacity to trapped sediments evolves on a ‘slow’ time scale. We formulate a multidimensional optimal control problem with singularly perturbed equations of motion to accommodate the disparate time scales. We apply singular perturbation methods to approximate (via polynomial series expansion) a ‘slow’ manifold reducing multi-dimensional solution space to the single-dimensional subspace confining long-term dynamics.     

Measuring local health care system development for public policy purposes; an exploratory analysis of physicians and hospitals.

This paper attempts to measure local health care development for public policy purposes using a systems approach. The tools of multivariate analysis including principal components analysis and Guttman Scale techniques are used to construct indices of the development of local systems of medical specialists and of hospital facilities. The data measuring these phenomena were gathered for 243 United States Standard Metropolitan Statistical Areas and for a set of 300 Eastern U.S. Counties. These structural measures of system development were compared and contrasted to the usual aggregate ratio measures and found preferable. The public policy implication of this research are presented.     

Preferences of citizens for public expenditures on elementary and secondary education

This paper presents an empirical analysis of citizens' preferences for public elementary and secondary education expenditures. Survey data collected in conjunction with a school tax referendum and a multinomial probit random utility model are used to make inferences concerning the preference mappings of citizens. These estimated mappings, in turn, imply unique estimates of the demands of citizens for public education expenditures. Citizens' beliefs concerning whether expenditures are wisely spent and will affect school quality are seen to be important determinants of demand. The impact of citizens' perceptions of tax costs is also considered.     

Expolynomial smoothing of autocorrelated time series

Summary In the following, causal pattern buried in autocorrelated noise is considered. The causal pattern may be described by models such as trends, polynomial trajectories, growing sines. Based on a new criterion — called expolynomial — estimators of coefficients of a polynomial model are obtained. Characteristic functions of the estimators are derived and the first two moments calculated. Continuous time series are briefly studied to show similarities between discrete and continuous observations. Popular exponential smoothing is a special case of the expolynomial smoothing.     

Efficient estimation for error component seemingly unrelated nonparametric regression models

Multivariate panel data provides a unique opportunity in studying the joint evolution of multiple response variables over time. In this paper, we propose an error component seemingly unrelated nonparametric regression model to fit the multivariate panel data, which is more flexible than the traditional error component seemingly unrelated parametric regression. By applying the undersmoothing technique and taking both of the correlations within and among responses into account, we propose an efficient two-stage local polynomial estimation for the unknown functions. It is shown that the resulting estimators are asymptotically normal, and have the same biases as the standard local polynomial estimators, which are only based on the individual response, and smaller asymptotic variances. The performance of the proposed procedure is evaluated through a simulation study and a real data set.     

What drives the liquidity premium in the Chinese stock market?

This paper examines the dynamics of the liquidity premium in the Chinese stock market by adopting a multivariate decomposition approach to measure the individual contributions of various driving forces of the premium (such as firm size, idiosyncratic volatility, and market liquidity betas). By employing a wide range of liquidity measures, we show that liquidity premium is generally significant in the Chinese stock market. Furthermore, this premium is increasing in recent years starting from 2011; this observation is different from the United States market, in which the premium has declined over the years. Moreover, the multivariate decomposition approach highlights several asset pricing factors as the main driving forces of the premium. Based on the Amihud liquidity measure, the decomposition approach indicates that the size factor contributes 45–65% to the liquidity premium. However, the measure based on turnover suggests that idiosyncratic volatility accounts for at least 60% of the liquidity premium. In contrast, the global market liquidity beta does not significantly contribute to the premium. However, there is some evidence that the local market liquidity beta has become more significant in its impact on the premium during the period from 2011 to 2015. Our results imply that the findings on the liquidity premium in the Chinese stock market could be sensitive to the liquidity measure used and period of analysis.     

Nonparametric estimation of conditional distribution functions with longitudinal data and time-varying parametric models

Nonparametric estimation and inferences of conditional distribution functions with longitudinal data have important applications in biomedical studies. We propose in this paper an estimation approach based on time-varying parametric models. Our model assumes that the conditional distribution of the outcome variable at each given time point can be approximated by a parametric model, but the parameters are smooth functions of time. Our estimation is based on a two-step smoothing method, in which we first obtain the raw estimators of the conditional distribution functions at a set of disjoint time points, and then compute the final estimators at any time by smoothing the raw estimators. Asymptotic properties, including the asymptotic biases, variances and mean squared errors, are derived for the local polynomial smoothed estimators. Applicability of our two-step estimation method is demonstrated through a large epidemiological study of childhood growth and blood pressure. Finite sample properties of our procedures are investigated through simulation study.