Explaining and Forecasting Online Auction Prices and Their Dynamics Using Functional Data Analysis

Online auctions have become increasingly popular in recent years, and as a consequence there is a growing body of empirical research on this topic. Most of that research treats data from online auctions as cross-sectional, and consequently ignores the changing dynamics that occur during an auction. In this article we take a different look at online auctions and propose to study an auction's price evolution and associated price dynamics. Specifically, we develop a dynamic forecasting system to predict the price of an ongoing auction. By dynamic, we mean that the model can predict the price of an auction “in progress” and can update its prediction based on newly arriving information. Forecasting price in online auctions is challenging because traditional forecasting methods cannot adequately account for two features of online auction data: (1) the unequal spacing of bids and (2) the changing dynamics of price and bidding throughout the auction. Our dynamic forecasting model accounts for these special features by using modern functional data analysis techniques. Specifically, we estimate an auction's price velocity and acceleration and use these dynamics, together with other auction-related information, to develop a dynamic functional forecasting model. We also use the functional context to systematically describe the empirical regularities of auction dynamics. We apply our method to a novel set of Harry Potter and Microsoft Xbox data and show that our forecasting model outperforms traditional methods.     

网上拍卖竞买者出价水平的动态演变模式研究

网上拍卖是将传统拍卖与网络相结合的一种新商务模式,是对资源进行有效配置的一种市场机制。尽管有关参与者行为的研究是网上拍卖中的一个重要论题,但是国际上鲜有文献从统计视角对竞买者出价水平的动态演变模式及其变异性进行研究。本文利用函数性数据分析方法及基于MatLab编写的计算程序,对从eBay网站收集到的27个拍卖子类的出价数据进行了分析,结果显示竞买者出价水平的动态演变呈现“c”形模式且其形状随 拍卖的不同特征而变化,“c”形模式变异的两个主要方式是“前期变化”和“后期变化”,其显著变异的时段是拍卖的早期阶段。本文为网上拍卖问题的实证研究引入了新方法并提供了技术支持,所得结论丰富和发展了现有相关研究文献的结论。     

Assessing the use of sample selection models in the estimation of fertility postponement effects

Several studies have shown that at the individual level there exists a negative relationship between age at first birth and completed fertility. Using twin data in order to control for unobserved heterogeneity as possible source of bias, Kohler et al. (2001) showed the significant presence of such "postponement effect" at the micro level. In this paper, we apply sample selection models, where selection is based on having or not having had a first birth at all, to estimate the impact of postponing first births on subsequent fertility for four European nations, three of which have now lowest-low fertility levels. We use data from a set of comparative surveys (Fertility and Family Surveys), and we apply sample selection models on the logarithm of total fertility and on the progression to the second birth. Our results show that postponement effects are only very slightly affected by sample selection biases, so that sample selection models do not improve significantly the results of standard regression techniques on selected samples. Our results confirm that the postponement effect is higher in countries with lowest-low fertility levels.     

消费者在C2C交易中的信任模型与数据检验

为了探究个体消费者怎样在C2C交易中形成对个体卖方的信任,提出了消费者的信任结构方程模型,并通过情景泛义模拟实验采集的数据进行检验。文章得出：消费者的感知网站质量是最主要因素,信任机制至关重要,C2C平台市场比个体卖方作用更大,声誉的影响强于规模,买卖方的交互比较关键等结论。     

HOW WELL DO SELECTION MODELS PERFORM? ASSESSING THE ACURACY OF ART AUCTION PRE-SALE ESTIMATES

Art auction catalogs provide a pre-sale prediction interval for the price each item is expected to fetch. When the owner consigns art work to the auction house, a reserve price is agreed upon, which is not announced to the bidders. If the highest bid does not reach it, the item is brought in. Since only the prices of the sold items are published, analysts only have a biased sample to examine due to the selective sale process. Relying on the published data leads to underestimating the forecast error of the pre-sale estimates. However, we were able to obtain several art auction catalogs with the highest bids for the unsold items as well as those of the sold items. With these data we were able to evaluate the accuracy of the predictions of the sale prices or highest bids for all item obtained from the original Heckman selection model that assumed normal error distributions as well as those derived from an alternative model using the t(2) distribution, which yielded a noticeably better fit to several sets of auction data. The measures of prediction accuracy are of more than academic interest as they are used by auction participants to guide their bidding or selling strategy, and similar appraisals are accepted by the US Internal Revenue Services to justify the deductions for charitable contributions donors make on their tax returns.     

Random-Time Aggregation in Partial Adjustment Models

Structural econometric auction models with explicit game-theoretic modeling of bidding strategies have been quite a challenge from a methodological perspective, especially within the common value framework. We develop a Bayesian analysis of the hierarchical Gaussian common value model with stochastic entry introduced by Bajari and Hortaçsu. A key component of our approach is an accurate and easily interpretable analytical approximation of the equilibrium bid function, resulting in a fast and numerically stable evaluation of the likelihood function. We extend the analysis to situations with positive valuations using a hierarchical gamma model. We use a Bayesian variable selection algorithm that simultaneously samples the posterior distribution of the model parameters and does inference on the choice of covariates. The methodology is applied to simulated data and to a newly collected dataset from eBay with bids and covariates from 1000 coin auctions. We demonstrate that the Bayesian algorithm is very efficient and that the approximation error in the bid function has virtually no effect on the model inference. Both models fit the data well, but the Gaussian model outperforms the gamma model in an out-of-sample forecasting evaluation of auction prices. This article has supplementary material online.     

Iterated Feasible Generalized Least-Squares Estimation of Augmented Dynamic Panel Data Models

This article provides the large sample distribution of the iterated feasible generalized least-squares (IFGLS) estimator of an augmented dynamic panel data model. The regressors in the model include lagged values of the dependent variable and may include other explanatory variables that, while exogenous with respect to the time-varying error component, may be correlated with an unobserved time-invariant component. The article compares the finite sample properties of the IFGLS estimator to that of GMM estimators using both simulated and real data and finds that the IFGLS estimator compares favorably.     

基于函数性数据方法的艺术品网上拍卖竞买者出价水平影响因素研究

在分析互联网艺术品拍卖中竞买者出价水平特有影响因素的基础上,运用函数性相平面图与线性回归方法,探究出价水平及各影响因素在整个拍卖期间的动态变化情况。结果表明,在拍卖的不同阶段,推动竞买者出价水平变化的影响因素各有不同,且作用大小与作用方向在整个拍卖期间不断变化。特别指出,拍卖次序在整个拍卖期间对出价水平具有正向影响,且作用程度随着拍卖的进行逐渐增强,即序号越大、越晚参与竞拍的艺术品的最终成交金额越大。     

Interregional Price Difference in the New Orleans Auctions Market for Slaves

Our article investigates the variation of winning bids in slave auctions held in New Orleans from 1804 to 1862. Specifically, we measure the variation in the price of slaves conditional on their geographical origin. Previous work using a regression framework ignored the auction mechanism used to sell slaves. This introduced a bias in the conditional mean of the winning bid because it depended on the number of bidders participating in the auction. Unfortunately, the number of bidders is unobserved by the econometrician.We adopt the standard framework of a symmetric independent private value auction and propose an estimation strategy to attempt to deal with this omitted variable bias. Our estimate of the mean number of bidders doubled from 1804 to 1862. We find the number of bidders had a significant positive effect on the average winning bid. An increase from 20 to 30 bidders in an auction raised the average winning bid by around 10%%. The price variation according to the geographical origin of slaves found in earlier work continues to persist after accounting for the omitted variable. We also find a new result that a considerable premium is paid for slaves originating from New Orleans. However, this price variation disappears once we account for regional productivity differences.     

Bayesian inference and prediction of the Rayleigh distribution based on ordered ranked set sampling

Based on ordered ranked set sample, Bayesian estimation of the model parameter as well as prediction of the unobserved data from Rayleigh distribution are studied. The Bayes estimates of the parameter involved are obtained using both squared error and asymmetric loss functions. The Bayesian prediction approach is considered for predicting the unobserved lifetimes based on a two-sample prediction problem. A real life dataset and simulation study are used to illustrate our procedures.     

A Weibull Regression Model with Gamma Frailties for Multivariate Survival Data

Frequently in the analysis of survival data, survival times within the same group are correlated due to unobserved co-variates. One way these co-variates can be included in the model is as frailties. These frailty random block effects generate dependency between the survival times of the individuals which are conditionally independent given the frailty. Using a conditional proportional hazards model, in conjunction with the frailty, a whole new family of models is introduced. By considering a gamma frailty model, often the issue is to find an appropriate model for the baseline hazard function. In this paper a flexible baseline hazard model based on a correlated prior process is proposed and is compared with a standard Weibull model. Several model diagnostics methods are developed and model comparison is made using recently developed Bayesian model selection criteria. The above methodologies are applied to the McGilchrist and Aisbett (1991) kidney infection data and the analysis is performed using Markov Chain Monte Carlo methods. This revised version was published online in July 2006 with corrections to the Cover Date.     

Two-Step Estimation of Incomplete Information Social Interaction Models With Sample Selection

ABSTRACT

This article considers linear social interaction models under incomplete information that allow for missing outcome data due to sample selection. For model estimation, assuming that each individual forms his/her belief about the other members’ outcomes based on rational expectations, we propose a two-step series nonlinear least squares estimator. Both the consistency and asymptotic normality of the estimator are established. As an empirical illustration, we apply the proposed model and method to National Longitudinal Study of Adolescent Health (Add Health) data to examine the impacts of friendship interactions on adolescents’ academic achievements. We provide empirical evidence that the interaction effects are important determinants of grade point average and that controlling for sample selection bias has certain impacts on the estimation results. Supplementary materials for this article are available online.     

Common threshold in quantile regressions with an application to pricing for reputation

The paper develops a systematic estimation and inference procedure for quantile regression models where there may exist a common threshold effect across different quantile indices. We first propose a sup-Wald test for the existence of a threshold effect, and then study the asymptotic properties of the estimators in a threshold quantile regression model under the shrinking threshold effect framework. We consider several tests for the presence of a common threshold value across different quantile indices and obtain their limiting distributions. We apply our methodology to study the pricing strategy for reputation through the use of a data set from Taobao.com. In our economic model, an online seller maximizes the sum of the profit from current sales and the possible future gain from a targeted higher reputation level. We show that the model can predict a jump in optimal pricing behavior, which is considered as “reputation effect” in this paper. The use of threshold quantile regression model allows us to identify and explore the reputation effect and its heterogeneity in data. We find both reputation effects and common thresholds for a range of quantile indices in seller’s pricing strategy in our application.     

Bayesian comparison of private and common values in structural second-price auctions

Private and common values (CVs) are the two main competing valuation models in auction theory and empirical work. In the framework of second-price auctions, we compare the empirical performance of the independent private value (IPV) model to the CV model on a number of different dimensions, both on real data from eBay coin auctions and on simulated data. Both models fit the eBay data well with a slight edge for the CV model. However, the differences between the fit of the models seem to depend to some extent on the complexity of the models. According to log predictive score the IPV model predicts auction prices slightly better in most auctions, while the more robust CV model is much better at predicting auction prices in more unusual auctions. In terms of posterior odds, the CV model is clearly more supported by the eBay data.     

Flexible Bivariate Count Data Regression Models

The article develops a semiparametric estimation method for the bivariate count data regression model. We develop a series expansion approach in which dependence between count variables is introduced by means of stochastically related unobserved heterogeneity components, and in which, unlike existing commonly used models, positive as well as negative correlations are allowed. Extensions that accommodate excess zeros, censored data, and multivariate generalizations are also given. Monte Carlo experiments and an empirical application to tobacco use confirms that the model performs well relative to existing bivariate models, in terms of various statistical criteria and in capturing the range of correlation among dependent variables. This article has supplementary materials online.     

Multistage sampling for latent variable models

I consider the design of multistage sampling schemes for epidemiologic studies involving latent variable models, with surrogate measurements of the latent variables on a subset of subjects. Such models arise in various situations: when detailed exposure measurements are combined with variables that can be used to assign exposures to unmeasured subjects; when biomarkers are obtained to assess an unobserved pathophysiologic process; or when additional information is to be obtained on confounding or modifying variables. In such situations, it may be possible to stratify the subsample on data available for all subjects in the main study, such as outcomes, exposure predictors, or geographic locations. Three circumstances where analytic calculations of the optimal design are possible are considered: (i) when all variables are binary; (ii) when all are normally distributed; and (iii) when the latent variable and its measurement are normally distributed, but the outcome is binary. In each of these cases, it is often possible to considerably improve the cost efficiency of the design by appropriate selection of the sampling fractions. More complex situations arise when the data are spatially distributed: the spatial correlation can be exploited to improve exposure assignment for unmeasured locations using available measurements on neighboring locations; some approaches for informative selection of the measurement sample using location and/or exposure predictor data are considered.     

Inference for the generalized Rayleigh distribution based on progressively censored data

In this paper, and based on a progressive type-II censored sample from the generalized Rayleigh (GR) distribution, we consider the problem of estimating the model parameters and predicting the unobserved removed data. Maximum likelihood and Bayesian approaches are used to estimate the scale and shape parameters. The Gibbs and Metropolis samplers are used to predict the life lengths of the removed units in multiple stages of the progressively censored sample. Artificial and real data analyses have been performed for illustrative purposes.     

Regression spline bivariate probit models: A practical approach to testing for exogeneity

Bivariate probit models can deal with a problem usually known as endogeneity. This issue is likely to arise in observational studies when confounders are unobserved. We are concerned with testing the hypothesis of exogeneity (or absence of endogeneity) when using regression spline recursive and sample selection bivariate probit models. Likelihood ratio and gradient tests are discussed in this context and their empirical properties investigated and compared with those of the Lagrange multiplier and Wald tests through a Monte Carlo study. The tests are illustrated using two datasets in which the hypothesis of exogeneity needs to be tested.     

Modeling Employment Dynamics With State Dependence and Unobserved Heterogeneity

This study extends existing work on the dynamics of labor force participation by distinguishing between full-time and part-time employment and by allowing unobserved heterogeneity in the effects of previous employment outcomes, children and education on labor supply behavior. In addition, unobserved heterogeneity may feature autocorrelation and correlated random effects. The results reveal significant variation in the effects of children and education on labor supply behavior. Moreover, the omission of random coefficients and autocorrelation biases estimates of state dependencies. On average, temporary shocks that increase the rate of part-time employment lead subsequently to lower rates of nonemployment than do shocks that temporarily increase the rate of full-time work. The article has additional online supplementary material.     

New HEAVY Models for Fat-Tailed Realized Covariances and Returns

ABSTRACT

We develop a new score-driven model for the joint dynamics of fat-tailed realized covariance matrix observations and daily returns. The score dynamics for the unobserved true covariance matrix are robust to outliers and incidental large observations in both types of data by assuming a matrix-F distribution for the realized covariance measures and a multivariate Student's t distribution for the daily returns. The filter for the unknown covariance matrix has a computationally efficient matrix formulation, which proves beneficial for estimation and simulation purposes. We formulate parameter restrictions for stationarity and positive definiteness. Our simulation study shows that the new model is able to deal with high-dimensional settings (50 or more) and captures unobserved volatility dynamics even if the model is misspecified. We provide an empirical application to daily equity returns and realized covariance matrices up to 30 dimensions. The model statistically and economically outperforms competing multivariate volatility models out-of-sample. Supplementary materials for this article are available online.