Reduced-Form Versus Structural Models of Water Demand Under Nonlinear Prices

Increasing-block prices are common in markets for water, cellular phone service, and retail electricity. This study estimates demand models under block prices and conducts a Monte Carlo experiment to test the small-sample bias of structural and instrumental variables (IV) estimators. We estimate the price and income elasticity of water demand under increasing-block prices using a structural discrete/continuous choice (DCC) model, as well as random effects and IV. Elasticity estimates are sensitive to the modeling framework. The Monte Carlo experiment suggests that IV and DCC models estimate both price and income elasticity with bias, with no clear best choice among estimators.     

非线性定价有效吗

非线性定价存在于日常生活的方方面面,如阶梯电、水、气价格以及累进税率、通话套餐等。然而,价格信号的复杂性,使得消费者常常并未基于边际价格做出经济决策,关于非线性定价对于需求是否存在抑制的争论亦是此起彼伏。有鉴于此,本文基于Ito（2014）所提模型,利用广东省2010-2013年间各城市阶梯水价在时间维度和横截面维度的变异性以及微观住户月度用水消费数据,对消费者认知价格进行了甄别,并指出既往研究存在的识别问题。实证结果显示,住户当月消费基本是对上月平均价格而非边际价格或者期望边际价格做出反应,弹性约为-0.24。这说明,阶梯水价并未如设计初衷那样,通过跳跃性的价格激励机制降低住户用水需求,而是通过提高平均价格实现了对于住户用水的抑制。本文对于税率设计以及其他能源价格、通信套餐定价也有一定启发意义。     

非线性定价、家庭人口特征和收入再分配效应调整

本文以分时阶梯定价为例,在人口老龄化及生育政策逐渐放宽的背景下,通过建立结构计量模型,实证分析了引入家庭人口特征后,非线性定价对收入再分配效应这一政策目标的影响。通过构建引入家庭人口特征的二次近乎理想需求（QUAIDS）函数,基于相对等价补偿方法建立收入再分配效应调整的测度模型。估计了为保持相同效用增加家庭不同类型的人口需要增加的电费补偿率及其金额。研究结论表明,引入家庭人口特征后收入再分配效应得到了强化;家庭人口特征对消费者行为选择有显著影响;不同人口规模的家庭的电费补贴结构存在明显差异;动态分析显示,随着预算水平的提高,家庭人口特征对收入再分配效应的影响在减小。     

Exact Estimation of Demand Functions under Block-Rate Pricing

This article proposes an exact estimation of demand functions under block-rate pricing by focusing on increasing block-rate pricing. This is the first study that explicitly considers the separability condition which has been ignored in previous literature. Under this pricing structure, the price changes when consumption exceeds a certain threshold and the consumer faces a utility maximization problem subject to a piecewise-linear budget constraint. Solving this maximization problem leads to a statistical model in which model parameters are strongly restricted by the separability condition. In this article, by taking a hierarchical Bayesian approach, we implement a Markov chain Monte Carlo simulation to properly estimate the demand function. We find, however, that the convergence of the distribution of simulated samples to the posterior distribution is slow, requiring an additional scale transformation step for parameters to the Gibbs sampler. These proposed methods are then applied to estimate the Japanese residential water demand function.     

Exact testing in multivariate regression

An F statistic due to Rao (1951,1973) tests uniform mixed linear restrictions in the multivariateregression model. In combination with a generalization of the Bera-Evans-Savin exact functional relationship between the W, LR, and LM statistics, Rao's F serves to unify a number of exact test procedures commonly applied in disparate empirical literatures. Examples in demand analysis and asset pricing are provided. The availability of exact tests of restrictions in certain nonlinear models when the model is linear under the null, originally explored by Milliken-Graybill (1970), is extended to multivariate regression. Generalized RESET, J-, and Hausman-Wu tests are resented. As an extension of Dufour (1989), bounds tests exist for nonlinear and inequality restrictions. Applications include conservative bound tests for symmetry or negativity of the substitution matrix in demand systems.     

西安市天然气阶梯价格城市家庭门槛消费量的估计

以西安市为例,通过分层随机抽样获取样本,对家庭天然气阶梯定价初始档的消费量及决定因素进行分析。通过调研发现,在燃气灶、燃气热水器和壁挂锅炉三个主要用能终端中,壁挂锅炉家庭和非壁挂锅炉家庭的消费特征显著不同。运用He和Reiner的能源消费门槛值(Threshold)模型,对这两类家庭样本进行估计,得到壁挂锅炉和非壁挂锅炉家庭天然气阶梯价格门槛值消费量分别为898.07立方米/年和182.74立方米/年,证实西安市实施中的天然气阶梯价格划定的门槛值(一档线)过高,不能实现高收入家庭交叉补贴低收入家庭的收入再分配效果。     

基于连续混合正态分布的期货定价偏差研究

挖掘期货理论价格和实际价格之间的关系有助于提高期货市场定价效率、发挥期货价格发现功能。基于持有成本定价模型计算期货定价偏差,利用连续混合正态分布模型对定价偏差的分布进行拟合,先采用基于牛顿迭代的极大似然估计法对未知参数进行估计,再进一步利用模拟退火算法对牛顿迭代的结果进行优化。结果发现,模拟退火算法可以有效提高估计精度,连续混合正态分布模型能够更好地拟合期货定价偏差分布。     

潜在流动性约束与城镇家庭消费

笔者认为,收入不平等与家庭消费的关系与信贷约束程度以及家庭社会地位偏好有关。住房是典型的地位性商品,收入差距扩大时,人们为了维持或提高现有的相对地位会努力改善居住条件,住房攀比最终会导致全社会住房面积标准提高和房价上涨。在信贷缺乏的环境中,购房标准提高和房价上涨意味着家庭未来遭遇流动性约束的风险加大,为此,家庭在增加购房预算的同时会抑制日常消费。利用2010年、2012年和2014年的微观跟踪调查数据所做的实证分析支持了我们的观点：（1）周围人群的住房面积的扩大,会促使家庭选择购买更大的房子。并且,攀比效应对住房需求的刺激作用明显大于房价上涨对住房需求的抑制作用。（2）家庭平均住房面积扩大和房价上涨都与收入不平等引发的住房攀比有关。（3）收入不平等对城镇家庭消费皆有拉动作用和抑制作用。（4）潜在流动性约束对家庭消费的抑制作用与家庭地位等级的高低有关。     

基于出口国偏好的天然气进出口均衡价格策略

天然气进口价格与国内销售价格是影响进口天然气获利的重要因素。将出口国偏好引入到天然气出口国的目标函数中,假设进口国的目标为谋求合理的国内天然气定价且使进口利润最大化,由此构建天然气出口国与进口国的主从博弈模型,并利用微分对策理论求得均衡情形下的天然气出口价格与进口国国内销售价格,结果表明:出口国对进口国具有较强的正偏好,可使进口国国内天然气价格降低、天然气销售利润和消费者剩余增加、价格趋于均衡的时间延长;进口国天然气市场需求对替代能源价格的交叉弹性较大时,天然气价格将以较快的速度趋于更低的均衡;进口国天然气价格相对于替代能源价格调整的速度较快时,天然气价格将以较慢的速度趋于更低的均衡,这两种情形都会提高进口国消费者剩余,但会使进口国天然气企业获利减少。进口国应该与出口国建立积极稳定的正偏好关系,这将有利其提升进口天然气的利润以及稳定国内市场。     

Estimation of systems of equations subject to curvature constraints

Two computationally manageable estimation procedures for maintaining curvature constraints are compared. Using an efficient nonlinear optimizing algorithm, the well-known Cholesky factorization is compared with the eigenvalue decomposition method for estimating a system of input demand and output supply equations. Statistical tests are provided. The Cholesky factorization is superior when efficient optimizers are used. The eigenvalue decomposition may become a better choice when the user is limited to less efficient algorithms.     

A multifactor transformed diffusion model with applications to VIX and VIX futures

Abstract

Transformed diffusions (TDs) have become increasingly popular in financial modeling for their model flexibility and tractability. While existing TD models are predominately one-factor models, empirical evidence often prefers models with multiple factors. We propose a novel distribution-driven nonlinear multifactor TD model with latent components. Our model is a transformation of a underlying multivariate Ornstein–Uhlenbeck (MVOU) process, where the transformation function is endogenously specified by a flexible parametric stationary distribution of the observed variable. Computationally efficient exact likelihood inference can be implemented for our model using a modified Kalman filter algorithm and the transformed affine structure also allows us to price derivatives in semi-closed form. We compare the proposed multifactor model with existing TD models for modeling VIX and pricing VIX futures. Our results show that the proposed model outperforms all existing TD models both in the sample and out of the sample consistently across all categories and scenarios of our comparison.     

非对称信息与高频价格变动

高频价格运动对金融市场微观结构具有非常重要的意义。由于高频价格的离散性和不等距变化的特点使得对该类变量建模较为困难,而在理论与实证研究中通常是根据特定的研究目的建立相应的高频价格运动模型。故从金融市场微观结构信息不对称理论出发,结合中国纯限价订单市场的实际情况和对中国市场交易者行为的分析,建立高频价格运动和非对称信息的联合模型,并同时估计和模拟了非对称信息状态和高频价格运动的轨迹。研究发现,知情交易者的比率对交易价格与市场流动性均有显著影响。     

基于BP神经网络的S＆P500指数期权定价

期权定价理论源于影响期权价格的变量和期权价格之间的非线性关系,传统的Black-Scholes期权定价公式过于严格的假设削弱了该公式在现实中的适用性,使其在理论与应用上均存在缺陷。因此,能够以任意精度近似复杂非线性系统的神经网络运用于期权定价。分别利用BP神经网络和Black-Scholes期权定价公式对S＆P 500指数看跌期权进行定价,实证结果表明BP神经网络的定价结果要优于Black-Scholes定价公式。     

Generalized Method of Moments Estimation When a Parameter Is on a Boundary

This article establishes the asymptotic distributions of generalized method of moments (GMM) estimators when the true parameter lies on the boundary of the parameter space. The conditions allow the estimator objective function to be nonsmooth and to depend on preliminary estimators. The boundary of the parameter space may be curved and/or kinked. The article discusses three examples: (1) instrumental variables (IV) estimation of a regression model with nonlinear equality and/or inequality restrictions on the parameters; (2) method of simulated moments estimation of a multinomial discrete response model with some random coefficient variances equal to 0, some random effect variances equal to 0, or some measurement error variances equal to 0; and (3) semiparametric least squares estimation of a partially linear regression model with nonlinear equality and/or inequality restrictions on the parameters.     

Weighted Median of the Data in Solving Least Absolute Deviations Problems

We consider the weighted median problem for a given set of data and analyze its main properties. As an illustration, an efficient method for searching for a weighted Least Absolute Deviations (LAD)-line is given, which is used as the basis for solving various linear and nonlinear LAD-problems occurring in applications. Our method is illustrated by an example of hourly natural gas consumption forecast.     

Threshold selection in jump-discriminant filter for discretely observed jump processes

Threshold estimation is one of the useful techniques in the inference for jump-type stochastic processes from discrete observations. In this method, a jump-discriminant filter is used to infer the continuous part and the jump part separately. Although there are several choices for the filter, statistics constructed via filters are often sensitive to the choice. This paper presents some numerical procedures for selecting a suitable filter based on observations.     

Efficient Monte Carlo option pricing under CEV model

One of the financial model with nonconstant volatiltiy is the constant elasticity of varinace model, or CEV model for short. The CEV model is an altrnative to the Black–Scholes model of stock price movements. In this diffusion process, unlike the Black–Scholes model, the volatility is a function of the stock price and involves two parameters. In this article, we propose an efficient Monte-Carlo algorithm for pricing arithmetic Asian option under CEV model. In an earlier work by Mehrdoust, an efficient Monte Carlo simulation algorithm for pricing arithmetic Asian options under Black–Scholes model is proposed. The proposed algorithm has proved extremely successful in decreasing the standard deviation and the error of simulation in pricing of the arithmetic Asian options. In this article, we find that the proposed algorithm under the geometric Brownian motion assumption in the Black–Scholes model can effectively apply for pricing arithmetic Asian options when the stock price process follows the CEV model. Numerical experiments show that our algorithm gives very accurate results.     

Nonresponse Assessment of a Consumer Price Index

A household budget survey often suffers from a high nonresponse rate and a selective response. The bias that may be introduced in the estimation of budget shares because of this nonresponse can affect the estimate of a consumer price index, which is a weighted sum of partial price index numbers (weighted with the estimated budget shares). The bias is especially important when related to the standard error of the estimate. Because of the impossibility of subsampling nonrespondents to the budget survey, no exact information on the bias can be obtained. To evaluate the nonresponse bias, bounds for this bias are calculated using linear programming methods for several assumptions. The impact on a price index of a high nonresponse rate among people with a high income can also be assessed by using the elasticity with respect to total expenditure. Attention is also given to the possible nonresponse bias in a time series of price index numbers. The possible nonresponse bias is much larger than the standard error of the estimate.     

Discrete associated kernels method and extensions

Discrete kernel estimation of a probability mass function (p.m.f.), often mentioned in the literature, has been far less investigated in comparison with continuous kernel estimation of a probability density function (p.d.f.). In this paper, we are concerned with a general methodology of discrete kernels for smoothing a p.m.f. f. We give a basic of mathematical tools for further investigations. First, we point out a generalizable notion of discrete associated kernel which is defined at each point of the support of f and built from any parametric discrete probability distribution. Then, some properties of the corresponding estimators are shown, in particular pointwise and global (asymptotical) properties. Other discrete kernels are constructed from usual discrete probability distributions such as Poisson, binomial and negative binomial. For small samples sizes, underdispersed discrete kernel estimators are more interesting than the empirical estimator; thus, an importance of discrete kernels is illustrated. The choice of smoothing bandwidth is classically investigated according to cross-validation and, novelly, to excess of zeros methods. Finally, a unification way of this method concerning the general probability function is discussed.     

A candidate-set-free algorithm for generating D-optimal split-plot designs

Summary.  We introduce a new method for generating optimal split-plot designs. These designs are optimal in the sense that they are efficient for estimating the fixed effects of the statistical model that is appropriate given the split-plot design structure. One advantage of the method is that it does not require the prior specification of a candidate set. This makes the production of split-plot designs computationally feasible in situations where the candidate set is too large to be tractable. The method allows for flexible choice of the sample size and supports inclusion of both continuous and categorical factors. The model can be any linear regression model and may include arbitrary polynomial terms in the continuous factors and interaction terms of any order. We demonstrate the usefulness of this flexibility with a 100-run polypropylene experiment involving 11 factors where we found a design that is substantially more efficient than designs that are produced by using other approaches.