Coexistence and segregation of two groups in a metropolitan area through externalities

This paper proposes to regard the population distributions of two groups in a metropolitan area as equilibrium solutions of systems of ordinary differential equations. This approach—an extension of the Miyao's single subarea model to a many subarea case—allows us to incorporate the effect of fiscal/pecuniary neighborhood externalities into the classic Alonso-Mills-Muth model. This paper investigates its three typical cases, and obtains one coexistent and two segregated solutions. Consideration on these cases leads to the conclusion that substantial neighborhood externalities other than simple tax redistribution exist between the groups in the United States. As by-products of this analysis, it is also shown that positive bid gradients and discontinuities of bid prices are realized under suitable conditions.     

Community income distributions in a metropolitan area

We extend de Bartolome and Ross [C.A.M. de Bartolome, S.L. Ross, Equilibrium with local governments and commuting: Income sorting vs. income mixing, Journal of Urban Economics 54 (2003) 1–20] to the case when the income distribution in the metropolitan area is a continuous distribution. In particular, we consider a circular central city surrounded by a suburban community. All households must commute to the metropolitan center and public service levels differ in the two jurisdictions. There is intra-jurisdictional and inter-jurisdictional capitalization. Our model has an equilibrium in which the income distributions of the central city and of the suburban community do overlap. Our finding contrasts with the traditional finding of Alonso–Mills–Muth-type models of spatial sorting and of Tiebout-type models of fiscal sorting, both of which have been shown to predict that the income distributions of the two communities do not overlap. In addition, the model explains the fixedness in jurisdictional boundaries.     

Stochastic volatility with leverage: Fast and efficient likelihood inference

This paper is concerned with the Bayesian analysis of stochastic volatility (SV) models with leverage. Specifically, the paper shows how the often used Kim et al. [1998. Stochastic volatility: likelihood inference and comparison with ARCH models. Review of Economic Studies 65, 361–393] method that was developed for SV models without leverage can be extended to models with leverage. The approach relies on the novel idea of approximating the joint distribution of the outcome and volatility innovations by a suitably constructed ten-component mixture of bivariate normal distributions. The resulting posterior distribution is summarized by MCMC methods and the small approximation error in working with the mixture approximation is corrected by a reweighting procedure. The overall procedure is fast and highly efficient. We illustrate the ideas on daily returns of the Tokyo Stock Price Index. Finally, extensions of the method are described for superposition models (where the log-volatility is made up of a linear combination of heterogenous and independent autoregressions) and heavy-tailed error distributions (student and log-normal).     

Über die Approximation von Wahrscheinlichkeitsverteilungen durch Grenzverteilungen

Zusammenfassung Der Fehler, der bei der Approximation einer Wahrscheinlichkeitsverteilung durch eine Grenzverteilung entsteht, wird mit Hilfe von Differential- (bzw. Differenzen-)gleichungen asymptotisch (bezüglich eines wachsenden Parameters) entwickelt. Diese Aussagen stellen Verallgemeinerungen des vonWasow [1956] behandelten Falles auf beliebige stetige oder gitterförmige Grenzverteilungen dar. Zwei Beispiele veranschaulichen die theoretischen Aussagen.

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Summary The error, which is caused by the approximation of a probability distribution by a limit distribution, is asymptotically expanded (to an increasing parameter) by means of differential (or difference) equations. These statements are generalizations ofWasow's [1956] theorem to arbitrary continous or lattice distributions. Two examples are given to show the practical effect of the stated theorems.

     

The employment interview: A review of current studies and directions for future research

The employment interview continues to be a prevalent device used by organizations and a popular topic of study among researchers. In fact, over 100 new articles have been published since Posthuma, Morgeson and Campion's [Posthuma, R. A., Morgeson, F. P., & Campion, M. A. (2002). Beyond employment interview validity: A comprehensive narrative review of recent research and trends over time. Personnel Psychology, 55, 1–81] review that are selectively examined and critiqued. During this timeframe, three main areas that have received considerable research attention are discussed: (1) understanding why “structured” interviews predict, (2) examining the constructs interviews may measure, and (3) investigating the applicant and interview factors that may affect the interview process. Despite advances made in our knowledge of employment interviews, numerous ideas for future research are advanced. Three key areas that deserve immediate research attention are: (1) establishing a common model and measurement of interview structure, (2) focusing on what constructs could be or are best measured, and (3) formulating consistent definitions, labeling and measurement of applicant factors. In this way, employment interview research can be advanced.     

Inference with dependent data using cluster covariance estimators

This paper presents an inference approach for dependent data in time series, spatial, and panel data applications. The method involves constructing t and Wald statistics using a cluster covariance matrix estimator (CCE). We use an approximation that takes the number of clusters/groups as fixed and the number of observations per group to be large. The resulting limiting distributions of the t and Wald statistics are standard t and F distributions where the number of groups plays the role of sample size. Using a small number of groups is analogous to ‘fixed-b’ asymptotics of [Kiefer and Vogelsang, 2002] and [Kiefer and Vogelsang, 2005] (KV) for heteroskedasticity and autocorrelation consistent inference. We provide simulation evidence that demonstrates that the procedure substantially outperforms conventional inference procedures.     

太沙基单向固结的差分计算及其Matlab实现

本文利用差分原理推导了Terzaghi一维固结微分方程的解法,借助Matlab矩阵工具进行实现,对具体工程实例进行计算,得到符合理想情况的Terzaghi固结方程解。得到结论:对于均匀的地层,满足Terzaghi基本假设条件下,借助差分法可以得到一维固结微分方程的解;对于不满足假设条件的情况,改变初始及边界条件后,仍然可以利用差分法进行求解。     

Changing energy parameters and the evolution of urban spatial structure

In this paper two different models of urban spatial structure are developed. The first is based on equilibrium analysis and the dynamics of the equilibrium solution are examined. The second is based on disequilibrium analysis and is formulated as a set of differential equations. The models are run to assess the effects of changing energy parameters, particularly in relation to transport costs, and it is shown that a range of different patterns of spatial structure emerge.     

An existence theorem of intertemporal recursive utility in the presence of Lévy jumps

This paper presents an existence theorem for a class of backward stochastic integral equations. The main contribution is a generalization of Duffie and Epstein's [Duffie, D., Epstein, L., 1992. Stochastic differential utility, (Appendix C with Skiadas C.), Econometrica 60, 353–394.] existence theorem of intertemporal recursive utility to allow the information structure to be driven by a Lévy jump process. The existence theorem applies also for a more general class of utility functions, such as recursive utility with habit-formation, and can be used to prove the existence of an equilibrium asset price process as a unique solution to the stochastic Euler equation derived by Ma [Ma, C., 1993b. Valuation of Derivative Securities with Mixed Poisson–Brownian Information and Recursive Utility, McGill University, mimeo.].     

A socio-economic activity distribution model for nonincorporated minor civil divisions; The case of Maryland

Planners and administrators alike increasingly recognize the need for a quantitative tool that could be used to evaluate the effects of policies and other socio-economic attributes on the level of activities in non-incorporated subcounty areas of the State. In this paper, a quantitative model that could be used for such a purpose in presented.To overcome the problem of insufficiency of census data, temporal administrative data were collected for 224 Minor Civil Divisions or Election Districts (MCD's or ED's) of 20 counties of the State of Maryland from eclectric sources and then processed through utilization of University of Maryland multi-variate computer programs. Regressional equations were then constructed for a host of socio-economic activities (e.g. population, employment, etc.). The outcome of this endeavor supports a proposition advocated by the author in an earlier working paper (June 1979) namely that variables denoting such activities and their respective attributes could be obtained by processing administrative data which is tabulated periodically by county, State and public utility organizations.Although only the general model is presented hereafter, the results obtained in this research endeavor reinforce the idea that a family of models rather than a single general model should be constructed for various types of MCD's of the State (e.g. rural and urban). Moreover, the results seem to support ideas advocated by the author [13] and Hill [11] in their respective studies that the equations of the model could be improved even further by transforming them into a “Semiendogenous” form.The model in its present form could be used as a tool for carrying out an impact analysis study. For instance, the impact of sewer and water facilities as well as land use policies on building permits could be examined through the utilization of this model. Another example of its applicability is the examination of employment opportunity impact on population or the average price of dwelling units. Although all needed data were assembled, to use the model as a forecasting tool requires consultation with county planning officials concerning future policies (e.g. land use, sewer/water) and some improvement of the mode(s).     

基于圆和圆环点的摄像机线性标定

本文提出了一种基于圆和圆环点的线性自标定方法。该方法的平面模板要求圆内有3组两两正交的直径,从3个或多个不同的方位摄取平面圆模板的图像。根据射影几何调和共轭和交比不变的性质,求出6条直径灭点的坐标。由3组两两正交的直径和拉盖尔定理的推论解出圆环点的图像坐标。利用圆环点的性质得到关于内参数的约束方程,从而线性的求出摄像机的5个内参数。模拟和真实图像实验表明,该方法精确度较高,鲁棒性较强,有一定的实用性。     

Asymmetry in first‐price auctions with affiliated private values

Collusion and heterogeneity across firms may introduce asymmetry in bidding games. A major difficulty in asymmetric auctions is that the Bayesian Nash equilibrium strategies are solutions of an intractable system of differential equations. We propose a simple method for estimating asymmetric first‐price auctions with affiliated private values. Considering two types of bidders, we show that these differential equations can be rewritten using the observed bid distribution. We establish the identification of the model, characterize its theoretical restrictions, and propose a two‐step non‐parametric estimation procedure for estimating the private value distributions. An empirical analysis of joint bidding in OCS auctions is provided. Copyright © 2003 John Wiley & Sons, Ltd.     

The taxation principle and multi-time Hamilton-Jacobi equations

Problems arising in economic theory are usually solved by use of mathematical techniques. Here, we propose an example of the contrary: every system of first order partial differential equations of a certain type can be solved by use of an economics principle. For the case of a single equation, our approach is in some sense dual to the usual optimal control method.     

Unit root quantile autoregression testing using covariates

This paper extends unit root tests based on quantile regression proposed by Koenker and Xiao [Koenker, R., Xiao, Z., 2004. Unit root quantile autoregression inference, Journal of the American Statistical Association 99, 775–787] to allow stationary covariates and a linear time trend. The limiting distribution of the test is a convex combination of Dickey–Fuller and standard normal distributions, with weight determined by the correlation between the equation error and the regression covariates. A simulation experiment is described, illustrating the finite sample performance of the unit root test for several types of distributions. The test based on quantile autoregression turns out to be especially advantageous when innovations are heavy-tailed. An application to the CPI-based real exchange rates using four different countries suggests that real exchange rates are not constant unit root processes.     

Tiebout's tale in spatial economies: Entrepreneurship, self-selection, and efficiency

This paper establishes the existence and efficiency of equilibrium in a local public goods economy with spatial structures by formalizing Hamilton's [Hamilton, B.W., 1975. Zoning and property taxation in a system of local governments Urban Studies 12, 205–211] elaboration of Tiebout's [Tiebout, C., 1956. A pure theory of local public expenditures. Journal of Political Economy 64, 416–424] tale. We use a well-known equilibrium concept from Rothschild and Stiglitz [Rothschild, M., Stiglitz, J.E., 1976. Equilibrium in competitive insurance markets: an essay on the economics of imperfect information. Quarterly Journal of Economics 40, 629–649] in a market with asymmetric information, and show that Hamilton's zoning policy plays an essential role in proving the existence and efficiency of equilibrium. We use an idealized large economy following Ellickson, Grodal, Scotchmer and Zame [Ellickson, B., Grodal, B., Scotchmer, S., Zame, W.R., 1999. Clubs and the market, Econometrica 67, 1185–1217] and Allouch, Conley and Wooders [Allouch, N., Conley, J.P., Wooders, M.H., The Tiebout Hypothesis: On the Existence of Pareto Efficient Competitive Equilibria, (2004), mimeograph]. Our theorem is directly applicable to the existence and efficiency of a discrete spatial approximation of mono- or multi-centric city equilibria in an urban economy with commuting time costs, even if we allow the existence of multiple qualities of (collective) residences, when externalities due to traffic congestion are not present.     

On the estimation of location parameters in the multivariate one sample and two sample problems

Summary In this paper we consider the problem of estimating the vectors of location parameters in the multivariate one sample and two sample problems. These estimators are obtained through the use of the multivariate rank order statistics such as theWilcoxon or the normal scores statistic considered by the authors inPuri, Sen [1966] andSen, Puri [1967] for the corresponding testing problems. The distribution of these estimators is shown to be symmetric with respect to the parameters being estimated. These estimators are translation invariant, robust and asymptotically normal. Their asymptotic relative efficiencies with respect to the estimators based on the vector of means and medians are discussed by applying the criterion ofWilks generalized variance [Anderson, p. 166]. In particular, it is shown that the estimators based on the multivariate normal scores statistics are asymptotically as efficient as the ones based on the method of least squares when the parent distributions are normal. Research sponsored by National Science Foundation Grant No. GP-12462, and by Research Grant, GM-12868 from the N.I.H., Public Health Service.     

Assessing value at risk with CARE, the Conditional Autoregressive Expectile models

In this paper we propose a downside risk measure, the expectile-based Value at Risk (EVaR), which is more sensitive to the magnitude of extreme losses than the conventional quantile-based VaR (QVaR). The index θ of an EVaR is the relative cost of the expected margin shortfall and hence reflects the level of prudentiality. It is also shown that a given expectile corresponds to the quantiles with distinct tail probabilities under different distributions. Thus, an EVaR may be interpreted as a flexible QVaR, in the sense that its tail probability is determined by the underlying distribution. We further consider conditional EVaR and propose various Conditional AutoRegressive Expectile models that can accommodate some stylized facts in financial time series. For model estimation, we employ the method of asymmetric least squares proposed by Newey and Powell [Newey, W.K., Powell, J.L., 1987. Asymmetric least squares estimation and testing. Econometrica 55, 819–847] and extend their asymptotic results to allow for stationary and weakly dependent data. We also derive an encompassing test for non-nested expectile models. As an illustration, we apply the proposed modeling approach to evaluate the EVaR of stock market indices.     

Existence of an equilibrium for infinite horizon economies with and without complete information

This work proves the existence of an equilibrium for an infinite horizon economy where trade takes place sequentially over time. There exist two types of agents: the first correctly anticipates all future contingent endogenous variables with complete information as in Radner [Radner, R. (1972). Existence of equilibrium of plans, prices and price expectations in a sequence of markets. Econometrica, 289–303] and the second has exogenous expectations about the future environment as in Grandmont [Grandmont, J. M. (1977). Temporary general equilibrium theory. Econometrica, 535–572] and information based on the current and past aggregate variables including those which are private knowledge. Agents with exogenous expectations may have inconsistent optimal plans but have predictive beliefs in the context of Blackwell and Dubbins [Blackwell, D., Dubins, L. (1962). Merging of opinions with increasing information. The Annals of Mathematical Statistics, 882–886] with probability transition rules based on all observed variables. We provide examples of this framework applied to models of differential information and environments exhibiting results of market selection and convergence of an equilibrium. The existence result can be used to conclude that, by adding the continuity assumption on the probability transition rules, we obtain the existence of an equilibrium for some models of differential information and incomplete markets.     

On a class of discrete distributions arising from the birth-death-with-immigration process

This paper considers a class of distributions which may be regarded as the convolution of a negative binomial and a stopped-sum generalized hypergeometric factorial-moment random variables. Some properties are derived and it is shown that this class of distributions is a subset of distributions for the birth-and-death process with immigration (also reversible counter system). Formulations by mixing, limiting distributions and maximum likelihood equations are also discussed.     

Bertrand oligopoly in a spatial context: The case of quantity independent transportation costs

The theory of spatial competition [for a review, see Gabszewicz and Thisse (1985)] is usually based on the assumption of transportation costs which are proportionate to distance and quantity. In reality, however, there exist frequently considerable economies of scale, especially with respect to the conveyed quantity of goods. A good case in point is transportation cost incurred by a consumer patronizing a shopping area. Cost economies of scale will in general influence consumers' optimal choice with respect to quantities and best market places. In the extreme, consumers' outlays on transportation can be considered independent of the purchased quantity, but approximately proportionate to distance. In the present paper, the impact of this assumption on spatial competition is analysed. It will be shown, that existence and uniqueness of spatial oligopolistic equilibrium is restored. Furthermore, due to some residual monopolistic power, prices do not converge to the perfectly competitive equilibrium prices when the distance between the firms shrinks to zero. In conclusion the model exhibits a fundamental difference in the market structure, when the spatial aspect is incorporated.