Nonlinear Hedonics and the Search for School District Quality

Since the pioneering work of Tiebout (1956), economists have recognized that the quality of public services, especially schools, influence house prices. Many empirical studies have attempted to discern the extent to which the quality of public education affects house prices. Initially, researchers estimated hedonic pricing equations (Rosen, 1974). In a simple hedonic pricing model, a house's value depends on its comparable neighborhood and school district characteristics. A house's comparable characteristics include aspects such as the number of bedrooms, square feet, etc. Neighborhood characteristics typically include the distance to the nearest major downtown area, racial composition, and median household income. Education quality may be proxied by variables such as per-pupil spending, pupil/teacher ratio, and property taxes, which are usually available at the school district level, or it may be measured directly by state or local standardized tests scores, which are usually available at the school level. In an influential study, Black (1999) argues that past research estimating hedonic pricing functions (see Rosen, 1974) may introduce an upward bias due to neighborhood quality effects that are unaccounted for in the data. Specifically, she notes that better schools may be associated with better neighborhoods, which could independently contribute to higher house prices. Black circumvents this problem by estimating a linear hedonic pricing function using data only from houses which border the school attendance zone boundaries. She rationalizes that, while test scores make a discrete jump at attendance boundaries, changes in neighborhoods are more smooth. Black's linear specification presupposes that the marginal valuation of worse-than-average schools is equal to the valuation of better-than-average schools and results in a constant premium on school quality. Moreover, if school quality is normalized (i.e., expressed in terms of deviations from the mean), the linear capitalization term implies a penalty (increasing as quality decreases) for houses in attendance zones of schools performing below average. Thus, a linear model implies there exists a substantive pecuniary penalty for a really bad school compared to just a bad school. In this paper, we formulate a simple housing search model that yields a theoretical nonlinear pricing function. The nonlinearity in our model reflects two aspects of the market for public education via housing. First, alternative schooling arrangements (e.g., private school, home schooling, magnet schools, etc) can provide home buyers with high quality education even if they choose to live in below average school districts. The existence of these options underlies our belief that an increasing penalty for below average quality school attendance zones may be theoretically unappealing. Second, if buyers have positive valuations for education, they may concentrate their efforts among the highest quality attendance zones, yielding an increasing market tightness as school quality increases. Thus, buyers may face incresed competition for the highest quality schools and a rapidly increasing premium for houses in those attendance zones. Motivated by our theoretical specification, we extend Black's analysis and examine the relationship between school quality and house prices in the St. Louis, Missouri metropolitan area. A previous study by Ridker and Henning (1967) found no evidence of education capitalization in St. Louis house prices. While their main concern was to determine the negative effect of air pollution on housing prices, they included a dummy variable which indicated residents' attitudes about the quality of the schools (above average, average, and below average). Our goal is to determine the degree of education capitalization in the St. Louis MSA. We first measure education capitalization employing Black's methodology of considering only houses near attendance zone boundaries to control for neighborhood quality. This allows us to determine the extent to which Black's results extend to the St. Louis metro area. Then, we advance Black's methodology by considering the possibility that education capitalization affects house prices nonlinearly, as indicated by our theoretical framework. Black, Sandra E. "Do Better Schools Matter? Parental Valuation of Elementary Education," Quarterly Journal of Economics, May 1999, 114(2), pp. 577-599. Ridker, Ronald G. and Henning, John A. "The Determinants of Residential Property Values with Special Reference to Air Pollution," Review of Economics and Statistics, May 1967, 49(2), pp. 246-257. Rosen, Sherwin. "Hedonic Prices and Implicit Markets: Product Differentiation in Pure Competition," Journal of Political Economy, January-February 1974, 82(1), pp. 34-55. Tiebout, Charles M. "A Pure Theory of Local Expenditures," Journal of Political Economy, October 1956, 64(5), pp. 416-424.education, captialization, hedonic pricing, search

Kinematics of Current Region Fragmentation in Semi-Inclusive Deeply Inelastic Scattering

Different kinematical regimes of semi-inclusive deeply inelastic scattering (SIDIS) processes correspond to different underlying partonic pictures, and it is important to understand the transition between them. This is particularly the case when there is sensitivity to intrinsic transverse momentum, in which case kinematical details can become especially important. We address the question of how to identify the current fragmentation region --- the kinematical regime where a factorization picture with fragmentation functions is appropriate. We distinguish this from soft and target fragmentation regimes. Our criteria are based on the kinematic regions used in derivations of factorization theorems. We argue that, when hard scales are of order a few GeVs, there is likely significant overlap between different rapidity regions that are normally understood to be distinct. We thus comment on the need to take this into account with more unified descriptions of SIDIS, which should span all rapidities for the produced hadron. Finally, we propose general criteria for estimating the proximity to the current region at large Q.Comment: 9 Pages, 5 figures; minor clarifications and corrections, version appearing in Physics Letters

Tetraquark spectroscopy

A complete classification of tetraquark states in terms of the spin-flavor, color and spatial degrees of freedom was constructed. The permutational symmetry properties of both the spin-flavor and orbital parts of the quark-quark and antiquark-antiquark subsystems are discussed. This complete classification is general and model-independent, and is useful both for model-builders and experimentalists. The total wave functions are also explicitly constructed in the hypothesis of ideal mixing; this basis for tetraquark states will enable the eigenvalue problem to be solved for a definite dynamical model. This is also valid for diquark-antidiquark models, for which the basis is a subset of the one we have constructed. An evaluation of the tetraquark spectrum is obtained from the Iachello mass formula for normal mesons, here generalized to tetraquark systems. This mass formula is a generalizazion of the Gell-Mann Okubo mass formula, whose coefficients have been upgraded by means of the latest PDG data. The ground state tetraquark nonet was identified with $f_{0}(600)$, $\kappa(800)$, $f_{0}(980)$, $a_{0}(980)$. The mass splittings predicted by this mass formula are compared to the KLOE, Fermilab E791 and BES experimental data. The diquark-antidiquark limit was also studied.Comment: Invited talk at 11th International Conference on Meson-Nucleon Physics and the Structure of the Nucleon (MENU 2007), Julich, Germany, 10-14 Sep 2007. In the Proceedings of 11th International Conference on Meson-Nucleon Physics and the Structure of the Nucleon (MENU 2007), Julich, Germany, 10-14 Sep 2007, eConf C070910, 163 (2007

Non-relativistic Extended Gravity and its applications across different astrophysical scales

Using dimensional analysis techniques we present an extension of Newton's gravitational theory built under the assumption that Milgrom's acceleration constant is a fundamental quantity of nature. The gravitational force converges to Newton's gravity and to a MOND-like description in two different mass and length regimes. It is shown that a modification on the force sector (and not in the dynamical one as MOND does) is more convenient and can reproduce and predict different phenomena usually ascribed to dark matter at the non-relativistic level.Comment: 4 pages, 2 figures. To appear in the proceedings of the 2011 Spanish Relativity Meeting (ERE2011) held in Madrid, Spai

The Transition State in a Noisy Environment

Transition State Theory overestimates reaction rates in solution because conventional dividing surfaces between reagents and products are crossed many times by the same reactive trajectory. We describe a recipe for constructing a time-dependent dividing surface free of such recrossings in the presence of noise. The no-recrossing limit of Transition State Theory thus becomes generally available for the description of reactions in a fluctuating environment

The Bayesian Decision Tree Technique with a Sweeping Strategy

The uncertainty of classification outcomes is of crucial importance for many safety critical applications including, for example, medical diagnostics. In such applications the uncertainty of classification can be reliably estimated within a Bayesian model averaging technique that allows the use of prior information. Decision Tree (DT) classification models used within such a technique gives experts additional information by making this classification scheme observable. The use of the Markov Chain Monte Carlo (MCMC) methodology of stochastic sampling makes the Bayesian DT technique feasible to perform. However, in practice, the MCMC technique may become stuck in a particular DT which is far away from a region with a maximal posterior. Sampling such DTs causes bias in the posterior estimates, and as a result the evaluation of classification uncertainty may be incorrect. In a particular case, the negative effect of such sampling may be reduced by giving additional prior information on the shape of DTs. In this paper we describe a new approach based on sweeping the DTs without additional priors on the favorite shape of DTs. The performances of Bayesian DT techniques with the standard and sweeping strategies are compared on a synthetic data as well as on real datasets. Quantitatively evaluating the uncertainty in terms of entropy of class posterior probabilities, we found that the sweeping strategy is superior to the standard strategy