Bias from ignoring price dispersion in demand estimation

Consumers often pay different prices for the same product bought in the same store at the same time. However, the demand estimation literature has ignored that fact using, instead, aggregate measures such as the “list” or average price. In this paper we show that this will lead to biased price coefficients. Furthermore, we perform simple comparative statics simulation exercises for the logit and random coefficient models. In the “list” price case we find that the bias is larger when discounts are higher, proportion of consumers facing discount prices is higher and when consumers are more unwilling to buy the product so that they almost only do it when facing discount. In the average price case we find that the bias is larger when discounts are higher, proportion of consumers that have access to discount are similar to the ones that do not have access and when consumers willingness to buy is very dependent on idiosyncratic shocks. Also bias is less problematic in the average price case in markets with a lot of bargain deals, so that prices are as good as individual. We conclude by proposing ways that the econometrician can reduce this bias using different information that he may have available.

Year 6 students' idiosyncratic notions of unitising, reunitising and regrouping decimal number places

Having flexible notions of the unit (e.g., 26 ones can be thought of as 2.6 tens, 1 ten 16 ones, 260 tenths, etc.) should be a major focus of elementary mathematics education. However, often these powerful notions are relegated to computations where the major emphasis is on "getting the right answer" thus procedural knowledge rather than conceptual knowledge becomes the primary focus. This paper reports on 22 high-performing students' reunitising processes ascertained from individual interviews on tasks requiring unitising, reunitising and regrouping; errors were categorised to depict particular thinking strategies. The results show that, even for high-performing students, regrouping is a cognitively complex task. This paper analyses this complexity and draws inferences for teaching.

Simulations of pollutant dispersion at toll plazas using three-dimensional CFD models

Toll plazas are particularly susceptible to build-ups of vehicle-emitted pollutants because vehicles pass through in low gear. To look at this, three-dimensional computational fluid dynamics simulations of pollutant dispersion are used on the standard k e turbulence model. The effects of wind speed, wind direction and topography on pollutant dispersion were discussed. The Wuzhuang toll plaza on the Hefei-Nanjing expressway is considered, and the effects of the retaining walls along both sides of the plaza on pollutant dispersion is analysed. There are greater pollutant concentrations near the tollbooths as the angle between the direction of the wind and traffic increases implying that retaining walls impede dispersion. The slope of the walls has little influence on the variations in pollutant concentration.

Difference and dispersion : educational research in a postmodern context

Difference and Dispersion is the fourth in a series of annual research papers produced by doctoral students from The Graduate School of Education, The University of Queensland, following their presentation at the School’s annual Postgraduate Research Conference in Education. The work featured herein celebrates the diversity of cultural and disciplinary backgrounds of education researchers who come from as far afield as Germany, Hong Kong, China, Nigeria, Russia, Singapore, Thailand and of course different parts of Australia. In keeping with a postmodern epistemology, ‘difference’ and ‘dispersion’ are key themes in apprehending the multiplicity of their research topics, methodologies, methods and speaking/writing positions. From widely differing contexts and situations, these writers address the consequences, implications and possibilities for education at the beginning of the third millennium. Their interest ranges from location-specific issues in schools and classrooms, change in learning contexts and processes, educational discourses and relations of power in diverse geographical settings, and the differing articulations of the local and the global in situated policy contexts. Conceived and developed in a spirit of ongoing dialogue with and insight to alternative views and visions of education and society, this edited collection exemplifies the quality in diversity and the high levels of scholarship and supervision at one of Australia’s finest Graduate Schools of Education.

On the nature of over-dispersion in motor vehicle crash prediction models

Statistical modeling of traffic crashes has been of interest to researchers for decades. Over the most recent decade many crash models have accounted for extra-variation in crash counts—variation over and above that accounted for by the Poisson density. The extra-variation – or dispersion – is theorized to capture unaccounted for variation in crashes across sites. The majority of studies have assumed fixed dispersion parameters in over-dispersed crash models—tantamount to assuming that unaccounted for variation is proportional to the expected crash count. Miaou and Lord [Miaou, S.P., Lord, D., 2003. Modeling traffic crash-flow relationships for intersections: dispersion parameter, functional form, and Bayes versus empirical Bayes methods. Transport. Res. Rec. 1840, 31–40] challenged the fixed dispersion parameter assumption, and examined various dispersion parameter relationships when modeling urban signalized intersection accidents in Toronto. They suggested that further work is needed to determine the appropriateness of the findings for rural as well as other intersection types, to corroborate their findings, and to explore alternative dispersion functions. This study builds upon the work of Miaou and Lord, with exploration of additional dispersion functions, the use of an independent data set, and presents an opportunity to corroborate their findings. Data from Georgia are used in this study. A Bayesian modeling approach with non-informative priors is adopted, using sampling-based estimation via Markov Chain Monte Carlo (MCMC) and the Gibbs sampler. A total of eight model specifications were developed; four of them employed traffic flows as explanatory factors in mean structure while the remainder of them included geometric factors in addition to major and minor road traffic flows. The models were compared and contrasted using the significance of coefficients, standard deviance, chi-square goodness-of-fit, and deviance information criteria (DIC) statistics. The findings indicate that the modeling of the dispersion parameter, which essentially explains the extra-variance structure, depends greatly on how the mean structure is modeled. In the presence of a well-defined mean function, the extra-variance structure generally becomes insignificant, i.e. the variance structure is a simple function of the mean. It appears that extra-variation is a function of covariates when the mean structure (expected crash count) is poorly specified and suffers from omitted variables. In contrast, when sufficient explanatory variables are used to model the mean (expected crash count), extra-Poisson variation is not significantly related to these variables. If these results are generalizable, they suggest that model specification may be improved by testing extra-variation functions for significance. They also suggest that known influences of expected crash counts are likely to be different than factors that might help to explain unaccounted for variation in crashes across sites