Louis de Grange

A Microeconomic Interpretation of the Maximum Entropy Estimator of Multinomial Logit Models and Its Equivalence to the Maximum Likelihood Estimator

Maximum entropy models are often used to describe supply and demand behavior in urban transportation and land use systems. However, they have been criticized for not representing behavioral rules of system agents and because their parameters seems to adjust only to modeler-imposed constraints. In response, it is demonstrated that the solution to the entropy maximization problem with linear constraints is a multinomial logit model whose parameters solve the likelihood maximization problem of this probabilistic model. But this result neither provides a microeconomic interpretation of the entropy maximization problem nor explains the equivalence of these two optimization problems. This work demonstrates that an analysis of the dual of the entropy maximization problem yields two useful alternative explanations of its solution. The first shows that the maximum entropy estimators of the multinomial logit model parameters reproduce rational user behavior, while the second shows that the likelihood maximization problem for multinomial logit models is the dual of the entropy maximization problem.

A Maximum Entropy Estimator for the Aggregate Hierarchical Logit Model

A new approach for estimating the aggregate hierarchical logit model is presented. Though usually derived from random utility theory assuming correlated stochastic errors, the model can also be derived as a solution to a maximum entropy problem. Under the latter approach, the Lagrange multipliers of the optimization problem can be understood as parameter estimators of the model. Based on theoretical analysis and Monte Carlo simulations of a transportation demand model, it is demonstrated that the maximum entropy estimators have statistical properties that are superior to classical maximum likelihood estimators, particularly for small or medium-size samples. The simulations also generated reduced bias in the estimates of the subjective value of time and consumer surplus.

An equivalent optimization formulation for the traffic assignment problem with asymmetric linear costs

Abstract In this paper, we present a general formulation for the deterministic traffic assignment problem, using an equivalent optimization problem applicable to the case of asymmetric linear cost functions. We present a resolution approach for this problem in such a way that in equilibrium Wardrops first principle or Nash equilibrium is satisfied. We conclude that many deterministic traffic assignment problems with asymmetric linear costs can be formulated as an optimization problem whose objective is defined by a line integral, and whose constraints correspond to non-negativity and flows conservation. By adequately defining the integration path, it is feasible to resolve the problem, obtaining Wardrops equilibrium. This approach can be applied in other economic contexts, including microeconomic theory and consumer surplus analysis.

Dealing with collinearity in travel time valuation

The value of travel time (VOT) is defined as the marginal rate of substitution between travel time and travel cost, and it is typically calculated using standard econometric techniques. However, it is very common for both variables (travel time and travel cost) to present high correlation, artificially increasing the variance of the VOT estimator. We propose a new approach to estimating VOT in the context of logistic regression models (that could also be applicable to classical discrete choice models), based on an application of the ridge regression approach. Using simulated data, we demonstrate that the ridge estimator reduces the variance and mean-squared error of the VOT. Additionally, we obtain a lower estimation bias for the VOT estimation, due to a geometric property of the ridge estimator that is applicable for VOT (defined as the ratio of the travel time and travel cost parameters in linear models). We applied the methodology to a large sample of interurban trips by bus and train in the South of Chile, achieving reductions of nearly 50% in the variance of the VOT.

Límites de la tarificación vial

Para muchos academicos y profesionales de la ingenieria de transporte, el concepto de tarificacion por congestion se ha transformado en el paradigma de la eficiencia en el uso de la escasa infraestructura vial y del desincentivo al uso excesivo del automovil. Si bien la tarificacion vial puede ser, en varios casos, una buena herramienta de gestion de trafico, comporta tambien una serie de riesgos y sobreexpectativas que es importante tener en consideracion a la hora de disenar, implementar y administrar un eficiente esquema de tarificacion vial. En este trabajo presentamos una serie de antecedentes, basados muchos de ellos en la literatura especializada y en evidencia empirica, que permiten describir los riesgos potenciales y eventuales sobreexpectativas que enfrenta una politica de tarificacion por congestion, lo que puede ser de gran ayuda para impulsar una correcta implementacion de esta politica de gestion de trafico.

Estimates of price elasticity of demand for urban freeway use with high-frequency control variables: the case of Santiago, Chile

Estimates are presented of toll and fuel price elasticities of demand for urban freeway use in Santiago, Chile. High-frequency toll and vehicle data were collected from four urban freeways for different route segments and times of day. Estimation was performed using log-linear regression models whose explanatory variables were tolls, fuel prices, city traffic levels and sets of dichotomous variables to control for daily, weekly and monthly seasonality. City traffic is a high frequency control of the activity level of the city. The elasticities to changes in tolls and fuel were all low in absolute value. The toll elasticities were below 0.05 for two freeways and 0.16 for the third, while for the fourth, which had more alternative routes, it was 0.47. The fuel price elasticities were also heterogeneous, with values of approximately 0.45 for two freeways and 0.21 for the third whereas for the fourth, which had the fewest alternatives, it was 0.07.

Assessing salesforce marginal productivity

Marginal productivity of salesforce (excluding checkout clerks) in a retail store is difficult to assess. An analytical model is presented here explaining this productivity using salesforce workers per hour as the factor of production (the explanatory variable) and sales transactions per hour as the level of production (the explained variable). The model incorporates self-service transactions, controls for various seasonal effects (time of day, day of the week, month of the year) and generates solutions for in-store salesforce assignment across opening hours and sales points. To control for possible endogeneity between the transactions and salesforce size variables, instrumental variables are employed in the calibration process. The model is calibrated using data from a major retail chain based in Latin America both at the storewide level and for groups of individual store departments. The results corroborate the existence of diminishing returns to scale for the workers per hour factor and a significant level of self-service transactions in the total number of sales. The application of the model to the stores supplying the data confirms the systematic understaffing reported in the literature for the retail industry.

Numerical Bounds on the Price of Anarchy

Theoretical upper bounds for price of anarchy have been calculated in previous studies. We present an empirical analysis for the price of anarchy for congested transportation networks; different network sizes and demand levels are considered for each network. We obtain a maximum price of anarchy for the cases studied, which is notably lower than the theoretical bounds reported in the literature. This result should be carefully considered in the design and implementation of road pricing mechanisms for cities.

A Road Pricing Model for Congested Highways Based on Link Densities

A road pricing model is presented that determines tolls for congested highways. The main contribution of this paper is to include density explicitly in the pricing scheme and not just flow and time. The methodology solves a nonlinear constrained optimization problem whose objective function maximizes toll revenue or highway use (2 scenarios). The results show that the optimal tolls depend on highway design and the level of congestion. The model parameters are estimated from a Chile’s highway data. Significant differences were found between the highway’s observed tolls and the optimal toll levels for the two scenarios. The proposed approach could be applied to either planned highway concessions with recovery of capital costs or the extension or retendering of existing concessions.

Estimating the impact of incidents on urban controlled-access highways: an empirical analysis

ABSTRACT An empirical analysis is developed that quantifies the impact of different types of traffic incidents on the speed and maximum flow averages of vehicles on a controlled-access highway. The incident types considered include damage to highway infrastructure, vehicle rollover, crashes (into stationary objects), collisions (with moving vehicles), rain, fog, vehicle breakdowns, pedestrians on roadway, etc. Using real-world data from Chile’s most heavily used urban motorway/freeway, estimates of incident impacts on speed are generated using a multiple linear regression model incorporating instrumental variables to correct for endogeneity. Flow results are then generated using the fundamental traffic equation relating speed, flow and density. A ranking of the impacts on highway traffic of the different incident types based on incident frequency as well as impact size demonstrates that for the real case studied, the incidents with the greatest cumulative effect are (in order of magnitude) vehicle breakdown, collisions and rain.