A theoretical analysis of the cross-nested logit model

The emergence of Intelligent Transportation Systems and the associated technologies has increased the need for complex models and algorithms. Namely, real-time information systems, directly influencing transportation demand, must be supported by detailed behavioral models capturing travel and driving decisions. Discrete choice models methodology provide an appropriate framework to capture such behavior. Recently, the Cross-Nested Logit (CNL) model has received quite a bit of attention in the literature to capture decisions such as mode choice, departure time choice and route choice. %The CNL model is an extension of the Nested Logit model, providing %more flexibility at the cost of some complexity in the model formulation. In this paper, we develop on the general formulation of the Cross Nested Logit model proposed by Ben-Akiva and Bierlaire (1999) and based on the Generalized Extreme Value (GEV) model. We show that it is equivalent to the formulations byby Papola (2004) and Wen and Koppelman (2001). We also show that the formulations by Small(1987) and Vovsha(1997) are special cases of this formulation. We formally prove that the Cross-Nested Logit model is indeed a member of the GEV models family. In doing so, we clearly distinguish between conditions that are necessary to prove consistency with the GEV theory, from normalization conditions. Finally, we propose to estimate the model with non-linear programming algorithms, instead of heuristics proposed in the literature. In order to make it operational, we provide the first derivatives of the log-likelihood function, which are necessary to such optimization procedure

A theoretical analysis of the cross-nested logit model

The emergence of Intelligent Transportation Systems and the associated technologies has increased the need for complex models and algorithms. Namely, real-time information systems, directly influencing transportation demand, must be supported by detailed behavioral models capturing travel and driving decisions. Discrete choice models methodology provide an appropriate framework to capture such behavior. Recently, the Cross-Nested Logit (CNL) model has received quite a bit of attention in the literature to capture decisions such as mode choice, departure time choice and route choice. %The CNL model is an extension of the Nested Logit model, providing %more flexibility at the cost of some complexity in the model formulation. In this paper, we develop on the general formulation of the Cross Nested Logit model proposed by Ben-Akiva and Bierlaire (1999) and based on the Generalized Extreme Value (GEV) model. We show that it is equivalent to the formulations byby Papola (2004) and Wen and Koppelman (2001). We also show that the formulations by Small(1987) and Vovsha(1997) are special cases of this formulation. We formally prove that the Cross-Nested Logit model is indeed a member of the GEV models family. In doing so, we clearly distinguish between conditions that are necessary to prove consistency with the GEV theory, from normalization conditions. Finally, we propose to estimate the model with non-linear programming algorithms, instead of heuristics proposed in the literature. In order to make it operational, we provide the first derivatives of the log-likelihood function, which are necessary to such optimization procedures

The Delinquency of Subprime Mortgages

The lag between the time that a borrower stops making payments on a mortgage and the termination of the loan plays a critical role in the costs borne by both borrower and lender on defaulted loans. While the prior literature uses a multinomial logit approach, statistical tests indicate that we cannot accept the associated assumption of Independence of Irrelevant Alternatives (IIA). Using a nested logit specification our results suggest that the recipe for delinquency involves young loans to low credit score borrowers with low or no documentation in housing markets with moderately volatile and flat or declining nominal house prices

The flexible coefficient multinomial logit (FC-MNL) model of demand for differentiated products

We show FC-MNL is flexible in the sense of Diewert (1974), thus its parameters can be chosen to match a well-defined class of possible own- and cross-price elasticities of demand. In contrast to models such as Probit and Random Coefficient-MNL models, FC-MNL does not require estimation via simulation; it is fully analytic. Under well-defined and testable parameter restrictions, FC-MNL is shown to be an unexplored member of McFadden’s class of Multivariate Extreme Value discrete-choice models. Therefore, FC-MNL is fully consistent with an underlying structural model of heterogeneous, utility-maximizing consumers. We provide a Monte-Carlo study to establish its properties and we illustrate the use by estimating the demand for new automobiles in Italy

On the Migration Decision of IT-Graduates: A Two-Level Nested Logit Model

Discrete choice models are used to investigate the individual’s choice among a discrete number of alternatives. The characteristics of each alternative, by means of a multinomial and nested multinomial models have been taken into account. Specifically, this study analyses the impact of choice specific characteristics (attributes) in a model of choice between different country locations. Individual IT-Graduates are assumed to choose a single type of move, stayhome or go-abroad, while simultaneously choosing a country of their choice. We demonstrate that a nested logit model is appropriate on both theoretical and empirical grounds. The sample consists of 1,500 IT-Graduates from Pakistan. The results show a high migration propensity for foreign destinations. While comparing the direct elasticities (at branch level) of home with the foreign destination types we observe that the economic factors such as self-employment and higher career position show greater effects than the sociopolitical as well as institutional factors (social networks and residence permit). A location comparison between the destinations Germany and USA/Canada (of the cross elasticities) shows that the magnitude of the values of elasticities are found to be higher for North American countries than for Germany. This suggests that IT-Graduates evaluate the factors self- employment, higher career positions, social networks and residence permit more important and significantly higher for North American destinations than for Germany. In addition we find a strong evidence for a competition between countries for high potentials from Pakistan. ZUSAMMENFASSUNG - (Migrationsentscheidung von IT-Hochschulabsolventen: Ein zweistufiges Nested-Logitmodell) Mit Hilfe von Modellen für diskrete abhängige Variablen untersuchen wir die individuelle Auswahl aus einer Anzahl von Alternativen bei der Migration. Die Charaktaristika der einzelnen Alternativen im Zusammenhang von Multinomial bzw. Nestedmodellen sind berücksichtigt worden. Wir untersuchen den Einfluss von auswahlspezifischen Charaktaristika in einem Modell zur Auswahl zwischen verschiedenen Empfängerländern. IT-Hochschulabsolventen wählen ausgehend von zwei Alternativmöglichkeiten (Migration oder im Land bleiben), eine Alternative aus und wählen simultan ein bestimmtes Land. Es zeigt sich, dass ein "Nestedlogit-modell" sowohl in theoretischer als auch in empirischer Hinsicht für die Untersuchung am besten geeignet ist. Die Stichprobe besteht aus ca. 1500 IT-Hochschulabsolventen aus Pakistan. Die Ergebnisse zeigen eine höhere Neigung auf, ein ausländisches Land zu wählen. Beim Vergleich der Direktelastizitäten für die erste Stufe beobacten wir für die Faktoren Selbstständigkeit und gute Karrieremöglichkiten einen höheren Einfluss als für die gesellschaftspolitische Determinaten (Soziale Netzwerke und Aufentshaltserlaubnis). Bei einem Standortvergleich zwischen Deutschland und dem klassischen Immigrationsland USA (basiert auf Kreuzelastizitäten) zeigt sich ferner, dass das Ausmaß der Elastisitätenwerte höher für Nordamerikanischen Länder ist als für Deutschland. Dies bedeutet, dass die ITHochschulabsolventen die Faktoren: die Selbstständigkeit, gute Karrieremöglichkeit, soziale Netzwerke und Aufenthaltserlaubnis für die Nordamerikanischen Länder signifikant höher bewerten als für Deutschland. Zusätzlich finden wir eine Evidenz für die Existenz von Wettbewerb zwischen Ländern für die IT-Hochschulabsolventen aus Pakistan.international migration, push- and pull factors, nested model

The decision to migrate: A simultaneous decision making approach

Discrete choice models are used to investigate the individual’s choice among a discrete number of alternatives. The characteristics of each alternative, by means of multinomial and nested multinomial models, have been taken into account. Specifically, this study analyses the impact of choice-specific characteristics (economic and socio-political attributes) in a model of choice between different country locations. Individual IT-graduates are assumed to choose a single type of move, stay-home or go-abroad, while simultaneously choosing a country of their choice. We demonstrate that a nested logit model is appropriate on both theoretical and empirical grounds. The sample consists of 1,500 IT-graduates from India. The results show on the one hand a high migration propensity for foreign destinations and on the other hand a quite large number of IT-Graduates who want to stay at home. By comparing the direct elasticities (at branch level) of home with those of foreign destination types we observe that both the economic as well as socio-political factors tend to have a greater impact for the foreign destinations. Based on the cross elasticities values, a location comparison between the destinations Germany and the USA/Canada shows that the magnitude of the values of elasticities are found to be higher for North American countries than for Germany. This suggests that IT-Graduates evaluate the economic as well as the socio-political factors as more important and significantly higher for North American destinations than for Germany. In addition we find strong evidence for a competition between countries with high potentials, with India emerging as an attractive location. -- Mit Hilfe von Modellen für diskrete abhängige Variablen untersuchen wir die individuelle Auswahl aus einer Anzahl von Alternativen bei der Migration. Die Charakteristika der einzelnen Alternativen im Zusammenhang von Multinomialbzw. Nestedmodellen sind berücksichtigt worden. Wir untersuchen den Einfluss von auswahlspezifischen Charaktaristika (ökonomische u. sozio-politische) in einem Modell zur Auswahl zwischen verschiedenen Empfängerländern. ITHochschulabsolventen wählen ausgehend von zwei Alternativmöglichkeiten (Migration oder im Land bleiben), eine Alternative aus und wählen simultan ein bestimmtes Land. Es zeigt sich, dass ein „Nested-Logit-Modell“ sowohl in theoretischer als auch in empirischer Hinsicht für die Untersuchung am besten geeignet ist. Die Stichprobe besteht aus ca. 1500 IT-Hochschulabsolventen aus Indien. Die Ergebnisse zeigen einerseits eine höhere Neigung, ein ausländisches Land zu wählen, und andererseits tendiert eine große Anzahl von IT-Hochschulabsolventen, in der Heimat zu bleiben. Beim Vergleich der Direktelastizitäten für die erste Stufe beobachten wir für beide ökonomische und sozio-politische Faktoren einen höheren Einfluss auf die Entscheidung, ins Ausland zu gehen. Bei einem Standortvergleich zwischen Deutschland und dem klassischen Immigrationsland USA/Canada (basierend auf Kreuzelastizitäten) zeigt sich ferner, dass das Ausmaß der Elastizitätswerte höher für nordamerikanische Länder ist als für Deutschland. Dies bedeutet, dass die ITHochschulabsolventen die ökonomischen und sozio-politischen Faktoren für die nordamerikanischen Länder signifikant höher bewerten als für Deutschland. Zusätzlich finden wir Evidenz für die Existenz von starkem Wettbewerb zwischen Ländern um die IT-Hochschulabsolventen aus Indien, das selbst als ein attraktiver Standort gilt.

International price discrimination in the European car market: An econometric model of oligopoly behavior with product differentiation

Car Industry;Oligopoly;Product Differentiation;Econometric Models;Price Discrimination

Assessing the Value of Time Travel Savings – A Feasibility Study on Humberside.

It is expected that the opening of the Humber Bridge will cause major changes to travel patterns around Humberside; given the level of tolls as currently stated, many travellers will face decisions involving a trade-off between travel time, money outlay on tolls or fares and money outlay on private vehicle running costs; this either in the context of destination choice, mode choice or route choice. This report sets out the conclusions of a preliminary study of the feasibility of inferring values of travel time savings from observations made on the outcomes of these decisions. Methods based on aggregate data of destination choice are found t o be inefficient; a disaggregate mode choice study i s recommended, subject to caveats on sample size

The delinquency of subprime mortgages

This paper focuses on understanding the determinants of the performance of subprime mortgages. A growing body of literature recognizes the substantial lag between the time that a borrower stops making payments on a mortgage and the termination of the loan. The duration of this lag and the method by which the delinquency is ultimately terminated play a critical role in the costs borne by both borrower and lender. Using nested and multinomial logit, we find that delinquency and default are sensitive to current economic conditions and housing markets. Credit scores and loan characteristics also play important roles.Mortgages ; Subprime mortgage