Existing Aggregate models focused on accumulation of household vehicle

Existingmodels for determining vehicle ownership were categorized by Patoglou andSusilo (2008) into two broad groups namely aggregate and disaggregate models. 3.1Aggregate modelsAggregatemodels focused on accumulation of household vehicle ownership at differentgeographical scales such as zonal, regional, state or national levels (Patoglouand Susilo 2008).

They can be applied to derive income elasticity of vehicledemand, make international comparisons, predict future vehicle stock; and canbe used as input in forecasting travel demand applying least square method ofregression techniques (Zegras and Hannan 2012). It consists mainly of three types namely timeseries, cohort models and car market models (Dargay and Gately, 1999; Madre andPirotte 1991; European Commission (DGII) et al 1999).  Aggregate time series model usually use sigmoid-shapedfunction and saturation level concept to develop vehicle ownership overtime.  They assume that vehicle ownershipis a function of income or gross domestic product which slowly increasesinitially.  It then rises steeply andapproaches saturation level at the end (De Jong et al 2004). The works ofIngram and Liu (1998); Dargay and Gately (1999); Whelan et al, (2000), andWhelan, (2001) were the more recent applications of aggregate time seriesmodels.  The studies used the models toexplain vehicle ownership in many countries of the world.  LowS data requirements have made aggregatetime series model attractive for application to developing countries (De Jonget al 2004)Aggregatecohort model divides the current population into five years age cohorts.

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  The cohorts are then projected into the future,explaining their vehicle ownership with respect to how they will acquire, keepand lose cars as they become older (De Jong et al, 2004).  Examples are the works of Van den Broecke(1987) and Madre and Pirotte (1991) in Netherlands and Francerespectively.  The studies used themodels to examine cohort effect as a major cause of significant growth in carownership in western European countries. The model is most suitable for forecasting the effect of changes in sizeand composition of population on car ownership. Aggregatecar market models operate by determining the equilibrium between demand andsupply side of car market.  The demandside is the number of cars purchased as predictable by number of people, numberof households, the average income and distribution income, and various prices.

Onthe other hand, the supply side is defined by the number of scrapped cars, ageingand new cars actually bought at the previous year. The number of purchased cars(supply function) and the price of a second hand car which is the demand functionare the two unknown endogenous variables in the model (Cramer and Vos1985).  The changes in car market areinfluenced by dynamics of demand for the existing number of old cars.  This operates through the price of used carsand its effects on demand for new cars.

 Consequently, a unit decrease in the price of used cars results inproportionate decrease in the demand for newcars (De Jong et al 2002).  Examples ofthese models include the Cramers car ownership model (Cramer and Vos 1985), Mogridge(1983); Manski (1983); and Berry et al (1995)3.2Disaggregate ModelsDisaggregatemodels examine vehicle ownership at household levels (Patoglou and Susilo,2008).  The advantage of disaggregatemodels over aggregate models lies on their behavioral structure and enhancedability in identifying causal relationship.

 This has made disaggregate models the most dominant in determiningvehicle ownership.  Their extensive usewas based on their robustness in developing vehicle ownership model.  This is because the models have overcome theweakness of aggregate models (Patoglou and Susilo 2008).  Disaggregate models use ordinal or nominaldiscrete variable to determine vehicle ownership, thus giving rise to two typesof model choice namely ordered and unordered. The ordered choice model is based on an assumption that household’schoice of number of vehicles is dependent on the propensity of a household toown vehicles.  The unordered responsemodel on the other hand assumes that utility value of household vehicle ownershipat different levels is determined by the one that gives the maximumutility.

  No study yet has proved thatordered response or unordered response models are the most appropriate(Potoglou and Susilo, 2008;  Bhat and Pulugurta1998; Potoglou and Kanoroglou 2007). Examples of disaggregate models include static disaggregate carownership models, joint discrete–continuous models, static disaggregate cartype choice models and Pseudo-dynamics models, (De jong, et al, 2004)Therelevance of these theories to this study cannot be overemphasized.  They were very critical to the choice ofmodel specification applied in this study. The aggregate time series model became the most appropriate model for thisstudy due to dearth of disaggregate data in the country.  This challenge has made the use ofdisaggregate models, despite their advantages, over aggregate models impossiblein this work.  Despite the challenges, itis hope that this study will be the foundation for future research. This isbasically because its prediction of future vehicle ownership would serve as astarting point for other more detailed models which require a broader and morecomplete data (Cirillo and Xu, 2011). This will be particularly useful for developing countries where studieson vehicle ownership at both aggregate and disaggregate levels are limited.