International Journal of Scientific and Research Publications, Volume 3, Issue 6, June 2013 1 ISSN 2250-3153 www.ijsrp.org Analysis by Panel Data Method Estimation of Car Fleet Models Rachid TOUMACHE*, Khaled ROUASKI**, Sabah FADEL*** * High National School of Statistics and Applied Economics, Ben Aknoun, 16028, Algeria, email : rtoumache@gmail.com ** High National School of Statistics and Applied Economics, Ben Aknoun, 16028, Algeria, email: khaled.rouaski@gmail.com. 3University of Algeria III, Ben Aknoun, 16028, Algeria, email: sabah.rouaski@gmail.com. Abstract- The car fleet evolution in Algeria is due to the non- linear variation of the income represented by the national wealth (GDP) rather than other infrastructural factors such as car prices, fuel prices, the transport network, population density, and the extent of the country. This study predicts the future image of the Algerian car fleet, based on the technique of time-series cross- sectional data. The evolution of the car fleet is modeled using three utilities models provided by the literature namely the Gompertz function, the function Quasi-Logistics and Logistics function. In addition, these models were calibrated using panel data or pooled data. 46 countries (sections) were captured during 32 years from 1971 to 2002 (source: World Bank) to build four panels which include Algeria, China, India and the United States. For this choice, it was considered the international trend of the development of the park in terms of GDP and the countries with the same characteristics as ours. As a result of the work, a set of future Algerian car fleet scenarios were identified by the different models statistically significant. Index Terms- car fleet, panel data, Gompertz function, Quasi- logistic and logistic functions, calibration of econometric models. I. INTRODUCTION mong the three Maghreb countries, Algeria owns the most important car fleet, it was stated that the car fleet rolling has 2 million tourism vehicles, 700,000 lightweight commercial vehicles, 536,000 heavyweight vehicles and 10,000 motorcycles. However, the average age of the car fleet is high, 55% of the vehicles have more than 20 years and 80% more than 10 years. The Algerian motorization rate is 71 vehicles for 1,000 inhabitants. Among the brands present, French carmakers are dominant; Peugeot and Renault represent half of the rolling car fleet (900,000 Peugeot vehicles and more than 600,000 of Renault vehicles). The total of other carmakers’ cars is below 200,000 vehicles throughout Algeria. Recent years, le car market has seen the apparition of a growing number of new brands which constitutes new competitors, with the particularity of being aggressive on price segment, for French carmakers historically present in Algeria. II. IDENTIFY, RESEARCH AND COLLECT IDEA The existing relationship between the vehicle ownership and the GDP per capita is represented by various non-linear models [1]:  Logistic model : Tanner proposed a logistic model by adding more variables as the GDP per capita and the cost of vehicle. The utility form suggested commonly is : Y=   ()() (1).  The quasi-logistic mode (l) : The same principle of the first model is applied in addition to a set of socioeconomic factors Xi. Y=             (2)  Gompertz Function: Theoretically, the Gompertz function is written as : Y=S   ( 3) i :represents the income per capita, S : saturation level, P : cost of the vehicle, b, c and d are parameters of the mode (l). Yi : the vehicle ownership level per capita, over the long run, GDP per capita income. Concerning our application, the database is characterized by : The inclusion of two variables : the car fleet as a dependant variable and the GDP as an explanatory variable. It is a time series having 46 sections (countries) covering the period 1971- 2002. This database is provided by the World Bank and the International Monetary Fund, gives us 1472 observations. In addition, the GDP is defined as the total of goods and services produced in the territory of any country during a given year, whichever the nationality of the producers; hence, it measures the wealth of a country. The model in S curve «GOMPERTZ Quasi-logistic» allows establishing a unique trend based on one or many sections or countries with the goal to classify correctly the members of the population, they seek combinations between several countries. For each model, a saturation threshold, set in advance, is equal to the threshold of the country situated in the upper extreme of the S curve. The utilities’ models for the case of Algeria are written under the following linear form[1]:  Logistic Model : Yi=     (4) ,Where the linear form is [3] : Log (    )= log(α) +β*log(PIB) (5)  Quasi- Logistic Model Yi=    (6) Where the linear form is[3] : Log (    )= log(α) +β*log(PIB) (7) A