Econometric Theory

Introduction

Whether travelling to and from work, escaping on a weekend vacation or most importantly just for general convenience a car is essential in today’s society especially with the expanding nature of cities. A limiting factor of owning a car however, are the costs associated with it, from the initial purchase to refilling the petrol tank, maintenance, etc., thus many seek to purchase a used car, forgoing a large sunk cost.

This report determines the major influences on the various prices of used cars since August 2004, also with the use of various techniques produce a superior model of predicting the price relative to certain features for consumers/businesses to have a better idea for future purchases.

The following investigates data of 1436 used cars with the first 1236 of them being used for this report leaving the remaining 200 as genuine test data. The variable of interest is named ‘price’ and is the ‘offer price in EUROs’, the price asked for the used car by the seller in euros as of August 2004. A second set of data is given that contains all the variables, their respective descriptions and whether to include them or not in the analysis.

The instructions from an expert at pricing cars are conflicting as many are labelled to be used however the total count of 15 is less than the number labelled. After a quick glance it seems 15 is the more correct figure as a few included seem similar to the not included in terms of personal preferences/extras, such as mist lamps, in used cars. However the greater number will be investigated first in case a few variables are in fact significant.

The investigation will be carried out through Stata, a computer software designed for regression analysis.

Results

At first a few tweaks are performed to set the data as required including the dropping of the variables according to the expert, creation of dummy variables for the categorical variable ‘fuel_type’ and dropping the last 200 observations for testing.

The initial model, as above, includes all the variables labelled to be used in the descriptive data and is regressed. The resultant (Appendix 1) adjusted R-squared of 0.9019 and an σ (RMSE) of 1127.8 indicate excellent goodness of fit with a very large standard deviation of the error. The cause of this large root mean square error lies in the units used which in this case the model is a level-level with prices of used cars in the thousands. This is noted though with the expectation of improvement.

It is also important to note that the dummy variable ‘cng’ created for the categorical variable ‘fuel_type’ has been omitted (Appendix 1), this is to allow comparison to each of the other dummy variables, both ‘petrol’ and ‘diesel’. In this case the dummy variable removed was the least common for a simpler reference. Another point