Expectations Concerning the Class Project for AGEC 317

  • Run the regression models using monthly observations from January 2000 to April 2012(148 observations) that express the number of new car purchases (CAR_SALES) and the number of light commercial vehicles (trucks) purchases (LCV_SALES) as the dependent variables; the data set is posted on the AGEC 317 website. The list of explanatory or right-hand side variables are:(1) the consumer confidence index (CONS_CONFID_INDEX); (2) the ratio of the price index of new vehicles to the price of used vehicles (CPI_NEW VEHICLES/CPI_USED_CARS_TRUCKS); (3) the unemployment rate (UNRATE); (4) the inflation-adjusted 3-month lag of the price index for gasoline (CPI_GASOLINE/CPI_ALL_ITEMS); (5) the inflation-adjusted prime rate (PRIME_RATE/CPI_ALL_ITEMS); (6) the debt-to-income ratio, defined as the level of consumer installment debt to income (DEBTINC_RATIO); (7) the great recession defined as the time period from December 2007 to June 2009; and (8) seasonality. Seasonality corresponds to the use of the seasonal dummy variables. We will cover this material later on in class.
  • Formulate expectations regarding the impacts of these explanatory variables on new car purchases and new light commercial vehicle purchases.
  • For the regression models, you must use the linear model and the logarithmic (multiplicative) model; do not take the logarithm of the dummy variables; the logarithm of zero is undefined.
  • Obtain the respectiveelasticities associated with the linear model and the logarithmic (multiplicative) modelassociated with these explanatory variables: consumer confidence index, the ratio of new of the price index of new vehicles to the price of used vehicles, the inflation-adjusted 3-month lag of the price of gasoline, the inflation-adjusted prime rate, and the debt-to-income ratio. The respectiveelasticities will vary from observation to observation in the linear model. So calculate these elasticities at every observation and then calculate the means of these elasticities across all observations. Plot the respective elasticitiesobtained from the linear model as well. In the use of the logarithmic (multiplicative) model, the estimated coefficients are the elasticities. Compare and contrast these elasticities for the multiplicative model and for the linear model for the number of new vehicle purchases and the number of light commercial vehicle purchases.
  • Provide a summary of the overall regression results for each type of vehicle purchases and for each type of functional form (linear, multiplicative). Use metrics such as goodness-of-fit, and standard error of the regression.
  • Now turn attention to the forecast performance of the regression models. Re-run the regression models using monthly data from January 2000 to April 2011 (136 observations). Essentially by doing so, a holdout sample of 12 monthly observations from May 2011 to April 2012 is created. Provide descriptive statistics of the holdout sample. Using the regression results for each type of vehicle purchase and for each functional form, obtain the respective forecasts. Compare these forecasted values to the actual values using the metrics ofroot mean squared error (RMSE), mean absolute error (MAE), and mean absolute percent error (MAPE). These are widely used measures of forecast performance. Contrast the results across the type of vehicle purchases and across the respective functional forms.
  • As alternative forecasting tools, you must use the linear trend model, the quadratic trend model, an AR(1) model, and an AR(2) model. AR(1) and AR(2) are specific types of autoregressive models. Use data from January 2000 to April 2011 in the construction of these forecasts. In this way, legitimate comparisons can be made with the forecasts obtained from the multiple regression models. Among these four models, indicate which model performs the best on the RMSE, MAE, and MAPE. The appropriate model may vary depending on the particular vehicle type. Do not use any moving average (MA) models for this project.
  • Compare the out-of-sample forecast accuracy for the multiple regression models in comparison to the trend extrapolation models as well as the autoregressive models.
  • Concentrate on the write-up of the technical report and the power point deck.