*Time Series in United States between 1999 and 2015*

This model attempted to derive an Engle curve for the demand of motor vehicles in the United States. Before addressing the results of the regression, we must define our variables. Our proxy for income was real median household income. The primary motivation for this metric was the fact that families generally pool resources to purchase large items like cars. Real disposable income pegged to 2009 was also used in models 3 and 4. The real consumer expenditure on vehicles and vehicle parts was our proxy for vehicle consumption measured in billions ($) pegged to 2009 dollar. A time series approach worked to unearth trends in vehicle consumption over time. Using real rather than nominal allows us to see a better picture of year to year changes.

Model 1 sought to find the relationship between vehicle purchases and income.

CEMV* _{i }* = β

_{0 }+ β

_{1 }RMHI

_{i}*u*

_{ + }

_{i}The initial regression exhibits a positive slope coefficient on CEMV meaning that vehicles are likely a normal good.

The results to model 1’s regression predict that an increase of $1000 to real median household income will predict that total expenditure in the American auto market will rise by $4.7 billion. Unfortunately only about 6% of variation in income can explain variation in consumer expenditure on vehicles.

With a p-value of 0.345 we may not claim that our variable is statistically significant.

A formal hypothesis test does suggest that the overall effect exists and is not subject to complete error.

In an attempt to adjust the model for better fit, I decided to log the model so that the data could be regressed in relative terms.

States lnCEMV* _{i }* = β

_{0 }+ β

_{1 }

*ln*RMHI

_{i}*u*

_{ + }

_{i}_{}

As expected the model yields a stronger R^{2} suggesting that 6.3% of variation income can explain changes in vehicle expenditure.

The model still does not retain statistical significance with a p-value of .33. This model suggests that a 10% increase to real median household income will result in a 7% increase in motor vehicle expenditure in the United States. While are new coefficient estimate is not statistically significant we can say that the consumer expenditure is subject to some influence from income, given our t-score.

To define a model with better fit, I found a new metric to describe income. Using real disposable income, I sought to draw a link between vehicle consumption and how much income consumers have to buy things other than necessities.

CEMV* _{i }* = β

_{0 }+ β

_{1 }RDI

_{i}*u*

_{ + }

_{i}_{}

This model yielded less conclusive results than the first. This model predicts that an increase of $100 in real disposable income will precede an increase of $0.4 billion in consumption in the auto market.

With an R^{2} 0.029, only about 2% of variance in auto consumption can be explained by variance in income. With a p-value of 0.51, our coefficient is not statistically significant.

It appears that all of the above models are not able to find a strong relationship between vehicle expenditures and income. In this case, there is a likely omitted variable bias. Our error term likely contains variables like gasoline prices and interest rates which would strengthen the model. The time-series method also makes overall analysis more difficult, especially considering that the period contains the great recession, a time when auto sales were negligible and incomes overall had taken a hit.

Further tests, including other explanatory variables could be conducted to control for influences to consumer vehicle consumption.

Source: FRED: Saint Louis Federal Reserve