Statistics and Finance
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The good that I decided to proc autoreg nlag option trading is total alcohol consumption per capita, measured in gallons of ethanol. I obtained this information from Statista.
I decided to use a time series approach for my analysis of the Engel Curve. The timespan of my data goes from through I proc autoreg nlag option trading the curve to be upward sloping because I think that alcohol is a normal good. People who are rich do not find alcohol less appealing to drink in general than those with less money. However, certain brands or types of alcoholic beverages may be inferior.
If people without much money suddenly became substantially more wealthy, they might decide to stop drinking cheap brands of beer proc autoreg nlag option trading Busch for example, and switch to drinking expensive wine instead. As I am not differentiating between brands or types of alcoholic beverages in my regression analysis, I am unable to test for this. I decided to put proc autoreg nlag option trading on the Y-axis and ethanol on the X-axis even though this made income the dependent variable in the regression, because Engel Curves always have income on the Y-axis.
Although ethanol should be the dependent variable in this situation, the results obtained when switching the two variables are still important and useful. The year has a much higher value for ethanol consumption than any of the other years, and looks like it is an outlier. Outliers are a problem in statistical models because they pull a regression line in their proc autoreg nlag option trading substantially, even though they are proc autoreg nlag option trading one observation among many.
In order to refine my estimate of the Engel curve, I took that data point out, and ran the regression again, using only the years through I expected that this would improve the fit of the model substantially. As it can be seen in the above graph, the Engel Curve here is upward sloping which indicates that Alcohol is a normal good as was expected, although there are a number of data points below the regression line aiming in a downward direction.
This regression line does not appear to fit the data very well because many of the data points are scattered fairly far away from it.
Also, I had a low R-Square value of 0. According to the way Proc autoreg nlag option trading arranged the variables, this means that variation in ethanol consumption only explains 8. However, I did check the R-Square results with ethanol as the dependent variable, and proc autoreg nlag option trading was exactly the same.
The t-statistic obtained for ethanol was not significant here, with a value of only 1. The F-value also indicates that the entire model is not significant, showing the same p-value as for ethanol, which is to be expected since ethanol was the only explanatory variable included, and it is not significant. The correlation between ethanol and income is 0. The graph of my refined Engel Curve also shows that ethanol is a normal good, as it is upward sloping.
As can be seen, taking the value out of my analysis improved the model. The R-Square value was increased substantially, from 0. This is still not a very high R-Square value, but it is clearly much better than the one before. The t-statistic increased far enough to become significant, with a t-value of 3. The F-statistic also shows that the model is significant, with a value of The correlation between ethanol and income in this increased substantially, from 0. Because this data is based on ethanol consumption, it may not be very reliable for an Engel curve.
As I mentioned earlier, the existence of many different types of alcoholic beverages with a wide variety in prices questions the analysis presented. It is possible that poor people drink more than rich people, but buy much cheaper brands and in the end spend far less money on alcohol. People also consume alcohol for different reasons, such as depression. A person who becomes clinically depressed may vastly increase their alcohol consumption without an increase in income, or even with a decrease in income if they are depressed because of losing a job.
In addition, my data on ethanol is for all people 14 years and older, which is problematic. It may be that in some years, more underage people, who do not have many monetary obligations decide to drink more, and influence others who are of age to buy the alcohol for them.
Median Family Income data is inflation adjusted and pulled from the St. Louis Federal Reserve website. Total motor gasoline consumption is in thousands of barrels sold in the U. Energy Information Administration website.
I chose motor gasoline for my independent variable because gasoline is generally considered to be price insensitive, meaning that consumers do not change their consumption of gasoline very much as factors like the price of oil or tax rates change, but I wanted to see if this trend was persistent across various income levels, as gasoline may be considered a luxury good in some circumstances.
The regression equation and resulting Engel Curve are shown below:. The Engel Curve above shows us that Gasoline is in fact a normal good, proc autoreg nlag option trading the Engel Curve has a positive slope. SAS Output for this model is shown below. The p-value associated with Median Family Income is less than 0. However, because this is a time-series analysis, we proc autoreg nlag option trading check our results for the presence of first-order autocorrelation, as autocorrelation is often present in time-series models.
To do this, I ran a Durbin-Watson test, the results proc autoreg nlag option trading which may be found below. These results show that there is a high degree of first-order positive autocorrelation in our data, meaning that we must now attempt to correct this problem.
As we can see from the above SAS output, the PROC AUTOREG procedure significantly reduced the level of positive first-order autocorrelation in the data, and in fact brings the Durbin-Watson statistic in between the dU and dL values for a regression with one independent variable and 29 observations, meaning that a hypothesis test to determine the presence of autocorrelation on this dataset would now be inconclusive. To do away with the remaining possibility of autocorrelation in the data and improve the R-Squared for this model, I decided to add a variable, the price of a new car PNCUS to this equation to reduce the likelihood of omitted variable bias.
The regression equation and SAS output are shown below. This model tells us that gasoline is in fact a normal good, as when median family income rises, so does demand for gasoline. There may still be issues in our model with autocorrelation, but it is not inconceivable that this autocorrelation is attributable to the fact that a model with many different independent variables is needed proc autoreg nlag option trading fully explain changes in demand for motor gasoline proc autoreg nlag option trading the United States.
Clearly, our model does not paint the entire picture, but it provides us with a good starting point for analyzing the factors which influence demand for motor gasoline. I used a measurement of income before taxes separated into 9 different brackets: I ran a cross sectional regression to observe changes in food consumption due to increases in annual income. For a second regression, I included alcohol consumption in dollars to observe its effect on food consumption under the same income brackets.
My R squared statistics of. These findings align with our common assumptions about food, that it is a highly normal good. The purpose of this assignment was to estimate an Engel curve on used car purchases. Proc autoreg nlag option trading, there were difficulties model in gathering data. The first issue was obtaining the proper data.
Luckily, the Bureau of Labor Statistics maintains consumer expenditure surveys. Each survey contained nine income categories, with the average amount spent on used cars in each income category. I used the after-tax income for this model. Also, I used the data from This gave me a data set of 36 observations. The first model that I created estimated had Income as the independent variable and average dollars spent on used cars per person as the dependent variable. After I ran the regression, the equation looked like: This model had very good predictive power.
However, I realized that gasoline prices might influence car purchases. There is a possibility that in times of high gas prices, consumers might be more hesitant to purchase a car. I thought that there might be an omitted variable bias. I then found data on the average gas price in the United States in the years used in the previous model.
The data was taken from energy. I then ran a new regression. This model had a slightly better R-Square at. What is very interesting about this model is that it predicted that gas prices have a significant deterrent effect. After analyzing the data and regression results, I found that increased income proc autoreg nlag option trading a positive effect on used car sales. In addition, increased gas prices had a negative effect on used car sales.
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 was also used in models 3 and 4. 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. The initial regression exhibits a positive slope coefficient proc autoreg nlag option trading CEMV meaning that vehicles are likely a normal good.
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.
As expected the model yields a stronger R proc autoreg nlag option trading suggesting that 6. The model still does not retain statistical significance with a p-value of.
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.
This model yielded less conclusive results than the first. With a p-value of 0. It appears that all of the above models are not able to find a strong relationship between vehicle expenditures and income.