For my Aggregate Engel Curve assignment, I ran OLS test to see if National Real GDP per capita has a significant impact on consumption spending of gambling. I was originally going to use a cross sectional data analysis, but gambling is only legal in 24 of the 50 states so, I went with a time series approach using data from 2009-2015. I also picked time series because even though gambling is not legal everywhere, all states still have some form of legal gambling, which is why I chose to look at data from Commercial Gambling and Lottery ticket consumption. The Commercial Gambling is your basic casino trip, and I still used this data because there are no barriers for anyone from any state to enter these casinos or play the lottery (except for ages 18+) and that is where I thought that using national income would be a better explanatory variable on my data. All data numbers were measured in billions (USD).
To start off my data, I ran a regression analysis for Real GDP per capita and Commercial Gambling expenditure (total per year), then ran another regression for both coefficients, Commercial Gambling, and Lottery ticket sales. When running the first analysis, Commercial gambling was statistically significant with a p-value of 0.0013. This meant that as income rose so did spending on Commercial Gambling, however, when running the regression for both, I found that they were not statistically significant. My reasoning for this was that when looking at Real GDP as income rises, compared against a single gambling event had a positive correlation (which can be seen from the R-squared values of my analysis), but when another gambling event was added, it showed how spending for one dropped (Commercial Gambling) and more went to the second event (Lottery). This was just my take on it though, of course several variables take into play such as age of household, transportation costs, geographic location, and median household income.
Commercial Gambling only:
Real GDP 2009 to 2015 and Consumption on Commercial and Lottery Gambling
The AUTOREG Procedure
Ordinary Least Squares Estimates
Fit Summary
| Ordinary Least Squares Estimates | |||
| SSE | 309516.773 | DFE | 5 |
| MSE | 61903 | Root MSE | 248.80385 |
| SBC | 98.6349617 | AIC | 98.7431414 |
| MAE | 183.536902 | AICC | 101.743141 |
| MAPE | 1.16479804 | HQC | 97.4060606 |
| Durbin-Watson | 1.2795 | Total R-Square | 0.8944 |
Parameter Estimates
| Parameter Estimates | ||||||
| Variable | DF | Estimate | Standard Error |
t Value | Approx Pr > |t| |
Variable Label |
| Intercept | 1 | 1377 | 2181 | 0.63 | 0.5555 | |
| Commercial | 1 | 387.7134 | 59.5939 | 6.51 | 0.0013 | Commercial |
For both Coefficients:
Real GDP 2009 to 2015 and Consumption on Commercial and Lottery Gambling
The AUTOREG Procedure
Ordinary Least Squares Estimates
Fit Summary
| Ordinary Least Squares Estimates | |||
| SSE | 206958.234 | DFE | 4 |
| MSE | 51740 | Root MSE | 227.46331 |
| SBC | 97.7634049 | AIC | 97.9256744 |
| MAE | 138.683857 | AICC | 105.925674 |
| MAPE | 0.89564805 | HQC | 95.9200533 |
| Durbin-Watson | 1.9107 | Total R-Square | 0.9294 |
Parameter Estimates
| Parameter Estimates | ||||||
| Variable | DF | Estimate | Standard Error |
t Value | Approx Pr > |t| |
Variable Label |
| Intercept | 1 | 11148 | 7221 | 1.54 | 0.1975 | |
| Commercial | 1 | -166.9237 | 397.6935 | -0.42 | 0.6962 | Commercial |
| Lottery | 1 | 159.3078 | 113.1520 | 1.41 | 0.2319 | Lottery |
So, even though these were not statistically significant in the second test, the total R-Square value is still high, which shows that rises in income have a positive correlation with increased consumer expenditure on gambling. This shows that my aggregate Engel curve estimation does still have a positive relationship, and to further see the correlation between the variables and Real GDP I ran a correlation test in SAS which gave Commercial Gambling a .9457 and Lottery sales a .96242 which is a strong relationship.
Real GDP 2009 to 2015 and Consumption on Commercial and Lottery Gambling
The CORR Procedure
Variables Information
| 3 Variables: | GDP Commercial Lottery |
Simple Statistics
| Simple Statistics | |||||||
| Variable | N | Mean | Std Dev | Sum | Minimum | Maximum | Label |
| GDP | 7 | 15555 | 698.77343 | 108883 | 14595 | 16597 | GDP |
| Commercial | 7 | 36.56714 | 1.70443 | 255.97000 | 34.28000 | 38.54000 | Commercial |
| Lottery | 7 | 65.97571 | 5.99054 | 461.83000 | 58.25000 | 73.87000 | Lottery |
Pearson Correlations
| Pearson Correlation Coefficients, N = 7 Prob > |r| under H0: Rho=0 |
|||
| GDP | Commercial | Lottery | |
| GDP
GDP |
1.00000
|
0.94570
0.0013 |
0.96242
0.0005 |
| Commercial
Commercial |
0.94570
0.0013 |
1.00000
|
0.99057
<.0001 |
| Lottery
Lottery |
0.96242
0.0005 |
0.99057
<.0001 |
1.00000
|
Finally, I ran a hypothesis test to see if the 2 coefficients were equal in importance for my analysis comparison to Real GDP increases. I set both coefficients equal, and at the 5% level of significance the two coefficients were not of equal importance. This relates back to the scenarios listed above on how gambling is legal some places and not others, and that there are several different types of gambling methods. Overall, I was not shocked by the findings about increases in income do have increases in gambling expenditure. I wish I would have found more data on the household income of ages 18+ only and compared that to overall household incomes, which may have presented different results.
Test:
Test 1
Results
| Test 1 Results for Dependent Variable GDP | ||||
| Source | DF | Mean Square |
F Value | Pr > F |
| Numerator | 1 | 21169 | 0.41 | 0.5572 |
| Denominator | 4 | 51740 | ||
Data on Commercial and Lottery Gambling provided by: State Gaming Regulatory Agency.
Data on Real GDP per capita provided by: Organization for Economic Co-operation and Development.