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.

 

Relationship between Real GDP per capita and Gambling using Commercial Gambling and Lottery Sales