For my project, I chose to evaluate the effect of Gross Domestic Income on personal consumption expenditures for alcoholic beverages purchased for off-site consumption between 1950 and 2015, at an annual frequency. Both data sets were set to an index where 1985 levels equaled 100.  I chose GDI because it displays the aggregate income of the US population, and would compare well to total expenditures for alcoholic beverages, excluding commercial purchases and purchases in bars and restaurants. The results of my initial regression are below:

 

These regression results suggest that the level of Gross Domestic Income affects the level of for personal consumption expenditures for alcoholic beverages purchased for off-site consumption. For this sample, a one percentage increase in the index (1985 = 100) for Gross Domestic Income was associated with a subsequent 0.75658 percent increase in the index (1985 = 100) for personal consumption expenditures for alcoholic beverages purchased for off-site consumption- holding all else constant.  The coefficient of personal consumption expenditures for alcoholic beverages purchased for off-site consumption was highly statistically significant (p<.0001). The regression fit very well (R2=.9945, adjusted R2=.9944) and was highly statistically significant (F=11522.8, p<.0001).

 

A Durban-Watson test revealed positive autocorrelation (DW=.1812, P<.0001). I ran the AUTOREG procedure with a 1 period lag to correct for first-order autocorrelation, and the corrected Durban-Watson test showed improved results using Yule-Walker estimates (DW=1.0787, p<.0001). The interpretation of the new corrected model is below:

 

These regression results suggest that the level of Gross Domestic Income affects the level of for personal consumption expenditures for alcoholic beverages purchased for off-site consumption. For this sample, a one percentage increase in the index (1985 = 100) for Gross Domestic Income was associated with a subsequent 0.7463 percent increase in the index (1985 = 100) for personal consumption expenditures for alcoholic beverages purchased for off-site consumption- holding all else constant.  The coefficient of personal consumption expenditures for alcoholic beverages purchased for off-site consumption was highly statistically significant (p<.0001). The regression fit very well (R2=.9549, total R2=.9999)

 

 

SAS outputs are listed below:

 

 

The REG Procedure

Model: MODEL1

Dependent Variable: AlcC AlcC

Number of Observations Read 66
Number of Observations Used 66

 

Analysis of Variance
Source DF Sum of
Squares
Mean
Square
F Value Pr > F
Model 1 620243 620243 11522.8 <.0001
Error 64 3444.94662 53.82729
Corrected Total 65 623688

 

Root MSE 7.33671 R-Square 0.9945
Dependent Mean 111.81589 Adj R-Sq 0.9944
Coeff Var 6.56142  

 

Parameter Estimates
Variable Label DF Parameter
Estimate
Standard
Error
t Value Pr > |t|
Intercept Intercept 1 12.67278 1.29174 9.81 <.0001
GDI GDI 1 0.75658 0.00705 107.34 <.0001

 

 

The REG Procedure

Model: MODEL1

Dependent Variable: AlcC AlcC

Durbin-Watson D 0.181
Pr < DW <.0001
Pr > DW 1.0000
Number of Observations 66
1st Order Autocorrelation 0.906

 

The AUTOREG Procedure

Dependent Variable AlcC
  AlcC

 

The AUTOREG Procedure

Ordinary Least Squares Estimates
SSE 3444.94662 DFE 64
MSE 53.82729 Root MSE 7.33671
SBC 456.709786 AIC 452.330477
MAE 6.27164079 AICC 452.520953
MAPE 14.4722973 HQC 454.06095
Durbin-Watson 0.1812 Regress R-Square 0.9945
  Total R-Square 0.9945

 

Durbin-Watson Statistics
Order DW Pr < DW Pr > DW
1 0.1812 <.0001 1.0000

 

Parameter Estimates
Variable DF Estimate Standard
Error
t Value Approx
Pr > |t|
Variable Label
Intercept 1 12.6728 1.2917 9.81 <.0001
GDI 1 0.7566 0.007048 107.34 <.0001 GDI

 

Estimates of Autocorrelations
Lag Covariance Correlation -1 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 1 
0 52.1962 1.000000 |                    |********************|
1 47.2653 0.905531 |                    |******************  |

 

Preliminary MSE 9.3960

 

Estimates of Autoregressive Parameters
Lag Coefficient Standard
Error
t Value
1 -0.905531 0.053454 -16.94

 

 

 Corrected for Autocorrelation using Yule-Walker

 

The AUTOREG Procedure

Yule-Walker Estimates
SSE 595.600715 DFE 63
MSE 9.45398 Root MSE 3.07473
SBC 346.778016 AIC 340.209052
MAE 2.24931649 AICC 340.596149
MAPE 3.10491344 HQC 342.804762
Durbin-Watson 1.0787 Regress R-Square 0.9549
  Total R-Square 0.9990
Durbin-Watson Statistics
Order DW Pr < DW Pr > DW
1 1.0787 <.0001 1.0000
Parameter Estimates
Variable DF Estimate Standard
Error
t Value Approx
Pr > |t|
Variable Label
Intercept 1 13.7445 4.6762 2.94 0.0046
GDI 1 0.7463 0.0204 36.52 <.0001 GDI

 

 

Relationship Between Gross Domestic Income and Personal Expenditures for Alcohol Consumed Off-Premisis