I chose to compare quarterly changes in Real Disposable Income measured in billions of chained 2009 dollars and changes in Real Personal Consumption Expenditure of Non-Durable Goods between 1/1/1991 and 12/1/2016. Following includes my time-series regression, its respective Engel Curve, another regression correcting for first-order auto correlation, and a conclusion based on my results.
| Engel Curve |
The REG Procedure
Model: MODEL1
Dependent Variable: NDGoods NDGoods
| Number of Observations Read | 72 |
| Number of Observations Used | 72 |
| Analysis of Variance | ||||||
| Source | DF | Sum of Squares |
Mean Square |
F Value | Pr > F | |
| Model | 1 | 96943 | 96943 | 2179.52 | <.0001 | |
| Error | 70 | 3113.52385 | 44.47891 | |||
| Corrected Total | 71 | 100056 | ||||
| Root MSE | 6.66925 | R-Square | 0.9689 |
| Dependent Mean | 310.61389 | Adj R-Sq | 0.9684 |
| Coeff Var | 2.14712 |
| Parameter Estimates | ||||||
| Variable | Label | DF | Parameter Estimate |
Standard Error |
t Value | Pr > |t| |
| Intercept | Intercept | 1 | -24.47984 | 7.22062 | -3.39 | 0.0012 |
| RDI | RDI | 1 | 0.03145 | 0.00067370 | 46.69 | <.0001 |
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| Engel Curve Controlling for Autocorrelation | ||||||
The AUTOREG Procedure
| Yule-Walker Estimates | |||
| SSE | 1530.46157 | DFE | 69 |
| MSE | 22.18060 | Root MSE | 4.70963 |
| SBC | 437.899022 | AIC | 431.069024 |
| MAE | 3.3598497 | AICC | 431.421965 |
| MAPE | 1.09144035 | HQC | 433.788066 |
| Durbin-Watson | 2.1735 | Regress R-Square | 0.8722 |
| Total R-Square | 0.9847 | ||
| Durbin-Watson Statistics | |||
| Order | DW | Pr < DW | Pr > DW |
| 1 | 2.1735 | 0.7512 | 0.2488 |
| NOTE: Pr<DW is the p-value for testing positive autocorrelation, and Pr>DW is the p-value for testing negative autocorrelation. |
| Parameter Estimates | ||||||
| Variable | DF | Estimate | Standard Error |
t Value | Approx Pr > |t| |
Variable Label |
| Intercept | 1 | -6.0331 | 14.6799 | -0.41 | 0.6824 | |
| RDI | 1 | 0.0297 | 0.001368 | 21.70 | <.0001 | RDI |
These regression results suggest that change in Real Disposable Income affects the change in Real Personal Consumption Expenditure of Non-Durable Goods. For this sample, an increase of 1 billion of chained 2009 dollars was associated with a subsequent rise of 0.0297 billions of chained 2009 dollars ($29,700,000) in Real Personal Consumption Expenditure of Non-durable goods. The coefficient of Real Disposable Income was highly statistically significant (p<.0001). The regression fit very well (R^2=0.9689, adjusted R^2=0.9847) and was highly statistically significant (F=2179.52 p<.0001).*
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