SAS Assignment #1

Engel Curve: Illustrating the effects of real personal disposable income on real personal consumption of musical instruments

The curve was derived using SAS. An index of real personal consumption of musical instruments is the dependent variable and average real personal disposable income is the explanatory variable. Both sets of time-series data came from the U.S. Bureau of Economic Analysis.

Initial Regression Equation: IPC = -.53161 + .00444*RI + µ

IPC = Percentage of real personal consumption consisting of musical instruments in a given year in the U.S.

RI = Average Real Personal Disposable Income in a given year in the U.S.

In this given sample, in any given year, an additional 1\$ increase in overall real personal disposable income results in a .0044% increase in musical instruments purchased in the United States. Analysis of Variance Source DF Sum of Mean Square F Value Pr > F Model 1 7.35460 7.35460 672.89 <.0001 Error 55 0.60115 0.01093 Corrected Total 56 7.95574

 Root MSE 0.10455 R-Square 0.9244 Dependent Mean 0.55759 Adj R-Sq 0.9231 Coeff Var 18.7497

 Parameter Estimates Variable Label DF Parameter Estimate Standard Error t Value Pr > |t| Intercept Intercept 1 -0.53161 0.04421 -12.02 <.0001 RI RI 1 0.00004440 0.00000171 25.94 <.0001

 Ordinary Least Squares Estimates SSE 6015.07544 DFE 55 MSE 109.36501 Root MSE 10.45777 SBC 435.406551 AIC 431.320448 MAE 8.70880226 AICC 431.54267 MAPE 25.3737896 HQC 432.908447 Durbin-Watson 0.1073 Total R-Square 0.9244

 Durbin-Watson Statistics Order DW Pr < DW Pr > DW 1 0.1073 <.0001 1.0000

 NOTE: PrDW is the p-value for testing negative autocorrelation.

 Parameter Estimates Variable DF Estimate Standard Error t Value Approx Pr > |t| Variable Label Intercept 1 -53.1807 4.4227 -12.02 <.0001 RI 1 0.004442 0.000171 25.94 <.0001 RI

The problem with my first regression: There is positive autocorrelation between my explanatory variable and dependent variable. In the second regression, I corrected this autocorrelation by using the “nlag” command. I also changed the dependent variable and explanatory variable so that the dependent variable would be expressed as a dollar amount rather than a percentage of consumption. The dependent variable changed from real personal consumption of instruments as an index to real personal consumption of instruments in billions of dollars. The explanatory variable changed from overall real personal disposable income to real personal disposable income per capita.

New Regression Equation: IPC = -3.151 + .00022*RI + µ

IPC = Real Consumption of Musical Instruments in Billions of dollars in a given year in the U.S.

RI = Real Personal Disposable Income Per Capita

In this given sample, an additional 1\$ increase in average real personal disposable income results in a \$220,000 increase in musical instruments purchased in the aggregate across in the United States in a given year.

 Number of Observations Read 57 Number of Observations Used 57

 Analysis of Variance Source DF Sum of Squares Mean Square F Value Pr > F Model 1 190.41259 190.41259 932.31 <.0001 Error 55 11.23303 0.20424 Corrected Total 56 201.64561

 Root MSE 0.45193 R-Square 0.9443 Dependent Mean 2.39123 Adj R-Sq 0.9433 Coeff Var 18.8993

 Parameter Estimates Variable Label DF Parameter Estimate Standard Error t Value Pr > |t| Intercept Intercept 1 -3.15128 0.19114 -16.49 <.0001 RI RI 1 0.00022594 0.00000740 30.53 <.0001

After changes my variables and accounting for autocorrelation, this is the refined Engel Curve for Musical Instruments using time-series data from 1959-2015. IPC = -3.151 + .00022*RI + µ

IPC = Real Consumption of Musical Instruments in Billions of dollars in a given year in the U.S.

RI = Real Personal Disposable Income Per Capita

Aggregate Engel Curve: Musical Instruments