Instead of equation 1) suppose we add a time trend to the Consumption Function model: Consumption=β_0+β_1 Income+β_2 tim

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Instead of equation 1) suppose we add a time trend to the
Consumption Function model:
Consumption=β_0+β_1 Income+β_2 time+ε_i (2)
Where T is a time trend. The GRETL output of OLS
estimates of adding a time trend to the model is given in Figure
2.
Figure 2: OLS estimates including a time trend
Model 2: OLS, using observations 1940-1975 (T = 36)
Dependent variable: Consumption
Coefficient Std. Error t-ratio p-value
const 1316.76 231.523 5.687 <0.0001 ***
Income 0.653009 0.0271478 24.05 <0.0001 ***
time 311.478 31.4617 9.900 <0.0001 ***
Mean dependent var 24664.17 S.D. dependent var 11195.21
Sum squared resid 7395011 S.E. of regression 473.3828
R-squared 0.998314 Adjusted R-squared 0.998212
F(2, 33) 9771.134 P-value(F) 1.75e-46
Log-likelihood −271.2721 Akaike criterion 548.5443
Schwarz criterion 553.2948 Hannan-Quinn 550.2023
rho 0.445874 Durbin-Watson 0.885368
Test that the marginal propensity to consume is zero. Use
a significance level of 0.05.
Test that the marginal propensity to save is zero. Use a
significance level of 0.05.
Test the consumption function for first order serially
correlated errors using the Durbin-Watson Statistic.
Use a significance level of 0.05.
Comparing the results of Figure 1 in Question 1 with figure 2 in
question 2, determine if the time trend is an omitted or
superfluous variable.