6. (a) Consider the following consumption function tested for the U.K. economy u

Question

6. (a) Consider the following consumption function tested for the U.K. economy using quarterly data over the period 195501-19870: c, = 1.78 + 0.8 l y, + 0.023s + 0.03%; + 0.077s, (0.062) (0.006) (0.004) (0.004) (0.004) R' =0.99 RSS =0.034 where c(the log value of) the real non-durable consumers' expenditure and y is (the log value of) the real personal disposable income. S,(i=2,3,4) are seasonal dummies for quarter i. Figures in parentheses are estimated standard errors. () Explain how the coefficients of the dummy variables should be interpreted, (i) The consumption function was tested again omitting the seasonal dummies c, = 1.744 + 0.81y, and describe the implied seasonal pattern. and the results are given as follows (0.122) (0.012) R-=0.97 RSS=0.136 Test the hypothesis that the estimated consumption function exhibits no autonomous seasonal pattern, explaining your approach carefully.

Explanation / Answer

6) (a)

(i) In the above regression the season for quarter 1 is taken as base category.

1) The coefficient for s2 tells that real non- durable consumption expenditure was on average 0.023 units higher in quarter 2 than in quarter 1.

2) The coefficient for s3 tells that real non- durable consumption expenditure was on average 0.039 units higher in quarter 3 than in quarter 1.

3) The coefficient for s4 tells that real non- durable consumption expenditure was on average 0.077 units higher in quarter 4 than in quarter 1.

(ii) Now let us consider the regression in part (i) as unrestricted regression (UR) and the one in part (ii) as restricted regression(R)

H0: R2UR = R2R

Ha: R2UR != R2R

To check for this we will use the F-test

F = [(R2UR - R2R )/(no.of restrictions)]/[(1- R2UR)/(n-k)]

F= (0.02/0.01)*(126/3) = 84.

Since the F-value is sufficiently high so we reject the null hypothesisthat consumption function exhibits no autonomous seasonal pattern.

Related Questions

Navigate

• Browse (All)
• Browse 6
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.