Simple Consumption Function
In this empirical analysis, I used the same method which was taught in the classroom
to estimate simple consumption function in Taiwan. And after that, I will use the
estimate to calculate marginal propensity to consume (MPC). In here, I used the
annual data, household disposable income and household consumption, from Taiwan
Statistical Data Book 2005 instead of seasonal data from total.gdt. The data is ranged
from 1977 to 2003. However, I only used fifteen observations from 1989 to 2003 to
run the regression since the behavior of data before 1989 has dramatic change which
will give bad result in estimation. The model is as follow:
log C t   0   1 log Yt d   t
where C t  household consumption
Yt d  household disposable income
 t  random var iable
Estimation Results:
Model 1: OLS estimates using the 15 observations 1989-2003
Dependent variable: lc
VARIABLE
COEFFICIENT
STDERROR
0) const
-1.11073
0.149147
4) lyd
1.05944
0.00966308
Mean of dependent variable = 15.2375
Standard deviation of dep. var. = 0.369875
Sum of squared residuals = 0.00206915
Standard error of residuals = 0.0126161
Unadjusted R-squared = 0.99892
Adjusted R-squared = 0.998837
Degrees of freedom = 13
Durbin-Watson statistic = 1.38228
First-order autocorrelation coeff. = 0.300505
T STAT
-7.447
109.638
2Prob(t > |T|)
< 0.00001 ***
< 0.00001 ***
Regression Diagnostics:
The result of this regression is good. ̂ 0 and ˆ1 are all significant in t test. R 2 is very
high and D-W statistic is acceptable although it is not very close to 2.
Test Diagnostics:
Test for autocorrelation and heteroskedasity indicate that there are no autocorrelation
and heteroskedasity problems in this regression. Test for stability of the regression,
which are Chow test and CUSUM test, indicate that there is no structural change in
this regression. Normality test shows that residuals are distributed normally. All test
results are shown as follows:
Test for autocorrelation:
LM test for autocorrelation up to order 1
Null hypothesis: no autocorrelation
Test statistic: LMF = 1.05147
with p-value = P(F(1,11) > 1.05147) = 0.327189
Test for heteroskedasticity:
White's test for heteroskedasticity
Null hypothesis: heteroskedasticity not present
Test statistic: TR^2 = 4.59807
with p-value = P(Chi-Square(2) > 4.59807) = 0.100356
Test for stability of the regression:
Chow test for structural break at observation 1997
Null hypothesis: no structural break
Test statistic: F(2, 11) = 0.618254
with p-value = P(F(2, 11) > 0.618254) = 0.5566
CUSUM test for parameter stability
Null hypothesis: no change in parameters
Test statistic: Harvey-Collier t(12) = 0.0691407
with p-value = P(t(12) > 0.0691407) = 0.946016
Test for normality:
Test for normality of residual Null hypothesis: error is normally distributed
Test statistic: Chi-square(2) = 0.404576
with p-value = 0.81686
Marginal Propensity to Consume (MPC):
To calculate MPC, I calculated average propensity to consume (APC) first. By using
the same data range, gretl calculated the following results for APC which has average
about 0.82.
Summary Statistics, using the observations 1989 – 2003
for the variable 'apc' (15 valid observations)
Mean
Median
Minimum
0.82425
0.82701
0.78870
Maximum
Standard deviation
0.84979
0.019684
By definition, MPC 
dC
 1  APC and it is equal to 0.87. This means people in
dY d
Taiwan consume NTD 0.87 out of every NTD1 earned.
Conclusion:
The overall results of the regression are good. There is no statistical problem in the
regression. As for MPC, compare to the MPC = 0.68 we calculated in the classroom,
my result is higher. Every NTD1 we earned, NTD0.87 will be consumed and
NTD0.23 will be saved.