"Life Cycle" Hypothesis of Saving: Aggregate ... - Arabictrader.com

1998
1993
1988
1983
1978
1973
1968
1963
1958
1953
188 The Life-Cycle Hypothesis
S/Y DS/Y g
ADF t-stat -4.0*** -0.47 -0.55
Dg M/E DE/M
ADF t-stat -3.3* 2.75 -2.75*
***:1 percent, **:5 percent, *:10 percent MacKinnon critical values for rejection
of hypothesis of a unit root.
The tests indicate that the three series contain a unit root. Given that each series
has a unit root, we now test whether the series are co-integrated over the sample
period and if so, what the co-integrating relationship is. To test co-integration we
use two methods, the first being the Engle and Granger (1987) two-step method.
The first stage consists of regressing the variables supposed to be co-integrated.
The second stage consists of testing for a unit root in the residuals. Since the
residuals are estimates of the disturbance term, the asymptotic distribution of the
tests statistic differs from the one for ordinary series. (The correct critical values
are obtained from Russell Davidson and James MacKinnon 1993, table 20.2).
Table 6.3 reports the results of the estimation (see also figure 6.5). The first
row of each equation contains the estimated coefficients. The second row
shows the corresponding t-values. The first two equations (I.1 and I.2) are the
regressions on the saving ratio on the long-term growth rate and the E/M ratio,
0.40
0.35
0.30
S/Y
S/Y (Eq 1.1)
S/Y (Eq 1.2)
0.25
Saving ratio
0.20
0.15
0.10
0.05
0.00
–0.05
Year
Figure 6.5
Saving ratio, long-term growth, and ratio of employment to minors