WEALTH, DISPOSABLE INCOME AND CONSUMPTION - Economics

Table 3
Cumulative growth factors used to evaluate human wealth
state xˆ \rˆ
1 2 3 ... 24 25
value xˆ \rˆ –0.0067 –0.0049 –0.0031 ... 0.0341 0.0359
1 –0.0270 114.1 112.9 111.7 ... 85.4 84.5
2 –0.0244 114.2 113.0 111.7 ... 85.5 84.6
3 –0.0219 114.3 113.1 111.8 ... 85.5 84.7
... ... ... ... ... ... ... ...
24 0.0320 116.1 115.0 113.7 ... 86.9 86.0
25 0.0346 116.2 115.0 113.8 ... 87.0 86.1
Comparing the cumulative growth factors across states we see that
the higher is the real interest rate in the current state, the lower is the
cumulative growth factor and, thus, human wealth. This largely reflects
the persistence of real interest rate movements as captured in the estimated
VAR. An above average realization of rt raises the probability of an above
average realization of rt + 1 and thus lowers the expected present value of
future net income growth. Reinforcing this own effect is a cross-effect stemming
from the negative relationship between the real interest rate and net
income growth. An above average realization of rt also lowers the
expected value of future net income growth, thereby further reducing
human wealth. The quantitative impact on human wealth of a rise in the
interest rate depends on the initial state of the system, which reflects the
non-linear nature of the problem. To be more concrete, the response of the
cumulative growth factor to a positive 25-basis-point shock to the real
interest rate (at quarterly rates) ranges between –1.4 and –1.8 per cent, with
the larger responses coming when r is near its mean.
The effects of innovations in net income growth are much smaller,
which reflects the fact that shocks to net income provide very little information
about the future. Net income growth exhibits very little serial correlation,
and there are no significant cross-effects in the estimated VAR of net
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