Table 2
Business Cycle Statistics
|
Variable |
OLG model |
Ramsey model | ||||
|
sx |
rxy |
rx |
sx |
rxy |
rx | |
|
Output |
0.89 |
1.00 |
0.69 |
0.89 |
1.00 |
0.69 |
|
Investment |
3.79 |
1.00 |
0.69 |
3.73 |
1.00 |
0.69 |
|
Consumption |
0.35 |
0.98 |
0.72 |
0.37 |
0.98 |
0.72 |
|
Effective Labor |
0.07 |
0.20 |
0.33 | |||
|
Hours |
0.07 |
-0.03 |
0.19 |
0.08 |
0.33 |
0.17 |
|
Real Wage |
1.09 |
0.78 |
0.43 |
1.08 |
0.79 |
0.43 |
|
Inflation |
1.66 |
-0.05 |
-0.09 |
1.66 |
- 0.05 |
-0.08 |
|
Gini Wealth |
0.07 |
-0.11 |
0.87 | |||
|
Gini Net Income |
0.31 |
-0.33 |
0.52 | |||
Notes: sx :=standard deviation of HP-filtered simulated series of variable x,
rxy :=cross correlation of variable x with output, rx :=first order autocorrela-
tion of variable x.
The second moments in Table 2 corroborate the impression conveyed by the impulse
response functions. The two models are very similar. There are negligible differences
in the standard deviations of investment, consumption, hours, and the real wage. Ex-
cept for hours and the inflation factor the first-order autocorrelations are the same in
both models. Merely the cross correlation of hours with output differs between the two
models. Hours are slightly procyclical in the Ramsey model (rxy = 0.33) and uncor-
related (rxy = -0.03) in the OLG model. Notice further that the wealth distribution
is almost unrelated to output (rxy = -0.11) and the inequality of the income distri-
bution is weakly anti-cyclical (rxy = -0.33). The behavior of the income distribution
is in good accordance with empirical evidence collected by Castaneda et al. (1998).
They find that the lower income quintiles of the income distribution in the US are
procyclical, while the fourth quintile and and next 15% of the income distribution are
negatively correlated with income. Consequently, the Gini coefficient of income in the
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