Johansen cointegration tests of crude birth rate (b), crude death rate (d), and log real wage (w)
| . | . | Critical Values . | ||
|---|---|---|---|---|
| Null Hypothesis . | Trace Statistic . | 10% . | 5% . | 1% . |
| Multivariate Series (b, d, w) | ||||
| 1730–1870 | ||||
| r = 0 | 87.02 | 39.06 | 42.44 | 48.45 |
| r ≤ 1 | 34.86 | 22.76 | 25.32 | 30.45 |
| r ≤ 2 | 7.10 | 10.49 | 12.25 | 16.26 |
| 1730–1799 | ||||
| r = 0 | 58.50 | 39.06 | 42.44 | 48.45 |
| r ≤ 1 | 24.07 | 22.76 | 25.32 | 30.45 |
| r ≤ 2 | 8.50 | 10.49 | 12.25 | 16.26 |
| 1816–1870 | ||||
| r = 0 | 59.29 | 7.52 | 9.24 | 12.97 |
| r ≤ 1 | 31.29 | 17.85 | 19.96 | 24.60 |
| r ≤ 2 | 9.55 | 7.52 | 9.24 | 12.97 |
| Bivariate Series (b, w) | ||||
| 1730–1870 | ||||
| r = 0 | 38.81 | 22.76 | 25.32 | 30.45 |
| r ≤ 1 | 6.50 | 10.49 | 12.25 | 16.26 |
| 1730–1799 | ||||
| r = 0 | 28.35 | 22.76 | 25.32 | 30.45 |
| r ≤ 1 | 6.13 | 10.49 | 12.25 | 16.26 |
| Bivariate Series (d, w) | ||||
| 1730–1870 | ||||
| r = 0 | 54.09 | 22.76 | 25.32 | 30.45 |
| r ≤ 1 | 14.59 | 10.49 | 12.25 | 16.26 |
| 1730–1799 | ||||
| r = 0 | 38.66 | 22.76 | 25.32 | 30.45 |
| r ≤ 1 | 12.16 | 10.49 | 12.25 | 16.26 |
| Bivariate Series (b, d) | ||||
| 1730–1870 (lag order = 3) | ||||
| r = 0 | 62.10 | 22.76 | 25.32 | 30.45 |
| r ≤ 1 | 19.76 | 10.49 | 12.25 | 16.26 |
| 1730–1799 | ||||
| r = 0 | 42.37 | 22.76 | 25.32 | 30.45 |
| r ≤ 1 | 13.88 | 10.49 | 12.25 | 16.26 |
| . | . | Critical Values . | ||
|---|---|---|---|---|
| Null Hypothesis . | Trace Statistic . | 10% . | 5% . | 1% . |
| Multivariate Series (b, d, w) | ||||
| 1730–1870 | ||||
| r = 0 | 87.02 | 39.06 | 42.44 | 48.45 |
| r ≤ 1 | 34.86 | 22.76 | 25.32 | 30.45 |
| r ≤ 2 | 7.10 | 10.49 | 12.25 | 16.26 |
| 1730–1799 | ||||
| r = 0 | 58.50 | 39.06 | 42.44 | 48.45 |
| r ≤ 1 | 24.07 | 22.76 | 25.32 | 30.45 |
| r ≤ 2 | 8.50 | 10.49 | 12.25 | 16.26 |
| 1816–1870 | ||||
| r = 0 | 59.29 | 7.52 | 9.24 | 12.97 |
| r ≤ 1 | 31.29 | 17.85 | 19.96 | 24.60 |
| r ≤ 2 | 9.55 | 7.52 | 9.24 | 12.97 |
| Bivariate Series (b, w) | ||||
| 1730–1870 | ||||
| r = 0 | 38.81 | 22.76 | 25.32 | 30.45 |
| r ≤ 1 | 6.50 | 10.49 | 12.25 | 16.26 |
| 1730–1799 | ||||
| r = 0 | 28.35 | 22.76 | 25.32 | 30.45 |
| r ≤ 1 | 6.13 | 10.49 | 12.25 | 16.26 |
| Bivariate Series (d, w) | ||||
| 1730–1870 | ||||
| r = 0 | 54.09 | 22.76 | 25.32 | 30.45 |
| r ≤ 1 | 14.59 | 10.49 | 12.25 | 16.26 |
| 1730–1799 | ||||
| r = 0 | 38.66 | 22.76 | 25.32 | 30.45 |
| r ≤ 1 | 12.16 | 10.49 | 12.25 | 16.26 |
| Bivariate Series (b, d) | ||||
| 1730–1870 (lag order = 3) | ||||
| r = 0 | 62.10 | 22.76 | 25.32 | 30.45 |
| r ≤ 1 | 19.76 | 10.49 | 12.25 | 16.26 |
| 1730–1799 | ||||
| r = 0 | 42.37 | 22.76 | 25.32 | 30.45 |
| r ≤ 1 | 13.88 | 10.49 | 12.25 | 16.26 |
Notes: Tests for 1730–1870 and the subperiod 1730–1799 include a trend; tests for the subperiod 1816–1870 include a constant.
Source: Own calculation based on series shown in Fig. 3. Where not stated otherwise, lag order is 2.