RDP 8903: The Relationship Between Financial Indicators and Economic Activity: Some Further Evidence 4. VAR Estimation Results
June 1989
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This section presents results for VAR tests of the relationship between financial indicators and measures of activity. Two measures of activity are used: gross domestic product, and private final expenditure. The two sets of results are discussed in turn.
Each VAR model includes four lags of each variable. The number of lags was determined by estimating models with eight lags, then using likelihood ratio tests to compare these with models with six or four lags. Neither of the shorter lag specifications were dominated by the eight-lag specification, and so four lags were used for all the causality tests^{[6]}.
(a) Financial Indicators and GDP
This section presents some results, using VAR methodology, for the relationship between GDP, as a measure of activity, and the various financial aggregates and short-term interest rates.
Table 1 shows the results for two-variable VARs, where each financial indicator is compared “one-on-one” with GDP. Both nominal and real GDP are tested. The table shows results over two time periods for the narrow financial aggregates and interest rates: 1969–88, and 1978–88. Tests involving the broader aggregates are restricted to the later period by availability of data.
1969:2–1988:3 | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
Nom GDP | M1 | Nom GDP | M3 | Nom GDP | Bank lend. | Nom GDP | Bill Rate | ||||
Nom GDP | 0.371 | 1.548 | Nom GDP | 0.290 | 1.942 | Nom GDP | 0.335 | 2.371 | Nom GDP | 0.947 | 2.275 |
M1 | 0.570 | 8.036** | M3 | 3.140* | 7.972** | Bank lend. | 3.042* | 13.000** | Bill Rate | 0.412 | 1.142 |
1978:1–1988:3 | |||||||||||
Nom GDP | M1 | Nom GDP | M3 | Nom GDP | Bank lend. | Nom GDP | Bill Rate | ||||
Nom GDP | 5.769** | 4.943** | Nom GDP | 2.001 | 0.636 | Nom GDP | 3.267* | 1.088 | Nom GDP | 2.557 | 1.842 |
M1 | 0.852 | 1.862 | M3 | 1.716 | 1.619 | Bank lend. | 0.731 | 5.413** | Bill Rate | 1.055 | 3.024* |
Nom GDP | Broad money | Nom GDP | AFI lend. | Nom GDP | Credit | ||||||
Nom GDP | 2.675* | 0.226 | Nom GDP | 1.823 | 0.413 | GDP | 2.776* | 1.370 | |||
Broad money | 2.534 | 0.688 | AFI lend. | 4.061** | 5.837** | Credit | 2.679* | 7.965 | |||
1969:2–1988:3 | |||||||||||
Real GDP | M1 | Real GDP | M3 | Real GDP | Bank lend. | Real GDP | Bill Rate | ||||
Real GDP | 1.476 | 1.761 | Real GDP | 1.405 | 0.877 | Real GDP | 1.589 | 1.587 | Real GDP | 1.553 | 0.761 |
M1 | 0.813 | 8.090** | M3 | 0.922 | 7.839** | Bank lend. | 0.802 | 15.650** | Bill Rate | 0.941 | 1.576 |
1978:1–1988:3 | |||||||||||
Real GDP | M1 | Real GDP | M3 | Real GDP | Bank lend. | Real GDP | Bill Rate | ||||
Real GDP | 1.380 | 2.082 | Real GDP | 0.878 | 0.860 | Real GDP | 1.917 | 0.812 | Real GDP | 1.405 | 0.981 |
M1 | 1.340 | 1.732 | M3 | 2.849* | 1.626 | Bank lend. | 1.394 | 3.882* | Bill Rate | 1.496 | 3.108* |
Real GDP | Broad money | Real GDP | AFI lend. | Real GDP | Credit | ||||||
Real GDP | 1.181 | 0.378 | Real GDP | 0.919 | 0.360 | Real GDP | 1.193 | 1.030 | |||
Broad money | 2.853* | 0.622 | AFI lend. | 7.586** | 3.687* | Credit | 6.486** | 5.297** | |||
^{1} Calculated values for F-tests of the hypothesis that the coefficients on lags of explanatory variables are jointly zero. An* denotes significance at the 5 per cent level, ** at the 1 per cent level. |
In interpreting the table, note that the rows of each cell represent the left-hand-side variables in the equation, and the columns represent the right-hand-side variables. The statistics quoted are the computed values of the F-statistic in a test of the hypothesis that lags of the right-hand-side variable are jointly zero in an equation determining the left-hand-side variable. In the top-left-hand cell of Table 1, for example, in an equation explaining growth in nominal GDP by lags of itself and lagged growth of M1, imposing the restriction that coefficients on the lags of nominal GDP are zero yields a test statistic of 0.371, which is below the critical value of 2.5 at the 5 per cent significance level, so that the hypothesis cannot be rejected. Similarly, a test of the hypothesis that lags of M1 have zero coefficients yields a test statistic of 1.548, also insignificant, so the hypothesis cannot be rejected.
In the next row of this cell, lags of nominal GDP do not add much explanatory power to an equation for M1 but lags of M1 itself do. (The test statistic for the latter is 8.036, well outside the critical value.) Clearly, in each cell, the results of most interest are the off-diagonal elements, where the explanation of current values of a variable require more than just the lags of that variable itself.
Interpreting the other cells in Table 1 in like manner suggests the following results:
- both real and nominal GDP tend to lead the broader financial aggregates;
- there is some evidence for GDP leading M3 and bank lending, though this is less consistent; and
- M1 leads nominal GDP in the 1978–88 period.
Table 2 shows results for three-variable VARs, where the bill rate is included in every model. The interpretation of the table is similar to that for Table 1 except that each cell now contains nine entries: the test statistics for the hypothesis of jointly zero coefficients for lags of each of the three variables in each of three equations.
1969:2–1988:3 | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
Nom GDP | Bill rate | M1 | Nom GDP | Bill rate | M3 | Nom GDP | Bill rate | Bank lend. | |||
Nom GDP | 0.707 | 2.943* | 2.229 | Nom GDP | 0.386 | 1.379 | 1.078 | Nom GDP | 0.452 | 1.809 | 1.898 |
Bill rate | 0.570 | 5.601** | 7.066** | Bill rate | 0.602 | 3.489* | 4.624** | Bill rate | 0.796 | 1.665 | 2.424 |
M1 | 0.759 | 4.596** | 1.734 | M3 | 2.609* | 5.107** | 5.876** | Bank lend. | 1.922 | 1.013 | 13.828** |
1978:1–1988:3 | |||||||||||
Nom GDP | Bill rate | M1 | Nom GDP | Bill rate | M3 | Nom GDP | Bill rate | Bank lend. | |||
Nom GDP | 5.613** | 1.586 | 4.311** | Nom GDP | .465 | 1.798 | 1.734 | Nom GDP | 3.389* | 2.201 | 1.494 |
Bill rate | .370 | 4.642** | 2.004 | Bill rate | .961 | 1.816 | 2.712* | Bill rate | 1.467 | 3.004* | 1.816 |
M1 | .889 | 1.880 | 0.558 | M3 | 1.912 | 16.941** | 1.733 | Bank lend. | 0.844 | 0.245 | 4.500** |
Nom GDP | Bill rate | Broad money | Nom GDP | Bill rate | AFI lend. | Nom GDP | Bill rate | Credit | |||
Nom GDP | 2.934* | 2.350 | 0.812 | Nom GDP | 1.730 | 1.349 | 0.126 | Nom GDP | 2.290 | 1.258 | 0.859 |
Bill rate | 1.459 | 5.403** | 4.222** | Bill rate | 2.033 | 2.927* | 1.775 | Bill rate | 2.051 | 3.375* | 2.658 |
Broad money | 1.872 | 3.322* | 1.055 | AFI lend. | 2.936* | 1.516 | 4.912** | Credit | 3.757* | 1.775 | 9.460** |
1969:2–1988:3 | |||||||||||
Real GDP | Bill rate | M1 | Real GDP | Bill rate | M3 | Real GDP | Bill rate | Bank lend. | |||
Real GDP | 1.484 | 0.879 | 1.831 | Real GDP | 1.233 | 0.658 | 0.767 | Real GDP | 1.469 | 0.268 | 1.026 |
Bill rate | 0.154 | 5.350** | 5.828** | Bill rate | 0.911 | 4.101** | 4.387** | Bill rate | 0.908 | 2.402 | 1.999 |
M1 | 0.867 | 4.445** | 2.020 | M3 | 0.956 | 5.613** | 9.081** | Bank lend. | 1.263 | 2.452 | 19.048** |
1978:1–1988:3 | |||||||||||
Real GDP | Bill rate | M1 | Real GDP | Bill rate | M3 | Real GDP | Bill rate | Bank lend. | |||
Real GDP | 1.402 | 0.659 | 1.606 | Real GDP | 0.893 | 0.607 | 0.504 | Real GDP | 1.922 | 1.375 | 1.217 |
Bill rate | .500 | 4.393** | 1.735 | Bill rate | 0.774 | 3.470* | 1.164 | Bill rate | 1.226 | 2.831* | 1.167 |
M1 | 1.598 | 2.167 | 0.276 | M3 | 3.367* | 0.963 | 1.886 | Bank lend. | 1.340 | 0.155 | 3.209* |
Real GDP | Bill rate | Broad money | Real GDP | Bill rate | AFI lend. | Real GDP | Bill rate | Credit | |||
Real GDP | 1.493 | 0.990 | 0.450 | Real GDP | 1.114 | 0.707 | 0.170 | Real GDP | 1.019 | 0.784 | 0.827 |
Bill rate | 0.748 | 4.407** | 2.816* | Bill rate | 1.891 | 2.178 | 1.233 | Bill rate | 1.829 | 2.872* | 1.984 |
Broad money | 2.644 | 3.885* | 0.747 | AFI lend. | 5.672** | 1.385 | 1.965 | Credit | 7.347** | 1.626 | 5.567** |
^{1} Calculated values for F-tests of the hypothesis that the coefficients on lags of explanatory variables are jointly zero. An* denotes significance at the 5 per cent level, ** at the 1 per cent level. |
Results here are similar to those for the two-variable models: GDP tends to lead AFI lending and credit, and also M3, though again the latter result is not as consistent: it occurs only on half the occasions on which M3 enters. There is one instance of the bill rate leading nominal GDP, and one of M1 leading nominal GDP, but overall there is not strong evidence of “Granger-causality” in these cases.
There are a number of instances of complex relationships between the bill rate and the financial aggregates, where lags of the aggregate help explain the bill rate and vice versa.
Appendix B contains results for the same tests based on data which are not seasonally adjusted. Similar conclusions are evident: the broad lending and credit aggregates tend to be led by GDP, and there is two-way dynamic interaction between the bill rate and the financial aggregates in a number of cases.
(b) Financial Indicators and Private Final Demand
The principal activity indicator in BMS was private final demand. This section presents results of tests parallel to those in Section 4(a), but using PFD as the activity indicator. The interpretation of Table 3 and 4 is analogous to that of the earlier tables.
1969:2–1988:3 | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
Nom PFD | M1 | Nom PFD | M3 | Nom PFD | Bank lend. | Nom PFD | Bill Rate | ||||
Nom PFD | 3.781** | 1.725 | Nom PFD | 3.330* | 0.879 | Nom PFD | 3.896** | 0.738 | Nom PFD | 5.772** | 0.351 |
M1 | 1.084 | 6.311** | M3 | 1.419 | 6.022** | Bank lend. | 0.970 | 13.218** | Bill Rate | 1.256 | 1.778 |
1978:1–1988:3 | |||||||||||
Nom PFD | M1 | Nom PFD | M3 | Nom PFD | Bank lend. | Nom PFD | Bill Rate | ||||
Nom PFD | 1.196 | 1.815 | Nom PFD | 1.969 | 1.871 | Nom PFD | 2.626 | 1.197 | Nom PFD | 2.133 | 0.100 |
M1 | 1.831 | 1.785 | M3 | 1.142 | 1.882 | Bank lend. | 0.670 | 4.955** | Bill Rate | 2.875* | 3.669* |
Nom PFD | Broad money | Nom PFD | AFI lend. | Nom PFD | Credit | ||||||
Nom PFD | 2.628 | 2.063 | Nom PFD | 2.882* | 0.730 | PFD | 2.403 | 0.230 | |||
Broad money | 2.507 | 1.253 | AFI lend. | 2.119 | 3.692* | Credit | 1.011 | 7.389** | |||
1969:2–1988:3 | |||||||||||
Real PFD | M1 | Real PFD | M3 | Real PFD | Bank lend. | Real PFD | Bill Rate | ||||
Real PFD | 1.178 | 1.257 | Real PFD | 1.634 | 0.882 | Real PFD | 1.988 | 1.734 | Real PFD | 2.501 | 1.377 |
M1 | 2.431 | 5.323** | M3 | 2.266 | 6.705** | Bank lend. | 0.499 | 14.670** | Bill Rate | 5.081** | 3.629** |
1978:1–1988:3 | |||||||||||
Real PFD | M1 | Real PFD | M3 | Real PFD | Bank lend. | Real PFD | Bill Rate | ||||
Real PFD | 1.085 | 1.255 | Real PFD | 2.234 | 1.087 | Real PFD | 2.532 | 0.977 | Real PFD | 2.335 | 0.098 |
M1 | 3.389* | 2.378 | M3 | 0.934 | 1.741 | Bank lend. | 1.170 | 4.519** | Bill Rate | 3.198* | 3.971** |
Real PFD | Broad money | Real PFD | AFI lend. | Real PFD | Credit | ||||||
Real PFD | 1.924 | 2.561 | Real PFD | 2.742* | 1.596 | Real PFD | 2.700* | 1.152 | |||
Broad money | 3.035* | 1.281 | AFI lend. | 4.929** | 1.335 | Credit | 2.306 | 4.033** | |||
^{1} Calculated values for F-tests of the hypothesis that the coefficients on lags of explanatory variables are jointly zero. An* denotes significance at the 5 per cent level, ** at the 1 per cent level. |
1969:2–1988:3 | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
Nom PFD | Bill rate | M1 | Nom PFD | Bill rate | M3 | Nom PFD | Bill rate | Bank lend. | |||
Nom PFD | 3.054* | 0.233 | 1.520 | Nom PFD | 3.093* | 0.328 | 0.825 | Nom PFD | 2.096* | 0.501 | 1.001 |
Bill Rate | 0.298 | 5.710** | 5.643** | Bill rate | 0.438 | 3.887** | 3.478** | Bill rate | 0.662 | 2.316 | 1.541 |
M1 | 1.093 | 4.408** | 1.543 | M3 | 1.441 | 5.631** | 5.975** | Bank lend. | 0.930 | 1.877 | 14.392** |
1978:1–1988:3 | |||||||||||
Nom PFD | Bill rate | M1 | Nom PFD | Bill rate | M3 | Nom PFD | Bill rate | Bank lend. | |||
Nom PFD | 1.018 | 0.610 | 2.227 | Nom PFD | 1.267 | 0.135 | 1.707 | Nom PFD | 2.291 | 0.243 | 1.123 |
Bill Rate | 0.764 | 4.170** | 0.883 | Bill rate | 1.671 | 3.689* | 0.939 | Bill rate | 3.208* | 3.935* | 1.845 |
M1 | 1.063 | 1.166 | 0.754 | M3 | 0.868 | 0.171 | 1.545 | Bank lend. | 0.618 | 0.085 | 4.028** |
Nom PFD | Bill rate | Broad money | Nom PFD | Bill rate | AFI lend. | Nom PFD | Bill rate | Credit | |||
Nom PFD | 1.801 | 0.537 | 2.372 | Nom PFD | 2.366 | 0.110 | 0.667 | Nom PFD | 2.057 | 0.190 | 0.306 |
Bill Rate | 1.608 | 5.191** | 2.510 | Bill rate | 2.680 | 3.411* | 0.819 | Bill rate | 2.735* | 3.633* | 1.643 |
Broad money | 1.328 | 2.719* | 1.363 | AFI lend. | 1.486 | 1.682 | 4.323** | Credit | 1.200 | 0.925 | 7.737** |
1969:2–1988:3 | |||||||||||
Real PFD | Bill rate | M1 | Real PFD | Bill rate | M3 | Real PFD | Bill rate | Bank lend. | |||
Real PFD | 1.336 | 0.845 | 0.736 | Real PFD | 1.834 | 0.918 | 0.463 | Real PFD | 1.975 | 1.203 | 1.377 |
Bill Rate | 1.834 | 6.662** | 3.576* | Bill rate | 4.655** | 6.471** | 4.230** | Bill rate | 5.022** | 4.904** | 2.244 |
M1 | 1.370 | 3.303* | 2.098* | M3 | 1.555 | 4.816** | 8.382** | Bank lend. | 1.052 | 2.467 | 16.943** |
1978:1–1988:3 | |||||||||||
Real PFD | Bill rate | M1 | Real PFD | Bill rate | M3 | Real PFD | Bill rate | Bank lend. | |||
Real PFD | 1.060 | 0.154 | 1.184 | Real PFD | 1.896 | 0.071 | 0.942 | Real PFD | 2.291 | 0.156 | 0.939 |
Bill Rate | 0.999 | 4.260** | 0.883 | Bill rate | 1.798 | 4.029** | 0.820 | Bill rate | 2.774* | 3.964* | 1.219 |
M1 | 3.003* | 1.737 | 1.514 | M3 | 0.773 | 0.251 | 1.356 | Bank lend. | 1.482 | 0.459 | 4.552** |
Real PFD | Bill rate | Broad money | Real PFD | Bill rate | AFI lend. | Real PFD | Bill rate | Credit | |||
Real PFD | 1.330 | 0.489 | 2.778 | Real PFD | 2.285 | 0.047 | 1.361 | Real PFD | 2.440 | 0.161 | 1.100 |
Bill Rate | 1.754 | 5.783** | 2.390 | Bill rate | 2.323 | 3.563* | 0.306 | Bill rate | 2.067 | 3.595* | 0.811 |
Broad money | 1.798 | 2.771* | 1.311 | AFI lend. | 4.362** | 2.085 | 1.754 | Credit | 2.647 | 1.149 | 4.609** |
^{1} Calculated values for F-tests of the hypothesis that the coefficients on lags of explanatory variables are jointly zero. An * denotes significance at the 5 per cent level, ** at the 1 per cent level. |
There is some support for the hypothesis that activity leads the broad aggregates, though it is not as strong as where GDP is used as the activity variable.
On a number of occasions lags of growth in PFD explain changes in the bill rate. This result is in apparent contrast to the conclusions of BMS, and some reconciliation is in order.
First, it is notable that in the three-variable models, the result occurs five times, and four of these are when bank lending is the third variable. In the thirteen sets of results in Table 4 which do not include bank lending, PFD leads the bill rate only once (when M3 is included). This suggests that perhaps there is some unique feature of the interaction of interest rates, PFD and bank lending which is reflected in the results.
Second, the result that PFD leads the bill rate hinges, to some extent, on the specification of the interest rate series in the present paper as a first difference, rather than as a level as in BMS. When the two-variable VAR tests in Table 3 are conducted with the level, rather than the change, of the bill rate, a unidirectional relationship between PFD and the bill rate can no longer be established.
Footnote
For models with seasonally adjusted data, two lags performed as well as four. But four lags were retained anyway for consistency. [6]