# RDP 8805: The Relationship Between Financial Indicators and Economic Activity: 1968–1987 4. Financial Indicators and Real Private Demand: Correlation Analysis

This section augments the graphs shown in the previous section by calculating simple correlation coefficients between each financial variable and real private demand. As well as helping to quantify the strength of the relationship between the pairs of variables, it also provides a simple quantitative test of whether a particular variable leads or follows private demand. The section is in two parts. Part (a) gives results for the complete data period; part (b) gives results for selected sub-periods.[10]

## (a) Full Sample Results

Table 1 summarises the results of tests to see whether each financial variable has a coincident or leading relationship with real private demand. The first column shows the correlation coefficients between current movements in demand and the current movements in the various financial indicators. The second column shows the correlation between the current movement in private demand and the movement in the financial indicators in the previous period, and so on.

Table 1: Correlation Coefficients Between Financial Indicators and Real Private Demand
0 1 2 3 4 5
Bill rate −.37** −.40** −.39** −.29** −.25** −.18
M1 .31** .32** .27** .11 .05 −.04
M3 .26** .17 −.01 −.15 −.22* −.05
Bank lending .09 −.04 −.15 −.28** −.39** −.24**
Broad money(a) .37** .14 .23 .09 −.02 .13
Lending(a) .09 .14 .11 .08 .04 −.05
Credit(a) .05 .15 .11 .08 .06 −.05

(a) The estimation period for these variables is from 1976–87. The others are for the full period of 1968–87. All financial aggregates and demand are in percentage change form, seasonally adjusted.
(b) An asterisk indicates significance at the 10 per cent level; two indicates the 5 per cent level.

The top row of Table 1 shows that the first five correlation coefficients between interest rates and domestic demand are all significant and of the expected (negative) sign. Not only are the current quarter's interest rates correlated with current private demand, but interest rates as long ago as a year are correlated with private demand. Expressed in a different way, a change in interest rates is associated with changes in private demand in the same quarter, and over the next year.

M1 also has a significant relationship to private demand, with M1 in the current quarter, and in the previous two quarters, positively correlated with demand. This establishes a clear leading relationship for M1, consistent with the graphical evidence. On balance, the relationship is not as strong for M1 as it is for interest rates. The correlation coefficients are a little smaller, and the lead time between movements in M1 and movements in private demand is shorter than for interest rates.

The results for M3 are noticeably weaker. The only significant coefficient of the correct (positive) sign is the coincident one, and its value is lower than for either M1 or interest rates. There is a significant coefficient on the fourth lead, but it is of the wrong sign. Bank lending is less satisfactory than M3, as there are no significant correlations of the correct sign (although there is a sequence with the wrong sign at leads from three to five quarters).

Among the broader aggregates, the results are also weak; the only significant coefficient is a coincident one between broad money and private demand. Neither lending nor credit show a coincident correlation at all.

An obvious explanation is that the broader aggregates do not lead demand, but lag it. Table 2, which contains correlation coefficients between lags of real private demand and current movements in the broad aggregates, confirms this. Most of these coefficients are significant and positive, i.e. movements in private demand occur before the associated movement in the financial aggregates. The strongest results are for lending. This supports the visual evidence that broad financial aggregates have a strong pro-cyclical behaviour, but lag the cycle in private demand.

Table 2: Correlation Coefficients Between Real Private Demand and Financial Indicators
Indicator Lag in quarters(b)
1 2 3 4 5
Bill rate −.25** −.13 −.05 .00 .06
M1 .21* −.16 −.24** −.31** −.36**
M3 .24** .04 −.24** −.19* −.22*
Bank lending (a) .07 .10 .03 .07 .04
Broad money (a) .43** .36** .39** .26* −.19
Lending (a) .30* .44** .51** .49** .24
Credit .25* .38** .45** .46** .19

(a) The estimation period for these variables is from 1976–87. The others are for the full period of 1968–87. All financial aggregates and demand are in percentage change form, seasonally adjusted.
(b) An asterisk indicates significance at the 10 per cent level; two indicates the 5 per cent level.

## (b) Variation Between Sub-Periods

The period over which these relationships have been tested contains major structural changes in the financial system; it has moved from being heavily regulated to being largely deregulated. This change occurred in a number of steps over the period; a full account of the various changes will be contained in a later paper in this series.[11]

Any division of the two-decade period into regulated and deregulated sub-periods will inevitably be partly arbitrary. For the present purposes, the major division has been made at December 1980. This was when all interest rate controls on bank deposits were removed. The period from 1968 to 1980 is regarded as being predominantly regulated and the period from 1980 to 1987 as predominantly deregulated. Within the latter period, the sub-period December 1983 to December 1987 corresponds to a further step in deregulation when the Australian dollar was floated, maturity restrictions on bank deposits were removed (in 1984) and open market operations became the main technique for implementation of monetary policy.

Table 3 shows correlation coefficients for those sub-periods. Like Table 1, it tests only for coincident and leading relationships between financial variables and real private demand.

Table 3: Correlation Coefficients Between Financial Indicators and Real Private Demand: Selected Sub-Periods
Indicator   Sub-periods(a)
Quarters
Mar. 1968 to
Dec. 1980
Dec. 1980 to
Dec. 1987
Dec 1983 to
Dec. 1987
Bill rate 0 −.37** −.37** −.76**
1 −.36** −.54** −.76**
2 −.33** −.56** −.61**
3 −.10 −.60** −.50**
4 −.08 −.47** −.35
5 .00 −.29 −.27
M1 0 .30** .30 .34
1 .24* .45** .48*
2 .12 .52** .36
3 .01 .24 −.11
4 −.13 .31 .24
5 −.15 .10 .13
M3 0 .24* .37* .62**
1 .21 .08 .15
2 −.05 .18 −.04
3 −.17 −.10 −.22
4 −.26* −.14 −.30
5 −.07 −.06 −.25
Bank lending 0 .09 .17 .02
1 −.04 −.05 −.30
2 −.18 −.09 −.56**
3 −.26** −.39** −.80**
4 −.41** −.40** −.70**
5 −.26* −.22 −.56**
1 .13 −.02
2 .08 .10
3 −.13 −.25
4 −.36* −.62**
5 −.32* −.48*
Lending 0 .16 −.11
1 .07 −.22
2 −.11 −.30
3 −.36* −.56**
4 −.43** −.63**
5 −.52** −.69**
Credit 0 .17 −.19
1 .13 −.11
2 −.07 −.23
3 −.31 −.51**
4 −.38** −.54**
5 −.53** −.72**

(a) An asterisk indicates significance at the 10 per cent level; two indicates the 5 per cent level.

The top panel shows results for the relationship between interest rates and real private demand. In all three sub-periods, there is a significant coincident and leading relationship with private demand. The strength of this relationship (indicated by the size of the correlation coefficients) increases in the more recent sub-periods. The correlations between real private demand and interest rates at leads from one to four quarters are the strongest identified in the various tests in this paper.[12]

The second panel shows results for the relationship between M1 and real private demand. Overall, the relationship is not as strong as that between interest rates and demand. It looks marginally stronger in the post-1980 period, with larger coefficients and slightly improved significance levels. It then seems to deteriorate post-1983, with coefficients noticeably less significant. This is consistent with the discussion of the graphical evidence that suggested some recent shift in the relationship between M1 and demand.

Somewhat surprisingly in view of the visual evidence, the correlation coefficients for M3 suggest that there has been no deterioration in its relationship with real private demand. The correlation is not as strong as for interest rates or M1 in the early period, and it has no leading characteristics, but it has not deteriorated on the basis of evidence in Table 3. In fact, the results suggest that the contemporaneous correlation has strengthened over the most recent period.

But it is clear from the graph that shifts in the relationship between M3 and activity that have occurred within our sub-samples, notably in 1982/83, and possibly also in 1985. A more detailed breakdown of the periods for the correlations suggests that M3 had a very strong leading relationship with demand between 1970 and 1977 (a significant correlation coefficient of 0.44). Between 1977 and 1983, this relationship disappeared, with no concurrent or leading coefficients being significant. After 1983, a strong concurrent relationship (evident in Table 3) is found. These results are consistent with views put forward elsewhere that the relationship between M3 and activity has at times been unstable over the past 20 years..3

Broad money shows a strong coincident relationship with real demand through both of the sub-periods. There is no evidence of broad money playing a leading role. There is also no evidence of coincident relationships for the broader lending aggregates in the sub-period analysis. Several leading coefficients are significant in these cases, but with unexpected signs (negative). This strengthens in the 1983–1987 period. One explanation for this apparently paradoxical result could lie in the number of turning points in the 1980s. If these aggregates in fact lag activity (as the evidence in Table 2 suggests), then negative correlations between leads of the aggregates and current demand might be expected where there are pronounced cycles in demand. In effect, these coefficients are picking up the fact that just after a turning point, demand is negatively correlated with lags of itself.

In summary, the evidence to this point suggests that nominal interest rates and M1 have had a consistent, leading relationship with real private demand over the past 20 years. Other bank-based aggregates have been less consistent as indicators. Broader aggregates have had reasonably good relationships, but have tended to be lagging or coincident indicators.

## Footnotes

The formula for the correlation coefficient is given in the appendix, along with notation on how significance levels are calculated. [10]

“Deregulation and the Behaviour of Financial Institutions”, Research Discussion Paper, (forthcoming). [11]

It should be noted that the results for the last sub-period are not as strong when real GDP is used as the indicator of activity rather than private demand. [12]