RDP 7902: Financial Modelling in Australia 2. Sectoral Studies of Portfolio Behaviour

2.1 The Corporate and Household Sectors

There are five studies considered here, Valentine (1973) examines the portfolio holdings of very liquid assets by the aggregate corporate and household sectors. Clements (1976), Parkin, Cooper, Henderson and Danes (1975) and Purvis (1975) consider the general portfolio behaviour of the household sector.^[2] Kiernan (1978) considers the financial asset allocation of the total non-official sector.

2.1.1 Theory

These studies have the following common aspects:

• They treat all assets and liabilities as demand determined with interest rates being predetermined.
• The general behavioural equations can be derived from an explicit theory of the decisions of a representative member of the group.

The equations are derived using three separate (but related) approaches:

• The estimating equations are derived by maximising a static utility function subject to a budget constraint. (Valentine (1973); Clements (1976))^[3]. Adjustment costs do not appear in the utility function of either of these studies. It is assumed that the agent achieves his desired position within each period. Consequently, in this paper, these models are labelled equilibrium models.
• A set of desired levels is obtained in a similar manner to the first approach, but it is recognised that, because of costs of adjustment, it may not be possible for the agent to achieve his desired position within one observation period. A first order multiple stock adjustment model is used. This can be derived by minimising a quadratic cost function subject to the budget constraint. (Purvis (1975), Kiernan (1978))^[4].
• Parkin et al (1975) obtain a set of demand equations by maximising a quadratic intertemporal utility function which includes costs of adjustment. A similar set of estimating equations to those in the second group is obtained whilst estimating equations like those of the first group would be obtained if adjustment costs were omitted from the utility function.

In the appendix, a cost function from which the multiple stock adjustment model can be derived is set out and the multiple stock adjustment model is derived.

2.1.2 Estimation

Because the demand equations are derived subject to the balance sheet constraint of private non-financial groups it is important that the estimated parameters be consistent with this constraint. The.necessary restrictions between the parameters are derived in the appendix for the first two cases. A similar set of restrictions apply for the third case. The following rules are used when estimating such demand systems:

1. If the same set of regressors is used in each estimating equation and there are no cross equation restrictions each equation can be estimated efficiently using ordinary least squares. The parameters of any one of the equations can be determined from the balance sheet identity or can separately be estimated. The results will be identical.
2. If a different set of regressors is used in any of the equations or there are cross equation restrictions in the system they can only be estimated efficiently using three pass least squares or full information maximum likelihood with any one of the equations being dropped and its parameters determined from the balance sheet identity.

Parkin et al and Purvis estimate totally general systems with the same set of regressors in each equation with no cross equation restrictions and obtain efficient estimates using ordinary least squares. Purvis estimates each equation whilst Parkin et al obtain the consumption equation from the balance sheet identity.

Clements estimates his model using full information maximum likelihood because there are cross equation restrictions on the parameters. These restrictions stem from the assumptions of symmetry, homogeneity and an additive utility function.

Because Valentine models the total corporate and household portfolio he finds it necessary to include additional variables in his estimating equations which are not derived explicitly from the underlying theory. These variables reflect distributional effects. Unlike the studies discussed above, Valentine also suppresses any coefficients which he finds to be statistically insignificant. This leads to the elimination of all interest rate effects in the model.^[5] Consequently, Valentine's final estimating equations bear little resemblance to those that are derived initially from the underlying utility function. A different set of regressors in each equation also requires that three-pass least squares be used to ensure efficient estimation. It is interesting that although Valentine restricts himself to the liquid asset portfolio whilst Clements integrates financial and real asset demand with expenditure, both these equilibrium studies show evidence of significant auto-correlation. One interpretation of this is that the models should have allowed for financial market disequilibrium.

Kiernan (1978) obtains efficient estimates using ordinary least squares. He does not include the same set of variables in each estimating equation but instead specifies a particular hierarchy of decisions. At the first stage the agent allocates his savings to either equities or the remainder of the portfolio. At the next stage this remainder is allocated to government securities and a second remainder. The process continues through certificates of deposit, trading bank fixed deposits and trading bank demand deposits. The imposition of a strict decision hierarchy has, as the author admits, “an element of arbitrariness”. It does however have the econometric advantage of allowing a simple estimation technique whilst overcoming the statistical problems experienced by some of the other studies.

2.1.3 The Results

There is considerable evidence of links between the real and financial sectors and for interdependences within the financial sector from these studies. The results of Clements (1976), Parkin et al (1975) and Purvis (1975) are discussed in this section because all these integrate the demands by the household for real assets, financial assets and expenditure.

2.1.4 Rate of return links

i) Parkin et al

Of the 168 freely estimated rate of return links in the model, only 44 are significantly different from zero. Only six of the 15 own rate links are significantly different from zero. Fixed deposits, building society deposits, and other durables had the expected sign, whilst debentures, instalment credit, and land had perverse signs.

The strongest intuitively plausible results from the study are:

• A rise in the fixed deposit rate leads to a reduction in the demand for savings deposits and an increase in the demand for bank advances.
• A rise in the instalment credit rate reduces the demand for motor vehicles and other durables.
• A rise in the return on land reduces the demand for bank deposits and equities.
• A rise in the debenture rate reduces the demand for land.
• A rise in the long-term bond rate reduces the demand for fixed deposits.

Less plausible results are:

• A rise in the long-term bond rate leads to an increase in the demand for debentures but has no effect on the demand for bonds, whilst a rise in the debenture rates leads to a fall in holdings of debentures.
• A rise in the rate on bank advances has no effect on bank advances but reduces the demand for instalment credit.

The results of the study, whilst suggesting some interesting and plausible portfolio interactions contain enough insignificant and intuitively implausible coefficients to render the results, at least, preliminary.

ii) Purvis

In this study, 180 rate of return links are estimated and 33 are significantly different from zero. The only significant own rate effects are for fixed deposits, equities, household durables and bank advances. All the first three are positive whilst the own rate effect for bank advances is significant and negative, suggesting that advances are demand determined.

Other statistically significant results which are intuitively plausible are:

• An increase in the savings deposit rate reduces holdings of note and coin.
• An increase in the rate on advances reduces the demand for government securities.
• An increase in the rate on fixed deposits reduces the demand for equities.
• An increase in the price of household durables reduces the demand for advances and increases the demand for equities.
• An increase in the return on equities reduces the demand for motor vehicles, household durables and land.

Results that are not intuitively plausible are:

• A rise in the fixed deposit rate increases current deposit holdings.
• A rise in the price of durables reduces non-durable consumption.
• A rise in the return on debentures increases holdings of dwelling.
• A reduction in non-durable consumption follows a rise in the price of durables.

Similar reservations to those expressed for the Parkin et al study are relevant here. These results also show some evidence for interdependencies both within the financial sector and between the financial and real sectors.

iii) Clements

Clements develops an approach to modelling portfolio demand by imposing restrictions on his system which are based on the system wide approach to consumer demand, (Theil (1975)). He estimates equations for liquid assets, government securities, equities, dwellings, durables and three categories of consumption. Theil (1975) discusses three ways in which prices of assets and consumption goods affect the demand for other assets and consumption. These are:

• income effect;
• general substitution effect;
• specific substitution effect.

In addition to these links developed from the consumer demand theory, Clements allows for a lagged wealth effect. This effect only works through financial and physical assets. A change in the price of an asset affects the current value of the stock of assets. If this change does not accord with preferences, it is allocated across other assets and consumption goods to restore equilibrium. In this specification, the new short run equilibrium is achieved within one quarter. The first two “consumer demand” effects refer to the impact that changes in asset and consumer good prices have on the allocation of current income. A rise in prices reduces the real value of current nominal income. The “income effect” causes adjustment of assets and consumption demand. In affecting the level of real income, the price change will also affect the marginal utility of income. The “general substitution effect” influences all assets and consumer goods through the first order conditions from which the demand equations are derived. The specific substitution effect measures the influence which the price change of an asset or good will have on the demand for another through their interdependence in the agent's utility function. An example of this would be the interdependence of assets with similar risk factors or terms to maturity. These interdependencies could be expected to be of particular importance within financial markets.

Clements derives his estimating equations from a separable utility function, which means that the specific substitution effects are suppressed. The failure to measure the specific substitution effects could explain the very low cross price elasticities in the empirical results.^[6] As discussed above, these consistently low cross effects are not supported by the evidence from the more general studies by Parkin et al and Purvis. Of course Clements pays the price of lack of generality so that he can obtain precise parameter estimates. If we are specifically interested in testing for the links between markets then this price is too high. An obvious solution would be to retain some of the structure imposed on Clements' model but relax the assumption of a separable utility function.

2.1.5 Quantity links

Both Parkin et al and Purvis estimate the effect of lagged stocks on the holdings of each asset. In the context of the multiple stock adjustment model used by Purvis these coefficients can be identified with the disequilibrium spillover effects between assets (see Appendix B). That is, they measure the speed with which the holdings of any asset adjusts to the disequilibrium of any other asset. Such an explicit interpretation for the Parkin et al model is not possible, although, given the similarity of the two estimating forms, a similar interpretation seems reasonable.

In the study by Clements, asset demands and expenditure respond to the total level of spending-power, and the separate influence of the specific holdings of any particular asset is not measured.

i) Parkin et al

Of the 196 estimated lagged stock effects, 46 were found to be statistically significant. Only six of the own lagged stock effects were significant and of the expected sign.

If we interpret these in the context of a multiple stock adjustment model we see that fixed deposits, bank advances, and current deposits showed rapid own adjustment, whilst debentures, motor vehicles and dwellings adjusted more slowly.

Of the significant spillover effects:

• An excess demand for credit leads to a fall in holdings of financial assets.
• An excess demand for fixed deposits reduces holdings of current and savings deposits.
• Government securities, equities, and building societies have low spillover effects.
• An excess demand for durables leads to a rise in bank advances.
• An excess demand for dwellings leads to a fall in holdings of financial assets and a rise in credit levels.
• There is little significant evidence for spillover effects from financial assets to real assets.
• The consumption function has not explicitly been calculated to test whether financial sector spillovers directly affect consumption.

ii) Purvis

In this study 210 spillover coefficients are estimated and 51 are found to be significant. All the own adjustment coefficients are significant and show that the holdings of an asset rise when there is excess demand for it; of these, household durables and motor vehicles show the most rapid adjustment.

The significant disequilibrium effects are generally of an unexpected sign, which suggests that, unlike the results of the study by Parkin et al, most quantity effects stem from the influence of the own asset disequilibrium.

2.1.6 Income Impact Effects

Table 1 compares the proportion of a change in income which is absorbed, on impact, into financial assets, real assets and expenditure. Different income measures are used in these studies. In the Parkin et al study, the income measure covers labour and other miscellaneous income but no income which accrues from holding assets. (The latter income is endogenously determined.) In the Purvis study income is defined to cover labour income as well as income from dividend and interest payments and changes in the market value of real and financial assets. Clements also uses a general measure of income (defined as spending-power in his study) which covers labour income as well as income from asset holdings. In Kiernan's study, the sources of income are allocated into three groups. These are:

1. Labour income plus interest and dividend payments.
2. The income which accrues from a change in the market value of equities.
3. The income which is derived from a change in the market value of government securities.

Kiernan is interested in identifying the separate impacts on the portfolio of changes in income from each of these three sources.

Table 1 lists the proportional allocation of the separate income measures for each of the studies.

The most remarkable aspect of Table 1 is the overwhelming importance given to equities in explaining the impact effects on the portfolio of an income change for three of the studies. In the Purvis study this result can be partly explained because his measure of income includes changes in the market value of assets. The sample period used in the study by Purvis (1961(1)–1974(4)) contained large fluctuations in equity prices. Helliwell (1977) and others have argued that income changes resulting from a change in the market value of assets can be expected to remain, in the short-run, in the asset in which the change accrues. The more interesting issue is how other income changes, which are not due to variations in the market value of securities, are allocated across the portfolio. The results from the Kiernan study and the Parkin et al study which measure the impact effect of a change in income measure which does not include changes in the market value of assets also suggest that about 50% of the income change accrues to equities. One possible explanation of the Kiernan results is that they are biased in favour of a large allocation to the asset which is at the top of the hierarchical allocation process.^[8] This conjecture, however, is not applicable to the results of Parkin et al who use a totally general structure and still find that about 50% of any change in “labour and miscellaneous” income is lodged in equities. It is difficult to provide an explanation for this result beyond further emphasising the caution which should be exercised in interpreting the results of all these studies.

Further doubt about the important impact effects of equities is raised by the vastly different results found by Clements. Major differences between the Clements study and the others are that the former:

• estimates an equilibrium model;
• imposes structural restrictions on the estimating equations, some of which stem from a highly restricted utility function;
• uses an entirely different series for equities.

Clements calculates his value of equity series by capitalising dividends paid, where the capitalisation rate is the average yield on equities. The other studies use a value of equities series calculated by Helliwell and Boxall (1978). Helliwell and Boxall use a sample of 60 companies to calculate the average market valuation ratio and adjust a depreciated sum of total investment (to generate a measure of the total capital stock in the economy) to obtain the series for the market value of equities. The end result is that the Clements series is much smaller than the Helliwell-Boxall series. Equities represent, on average, 10% of the households portfolio in the Clements study and 30% in the other studies. In contrast, liquid assets represent 22% of the Clements portfolio and only 15% for the others. These great disparities between the series highlight the importance and problems with obtaining reliable equity data. It is, furthermore, interesting to note that Clements finds that by far the largest impact effect is found in the asset with the lowest cost of adjustment i.e. liquid assets.

2.2 Portfolio Models of Financial Institutions

Apart from the studies using full econometric models, which are discussed in Section 3, the only complete portfolio studies of Australian financial institutions are by Sharpe (1973; 1974) for the savings banks and Shaw (1973) for the life assurance companies.

Sharpe estimates a general stock adjustment model which he derives in a two step procedure using a utility function of similar mathematical form to that used by Valentine (Appendix A) and a cost function of the form outlined in Appendix B. The asset portfolio of the savings banks is disaggregated into: cash and Reserve Bank deposits; deposits with the major trading banks; Commonwealth government securities; local and semi-government securities; mortgage loans; and other loans and advances. Of the 24 interest rate effects estimated, only five are found to be significant. All own quantity adjustment effects are significant, but there is little significant evidence for the quantity disequilibrium of one asset affecting the holdings of others. The constraint variable used in Sharpe's study is total savings bank deposits. He finds that, on impact, 72% of an increase in deposits is absorbed into the most liquid assets i.e. cash, and deposits with other banks. On the other hand, 76% of the long-run increase in deposits goes into loans.

Shaw derives his estimating model using the same approach as Sharpe. He disaggregates the “free” asset portfolio of the life assurance companies into: fixed assets (including building and property); total shares; public securities held above the 30/20 requirement; mortgages, other loans and debentures. There was little significant evidence for interest rate influences (only 5 of the 30 estimated interest rate coefficients were significant). Furthermore, all the own rate effects were insignificant. In contrast to Sharpe's results, however, Shaw finds considerable evidence for the disequilibrium quantity effects of assets affecting the holdings of others. He points out that the results highlight the interdependency of the portfolio allocation process for the life assurance companies. The impact effect of a change in wealth were significant in all cases except excess public securities. The largest proportion of the wealth change was lodged in “other loans” (30%) and fixed assets (22%). This result is in marked contrast to the savings banks where a deposit increase is lodged, on impact, mainly in liquid assets. Further divergence from the savings banks comes from the long-run portfolio behaviour of the life assurance companies. In the long-run 28% of a wealth change is lodged in excess public securities, whilst other, less liquid investments, fall back from their impact levels.

2.3 Summary

At this stage the clear dichotomy between theoretical completeness and econometric pragmatism is evident. Those studies which faithfully estimate the structures suggested by very general theoretical underpinnings suffer from results that are usually statistically imprecise and not always intuitively plausible. Explanations for these problems range from: multicollinearity; insufficient and unreliable data; and inappropriate dynamic specification.

Kiernan attempts to overcome the problems caused by multicollinearity and low degrees of freedom by using a set of restrictions which originate from a rigidly imposed, but theoretically and empirically untested, decision hierarchy. Because Valentine considers a very small subset of assets he does not encounter such formidable statistical problems. Nevertheless, he does suppress the influence of variables with insignificant parameters, although the underlying theory of the model provides no justification. Clements chooses a less general dynamic specification and imposes cross equation restrictions derived from a utility function which suppresses interdependencies between asset holdings.

None of these approaches is entirely satisfactory. It can only be concluded that the portfolio study which imposes sufficient statistically testable and theoretically reasonable restrictions, to generate precise parameter estimates has not yet been done for Australia.

Some of the data problems are highlighted in the vastly different implications for the role of the equity market. It is also true that a good deal of the imprecision of the parameter estimates in the general portfolio studies could be explained by the low variability of many of the rates of return over the sample period. A study which used data for the mid and late 1970's, when much more variation in rates of return has been evident, may meet with more success than has been reported here.

It would be inappropriate, however, fully to discount the lessons that have been learnt from the sectoral studies. Among their most important contributions has been to establish a theoretical framework which later researchers may modify and, with more reliable and variable data, obtain more satisfactory results. On the empirical side, also, some lessons have been learnt. The general studies in particular have uncovered significant evidence of both price and quantity links between the real and financial sectors, as well as further evidence for interdependencies within the financial sector. It is hoped that further work is done in this field.

There are however, considerable costs in restricting studies of financial interactions to particular sectors. The important links between sectors from the information that the assets of one agent are the liabilities of another cannot be used in the equation specification. The studies discussed above all assume that asset holdings are demand determined. Furthermore, these studies have assumed either the increment to the total value of the portfolio or some component of income to be exogenous. Full model studies can explain the determination of total savings and income and model the interplay of the supply and demand for assets. These studies are examined in Section 3.

Footnotes

Parkin et al also model the portfolio behaviour of the corporate Sector. For purposes of comparison with the other studies their household sector work is discussed here. [2]

Specifically, Valentine considers a subset of the financial assets i.e. the very liquid assets, whilst Clements examines all financial assets as well as integrating decisions about real assets and expenditure. Clements derives his model from an intertemporal utility function but uses a collapsability theorem to represent the problem with a static utility function. [3]

Purvis integrates the portfolio allocation decision with the expenditure decision whilst Kiernan allocates across a predetermined sub-sector of savings. [4]

It is claimed that this is not surprising since Valentine considers the allocation of the portfolio of very liquid assets and it is reasonable that such a portfolio is determined mainly by transaction requirements and is not sensitive to interest rate changes. [5]

Price elasticity measures (Table 2, Clements (1976)) show the own elasticity being, on average, 3–5 times larger than the highest cross elasticity in each demand expression. [6]

See categories in text. [7]

Some supporting evidence of this conjecture comes from the result that Kiernan finds, that, on impact, 49% of the change in income resulting from a change in the market value of government securities is allocated to equities and only 20% stays in government securities. [8] [8]