|Abstract: ||The aim of this thesis has been to investigate the relationship between state and private pensions and personal savings. A theoretical framework has been developed to facilitate the a priori determination of the
relationship and an empirical investigation then undertaken using data for the U. K. in the postwar period. These two aspects of the thesis will firstly be summarised.
Initially, the standard life cycle model of individual accumulation is extended to include a flat rate pension scheme. The
introduction of the scheme will have an impact on savings determined by a savings replacement effect, where pension saving is substituted for alternative forms personal saving, and an induced retirement effect,
where savings is increased to finance a longer retirement period. The net effect on savings will depend on the rate of return to pension contributions, and therefore lifetime income, implied by the combination
of the two effects. As membership of state pension schemes is usually compulsory there exists the possibility that the implied rate of return can be above or below the market rate, indeed it may even be negative, with the result that lifetime income may be higher or lower than prior to the introduction of the pension scheme. The impact on savings cannot therefore be determined at a theoretical level. Increasing
pension contributions and benefits always lead to a reduction in work period and, under the usual assumptions, aggregate savings. These changes also induce early retirement. Having analysed the state pension case the model is further modified to include private pension schemes, in particular a terminal salary scheme, membership of which is assumed to be compulsory, and a money purchase scheme, the joining of which is a voluntary decision.
Again, for the reasons outlined above, the effect on personal savings of introducing the private schemes cannot be determined a priori. It is still possible though to say something about the effect of changes in pension contributions and benefits. When considering the increasing of pension contributions and state pension benefits, the
outcomes are as in the state pension case alone. If attention is confined to increasing private pension benefit functions by constant absolute amounts then early retirement and a reduction in work period
savings are the unambiguous outcomes. In the case of the money purchase scheme early retirement also implies a larger private
The empirical estimation of the relationship has been attempted through the inclusion of pension wealth variables in the aggregate
life cycle consumption function. Two definitions of pension wealth were used. Gross pension wealth has been defined as the discounted present value of future pension receipts weighted by survival probabilities whilst net pension wealth is gross pension wealth less the discounted present value of future pension contributions weighted by survival probabilities (termed liabilities). Unfortunately these definitions could only be used with state pensions - data was not available to evaluate these types of wealth variable in the case of private pensions. Over the period 1949-73 gross state pension wealth appears to have no impact on consumption, and therefore savings, whilst
net pension wealth depresses consumption. The growth of the market value of the assets of superannuation- funds was used as a proxy for the growth of private pension wealth. This data was available for the period 1958-73. Whilst private pension wealth was found to be insignificant in the regressions in these same equations gross state pension wealth becomes significant and positive. If net pension wealth is substituted for the gross alternative its coefficient remains
negative but its significance falls. Over both periods there was found to be no evidence of an induced retirement effect. Various estimates of the effect of the existence of pension schemes and changes in pension contributions and benefits were made on the basis of a range of estimated coefficients. As one would expect these estimates varied widely given the different signs of the coefficients on gross and net
state pension wealth.
There are four aspects of the work that, at the end of the day, give cause for concern. The two relating to the theoretical work are
probably less serious than the two relating to the empirical work.
In the development of the theoretical analysis the individuals work/leisure decision was given only passing consideration. Indeed it was only shown that if the individual moved continuously from the work to the retirement period then leisure considerations would be irrelevant. Nevertheless recognition was accorded to the possibility that if this move is discontinuous, which is highly likely to be the case, not only might the optimal retirement date be different to that derived in the basic model but also the earlier comparative statics results might no longer apply. In a recent paper Ulph (58) has begun
to consider this problem in a model incorporating a terminal salary based private pension scheme. Employing an iso-elastic utility function in consumption and leisure he shows that certain assumptions relating to the parameters of the utility function imply that not all the comparative
statics results of earlier chapters necessarily go through. Thus leisure
considerations are not irrelevant to the analysis of pensions. The results also imply that analyses of the individuals life cycle problem which do not include pensions, and where the individual retires when the
marginal utility of consumption falls below the marginal utility derived from spending all ones time in leisure, might be substantially changed when leisure considerations are taken into account. An obvious, extension of pension theory would then be to integrate it into a model of the above type, such as that of Blinder (13).
Another important feature of the pension decision,, which again has only been covered rather briefly, is uncertainty about the length of lifetime. It has been shown that if it is assumed that there exists a perfect insurance market then the problem reduces to an analysis under certainty, the insurance asset obviating any problem arising from a
probabilistic date of death. Ulph and Hemming (59) have since dropped this last assumption and shown how the results of this thesis are affected. Although this turns out to be to an extent: that gives little cause for concern, the new model does produce the results within a framework that is more realistic. The above paper also has important implications for another aspect of pension analysis. When lifetime is
uncertain the purchase of a pension asset or annuity provides insurance and the individual should therefore be prepared to purchase it even if its return were less than actuarially fair. Now in evaluating the
value of anticipated state pension wealth the average market rate of interest has been used to discount the expected value of future returns.
This is an approximation of the actuarially fair rate of interest. But under uncertainty this is not the appropriate rate of discount - what ought to be used is the lowest rate of return at which the individual
is just willing to purchase the annuity. In fact Ulph and Hemming show that whilst the individual is holding non-pension assets the
appropriate rate of discount is the rate on those assets. Once the individual has run down his stock of these assets the appropriate rate of discount will be the subjective rate of discount incorporating a
risk factor. Thus if the individual is holding the alternative asset the appropriate rate of discount is less than the actuarially fair rate, (see (3.6.4)). Pension wealth will therefore be underestimated. When none of the alternative assets are held the value of pension wealth can be under- or over-estimated depending on the relative magnitudes of the rates of interest and the subjective rate of discount. Not only do these results suggest that pension wealth might be evaluated
incorrectly but it could be that the optimal bequest decision, which did not affect the earlier analysis, now becomes important in that individuals will be holding capital through the later part of their life.
When they choose to make their bequest will affect their valuation of pension wealth. This interrelationship could produce some interesting results and is worth exploring further. Turning now to the problems arising on the estimation side one can consider firstly the general insignificance of the pension variables in the regression equations and the inconsistency of the
short and long period estimates. In retrospect, it should have been realised that the wealth approach could present a problem in attempting to reconcile the theoretical and empirical results. Recall that increases in both state pension contributions and benefits always lead
to a reduction in savings - when using the net state pension wealth variable in the estimated equations, no matter what the sign of its coefficient, both the above predictions cannot be confirmed
simultaneously. This follows since increasing contributions and benefits
respectively decreases and increases net state pension wealth. Only if the coefficient on gross state pension wealth had been positive and significant could both predictions have been borne out, That net state pension wealth alone should turn out to be significant, and then negative, implies that only the effect on savings of increasing contributions is confirmed. Possibly this result was to have been
expected since the only acceptable way of explaining the difference between the coefficients on the two pension wealth variables is through the significance of liabilities. Unfortunately there appears to be no reasonable argument which explains why individual behaviour should be determined by liabilities rather than gross wealth.
One has to be rather surprised about the apparent change in the relationship between the long and short data periods. A somewhat
similar case of this arose when Feldstein (19) changed his data period. Since in both analyses the regressors: are all income and wealth variables it is difficult to believe that this is not a classic symptom of the multi-collinearity which is quite clearly present rather than some structural change in the relationship over time.
In the theoretical developments an induced retirement effect played a prominent part in the discussion. When it came to estimation
the effect was found to be non-existent. Indeed the data suggested that retirement patterns had not changed markedly over the postwar period. This is not surprising. Under the state pension scheme coverage was universal by 1946 and whilst subsequent changes in contributions and benefits have hardly had marginal effects on lifetime
income it is unlikely that this will be affected by induced retirement because either many people will retire at the official retirement date or, for those retiring later, the retirement date is not a continuous variable. Even if this were not the case in practice estimation of the effect would be difficult since the retirement date is discrete as far as official statistics are concerned. As far as private pensions are concerned significant growth has taken place over the postwar
period but still only half the working population are covered - many of these are younger workers whose retirement behaviour will not yet have been observed.
Indeed this last point is one that applies to the study of private pensions as a whole. The empirical analysis of relationships
involving private pensions has been scant and highly unsatisfactory.
That no attempt was made to calculate a private pension wealth variable was simply due to data inadequacy: that no attempt was made to collect the data is explained by comparative advantage. As mentioned earlier the Government Actuaries Department are currently engaged in providing estimates. When these are available and the regression equations re-estimated some more useful results may emerge.
Even when the specification and data problems are overcome there still might exist one reason why the results produced might not be convincing. When a life cycle model of individual behaviour has carefully been built up, and no one could disagree that when considering pension problems this is the appropriate type of model, it will always be disappointing that the model cannot truly be tested with the data
currently available. All the methods considered for estimating such a
model are only approximations - there can be no substitute for cross-section data relating to the behaviour of the same individuals over fairly long periods of time.
Whilst this pessimism about the reliability of the results is clearly very healthy one is now only left to ponder whether the
attitude would have been the same if the estimated coefficients had all been statistically significant and of the theoretically anticipated signs. One has to hope so!|