State and private pensions, retirement behaviour and personal capital accumulation

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 \nrelationship 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. \nInitially, the standard life cycle model of individual accumulation is extended to include a flat rate pension scheme. The \nintroduction 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, \nwhere 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 \nof 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 \npension 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. \nAgain, 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 \noutcomes 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 \nsavings are the unambiguous outcomes. In the case of the money purchase scheme early retirement also implies a larger private \npension fund. \nThe empirical estimation of the relationship has been attempted through the inclusion of pension wealth variables in the aggregate \nlife 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 \nnet 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 \nnegative 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 \nstate pension wealth. \nThere 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 \nprobably less serious than the two relating to the empirical work. \nIn 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 \nto 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 \nstatics results of earlier chapters necessarily go through. Thus leisure \nconsiderations 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 \nmarginal 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). \nAnother 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 \nprobabilistic 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 \nuncertain 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 \nvalue of anticipated state pension wealth the average market rate of interest has been used to discount the expected value of future returns. \nThis 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 \nis just willing to purchase the annuity. In fact Ulph and Hemming show that whilst the individual is holding non-pension assets the \nappropriate 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 \nrisk 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 \nincorrectly 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. \nWhen 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 \nshort 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 \nto 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 \nsimultaneously. This follows since increasing contributions and benefits \nrespectively 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 \nexpected 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 re