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Ricardian equivalence are the required assumptions defensible?
economics letters
Economics
Letters
46 (1994) 223-227
Ricardian Equivalence Are the required assumptions defensible? James Pemberton Department of Economics, Received
Faculty of Letters and Social Sciences, P.O. Box 218, Whiteknights, Reading, Berkshire, RG62AA, UK
13 July 1992; final revision
received
1 March
1993; accepted
29 March
1994
Abstract Ricardian Equivalence (RE) requires universal provision of bequests for purely altruistic reasons. This paper argues that no defensible set of values for relevant parameters is consistent with this requirement; hence observed bequests must at least partly reflect motives inconsistent with RE. JEL
classification: D10
1. Introduction
Barro (1974) generated a large and continuing literature with his well-known model of intergenerational altruism and debt neutrality. Subsequently, theoretical work has concentrated on analysing conditions in which strict neutrality breaks down, and empirical work has tested, with varying results, the extent to which the neutrality predictions hold in practice. Barro (1989) and Bernheim (1987) provide recent literature surveys. This paper considers evidence concerning the assumptions required for, rather than the predictions of, full neutrality. The following three assumptions are all necessary. (a) Each household must be linked by operative intergenerational transfers to all (not some) of its children. No one must be at a zero bequest corner solution. (b) All such transfers must reflect pure altruism, rather than a mixture of altruistic and ‘strategic’ motives (Bernheim et al., 1985). Neither must they be ‘accidental’ bequests occurring because parents cannot know their date of death (Davies, 1981).’ (c) Th ere must be no uncertainty about future income levels, of ’ A referee has argued that neutrality may still be possible if bequests result for both altruistic and ‘accidental’ reasons (e.g. altruism may determine bequest levels at the margin, with intramarginal bequests being ‘accidental’). A fully worked out model on these lines would be quite complex - it would need to incorporate uncertain lifetimes for future as well as current generations - and to my knowledge has not been attempted. In general, neutrality is overturned by uncertainty (e.g. about future income, future tax policy, etc.) and it is not a priori obvious that it could plausibly be consistent with uncertainty about the length of life. 0165-1765/94/$07.00 0 1994 Elsevier SSDI 0165-1765(94)00475-H
Science
B.V. All rights reserved
J. Pemberton
224
I Economics Letters 46 (1994) 223-227
either the parent or any of the children (Barsky et al., 1986).2 Assumption (b) can hold if a market for life-time annuities develops. As for (c), it is possible in principle that people behave as if they are subjectively certain about future incomes. In this paper I assume that (a), (b) and (c) all hold, and then assess whether or not this combined assumption is plausible in the light of observed or estimated values for relevant parameters. The conclusion is negative. Since the parameter values refer to contexts in which bequests are believed to explain a significant, and perhaps an overwhelming, proportion of total wealth accumulation, the implication is that these bequests cannot plausibly be fully explained in a way which is consistent with Ricardian Equivalence. Section 2 develops the model; Section 3 assesses its plausibility and draws conclusions.
2. The altruistic
model with certainty
I specify the simplest possible Barro-type model. There are many dynasties with finite-lived overlapping generations, a constant population, and parthogenesis. Hence each household contains one parent and one child.3 Since life-cycle considerations are not central, adult life is modelled as a single ‘period’. All adults in any given period t receive an identical exogenously determined labour income y(t) and they all have identical preferences. (Hence all dynasties are effectively identical.) Each adult may also receive a bequest b(t - 1) from his ancestor. All resources are available at the start of the period, when they are allocated to consumption c(t) and when some may be invested, at an annual interest rate r, in a bequest b(t) to the child. The span of a generation - i.e. the length of a ‘period’ - is assumed to be 25 years. There is no uncertainty. The household’s objective function is V(t) = u(c(t))
+ aDV(t
u(c) = (1 - a)
+ 1) ;
‘c’-“(a>O,o#l);
c(t) = y(t) + Rb(t - 1) - b(t) ;
R = (1 + r)*“;
a > 0
)
=logc((T=l) b(t - 1) ) b(t) 2 0
W
D = (1+ d))25 .
d is the annual rate of time preference. (Y is measuring the weight which the household gives non-negativity constraint on b follows Barro and The only allocation decision for each generation The first-order condition is dV(t)ldb(t)
= -[c(t)-”
- aRDc(t + l))“]
(14
the intergenerational altruism parameter, to its heirs’ utility relative to its own. The most of the subsequent literature. t adult is her choice of bequest b(t), if any.
< or = 0 as b(t) = or > 0 .
‘There are of course other important requirements for neutrality, e.g. that all taxes are lump-sum. This and other conditions are not the subject-matter of the present paper. 3 Bernheim and Bagwell (1988) introduce marriage and argue that this may guarantee full neutrality because each household is then indirectly linked to many (perhaps all) others in its generation. Blanchard and Fischer (1989, p. 151) characterise this as a reductio ad absurdum, as is implied also by the authors themselves. Their argument can be criticised (e.g. because its information requirements seem too demanding, so that parents may ignore linkages when choosing bequests, hence continuing to behave like isolated dynasties), but this goes beyond the scope of the present note; hence parthogenesis is assumed.
J. Pemberton
I Economics
Letters 46 (1994) 223-227
22.5
To analyse (2) I consider a long-run steady state in which labour income grows at a constant annual rate g. Defining G = (1 + g)25, y(t + i + 1) = Gy(t + i). Along the steady-state path, c(t + i + 1) = Gc(t + i) is also required. Substituting this in (2), and setting (2) to equality: a = a* = G”IRD ,
(3)
where (Y” is the value of the intergenerational altruism parameter required for steady growth with positive bequests. If the actual value of (Yis less than (Y*, bequests are zero and there are no operative altruistic linkages.
3. The degree of intergenerational
altruism
In this section I consider the values of (Y* which are generated by (3) for observed or estimated parameter values. For R, I use the annual value Y= 0.045 calculated by Kotlikoff and Summers (1981) for the U.S. economy over the period 1900-1974. Using (Id) this gives R = 3.01. For G, I again use the Kotlikoff and Summers’ estimate of an annual productivity growth rate of g = 0.022, whence G = 1.72. Use of the Kotlikoff-Summers’ estimates is appropriate, since their paper argues that over the period in question, around 81% of total U.S. wealth was the result of intergenerational transfers rather than life-cycle saving. Whilst this figure can be disputed (it exceeds various other estimates), the broad conclusion that intergenerational transfers account for a non-negligible proportion of twentieth-century wealth accumulation (not only in the United States) is quite widely accepted. (See, for example, Modigliani, 1988, and Kotlikoff, 1988, for further discussion.) If debt neutrality is to hold, these transfers have to be interpreted as resulting solely from altruism, and the basic model of (l)-(3) should then predict positive bequests when it is calibrated with values of r and g calculated by Kotlikoff and Summers, together with other appropriate parameter values. The utility function parameter u in (lb) can be interpreted either as the coefficient of relative risk aversion, or as the inverse of the elasticity of intertemporal substitution. In the context of risk aversion, most estimates of u lie between 1 and 5 (mainly in the lower part of the range); a few estimates are below 1. Pemberton (1991b) provides a survey. Concerning the elasticity of intertemporal substitution, Hall (1988) has recently argued that the latter is small (perhaps zero), implying a large (perhaps infinite) value for u. As Hall argues (1988, pp. 343-345) one cannot sensibly believe in an infinite risk aversion coefficient, and this emphasises that the time additive Von Neumann-Morgenstern (VNM) preferences in (lb) may be restrictive in forcing (T to play two roles. Weil (1990) proposes a form of KrepsPorteus preferences in which risk aversion and intertemporal substitution are represented by separate parameters. Whilst this suggests various interesting possibilities, the overwhelming majority of work on intertemporal choice (including Hall’s work just mentioned) has used, and continues to use, VNM preferences, and the present paper follows this tradition. I therefore assume values for u consistent with typical estimates from the risk aversion literature. In the context of the paper this is a conservative approach to the extent that Hall’s findings might justify higher values, since the latter would strengthen the paper’s main conclusion. Regarding the annual rate of time preference d (and the resulting time preference
J. Pemberton
226
I Economics
Letters
46 (1994) 223-227
parameter D = (1 + d))“), Pemberton (1991a) surveys a number of empirical studies which typically estimate d to be between 0.1 and 0.25, though some are considerably higher. However, most simulation studies assume much smaller values for d: e.g. Lucas (1987) assumes (1 + d)-’ = 0.95, and Kotlikoff and Spivak (1981) assume (1 + d))’ = 0.99. Whilst there are no estimates of which I am aware which support such assumptions, at least when applied to representative agents, I consider a value of d within this range, in addition to values within the typically estimated range. Table 1 calculates the values of a* defined by (3) using the range of parameter values For typically estimated values of (T and d, (Y” far suggested by the preceding discussion. exceeds unity: the parent needs to weight her child’s utility much more highly than her own. A benchmark case is (7 at or near to 2, and d between 0.1 and 0.2 (probably nearer the latter); then (Y* is between 10 and 100 (probably nearer the latter). Whilst (Y> 1 is not impossible (“I want my child to have the opportunities I missed”), these orders of magnitude seem unrealistically high. The main source of this high level of required altruism is, of course, economic growth, which makes children richer than their parents. If (Y
Table 1 Values of the intergenerational
altruism
parameter
CX*defined
by (3)
d CT
0.02
0.10
0.20
0.5 1 2 5
0.71 0.93 1.61 8.18
4.85 6.34 10.96 55.71
43.67 57.33 98.67 501.67
Note: Each cell gives the value of LY* calculated R = (1 + r)*’ = 3.01; and D = (1 + d)mZT.
from
(3),
with g = 0.022;
G = (1 + g)” = 1.72; r = 0.045;
J. Pemberton
I Economics
Letters 46 (1994) 223-227
227
Hence I conclude from Weil’s analysis that pure lower values for relevant parameters4 altruism may plausibly generate some positive level of bequests; whether or not this equals the actually observed level cannot be answered using Weil’s procedure. The present paper’s conclusion suggests the following answer: Pure altruism alone cannot fully explain, though it
may well contribute to, observed bequest behaviour; hence the latter must also reflect one or more further motives, the existence of which is generally inconsistent with Ricardian Equivalence. References Barro, R.J., 1974, Are government bonds net wealth?, Journal of Political Economy 82; 1095-1117. Barro, R.J., 1989, The Ricardian approach to budget deficits, Journal of Economic Perspectives 3, 37-54. Barsky, R.B., N.G. Mankiw and S.P. Zeldes, 1986, Ricardian consumers with Keynesian propensities, American Economic Review 76, 676-691. Bernheim, B.D., 1987, Ricardian equivalence: An evaluation of theory and evidence, NBER Macroeconomics Annual 2, 263-303. Bernheim, B.D. and K. Bagwell, 1988, Is everything neutral?, Journal of Political Economy 96, 308338. Bernheim, B.D., A. Shleifer and L.H. Summers, 1985, The strategic bequest motive, Journal of Political Economy 93, 1045-1076. Blanchard, O.J. and S. Fischer, 1989, Lectures on macroeconomics (M.I.T. Press, Cambridge, MA). Davies, J., 1981, Uncertain lifetime, consumption and dissaving in retirement, Journal of Political Economy 89, 561-577. Hall, R.E., 1988, Intertemporal substitution in consumption, Journal of Political Economy 96, 339-357. Kotlikoff, L.J., 1988, Intergenerational transfers and bequests, Journal of Economic Perspectives 2, 41-58. Kotlikoff, L.J., and A. Spivak, 1981, The family as an incomplete annuities market, Journal of Political Economy 89, 372-391. Kotlikoff, L.J. and L.H. Summers, 1981, The role of intergenerational transfers in aggregate capital accumulation, Journal of Political Economy 89, 706-732. Lucas, R.E., Jr., 1987, Models of business cycles (Blackwell, Oxford). Modigliani, F., 1988, The role of intergenerational transfers and life cycle saving in the accumulation of wealth, Journal of Economic Perspectives 2, 15-40. Pemberton, J., 1991a, Trends, cycles and utility, mimeo., Reading. Pemberton, J., 1991b, Risk aversion, leisure, and wage determination, mimeo., Reading. Weil, P., 1987, Love thy children: Reflections on the Barro debt neutrality theorem, Journal of Monetary Economics 19, 377-391. Weil, P., 1990, Nonexpected utility in macroeconomics, Quarterly Journal of Economics 105, 29-42.
4 Using Weil’s terminology in his Table 1, h = /3/( 1 + /3), where /3 is equivalent to my time preference factor D except that Weil assumes 35 rather than 25 year generation spans. Hence his assumed values h = 0.5 and 0.75 imply /3 = 1 and 3, respectively, implying zero or negative time preference. Only the first row of his table, when h = 0.25 (/3 = 0.33), allows positive time preference. Hence only the entries in this row seem to correspond to orthodox assumptions, and in this row the calculated values are much lower than elsewhere in the table. Moreover, the entries refer to his ‘intercohort discount factor’, y, which is not a true measure of the altruism parameter, y ’ (cf. his footnotes 5 and 9). Calculating y’ alters the values: for example, for h =0.25 and rz’ = 7%, the ‘intercohort discount factor’ is 0.70 as entered in the table, but the altruism parameter is only 0.20.
Economics
Letters
46 (1994) 223-227
Ricardian Equivalence Are the required assumptions defensible? James Pemberton Department of Economics, Received
Faculty of Letters and Social Sciences, P.O. Box 218, Whiteknights, Reading, Berkshire, RG62AA, UK
13 July 1992; final revision
received
1 March
1993; accepted
29 March
1994
Abstract Ricardian Equivalence (RE) requires universal provision of bequests for purely altruistic reasons. This paper argues that no defensible set of values for relevant parameters is consistent with this requirement; hence observed bequests must at least partly reflect motives inconsistent with RE. JEL
classification: D10
1. Introduction
Barro (1974) generated a large and continuing literature with his well-known model of intergenerational altruism and debt neutrality. Subsequently, theoretical work has concentrated on analysing conditions in which strict neutrality breaks down, and empirical work has tested, with varying results, the extent to which the neutrality predictions hold in practice. Barro (1989) and Bernheim (1987) provide recent literature surveys. This paper considers evidence concerning the assumptions required for, rather than the predictions of, full neutrality. The following three assumptions are all necessary. (a) Each household must be linked by operative intergenerational transfers to all (not some) of its children. No one must be at a zero bequest corner solution. (b) All such transfers must reflect pure altruism, rather than a mixture of altruistic and ‘strategic’ motives (Bernheim et al., 1985). Neither must they be ‘accidental’ bequests occurring because parents cannot know their date of death (Davies, 1981).’ (c) Th ere must be no uncertainty about future income levels, of ’ A referee has argued that neutrality may still be possible if bequests result for both altruistic and ‘accidental’ reasons (e.g. altruism may determine bequest levels at the margin, with intramarginal bequests being ‘accidental’). A fully worked out model on these lines would be quite complex - it would need to incorporate uncertain lifetimes for future as well as current generations - and to my knowledge has not been attempted. In general, neutrality is overturned by uncertainty (e.g. about future income, future tax policy, etc.) and it is not a priori obvious that it could plausibly be consistent with uncertainty about the length of life. 0165-1765/94/$07.00 0 1994 Elsevier SSDI 0165-1765(94)00475-H
Science
B.V. All rights reserved
J. Pemberton
224
I Economics Letters 46 (1994) 223-227
either the parent or any of the children (Barsky et al., 1986).2 Assumption (b) can hold if a market for life-time annuities develops. As for (c), it is possible in principle that people behave as if they are subjectively certain about future incomes. In this paper I assume that (a), (b) and (c) all hold, and then assess whether or not this combined assumption is plausible in the light of observed or estimated values for relevant parameters. The conclusion is negative. Since the parameter values refer to contexts in which bequests are believed to explain a significant, and perhaps an overwhelming, proportion of total wealth accumulation, the implication is that these bequests cannot plausibly be fully explained in a way which is consistent with Ricardian Equivalence. Section 2 develops the model; Section 3 assesses its plausibility and draws conclusions.
2. The altruistic
model with certainty
I specify the simplest possible Barro-type model. There are many dynasties with finite-lived overlapping generations, a constant population, and parthogenesis. Hence each household contains one parent and one child.3 Since life-cycle considerations are not central, adult life is modelled as a single ‘period’. All adults in any given period t receive an identical exogenously determined labour income y(t) and they all have identical preferences. (Hence all dynasties are effectively identical.) Each adult may also receive a bequest b(t - 1) from his ancestor. All resources are available at the start of the period, when they are allocated to consumption c(t) and when some may be invested, at an annual interest rate r, in a bequest b(t) to the child. The span of a generation - i.e. the length of a ‘period’ - is assumed to be 25 years. There is no uncertainty. The household’s objective function is V(t) = u(c(t))
+ aDV(t
u(c) = (1 - a)
+ 1) ;
‘c’-“(a>O,o#l);
c(t) = y(t) + Rb(t - 1) - b(t) ;
R = (1 + r)*“;
a > 0
)
=logc((T=l) b(t - 1) ) b(t) 2 0
W
D = (1+ d))25 .
d is the annual rate of time preference. (Y is measuring the weight which the household gives non-negativity constraint on b follows Barro and The only allocation decision for each generation The first-order condition is dV(t)ldb(t)
= -[c(t)-”
- aRDc(t + l))“]
(14
the intergenerational altruism parameter, to its heirs’ utility relative to its own. The most of the subsequent literature. t adult is her choice of bequest b(t), if any.
< or = 0 as b(t) = or > 0 .
‘There are of course other important requirements for neutrality, e.g. that all taxes are lump-sum. This and other conditions are not the subject-matter of the present paper. 3 Bernheim and Bagwell (1988) introduce marriage and argue that this may guarantee full neutrality because each household is then indirectly linked to many (perhaps all) others in its generation. Blanchard and Fischer (1989, p. 151) characterise this as a reductio ad absurdum, as is implied also by the authors themselves. Their argument can be criticised (e.g. because its information requirements seem too demanding, so that parents may ignore linkages when choosing bequests, hence continuing to behave like isolated dynasties), but this goes beyond the scope of the present note; hence parthogenesis is assumed.
J. Pemberton
I Economics
Letters 46 (1994) 223-227
22.5
To analyse (2) I consider a long-run steady state in which labour income grows at a constant annual rate g. Defining G = (1 + g)25, y(t + i + 1) = Gy(t + i). Along the steady-state path, c(t + i + 1) = Gc(t + i) is also required. Substituting this in (2), and setting (2) to equality: a = a* = G”IRD ,
(3)
where (Y” is the value of the intergenerational altruism parameter required for steady growth with positive bequests. If the actual value of (Yis less than (Y*, bequests are zero and there are no operative altruistic linkages.
3. The degree of intergenerational
altruism
In this section I consider the values of (Y* which are generated by (3) for observed or estimated parameter values. For R, I use the annual value Y= 0.045 calculated by Kotlikoff and Summers (1981) for the U.S. economy over the period 1900-1974. Using (Id) this gives R = 3.01. For G, I again use the Kotlikoff and Summers’ estimate of an annual productivity growth rate of g = 0.022, whence G = 1.72. Use of the Kotlikoff-Summers’ estimates is appropriate, since their paper argues that over the period in question, around 81% of total U.S. wealth was the result of intergenerational transfers rather than life-cycle saving. Whilst this figure can be disputed (it exceeds various other estimates), the broad conclusion that intergenerational transfers account for a non-negligible proportion of twentieth-century wealth accumulation (not only in the United States) is quite widely accepted. (See, for example, Modigliani, 1988, and Kotlikoff, 1988, for further discussion.) If debt neutrality is to hold, these transfers have to be interpreted as resulting solely from altruism, and the basic model of (l)-(3) should then predict positive bequests when it is calibrated with values of r and g calculated by Kotlikoff and Summers, together with other appropriate parameter values. The utility function parameter u in (lb) can be interpreted either as the coefficient of relative risk aversion, or as the inverse of the elasticity of intertemporal substitution. In the context of risk aversion, most estimates of u lie between 1 and 5 (mainly in the lower part of the range); a few estimates are below 1. Pemberton (1991b) provides a survey. Concerning the elasticity of intertemporal substitution, Hall (1988) has recently argued that the latter is small (perhaps zero), implying a large (perhaps infinite) value for u. As Hall argues (1988, pp. 343-345) one cannot sensibly believe in an infinite risk aversion coefficient, and this emphasises that the time additive Von Neumann-Morgenstern (VNM) preferences in (lb) may be restrictive in forcing (T to play two roles. Weil (1990) proposes a form of KrepsPorteus preferences in which risk aversion and intertemporal substitution are represented by separate parameters. Whilst this suggests various interesting possibilities, the overwhelming majority of work on intertemporal choice (including Hall’s work just mentioned) has used, and continues to use, VNM preferences, and the present paper follows this tradition. I therefore assume values for u consistent with typical estimates from the risk aversion literature. In the context of the paper this is a conservative approach to the extent that Hall’s findings might justify higher values, since the latter would strengthen the paper’s main conclusion. Regarding the annual rate of time preference d (and the resulting time preference
J. Pemberton
226
I Economics
Letters
46 (1994) 223-227
parameter D = (1 + d))“), Pemberton (1991a) surveys a number of empirical studies which typically estimate d to be between 0.1 and 0.25, though some are considerably higher. However, most simulation studies assume much smaller values for d: e.g. Lucas (1987) assumes (1 + d)-’ = 0.95, and Kotlikoff and Spivak (1981) assume (1 + d))’ = 0.99. Whilst there are no estimates of which I am aware which support such assumptions, at least when applied to representative agents, I consider a value of d within this range, in addition to values within the typically estimated range. Table 1 calculates the values of a* defined by (3) using the range of parameter values For typically estimated values of (T and d, (Y” far suggested by the preceding discussion. exceeds unity: the parent needs to weight her child’s utility much more highly than her own. A benchmark case is (7 at or near to 2, and d between 0.1 and 0.2 (probably nearer the latter); then (Y* is between 10 and 100 (probably nearer the latter). Whilst (Y> 1 is not impossible (“I want my child to have the opportunities I missed”), these orders of magnitude seem unrealistically high. The main source of this high level of required altruism is, of course, economic growth, which makes children richer than their parents. If (Y
Table 1 Values of the intergenerational
altruism
parameter
CX*defined
by (3)
d CT
0.02
0.10
0.20
0.5 1 2 5
0.71 0.93 1.61 8.18
4.85 6.34 10.96 55.71
43.67 57.33 98.67 501.67
Note: Each cell gives the value of LY* calculated R = (1 + r)*’ = 3.01; and D = (1 + d)mZT.
from
(3),
with g = 0.022;
G = (1 + g)” = 1.72; r = 0.045;
J. Pemberton
I Economics
Letters 46 (1994) 223-227
227
Hence I conclude from Weil’s analysis that pure lower values for relevant parameters4 altruism may plausibly generate some positive level of bequests; whether or not this equals the actually observed level cannot be answered using Weil’s procedure. The present paper’s conclusion suggests the following answer: Pure altruism alone cannot fully explain, though it
may well contribute to, observed bequest behaviour; hence the latter must also reflect one or more further motives, the existence of which is generally inconsistent with Ricardian Equivalence. References Barro, R.J., 1974, Are government bonds net wealth?, Journal of Political Economy 82; 1095-1117. Barro, R.J., 1989, The Ricardian approach to budget deficits, Journal of Economic Perspectives 3, 37-54. Barsky, R.B., N.G. Mankiw and S.P. Zeldes, 1986, Ricardian consumers with Keynesian propensities, American Economic Review 76, 676-691. Bernheim, B.D., 1987, Ricardian equivalence: An evaluation of theory and evidence, NBER Macroeconomics Annual 2, 263-303. Bernheim, B.D. and K. Bagwell, 1988, Is everything neutral?, Journal of Political Economy 96, 308338. Bernheim, B.D., A. Shleifer and L.H. Summers, 1985, The strategic bequest motive, Journal of Political Economy 93, 1045-1076. Blanchard, O.J. and S. Fischer, 1989, Lectures on macroeconomics (M.I.T. Press, Cambridge, MA). Davies, J., 1981, Uncertain lifetime, consumption and dissaving in retirement, Journal of Political Economy 89, 561-577. Hall, R.E., 1988, Intertemporal substitution in consumption, Journal of Political Economy 96, 339-357. Kotlikoff, L.J., 1988, Intergenerational transfers and bequests, Journal of Economic Perspectives 2, 41-58. Kotlikoff, L.J., and A. Spivak, 1981, The family as an incomplete annuities market, Journal of Political Economy 89, 372-391. Kotlikoff, L.J. and L.H. Summers, 1981, The role of intergenerational transfers in aggregate capital accumulation, Journal of Political Economy 89, 706-732. Lucas, R.E., Jr., 1987, Models of business cycles (Blackwell, Oxford). Modigliani, F., 1988, The role of intergenerational transfers and life cycle saving in the accumulation of wealth, Journal of Economic Perspectives 2, 15-40. Pemberton, J., 1991a, Trends, cycles and utility, mimeo., Reading. Pemberton, J., 1991b, Risk aversion, leisure, and wage determination, mimeo., Reading. Weil, P., 1987, Love thy children: Reflections on the Barro debt neutrality theorem, Journal of Monetary Economics 19, 377-391. Weil, P., 1990, Nonexpected utility in macroeconomics, Quarterly Journal of Economics 105, 29-42.
4 Using Weil’s terminology in his Table 1, h = /3/( 1 + /3), where /3 is equivalent to my time preference factor D except that Weil assumes 35 rather than 25 year generation spans. Hence his assumed values h = 0.5 and 0.75 imply /3 = 1 and 3, respectively, implying zero or negative time preference. Only the first row of his table, when h = 0.25 (/3 = 0.33), allows positive time preference. Hence only the entries in this row seem to correspond to orthodox assumptions, and in this row the calculated values are much lower than elsewhere in the table. Moreover, the entries refer to his ‘intercohort discount factor’, y, which is not a true measure of the altruism parameter, y ’ (cf. his footnotes 5 and 9). Calculating y’ alters the values: for example, for h =0.25 and rz’ = 7%, the ‘intercohort discount factor’ is 0.70 as entered in the table, but the altruism parameter is only 0.20.