Appendix II Notes on the Empirical Literature on Pensions and Saving
- Alfredo Cuevas, George Mackenzie, and Philip Gerson
- Published Date:
- September 1997
Given the theoretical ambiguity of the precise relationship between pensions and saving, the various statistical techniques that have been used to analyze it, and the diversity in actual pension systems and in the underlying socioeconomic and demographic profiles of different countries at different times, it is not surprising to find a wide range of results in the empirical literature. In general, the evidence is rather weak, although it suggests that public pension systems have a small negative effect (a positive effect, however, has been found in a few countries) on aggregate saving rates and that private retirement schemes have a more clearly positive effect on saving. First, this appendix reviews the literature on public pensions, with a special emphasis on a group of studies that rely on the construction of a social security wealth variable. Then, it discusses the results concerning private retirement schemes.
Some Empirical Findings on Public Pensions
Studies of the United States
Experience with the public pension system of the United States has been studied extensively. However, the results of this effort have not been conclusive. Cross-sectional studies tend to find considerable substitution between private wealth and social security wealth (SSW), but the offset is generally less than dollar for dollar: in several studies offsets were found to range from 39 cents to 69 cents per dollar of SSW.37 Working with total (public and private) pension wealth, Gale (1995) attempts to control for a number of factors that may bias the estimated offset toward zero and succeeds in obtaining offset estimates as high as 82 cents per dollar. However, the author recognizes possible sample bias away from zero as well and concludes that extending pension coverage may well increase saving because this would increase involuntary saving by finandaily naive or liquidity-constrained individuals who would not engage in offsetting behavior.
Feldstein (1974) was the first researcher to incorporate the effect of pensions into an estimable version of the life-cycle model for the United States through an SSW variable. Under the LCH, individuals make consumption decisions on the basis of their total human and nonhuman wealth. Therefore, the total (current and future) anticipated financial flows, appropriately discounted, expected to be derived from participation in a pension plan must be taken into account to explain current consumption and saving. Using aggregate data, Feldstein estimates a model of the following form:
Ct = a + bYt + c Wt-1 + d SSWt.
This model makes current consumption depend on contemporaneous disposable income Y, accumulated financial and real wealth W, and anticipated SSW. SSW is the present value of the expected retirement benefits payable to those currently at work or currently retired, from the present time onward. It can be calculated net or gross of future contributions to the social security system.
This type of formulation has been used extensively, and results can vary widely according to how the SSW series is constructed. The basic building block is the social security wealth of a representative individual from a well-defined group (e.g., active worker of a certain sex, age, and marital status; current retiree of a certain sex, age, and marital status; spouse and children eligible for survivor benefits). The SSW variable is constructed by first summing the individuals in each category, and then summing over the categories.
A useful example is that of an unmarried worker of age A in year t who is eligible to retire with a full pension at age 65 without ever having married. With some probability, this individual will live to see his sixty-fifth birthday, and thus 65 −A years from year t, in year t + 65 - A, he will begin collecting retirement benefits. In his first year as a retiree, he will collect Bt + 65−A, and with some probability, he will survive another year to collect Bt + 66 -A, and so forth. Then, as of his sixty-fifth birthday, it is assumed that he can compute the present value of the total stream of pension payments he will henceforth receive, discounting them year by year at some appropriate rate and by the probability that he will not live to receive the payments. This is the expected present value of his pension at the time of retirement. In year t, when the worker is still A years old, he is assumed to be able to foresee and estimate this value, and to discount it to time t, taking into account the probability of his not reaching retirement age. This is his gross social security wealth in year t. To arrive at a net measure of SSW, the present value of the contributions the worker will pay between the years t and t + 65 − A is computed and then subtracted from gross SSW. For other categories of covered individuals, the computations are analogous.
This description of the method for computing SSW has left many details unresolved: What is the appropriate discount factor? What measure of benefits in, say, 1970, B70, do we use when constructing a 45-year-old individual’s SSW 20 years earlier?38 In particular, how do we deal with changes in the rules for computing benefits that have taken place? Do we assume that people could anticipate these changes, and if so, since when? How do we deal with the possibility of early or late retirement? How do we incorporate those currently unemployed who may be rehired later and the possibility that those currently at work may face unemployment at some future time? How do we take into account the possibility that a worker, unmarried at some point, may have expected to marry later and have children who might eventually collect survivor benefits? We could resolve some of these issues, at least for the average member of each category, if we had enough data at our disposal, but at the cost of making estimation impractical.39 For example, we could probably deal with changes in marital status or retirement at ages other than 65, but other issues have no “best” answer, and the choices may crucially affect the results.40
The most important and controversial issue relates to the way people form expectations about the level of future benefits. Feldstein (1974) assumes that people expect the average replacement ratio to be constant, which leads him to set expected benefits for every year at 41 percent of disposable income per head (its mean value in the sample period 1947–71). Feldstein also assumes that people expect disposable income to grow at 2 percent a year in real terms. He finds that the marginal propensity to consume pension wealth is higher than the propensity to consume financial and real wealth, something he ascribes to the higher concentration in the distribution of the latter across households. He concludes that, in the absence of social security, private saving would have been between 40 percent and 50 percent higher than it was at the time of his study. He reaches similar conclusions in later versions of his work (Feldstein, 1982 and 1995); in his most recent exercise, Feldstein (1995) estimates that the social security program reduces private saving by close to 60 percent.
However, different assumptions can be made to compute future benefits. Leimer and Lesnoy (1982) start with the same primitive data as Feldstein (1974), but do more refined actuarial work on the demographic and labor market assumptions required to construct SSW. They then try different approaches to computating benefits: perfect foresight (benefits are anticipated exactly), myopia (current levels are expected to remain unchanged in real terms), and constant average replacement rates. In most cases, their results indicate that pensions have no statistically discernible influence on saving—the exception is the model with the Feldstein-type of assumption. They then try estimating over different periods, and the results turn out to be highly sensitive to even small changes in, for example, the starting year of the sample.
Other studies have been inspired by the SSW approach. Using the SSW variable constructed by Leimer and Lesnoy (1982), Burkhauser and Turner (1982) find that one effect of social security in the United States has been to increase the work week by two or three hours among “prime-aged” men. Exclusion of this effect from the saving regressions discussed above will tend to produce results that exaggerate the negative effect of pensions on saving.
Using a somewhat different approach, Leimer and Richardson (1992) study the effect of social security on saving and on economic efficiency by estimating a model that incorporates the benefits from reducing longevity risk (the risk that an old person may out-last his savings). They conclude that social security does reduce voluntary saving by a significant amount, but still less than dollar for dollar. In fact, they must reject extreme life-cycle and Ricardian versions of their consumption equations, because they find negative effects on saving through life-cycle channels, but also some offsets to these effects through private transfers. Perhaps more important, their findings suggest that over one-half of saving reductions attributable to social security represent efficiency gains because pensions satisfy a need that imperfect annuities markets do not fully meet.
Studies of Other Countries
The impact on saving of pension systems in other countries has received less intense scrutiny, but some analyses are available. In Italy, an SSW series has been constructed to study the decline in saving over recent years that has coincided with marked growth in the ratio of pension expenditure to GDP (Rossi and Visco, 1992). The study assumes a myopic formation of expectations about future benefits and finds that the social security system reduced private saving by about one-third in 1990. It also states that, while about one-fourth of the fall in private saving between the 1960s and the 1980s can be attributed to rising SSW, virtually all of the fall in private saving during the 1980s is attributable to that source.
Another study of the Italian experience also finds that SSW partially substitutes for other assets, but the offset effect is in the range of 10–20 percent (Jappelli, 1995).41 The Italian pension system is one of the most generous among OECD countries; given the levels of contributions, current benefits are estimated to be at least 21 percent higher than they would be if the system were funded.42
Japan’s social security system, introduced in 1942, underwent significant changes in 1965 and 1973 that offer an opportunity to study the effects of successive and drastic increases in the coverage and generosity of pensions. Yamada and Yamada (1988) and Yamada, Yamada, and Liu (1990) study time-series data for Japan following the extended life-cycle model proposed by Feldstein (1974), but attempt to separate more carefully the impact of pensions on private saving into a negative “benefit” effect and a positive “retirement” effect. The 1988 study finds that the benefit effect is about ten times larger than the retirement effect in Japan, and that, on balance, saving was depressed by 68 percent as a result of growth in pension wealth during 1970–80.
Another study (Yamada, Yamada, and Liu, 1992) also tries to disentangle the retirement and benefit effects, using a system of equations with personal saving rates and labor force participation as endogenous variables. It estimates that the real increase in social security wealth since 1960 caused personal saving to be reduced by 34–38 percent in 1980. The findings are robust to the choice of social security variable (social security contributions, gross or net SSW), and the authors conclude that social security does depress savings in Japan. An earlier paper by Yamada, Yamada, and Liu (1990) focuses on the effects of the institutional changes of 1965 and 1973, which increased benefits and relaxed eligibility criteria. It finds that each of these reforms magnified the depressing net effect of social security on private saving.
A study of Canada (Denny and Rea, 1979), how-ever, finds that the saving rate is higher than it was prior to the introduction of the Canada Pension Plan in 1966, instead of lower by 5.2 percentage points as it should be under the dollar-for-dollar replacement hypothesis. These authors suggest that the induced-retirement effect may be responsible for this result. A government study in Ontario covering 1951–7543 finds a negative but statistically insignificant direct effect of benefits on saving ratios, a negative and significant direct effect of coverage, and an insignificant but positive retirement effect. However, retirement itself is significantly increased by pension coverage and benefits. On the whole, the latter study finds that the overall impact of pensions on saving was positive but statistically insignificant. It concludes that the saving rate may have increased by up to 3.8 percentage points as a result of the pension plan, but also that as the proportion of people who retire reaches a plateau, the negative benefit effects will become preponderant.
One survey of the United Kingdom (Barros, 1979) focuses on the natural experiment created by the social security reforms undertaken there during the 1970s. It reports that studies have tended to find small negative, or even positive, effects of pensions on other forms of personal saving. While inconclusive, these studies are interpreted as lending support to the hypothesis that pensions induce retirement, not just by making it more affordable (feasible), but also by making people aware that they should make provisions toward their old age (the “recognition effect”). At any rate, no evidence is presented to the effect that pensions depress saving. Elsewhere, impressionistic arguments have been advanced to the effect that private savings growth has been hampered by the presence of social security (Seldon, 1994).
A study of France (Oudet, 1979), while using very rough data and simple methods, finds that pensions do not depress saving. The study suggests that, in France, (1) wealth is largely held in real estate, for which pensions are poor substitutes; (2) wealth and savings are quite concentrated; and (3) old people do not run down their financial wealth to a significant extent. These findings would point to a system of private intergenerational transfers through which some of the negative “benefit effect” can be undone (40 percent of net worth in France as of the mid-1970s was estimated to be the result of inheritance). In addition, the recognition effect is mentioned again as a contribution made by pension systems to promote saving.
A study of Germany (Blum and Gaudry, 1987) uses a cross-sectional approach in which household saving is related to gross income, taxes, household composition, and contributions to the public pension system. Its main finding is that the sign on the social security variable is not robust to changes in the regression equation’s functional form.
A study of Belgium (Perelman and Pestieau, 1984) adopts an approach similar to Feldstein’s, with results that are consistent with the Feldstein hypothesis; moreover, the results are robust with respect to changes in the specification of the regression equation.
In Sweden, where a partially funded system has been in place since 1960, studies suggest that voluntary saving may have fallen as a result of the operation of the public pension scheme. The drop in the household saving ratio is estimated at between 1.5 percentage points and 4.0 percentage points in different studies.44 However, the growth of the general pension fund during 1960–80 represents a saving of between 2 percent and 4.5 percent of GDP. On balance, therefore, aggregate saving does not seem to have been affected by the pension scheme and may even have increased slightly.
Voluntary saving has been declining as a proportion of total income in the Netherlands for over three decades. Draper (1994) argues that an important factor in this development has been the generosity of pensions. The model used to generate this result rests on the idea that people may make medium-term decisions on consumption and asset accumulation, because lifelong planning may be impossible or too onerous in view of the uncertainty surrounding income flows. The results indicate that a unit decrease in pension rights will lead to an offsetting increase in financial wealth of about 40 percent.
Shome and Saito (1980) explore the economic impact of social security systems in five Asian countries: India, Malaysia, Philippines, Singapore, and Sri Lanka. In each of these countries, saving through social security schemes (contributions to funded schemes and surpluses of PAYG schemes45) comprised between 20 percent and 45 percent of gross household financial saving during the 1970s. The importance of social security would lead one to expect a crowding out of “noncompulsory saving.” The authors run simple regressions to test this conjecture and find that pension saving does not significantly reduce voluntary saving; if anything, it seems to increase it in some cases (India, Singapore, and Sri Lanka). In fact, in all five countries, voluntary and compulsory saving seem to follow parallel and usually upward trends. The authors suggest that, except in Singapore, urbanization may be one cause underlying the increases in both types of saving. As more workers migrate to cities, they take jobs in the formal economy, which makes them subject to social security contributions; at the same time, they face the need to build savings to substitute for the more traditional safety nets provided by the networks of transfers left behind in rural areas.
A study of prere form Chile (Wallich, 1981) tries to estimate the benefit and retirement effects of the old PAYG social security scheme, loosely following the extended life-cycle model. The main result is that, although a clear retirement effect can be identified, the benefit effect is consistently positive and statistically significant under different model specifications. On balance, the pension scheme in Chile stimulates voluntary saving. This study offers numerous possible explanations for the absence of an offsetting effect on private saving, among them the weak credibility of the scheme and problems with the data.
A review of econometric studies of the effects of compulsory saving on national saving in Malaysia reports that most of the studies cited find that the presence of the compulsory defined-contributions plan reduces national saving (Chang, 1995). The reason, apparently, is that the compulsory saving plans do not induce households to increase their saving, but simply lead them to reduce their discretionary saving by an offsetting amount. However, the employer contribution redistributes income from the high-saving corporate sector to the low-saving household sector, leading to a decline in aggregate private saving. Public saving may also decline as a result of the compulsory saving plan, with the presence of ready credit from the Employees’ Provident Fund (which must invest 50 percent of its assets in government securities, down from 70 percent earlier) inducing the government to spend more than it otherwise might.
Cross-Sectional or Panel Approaches
From a different methodological perspective, Feldstein (1977) attempts to explain variations in saving rates across countries by estimating an extended life-cycle model for a cross section of 15 countries with well-established social security systems. He concludes that pension systems reduce national saving rates and thus endanger the prospects for capital accumulation. In particular, he notes that the benefit effect reduces the saving rate by over 4 percentage points in the United States. On average for the sample, the net impact of the benefit (negative) and retirement (positive) effects is to reduce the saving rate by 1.5 percentage points.
Barro and MacDonald (1979) use a pooled cross-sectional time-series sample of data on 16 Western industrial countries during 1951–60 to test a model of consumer spending. They find that their results depend strongly on whether the model is estimated with a single intercept term, or if individual country intercepts are introduced. Using a common intercept, the social security variable (total payments for old-age, survivors’ and disability programs, divided by the number of individuals aged 65 and over, as a share of per capita income) has a significant, negative effect on consumption. However, when individual country intercepts are used, the results indicate that social security has a significant, positive effect on consumption. (In addition, the assumption of a common intercept is rejected at the 1 percent level.) One implication of these results is that time-series properties of the data set (captured by the individual intercept model) imply a negative relationship between saving and social security, while the cross-sectional properties, more fully captured in the common intercept specification, imply a positive one. A second implication is that the results of cross-sectional studies like this one are extremely sensitive to model specification.
Kopits and Gotur (1980) adopt a cross-sectional approach, but examine data from both industrial and developing countries. (Specifically, they look at averaged data covering 1969–71 for 14 industrial and 40 developing countries.) They estimate a separate labor force participation function for individuals aged 65 and over, and include old-age pensions, oldage lump-sum payments, other social security transfers, and loans from social security funds as separate variables, rather than lumping all social security payments into a single variable. In addition, they use private household saving, rather than total private saving, as their dependent variable. For industrial countries, they find that increases in social security pensions tend to increase household saving (as do increases in social security tax rates), while increases in other social security benefits tend to reduce saving. The implication is that the indirect effect of higher social security pensions on saving that operates through labor force participation rates (they find that the presence of social security payments— in the form of pensions or lump-sum payments—reduces labor force participation rates for those over 65) outweighs the direct wealth effect. Social security pensions also tend to reduce labor force participation in developing countries, but the overall impact of pensions on saving in these countries is close to zero, because the direct and indirect effects almost cancel each other out. As in industrial countries, other forms of social security benefits tend to reduce saving.
Modigliani and Sterling (1983) examine a cross section of 21 OECD countries using period averages covering 1960–70, modeling private saving and participation rates of older workers as functions of—among other variables—replacement ratios for social security systems. They find that their results are extremely sensitive to the specification of the variables other than social security included in the study and to the presence of extreme observations within the sample. In addition, they gather data on replacement ratios from two different sources (neither of which covers all countries in the sample) and find that their results depend on which replacement ratios are used.46 They find that social security has a small, negative direct effect on private saving, but a large, negative effect on participation rates. The net effect of these two forces on savings is insignificant, meaning that the direct and indirect effects largely cancel each other out.
Koskela and Viren (1986) also follow a cross-sectional approach, using a model with pooled cross-country data under a variety of assumptions about the error term. The data consist of annual observations for the period 1960–77 drawn from 16 OECD countries. The model regresses the saving-to-GDP ratio on country dummies, a number of macroeconomic and demographic controls, and the ratio of social security benefits per retiree to per capita GDP. The authors cannot reject the null of a zero coefficient on the social security variable. They also run separate regressions for each country with a reduced number of regressors. These tend to yield the same result; only in Portugal and Sweden are significant and negative coefficients found. The authors conclude, as they did in an earlier study (Koskela and Viren, 1983) that used essentially the same model, that social security has no effect on household saving.
In summary, several cross-sectional studies have found a negative direct effect of social security on saving, but they have also often found that social security induces earlier retirement, which indirectly leads to higher saving. Overall, the two effects appear to cancel each other out, meaning that social security has no net impact on saving. These studies have also demonstrated that results are extremely sensitive to the specifications researchers choose to employ.
What may be concluded from this survey? Clearly, different studies have come to widely varying conclusions about the impact of social security on saving. A number of studies—particularly those of the United States—tend to find some, but less than full, offset of public pension saving through reduced private saving. Others conclude that pension schemes may actually increase private saving. To this extent, offering a general conclusion—one that applies across countries—on the impact of pensions on saving is not possible.
Occupational Pensions and Saving: Some Empirical Results
As is often the case, economic theory is considerably better at identifying the various forces through which participation in occupational pension programs influences individuals’ saving decisions than it is at providing insight into the likely magnitudes, and hence overall effect, of these forces.
To resolve this theoretical ambiguity, a number of economists have undertaken empirical studies of the extent to which participation in pension plans affects aggregate saving. The simplest estimating equation for such a study would take the form
W = a’z + bP + e,
where W is nonpension wealth or savings, z is a vector of explanatory (usually demographic) variables, P is a scalar measuring pension wealth, e is an error term, and [a’, b] is a vector of coefficients to be estimated. If b = -1, then pension savings fully offset other savings, and total savings, W + P, are unaffected by increases in pension wealth. If b > -1, then the offset is less than full (and if b > 0, the offset is negative), and increases in pension wealth would lead to increases in aggregate wealth.47
Cagan (1965), in an early study, finds that house-holds with pensions tend to have higher nonpension savings than households that are not covered by pension plans, but he fails to control for any demographic variables that might also affect saving behavior. When Munnell (1974) controls for age, education, income, and other factors, she finds a negative impact of pension saving on other saving, but the effect is not statistically significant. In a subsequent paper, she adds controls for the desire to leave an inheritance, expected retirement age, and life expectancy—high values of these variables would tend to increase saving—and finds that about 62 percent of pension wealth is offset by reductions in other savings (Munnell, 1976). However, Kotlikoff (1979) uses the same data set and finds no significant effect of pension coverage on wealth or saving. Blinder, Gordon, and Wise (1980) find a positive but insignificant effect of private pension wealth on other wealth, while Waters (1981) looks at Canadian data and finds that, on average, homeowners reduce their nonpension wealth by about 50 cents for every dollar they contribute to their pension plans. Diamond and Hausman (1984) find that, while more generous annual pension benefits induce earlier retirement, they have little direct effect on saving rates or wealth.
Dicks-Mireaux and King (1984) use Canadian data to examine the impact of pension wealth on the ratio of private wealth to permanent income. They find that the offset for pension wealth is between 27 percent and 51 percent, meaning that each increase of a dollar in pension wealth leads to a reduction of between 27 cents and 51 cents in nonpension wealth (or to an increase of 49 cents to 73 cents in total wealth). Pitelis (1985) examines postwar U.K. data and finds no evidence of an offset of nonpension saving from contributions to pension funds or life insurance. Hubbard (1986) uses data on American households and finds that the average offset is 16 percent (which is much lower than the offset he finds for social security), while Avery, Elliehausen, and Gustafson (1986) find (using a sample of American households headed by persons aged 50 and over) that the offset is 66 percent when a broad measure of nonpension wealth is used, but only 11 percent when nonpension wealth includes only liquid assets. Venti and Wise (1986) examine the likely impact of raising the ceiling on contributions to IRAs in the United States and find that on average, only about 10–20 percent of increased IRA contributions come at the expense of holdings of other financial assets, with 45–55 percent of that from reduced consumption and about 35 percent from lower taxes. Bernheim and Scholz (1993) find that pension coverage reduces nonpension wealth for households headed by college graduates but not for others. Poterba, Venti, and Wise (1993) find that saving in IRAs and 401(k) plans has little impact on other forms of saving, while Venti and Wise (1996) find very little (or even negative) offset from pension wealth.
Not surprisingly, these empirical studies have produced a wide variety of results. In some, the offset is as large as 66 percent, while in others it is close to zero, and in still others it is negative. However, none of the studies finds an offset of 100 percent, and thus all the studies imply that increases in occupational or private pension saving will induce increases in aggregate saving. Whether an increase of a dollar in pension saving leads to an increase of 33 cents, a dollar, or more than a dollar in aggregate saving remains an open question. However, none of the studies supports the contention that increases in pension saving have no impact on the level of aggregate saving. From a public policy perspective, the implication is that an expansion of private pension systems could lead to a significant increase in private saving. In addition, to the extent that wealthier households are more likely than poorer ones to offset higher pension saving with reduced nonpension saving, an expansion of private pension programs could have positive social implications by redistributing wealth.
As Gale (1995) notes, a number of econometric problems—mostly related to omitted variables or measurement errors—can arise in estimating the effects of private pensions on aggregate saving and can bias the results. For example, if saving is calculated from cash earnings rather than from total compensation (including deferred compensation), the offset will tend to be underestimated because it will not take into account the income effect arising from higher future compensation.48 Omitting variables for life expectancy, retirement age, and current age (as some studies have done), or ignoring the fact that employment choices are endogenous and that people with high propensities to save may self-select into jobs that offer pensions, may also introduce a bias that understates the extent of the offset. Having corrected for many of these factors, Gale obtains an estimated offset of 82 percent in one exercise and 39 percent in another. Although these estimates are substantially larger than those from most of the studies cited above, they are still less than 100 percent. Moreover, because Gale’s sample is wealthier than average, and because the degree of offset tends to increase with wealth, his results may overstate the extent of the offset for the population as a whole. In any case, the bulk of the available econometric evidence does not reject the view that nonpension wealth is insensitive to private pension wealth, implying that any offset of nonpension saving arising from increases in pension saving is small.
In other words, what benefits did a 45-year-old worker think, in 1950, that he would receive as a retiree in 1970?
Not to mention the fact that the more complex the method for constructing SSW, the more prone to error the actual construction will be.
See Auerbach and Kotlikoff (1983) for a discussion of how different assumptions, such as the choice of the sample period to analyze, can determine the results of this type of research.
This study controls for desired retirement age, which should in principle result in more accurate estimates of SSW.
See Palmer (1988) for a summary of the findings of these studies and a description of Sweden’s pension system.
Shome and Saito (1980) explain that defined-benefits plans mobilize at least as much savings as funded systems in these countries, largely as a consequence of the immaturity of the schemes.
They also find that among countries covered by both sources, the replacement rates differ significantly for individual countries.
Given that W = a’z + bP + e, it is clear that W + P = a’z + (1 + b)P + e. Therefore, if b =−1, total wealth, W + P, is independent of P. If b >–1, then total wealth is increasing in P, while if b <−1, then total wealth is decreasing in P.
Consider two individuals, each of whom earns a cash wage of 100 in period 1 and lives off of his savings and retirement income in period 2. The first individual will receive a pension of 10 in period 2, while the second individual will receive no retirement income. If each smooths his consumption perfectly over the two periods, the first individual will consume 55 in period 1 and enter period 2 with 45 in savings, while the second will consume 50 in period 1 and enter period 2 with 50 in savings. Thus, the increase of 10 in pension wealth appears to have led to a decline of 5 in nonpension wealth, implying an offset of 50 percent. However, the true offset is 100 percent, because if the first individual had received his true income of 110 in cash he would have entered period 2 with 55 in savings rather than the 45 he actually began with.