Social Security's Five Oasi Inflation Indexing Problems

This paper examines five problems with the indexing procedures used by the Social Security Administration of the United States in taking inflation into account when calculating Old Age and Survivor Insurance (OASI) Benefits. Because of the commin-gling of unindexed with indexed earnings, a retiree born in 1930 who continued in a high earning career until age 75 receives an annual benefit more than $1,800 larger than would have been generated with full indexing. While the inflation indexing problems identified in this paper do not attract much attention in normal times, they can contribute to serious short-run financial instability for the OASI trust fund in periods of substantial inflation or deflation. They make the percentage increase in your inflation adjusted (CPI-W) benefit if you elect to postpone retirement and the start of OASI benefits depend in part on the pace of inflation. This paper explains how these problems could be resolved in a way that would not hurt and might help resolve Social Security's longrun solvency problems. --


Introduction
This paper examines five problems with the inflation indexing procedures used by the Social Security Administration in calculating Old Age and Survivors Insurance (OASI) Benefits. Because of these indexing problems, a proper evaluation of how progressive OASI actually is-who benefits the most--requires that the pace of inflation be explicitly taken into account. These problems also mean that inflation can affect the incentives provided for delaying retirement and the start of OASI benefits. Although indexing problems do not attract much attention in normal times, they will generate serious short-run financial instability for the OASI trust fund if our economy again experiences stagflation like that generated during the OPEC oil price surges almost a third of a century ago. This paper shows that how an index is used or misused may be just as important as which index or combination of indexes is used in adjusting OASI benefits for inflation. The most serious problem involves the commingling of the worker's earnings adjusted for wage inflation up through age 60 with unadjusted earnings from age 61 to retirement. As a result, a successful lawyer born in 1930 who earned at or above the taxable maximum cap on earnings subject to OASI taxes ($90,000 in 2005) and postponed full retirement until her 75th birthday might enjoy an annual benefit of $25,812 instead of the $24,000 that would be received if the earnings were fully adjusted for wage inflation in calculating benefits. This $1,812 annual bonus is 7.0% of the annual benefit. In contrast to this $1,812 annual bonus, a worker who always earned the minimum wage over an equally long career receives a benefit of $10,296 instead of $10,164 with full wage indexing-a $132 annual bonus amounting to only 1.3% of the annual benefit. These bonuses, adjusted for inflation with the consumer price index (CPI-W), are received in every year of retirement, and beyond if claimed by the worker's surviving spouse. 1 Social Security has evolved over the years since President Roosevelt signed it into law in 1935 into a program that must be judged to be in many ways a tremendous success: It has contributed to the dramatic reduction in the rate of poverty among the elderly. And it is remarkably efficient-OASI administrative expenses in FY 2007 were only 0.6% of benefit payments. But it also has serious problems. As everyone knows, it is underfunded and its trust funds are threatened with eventual exhaustion. But there are also serious problems with the way in which the program indexes for inflation.
Attempting to modify the way in which Social Security Benefits are adjusted for inflation can turn into a political minefield. A case in point is provided by the serious political controversy generated in the 1970s when Social Security was first indexed for inflation. The initial attempt at indexing, signed into law in 1972, was flawed--it overcompensated for inflation to such an extent that it is said to have threatened to exhaust the trust funds. After the indexing procedure was revised in 1978, those born _________________________ between 1917 and 1921 become known as the "Notch Generation" because their benefits fell short of those received by both the immediately preceding and following birth cohorts (Duggan et al., 1996). In response to their protests, over the years more than 100 legislative bills attempting to redress the problems of the Notch Generation were introduced in both houses of Congress. A bipartisan Commission on the Social Security 'Notch Issue ' (1994) concluded after extensive hearings that no remedial action should be taken. That report may have put the Notch Issue more or less to rest, but serious underlying problems with the indexing procedures are still not resolved.
The next section of this paper reviews how OASI benefits are calculated. Section 3 investigates five indexing problems and recommends steps that would contribute to their resolution. Computer experiments in Section 4 test how well alternative indexing procedures respond to accelerated inflation or deflation. Section 5 explains how the price and wage indices used by the SSA are constructed. Section 6 examines the task of phasing in reform, Section 7 summarizes how the choice of index affects retirement incentives and Section 8 concludes.
Throughout we shall be focusing on the wage earnings and OASI benefits of workers but will not consider how the financial wellbeing of workers and retirees may be influenced by the income tax, the Earned Income Tax Credit, Supplementary Social Security payments, pensions, inheritances, personal saving and investments.

Calculating OASI Benefits
Before we can appreciate OASI indexing problems we must examine the procedure for calculating a retiree's benefits. First we will calculate the worker's Average Indexed Monthly Earnings (AIME), then we will show how the Primary Insurance Amount (PIA) is derived from the AIME, and finally we will explain how the benefits are calculated from the PIA. 2

Calculating a Worker's Average Indexed Monthly Earnings (AIME)
The OASI benefit is based on earnings reported on the worker's W-2 forms, , but only up to the Taxable Maximum (aka the Contribution and Benefit Base) ceiling t C on earnings subject to the OASI payroll tax; e.g., C 2008 = $102,000. Earnings above C t are not subject to the payroll tax and are nor tabulated in computing OASI benefits. These capped earnings, are adjusted for wage inflation with w t , the Average Wage Index. This index, plotted along with the consumer price index (CPI-W) on Figure 1, is based on 2 w t E − , the average of all workers' W-2 income, and is normalized to equal 100 in the workers 60 th year, _________________________ where t b is the year of birth. But our worker's "indexed earnings", , are in fact only indexed up through the year of the worker's 60 th birthday; subsequent earnings are not adjusted for inflation:  where ( I ) R E τ is the descending rank of earnings up to year t. Earnings that are too small to be included in the top 35, although subject to the OASI wage tax, do not count in computing OASI benefits.
The worker's Average Indexed Monthly Earnings (AIME) is this 35 year sum divided by 35×12: t E = .
(5) 35 / (35 12) I t E × If there are fewer than 35 years of employment, the sum is still divided by 35x12.
Here the ratio , where p t , the CPI-W price index, adjusts the PIA for inflation.
The bend point coefficients b 1 and b 2 are adjusted for inflation according to the level of the wage index in the year of the worker's 60 th birthday. The bendpoint kinks on the graph have coordinates <b 1 , 0.9b 1 > and <b 2 , 0.9b 1 +0.32(b 2 -b 1 ) >. The dashed line is the original PIA function, which applied for workers born in 1917 and enjoying their 60 th birthday in 1979. Because the wage index increased by 115% from 1977 to 1990, the bend points for workers reaching 60 in 1990 are 115% larger than they were for the 1917 age cohort.
The PIA is a progressive function of earnings because the ratio of benefits to earnings, PIA/AIME, declines with AIME, as can be observed on Figure 2. However, the progressive feature of the function linking annual benefits to AIME is more or less offset because life expectancy increases with socioeconomic status and is sensitive to both race and life style. 4 Note that the worker's PIA will increase over time for two reasons: First, it is adjusted for price inflation by the ratio p + . Second, the PIA increases with the passage of time if the beneficiary continues to work after the 62 nd birthday, but only if the earnings are large enough to increase the AIME, which means they must count among the best 35 years.

Benefit Calculation
The monthly OASI benefit that a worker born in year t b will receive at age a, according to SSA statutes, depends partly on that year's PIA, as determined by (6), but subject to an adjustment factor A(t b ,a s ) that penalizes workers if the age a s at which they initially claimed benefits is before the normal retirement age and rewards those who delay the start of benefits beyond the normal retirement age: b 1 1 61 t +60 61 60 ( , , / , ,w ) ( , ) ( , , / , , ) for 62, 0 otherwise.
For example, a worker born in 1930 who started benefits when first becoming eligible at age 62 will receive only A (1930,62) = 80% of the benefit that would be received if the start of benefits were postponed until age 65. which is the normal retirement age for that age cohort; i.e., A(1930,65) =1. But the adjustment factor would be A (1930,70) = 122.5% if the worker decided to refrain from drawing benefits until age 70, receiving a larger benefit over a shorter remaining lifetime. As indicated by Table 1, the adjustment factors have been modified over time, in part to reflect the increased longevity of the population.
The Average Indexed Monthly Earnings, the Primary Insurance Amount and the benefit are updated in each year after age 62 in which our worker has W-2 earnings, but the worker's PIA function bend points do not change and the wage index remains normalized at 100 in the worker's 60 th year. The maximum benefit that can be received by anyone who always earned at or above the taxable maximum depends on the year of retirement, for that limits the sum of the capped earnings that is used in calculating the AIME. For a worker born in 1930 who retires at 62, the maximum AIME is $2,985 and the resulting cap on the PIA is $1,069. 4 Gustman and Steinmeier (2001) report that there is significant income redistribution when only own benefits are taken into account; but progressivity is substantially reduced when spouse and survivor benefits are included and redistribution is measured among families. A Congressional Budget Office (2006) study reports that the degree of progressivity is strengthened when OASI and Disability Insurance benefits are combined and when benefits are measured net of the personal income tax.
www.economics-ejournal.org Married workers receive a benefit equal to ½ that of their spouse if it is larger than the benefit based on their own earnings. 5 Dependent children may also receive a benefit based on the retiree's earnings record. Surviving marital partners receive a benefit equal to that of their deceased spouse if it is larger than the benefit based on their own earnings. 6

Indexing Problems
We will illustrate the effects of various indexing problems by considering how they affect the OASI benefits received by four quite differently situated workers: • The Maximum Wage Earner always earned at or above the taxable maximum cap. This category includes successful accountants, lawyers, physicians, business school professors, and many other professionals and business leaders. Some may continue to earn above the taxable maximum cap even in part-time retirement (http://www.socialsecurity.gov/cgi-bin/netcomp.cgi?year=2006).

•
The Average Wage Earner enjoyed the average (mean) W-2 income of all workers subject to the Social Security tax throughout their careers.

•
The Median Wage Earner always earned the median of the W-2 earnings distribution, half of the population earning more and half less. Because the distribution of income is highly skewed, the median wage is substantially below _________________________ 5 The maximum family benefit caps the sum of retirement or survival benefits that can be paid to a worker's spouse and eligible children, usually equals 150% to 180% of the basic benefit. Any benefits paid to a surviving divorced spouse do not count against the maximum family benefit. 6 A divorced spouse who does not remarry before age 60 may still elect the survivor benefit, provided the marriage had lasted at least 10 years. A divorced spouse who remarried after age 60 could still collect survivor benefits on the former spouse's record or choose instead to receive retirement benefits based on the record of the new spouse. Several former wives of a serially marrying spouse may be able to claim benefits on the basis of that former spouse's earning history, provided each marriage lasted at least 10 years. The Social Security Administration accepts common law marriages if recognized by the state where the couple resides. Gay Marriages are not accepted even if recognized in the state of residence (e.g., Massachusetts or Connecticut). the average. For example, average income in 1990 was $21,028,  In order to learn about the OASI benefit experience of workers who occupy quite different positions on the income distribution, we will be analyzing how the benefits of these four hypothetical workers are affected by inflation.
The income histories of these four stylized classes of workers are reported on Table  2 and plotted on Figure 3. Their incomes deflated with the CPI-W (1990=100) are plotted on Figure 4 and with the Average Wage Index on Figure 5. In 2006 our minimum wage worker's W-2 income was in the 35th percentile of all workers, including part timers. The median worker was, by definition, at the 50th percentile, our average worker was in the 73rd percentile and the maximum in the 94th percentile; only about 6% of W-2 earners having an income at or above the taxable maximum cap. In 1979, the earliest year for which data are readily available, 13.4 percent of hourly workers were paid at or below the minimum wage; by 2006 that percentage had declined to 2.3%. 8 In order to keep the analysis tractable, it is assumed that each of the four hypothetical workers earned the specified amount throughout their careers. 9 _________________________ 7 Alternative measures of median income are examined in detail by L. Scott Muller (2008). The median figures referred to in the text are from www.socialsecurity.gov/OACT/COLA/central.htm, but this series only goes back to 1990. Elsewhere this study uses the series compiled by Muller from back issues of the Annual Statistical Supplements, Social Security Bulletin because it covers the entire historical period of interest. While not fully comparable to the Average Wage Index, it is close enough for the purposes of this study. 8 http://www.bls.gov/cps/minwage2007tbls.htm#10 9 In practice, a worker's relative position in the income distribution tends to change over the years, rising early in their careers as they develop skills and obtain seniority and dropping in later years if they suffer a decline in physical stamina or their human capital suffers from obsolescence. Clingman and Nichols (2006) of the Social Security Administration suggest that earnings typically peak at age 48 or 49. They have developed "scaled factors" to take this age-earning profile complication into account, but only through age 64, which is too short for our study. This is not a problem for either the maximum or minimum wage earners. High income workers earning rewards in excess of the taxable maximum do have their income time path for OASI tax and benefit calculations accurately captured by the cap. And our minimum wage earner reflects the position of those who are frozen in minimum wage jobs throughout their career. But the complication does mean that the Average and Median Wage Earner income paths only approximate the typical earning histories of the majority of workers near the center of the income distribution. More may be learned in future research based on micro data sets. www.economics-ejournal.org

Indexing Problem #1: Incomplete Wage Indexing
Because earnings adjusted for wage inflation up through the 60 th year are commingled with undeflated earnings in subsequent years, as shown by (3), many workers are credited with exaggerated Average Index Monthly Earnings. This results in an enlarged Primary Insurance Amount, leading to a larger OASI benefit than would be awarded if the entire earning history were wage indexed. We shall consider how three alternatives to this incomplete indexing procedure would affect workers in different income classes. After first considering the extreme case of wage earners who continue working until age 75, we shall look at how the choice of retirement date affects the benefits generated by alternative inflation indexing procedures. The top four rows of Table 3 contrasts the benefit of the Maximum Wage Earner under the current incomplete wage indexing procedure with three alternatives: (1) indexing earnings after age 60 with the Average Wage Index, (2) wage indexing of earnings to age 60 and the CPI-W in subsequent years, and (3) indexing all earnings with the CPI-W. Because the choice of deflation procedure for calculating benefits does not change the income paths of the four classes of workers, the same amount of tax revenue is raised regardless of the indexing procedure. 10

_________________________
10 The possible secondary effects of changes in benefits on the incentives to work and to save and the tertiary effect of such changes on capital accumulation and worker productivity in future years are beyond the scope of this paper. In the full CPI-W row the bend points determining the position of the PIA function that was plotted on Figure 2 are also indexed with the CPI-W instead of the wage index, but this happens to have only a small effect on the benefits of workers born in 1930 because the increase in the CPI-W from 1977 to 1990 was almost identical to that of the wage index, as can be seen from Figure 1.
As an extreme example, consider a maximum wage earner who continued working until age 75. With wage indexing only until age 60, the maximum wage earner's annual benefit is $25,812 per year (see Table 3). If, however, full wage indexing were extended to W-2 income earned after age 60, this worker would receive $24,000. Thus our worker enjoys an undeflated OASI benefit bonus of $1,812 in the first year of retirement. Or to put it another way, the adoption of full wage indexing would save the Social Security Administration $1,812 in the first year of retirement. This benefit bonus continues, indexed for inflation with the CPI-W, throughout the retirement years. If the spousal benefit is also claimed during retirement, the combined benefit for worker and spouse would be $38,718 with incomplete indexing versus $36,000 with full wage indexing, a difference of $2,718. This annual undeflated benefit bonus will continue until one or the other of the marital partners dies-at age 65 the life expectancy of the first to die is 80. More than this, a surviving partner may continue to claim a bonus because a widow(er)'s benefit equals that of the deceased spouse if it is higher than that based on one's own earning history-the life expectancy of the second to die at age 65 is 91. 11 The experience of the Average Wage Earner, the Median Wage Earner and the Minimum Wage Earner are presented in subsequent rows of this table. Note that the maximum wage earner's case is extreme. The minimum wage earner would lose only $132 per year from a shift from incomplete wage indexing to either mixed earnings/CPI-W indexing or full earnings indexing. However, a shift from the current incomplete indexing procedure to full CPI-W indexing would result in a $672 reduction in the minimum wage earner's annual benefit, which in percentage terms looms larger than the reduction for the maximum income worker.
As was reported on Table 1, workers who retire before the normal retirement age are penalized by a reduction in OASI benefits while those working later in life are rewarded. Thus a worker born in 1930 who elects to retire at age 62 is scheduled to receive only 80% of the PIA. According to the schedule on Table 1, that worker could receive a 122.5% of the PIA by postponing the start of retirement benefits until age 70. But the worker's PIA itself may be affected by how late in life our worker continues to earn W-2 income. Extra large benefits may result from postponing retirement until age 75, but only if those extra current dollar earnings are large enough to count among the highest 35 years. Table 4 shows in successive columns how the benefits depend on how late in life our worker continued to work and when she started to receive benefits. In all cases, benefits after the first year of retirement continue to be indexed by the CPI-W to the initial benefit. Panel A reports benefits when W-2 income is indexed only through age 60, the current procedure. Thus the first three entries in the top row show the benefits with partial wage indexing for the first year of retirement for maximum wage earners who began receiving benefits at age 62, at age 65 or at age 70; and the fourth entry in that row reports the benefit for a worker who continued working to age 75 but started benefits at age 70. Panel B shows what the benefits for these workers would be with complete wage indexing. The columns of Panel C are wage indexed until 60 and then indexed with the CPI-W. Those of Panel D are fully indexed by the CPI-W; _________________________ 11 Life expectancy estimates for 2 nd to die from Mahaney and Carlson (2007), p 39.
www.economics-ejournal.org furthermore, the bend points for that panel are indexed with the CPI-W instead of the wage index. The increase in nominal benefits for workers who delay retirement results in part from the additional earnings after age 62, provided they are large enough to be counted among the 35 highest income years. But as is clear from the real benefit figures on Panel A of Table 4, the reward for postponing retirement is far from uniform. Why is it that under the current SSA procedure of wage indexing only until age 60, the maximum wage earner receives an 81% increase in CPI-W deflated benefits for delaying retirement and continuing to work until 75, the average wage earner a 67% gain, the median earner a 62% gain and the minimum wage earner only 54%? And why is the incentive to delay retirement less with complete wage indexing, particularly for high income workers? Why do late working high income workers fair better with CPI than with wage indexed earnings (Panel B versus Panel D)? Are these variations in the incentive to retire the unintended consequence of arcane provisions in the Social Security statutes rather than the result of intelligent design or legislative intent? To answer such questions we will have to look closely at the earning history of our representative workers.

Maximum Wage Earner
Column 1 of Table 5, reports the partially indexed earnings of a worker who always earned at the taxable maximum cap as calculated with (3) in accordance with the OASI procedure by indexing the earnings at the cap (column 4 of Table 2) with the Average www.economics-ejournal.org Wage Index (column 6 of Table 2) only through the worker's 60 th birthday. Assuming there is inflation, each year worked beyond age 60 by our high income worker results in a high undeflated year replacing an earlier year which had been inflated only to age 60. Columns 3 through 5 on Table 5 shows that the number of unindexed years included among the highest 35 that count in determining benefits depends upon when the worker retires. All this means that under the provisions of the Social Security statutes, the number of unindexed years that are commingled with wage indexed years in calculating the sum of the top 35 depends upon how late in life the worker earns substantial income. 12 The two rows after the age 74 row decompose the sum of the best 35 years into earnings through age 60 and earnings from age 61 to retirement. Observe from columns (5), (7) and (9) that the sum through age 60 is the same for the first three indexing procedures. The second half of the sum in the next row, age 61 to retirement, depends upon whether these observations are not indexed, are wage indexed, or are CPI-W indexed. Comparing column 5 with column 3 reveals that working to age 75 instead of to 62 replaces thirteen low earning years in the 1950s, 1960s and early 1970's with higher unindexed earnings from 1991 on. That explains why the benefits of long career workers are more sensitive to the choice of index than shorter career workers whose post 60 earnings make up a smaller share of their 35 highest earning years.
As a result of the partial indexing procedure, less than half of the total earnings for the worker who continues to earn the cap to age 75, column 5, are indexed. The PIA at eligibility, used in calculating the worker's benefits, is 7.6% higher with incomplete wage indexing than would be generated by the case of full wage indexing of column 7. Columns 9 and 11 show how the PIA and hence the benefit for a worker retiring at 75 would be affected by the adoption of alternative full indexing procedures.

Minimum Wage Earner
A worker who earned only the minimum wage throughout an equally long career has a quite different outcome. As was reported on Table 4, with only two exceptions, the Minimum Wage Earner's benefits are the same with wage indexing only to age 60, full wage indexing, or wage indexing to age 60 then CPI; the exception is partial indexing for a worker who manages to postpone retirement until 70 or 75. Why? Table 6 shows that with that one exception our worker's earnings after age 60 are dropped rather than counted among the 35 highest earning years of (4). This happens because the minimum wage was allowed to fall so far behind inflation-see columns (3), (4), (7) and (9). Indeed, the real minimum wage, indexed with either the wage index or CPI-W (columns 6 or 10), was lower in 2004 than it was in 1951.

Average Earner
The average workers indexed income is recorded in column (12) of Table 6. It is a constant $21,028 through our worker's 60 th birthday because it is deflated with the wage _________________________ 12 The table may over or understate the contribution to the OASI benefit of earnings after age 62 for women who were not in the labor force when their children were young. It will understate the benefit of a women who had worked fewer than 35 years before reaching age 62 because then the dropped years involve zero rather than positive earnings. But the spousal benefit complicates the story: delaying retirement from the workforce will not increase her OASI retirement benefit if her husband's benefit remains more than twice the benefit based on the women's own earnings history. index constructed with the same nominal series. After the 60th birthday the undeflated wage data is used by the SSA. Because of the wage inflation, the income for all years worked after age 60 is included among the 35 highest. None the less, the gain in benefits from postponing retirement is not as great as that of the maximum income worker because of the increased skewness of the income distribution.

Recommendation:
Partial indexing is hard to defend. It obviously contributes to Social Security's financial problems, although a precise estimate of its total impact must be left for future research  193 11,193 11,193 11,193 11,193 11,193 11,193 11,193  based on a detailed analysis of micro data sets. 13 As shown on Table 3, in some cases it awards the largest benefit bonus to the highest income earners. Correcting this problem would probably not affect a worker's decision as to when to retire because it is doubtful that many contemplating delayed retirement either know about the bonus or can predict its magnitude with much precision.

Indexing Problem #2: Skipped 61 st Year Inflation Adjustment
In computing benefits, a worker's earnings are adjusted for wage inflation with an index normalized to equal 100 in the year of the workers 60 th birthday (t = t b +60). But the inflation adjustment ratio in were not so fortunate, for their 61 st year inflation rate was 5.32%. If in the future we encounter an inflation rate on the order of 12.77%, such as the U.S. experienced in 1980, workers 61 years of age will suffer a 12.77% reduction in the purchasing power of their benefits in every year of their retirement. 14

Recommendation:
The obvious remedy is to make the calculation include the CPI-W inflation that is experienced in the 61 st year. Historically, inflation as measured by the SSA has averaged about 3.8% over the years. This suggests that the omission of the 61 st year in computing OASI benefits saves 3.8% of the OASI benefit budget on average, which it can ill afford to lose. Given the financial pressures on the SSA, it might be most appropriate to maintain budget neutrality when making the correction by coupling the "reform" with a proportional reduction of benefits across the board, as has been suggested by Diamond and Orszag (2005:112). Essentially, this replaces the skipped 61 st year inflation lottery with an estimate of average inflation, which is an obvious benefit for the risk averse. 13 Diamond and Orszag briefly mention the incomplete indexing problem (2005: 274, fn 24), but its budget implications were not evaluated by either the Social Security Administration or the Congressional Budget Office(2004) in estimating the long run financial implications of the program changes they proposed. 14 Workers who were 61 in 1980 did not suffer this big a reduction in real benefits because the 1977 Amendments to the Social Security Act to Correct the Original Indexing Procedures included a special "Transitional Guarantee Method" for calculating benefits for workers born in 1917-21 (McKay, 1980. Nevertheless, the reductions were substantial, leading to the formation of the politically active "Notch Generation."

Indexing Problem #3: The One Year Indexing Lag
As can be seen from (6), there is a one year lag in adjusting benefits for price inflation because inflation is missed in the benefit year for the obvious reason that it has yet to be experienced-the current year p t will not be known until near the end of that year. 15 Because the one year inflation indexing lag treats equally every age cohort of those currently receiving OASI benefits, the erratic year-to-year fluctuation in the purchasing power of OASI benefits is not nearly as serious as the Skipped 61 st year problem, which penalizes those who had the misfortune to experience particularly severe inflation in their 61 st year. Furthermore, retirees generally have expenditures with sticky prices, such as real estate taxes, Medicare payments and rents. Therefore, the one year indexing lag is not too serious as long as inflation does not become intense.

Recommendation:
The problem is that benefits are determined in advance when obviously the rate of inflation that will prevail is not known. It would be possible to use a predicted rate of inflation,ˆt p , together with a simple error-correction adjustment to correct for the prediction error of the preceding year. Here is how such a procedure might operate for a worker born in year t b who started to draw benefits at age a s . For the first year of retirement: This differs from , which can be interpreted as using the p t-1 forecast, in that it corrects for both the prior year prediction error and the skipped 61year problem. It would be better to use a Box-Jenkins forecast of p t instead of p t-1 or, alternatively, a forecast provided by an accepted authority, such as the Chairman of the Federal Reserve Board or the Commissioner of Labor Statistics. The same revision procedure might also be used to avoid the two year lag involved in the adjustment of the PIA function bend points, (6), for changes in the Average Wage Index.
The adoption of a revision procedure has an additional benefit: it will allow the fixed weight CPI-W index, which has as its primary advantage that it is seldom revised, to be replaced with a more appropriate superlative index recognizing that in response to price changes consumers adjust the composition of their market basket of purchases, substituting away from commodities that increase most in price. The National Research Council's Panel on Conceptual, Measurement, and Other Statistical Issues in Developing Cost-of-Living Indexes, proposed in At What Price (2002, Conclusion #7.1:194): "It would be feasible and appropriate to calculate cost-of-living allowances provided for by social security and other programs from an advance estimate of the BLS published superlative index. Any divergence between that estimate and the superlative that appears 2 years later could be incorporated as a correction to the cost-of-living allowance provided for that year."

3.4
Indexing and elasticity 2 60 Consequently, the percentage change in indexed earnings up to year 60 is also equal to the percentage change in 2 60 b w t E − + . However, indexed earnings in year t b +60 do not change because by construction 60 1 b t w + = . Further, post age 60 earnings are not affected by the wage index bounce because earnings after age 60 are not deflated. Therefore, a worker's AIME will not change by as large a percentage as the increase in the average wage in the 60 th year. However, benefits derived from the new AIME will increase because the bend points defining the function plotted on Figure 2 will shift upwards in proportion to the wage inflation.
To illustrate the index bounce problem, consider an experimental shift of $480 from the National Average Wage income of 1991 to 1990; i.e., we increase the 1990 average wage from $21,028 to $21,508 (2.3%) and decrease the 1991 level from $21,812 to $21,332, as illustrated on column E1 of Table 7. This perturbation is equal to the standard deviation of annual changes in the NAW. It is small relative to the $1,208 jump in the NAW from 1995 to 1996. It does not affect the total undeflated lifetime income or the total OASI tax payments of the Average Wage Earner born in 1930. And there is no change in either the income or the taxes of the Maximum Income or the Minimum Wage Worker. Nevertheless, the perturbation does make quite a difference to the worker's OASI benefit throughout retirement. Table 7 shows how the wage index used for calculating the benefits for this and all other workers of the same age, because they are normalized to equal 100 in the 60th year, will be lower in all the other working years (Compare experiment column E6 with control column C6). When the worker's nominal earnings for all years prior to the 60th are divided by the revised index, the indexed earnings will be about 2.3% higher than if the shift had not occurred (column E10). Also, the change in the National Average Wage in 1990 increases the bend points of the PIA function, which provides a further push to benefits. As can be seen from the bottom line of Table 7, the income shift plus the Bend Point adjustments increases our M<aximum Wage Earner's annual benefit by $432, or 1.7%, if she continues working to age 75. Table 8 shows that the magnitude of the effect of the wage index bounce on retirement benefits depends on the age of retirement, the indexing procedure used in computing benefits, and the income history of the worker. The bounce has a larger percentage effect on the benefits of workers whose income is below the top break point on the piecewise linear PIA function plotted on Figure 2. If wages are fully CPI indexed, the bounce will be small as it reflects only the shift in the bend points because the CPI index is not affected by the bounce in the average worker's 60 th year income (it would be affected by revisions of the CPI in the 60 th year).
The shift would cause an increase in the OASI benefit throughout the retirement for all workers turning 60 in 1990-the 1930 birth cohort. This stream of higher benefits would be approximately offset in subsequent years by lower payments to workers in the 1931 birth cohort. And assuming roughly equal mortality rates, in the long run the revisions would approximately cancel out so that there is no serious effect on OASI's fiscal posture. The problem is that it is manifestly unfair to have benefits vary between different birth cohorts of workers because the calculation procedure is hypersensitive to movements in income in the year of one's 60 th birthday. In our $480 shift experiment the change in annual benefits with partial wage indexing ranges from 1.3% to 1.9%. This would not be deemed insignificant, at least by the minimum wage earner. And its size is roughly proportional to the size of the shift.

Recommendation:
It is not easy to devise a remedy for the 60th year bounce, but it would mitigate the problem somewhat if the SSA, instead of indexing to just age 60, would smooth the wage index, perhaps by using a three year average (ages 59 through 61), as is the practice of the BLS in constructing CPI indexes. 16 Also, employing a Median Wage Index instead of the Average (arithmetic mean) Wage Index might help because it may be more stable than the average. 17

Indexing Problem #5: Taxing OASI Benefits
The IRS has collected income taxes on OASI benefits since 1983. Initially, only 50% of OASI benefits were counted in taxable income by the IRS, and then only if the married couple's combined income was more then $32,000; for single tax payers the income threshold was $25,000. In 1993, the tax rate was imposed on 85% of OASI benefits for joint-filers with combined income above $44,000; for single taxpayers this second threshold is $34,000. Because the OASI tax paid by a worker from after-tax income is matched by the employer, which is before-tax income, the tax on 50% of OASI benefits that was imposed in 1983 is roughly comparable to the tax imposed on a worker who places equal amounts in a Roth IRA purchased with after tax money and a traditional IRA financed with before-tax money. In this sense, taxing 85% of OASI benefits appears to involve less favorable tax treatment than is currently available with an even mix of Roth and traditional IRA's.
Although tax bracket thresholds for the personal income tax have been indexed since 1985, the thresholds for the tax on OASI benefits have not been adjusted for inflation. This means that the income tax imposed on OASI benefits has gradually reached further and further down the income distribution. If the $32,000, $25,000 brackets established in 1983 had been indexed to the CPI, by 2008 they would have been adjusted to $64,805 for married and $50,629 for single tax fillers because the CPI-W slightly more than doubled during that 25 year time span. Burman and Saleem (2004) estimate that the percentage of households paying taxes on their OASI benefits will increase from 36% in 2004 to 40% in 2014. See also Munnell and Muldoon (2008).

Recommendation:
The income thresholds for imposing the personal income tax on OASI benefits should be indexed for inflation. The failure to index tax brackets for inflation has allowed rising prices to impose what amounts to a new tax on middle income retirees. The fact that the income tax revenue collected from taxing OASI benefits is dedicated to the Medicare Trust Fund does not justify failing to index the exemption thresholds. to extreme values because the deviations from the mean are squared. It might also be argued that the median is a better measure of wellbeing because maximizing the median is the same as maximizing average utility if income is approximately log normally distributed and utility(x i ) = log(x i ).

Inflation Experiments
Compared to many countries, the United States has enjoyed fairly stable prices over the years. But suppose the long run rate of inflation were to accelerate? How would this affect different income groups? And how would it affect the financial viability of the Old Age and Survivor Trust Funds? Incomplete indexing of OASI benefits means that the system is exposed to financial disruption from fluctuations in the rate of inflation. Three experiments will show how the choice of deflator affects the sensitivity of real benefits to changes in the trend inflation rate. For comparison, the results for counterfactual inflation trends will be contrasted with the control provided by the historical inflation experience reported on Table 4.

Experiment #1: 5% More Inflation
The first experiment, reported on Table 9, involves tilting both the CPI-W and the AWI by an extra 5% of inflation per annum, starting in 1991. This superimposes a steeper www.economics-ejournal.org trend on the two series but preserves the historical fluctuations in the gap between them. Because the increased inflation did not start until 1991, the wage index is at the original historical level of 1990, which means that precisely the same bend points could be utilized as before and Figure 2 still shows how the PIA is determined by the AIME. In this experiment the CPI-W (1990 = 100) had increased to 308 by 2005, substantially above the control level of 148 for that year. As a result, the CPI deflated benefit data (real) are more revealing, particularly when they are compared with the real outcomes of the control. Almost everybody loses from the higher inflationary trend. The primary exceptions are maximum, average and median earners who continue working to age 75 while their earnings, under current SSA procedures, are indexed only through age 60-their increased incomplete indexing bonus more than offsets their loss from the skipped 61st year and the one year indexing lag. Further, the reward for postponing retirement from 62 to 75 is magnified, as can be seen by comparing the results on Panel A with those of Table 4 With any of the three alternatives to the SSA's incomplete indexing procedure, everyone's real benefit is reduced by the skipped 61st year indexing problem to 91% of the control benefit. Table 10 reports that with 10% inflation the maximum wage earner who continues to receive the cap through to age 75 is the big winner, gaining 13% per annum under incomplete indexing; the average earner gains 6%, the median 14% and the minimum wage earner 2%. With any of the three complete indexing procedures, real income is reduced by 17%.

Experiment #3: Deflation
With a reduction in the inflation rate to 5% below its historic value, every thing is reversed: the undeflated earnings bonus turns negative while the skipped 61 st year and one year indexing lag contribute to an increase in benefits. As a result, every OASI recipient gains from the deflation, as reported on Table 11. This time the maximum wage earner who continues working until age 75 experiences the smallest real gain, only one percent, because falling wages yield a sizable undeflated earnings penalty that counters the gain workers enjoy from the skipped 61 st year and the one year indexing lag.

Summary
Observe on Table 11 that the 5% reduction in inflation caused a uniform 11% increase in the real value of benefits for all except the incompletely indexed SSA benefits of Panel A. Similarly, 5% increased inflation caused a uniform 9% reduction in benefits and 10% inflation a uniform 17% reduction in benefits. This unexpected result is due to the skipped 61 st year inflation adjustment and one year indexing lag problems, as can be verified by looking back to PIA (6). The price ratio in that equation Thus our 5% inflation experiment generated a reduction in real benefits to 90.2% and the 10% experiment generated a reduction to 83%. A 5% reduction in inflation results in a benefit increase to 111% as reported on the tables. These under-indexing distortions could be mitigated by using a predicted rate of inflation together with the error correction procedure of equations (8) and (9). Thus our experiments show that while the correction of the incomplete wage indexing problem would substantially reduce inflationary distortions, inflation would still have a substantial impact on the purchasing power of OASI benefits.

Recommendation:
These experiments strengthen the case for correcting Indexing Problem #1: Incomplete Wage Indexing. But just changing from incomplete wage indexing to full indexing still allows inflation to have a substantial impact on benefits. Indexing with the wage index, the CPI or a blend does not stop inflation from imposing a proportional reduction in the purchasing power of the benefits received by practically all beneficiaries, regardless of the age when benefits start or income class. Full indexing requires in addition the correction of the skipped 61 st year and the one year indexing problem. It also requires the indexing of the brackets in the income tax imposed on OASI benefits.

Unanticipated Inflation
While the resolution of the five indexing problems discussed in this paper would help insulate the real value of OASI benefit payout from inflation, which does not mean that the inflation would not have other consequences for the OASI trust funds. Those funds are invested with an average maturity of 7.3 years. A bout of inflation, unless it is anticipated, will cause a sustained reduction in the real rate of interest earned on those investments. 18

Wage and Price Indices
The two indexes used by the Social Security Administration in adjusting nominal figures for inflation were recorded on columns (5) and (6) of Table 2. The Average Wage Index (AWI) is used to index earnings up to the year of the worker's 60 th birthday and a modified version of the Bureau of Labor Statistics CPI-W price index is used to adjust benefits for workers from the year of the 61 st birthday through retirement. 19 Both were plotted on Figure 1. On Table 2 we have the level and annual inflation rates for both indexes from 1960 to 2007. Table 2 also reports the effective interest rate r earned on Social Security's OASI trust fund and two implied ex post real rates of interest, defined as r where p − & p & is the rate of change in either the CPI-W or AWI. 20 The OASI procedure for computing the sum of indexed earnings in the highest years implicitly uses a zero real AWI interest rate, while in practice the trust funds have earned a real rate of about 1.3% relative to the AWI or 2.4% relative to the CPI-W, as indicated on Table 2. In contrast to Social Security, when individuals place some of their retirement funds in a private savings account or purchase bonds, their savings in earlier years make a larger contribution toward retirement, cumulating more interest earnings because they are invested for a longer period of time.

Consumer Price Index (CPI-W):
The Consumer Price Index for Urban Wage Earners and Clerical Workers (CPI-W), compiled by the Bureau of Labor Statistics, is used in slightly modified form by the SSA in annually adjusting benefit figures for changes in the cost of living (COLA). The annual CPI-W index cannot be used without modification because of the need to have the figure available before the end of the year. Instead, the SSA compiles an index based on the average of the index in the 3 rd quarter-July, August and September.

_________________________
18 The accelerated inflation experiments reported in this paper have the CPI-W and the wage index both increase by the same percentage, which might be the case if the rate of productivity growth was unaffected. The complications generated when this assumption is relaxed must be left for future research.
19 At What Price (2002, ch. 7), a study produced by an expert panel chaired by Charles L. Schultze for the National Research Council, presents a comprehensive analysis of the issues involved in the construction of wage and price indexes appropriate for adjusting Social Security benefits for inflation. That study emphasized the advantage of using a superlative index recognizing that consumers substitute away from commodities that have the largest price increases. In contrast, the primary focus of this study is on the way in which the indexes are used. 20 The effective interest rate on OASI trust funds was downloaded from http://www.socialsecurity.gov/OACT/ProgData/effectiveRates.html www.economics-ejournal.org

Average Wage Index (AWI):
The wage index used in calculating Social Security benefits is based on the average income reported on W-2 forms for workers subject to Social Security Taxes. The Social Security web site explains: "In keeping with the legal term 'average wage index' (AWI), we often loosely refer to the basis for the index as average wages. To be more precise, however, the index is based on compensation (wages, tips, and the like) subject to Federal income taxes, as reported by employers on Form W-2. Beginning with the AWI for 1991, compensation includes contributions to deferred compensation plans, but excludes certain distributions from plans where the distributions are included in the reported compensation subject to income taxes. We call the result of including contributions, and excluding certain distributions, net compensation." 21 While the AWI now incorporates employer contributions to retirement plans, it excludes many forms of worker compensation, including employer provided health benefits.
And it does not include the income sole proprietors report to the IRS on Schedule C, although such income is subject to OASI taxes (IRS Schedule SE). Needless to say, it also excludes the compensation of hedge fund managers (who are taxed at the 15% capital gains rate by the IRS even when they do not have their own capital at risk) and the "carried interest" of private placement specialists. Employers do not have to submit the W-2 tax forms used by the SSA in calculating the average wage index until as late as March 31 of the following year, provided they file electronically. As a result, there is a lag in the availability of the average earnings index used in calculating bend points. Thus the National Average Wage for 2006 of $38,651.41 from which the average earnings index is calculated was not posted on the SSA website until October 17, 2007.
A number of non-inflationary factors can influence the path of the Average Wage Index, including demographic trends in the age structure of the labor force, the current recession, and financial sector restructuring. The decline in the teenage fraction of total employment from a peak of 8.6% in 1974 to 4% in 2007 would tend to reduce the index. The index would be boosted by an increase in the proportion of the work force composed of part-time workers, which might occur if the aging of the population led to an increase in the proportion of the workforce composed of seniors who had cut back on hours worked. The index will have a downward bias in recession because the cutback of workers to a shorter work week will reduce the numerator of the index but will cause a corresponding reduction in the denominator only to the extent that laid off workers are unemployed throughout a full calendar year. It will climb if there is an increase in W-2 incomes of high earning workers that is not matched by similar increases for the majority of the work force. In fact, mean income has risen much more rapidly then the median in the last decade and a half, reflecting at least in part the increased skewness of _________________________ 21 http://www.ssa.gov/OACT/COLA/netcomp.html The growing popularity of deferred compensation pension plans in the 1980s meant that the wage index, because it excluded this expanding component, did not grow as fast as Social Security tax revenue, which did reflect it (Clingman and Kunkel, 2008). The inclusion of deferred compensation plans after 1991 may partly explain the rapid rise in the wage index after that date. the income distribution, the ratio of median to mean income declining between 1990 and 2006 from 72% to 67%. The OASI benefits might be lower today if a Median Wage Index instead of the Average Wage Index had been used, but that could be a temporary effect if the trend toward a more highly skewed income distribution were to reverse. Figure 1 compared the time path of the Average Wage Index (AWI), used to inflate wages up to the worker's 60 th birthday, with the CPI-W, which is used to inflate benefits in step with rising prices during the retirement years. Observe that the upward trend in wages has averaged out above that of prices, yielding an upward trend in the standard of living that reflects the rise in worker productivity. The primary exception is the decline in real wages during productivity slowdown of the 1970s and early 1980s. The use of the wage index up to the 60 th year allows each generation of workers to enjoy in retirement the fruits of rising productivity that occurred during the bulk of the time they were in the work force. It helps to stabilize the replacement ratio-the ratio of retirement income to the worker's average income. 22 Evidence that the choice of deflator makes a difference is provided by a comparison of Figure 3 with Figure 4 and Figure 5. Figure 3 reported the income streams for a taxable maximum earner, an average wage earner, a median wage earner, and a worker who always earned at the federal minimum wage. Figure 4, utilizing the CPI-W deflator, indicates that workers earning the Taxable Maximum enjoyed a substantial increase in real income, that the Average Wage earner had only a moderate gain since the 1970s but did better than workers at the median. Workers earning only the federal minimum wage throughout their careers have suffered a decline in purchasing power since its peak in the late 1960s. Note on Figure 5 that the wage deflated earnings of a worker receiving the National Average Wage are represented by a horizontal line, as must be the case by construction because the Average Wage Index is the deflator.

Comparisons
The Taxable Maximum, adjusted by the wage deflator, increased dramatically in the 1970s and 80s. The immediate effect of an increase in the Taxable Maximum is to raise OASI tax revenue. The Congressional Budget Office (2004, Appendix A) has commented as follows: "Since 1982, the taxable maximum-the level above which earnings are not subject to the Social Security payroll tax-has been indexed to overall wage growth. However, due to increasing earnings inequality, the portion of covered wages that are subject to tax has declined since then, from about 89 percent to about 83 percent." Even with indexing, the Taxable Maximum has been subject to considerable variation since 1982, in part because the indexation is executed with a two year lag necessitated _________________________ 22 Age 60 provides a convenient base for calculations because it allows time for the compilation of relevant data about wage inflation before the worker turns 62, which is the earliest age at which workers can claim OASI benefits. A case can be made for indexing to the year in which the worker first claims OASI benefits, although this would introduce the complication of correcting initial payments that had to be made on the basis of preliminary data with the revision procedure of (8) and (9). www.economics-ejournal.org by the delay involved in the construction of the wage index, which is based on W-2 tax information.
Be that as it may, the fall in covered wages that are subject to the OASI tax to 83% implies that if the payroll cap were removed, as is already the case for Medicare, OASI tax revenue might increase by 17%/83% = 20.5%! This would be a gain in the short run, but it would be at least partially offset when the high income workers paying the tax on their full W-2 earnings retired because their benefit payments are also based on their taxable earnings, and this effect is compounded because of the longer expected lifespan of higher income workers. If the Taxable Maximum cap remained on employee contributions but was removed from employer contribution, the revenue gain would be cut to 10.25%, but there would be no offsetting increase in benefit payments down the road if they were still based on the unmodified Taxable Maximum.
Because this paper focuses on data for only the single cohort of retirees born in 1930, it leaves for subsequent research the task of determining the most appropriate index or combination of indexes to use in adjusting OASI for inflation. The choice should not be limited to the Average Wage Index versus the CPI-W. The primary advantage of CPI-W is that it is seldom revised, but (8) provides a procedure for coping with revisions that would also facilitate the adoption of a superlative price index. Because the median rather than the mean is likely to be less subject to erratic year to year movements and less sensitive to the growing income inequality that has contributed to the upward surge in the taxable maximum, consideration should also be given to shifting from using the National Average Wage to a National Median Wage in the construction of the wage index, in adjusting bend points, and in calculating the taxable maximum. Whether based on the average (mean) or median, it would also be somewhat more stable-and hence reduce the seriousness of Problem #4, the 60 th year bounce-to have the wage index normalized to equal 100 not in the worker's 60 th year, but on the average of wages in the adjacent years (ages 59-61= 100), just as the Bureau of Labor Statistics CPI is normalized: (1982-84 = 100).

Phasing in Reform
Easing the transition into a reform is not easy. When SS indexing procedures were revised in 1978, a special Transition Benefit procedure was included to protect workers who attained the age of 62 between the years 1979-83. It did not work, giving rise to the famous Notch Generation controversy. When President George W. Bush promulgated his Social Security reform, he stressed that there would be no changes for those already over 55 23 -implicit in his pronouncement was a warning to those under 55, the majority of voters, that they had better look out.

_________________________
Using an index that gradually reduces benefits over time might minimize political repercussions if the slippage is so slow as to fall below the representative voter's horizon-so much for transparency. 24 This is the argument for replacing wage indexing with CPI-W price indexing in dealing with the serious longrun financial problems of OASI.
Shifting from wage to price indexing during the working years might reduce financial pressure on the trust funds, provided that on average the CPI continues to rise less rapidly than wages. But the adjustment toward financial viability might well be by fits and starts, judging by the historical comparison of the CPI-W and the AWI on Figure 1. Further, Biggs et al. (2005) point out that a switch to price-indexing in computing benefits might be destabilizing, leading to a divergence over time between the path of expenditures and revenue, because benefits would depend on price movements while the OASI tax revenue is based on wage income. Biggs et.al. (2005:29) explain that "the same level of expected cost savings could be achieved without decreasing stability by simply choosing a predetermined path by which PIA factors are reduced that is not conditional on ex post realizations of wage and price growth." More than this, adopting a predetermined schedule will mean that discussions of how best to index benefits can focus on the proper task of insulating benefits from the vicissitudes of inflation.
A predetermined schedule for phasing in adjustments has several advantages. It will minimize the disruption of the financial plans that workers may have developed based on the good faith assumption that scheduled benefits would be received while at the same time facilitating adjustments that might contribute to financial equilibrium. Furthermore, the primary effect will be upon younger voters at a stage of life when they will be less certain about what their health and marital status will be when they reach retirement age, which means that they will be able to make a judgment that will not be dominated by their own personal situation on eve of retirement. They will be closer to making an impartial judgment based on probabilities, operating closer to John Rawls' "veil of ignorance," rather than making a judgment clouded by their own personal situation. And older voters, because they will not feel the full thrust of the change, will also be able to reach a judgment that will be less clouded by their own position in life.
Here is one way of generating a predetermined schedule that would gently phase in an OASI "reform." Each worker's benefit would be calculated twice: Let , It would also be possible to use indexes indirectly to gradually slow the growth of benefits generated by wage-indexing, as in the PIA Factor Indexing procedure considered by Biggs, Brown and Springstead (2005). This procedure would adjust the 90%, 32% and 15% parameters of the equation plotted on Figure  2 from the value in the preceding year by the ratio in the beneficiary's 60 th year; bend points would still be adjusted by current procedures. This would adjust the benefits of all workers in the same birth cohort by the same percentage, but it could make benefits for workers with similar wage histories vary rather erratically from one age cohort to the next. For The parameter ρ affects the speed of adjustment: with ρ = 1, the case of linear interpolation, weighting is proportional to the years spent before and after reform; for example, w i = ½ for a worker who was 40 when the reform measure was instituted. The reform is phased in more rapidly with ρ > 1; for example, with ρ = 2, a worker who was aged 49 when the reform was passed would have w i = ½. While this equation takes 44 years fully to complete the adjustment process, it can easily be modified to shorten the adjustment period.

Retirement Incentives
Workers receive higher OASI benefits if they postpone retirement beyond age 62, the first year of eligibility. Part of the increase arises from their after age 62 earnings adding to their Average Indexed Monthly Earnings, provided they are large enough to count among their highest 35 earning years. And part of the increase is deliberate built in by the OASI statutes in order to encourage workers to postpone their departure from the labor force, pay more taxes, and have a more adequate income when they do retire-this is the factor, tabulated in ( , ) b s A t a Table 1, that enters into (7) for the Primary Insurance Amount.
Calculations presented in this paper show that in practice the reward for postponing retirement depends in part on both ones position in the income distribution and the pace of inflation. Table 12 summarizes the results from Tables 4, 9, 10 and 11 for the extreme case of workers born in 1930 who kept working full time until age 75 rather than retiring at 62. The first column of Panel A of the table shows the gain with the actual inflation experience as reported on Table 4 and the next three columns report the gain with 5% more, 10% more or 5% less inflation, as was reported on Table 9, Table  10 and Table 11.
The top four entries in the first column of the table reveal that under current procedures the percentage benefit gain from delaying retirement has been much larger for those at the top of the income distribution. This result arises at least in part because maximum wage earners born in 1930 enjoyed an exceptional increase in earnings near the end of their careers. Subsequent columns reveal that accelerated inflation would substantially increase the incentive. And Sections B, C and D of the table show that a switch from the current incomplete indexing procedure to any one of the three full wage indexing procedures would help equalize the percentage benefit gain among different income classes. The estimates on Table 12 reveal only the direct effects of alternative indexing procedures on OASI benefits. The possible effects of the shift in the incentive for delaying retirement on the choice of retirement dates, on private savings, and worker productivity are complex topics that cannot be explored here but must be left for subsequent research. In fact, high earners do tend to retire later. While it is tempting to conclude that high earners retire later because of the greater incentive, such an argument, which assumes that the substitution effect is stronger than the income effect, would rest on the presumption that those approaching retirement perceive with considerable precision the gain in benefits that they will realize if they postpone retirement. But the table does make clear that the size of the incentive that will be enjoyed by an age cohort depends in part on what happens to the taxable maximum cap and the speed of inflation after the 60th year. Table 12, like the preceding tables on which it is based, does not state the gain from postponing retirement for workers whose earnings do not track one of the four specified income paths throughout their careers. Consider, for example, a college professor who received a substantial raise to the Taxable Maximum when promoted to full at the age of 40. And suppose that from then on her salary increased from year to year in proportion to increases in the National Average Wage Index; i.e., her income coincided with that of the Taxable Maximum path on Figure 3 only from age 40 on. As a result, each year that she works after 60 will displace an earlier year's income that is substantially below that for the worker on Table 5. This means that each year she decides to continue working full time will yield a net increase in her Average Indexed Monthly Earnings that is bigger than was reported on the tables. As a result, delaying retirement will yield a larger increase in OASI benefits than was indicated on Table 12.
Note that earnings in the last year of employment, while subject to tax, are not counted in computing OASI benefits. This means that if our college professor stops work at the end of the first semester of an academic year she will have nothing to show for a full year of taxed income. If she does stop full-time teaching in December she should consider saving that final year of teaching by taking a temporary position in the new year, even if it only involves retrieving shopping carts at the supermarket.
Our professor's OASI picture will be further complicated if she decides to cut back to part time later in her career. During her part-time years the OASI tax on her earnings will not yield any increase in OASI benefits if they are too low to displace the earnings of any of her earlier working years.

Summary and Conclusions
This paper demonstrates that full wage, mixed wage/CPI and full CPI indexing are all better at avoiding the distortions of inflation than the incomplete wage indexing procedure currently used by the Social Security Administration in computing OASI benefits. And Section 3 recommends strategies for addressing the other four indexing problems of the procedure currently used to calculate OASI benefits. How would resolving the five indexing problems examined in this paper affect the financial viability of OASI? A precise estimate must be left for future study because it will require the examination of detailed survey data sets instead of just the experiences of the four representative workers, all born in 1930, that were evaluated in this paper. But examination of Table 4 does reveal that resolving Indexing Problem #1, the commingling of indexed with unindexed earnings, would reduce the retirement benefits of all four classes of workers. The exception is workers retiring at 62, who would be held harmless. Thus switching from incomplete to the full indexing of earnings could help resolve OASI's financial problems. We also saw that Problem #2, the skipped 61 st year inflation adjustment, and Problem #3, the one year indexing lag, could be resolved in a financially neutral way. And mitigating Problem #4, the 60 th year wage index bounce, would reduce the erratic variance of benefits among different age cohorts but not average annual benefit expenditures. Indexing for inflation the brackets of the income tax imposed on OASI benefits would resolve Problem #5 without affecting OASI's budget. 25 Thus it seems reasonable to conclude, pending further study, that correcting these five indexing problems could help resolve OASI's financial problems.
Adopting CPI-W indexing instead of wage indexing might help resolve OASI's longrun financial problem by gradually reducing most benefits over time. But the adjustment would not be smooth, judging by the rather erratic historical movement in the gap between the CPI-W and the wage index displayed on Figure 1. Instead, a predetermined schedule, generated perhaps with (14), could be used to provide a smooth phasing in of a reform while retaining the advantages of wage indexing of earnings.
The various experiments presented in this paper provide ample reason for making the procedure for calculating OASI benefits inflation neutral by resolving the five indexing problems. Not only will the resolution of these five problems eliminate certain _________________________ capricious and regressive effects of inflation on the distribution of retiree benefits. It will make it easier for workers to evaluate more accurately the effect of delaying retirement on their OASI benefits. It will help insulate the financial viability of the trust funds from the vicissitudes of inflation.

Step #3: Summing the 35 Best Years
The Social Security benefit is calculated from the sum of indexed earnings for the 35 highest years; earnings in remaining years do not count. Column 4 of the AnyPIA output selects the highest 35 years from column 3. The sum of this column, $1,840,807.52, will be carried over to the next table for the subsequent steps in calculating our worker's retirement benefit. As indicated by the bottom italicized rows that have been added to the AnyPIA output, more than half this sum for this late retiring worker has not been indexed for inflation. The fully indexed best 35 year sum reported at the bottom of column 9 is only $1,588,856.78, which would yield substantially lower retirement benefits for our high income worker.

Step #4: Calculating Average Indexed Monthly Earnings (Page 5 of AnyPIA output)
At the beginning of the second line of Table 14, AnyPIA calculates the worker's Average Indexed Monthly Earnings (AIME) by dividing the sum of indexed earnings for the best 35 years from the bottom of the preceding table by 35x12: AIME = $1,840,807.52/(35x12) = $4,382. The columns added to the right of the verticsl line show the effects of full indexing. As shown near the top of the rightmost column, full wage indexing of earnings yields AIME = $3,782, or only 86% of the figure obtained with incomplete indexing.
Step #5: Calculating the Primary Insurance Amount at Eligibility (Page 5 of AnyPIA output) Age 62, the first year one may elect to start receiving OASI benefits, is called the year of eligibility. The PIA at eligibility is a piecewise linear function of the AIME, as graphed on Figure 2 for a worker born in 1930. The PIA function is the same for all workers born in the same year, but it shifts from birth cohort to birth cohort because the bend points shift in response to changes in the Average Wage Index.  (2) With full wage indexing (column 4), the PIA at benefit date 2005 would be $1,632.90, or 7% less than with incomplete indexing.
Step #7: Determining the Benefit (Page 1 of AnyPIA output) How our maximum earner's monthly benefit is affected by the choice of when to retire from work and when to start claiming OASI benefits is revealed by Table 15. Thanks to the delayed increment factor, workers who delay starting benefits until 70 enjoy benefits that are 22.5% higher than they would have been if they had started taking benefits at age 65. Working beyond age 70 will involve enjoying a higher benefit as a result of paying more taxes, but the delayed increment factor will remain at 22.5%.