Social Security Finds Later Retirement Age Reduces
Benefits, Costs but Increases Poverty
'Distributional Effects of
Accelerating and Extending Increase in the Full Retirement Age'
policy brief finds pluses and minuses in higher retirement age
by Glenn R. Springstead, Social
Security Office of Retirement Policy
Jan.
28, 2011 - This policy brief analyzes the distributional effects of increasing
Social Security's full retirement age (FRA),
the age at which Social Security pays full unreduced benefits. Under
current law, the FRA is 66 years for newly
eligible beneficiaries and is scheduled to increase incrementally to
67 years between 2017 and 2022.
This brief compares the effects of two
FRA options studied by the Social Security
Advisory Board. Both options would set an earlier date by which the
FRA is increased to 67 years. The first
option would subsequently increase the FRA to
68 years (FRA 68), and the second option
would subsequently increase the FRA to
70 years (FRA 70).1
The distributional effects were estimated using data from the Modeling
Income in the Near Term (MINT) microsimulation model.
MINT's comparison of projected benefits under current law with
those under each option is staticthat is, it does not assume any
changes in retirement behavior caused by either option's effect on
benefits or income.2
Consequently, for the purpose of this analysis, beneficiaries were not
assumed to retire later in response to the increase in the
FRA. Solvency estimates were developed by the
Social Security Administration (SSA)'s Office
of the Chief Actuary.
Major Findings
Selected Abbrevations
EEA
early eligibility age
FRA
full retirement age
PIA
primary insurance amount
SSA
Social Security Administration
FRA 68 and
FRA 70
would reduce benefits and improve solvency. When fully phased in,
FRA 68 could reduce average Social
Security benefit amounts from 6.2 percent to 7.4 percent relative to
current-law benefits, and eliminate 23 percent of Social Security's
actuarial imbalance. When fully phased in, FRA 70
could reduce average Social Security benefit amounts from
18.1 percent to 20.0 percent, and eliminate 31 percent of Social
Security's actuarial imbalance.
Average benefit reductions would be proportional across
different income and lifetime wage groups under FRA 68 and
FRA 70.
Microsimulations project that FRA 68
would reduce benefits by a median of 6.5 percent in 2070 relative to
current-law benefits. FRA 70 would reduce
benefits by a median of 11.3 percent relative to current-law
benefits in 2070 but, because it would still be phasing in,
FRA 70 would reduce benefits more for
those aged 6269 (13.9 percent) than for older beneficiaries (for
example, 6.4 percent for those aged 90 or older).
FRA 68 and
FRA 70
would shield large numbers of surviving spouse and disabled
beneficiaries. Social Security's benefit rules would shield more
than 40 percent of surviving spouse beneficiaries from any benefit
reduction under FRA 68 and
FRA 70. Likewise, the structure of
disability benefits would shield approximately 90 percent of
disabled and retired disabled beneficiaries from any reductions
under FRA 68 and FRA 70.
FRA 68 and
FRA 70
would reduce spouse benefits more than other benefit types.
FRA 68 and FRA 70
would affect slightly more spousal beneficiaries and reduce benefits
more for spousal beneficiaries than for other beneficiary types.
Based on the MINT simulations, the median benefit
reduction relative to current-law spouse benefits in 2070 would be
7.0 percent under FRA 68 and 14.1 percent
under FRA 70.
FRA 68 and
FRA 70
would increase poverty slightly. FRA 68
would increase poverty among aged beneficiaries in 2070 from
0.9 percent under current-law benefits to 1.1 percent.
FRA 70 would increase the poverty rate to
1.2 percent. Poverty under FRA 68 and
FRA 70 would remain substantially lower
than the 2.2 percent rate projected under current law assuming Trust
Fund exhaustion in 2037.
Current-Law
FRA
The system of old-age insurance established
by the Social Security Act of 1935 provided retirement benefits to
insured workers aged 65 or older. Benefits for wives and widows aged 65
or older were added in 1939. Benefits for husbands and widowers were
added in 1950. Between 1956 and 1961 an early eligibility age (EEA)
of 62 years was established for insured workers, spouses, and surviving
spouses. The EEA for surviving spouses was
reduced to 60 years in 1965.
In 1983 Congress scheduled gradual increases in the
FRA to begin in 2000. In the first stage, the
FRA would increase in
2-month increments each year, starting with 65 years and 2 months
in 2000, until reaching 66 years for newly eligible beneficiaries by
2005. After a 12-year hiatus, the
FRA would again begin to increase in
2-month increments in 2017, until reaching
67 years for new beneficiaries eligible in 2022. The
FRA for surviving spouses was also scheduled to increase to
67 years for new surviving spouses eligible (that is, attaining age 60)
in 2022.
Benefits received prior to reaching the FRA
are actuarially reduced for early retirement. These reductions are
permanent and are designed to ensure that lifetime benefits are
approximately equivalent, on average, whether a beneficiary claims upon
reaching the EEA or waits until reaching the
FRA.3
Under current law, benefits for insured workers are reduced by
6.67 percent for each of the first 3 years prior to reaching the
FRA and by 5 percent for the fourth and fifth
years prior to reaching the FRA (Table 1).
Workers with an FRA of 66 years who take
benefits at age 62 would have 4 years of "early retirement" and a
benefit reduction of 25 percent (3 years at 6.67 percent plus 1 year at
5 percent). Once the FRA reaches 67 years,
workers who take benefits at age 62 would have 5 years of early
retirement and a benefit reduction of 30 percent (3 years at
6.67 percent plus 2 years at 5 percent). Insured workers are also
eligible to receive a delayed retirement credit (DRC)
of 8 percent for each year of deferred benefits after reaching the
FRA (up to age 70).
Table 1. Effects of FRA 68 on benefits for a
retired worker with primary insurance amount (PIA)
equal to the average PIA in 2008
Age
when benefits first claimed
Current
law
FRA 68
Monthly PIA
($)
Early retirement reduction (%)
Delayed retirement credit (%)
Monthly benefit amount ($)
Early retirement reduction (%)
Delayed retirement credit (%)
Monthly benefit amount ($)
Change from current-law benefit (%)
62
1,298
30.0
. . .
908
34.5
. . .
850
-6.4
63
1,298
25.0
. . .
973
30.0
. . .
909
-6.7
64
1,298
20.0
. . .
1,038
25.0
. . .
974
-6.2
65
1,298
13.3
. . .
1,125
20.0
. . .
1,038
-7.7
66
1,298
6.7
. . .
1,211
13.3
. . .
1,125
-7.1
67
1,298
. . .
. . .
1,298
6.7
. . .
1,211
-6.7
68
1,298
. . .
8.0
1,402
. . .
. . .
1,298
-7.4
69
1,298
. . .
16.0
1,506
. . .
8.0
1,402
-6.9
70
1,298
. . .
24.0
1,610
. . .
16.0
1,506
-6.5
SOURCES: Author's
calculations and SSA Annual
Statistical Supplement to the Social Security Bulletin,
2009, Table 6.A2.
NOTE: . . . = not
applicable.
The spouse's benefit is one-half of the
insured worker's monthly primary insurance amount (PIA),
minus any early retirement reduction if the benefit is claimed before
the spouse reaches the FRA. Spouse benefits
are reduced 8.33 percent for each of the first 3 years, or a total of
25 percent for the first 3 years of early retirement, and 5 percent for
the fourth and fifth years of early retirement. Spouse beneficiaries
with an FRA of 66 years who take benefits at
age 62 would have their benefits reduced by 30 percent (3 years at
8.33 percent plus 1 year at 5 percent). Spouse beneficiaries with an
FRA of 67 years who take benefits at age 62
would have their benefits reduced by 35 percent (3 years at 8.33 percent
plus 2 years at 5 percent). A spouse's benefit is not affected by the
age at which insured worker claims benefits.
Survivor benefits for an aged spouse, with some important exceptions,
range from 71.5 percent of PIA (if claimed at
age 60) to 100 percent of PIA (if claimed at
or after reaching the FRA for surviving
spouse benefits). Prorated amounts are paid for claiming between age 60
and the FRA. The formula has two important
exceptions, which depend on the insured worker's age when claiming
benefits.
First, if the insured worker claimed retirement benefits
before his or her FRA, the surviving spouse's
benefit is limited to the highest of 82.5 percent of the
PIA or the monthly benefit amount the
deceased insured worker would be receiving if alive. Thus, if the worker
claimed benefits prior to reaching the FRA,
the surviving spouse would not be eligible for the worker's full
PIA even if the surviving spouse first
received the survivor benefit at or after reaching his or her own
FRA. The cap on the amount a surviving spouse
can receive from the record of a worker who claimed benefits prior to
reaching FRA is called the
"widow(er)'s limit."4
However, the 82.5-percent-of-PIA feature of
the widow(er)'s limit ensures that the
surviving spouse's benefits would not be reduced by the full amount of
the worker's reduction if the worker claimed upon reaching the
EEA. The other exception to the general
formula is that surviving spouses inherit delayed retirement credits
earned by their deceased spouses.
Implementing FRA 68 and
FRA 70
Both FRA 68 and FRA 70
would increase the FRA from 66 years at the
rate of 2 months per year beginning in 2010 until reaching 67 years for
new beneficiaries in 2015. FRA 68 would
continue increasing the FRA by 1 month every
2 years until reaching 68 years for new beneficiaries beginning in 2038.
FRA 70 would continue increasing the
FRA by 1 month every 2 years until reaching
70 years for new beneficiaries beginning in 2086.
Benefit Reductions
Under FRA 68, benefits in the new sixth
year of early retirement would be reduced by ⅜ of 1 percent per month
(or 4.5 percent for the year) relative to current-law benefits for
insured workers and spouses. Under FRA 70,
benefits in the new sixth and seventh years of early retirement would be
reduced by ⅜ of 1 percent per month (or 4.5 percent per year) relative
to current-law benefits for insured workers and spouses, and in the
eighth year benefits would be reduced by ⅓ of 1 percent per month (or
4.0 percent for the year). Surviving spouses would continue to receive
71.5 percent of PIA for benefits claimed at
age 60 under FRA 68 and
FRA 70, but benefit amounts would be lower than under current law
if benefits were claimed after age 60 and prior to ages 68 and 70,
respectively.
Tables 1 and 2 show how FRA 68 and
FRA 70, when fully phased in, would affect a
retired-worker beneficiary whose PIA equals
the average PIA in the aged population
according to age of first entitlement. Depending on when the
retired-worker beneficiary began receiving benefits,
FRA 68 would reduce his or her benefits by between 6.2 percent
and 7.4 percent (Table 1). FRA 70
would reduce benefits for the same PIA-level
retired worker by between 18.1 percent and 20.0 percent. Interestingly,
these stylized examples suggest the greatest reduction in benefitsin
percentage termswould apply to those first taking retirement benefits
at age 65 (FRA 68) and 67 (FRA 70).
Table 2. Effects of FRA 70 on benefits for a
retired worker with primary insurance amount (PIA)
equal to the average PIA in 2008
Age
when benefits first claimed
Current
law
FRA 70
Monthly PIA
($)
Early retirement reduction (%)
Delayed retirement credit (%)
Monthly benefit amount ($)
Early retirement reduction (%)
Monthly benefit amount ($)
Change from current-law benefit (%)
62
1,298
30.0
. . .
908
43.0
740
-18.6
63
1,298
25.0
. . .
973
39.0
792
-18.7
64
1,298
20.0
. . .
1,038
34.5
850
-18.1
65
1,298
13.3
. . .
1,125
30.0
909
-19.2
66
1,298
6.7
. . .
1,211
25.0
974
-19.6
67
1,298
. . .
. . .
1,298
20.0
1,038
-20.0
68
1,298
. . .
8.0
1,402
13.3
1,125
-19.8
69
1,298
. . .
16.0
1,506
6.7
1,211
-19.6
70
1,298
. . .
24.0
1,610
. . .
1,298
-19.4
SOURCES: Author's
calculations and SSA Annual
Statistical Supplement to the Social Security Bulletin,
2009, Table 6.A2.
NOTE: . . . = not
applicable.
Some surviving spouses are likely to be affected by the 82.5 percent
limit because of the way Social Security computes their benefits.
FRA 68 or FRA 70
would not affect those surviving spouses, and would also not affect
disability benefits, although the FRA options
might reduce benefits for disability beneficiaries who also receive
old-age benefits.
Benefit Reductions Would Improve Solvency
As measured by the actuarial balance, FRA 68
and FRA 70 would improve system solvency by
reducing lifetime benefit payments, but neither option would eliminate
Social Security's long-term imbalance. The
actuarial balance is the amount by which the Social Security payroll tax
would have to be increased today to eliminate the
75-year funding shortfall. FRA 70
would reduce the program's actuarial imbalance from -2.00 percent of
taxable payroll to -1.39 percent (Table 3). FRA 68
would reduce the imbalance to -1.55 percent.
Table 3.
Effects of FRA 68 and
FRA 70 on Social Security Trust Fund
solvency (as a percentage of taxable payroll)
NOTE: "Result of
option" values do not necessarily equal the sum of
rounded "current law" and "change from current law"
values.
Microsimulation Results
Chart 1 illustrates how FRA 68 and
FRA 70 would affect benefits relative to
those scheduled under current law, along with payable benefits assuming
no change in current law. Reductions from current-law benefits would
level off under FRA 68 by 2060, but would
continue under FRA 70 through 2080.
Chart 1. Average benefit change from current law,
20102080 (in percent)
SOURCE: Author's calculations using Modeling Income in the
Near Term (MINT) data, based on
SSA Office of the Chief Actuary
projections under intermediate assumptions.
NOTE: The Trust Fund is projected to be exhausted in 2037.
The Median Benefit Reduction Would Be 6.5 Percent under
FRA 68 and between 11.1 Percent and
11.6 Percent under FRA 70
Table 4 shows effects of FRA 68 and
FRA 70 on scheduled benefits in 2070 by sex,
age, household income quintile, and lifetime wage quintile.5
Because it would be fully phased in by 2070, the distributional
estimates for FRA 68 are more apt to remain
relatively consistent across groups in future years (everything else
being equal) than those for FRA 70, which
would still be phasing in after 2070.
Table 4.
Effects of FRA 68 and
FRA 70 in 2070 relative to
current-law benefits, by beneficiary sex, age, household income,
and lifetime wages
FRA 68
FRA 70
Beneficiaries affected (%)
Median change in benefit amount (%)
Beneficiaries affected (%)
Median change in benefit amount (%)
Total
80.5
-6.5
82.1
-11.3
Sex
Male
81.2
-6.5
82.9
-11.6
Female
80.0
-6.5
81.5
-11.1
Age
6269
82.3
-6.5
83.2
-13.9
70-79
81.5
-6.5
83.7
-11.4
80-89
78.9
-6.5
80.8
-9.0
90+
72.2
-6.3
72.5
-6.4
Household income quintile
Highest
87.7
-6.5
89.7
-11.2
Second highest
84.4
-6.5
85.8
-11.4
Middle
80.5
-6.5
82.6
-11.6
Second lowest
77.9
-6.5
78.9
-11.5
Lowest
72.4
-6.5
73.9
-11.1
Lifetime wages quintile
Highest
88.3
-6.5
90.5
-11.1
Second highest
85.1
-6.5
86.5
-11.3
Middle
79.6
-6.5
80.5
-11.4
Second lowest
70.9
-6.5
72.8
-11.6
Lowest
72.5
-6.5
74.3
-11.6
SOURCE: Author's
calculations using Modeling Income in the Near Term (MINT)
data.
NOTE: For newly
eligible retired workers in 2070,
FRA 68 would be fully phased in, but the
FRA would only have reached
69 years and 3 months under FRA 70
(the FRA would reach 70 years
in 2088).
FRA 68 would affect 80.5 percent of all
aged beneficiaries and the median benefit reduction relative to
current-law benefits would be 6.5 percent in 2070.
FRA 68 would affect 82.3 percent of retirement beneficiaries
aged 6269 and 72.2 percent of those aged 90
or older. FRA 68 would affect 87.7 percent of
those in the highest income and wage quintiles and about 72.4 percent of
those in the lowest income and wage quintiles, but the median reduction
would be 6.5 percent for each quintile.
FRA 70 would reduce benefits by about the
same proportion for different income and lifetime wage groups.
FRA 70 would also reduce benefits by about
the same proportion for men as for women. Because of its long
phase-in period, however,
FRA 70 would have substantially different impacts by age from
FRA 68 in 2070. Those between ages 62 and 69
would face median reductions of 13.9 percent, while those aged 90 or
older would see median reductions of 6.4 percent.
More Than 40 Percent of Surviving Spouse Beneficiaries Would Be
Shielded from Any Benefit Reductions
As suggested above, increases to the FRAwithout
other changes to the benefit structurewould generally have less effect
on surviving spouses because of current-law treatment of survivor
benefits. Because benefits for surviving spouses depend on when the
insured worker claimed benefits, however, FRA 68
or FRA 70 could reduce the insured worker's
benefit and thus reduce benefits for surviving spouses.
Nevertheless,
also recall that the widow(er)'s limit is
never below 82.5 percent of the insured worker's PIA.
This would help to limit any benefit losses to the surviving spouse
stemming from FRA 68 or
FRA 70's reductions to the insured worker's benefits.
The modeling results shown in Table 5 support this prediction.
Although FRA 68 would affect 98.0 percent of
retired workers in 2070 relative to current-law benefits, it would
affect only 53.6 percent of dually entitled surviving spouses and
24.0 percent of surviving spouse-only beneficiaries.
Table 5. Effects of FRA 68 and
FRA 70 in 2070 relative to
current-law benefits, by beneficiary marital status and benefit
type
Characteristic
FRA 68
FRA 70
Beneficiaries affected (%)
Median change in benefit amount (%)
Beneficiaries affected (%)
Median change in benefit amount (%)
Total
80.5
-6.5
82.1
-11.3
Marital status
Never married
86.9
-6.5
86.9
-11.8
Married
87.1
-6.5
88.9
-12.0
Divorced
80.1
-6.5
81.0
-11.0
Widowed
58.3
-5.9
61.2
-6.2
Benefit type
Retired worker
98.0
-6.5
99.3
-11.8
Spouse and worker
99.6
-6.6
100.0
-11.9
Spouse only
84.7
-7.0
86.5
-14.1
Surviving spouse and worker
53.6
-2.8
57.3
-3.6
Surviving spouse only
24.0
-4.8
28.0
-4.2
Retired disabled
9.2
-2.6
10.5
-2.9
Current disabled
5.2
-1.3
5.8
-2.4
SOURCE: Author's
calculations using Modeling Income in the Near Term (MINT)
data.
About 90 Percent of Retired Disabled Beneficiaries Would Be Shielded
from Any Benefit Reduction
Current benefit rules would also shield nearly all disabled
beneficiaries from any benefit reductions under FRA 68
and FRA 70. By design, the
FRA increases would not affect disability
benefits. However, FRA 68 and
FRA 70 could affect disabled beneficiaries if
they receive old-age benefits as well. Such
beneficiaries would receive disability benefits until converting to
old-age benefits at retirement age, but their
disability benefits would not change. However, disabled beneficiaries
claiming spousal or survivor's benefits based on the record of a worker
who retired before reaching FRA would face
reductions under the FRA options. As Table 5
shows, FRA 68 would affect less than
10 percent of disabled beneficiaries in 2070, while only slightly more
would be affected under FRA 70. The median
benefit reduction for retired and current disabled beneficiaries would
range from 1.3 percent to 2.9 percent.
Spousal Benefits Reduced More Than Other Benefits
Because spousal benefit levels are determined by the insured worker's
earnings record rather than the worker's benefit-claiming behavior, any
reduction to the insured worker's benefit stemming from
FRA 68 or FRA 70
would not affect the spouse. However, a spousal benefit claimed in the
first 3 years prior to the spouse's reaching the FRA
faces a higher annual reduction (8.3 percent) than that for
retired-worker benefits (6.7 percent).
Relative to current-law benefits, the median benefit reduction for
spouse-only beneficiaries would be only 0.5 percentage points greater
than that for retired workers under FRA 68 in
2070. The difference in median benefit reduction between the two benefit
types would widen under FRA 70 to
2.3 percentage points.
One potential cause of the greater benefit reduction for spouse-only
beneficiaries is age. As Table 4 shows, the median
benefit reduction under FRA 70 for those
aged 6269 would be 13.9 percent, compared
with a median reduction of 11.4 percent for those
aged 7079. This age gap stems from the fact that in 2070
FRA 70 would still be phasing in. Moreover,
affected spouse-only beneficiaries in 2070 would be younger (with a
median age of 69) than retired-worker beneficiaries (with a median age
of 73).
Slight Increases in the Poverty Rate
Compared with current law, FRA 68 and
FRA 70 would increase the number of aged
beneficiaries in poverty (Table 6). FRA 68
would increase the poverty rate from 0.9 percent under current-law
benefits to 1.1 percent in 2070; FRA 70 would
increase the poverty rate to 1.3 percent. Compared with the current-law
benefits and Trust Fund exhaustion scenario, poverty rates under
FRA 68 and FRA 70
would be lower in 2070. Because it would continue phasing in after 2070,
FRA 70 would likely raise poverty rates
slightly in later years. Overall, because the federal government
automatically adjusts poverty thresholds according to price changes
rather than economywide wage growth (as used for initial Social Security
benefits), poverty rates would tend to decline over time.6
Table 6.
Measures of poverty among beneficiaries in 2070 under current
law, FRA 68, and
FRA 70
Economic
characteristic
Current law
FRA 68
FRA 70
Scheduled
Payable a
Percentage of
beneficiaries in poverty in 2070
Total
0.9
2.1
1.1
1.3
Household income
quintile
Second lowest
0.0
0.0
0.0
0.0
Lowest
5.5
12.7
6.6
7.7
Lifetime wages
quintile
Second lowest
0.1
1.3
0.2
0.2
Lowest
8.2
17.3
9.8
11.4
Number of
beneficiaries in poverty in 2070 (in thousands)
Total
713
1,636
858
1,009
Household income
quintile
Second lowest
0
0
0
0
Lowest
713
1,636
858
1,009
Lifetime wages
quintile
Second lowest
17
173
25
31
Lowest
697
1,464
834
978
SOURCE:
Author's
calculations using Modeling Income in the Near Term (MINT)
data.
a. Represents benefits
that could be paid under the conditions of Trust Fund
exhaustion. Under intermediate assumptions, the
SSA Office of the Chief
Actuary projects that the Trust Fund will be exhausted
in 2037.
Notes
1 For more information, see Social
Security: Why Action Should be Taken Soon, Social Security Advisory
Board (2005),
http://www.ssab.gov/documents/WhyActionShouldbeTakenSoon.pdf.
The Board also discusses, and I have modeled, an option in which the
only change is to speed up the FRA
increase to 67. Microsimulation results for that option are not
presented here because of space limitations and the option's minimal
effects. Tabulations are available on request from the author.
2 MINT is based on Social
Security administrative data matched to the Census Bureau's Survey
of Income and Program Participation. Work, marriage, death, and
retirement are projected for real and imputed individuals based on
real earnings, marital histories, and education levels.
4 For more information, see "The
Widow(er)'s Limit Provision of Social
Security" by David A. Weaver, Social Security Bulletin 64(1):
115 (2001/2002).
5 The Lifetime Wages measure is the
present value of a person's yearly shared earnings.
6 For more information, see "Projections
of Economic Well-Being for Social Security Beneficiaries in 2022 and
2062" by Barbara A. Butrica, David B. Cashin, and Cori E. Uccello,
Social Security Bulletin 66(4): 119
(2005/2006) and "Income Growth and Future Poverty Rates of the Aged"
by Seyda G. Wentworth and David Pattison, Social Security Bulletin
64(3): 2337 (2001/2002).
NOTES
Policy Brief No. 2011-01
January 2011
This policy brief compares two options set forth
by the Social Security Advisory Board to increase the full
retirement age (FRA), the age at which
claimants may receive unreduced Social Security
old-age benefits.
One option would raise the
FRA from the current target of 67 years
to 68 years; the other would raise the FRA
to 70 years.
The brief examines the effects of both options on the
level of benefits of Social Security beneficiaries aged 62 or older
in 2070 using Modeling Income in the Near Term (MINT)
projections, and on Trust Fund solvency using estimates from the
Social Security Administration's Office of the Chief Actuary.
The
brief finds that both options would reduce benefits, improve
solvency, and slightly increase the poverty rate. Within each
option, effects on benefits are relatively uniform across
beneficiary characteristics, although some surviving spouse and
disabled beneficiaries would be shielded from benefit reductions.
U.S. Social Security Administration, Office of
Retirement and Disability Policy
Glenn R. Springstead is with
SSA's Office of Retirement Policy, Office
of Policy Analysis. Questions about the analysis should be directed
to the author at (202) 358-6234.
The findings and conclusions presented in
this brief are those of the author and do not necessarily represent
the views of SSA.
Acknowledgments: The author thanks
David Weaver, Mark Sarney, Sven Sinclair, Dena Berglund, Irena Dushi,
David Pattison, Kwaku Abrokwah, and Amy Shuart for their helpful
comments and suggestions.