This document provides a theoretical framework on how inflation impacts retirement decisions and security. It summarizes several simplified lifecycle models showing how different levels and volatility of inflation can reduce real income, consumption, and savings over a person's working life. Higher and more volatile inflation is shown to lead people to accumulate less savings for retirement. The models also explore how inflation may impact labor supply decisions, finding that higher inflation could cause both earlier retirement through income effects, but also longer work through consumption constraints. The document reviews relevant data on how inflation is negatively impacting households currently and expectations around retirement. It previews how firm behavior and policy tools like COLAs could also be factors.

1. A theoretical
framework on
Inflation and
Retirement
Naomi Fink, CEO & Founder, Europacifica Consulting
Chairperson, EBRI Retirement Security Research
Center
June 2023

2. Inflation impacts aggregate choices
-2%
0%
2%
4%
6%
8%
10%
12%
14%
16%
1975-01-01
1979-01-01
1983-01-01
1987-01-01
1991-01-01
1995-01-01
1999-01-01
2003-01-01
2007-01-01
2011-01-01
2015-01-01
2019-01-01
CPI, Urban Wage-earners (%y/y)
R-CPI-E (% y/y)
Social Security COLA (%)
-5
0
5
10
15
20
1959-01-01
1964-01-01
1969-01-01
1974-01-01
1979-01-01
1984-01-01
1989-01-01
1994-01-01
1999-01-01
2004-01-01
2009-01-01
2014-01-01
2019-01-01
Personal Consumption Expenditures, % y/y SAAR
Personal Saving Rate, % y/y SAAR
Source: St. Louis Fed

3. ¡ For example:
Lower-income households
(with higher proportion of
basic living expenses) may
be harder-hit by inflation.
Source: www.markuspettersson.net
But households experience inflation
in different ways

4. Problem #1:
inflation in retirement
¡ Why is understanding inflation important to
retirement security?
¡ Inflation, all else equal, reduces real income and
therefore purchasing power.
¡ In retirement, income is commonly fixed (though
possibly adjusted for inflation, in retrospect) and it may
not be possible to demand additional wage income to
offset the real income erosion.
¡ Uncertainty and/or volatility in real income may
contribute to financial stress and/or detract from
peace of mind for consumers in retirement.

5. ¡ Understanding inflation also involves
understanding the policymaker’s (central bank’s)
policy response to inflation
¡ The Lucas critique: don’t draw policy conclusions
from large econometric models alone – households
adapt to – and anticipate – policy.
¡ So backward-looking analysis of data is naïve for
macro policymakers.
¡ How about households? Human behavior may be
more consistent, if disentangled from structural
factors
¡ What to do? Microfoundations of Macro models
Problem #2: Macro policy is
reactive, blunt, aggregate

6. Microfoundations: a bridge
between macro & micro
¡ Policymakers must seek to understand human
behavior and seek parameters that are deep
and policy neutral
¡ Central Banks’ General Equilibrium models are
now micro-founded. For example:
¡ The household’s problem: the household maximizes
its lifetime welfare subject to constraints.
¡ Firms maximize profits in competitive markets for
output, labor, capital (via production function)
¡ The planner’s problem: the planner maximizes
aggregate welfare such that households are at least
as well off as in the planner’s absence.

7. ¡ Start with Partial Equilbirum (household, firm) then
identify possible frictions that policy could impact
¡ We start by exploring the household’s problem with
several simple models to explore:
¡ Impact of inflation (reduced real income) on
consumption and savings
¡ Impact of volatility of inflation on consumption and
savings
¡ Impact of inflation (reduced real income) on labor
supply decisions, introducing consumption constraints
¡ Then use models to derive intuition from data – side-
stepping the Lucas critique
Using models to understand
Inflation & Retirement

8. ¡ Simplified lifecycle model
shows the impact of trend
inflation on consumption and
savings/household assets
¡ Inflation and real income
volatility affect consumption
and savings in accumulation
phase
• Assumptions:
• Maximum asset constraint
• No borrowing allowed (to
demonstrate impact of real
income on savings and
consumption)
• CRRA preferences
• First working age of 25
• Random real income (which
halves in ‘bad’ times vs ‘good’).
Inflation and lifecycle consumption
and savings simulation

9. 1.35
1.4
1.45
1.5
1.55
1.6
1.65
1.7
25 30 35 40 45 50 55 60 65 70 75 80
Average Consumption Path
2% constant inflation
-2
0
2
4
6
8
10
12
25 29 33 37 41 45 49 53 57 61 65 69 73 77 81 85
Average Savings Path
2% constant inflation
With first working age of 25, average of 1000 paths with
random real income (which halves in ‘bad’ times vs ‘good’).
‘Smooth’ consumption and
accumulation/decumulation

10. $12,000.00
$13,000.00
$14,000.00
$15,000.00
$16,000.00
$17,000.00
25 30 35 40 45 50 55 60 65 70 75 80
Average Consumption ($10k
numeraire)
2% constant inflation
5% constant inflation
8% constant Inflation
$0.00
$20,000.00
$40,000.00
$60,000.00
$80,000.00
$100,000.00
$120,000.00
25293337414549535761656973778185
Average Savings/ Assets
($10k numeraire)
2% constant inflation 5% constant inflation
8% constant Inflation
Rising inflation erodes consumption
as well as savings
Where Inflation acts as a
constant tax on real income

11. $14,000.00
$15,000.00
$16,000.00
$17,000.00
$18,000.00
$19,000.00
$20,000.00
$21,000.00
$22,000.00
25 30 35 40 45 50 55 60 65 70 75 80
Average Consumption
(max real income=$20k)
Min Real Income = $10,000
Min Real Income = $15,000
Constant Real Income = $20,000
-$20,000.00
$0.00
$20,000.00
$40,000.00
$60,000.00
$80,000.00
$100,000.00
$120,000.00
$140,000.00
25 30 35 40 45 50 55 60 65 70 75 80 85
Avg. Savings/Assets
(max real income=$20k)
Min Real Income = $10,000
Min Real Income = $15,000
Constant Real Income = $20,000
What is the impact of volatility in
real income?
More smoothing and earlier saving under uncertainty

12. ¡ 33% of adults age 30+ indicated (as of July 2022) that their situation was
worse off than a year prior; common reasons cited were higher expenses
(65%) and the decline in value of investments (36%) and 78% were
worried about prices rising faster than income (decline in real income)
¡ 80% of adults 30+ reported higher basic expenses (transportation and
grocery) than a year ago. As a result, 45% cut back on basic expenses
and 50% cut back on Extras (inflation eroding consumption)
¡ Although only 17% of adults age 30+ expect their financial situation to be
worse in 12 months,. one in five (21%) of adults age 50+ expected their
situation to decline between July 2022 to July 2023 (near retirees and
retirees are sensitive to changes in inflation expectations)
¡ Everyday expenses, housing costs and debt are the top barriers to saving
both for emergencies and retirement. Roughly 60% of adults age 30+
cite everyday expenses as barriers to savings (inflation erodes savings)
¡ Among adults age 30+ who are not retired, more than half (52%) expect
to work in retirement or never retire (can inflation impact labor supply
choices?)
Next, we examine those labor
supply choices…
July 2022
8.4
-4.0
-2.0
0.0
2.0
4.0
6.0
8.0
10.0
2001-09-01
2004-06-01
2007-03-01
2009-12-01
2012-09-01
2015-06-01
2018-03-01
2020-12-01
US CPI % y/y (Urban)
Source: St. Louis Fed
What does (AARP) data say on
inflation impact?

13. Produces an income effect (lower) –
work longer to achieve same
consumption
Produces a substitution effect:
leisure is cheaper… substitute
leisure for consumption
According to theory, a lower real wage…
Labor supply choice:
Deriving retirement timing

14. 0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
Real Income of
100
2x Real Income
(e.g. 200)
Work/retire tradeoff (%)
by real income
Work (%) Retire (%)
0%
20%
40%
60%
80%
100%
0.1 25 50 100
Level of basic expenses(with real
income=100)
Work/retire tradeoff (%)
with consumption floor
Work (%) Retire (%)
Lower
real
income
⇒
retire
earlier
Higher
consumption
floor
⇒
work
longer
At first glance, substitution wins
but consumption constraints
change the game

15. Where substitution effect is
winning:
¡ “[W]e find that high inflation is
associated with exit from the
labor force, through partial as
well as full retirement. One
explanation for this may be that
during high inflation episodes
wages do not keep up with
inflation, and lower real wages
discourage labor force
participation.” –
¡ Source: Michigan Retirement
Research Center Issue Brief
#281
Where income effect is still in
play:
What does the data say about
retirement timing?

16. Production: how do firms
allocate labor & capital?
80.0
90.0
100.0
110.0
120.0
130.0
140.0
150.0
1960
1965
1970
1975
1980
1985
1990
1995
2000
2005
2010
2015
US GROWTH ACCOUNTING,
SHARE OF GDI(1960=100)
LABOR
CAPITAL
TFP
Policy: COLA’s influence
experience of inflation
The household ‘owns’ the firm in its portfolio
¡ Source: Aon/NIRS
Pension design is one policy lever
Preview:
firm’s problem & planner’s problem

17. • AARP Financial Security Trends: Wave 2 Report
• ‘The Real Deal for the Public Sector’: Retirement Income Adequacy Among US Public Sector Employees (NIRS and AON)
• ‘Public Pensions Contend with Falling Markets and Rising Inflation’, (Aubry, CRR (Boston College), 2022)
• ‘Wealth Effects and Macroeconomic Dynamics’, Dynan, Journal of Economic Surveys (2016)
• ‘Macroeconomic Determinants of Retirement Timing’, Gorodnichenko et al, Univ. Michigan Retirement Research Center (2013)
• ‘31% of Retirees Say Continued Inflation Would Motivate Them to Rejoin the Workforce’, American Staffing Association (2022)
• ‘The Best Strategies for Inflationary Times’, Neville et al (2021)
• ‘A Non-homothetic Price Index and Inflation Heterogeneity’, Petersson et al (2022)
• NASRA Issue Brief: Cost of Living Adjustments Brainard and Brown (2022)
• With Special Thanks to Niku Maattanen, University of Helsinki and Helsinki Graduate School of Economics
References

18. THANK YOU!
この度有り難う御座いました

19. Appendix
Analytical frameworks for models used in
numerical simulations of household’s problem
and labor supply

20. The model we use is a parsimonious version of a stochastic life cycle
model. The numerical solution method is based on dynamic
programming (Value Function Iteration).
The basic model is set up as follows:
The individual (i) starts working in period 1 (e.g. at age 25) and lives
for (j) periods until max age J. Each period until retirement the
individual receives an income (w), dependent on random shock z, and
accumulates savings (a). It is not possible to borrow (𝑎 ≥ 0). This is
to clearly display the relationship between real income, savings and
consumption. After retirement age (j=40 in this case), the individual
receives retirement income (b).
We start by solving the following value function iteratively from
period J to period 1:
𝑉
! 𝑎, 𝑧 = max
"
𝑢 𝑐 + 𝛽𝐸 𝑧# 𝑧 𝑉
!$% 𝑎#, 𝑧#
𝑠. 𝑡.
𝑐 + 𝑎# = 1 + 𝑟 𝑎 + 𝑤!(𝑧)
𝑎′ ≥ 0
where
𝑈 𝑐 = <
𝑐%&∝
1 −∝
,for σ > 0,σ ≠ 1
log 𝑐 ,for σ = 1
and
𝑤! 𝑧 = G
𝑧,for 𝑗 < 40
b,for j ≥ 40
The income shock process is specified as follows:
𝑧 ∈ 𝑧%, 𝑧( 𝑤ℎ𝑒𝑟𝑒 𝑧% = 2, 𝑧( = 1
With transition probabilities of :
𝑃 =
0.8 0.2
0.2 0.8
Model parameters
Life cycles simulated 1000
Personal discount factor 0.9
Interest rate 10%
Real Income, ‘good’ state 2
Real Income, ‘bad’ state 1
Pension Income 0.25
Min Assets/Savings 0
Max Assets/savings 25
Risk preference (CRRA) parameter 2.0
Retirement Age (from first working age) + 40 yrs
Max age (from first working age) + 60 yrs
Model 1: Lifecycle consumption/savings

21. The model that we use derives from the academic literature of Real
Business Cycle Theory (e.g. Kydland & Prescott, 1982) where
macroeconomic shocks affect the decisions of workers, wherein
workers face two tradeoffs:
(1) Individuals’ consumption-investment decision, under the life-cycle
hypothesis that individuals make decisions based on expected
lifetime income and prefer to smooth consumption over their
lifetime and;
(2) The labor-leisure tradeoff: in times of higher productivity, workers
supply more labor as to make the most of their higher income.
Meanwhile, disutility of labor means that there is an opposing
force –an income effect: workers, when earning more may afford
to work less. Cyclically, it appears as though the substitution
effect dominates in aggregate, although upon disaggregation, the
calculus of labor supply (and retirement timing) may depend on
many factors (such as the proportion of consumption dedicated to
basic living expenses).
Represented mathematically, for each period t the household maximizes
both consumption (c) and leisure (1-h, where h is labor supply and h+l
=1), earning a wage (w) and saving (k) the household’s problem may be
represented as follows:
max
{"!,$!,%!"#}
𝐸' &
()'
*
𝛽( 𝑈 𝑐(,1 − ℎ(
subject to:
𝑐( + 𝑘(+, ≤ 𝑅( − 𝛿 𝑘( + 𝑤(ℎ(,∀𝑡
and 𝑐 ≥ 0; 𝑘 ≥ 0; 0 ≤ ℎ ≤ 1;ℎ + 𝑙 = 1
taking prices as given
Equilibrium conditions may be derived analytically, yielding us analytical
representations of both the above-mentioned trade-offs, first the Euler
equation (intertemporal substitution problem):
𝑢′(𝑐() = 𝛽𝐸[𝑢′(𝑐(+,) 𝑅( − 𝛿 ]
and secondly the labor supply trade-off
𝑛- 1 − ℎ( = 𝑢- 𝑐( 𝑤(
Using the latter equation, we may obtain the marginal rate of substitution
between leisure and consumption,
𝑛- 1 − ℎ(
𝑢- 𝑐(
which in equilibrium equates to the wage (𝑤().
We assume utility of consumption of the following form:
𝑈 𝑐 = B
𝑐,.∝
1 −∝
,for σ > 0,σ ≠ 1
log 𝑐 ,for σ = 1
We assume labor disutility of the following form:
𝑁 1 − ℎ = B
1 − ℎ ,.0
1 − 𝛾
,𝑓𝑜𝑟 𝛾 > 0,𝛾 ≠ 1
log 1 − ℎ ,𝑓𝑜𝑟 𝛾 = 1
Where σ = 2 and 𝛾 = 2 for the purposes of illustration.
Model 2: Labor supply tradeoffs

22. 22
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