Sustainable retirement ageΒΆ
AIM: assuming that the current situation of working / retired people is sustainable, and keeping that as reference, what is the retirement age for the whole century, considering the forecast model of the population I have built in my previous Notebook?
InΒ [1]:
import io
import numpy as np
import pandas as pd
import plotly.graph_objects as go
import plotly.io as pio
pio.renderers.default = 'vscode+notebook'
pd.options.plotting.backend = "plotly"
InΒ [2]:
dfp=pd.read_csv("../data/pop_by_age_year.csv", index_col=0).rename(columns=int) # From Notebook#14
InΒ [3]:
retirement_age = pd.read_csv( # Digitized from source: https://www.linkedin.com/posts/federica-nerini-71222a2b0_a-che-et%C3%A0-si-va-in-pensione-in-italia-activity-7459644370825228288-lWXf
io.StringIO("""
year,male,female
1974,62.1,59.7
1975,62.0,60.0
1976,62.0,60.4
1977,61.2,60.8
1978,60.9,60.7
1979,60.7,60.5
1980,60.8,60.4
1981,60.7,60.2
1982,60.9,61.0
1983,61.2,60.5
1984,61.1,60.2
1985,61.2,60.3
1986,60.9,60.0
1987,61.0,60.3
1988,60.5,60.1
1989,60.6,58.7
1990,60.7,58.2
1991,60.5,58.0
1992,59.5,57.5
1993,58.8,59.0
1994,58.5,58.8
1995,58.2,58.7
1996,58.2,58.5
1997,58.4,58.1
1998,58.3,57.9
1999,58.8,57.3
2000,59.2,57.2
2001,59.0,58.2
2002,59.5,58.9
2003,59.9,58.0
2004,60.0,58.1
2005,59.9,57.9
2006,60.2,57.8
2007,60.4,57.8
2008,60.5,57.8
2009,60.0,57.9
2010,59.7,58.6
2011,60.1,58.9
2012,60.5,60.1
2013,60.5,60.2
2014,60.8,59.8
2015,60.9,60.2
2016,61.2,60.7
2017,61.5,60.7
2018,62.3,61.0
2019,62.8,61.9
2020,62.6,61.5
2021,62.3,61.5
2022,62.7,61.8
2023,63.1,62.2
""".strip()))
retirement_age["average"] = retirement_age[["male", "female"]].mean(axis=1)
(
retirement_age
.plot(x="year", y=["male", "female", "average"])
.update_layout(
title="Effective retirement age in Italy (source: OCSE)",
width=800
)
.show()
)
Visualize the past distribution of working / retired people, to spot some ratio to keep as reference for the future.
InΒ [4]:
# I'm making some assumptions on the average age of retirement and start working
first_year = dfp.columns[0]
last_year = dfp.columns[-1]
print("First and last year in the dataset:", first_year, last_year)
past_retirement_lookup = retirement_age.set_index("year")["average"].to_dict()
working_age = { y: 18 + 4*(y-first_year)/(last_year-first_year) for y in dfp.columns } # Assumption: it was 18 in first year and 22 in last
retirem_age = { y: past_retirement_lookup.get(y, 61 if y < 1980 else 64) for y in dfp.columns } # Assumption: following the retirement_age data
# ratio of people in working age over retired age
wr_df = pd.DataFrame(index=dfp.columns)
wr_df["working-age / retirement-age ratio"] = np.nan
for y in wr_df.index:
wa = working_age[y]
ra = retirem_age[y]
wr_df.loc[y, "working-age / retirement-age ratio"] = dfp.loc[wa:ra,y].sum() / dfp.loc[ra:,y].sum()
wr_df.plot().update_layout(
xaxis_title="Year",
yaxis_title="Working-age / Retirement-age ratio",
showlegend=False,
height=500,
width=800,
).show()
InΒ [5]:
# Compute the mean wr ratio, but only the recent one, which seems stabilized
starting_year_mean = 2000
wr_ratio = wr_df.loc[wr_df.index >= starting_year_mean, "working-age / retirement-age ratio"].mean().round(2)
print(f"Mean working-age/retirement ratio since {starting_year_mean}:", wr_ratio)
InΒ [6]:
dfs = pd.read_csv("../data/pop_by_age_year_proj.csv", index_col=0)
dfp_projs = {
scenario: ( # convert to the usual dataframe age-x-year format
dfs
.reset_index()
[["year", "AGE", scenario]]
.pivot(index="year", columns="AGE", values=scenario)
.transpose()
)
for scenario in dfs.columns[1:]
}
Note that I'm not consideting unemployment, assuming it is constant, and what matters is the ratio between working and retired people not if working people are actually employed or not.
I will now compute the projected retirement age that it is necessary to maintain an average working/retirement ratio of 2.2
InΒ [7]:
past_retirement_cohort = (
retirement_age
.assign(Born_year_retiring=lambda df: (df.year - df.average).astype(int))
.sort_values("Born_year_retiring")
)
past_retirement_cohort
Out[7]:
InΒ [8]:
# Same data plotted in two variants
fig = go.Figure()
for scenario_label, dfpproj in dfp_projs.items():
raproj_df = pd.DataFrame(index=range(2002,2100+1))
raproj_df["Sustainable retirement age"] = np.nan
for y in raproj_df.index:
wa = 22 # Assumption: people will start working at 22 on average
for ra in range(50, 100): # I'm testing different retirement ages (ra) untill the wr_ratio is reached
if dfpproj.loc[wa:ra,y].sum() / dfpproj.loc[ra:,y].sum() > wr_ratio:
raproj_df.loc[y, "Sustainable retirement age"] = ra - 1
break
raproj_df["Born year retiring"] = raproj_df.index - raproj_df["Sustainable retirement age"]
raproj_df = (
raproj_df
.reset_index()
.rename(columns={"index": "Year of Retirement"})
.astype(int)
)
fig.add_trace(
go.Scatter(
x=raproj_df["Born year retiring"],
y=raproj_df["Sustainable retirement age"],
mode='lines',
text=[f'With scenario `{scenario_label}` <br>someone born in {raproj_df.at[i, "Born year retiring"]} will retire in {raproj_df.at[i, "Year of Retirement"]} at {raproj_df.at[i, "Sustainable retirement age"]}yo'
for i in raproj_df.index],
hoverinfo='text',
name=scenario_label
))
fig.add_trace(
go.Scatter(
x=past_retirement_cohort["Born_year_retiring"],
y=past_retirement_cohort["average"],
mode='lines',
text=[f'Past data <br>someone born in {past_retirement_cohort.at[i, "Born_year_retiring"]} retired on average in {past_retirement_cohort.at[i, "year"]} at {past_retirement_cohort.at[i, "average"]:.0f}yo'
for i in past_retirement_cohort.index],
hoverinfo='text',
name="Past effective retirement age",
line=dict(color='black', width=2)
))
fig.update_layout(
xaxis_title="Year of Birth",
yaxis_title="Retirement Age",
legend_title="Scenarios",
showlegend=True,
margin=dict(l=0, r=15, t=20, b=0),
width=780,
height=320,
)
print(f"Sustainable retirement age to maintain the same ratio of working/retired people of {wr_ratio:.2f}:")
fig.write_html("../images_output/sust_retirement_age.html")
fig.show()
ConclusionsΒΆ
- I made some assumptions on the age at which people starts to work and retired in the past
- I took the average
wr_ratioof working-age/retirement-age people since 2000, which seems stabilized, as reference for the future - Based on my projection of Italian future population, being born in 1990, I expect to retire at 68-73 year old (2058-2064) depending on the scenario
- Whoever born after 1980 can not expect to retire before 68 years old, with a range of 5 year more depending on the scenario
NOTE: all previous assumptions are based solely on the demographic, not considering wage evolution.
A severe blindspot of this model is that the lower salaries of the newer generations may need a hither wr_ratio to be sustainable, which would lead to an even higher retirement age.
Follow-upΒΆ
- Consider unemployment: this is a self-balancing secondary effect as less woking people might compensate lower unemployment too
- Run a sensitivity test on the "reference" ratio of working-age/retirement-age people as it is a very handwavy estimate
- Get more data on effective historical start age (historical retirement age added on 2026-06-01)
- Run a sensitivity test on the age at which people will start to work
- Compute the life expectancy after retirement: is it fair w.r.t. those who retired in the past years?