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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 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

Visualize the past distribution of working / retired people, to spot some ratio to keep as reference for the future.

InΒ [3]:
# I'm making some assumptions on the average age of retirement and start working
first_year = dfp.columns[0]
last_year = dfp.columns[-1]

working_age = { y: 20 + 2*(y-first_year)/(last_year-first_year) for y in dfp.columns } # Assumption: it was 20 in 2002 and it is 22 in 2022
retirem_age = { y: 58 + 7*(y-first_year)/(last_year-first_year) for y in dfp.columns } # Assumption: it was 58 in 2002 and it is 65 in 2022

# 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()

print("Mean working-age/retirement-age ratio:", wr_df["working-age / retirement-age ratio"].mean().round(2))

Mean working-age/retirement-age ratio: 2.2
InΒ [4]:
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 [5]:
wr_ratio = 2.2

# 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 ratio is 2.2 is reached
            if dfpproj.loc[wa:ra,y].sum() / dfpproj.loc[ra:,y].sum() > wr_ratio:
                raproj_df.loc[y, "Sustainable retirement age"] = ra
                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.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("Sustainable retirement age to maintain the same ratio of working/retired people of 2.2")
fig.write_html("../images_output/sust_retirement_age.html")
fig.show()

Sustainable retirement age to maintain the same ratio of working/retired people of 2.2

ConclusionsΒΆ

  • I made some assumptions on the age at which people starts to work and retired in the past
  • I computed a ratio between working-age and retired-age people of 2.0 - 2.4 in the historical data, and picked an average value of 2.2 as the "referance" one to keep constant in the future
  • Based on my projection of Italian future population, being born in 1990, I expect to retire at 69-74 year old (2058-2064) depending on the scenario
  • This year is 2025 and we expect to have people going to (average effective) retirement at 65, born in 1960. Officially, the pension by old-age is 69. My graph shows that in the next 20 years this retirement age will go straight up: variations in fertility are not impacting, while the migration balance is impacting, but not that much.

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 and retirement age
  • 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?
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