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Modelling and Forecasting Suicide Rates
Yunus Emre Ergemen and Malene Kallestrup-Lamb
CREATES and Aarhus University
September 21, 2018
14th International Longevity Risk and Capital Markets SolutionsConference,Amsterdam
Ergemen & Kallestrup-Lamb (AU) Modelling and Forecasting Suicide Rates September 21, 2018 1 / 19
Motivation – Why suicide rates?
WHO Report 2014 on suicide:Every year, more than 800,000 deaths by suicideDeaths every 40 seconds in the worldSecond leading cause of death globally for 15-29 years of ageTop 10 cause of death for several countries including the US
Spillover effectsImpact on families, friends and communitiesLoss of knowledge accumulation
Recent increasing trends in the US and several other countries
Ergemen & Kallestrup-Lamb (AU) Modelling and Forecasting Suicide Rates September 21, 2018 2 / 19
Increasing Trends in US Suicide Rates
Ergemen & Kallestrup-Lamb (AU) Modelling and Forecasting Suicide Rates September 21, 2018 3 / 19
Characteristics of Suicide Rates Data
Reflecting a complex phenomenon influenced by the interplay ofseveral factors
Social, economic, psychological, cultural, biological, environmental
Measurement errorsTaboo, stigma, shame and guilt leading to under-reportingMiscoding as a mental illnessDifficult to analyze in a cross-state (or cross-country) study
Complex, possibly nonlinear, dynamics
Ergemen & Kallestrup-Lamb (AU) Modelling and Forecasting Suicide Rates September 21, 2018 4 / 19
Overview of the Talk
1 Introduction
2 Data
3 Methodology
4 Forecasts
5 Conclusion
Ergemen & Kallestrup-Lamb (AU) Modelling and Forecasting Suicide Rates September 21, 2018 5 / 19
Analyzing Suicide Rates
In the literature,
either psychological or economic factors considered
oversimplified specifications disregarding interplays of suicide riskfactors
measurement errors neglected
In this paper, we can
include a combination of all relevant factors affecting suicide rates.
study possibly nonlinear characteristics.
account for measurement errors.
obtain post-available-data forecasts.
Ergemen & Kallestrup-Lamb (AU) Modelling and Forecasting Suicide Rates September 21, 2018 6 / 19
Age Grouping in Suicide Rates
Correlation in suicide rate - Male
All
10-14
15-19
20-24
25-29
30-34
35-39
40-44
45-49
50-54
55-59
60-64
65-69
70-74
75-79
80-84
85+
All
10-14
15-19
20-24
25-29
30-34
35-39
40-44
45-49
50-54
55-59
60-64
65-69
70-74
75-79
80-84
85+
California
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
All
10-14
15-19
20-24
25-29
30-34
35-39
40-44
45-49
50-54
55-59
60-64
65-69
70-74
75-79
80-84
85+
All
10-14
15-19
20-24
25-29
30-34
35-39
40-44
45-49
50-54
55-59
60-64
65-69
70-74
75-79
80-84
85+
New York
-0.2
0
0.2
0.4
0.6
0.8
1All
10-14
15-19
20-24
25-29
30-34
35-39
40-44
45-49
50-54
55-59
60-64
65-69
70-74
75-79
80-84
85+
All
10-14
15-19
20-24
25-29
30-34
35-39
40-44
45-49
50-54
55-59
60-64
65-69
70-74
75-79
80-84
85+
Texas
-0.2
0
0.2
0.4
0.6
0.8
1
All
10-14
15-19
20-24
25-29
30-34
35-39
40-44
45-49
50-54
55-59
60-64
65-69
70-74
75-79
80-84
85+
All
10-14
15-19
20-24
25-29
30-34
35-39
40-44
45-49
50-54
55-59
60-64
65-69
70-74
75-79
80-84
85+
Illinois
-0.2
0
0.2
0.4
0.6
0.8
1
Ergemen & Kallestrup-Lamb (AU) Modelling and Forecasting Suicide Rates September 21, 2018 7 / 19
Age Grouping in Suicide Rates
Correlation in suicide rate - Female
All
10-14
15-19
20-24
25-29
30-34
35-39
40-44
45-49
50-54
55-59
60-64
65-69
70-74
75-79
80-84
85+
All
10-14
15-19
20-24
25-29
30-34
35-39
40-44
45-49
50-54
55-59
60-64
65-69
70-74
75-79
80-84
85+
California
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
All
10-14
15-19
20-24
25-29
30-34
35-39
40-44
45-49
50-54
55-59
60-64
65-69
70-74
75-79
80-84
85+
All
10-14
15-19
20-24
25-29
30-34
35-39
40-44
45-49
50-54
55-59
60-64
65-69
70-74
75-79
80-84
85+
New York
-0.2
0
0.2
0.4
0.6
0.8
1All
10-14
15-19
20-24
25-29
30-34
35-39
40-44
45-49
50-54
55-59
60-64
65-69
70-74
75-79
80-84
85+
All
10-14
15-19
20-24
25-29
30-34
35-39
40-44
45-49
50-54
55-59
60-64
65-69
70-74
75-79
80-84
85+
Texas
0
0.2
0.4
0.6
0.8
1
All
10-14
15-19
20-24
25-29
30-34
35-39
40-44
45-49
50-54
55-59
60-64
65-69
70-74
75-79
80-84
85+
All
10-14
15-19
20-24
25-29
30-34
35-39
40-44
45-49
50-54
55-59
60-64
65-69
70-74
75-79
80-84
85+
Illinois
-0.2
0
0.2
0.4
0.6
0.8
1
Ergemen & Kallestrup-Lamb (AU) Modelling and Forecasting Suicide Rates September 21, 2018 8 / 19
Suicide Rates across States
Suicide rate - Male
1980 1985 1990 1995 2000 2005 2010 2015 2020
0
0.2
0.4
0.6
0.8
1
1.2California
1980 1985 1990 1995 2000 2005 2010 2015 2020
0.1
0.2
0.3
0.4
0.5
0.6
0.7New York
1980 1985 1990 1995 2000 2005 2010 2015 2020
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8Texas
1980 1985 1990 1995 2000 2005 2010 2015 2020
0
0.2
0.4
0.6
0.8
1Illinois
All
20-24
50-54
85+
Ergemen & Kallestrup-Lamb (AU) Modelling and Forecasting Suicide Rates September 21, 2018 9 / 19
Suicide Rates across States
Suicide rate - Female
1980 1985 1990 1995 2000 2005 2010 2015 2020
0
0.05
0.1
0.15
0.2California
1980 1985 1990 1995 2000 2005 2010 2015 2020
0
0.02
0.04
0.06
0.08
0.1New York
1980 1985 1990 1995 2000 2005 2010 2015 2020
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14Texas
1980 1985 1990 1995 2000 2005 2010 2015 2020
0
0.02
0.04
0.06
0.08
0.1
0.12Illinois
All
20-24
50-54
85+
Ergemen & Kallestrup-Lamb (AU) Modelling and Forecasting Suicide Rates September 21, 2018 10 / 19
Data
For the period 1981-2016 in California, Texas, New York and Illinois, andfor age groups 20-24, 50-54 and 85+,
mean female suicide rates highest in California
mean male suicide rates highest in Texas
male suicide rates around 4x female suicide rates
nonlinear dynamics
recent increasing trends in male and female suicide rates
similarly evolving dynamics for the states pointing at cross-statedependence
Ergemen & Kallestrup-Lamb (AU) Modelling and Forecasting Suicide Rates September 21, 2018 11 / 19
Cross-State Dependence in Suicide Rates
Cross-state correlation - Male
Californ
ia
New York
Texas
Illinois
California
New York
Texas
Illinois
All
0.713
0.8449
0.713
0.761
0.6797
0.761
0.9149
0.8449
0.6797
0.9149
1
0.9245
1
0.9245
1
1
0.7
0.75
0.8
0.85
0.9
0.95
1
Californ
ia
New York
Texas
Illinois
California
New York
Texas
Illinois
20-24
0.734
0.8054
0.659
0.734
0.6961
0.5975
0.8054
0.6961
0.6539
0.659
0.5975
0.6539
1
1
1
1
0.6
0.65
0.7
0.75
0.8
0.85
0.9
0.95
1
Californ
ia
New York
Texas
Illinois
California
New York
Texas
Illinois
50-54
0.3674
0.3975
0.378
0.3674
0.4907
0.6111
0.3975
0.4907
0.6811
0.378
0.6111
0.6811
1
1
1
1
0.4
0.5
0.6
0.7
0.8
0.9
1
Californ
ia
New York
Texas
Illinois
California
New York
Texas
Illinois
85+
0.7217
0.3431
0.577
0.7217
0.3089
0.6278
0.3431
0.3089
0.3982
0.577
0.6278
0.3982
1
1
1
1 0.4
0.5
0.6
0.7
0.8
0.9
1
Ergemen & Kallestrup-Lamb (AU) Modelling and Forecasting Suicide Rates September 21, 2018 12 / 19
Cross-State Dependence in Suicide Rates
Cross-state correlation - Female
Californ
ia
New York
Texas
Illinois
California
New York
Texas
Illinois
All
0.6867
0.8578
0.871
0.6867
0.7278
0.7443
0.8578
0.7278
0.871
0.7443
1
1
1
0.9234
0.9234
1
0.7
0.75
0.8
0.85
0.9
0.95
1
Californ
ia
New York
Texas
Illinois
California
New York
Texas
Illinois
20-24
0.3035
0.5601
0.4588
0.3035
0.2588
0.4413
0.5601
0.2588
0.6471
0.4588
0.4413
0.6471
1
1
1
1
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Californ
ia
New York
Texas
Illinois
California
New York
Texas
Illinois
50-54
0.11
0.2606
0.4077
0.11
0.5429
0.3566
0.2606
0.5429
0.3421
0.4077
0.3566
0.3421
1
1
1
10.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Californ
ia
New York
Texas
Illinois
California
New York
Texas
Illinois
85+
0.6083
0.2936
0.4644
0.6083
0.3724
0.5685
0.2936
0.3724
0.6402
0.4644
0.5685
0.6402
1
1
1
1
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Ergemen & Kallestrup-Lamb (AU) Modelling and Forecasting Suicide Rates September 21, 2018 13 / 19
Further Characteristics for the All-Age Group – Stochastics
Unit roots in log male and female suicide rates in California, NewYork, Texas, Illinois
Lack of mean reversion due to the existence of unit roots and thenecessity for policy interventions
The first principal component, measuring cross-state dependence,accounting for 86.15% and 85.76% of the total variation in log maleand female suicide rates, respectively
Possibility of developing a suicide index
Ergemen & Kallestrup-Lamb (AU) Modelling and Forecasting Suicide Rates September 21, 2018 14 / 19
Methodology
Denoting Xit the logarithm of suicide rate in state i at time t, we write
Xit = αi + λ′iFt + εit
Ft account for common causes of suicide death, λi adjust themagnitude.
Measurement errors contained either by λ′iFt or idiosyncratically by εitPersistence allowed in model components
Ergemen & Kallestrup-Lamb (AU) Modelling and Forecasting Suicide Rates September 21, 2018 15 / 19
Forecast Model Considerations
AR
Xit+h = µih + βih(L)Xit + εit+h,
AR + common factor(s)
Xit+h = µih + βih(L)Xit + γih(L)′F̂t + εit+h
Nonlinear AR Artificial Neural Network
Xit+h = µi0h +
q∑j=1
µj0h g
(βi0j +
p∑k=1
βikjXit−k
)+ εit+h.
Nonlinear AR Artificial Neural Network + common factor(s)
Ergemen & Kallestrup-Lamb (AU) Modelling and Forecasting Suicide Rates September 21, 2018 16 / 19
Data and Post-Data Forecasts for Male Suicide Rates (AllAges)
1980 1990 2000 2010 2020 20300.1
0.15
0.2
0.25
0.3
0.35California
1980 1990 2000 2010 2020 20300.1
0.12
0.14
0.16
0.18
0.2New York
1980 1990 2000 2010 2020 20300.15
0.2
0.25
0.3
0.35Texas
1980 1990 2000 2010 2020 20300.1
0.15
0.2
0.25
0.3Illinois
Ergemen & Kallestrup-Lamb (AU) Modelling and Forecasting Suicide Rates September 21, 2018 17 / 19
Data and Post-Data Forecasts for Female Suicide Rates(All Ages)
1980 1990 2000 2010 2020 20300.2
0.25
0.3
0.35
0.4California
1980 1990 2000 2010 2020 20300.1
0.2
0.3
0.4New York
1980 1990 2000 2010 2020 20300.2
0.25
0.3
0.35
0.4Texas
1980 1990 2000 2010 2020 20300.15
0.2
0.25
0.3
0.35
0.4Illinois
Ergemen & Kallestrup-Lamb (AU) Modelling and Forecasting Suicide Rates September 21, 2018 18 / 19
Conclusion
Analyzing suicide rates is important.Our data-driven approach shows
there are heterogeneities across the states in terms of theircharacteristics.there are common characteristics between the states.suicide rates are forecast to increase in some states and/or fail to meanrevert.
Possible implications for pension and insurance planning
Ergemen & Kallestrup-Lamb (AU) Modelling and Forecasting Suicide Rates September 21, 2018 19 / 19