modelling and forecasting suicide rates€¦ · modelling and forecasting suicide rates yunus emre...

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


Increasing Trends in US Suicide Rates


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


Overview of the Talk

1 Introduction

2 Data

3 Methodology

4 Forecasts

5 Conclusion


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.


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


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


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+


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+


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


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


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


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


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


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)


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


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


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


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