A model to generate lifetime incomes for a population cross-section

The Lifetime INcome Distributional Analysis Model:

LINDA

Justin van de Ven (jvandeven@niesr.ac.uk) Martin Weale & Paolo Lucchino

January 2014

Outline• Objectives of the analytical framework• Choice of analytical approach• Model framework• Model validation• Suitable issues for analysis• Use in practice

09:00-10:30: Presentation 10:45-12:30: Hands-on use of the model

Analytical Objectives• HM Treasury and HMRC want to commission a

behavioural, structural, dynamic microsimulation model, which would allow us to produce analysis in terms of lifetime incomes.

• The new model would allow us to simulate lifetime net incomes of a representative cross-section of the UK population, before and after a change to tax and/or benefit policy.

• This new model would fill a gap in our analytical capability.– Project Specification, 14 January 2012

Analytical Objectives• HM Treasury and HMRC want to commission a

behavioural, structural, dynamic microsimulation model, which would allow us to produce analysis in terms of lifetime incomes.

• The new model would allow us to simulate lifetime net incomes of a representative cross-section of the UK population, before and after a change to tax and/or benefit policy.

• This new model would fill a gap in our analytical capability.– Project Specification, 14 January 2012

Analytical Objectives• HM Treasury and HMRC want to commission a

behavioural, structural, dynamic microsimulation model, which would allow us to produce analysis in terms of lifetime incomes.

• The new model would allow us to simulate lifetime net incomes of a representative cross-section of the UK population, before and after a change to tax and/or benefit policy.

• This new model would fill a gap in our analytical capability.– Project Specification, 14 January 2012

Choice of Analytical Approach• Focus on the implications of policy for

lifetime net incomes motivates simulation approach– lags involved to observe lifetime incomes in

survey data• Choice of the simulation approach

characterised by two key dimensions:– simulated population– approach to modelling behaviour

Choice of Analytical Approach• Simulation alternatives in relation to the

population:– case-study– birth cohort– population cross-section at a point in time– evolving population cross-section

Choice of Analytical Approach• Simulation alternatives in relation to the

population:– case-study– birth cohort– population cross-section at a point in time– evolving population cross-section

Interested in “a representative cross-section for the UK population”

Choice of Analytical Approach• Simulation alternatives in relation to the

population:– case-study– birth cohort– population cross-section at a point in time– evolving population cross-section

Interested in “a representative cross-section for the UK population”

Choice of Analytical Approach

• A spectrum of behavioural assumptions

very broad behavioural assumptions

back of the envelope

detailed statistical analysis

no formal model of behaviour

detailed statistical analysis

formal model of behaviour –

poor approx. of uncertainty

detailed numerical analysis

formal model of behaviour –

uncertainty explicitly considered

BEHAVIOURAL ASSUMPTIONS

ANALYTICAL APPROACH

Choice of Analytical Approach• Structural

– based on a formal model of behaviour• Dynamic

– projects circumstances through time• Microsimulation

– generates temporal variation for individual decision units

• Model of the population cross-section observed at a point in time

Choice of Analytical Approach

LINDA is the first dynamic microsimulation model of the population cross-section that

uses current best-practice economic methods to project savings and labour

supply decisions through time

LINDA: A model for Whitehall• Structural model of household consumption, labour supply, and

investment decisions (van de Ven, 2013)• Life-cycle framework

– Resolution of puzzles– Motivating observations (Attanasio & Webber, 2010)

• Unit of analysis– Benefit units, defined as a single adult or adult couple, and their dependent

children (to age 17)

• Population cross-section– All adults reported by the WAS for the population cross-section of Great

Britain observed between July 2006 and June 2007

• Period of analysis– Projects at annual intervals forward and backward through time, building up a

complete life history for each adult from age 18.

LINDA: A model for Whitehall• Characteristics that distinguish benefit units- year of birth - age- relationship status - number of children by age- student status - education- self-employed/employee - wage potential reference

adult- wage potential of spouse - savings held in ISAs- eligible private pension - private pension wealth- timing of pension access - state pension based on

BSP- state pension on S2P - wealth not otherwise

defined- time of death

LINDA: A model for Whitehall• Characteristics that distinguish benefit units- year of birth - age- relationship status - number of children by age- student status - education- self-employed/employee - wage potential reference

adult- wage potential of spouse - savings held in ISAs- eligible private pension - private pension wealth- timing of pension access - state pension based on

BSP- state pension on S2P - wealth not otherwise

defined- time of death

LINDA: A model for Whitehall• Characteristics that distinguish benefit units- year of birth - age- relationship status - number of children by age- student status - education- self-employed/employee - wage potential reference

adult- wage potential of spouse - savings held in ISAs- eligible private pension - private pension wealth- timing of pension access - state pension based on

BSP- state pension on S2P - wealth not otherwise

defined- time of death

LINDA: A model for Whitehall• Decisions (utility maximising)

• Uncertainty may be considered in relation to:

- consumption - employment of each adult

- private pension participn - timing of access to pension- investments in ISAs - investments in risky assets

- relationship status - dependent children - student status - education status- self-employed/employee - wage potential- ISA investments - private pension terms- private pension wealth - other wealth- time of death

LINDA: A model for Whitehall• Decisions (utility maximising)

• Uncertainty may be considered in relation to:

- consumption - employment of each adult

- private pension participn - timing of access to pension- investments in ISAs - investments in risky assets

- relationship status - dependent children - student status - education status- self-employed/employee - wage potential- ISA investments - private pension terms- private pension wealth - other wealth- time of death

LINDA: A model for Whitehall• Decisions (utility maximising)

• Uncertainty may be considered in relation to:

- consumption - employment of each adult

- private pension participn - timing of access to pension- investments in ISAs - investments in risky assets

- relationship status - dependent children - student status - education status- self-employed/employee - wage potential- ISA investments - private pension terms- private pension wealth - other wealth- time of death

Analytical Framework• Preferences:

• Budget constraint:

• Evolution of wages:

• Dynamic programming…

tttttt clhrwww )1(1

tttt lhh 1loglog 1

A

ajji

baajji

baaj

ajaaiai wuEuU

1

1,10,

1,,

1,, 1

11

aiaiai

aiai l

cu ,

/111

/11,

/1

/11

,

,,

Analytical Framework

hA

wA

hA-1

wA-1

hA-2

wA-2

h18

w18

age

Model Validation• Model parameters and statistical implications

– Model has been parameterised to reflect a wide range of statistics estimated from survey data sources

– Model fit has been checked in a high degree of detail in conjunction with HMT (process lasting > 1 year)

– Technical details reported in Lucchino and van de Ven (2013)

• Model code structure and personnel risk – Tax and transfer code checked over with HMT analysts– Source code of remaining model held by 4 personnel at

the NIESR

Suitable Issues for Analysis• Model is an appropriate tool for considering two

types of research question:1. What are the plausible implications of a given policy

environment for the distribution of lifetime income?• How does lifetime income vary by individual characteristics

such as birth year, education, relationship status, children, etc?

2. What are plausible behavioural responses to a given change in the policy environment?• How do such effects vary by individual characteristics, and

what are the associated implications for lifetime income?

Using LINDAa brief introduction

Use of the Model in Practice• Each simulation is comprised of 4 discrete steps:

1. Define the policy environment2. Solve for utility maximising decisions for any

potential combination of benefit unit characteristics3. Simulate the circumstances of a reference

population cross-section forward and backward through time, eventually building up panel data describing the complete life-history of each.

4. Run secondary analyses on the panel data to explore issues of interest

Use of the Model in Practice• Each simulation is comprised of 4 discrete steps:

1. Define the policy environment2. Solve for utility maximising decisions for any potential

combination of benefit unit characteristics3. Simulate the circumstances of a reference population cross-

section forward and backward through time, eventually building up panel data describing the complete life-history of each.

4. Run secondary analyses on the panel data to explore issues of interest

• Key to using the model appropriately is to allow sufficient time for stage 4

Use of the Model in Practice1. Defining the policy environment

– Excel front-end to facilitate variation of selected model parameters

– Programming access to tax and benefits structure

Use of the Model in Practice1. Defining the policy environment

– Excel front-end to facilitate variation of selected model parameters

– Programming access to tax and benefits structure

4. Analysing model output:– Excel summary statistics– Panel data for the simulated population

Use of the Model in Practice1. Defining the policy environment

– Excel front-end to facilitate variation of selected model parameters

– Programming access to tax and benefits structure

4. Analysing model output:– Excel summary statistics– Panel data for the simulated population