1. The Lifetime INcome Distributional Analysis model: LINDA
A model to generate lifetime incomes for a population cross-section
Justin van de Ven Martin Weale & Paolo Lucchino
July, 2014

2. Outline Purpose of the model A model design fit for purpose
Selected model features
Suitable issues for analysis
Desirable extensions
A practical example

3. Purpose of the model
A model 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
a model to produce analysis in terms of lifetime incomes
not possible with pre-existing analytical tools

4. A model design fit for purpose
A wide range of alternative analytical approaches exist, which can be organised according to two key dimensions:
the dimensionality of the considered population
the basis for projecting behavioural responses
The selected modelling approach is tailored to the analytical purpose

5. A model design fit for purpose
Principal model alternatives concerning the dimensionality of the considered population:
case-study
birth cohort
population cross-section at a point in time
evolving population cross-section

6. A model design fit for purpose
Principal model alternatives concerning the dimensionality of the considered population:
case-study
birth cohort
population cross-section at a point in time
evolving population cross-section

7. A model design fit for purpose
Principal model alternatives concerning the basis for projecting behavioural responses:
exogenous “rule-of thumb”
static reflection of past decisions
non-structural reduced form relationships
explicit behavioural assumptions, ignoring uncertainty
structural relationships with analytical solutions
explicit behavioural assumptions, accommodating uncertainty
structural relationships without analytical solutions

8. A model design fit for purpose
Principal model alternatives concerning the basis for projecting behavioural responses:
exogenous “rule-of thumb”
static reflection of past decisions
non-structural reduced form relationships
explicit behavioural assumptions, ignoring uncertainty
structural relationships with analytical solutions
explicit behavioural assumptions, accommodating uncertainty
structural relationships without analytical solutions

9. Selected model features
Reference population cross-section:
all individuals aged 18+ reported in the WAS between July 2006 and June 2007
weights adjusted to reflect the UK
Unit of analysis:
benefit units, defined as a single adult or adult couple, and their dependent children (to age 17)
Period of analysis:
model projects at annual intervals forward and backward through time, building up a complete life history for each adult (from age 18)

10. Selected model features
Behavioural assumptions:
life-cycle model of behaviour
allow for uncertainty
implies no analytical solution to the decision problem
model is consequently based on (numerical) dynamic programming methods

11. Selected model features
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

12. Selected model features
Decisions (utility maximising)
consumption - employment of each adult
private pension participn - timing of access to pension
investments in ISAs - investments in risky assets

13. Suitable issues for analysis
Model is an appropriate tool for considering two types of research question:
What are the plausible implications of a given policy environment for the distribution of lifetime income?
e.g. How does lifetime income vary by individual characteristics such as birth year / education / relationship status / children / etc?
What are plausible behavioural responses to a given change in the policy environment?
e.g. How do responses to a given policy change vary by lifetime income decile?

14. Suitable issues for analysis
Focussed on the healthy population
Includes a broad range of taxes and benefits
2006 and 2010 transfer systems explicitly modelled and altered through an Excel front-end
Taxes and benefits programming code can be accessed and altered as desired
Individual transfer schemes are separately represented in code
Allows for a reasonable degree of flexibility in relation to pensions

15. Desirable extensions
We are a long way short of a “model of everything”
Primary model extensions:
allowing for the evolving population cross-section
allowing the model to switch between structural decision making and reduced form decision making
explicit allowance for owner-occupied housing wealth

16. A practical example
Policy reform involving the introduction of a citizen’s pension set equal in value to the Pension Guarantee, off-set by a rise in the basic rate of tax
Citizen’s pension replaces the Pension Credit
Value of citizen’s pension:
£ pw for singles, £ pw for couples
Basic rate of tax increased from 22% to 34%
Without tax increase, tax revenue net of benefits reduced by £34Bn in 2006

17. A practical example – behavioural effects

18. A practical example – behavioural effects

19. A practical example – welfare effects

20. A practical example – welfare effects

21. A practical example – income effects

22. A practical example – income effects