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 BerkovecSternEmet1991.ox

BerkovecSternEmet1991.ox replicates results shown in Figure 1 of Berkovec and Stern (1991).

• Models retirement and work for males age 55+
• New job match value arrives each year, or can continue with current full/part-time wage
• Wages grow with duration on the job
• Choices made until age 76, then retired for 10 years
• Probability of early death depends on age and health (constant)
• Figure 1 simulates choice probabilities assuming 10 years tenure on full-time job

The Model

Solution/smoothing:

Extreme Value ex ante, ρ = 1/τ.

Clock:

RandomMortality (T = 21)

Mortality probability mprob (in the paper called δ) a function of age and constant health.

Paper does not report probabilities. Stern contacted and could not find them.

Rates are approximated using: CDC Data

Action Vector:

\(\alpha = (i)\),

i       Means
-----------------------------------
0       Retire
1       Work Part-time new match
2       Work Full-time new match
3       Stay in current job

Semi-Exogenous Variables

\(\eta = (h)\), new job match value.

Endogenous State Variables

\(\theta = \pmatrix{ m_0& m_1 & s & d & M &t}\),

\(m_0\) and \(m_1\) and \(s\) are lagged action trackers (full-time implied).

\(d\) duration of current match (t-s) in the paper

\(M\) current match value if a job was held last year (\(M'=h\) if \(i=1\) or \(i=2\)).

Random Effects (elements of the group vector \(\gamma\))

\(\gamma = \pmatrix{g_0& g_1&g_2&g_3& g_I}\).

Each is a permanent normal random effect associated with sector i. \(g_I\) is an individual specific wage effect.

Utility:

U = Xβ0 + σ1gI + σ2g0  + τz.0
    Xβ1 + σ1gI + σ2g1 + σ3hs+ τz.1
    Xβ2 + σ1gI + σ2g2 + σ3hs+ τz.2
    Xβ0 + d  +  σ3M+ τz.3

z.i IID extreme value error

Feasible Actions

only retirement (i=0) after age 75

cannot choose stay (i=3) if retired last period (\(m_0=1\))

Reachable States

duration must be feasible

new and current match value irrelevant after age 75

current match value irrelevant if retired

Notes:

Paper used ?? Monte Carlo draws per normal component.

Implementation in DDP

Header File: 

Ox File:

Output niqlow/examples/output/BerkovecSternEmet1991.txt

 Retirement

Public fields
acteqpars	static	βi
Changing	static const
col	static	Column of table to get params from
disc	static const
drates	static const
dur	static	duration of existing job
eI	static	individual wage effect
ejob	static	array of choice-specific draws
eqpars	static const
eS	static	new match draw
HThous	static const
i	static	Action variable
iacc	static const	age bracket death rates per 100000.
M	static	match value if worked last year
m	static	move/match decision.
p	static const
PrevJob	static	choice previous period
sig1	static const
sig2	static const
sig3	static const
tau	static const
Xn	static
Public methods
FeasibleActions
mprob	static	Age-dependent mortality probability.
Reachable		Duration must be feasible, do not track current eta if retired.
Run	static	Setup and solve the model for both columns.
Sig1	static
Sig2	static
Utility		The one period return.
Enumerations
Anonymous enum 1
Dimens		State space dimensions.
mortbrackets		Mortality brackets.
regressors		Wage regressors.
sectors		Choices & Sectors.

 XLagged

Public methods
Transit
XLagged

 Retirement

 acteqpars

β_i

 Changing

 col

Column of table to get params from

 disc

 drates

 dur

duration of existing job

 eI

individual wage effect

 ejob

array of choice-specific draws

 eqpars

 eS

new match draw

 FeasibleActions

 HThous

 i

Action variable

 iacc

age bracket death rates per 100000. Paper does not report δ, state-dependent survival probability. Stern was contacted and said they could not be found. These rates are used as an approximation.

Source http://www.cdc.gov/nchs/data/dvs/mx196878.pdf

Table: 82/10/14 TABLE 290 82/10/14 TABLE 290. DEATH RATES FOR 69 SELECTED CAUSES, BY 10-YEAR AGE GROUPS, RACE, AND SEX: UNITED STATES, 1968-78

Row: White Male 1969, Age55-85+

 M

match value if worked last year

 m

move/match decision.

 mprob

Age-dependent mortality probability.

 p

 PrevJob

choice previous period

 Reachable

Duration must be feasible, do not track current eta if retired.

 Run

Setup and solve the model for both columns.

 Sig1

 sig1

 Sig2

 sig2

 sig3

 tau

 Utility

The one period return.

 Xn

 XLagged

 Transit

 XLagged