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Schooling and Occupational Destination in
India and Brazil
Geraint Johnes
Aradhna Aggarwal (Delhi)
Ricardo Freguglia (Juiz de Fora)
Gisele Spricigo (UNISINOS)
In each period an individual faces choices about how she will allocate her time: will
• work in a skilled job?
• work in an unskilled job?
• undertake education/training?
• pursue other activities unrelated to the labour market?
The decision depends in part on her past actions:
• how much experience she has in different types of work
• how much education and training she has received
…but also on expected future actions. So, for example, she is more likely to
undertake education this year if, as a result, her earnings in skilled work are likely to
be greater in future years.
Decisions are therefore best modelled in a dynamic framework, but…
… where there are many choices that can be made in many periods, the number of
different pathways through life (the ‘state space’) is huge.
The huge state space makes estimation of dynamic discrete choice models difficult.
But methods have been developed. Aguirregabiria and Mira (2007) provide a survey,
and have compiled a set of programs that can be used in estimation. Another recent
survey is by Keane and Wolpin (2009).
Rust (1987) devised a model to analyse the timing of machine replacement. This is an
optimal stopping problem. The model has become popular owing to the tractability of
the nested fixed point algorithm used in its solution.
But Rust’s model assumes conditional independence of future values of variables, and
so is not suited to our purpose.
Keane and Wolpin (1994, 1997) develop an approximation method based on predicted
values of expected returns associated with a regression line fitted on a sample of the
points in the state space. They use this to evaluate career decisions of young men in
the US, using NLSY data. Similar approaches have been used by eg Stinebrickner
As Keane (2009) observes: ‘a common criticism of structural econometric work is that it
relies on too many assumptions’ (but so does conventional econometric work). He also
notes that ‘structural econometric work is just very hard to do’ – so is not fashionable.
More on the Keane and Wolpin model
1. Define period-specific reward functions for each labour market outcome, eg
R1 = f1(x1,x2,s)
R2 = f2(x1,x2,s)
R3 = f3(s,p)
R4 = f4(.)
where Ri is the reward from outcome i (i=1 skilled work; i=2 unskilled work; i=3
education; i=4 not in work or education), xi is experience in outcome i, s is years of
schooling, p is a policy variable. There may or may not be data (eg wage data) on
the Ri – if there are not, the Ri are latent (cf logit).
2. Maximising lifetime reward involves making a choice between outcomes in each
time period. With 4 choices and, say, 15 periods, there are over a billion possible
outcomes to compare.
3. Use Monte Carlo integration to approximate the expected maximum function for a
sample of points in the state space, and use these approximations as data points in
a regression that allows predictions to be made about the expected maximum
function for all other points in the state space.
4. Use standard maximum likelihood methods to evaluate the parameters of the model
in (1) above, given the approximation method described in (3) above.
Since this begins with defining a particular theoretical model, estimation has to be
by way of a program that is coded specifically for the model being estimated.
The outcome is a model that explains how changes in policy in one period can affect
outcomes in all subsequent periods.
If p changes now, s may change now, and so s, x1 and x2 may change in future periods.
Possible in the current project?
REDS dataset for India has panel data for individuals over 20 year period. But…
• it’s a rural survey only
• short panel - not annual data
• balanced panel only for small number of observations
NSS provides a large repeated cross-section dataset for India. Some questions are
asked annually, others more sporadically. Propensity score matching methods can be
used to match individuals in one year with similar individuals in another year, thus
generating a synthetic panel.
A similar approach could be adopted in Brazil using the PNAD data, but…
… here we have access to a true panel of administrative data, providing census
information about all workers in the formal sector.
We know the duration of schooling for each worker; we do not know what workers are
doing in years when they are not observed (they could be not working, they could be
in informal sector work…); our sample will contain only workers who are at some point
employed in the formal sector – so some sample selection bias for which we cannot
Results so far
Very preliminary results so far are from standard (static) multinomial logit analysis of
data from a single year (2005) for India:
Primary school or less
Middle school
High school
+ controls for religion, class, land holdings, household literacy. These are marginal
effects; all highly significant apart from a couple of the age terms.
Aguirregabiria, Victor and Pedro Mira (2008) Dynamic discrete choice structural models: a survey,
forthcoming in the Journal of Econometrics.
Johnes, Geraint (2009) Occupation and the labour market participation of women: why do some
people trade down jobs when careers are interrupted?, Applied Economics Letters, 16, 1093-1096.
Keane, Michael P. (2009) Structural vs atheoretic approaches to econometrics, Journal of
Econometrics, forthcoming.
Keane, Michael P. and Kenneth I. Wolpin (1994) The solution and estimation of discrete choice
dynamic programming models by simulation and interpolation: Monte Carlo evidence, Review of
Economics and Statistics, 76, 648-672.
Keane, Michael P. and Kenneth I. Wolpin (1997) The career decisions of young men, Journal of
Political Economy, 105, 473-522.
Keane, Michael P. and Kenneth I. Wolpin (2009) Empirical applications of discrete choice dynamic
programming models, Review of Economic Dynamics, 12, 1-22.
Rust, John (1987) Optimal replacement of GMC bus engines: an empirical model of Harold Zurcher,
Econometrica, 55, 999-1033.
Stinebrickner, Todd (2001) A dynamic model of teacher labor supply, Journal of Labor Economics, 19,