Schooling and Occupational Destination in India and Brazil

1. Schooling and Occupational Destination in India and Brazil Geraint Johnes Aradhna Aggarwal (Delhi) Ricardo Freguglia (Juiz de Fora) Gisele Spricigo (UNISINOS)

2. In each period an individual faces choices about how she will allocate her time: will she • 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.

3. 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 egStinebrickner (2001). 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.

4. More on the Keane and Wolpin model 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 Riare latent (cflogit). 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.

5. 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.

6. 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 correct.

7. Results so far Very preliminary results so far are from standard (static) multinomial logit analysis of data from a single year (2005) for India: + controls for religion, class, land holdings, household literacy. These are marginal effects; all highly significant apart from a couple of the age terms.

8. References 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 vsatheoretic 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, 196-230.