of worker would be from non-agriculture to non-agriculture, and most would not work in
agriculture at all. It may be difficult to estimate the whole migration pattern without data from all
sectors. In this presentation, we present an alternative method (duration model with sample bias
correction) to estimate the effect of the legal status of a worker on duration in farm work. Based on
the existing studies which have used the duration model (Hashida and Perloff 1996, Emerson and
Napasintuwong 2002), we develop the Heckman-type two-stage method, with the ordered probit
model in the first stage and the duration model in the second stage.
The sample selection bias issue should be investigated first. Duration for a worker with a
legal status is observed only if the worker is in that legal status. Each foreign-born worker chooses
his/her legal status, considering conditions such as his/her individual demographic characteristics,
cost of application, and benefit of the status. Without correcting for this selection process, the
duration model will yield biased estimators. Hashida and Perloff (1996) correct selection bias
using Lee’s extension of Heckman’s two-stage sample selection method (Lee 1983). In the first
stage, the multinomial logit model is run to calculate a correction term assuming the error term has
a Gumbel distribution. The second-stage duration model with this correction term does not
generally yield consistent estimates with the normal distribution assumption of error term in the
duration model.2 We will use the ordered probit model in the first stage for two reasons: (1) this is
consistent with the assumption about the error term in duration model in the second stage and (2)
the multinomial logit does not account for the ordinal nature of the legal status. Considering the
advantages in the labor market, they can be ordered as “citizen, permanent resident, authorized,
and unauthorized workers.”3
2 Lee’s method yields consistent estimator under very restrictive condition (Bourguignon et al. 2004).
3 The definition of each legal status is given in the Data section.
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