Hi,
I want to estimate in Stata a joint model for labour market choices and wages: multinomial logit panel data model with random effects for the choices and two linear random effect wage equations for the wages in the two sectors (public and private).
The wage equations are specified as follows (subscripts for individuals are omitted):
(1) lnwtj=MtVj + Lj + Ctj, j=1,2
where:
j denotes the sector (1-public 2-private)
Mt is a vector of individual characteristics (including a constant term, educational dummies and age)
Lj denotes the random individual effect
Ctj - error terms
Vj - parameter to be estimated
In the sector choice part of the model, wages will play a role, so I use a wage variable cleaned for measurement error - predicted log wages plnwtj given by:
plnwtj=lnwtj-Ctj, j=1,2
The choice part of the model is specified as follows:
(2) Ujt=Xt Bj + Aj + kplnwtj + Ejt, j=1,2,3
An individual can be in any of 3 possible labour market states, plnwt3 is set to 0 (j=3 means that respondent is unemployed).
How attractive the various labour market states are depends on potential wages, so predicted wage rates are used as explanatory variables with coefficient k.
Xt is a vector of explanatory variables including age, regional dummies, etc. To identify the model educational dummies are excluded from (2).
Aj - random individual effects
Bj - parameter to be estimated
With reference to the information above I have several questions:
(1) How to estimate wage equations if respondents wage rate in a given sector in a given year is only observed if the respondent works in that sector during that year? I thought about xtreg.
(2) I want to assume that the effect of wages on utility U is the same in public and private sector. How to impose this restriction in gllamm, because this is what I would have to do? In other words: how to make k to be the same over j=1 and j=2 if j=3 is taken as a reference state?
(3) How to impose on random effects restriction of no correlation between random effects in the wage and the choice equations in gllamm?
I would be very grateful if you could send me any suggestions. In advance thank you for help,
Best wishes,
Sebastian
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