Forum: help

RE: Only intercept term but no other variables in the selection function? [ Reply ] By: Fei Jin on 2015-12-10 15:34	[forum:42785]
Thank you very much! It works.

RE: Only intercept term but no other variables in the selection function? [ Reply ] By: Fei Jin on 2015-12-10 15:20	[forum:42784]
By the way, if the selection equation only includes an intercept term, the Inverse Mills Ratio is a constant. Because in the two step method, an intercept term has been added to the regression equation, there will be two intercept terms. Thus there is a pefect multicollinearity problem.

RE: Only intercept term but no other variables in the selection function? [ Reply ] By: Arne Henningsen on 2015-12-10 15:20	[forum:42783]
You can try to manually specify starting values of the parameters so that the ML estimation can be started without a prior two-step estimation.

RE: Only intercept term but no other variables in the selection function? [ Reply ]
By: Fei Jin on 2015-12-10 15:14

[forum:42782]

Dear Arne,
Thank you very much for your reply. You are right, the two step method will fail because of the perfect mulcollinearity. The first error is due to the perfect multicollinearity in the selection equation. The warning message is because of the perfect multicollinearity in the two step estimation method, which computes the initial value for the MLE. But the maximum likelihood can still work, if we use some other initial estimate instead of the two step estimate. What I am looking for is to solve the first error: an option to only include an intercept term but no other variables in the selection equation. In a paper (Lee and Chesher 1986, Journal of Econometrics, Specification testing when score test statistics are identically zero) , it is shown that, if the selection equation only includes an intercept term, there can be some irregular phenomenon, but the MLE is still consistent.

Thanks again!

RE: Only intercept term but no other variables in the selection function? [ Reply ]
By: Arne Henningsen on 2015-12-10 14:34

[forum:42781]

Dear Fei Jin

You can specify a model with just an intercept with using "1" as explanatory variable, e.g.:

R> selection( lfp ~ 1, wage ~ exper, Mroz87 )

However, you get an error message and a warning message:

Error in solve.default(crossprod(xMat)) :
system is computationally singular: reciprocal condition number = 9.88532e-18
In addition: Warning message:
In heckit2fit(selection, outcome, data = data, print.level = print.level, :
Inverse Mills Ratio is (virtually) collinear to the rest of the explanatory variables

If you do not have any (varying) explanatory variables in the selection equation, the Inverse Mill's Ratio is the same for all observations, e.g.:

R> pr <- probit( lfp ~ 1, data = Mroz87 )
R> range(invMillsRatio(pr)[,1])
[1] 0.6915378 0.6915378

Hence, you have perfect multicollinearity in the outcome equation.

In any case, it is recommended to have at least one "exclusion restriction" (an explanatory variable in the selection equation that is not used as explanatory variable in the outcome equation; sometimes called "instrumental variable") so that the identification of the parameters is not only based on the assumptions about the functional form and the distribution of the error terms.

Best regards,
Arne

Only intercept term but no other variables in the selection function? [ Reply ]
By: Fei Jin on 2015-12-10 14:13

[forum:42780]

Hi all,
I am using the sampleSelection package for the ML estimation of the standard sample selection model (Tobit 2). Can I only include an intercept term but no other variables in the selection function. For example, on p. 31 in the document, we have the code:

data( Mroz87 )
Mroz87$kids <- ( Mroz87$kids5 + Mroz87$kids618 > 0 )
# ML estimation
summary( selection( lfp ~ age + I( age^2 ) + faminc + kids + educ,
wage ~ exper + I( exper^2 ) + educ + city, Mroz87 ) )

In the selection equation, we have the variables: age, I(age^2), faminc, kids, educ. In addition, an intercept term is added to the equation automatically. Is it possible to include only an intercept in the selection equation? It is something like

summary( selection( lfp ~ z,
wage ~ exper + I( exper^2 ) + educ + city, Mroz87 ) )

where z is a column of ones. However, this will lead to perfect collinearity because another intercept term will be added automatically.

Thanks!