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st: endogenous switching regression


From   "fmodena" <fmodena@economia.unitn.it>
To   <statalist@hsphsun2.harvard.edu>
Subject   st: endogenous switching regression
Date   Mon, 15 Oct 2007 11:54:59 +0200

Dear all,

I repost my question from Mon Oct 08.

The regression I want to estimate is the following:
Y = b0 + b1X1 + b2CL*X2 + b3LS*X2 + u	(1)

Where Y is the household income, CL is a dummy equals to 1 if the household had a crop loss and it is interacted with X2 (the value of farm assets), LS is a dummy equals to 1 if the household responded with the labor supply to the crop loss. LS is interacted with the continuous variable X2 (farm assets). Note that LS=0 if CL=0.

The labour supply response to a crop loss may be endogenous in the income equation (least squares estimation of (1) may lead to biased estimates of the parameter). To solve this problem, I followed the procedure proposed by Cameron and Worswick (1999) ("The labor market as a smoothing device: labor supply responses to crop loss in Indonesia". The paper is published on the Review of Development Economics (2003), but the previous version to which I refer provides a more detail description of the switching regression). The authors employ a switching regression model with endogenous switching. This method involves a two stage procedure:

1)	estimate a probit equation with the dummy LS as dependent variable (using the sub-sample for which CL=1). Calculate the two selection terms (inverse Mill's ratio) for labor supply respondents (LS=1) and non labor supply respondents (LS=0)

2)	the two selection terms are included into the income equation (using the entire sample), so that equations (1) becomes:

Y = a0 + a1X1 + a2CL*X2 + a3LS*X2 + a4(LS*first selection term) + a5(CL*(1-LS)*second selection term) + u	(2)

Equation (2) is estimated by OLS

I am not completely satisfied by that procedure (the two selection terms seem not able to capture the endogeneity of LS in the income equation). I am also wondering weather the movestay command could help me (instead of using the two stage approach). 
Nicola suggests me to use -ivreg- and search in Statalist archivers for how to deal with interacted endogenous variables (see the reply to my first question from Oct 14).


What do you think about these procedures? 
Francesca 





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