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st: endogenous switching regression

From   "fmodena" <>
To   <>
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? 

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