Hello everyone,
I have a question regarding estimated dependent variable regressions.
I have two regression stages where I use estimated coefficients from the first stage as dependent variables in the second. More precisely, I estimated a wage regression on the individual level in the first stage including firm fixed effects. These fixed effetcs estimates are used in the second stage as dependent variable. The fixed effect estimates are in the second stage regressed on firm level characteristics.
As you probably know, using estimated values from a previous stage as a dependent variable in a second stage introduces biased standard errors because the second step ignores the estimaton error from the first stage. I would like to ask about the most effective way to remedy this problem.
I have already read about WLS and FGLS as the best estimation approaches, but I'm not sure how to implement it in Stata.
Lewis and Linzer (2005) (http://www.sscnet.ucla.edu/polisci/f...ewisLinzer.pdf) argue to use an FGLS estimator which uses the variance-covariance matrix from the standard errors of the first stage to generate a weight, which can be used to adjust the second stage regression (basically a weighted least squares regression with country-time specific weights). The weights (adjusted for a panel dimension) are calculated as follows:
wi,t = 1 / [sqrt(se_DependVariablei,t + SigmaHati,t)]
where se_DependVariablei,t are the standard errors of the dependent variable from the first stage and SigmaHati,t is an estimate for the variance of the error term in the second stage that is not due to the sampling error of the dependent variable. This sounds reasonable to me and I have seen some papers claiming that they use this adjustment. However, is there a Stata command which does this adjustment automatically or do the weights have to be calculated step by step? If there is no command, can someone provide a code how to do it?
So, to sum up my questions:
1) Do you know of a method that fixes the two-stage-error most efficiently? If there is an established way to solve this problem (maybe with a ready Stata command) I would be most happy to know about it!
2) Do you think FGLS will suffice? And do you know of a Stata command that implements the Lewis, Linzer weights?
3) Is there a ready WLS code?
Any help is greatly appreciated!
Best, Julia
I have a question regarding estimated dependent variable regressions.
I have two regression stages where I use estimated coefficients from the first stage as dependent variables in the second. More precisely, I estimated a wage regression on the individual level in the first stage including firm fixed effects. These fixed effetcs estimates are used in the second stage as dependent variable. The fixed effect estimates are in the second stage regressed on firm level characteristics.
As you probably know, using estimated values from a previous stage as a dependent variable in a second stage introduces biased standard errors because the second step ignores the estimaton error from the first stage. I would like to ask about the most effective way to remedy this problem.
I have already read about WLS and FGLS as the best estimation approaches, but I'm not sure how to implement it in Stata.
Lewis and Linzer (2005) (http://www.sscnet.ucla.edu/polisci/f...ewisLinzer.pdf) argue to use an FGLS estimator which uses the variance-covariance matrix from the standard errors of the first stage to generate a weight, which can be used to adjust the second stage regression (basically a weighted least squares regression with country-time specific weights). The weights (adjusted for a panel dimension) are calculated as follows:
wi,t = 1 / [sqrt(se_DependVariablei,t + SigmaHati,t)]
where se_DependVariablei,t are the standard errors of the dependent variable from the first stage and SigmaHati,t is an estimate for the variance of the error term in the second stage that is not due to the sampling error of the dependent variable. This sounds reasonable to me and I have seen some papers claiming that they use this adjustment. However, is there a Stata command which does this adjustment automatically or do the weights have to be calculated step by step? If there is no command, can someone provide a code how to do it?
So, to sum up my questions:
1) Do you know of a method that fixes the two-stage-error most efficiently? If there is an established way to solve this problem (maybe with a ready Stata command) I would be most happy to know about it!
2) Do you think FGLS will suffice? And do you know of a Stata command that implements the Lewis, Linzer weights?
3) Is there a ready WLS code?
Any help is greatly appreciated!
Best, Julia
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