re-transformation of logged DV give ridiculous value

[Vatana Chea]

Dear All,

I have a quick question. I am not sure what I did wrong here. After I run ivregress 2sls, I tried to re-transform the logged dependent variable using Duan's (1983) Smearing Estimate (using Stata user's written command "levpredict"), but the predicted value is ridiculously large. The mean of real value is around 177 while the mean of the predicted value was 4,465. I did try to do it manually, but it gave the same result. I also tried another method using exp(lny)*exp(0.5*rmse^2) , but mean of the predicted value is still ridiculously unbelievable ; more than 4000. But if I just exp(lny) without multiplying it by exp(u) , the mean of the predicted value is 217, which is close but I know it is not correct without taking into account the residual. But I think the problem is the residual. Mean of the exponentiated residual is 27.

Is there anything I may have done incorrectly? Any suggestion?

[John Mullahy]

How do the predictions perform if you estimate the reduced form of the model for ln(y) (e.g. using OLS) and then doing the retransformation? I think you will get different residuals for the reduced form than for 2SLS if you use the predict command after ivregress 2sls (which is what I assume you are doing).

I think this distinction is technically relevant since you are (presumably) trying to recover E[ y | something ] and if the "something" includes the endogenous RHS variable(s) then the computation of E[ y | something ] is more complicated than just using the standard retransformation approaches. But if you compute E[ y | exogenous variables ] (i.e. the reduced form) then the standard retransformation approaches should be applicable (although even then no guarantee that the predictions will be well behaved).

[Vatana Chea]

You assumed correctly. I try to predict the second stage ln(y) in which case the model includes the endogenous RHS variable, not the reduced form. Can you suggest something I can read to learn how to do it properly?

[Vatana Chea]

Actually I understand what happened. The residual is still heteroskedastic even if I transform the dependent variable. So what should I do now?

[John Mullahy]

This is a classic reference on heteroskedastic retransformation that may be useful:
https://www.sciencedirect.com/scienc...67629600000461

However it is not immediately evident that this approach (or others) is suitable when 2SLS residuals are used.

As this reference (https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2442231/) notes: "The properties of the smearing estimator in the presence of endogenous regressors are unknown."

[Vatana Chea]

thank you very much sir ^_^

[Joao Santos Silva]

Dear Vatana Chea,

Adding to the very useful comments that John made, I suggest you also consider estimating the model in its multiplicative form. The advantage of this is that you do not need to transform your dependent variable and therefore you do not have the re-transformation problem. Please check the command ivpoisson and the references in the help file. These estimators were designed for count data, but work fine when the dependent variable is continuous.

Best wishes,

Joao

[Vatana Chea]

Joao Santos Silva thank you very much for your suggestion. I will do it immediately.