Prediction adjustment factor for panel model with natural logged dependent variables

[Wayne Day]

Hi. I've been trying to find documentation of some sort on adjusting predicted values from a panel model with natural logged dependent variables. I haven't found anything confirming or rejecting to do such an adjustment. In Wooldridge's Introduction to Econometrics book, he says that when a model has a logged dependent variable, simply exponentiation the prediction (which would be in log form) will systematically underestimate the expected value of the dependent variable. This discussion is in the cross-sectional OLS case. He then goes on to discuss 2 or 3 methods on how to derive an adjustment factor, and that factor is greater than 1 because of the systematic underestimation.

In Wooldridge, the basic adjustment procedure is to:

1. estimate the model with logged dependent variable
2. predict the predicted/expected value of the dependent variable
3. exponentiate the predicted/expected value since it is in logged form
4. multiply the exponentiated value by the adjustment factor since it is systematically underestimated.

The issue is that I haven't found any discussion of this adjustment for the panel model case. I have a panel model with 8 years of data, the dependent variable is logged, and random effects are used.

Can anyone say with certainty that you need to or do not need to adjust the predicted values for panel models with logged dependent variables? And what would the procedure be for a panel model with random effects? The STATA code that I'm using to estimate the model is:

xtreg ln_dvar i.year ivar#i.year, re

where,

• xtreg is the command for panel model regression
• ln_dvar is the natural logged continuous dependent variable
• i.year is a indicator (dummy) variable for year, there are 8 years of data
• ivar is the independent variable(s)
• re for random effects at the observation level