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st: dependent var. that is a logged percentage

Subject   st: dependent var. that is a logged percentage
Date   Tue, 27 Feb 2007 11:02:27 +0100


Using ‘regress’, I have estimated a model in which the dependent variable is the natural log of a percentage (that is, I take ln of a variable that varies between 0 and 1, which represents market shares over different years). I have two questions:

1.	After fitting the model, I want to estimate the predicted values and convert back to a percentage by taking the antilog. It is my understanding that this introduces bias. How can I generate predicted values, expressed as percentages, that are not biased?

2.	Even if I am able to generate unbiased predictions, I suspect that when I sum them up, they will not add to one for each year in the data. Is there any logical way of imposing the restriction that the transformed predicted values sum to one? In a 1995 Econometrica article (63(4): 841-890), Berry, Levinsohn, and Pakes employ a “simulator for market shares” that has this property, but its unclear how to implement in Stata.

Any insights would be greatly appreciated.


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