I am modeling stock exchange according to the present value model as defined by Gregory Chow in this paper. Model operates on natural logarithms of stock prices and dividends in order to "eliminate the effect of the arbitrary number of shares issued". But the companies do not always pay dividends. What should I do when there is a one-year gap in payments? As for now logarithm makes it explode to infinity.

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    $\begingroup$ The model refers to the expectation of the dividends rather than the dividends themselves. Thus, a zero dividend should not cause any problems. $\endgroup$ – whuber Sep 17 '12 at 1:12
  • $\begingroup$ @whuber I want to estimate such model through nonlinear least squares. Indeed it is a problem that one of the variables takes minus infinity as a value. $\endgroup$ – infoholic_anonymous Sep 17 '12 at 11:14
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    $\begingroup$ That demonstrates that your fitting method is not appropriate for this model. You should be thinking in terms of changing your method rather than fiddling with the data to make an inappropriate method yield some kind of answer. $\endgroup$ – whuber Sep 17 '12 at 13:58
  • $\begingroup$ @whuber You seem to be right but I can't help thinking that G. Chow being such an authority must have known what he was doing. Or is the present value model already vintage? Maybe someone could suggest any alteration to it that would solve the problem? $\endgroup$ – infoholic_anonymous Sep 17 '12 at 17:49
  • $\begingroup$ I think you misread that paper. The model is not for the logarithms; it's for the prices themselves: see equation (2). $\endgroup$ – whuber Sep 17 '12 at 17:54

Although this is not something I would favor, sometime when an analyst wants to do a log transformation of a variable Y but Y can take on values greater than or equal to 0, they modify the transformation to be Y=log(X+a) wher a is some small positive constant. Then the minimum value is log(a) rather than negative infinity.

  • $\begingroup$ On what grounds am I to choose a? It seems that this has influence on the model itself. $\endgroup$ – infoholic_anonymous Sep 17 '12 at 0:45
  • $\begingroup$ Yes. I didn't say I would recommend it. But you are free to pick your transformation. It will have the shape of a log and the transformed values depend on the choice of a, of course. $\endgroup$ – Michael R. Chernick Sep 17 '12 at 1:04
  • $\begingroup$ What would you recommend then? $\endgroup$ – infoholic_anonymous Sep 17 '12 at 1:07
  • $\begingroup$ It doesn't matter. Take a=0.1. $\endgroup$ – Michael R. Chernick Sep 17 '12 at 1:13
  • $\begingroup$ My answer is an answer to the OPs question. The fatc that I don't recommend doing it doesn't make it an inappropriate answer. The approach does work and the choice of a only affects what the minimum value of Y can be. So it shouldn't matter for the analysis what value of a you choose. I picked 0.1 only because the OP asked for a choice. I think 0.1 is as good as any. Does anyone see something wrong in my answer that I don't see? $\endgroup$ – Michael R. Chernick Sep 17 '12 at 16:43

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