I am reading a article, whose title is Paywalls and the Demand for News (L Chiou ， C Tucker, 2013 ).
In it's chapter of Empirical Analysis, we can find two equations. In this chapter, the authors want to discuss how the adoption of paywalls affected visits to the paywall sites.
Equation 1 is a regression
Equation 2 is about the "ratio-of -ratios"
According to the authors, equation 2 offers a natural interpretation for the estimated coefficients in equation 1.
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Here are my quesitons:
1. What is the relationship between equation 1 and 2? Why do they both show in the paper? Can I understand that equation 2 is just an other way to explain the β1 in regression?
2. Although I can understand equation 1 as a regression, but I don't really know how does it works.
3. Why equation 2 equals to exp(β1)？I mean why “exp” exists?
Thank you!
(The paper has been atteched both in the link and the file)
http://sites.oxy.edu/lchiou/papers/chiou%20and%20tucker%20paywalls.pdf
Equation (1) is
log(visitsit + 1) = b0 + b1Postt x Paywalli + ai +gt + eit . Post and Paywall are indicator variable of possible values 0 and 1. Visitsit can be zero. Since log0 is not defined, 1 is added to visitsit as the log argument to validate the logarithm even if visitsit is zero. I believe that equation (2) is a particular case of equation (1). The inverse function to logarithm is the exponential function. Equation (1) may be inversely expressed as
visitsit + 1 = exp[b0 + b1Postt x Paywalli + ai + gt + eit].
If b0=0 and Postt = 1 and Paywall=1, ai = 0 = gt, equation (2) results from equation (1). Since eit is the error term its expectation E(eit)=0. I hope my explanation is helpful.
Dear Etuk
Your interpretation is really illuminating.
Thank you so much!
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