I am working on a paper where I have to model the long run relationship between earnings and dividends. I have downloaded the raw data from shillers website. I have converted the series to log(dividend) and log(earnings), and tested for stationarity in both variables. Both are non stationary before differencing once. The result from the test of cointegration between the variables conclude that they are cointegrated. Studying the raw data (levels without log), both variables have an exponential growth, but after using log there is a linear relationship. I have run a regression with both log and levels but I do not understand which of the models that are correct when describing the long run relationship between the variables.
Log(dividend) = a + b(log(earnings)) + u --> -0.44 + 0.88(log(earnings))
Dividend = a + bEarnings + u --> 0.87 + 0.35Earnings
From the book I am using it is stated that i do not need to work with stationary variables when modelling the long run relationship between two cointegrated variables, and that cointegration allows me to use levels (where the variables separately are non stationary). But when both variables possess an exponential growth, am I supposed to use equation 1 or 2? And Why choose one model over the other one? Also is there a problem with omitted variable bias when modelling the long run relationship between two cointegrating variables?