Choosing Levels or Logarithms for Cointegrated Dividends and Earnings

Summary

The document describes an empirical question about the long-run relationship between dividends and earnings. Both series are reported as nonstationary before first differencing, while a cointegration test indicates a shared long-run relation. The researcher compares a linear regression in levels with a log-log regression and asks which specification is appropriate given the series' exponential growth and the possibility of omitted-variable bias.

The text provides the data context and competing model forms, but it contains no answer or supporting analysis. It does not report the stationarity or cointegration test details, sample period, diagnostics, or evidence comparing the specifications. Consequently, it cannot establish whether the level or log relationship is preferable, whether the estimated cointegrating relation is robust, or whether omitted variables distort the interpretation. It is useful as a framing of model-selection issues in time-series research, rather than as a resolved method or finding. Researchers would need additional economic justification and diagnostics to make that choice.

Key ideas

• The researcher reports nonstationary dividend and earnings series that appear cointegrated.
• The question compares a levels regression with a log-log specification.
• Exponential growth in the raw series motivates examining a linear relation in logarithms.
• The document raises omitted-variable bias but supplies no analysis or conclusion on it.
• Model choice and cointegration robustness remain unresolved in the source.

Tags

# Modelling long run relationship between dividend and earnings


# Modelling long run relationship between dividend and earnings












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?

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.