Near-Unit AR(1) Estimates in a Dynamic Gordon Stock Valuation Model

Summary

The document raises a modeling problem in a dynamic Gordon framework where autoregressive coefficients govern changing price-dividend ratios. In the described application, estimated coefficients near one produce price-dividend ratios the author considers excessively volatile. The author reports applying an ad hoc proportional reduction to those estimates and asks for a more principled way to handle the issue.

The context is a heterogeneous dividend-expectations model applied to the COVID-19 crisis, with references to prior work on behavioral heterogeneity in stock prices. No proposed correction, diagnostic comparison, or empirical evidence for the adjustment is supplied, so the document does not establish that the reported fix is statistically justified. Its value is as a statement of an estimation and model-stability concern: any adjustment should be motivated and assessed against the model assumptions and data rather than selected solely because it makes valuations look more realistic.

Key ideas

• In a dynamic Gordon model, autoregressive coefficients affect the evolution of price-dividend ratios.
• Estimates close to one are reported to generate highly volatile ratios in the author's application.
• The author describes reducing each coefficient proportionally as a pragmatic but insufficiently justified fix.
• The document poses the methodological question without evaluating alternative estimators or validating the adjustment.

Tags

# Correcting high AR(1) coefficients in dynamic Gordon model


# Correcting high AR(1) coefficients in dynamic Gordon model












I have just finished my thesis on a heterogeneous dividend expectations model applied to the COVID-19 crisis. However after receiving some feedback there is one last issue I want to resolve. I'm using a dynamic Gordon model where estimated AR(1) coefficients (rho and tau) determine variable price-dividend ratios instead of one static value. See the references below for more information on this model.

The problem is that some of my estimated AR(1) coefficients are very high (close to 1) which results in very volatile and unrealistic price-dividend ratios. To pragmatically solve this issue I have corrected these high coefficients by subtracting 1/100 of themselves like this: $\rho_{new} = \rho_{old} - \frac{1}{100}\rho_{old}$.

This works very well (price-dividend ratios take on realistic values with only a small correction) but it is not very elegant and scientific. Therefore my supervisor asked me to look into this a bit more but I haven't been able to find any related literature on the problem. Does anyone know how to solve this issue in a more elegant way? Any tips and tricks are very welcome!

References:

Hommes, C., & Veld (2017). Booms, busts and behavioural heterogeneity in stock prices. Journal of Economic Dynamics and Control, 80, 101–124

Boswijk, H. P., Hommes, C. H., & Manzan, S. (2007). Behavioral heterogeneity in stock prices. Journal of Economic dynamics and control,31(6), 1938–1970, Appendix B1

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