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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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