# 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

• HI: You should write out the model unless those papers are directly available on the net. Based on the journal, my guess is that they aren't. Also, given what you said, it sounds like you may have a non-stationary series so doing what you're doing as a fix wouldn't be a good idea. – mark leeds Jun 28 at 16:00
• Hi, I believe the mentioned articles are freely available on google scholar. As for your other comment; the AR(1) coefficients are all below 1, so the process is not explosive I believe. However, the almost-1 coefficients make the ratios to volatile. – Niek de Meijier Jun 28 at 18:21
• @Nike de Meikiet: I don't have time to look now ( I don't even know what the dynamic Gordon model is but it seems pretty well known ) but you should be careful of even almost 1.0. That could indicate unit root which has repercussions as far as modelling. Hopefully someone else can say more. – mark leeds Jun 28 at 21:12
• here are links for those interested. ideas.repec.org/p/ams/ndfwpp/05-12.html AND THE OTHER ONE papers.tinbergen.nl/15088.pdf – mark leeds Jun 28 at 21:18
• How are you computing the likelihood of the coefficient? If you are doing it correctly you shouldn't get explosive estimates. – Freelunch Jun 30 at 10:39