How AR(1) Persistence Changes Consumption Growth

Summary

The document asks how the persistence coefficient in an AR(1) model for consumption growth affects the process. It identifies a zero coefficient as the case where growth has no dependence on its previous value; if the innovations are independent and identically distributed, growth is then iid. A coefficient of one gives the process a unit root, so it is nonstationary.

The explanation is brief and gives no derivation, data, or discussion of intermediate coefficient values. The iid conclusion also depends on assumptions about the innovations: setting the autoregressive coefficient to zero alone does not ensure that the shocks are identically distributed or independent over time. The note is useful as a starting point for understanding persistence and stationarity, but it does not develop a consumption-based pricing model or its asset-pricing implications.

Key ideas

• With an AR(1) coefficient of zero, consumption growth does not depend on its lagged value.
• If the innovations are iid, zero autoregressive persistence makes consumption growth iid.
• A coefficient of one gives the process a unit root and makes it nonstationary.
• The coefficient alone does not establish that innovations are independent and identically distributed.

Tags

# Consumption Based Asset Pricing


# Consumption Based Asset Pricing












I am working on some consumption based asset pricing models. I am modelling consumption growth in several different ways. An obvious one is to model consumption growth as an AR(1) process:

$g_{t+1} = \phi_0 + \phi_1 g_t +\epsilon_{t+1 }$

Where $g_{t+1}$ is consumption growth. What are the implications of having $\phi_1=0$? What about $\phi_1=1$?

In which case is consumption growth iid?

## Answer by phdstudent (score 2, accepted)

https://quant.stackexchange.com/a/21089

After some careful thought, the answer is trivially simple, actually.

If $\phi_1=0$ then consumption growth is iid. If If $\phi_1=1$ then consumption growth is has a unit root and is not stationary, and so will be the model.

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