# Time varying volatility and expectations

I have a model with oil which includes a stream of income, and so a present value price that looks like:

``````PV = param1 * bETA * oilprice(+1)+param2 * bETA^2 * oilprice(+2) … (+100).
``````

When I use the following specs for the oil price (as in Plante and Traum (2012)),…

``````Log(P/P_ss) = rHO * Log(P(-1)/P_ss) + **exp(eTA)** * ePSILON_OIL

**eTA** = (1-nU) * eTA_BAR + nU * **eTA(-1)** + ePSILON_ETA
``````

(With eTA_BAR = -4.7006, P_ss=0.1394, nU=0.9, starting value for eTA=-4.7006, eTA upon shock = -0.25)

…then when shocking the oil price volatility variable eTA (at the stochastic steady state), the PV variable declines as expected, but manufacturing output, capital investment and consumption rise.

When instead I use the following specs (as in Baskaya et al (2013))…

``````Log(P/P_ss) = rHO * Log(P(-1)/P_ss) + **eTA** * ePSILON_OIL

**Log(eTA)** = (1-nU) * eTA_BAR + nU * **Log(eTA(-1))** + ePSILON_ETA
``````

(With eTA_BAR=-4.7006, P_ss=0.1394, nU=0.9, starting value for eTA=0.0091, eTA upon shock=0.7788)

…then when shocking the oil price volatility variable, manufacturing output, capital investment and consumption decline as expected, but the PV variable rises…

Could someone explain why this is happening? I am using Dynare 5.4.

Which order of approximation are you using? And what type of IRFs are you using?