Autocorrelation parameter of AR(1) exogenous shocks

My understanding is that when a variable is declared as an exogenous shock, Dynare assumes that it is mean-zero iid with normal distribution, and in the shock block, shock covariance matrix is set. Given that almost always exogenous shocks follow an AR(1) process, would it be possible to specify the autocorrelation parameter of the shock? I can see that the standard way is to write the AR(1) process as one of the equations of the model, but the above suggestion makes it possible to see the policy functions evaluated by Dynare directly in terms of exogenous state variables, which is especially useful in higher (2nd or 3rd) order approximations.


neo1.mod (596 Bytes)
For instance in the above mod file, z is defined as an endogenous variable whereas it is in effect an AR(1) exogenous variable. The Dynare output for policy functions is in terms of epsz rather than z.

                                   c               k               z
Constant                    0.388069        0.188300               0
k(-1)                       0.680101        0.330000               0
z(-1)                       0.368666        0.178885        0.950000
epsz                        0.388069        0.188300        1.000000
k(-1),k(-1)                -1.209954       -0.587096               0
z(-1),k(-1)                 0.646096        0.313500               0
z(-1),z(-1)                 0.175116        0.084970               0
epsz,epsz                   0.194034        0.094150               0
k(-1),epsz                  0.680101        0.330000               0
z(-1),epsz                  0.368666        0.178885               0

No, that is not possible. Dynare has adopted this particular way of conceptualizing shocks as it is very general. This comes with the downside that there may be special cases that can be handled easier.


I have a similar problem. I am wondering if it is possible to treat my AR(1) exogenous shocks as “shocks” instead of “variables”, so that Dynare can compute the impulse response functions to those shocks?

For example, for now I have z=0.6*z(-1)+0.4ez, where ez is a iid shock. Dynare computes impulse response to ez instead of response to z. Is there a way to compute IRF to z?


As discussed above that is not possible. But I also do not understand what you mean with

Thanks for the quick reply.

I meant impulse response of other variables like y (output per capita), H (labor hours) to z (productivity shock, which is AR(1)). Currently I have IRF of those to ez (the volatility component).

I think you are confusing something. ez is not the volatility component, but the regular shock.

Yes, I confused about it. But you are right. In the way I model it, ez can be regarded as the shock.


I also have a very basic question regarding the autocorrelation parameter of AR(1) exogenous shock. Is it a norm to use a positive autocorrelation parameter of AR(1) exogenous shock. I have hardly seen any study using a negative coefficient (it may be a lacking on my part). While dealing with data we come across oscillatory patterns also. If estimated AR(1) coefficient (s) turn out to be negative, should we ignore the sign or calibrate it with negative sign?




It is usual practice to restrict autoregressive parameters to be positive because otherwise the variable is oscillatory (flipping sign in each consecutive period). So unless we believe the variable has this kind of behaviour, we do not consider negative values.

You might be more interested in having a cyclical behaviour (which is not the same than an oscillating pattern). If you want to have cycles in the (exogenous) TFP, for instance, you should increase the number of lags in the autoregressive process and choose a calibration (for the autoregressive parameters) such that the roots of the lag polynomial are complex.


Thank you for your reply. I hope you would spare some more time to consider the issue I am facing. Precisely, I estimated fiscal policy rule of automatic stabilization type just to have some idea about parameters. I got the unobserved series after estimation which is fiscal policy shock (government spending shock). The autocorrelation parameter of this AR(1) shock appeared negative. I used data for Pakistan. When I incorporated this parameter with negative sign, response of output to almost all shocks showed oscillatory pattern. So should I explore the reason to justify it or to use the parameter calibrated in previous studies.

Thanks in a advance


This is strange and usually indicates a problem with estimation. Are your observation equations correct and was the data seasonally adjusted?

Thanks for your reply and sorry for delayed response. I did estimation of fiscal rule outside Dynare /DSGE on annual data as for Pakistan quarterly data is not available.