Question about understanding irfs in dynare

Stochastic simulations
4

To be more precise: it depends on how the variables in your model are measured. As @stepan-a says, Dynare conducts a linearization.

  1. If you for example have a nonlinear model and your model variable is simply the level of output, the IRF will measure the difference between the variable and its steady state (or its mean at higher order). This is the case with https://github.com/DynareTeam/dynare/blob/master/examples/example1.mod

  2. In contrast, if your model variable already measures percentages, you will get the percentage deviation from the steady state, because that is what the simple deviation from steady state measures in this case. This is for example the case when you entered an already log-linearized model where all variables are percentage deviations from trend.

  3. Now there are cases where in a nonlinear model you want percentage deviations from steady state instead of simple deviations. There are three ways to do this:

    1. Use the loglinear option. The downside is that all variables in the model will be log-linearized using a Jacobian transformation, leading to trouble if you have variables with 0 or negative steady states. See the example at https://github.com/DynareTeam/dynare/blob/master/tests/loglinear/example4_exp.mod
    2. Perform an exp()-substitution, i.e. put the variable you want to be in percentage deviations consistently in exp() and adjust the steady state accordingly. Thereby, Dynare will do a linearization with respect to a variable that is effectively the log of the original variable, leading to a log-linearization instead of a linearization. See Section “4.4 Linearization vs. Log-linearization” in Pfeifer(2013): “A Guide to Specifying Observation Equations for the Estimation of DSGE Models” and as an example https://github.com/DynareTeam/dynare/blob/master/tests/loglinear/example4_loglinear.mod
    3. You can simply append the logs of the variables that interest you as auxiliary variables to your nonlinear model and consider these variables, which then measure percentage deviations from trend. An example is DSGE_mod/RBC_baseline/RBC_baseline.mod at master · JohannesPfeifer/DSGE_mod · GitHub
      Starting with Dynare 6, the process can be automated using the var(log) syntax. var(log) y for example will create a variable LOG_y and the associated auxiliary equation.
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