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plans with exogenise

Topics: IRIS in General, Models
Apr 1, 2014 at 4:44 PM
Hi all,

I am a new Iris user. My colleague told me that the toolbox is useful especially when doing judgments (as we mostly do in policy institutions). I would like to know more about "endogenise" and "exogenise" functions. How exactly are solutions found when these plans are specified? More specifically, if I want to fix policy interest rate for a couple of period in a new Keynesian model and use exogenise function (by endogenising policy shock), does IRIS simply switch Taylor rule to the specified value for those specific periods? Do i have to use "anticipate, true" option to guarentee that this path of interest rates are known by the agents?

I hope these questions are clear and you can help me on this. Thanks
Apr 2, 2014 at 8:51 AM
For an introduction see this blog post:

By default all judgmental adjustments are anticipated. You can change this for particular shocks or change the default setting for all shocks (the 'anticipate' option controls the default: anticipated vs. not). IRIS essentially adds state variables for future realizations of shocks so that they enter agents' information sets. In the case of exogenise/endogenise with an interest rate path, IRIS would use an anticipated shock to the interest rate rule which enforces the desired deviation from the Taylor rule (as specified in your input database).

Hope this makes sense.

Apr 4, 2014 at 4:18 PM
Hi Mike,

Thanks for your response. As far as I understand from your response, IRIS does this similar to a news shock implementation. Right? However, the blog link confused me a bit. It says: "we re-write the system so that the shock temporarily occurs in the state-space vector on the left-hand side, while the variable becomes an exogenous thing and moves to right-hand side (yes, this is possible in both unanticipated and anticipated modes). " This statement made me to think that IRIS solves this using a perfect foresight approach. I would be grateful if you can make a clarification. Thanks!
Apr 4, 2014 at 5:21 PM

let's say your model only has one type of shocks (e.g. demand shocks or productivity shocks, or whatever). If any occurrence of such a shock is unexpected, then a forward-looking model can be converted to its state-space representation like this (leaving out constant terms, etc. for simplicty)

x(t) = T x(t-1) + R e(t).

However, if you want to include the effect of expected shocks (or, more correctly, shock expectations), you arrive at a more generalized form,

x(t) = T x(t-1) + R0 e(t) + R1 E[e(t+1)] + R2 E[e(t+2)] + ... + Rk E[e(t+k)] + ...

where E[e(t+k)] is what I expect today about the mean of the shock at a future date t+k. Of course, my expectations E[e(t+k)] do not need necessarily coincide with the actual realization of the shock e(t+k). Note also that all the matrices R0, R1, R2, ... follow from (can be computed from) the original unsolved model. People sometimes get confused about this, I always recommend to look into the original paper by Blanchard and Kahn (1980). They explicitly do and discuss this kind of forward expansion of the solution. For some strange reason, the ideas got forgotten and lost for most of the academia :)

Now you see that the model has become a system with x(t) on the LHS, and x(t-1), e(t) and all those expectations on the RHS, with a big matrix consisting of all those T, R0, R1, ... Rk, ... and their corresponding products in between. You stack the system for several periods x(t), x(t+1), x(t+2), etc. and you get basically a static system of equations, in which you can swap the endogeneity (i.e. things being on the LHS) and the exogeneity (i.e. things being on the RHS) to your liking...

Hope this helps. Let us know if something needs further clarification...