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I have dummy variables (DV) which measure policy reforms (e.g. Independence of the judiciary, barriers-to-entry in a market etc.). These can be either “0,1” or, say, “0,1,2,….. upper”.

Say I have a VAR or VECM with these dummies in them. Two problems follow:

  1. Is it legitimate to do impulse responses on dummies? They are after all categorical variables, bound on a given interval. Does a temporary shock to a DV even make sense (=> a policy maker implements a reform, then withdraws it??). And if only permanent reforms make sense, how do you model agents’ learning of the reform since presumably you need to shock the dummy down in each period.

  2. The policy reforms on which the dummies are predicated aren’t exogenous events. They can reflect past poor economic performance, electoral changes etc. And yet the dummies (taken from external databases) are notionally considered exogenous.

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  • $\begingroup$ Regarding 2., you could either ignore the dummies being endogenous and assume they are exogenous, or you could endogenise the dummies by including equations describing how the dummies are determined. That could be a logit or probit equation for each "0,1" dummy. Also, regarding dummies with levels "0,1,2,...,upper", how do you include those in the model? If you enter them as simple regressors, then they will also work as simple regressors where larger values mean stronger/more intensive effects. If the increasing values mean different situations but not intensity, you should reconsider that. $\endgroup$ – Richard Hardy Mar 16 '15 at 19:53
  • $\begingroup$ Regarding 1., it would make sense to look at impulse responses where the impulses are like the actual impulses that you normally observe. If you have a regime change and a corresponding dummy with values 0,0,...,0,1,1,...,1, it would not make much sense to look at an impulse response where the impulse is 1,0,0,...,0 because that is not what you care about; the actual impulse is 1,1,...,1. I would try to stick to situations that I care about rather than some unrealistic cases that would not happen in reality. But that is just my gut feeling; I do not have much experience with such problems. $\endgroup$ – Richard Hardy Mar 16 '15 at 19:57
  • $\begingroup$ Thanks Richard. Indeed I considered Probit, but I wanted to see if there were any other ideas out there. The 0, .. upper thing was just reflecting that some indexes have coded upper bounds like 0, ... 10, but they're still categorical variables. One other interesting feature is that once reforms are implemented (for example a public utility is privatized) it's not likely that they're reversed. So it seems that these are not just dummy variables but somehow truncated. On 2) the permanent IRF is better but again I just wonder permanent dummy IRFS have been done in the literature. $\endgroup$ – user71264 Mar 16 '15 at 20:17
  • $\begingroup$ If they are categorical, including such variables could bring trouble. As I said, the categories will be interpreted as intensities if your variable will have levels like 0,1,...,10. What you could do is have 10-1=9 dummies. This is much like dummy variables for seasonal periods. When you have 12 months, you do not have a variable with levels 1,...,11 but rather you have 11 dummies. $\endgroup$ – Richard Hardy Mar 16 '15 at 20:20
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If the policy dummies were exogenous you could use a VAR-X model and do dynamic multiplier analysis (see Lutkepohl 2005 Chp. 10). But since you are sure that the dummy variable is endogenous you might take a look at the Qual-VAR model due to Dueker JBES 2005, which essentially includes a dynamic probit equation in a standard VAR model. His application is to forecasting, but I don't see a reason why you could not do IRFs as well, as in a standard VAR. You'll have no choice but to do a Bayesian estimation via MCMC as Dueker does. Dueker and others have follow up papers on the Qual-VAR model.

Hope this helps!

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