Cointegration with dummy variables? Let's say I'm interested in the relationship between poverty (measured by some continuous variable) and different types of financial reforms (which are dummies). 
Given this does it make sense to consider that the variables (given their different types - continuous, dummies) could be cointegrated? 
 A: No. 
In order to consider meaningfully the possibility of co-integration, it must be the case that the variables are not stationary, but that a linear combination of them is stationary. So poverty should be non-stationary, and let's say that the realization of the stochastic process that represents "poverty", does exhibit the signs of a non-stationary process (in the mean and/or in the covariance level).
But, can you model the dummies as random variables? If the financial reforms they represent have taken place, and are not considered likely to be implemented again, then these dummy variables are deterministic. I presume they are $0/1$ binary variables. Then they will take the value $1$ for the specific period(s) during which the reforms were active -but can you really argue that the proportion of $1$'s in the sample is an estimator of some underlying probability of the same reforms occurring again at any given future time period?
If you cannot make that argument, then linearly combining these deterministic dummies with the non-statitonary poverty-process, won't give you a stationary process: in the linear combination, the (possibly time-variant) variance of poverty may be scaled but it will remain time-variant, and its possibly time-variant mean may shift, but it will remain time-variant.  
But assume now that you can argue that the dummies are bona fide Bernoulli random variables. If they are assumed i.i.d., by construction they form a strictly stationary and covariance stationary process. This means that they do not posses a non-stationary element that "offsets" the non-stationary aspects of the poverty process (which is what co-integration is all about, in an informal sense). So again, co-integration will not exist.  
Of course, the usual route here is to attempt to make the poverty-process stationary (by e.g. differencing), and then construct and estimate your model.
