A reader emails me:
When doing econometrics on quarterly time series data, if there are some key variables that are available only annually, is there merit in interpolating the annual data to create a quarterly series or should the variables be discarded? What is the general advice on interpolation?
As a general rule, you should not discard the annual data. As with any econometric problem, the question is: do the additional data contain potentially useful information? If the answer is yes, then the next step is to find the best way to disaggregate the annual observations into quarterly ones.
There are many ways to do this, and the most appropriate one will depend on the problem at hand. Also, keep in mind that determining the appropriate standard errors for your included variables, especially the disaggregated ones, can be a bit tricky in this setting.
Here are some relevant papers (only the first free access)
Also keep in mind that, depending on the problem you are facing, it may even make sense to aggregate variables – e.g. making annual variables out of quarterly ones. Yes, you shed information in that case, but an even more critical question to ask is whether your assumptions are satisfied (usually E(u|X)=0). In many cases, you would have reason to expect the error to be correlated with your dependent variables in a ‘quarterly’ model but not in an ‘annual’ model, in which case it would be most probably preferable to use the latter.