A bit of philosophizing in this post — if that’s not for you, avert your eyes!
A theory is always about something that you think is going on in the world, so you can’t have something to theorize about without first seeing something happen in the world (i.e. data). For example, suppose my theory – which I deduced from some sort of a priori assumptions – is that watching Charlie Kaufman movies ruins one’s sex life. I couldn’t have made that theory without observing the existence of Charlie Kaufman movies.
Hmm. I see Noah’s point: generally our economic theory has some grounding in reality — economists don’t usually theorize about flying purple elephants (though I’ve read set-theory questions that do make claims about flying purple elephants; I’ll spare you). But Noah is kind of stretching the definition of data as it is applied in economics. Sure, that Charlie Kaufman movies exist is technically a piece of data that we observe, but it is not data that we have collected for the purpose of analysis.
One can theorize plenty without that kind of data. I could very easily make up an industrial organization model without having any prior data (this would be easier to make up without data than making up a model of the macroeconomy, about which I have bits of data floating around in my head). And technically, I suppose it would be based on data I’ve seen in my work life and the bit of facts I’ve collected through the years. But it most certainly would not be based on datasets collected by economists or statisticians. In other words, I could build a perfectly functioning model without any more than the bits of facts I’ve collected in my head.
And, technically, if I wanted to push the envelope a bit, I could come up with an economic model about things I have never observed, things that I just made up in my head. That is, I could make a theory without data. Say, for instance, I was interested in the flying purple elephants I mentioned earlier because, while I have never seen one myself, I believe they exist. I could make a well-functioning model that describes how they choose between labor and leisure. Now there’s a model with no data at its foundation.
So, contra Noah, I would say than you can theorize without data, though it’s probably not a common practice in economics because even the pure-theory papers are usually based on at least a little bit of data.