WWP: Development in spaaaaace (and tiiiiiiime)

I've been reading a lot recently, but very little of it is brand-new-not-yet-published research! So I was a little bit at a loss for what to highlight in this week's WWP. But then I remembered that I was at this awesome conference last week, and saw a bunch of great papers, so I'm going to highlight one of them. 

Integrating geography into trade models in a realistic way is a fairly new development. That's because it's hard to do - trade models are usually large and complicated, because they're built on micro-foundations. This is important, because it helps us believe the models and makes them less black box-like, which in turn contributes to trade being one of the few fields where the models can be taken very seriously, but the econometrics can too (since trade economists often derive estimating equations straight from the big micro-founded model, and then think carefully about causal inference when actually running the implied regressions).

Of course, in order to get a model that includes a complicated general equilibrium system to be solvable (either analytically, or more commonly, numerically given the computing power available to us), we often need to make simplifying assumptions. One of the assumptions that is often made is that we can write down the matrix of distances between every two regions or countries in the economy, but we don't have to think about the locations of those regions in two dimensions.

Ok, these are plants in space. That was the best I could do!

Ok, these are plants in space. That was the best I could do!

Another important piece of how these models work is that they're almost always static. That is, we don't have to worry about dynamics and growth and development - the economy exists wholly within one period, and each model has a static equilibrium (99% of the time there's a hairy proof showing how that equilibrium both exists and is unique. Yay GE!)

These assumptions are really important for us to be able to actually make progress - but it's also understood that they can be problematic when we want to think about how, for example, locational amenities endogenously influence growth over time. There are important questions that these trade models can't answer, because they're not set up to do so (for good reason).

Enter Desmet, Nagy, and Rossi-Hansberg. In a new working paper, these guys cleverly introduce both geography and dynamics to a trade model that's built off of some of the same technology as Eaton and Kortum (2002).  The really cool thing is that the geographic units in their model  are 1 degree x 1 degree pixels - really small compared to countries or states! In their abstract, they describe their work:

We study the relationship between geography and growth. To do so, we first develop a dynamic spatial growth theory with realistic geography. We characterize the model and its balanced growth path and propose a methodology to analyze equilibria with different levels of migration frictions. We bring the model to the data for the whole world economy at a 1 degree x 1 degree geographic resolution. We then use the model to quantify the gains from relaxing migration restrictions as well as to describe the evolution of the distribution of economic activity in the different migration scenarios. Our results indicate that fully liberalizing migration would increase welfare more than three-fold and would significantly affect the evolution of particular regions in the world. We then use the model to study the effect of a spatial shock. We focus on the example of a rise in the sea level and find
that coastal flooding can have an important impact on welfare by changing the geographic-dynamic path of the world economy.
A figure from the paper. The blue line floods 6m of the global coastline with current migration restrictions, and the red and green are with less and less restricted movement. Interesting to note: in the current scenario, flooding actually helps us - this is because when regions are flooded, people have to move, which then increases agglomeration spillovers. In the free-mobility versions, when regions are flooded, we lose out (as we might expect). This type of effect is only estimable in a model like this. 

A figure from the paper. The blue line floods 6m of the global coastline with current migration restrictions, and the red and green are with less and less restricted movement. Interesting to note: in the current scenario, flooding actually helps us - this is because when regions are flooded, people have to move, which then increases agglomeration spillovers. In the free-mobility versions, when regions are flooded, we lose out (as we might expect). This type of effect is only estimable in a model like this. 

Are my super-reduced-form friends going to love this paper? Maybe not. There's no big randomized experiment to establish causality here. But what I really like about this is that these guys develop some cool machinery to think about both space and growth - which in turn can let us think about the long-run effects of things like climate change (flooding is the climatic example used in this paper) or migration restrictions, which have explicitly spatial components, and also to think about how short-run shocks might play out in the long run when the economy makes investments in some places and not others. 

This isn't necessarily a paper for the faint of heart - as with all modern trade papers, the machinery is pretty big and complicated - but I'd urge you to take a look. It's clever and interesting.