|Figure 5 in Caliendo, et al. (change is 2002-2007)|
Click for larger image
From a new paper by Caliendo, Parro, Rossi-Hansberg, and Sarte:
We develop a quantitative model of the U.S. economy broken down by regions and sectors. In each sector and region, there are two factors of production, labor and a composite factor comprising land and structures. . . . Labor is allowed to move across both regions and sectors. Land and structures can be used by any sector but are fixed locally. Sectors are interconnected by way of input-output linkages but, in contrast to Long and Plosser (1983) and its ensuing literature, shipping materials to sectors located in other regions is costly in a way that varies with distance. . . . We calibrate the model and explore the regional, sectoral, and aggregate effects of disaggregated productivity changes. Specifically, for a given productivity change located within a particular sector and region, the model delivers the effects of this change on all sectors and regions in the economy. (2)
Here we can think about the elasticity of GDP (or TFP, or welfare) to things happening in specific regions and/or sectors, accounting for flows of labor, intermediate goods, and final goods across regions. This reminded me of Gabaix 2011, which finds:
In the granular view, idiosyncratic shocks to large firms have the potential to generate nontrivial aggregate shocks that affect GDP, and via general equilibrium, all firms. . . The idiosyncratic shocks to the top 100 firms in the United States can explain one-third of the fluctuations of GDP. (735, 736)
Gabaix's approach to heterogeneity was all about firms; Caliendo, et al. look at sectors and regions. This is a static model with two factors (capital/structures and labor). Labor is costlessly mobile. There is a rich interregional trade and input/output structure. The paper is worth looking at for the charts alone, which include GDP and GDP growth by region, geographic concentration of sectors, sectoral productivity by region, and others. Take a look.
The authors have a lot of interesting results. "We find that disaggregated productivity changes can have dramatically different implications depending on the regions and sectors affected" (2), in part because of these fixed factors of production that are durable. "A productivity change of the same national magnitude in California increases national output 46% more than in Florida" (27). They can "infer the regional distribution of income from land and structures across U.S. states" (8). And there's this:
We find that eliminating U.S. regional trading costs associated with distance would result in aggregate TFP gains of approximately 50 percent, and in aggregate GDP gains on the order of 126 percent. These figures are evidently significant, and may be interpreted as upper bounds on the extent to which advances in shipping and other transportation technology can eventually contribute to productivity and value added.
I wonder what 3D printers will do.
This regional stuff is really important. In the past I've looked a bit at startup activity by region (, ). I thoroughly enjoyed Moretti's book on the geography of jobs (that's a quick and easy read, by the way). Thinking about transportation, regions, and sectors may help us move toward a formal theory of the Leamer business cycle model ("supply-chain bull whip", etc.). The authors mention a large relevant literature, another reminder that the macro field likes to think about heterogeneity (and the derivative is positive).