Must-Read: Dietz Vollrath: What Assumptions Matter for Growth Theory?
Must-Read: The extremely sharp Paul Romer sends us to the very patient and clever Dietz Vollrath. I am broadly with Paul Romer here: papers that do not clearly and succinctly explain (1) what they are doing, (2) why they are doing it, and (3) why the result is of interest to those of us who want to understand the world are wasting electrons, wasting photons, and wasting attention:
What Assumptions Matter for Growth Theory?: “Somewhere along I-40 and I-81 I was able to get a little clarity…:
…Non-rival inputs are things like ideas that can be used by many firms or people at once without limiting the use by others. Think of blueprints. Rival inputs are things that can only be used by one person or firm at a time. Think of nails. The income earned by both rival and non-rival inputs has to add up to total output…. Here are three statements that could be true. (1) Output is constant returns to scale in rival inputs. (2) Non-rival inputs receive some portion of output. (3) Rival inputs receive output equal to their marginal product. Pick two. Romer’s argument is that (1) and (2) are true. (1) he asserts through replication arguments…. (2) he takes as an empirical fact. Therefore, (3) cannot be true. If the owners of non-rival inputs are compensated in any way, then it is necessarily true that rival inputs earn less than their marginal product….
McGrattan and Prescott abandoned (1)…. Boldrin and Levine dropped (2)…. Romer’s issue with these papers is that (1) and (2) are clearly true, so writing down a model that abandons one of these assumptions gives you a model that makes no sense…. From Romer’s perspective, abandoning (1) makes no sense due to replication…. [And] abandoning (2) also does not make sense… [because] some… non-rival ideas are remunerated in some way…. The ‘mathiness’ comes from authors trying to elide the fact that they are abandoning (1) or (2). McGrattan and Prescott have this stuff about location…. Lucas… is abandoning (2), and asserts that this is something we know as a result of prior work. It’s not…. The issue with Boldrin and Levine is… that they dismiss the whole idea of non-rival ideas and abandon (2)….
What does all this have to do with Euler’s Theorem? This theorem is the reason (1), (2), and (3) cannot all be true at once…