1/ What can the flight patterns of birds teach us about innovation and economic growth?
Vasco Carvalho & I take a stab at this question in a new paper: Firms as Foragers
We develop an empirically grounded theory of growth in which firms forage in idea space.
🧵 (link below)
2/ Link to paper: lukasbfreund.github.io/files/CF_FaF.p…
3/ Motivation. Behavioral ecologists document that foraging animals traverse space in a distinctive rhythm: many small steps, an occasional long jump. Optimal foraging theory rationalizes this as an explore-exploit strategy in a world where food sits in sparse patches that deplete as you feed.
@QuantaMagazine has a great write-up: quantamagazine.org/random-search-…
4/ So…how do we get from that to innovation and growth?
Firms’ innovation follows a similar rhythm.
Take Apple: breakthroughs as it entered new categories -- the iPod (2001), the iPhone (2007), wearables thereafter -- each followed by years of iterative refinement. Apple's patents trace this path.
5/ We take this image seriously and develop a theory of growth in which firms forage in idea space: they exploit a patch of related ideas until it thins, then search for a new one. We ask how this cycle shapes the pace and composition of aggregate growth.
6/ Empirics. We embed the text of millions of US patents, cluster related patents into patches, and document 3 facts:
(A) Within a patch, the quality of successive patents declines (see figure): diminishing returns, or local 'good ideas are getting harder to find'.
(B) Firms routinely enter new patches, and stay longer on richer ones.
(C) Entering a new patch raises the quantity & quality of a firm's patents and, with a lag, its sales.
7/ Theory. The central tradeoff is how long should a firm exploit a patch to improve its product (subject to diminishing scope for improvement) vs. explore for a new patch whose quality it cannot know in advance.
We cast this as an optimal stopping problem, making it tractable enough to embed in an otherwise standard endogenous growth model.
8/ The model speaks to a margin that standard models (where ideas behind a product line never run dry) lack: when firms move on.
We show growth decomposes into how productively firms exploit a patch × the share of time spent exploiting rather than exploring.
One exciting feature: we can approximately characterize many comparative statics in closed form.
9/ Applications. We calibrate the model and study 2 questions.
1⃣ How much growth comes from old vs. new patches?
In our calibration, patches new to the firm account for roughly 2/3 of quality-improvement growth over a 20 year horizon.→ sustained growth rests on exploration.
10/
2⃣ What drives changes in the pace of growth?
In our model, a slowdown can originate in worsening exploitation or worsening exploration.
The model yields a diagnostic to identify the driver based on the duration of exploitation spells. Applied to the U.S. the data -- where avg. patch duration has, if anything, risen -- point away from worsening exploitation and, tentatively, toward harder exploration as the driver behind the productivity slowdown over the last four decades.
We can apply this diagnostic prospectively: If AI is a method of invention that ‘only’ accelerates exploitation, it restores growth, but narrows innovation further into familiar territory.
11/ Link to paper once more:
This is the first version of what's been a very fun project with Vasco -- comments are very welcome!lukasbfreund.github.io/files/CF_FaF.p…
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