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)
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-…
@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.
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.
(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.
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.
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.
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.
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…
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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