📈 economics

A Quest for Knowledge

This paper presents a model demonstrating that the benefits of research novelty are nonmonotonic, showing that "moonshots"—investigating questions more novel than myopically optimal—can enhance the long-term evolution of knowledge by inducing research cycles that connect new discoveries to existing foundations.

Original authors: Christoph Carnehl, Johannes Schneider

Published 2026-06-25

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Christoph Carnehl, Johannes Schneider

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

The Big Picture: The "Safe Bet" vs. The "Moonshot"

Imagine a vast, foggy landscape representing all the things we don't know yet. Scientists are explorers trying to map this terrain. They have a map of the parts they already know (existing knowledge), but the rest is hidden in fog.

The paper asks a simple question: Should scientists stick to exploring the edges of the known map (safe bets), or should they take huge risks to jump far into the fog (moonshots)?

The authors build a mathematical model to answer this. They find that while scientists naturally prefer safe bets, this actually slows down progress. Sometimes, a risky "moonshot" that seems useless at first is actually the best way to speed up discovery for everyone later.

1. How Knowledge Works: The "Foggy Map" Analogy

The authors imagine that every possible question (like "How does this protein fold?" or "What causes this disease?") is a point on a line.

Existing Knowledge: These are the points we have already discovered. They are like lighthouses on the shore.
The Fog: The further you get from a lighthouse, the harder it is to guess what the terrain looks like.
The Goal: Society wants to know the entire map. The value of a new discovery isn't just about that one specific point; it's about how much it clears up the fog for the points between the old lighthouses and the new one.

The Insight:
If you discover a point right next to a lighthouse, you only clear up a tiny bit of fog.
If you discover a point very far away, you clear up a huge area of fog, but the area in between is still very foggy.
The "sweet spot" is finding a point at a medium distance. It clears up a lot of fog without leaving a massive gap in the middle.

2. The Problem: Scientists Play It Too Safe

In the real world, scientists are rewarded for finding answers now.

The Cost of Risk: It is much harder (and more expensive) to find an answer in the deep fog than near the lighthouse.
The Scientist's Choice: Because it's hard to succeed in the deep fog, scientists naturally choose to explore the edges of the known map. They pick questions that are easy to answer.

The Result:
Scientists end up creating a "ladder" of knowledge. They take small, safe steps, adding one rung at a time.

The Flaw: They fail too often. Because they are so close to what they already know, they aren't pushing the boundaries enough to inspire the next big leap. They are "deepening" knowledge in small areas rather than "expanding" it to new frontiers.

3. The Solution: The "Moonshot" and the "Research Cycle"

The paper suggests that a funder (like a government or a grant agency) should sometimes force a scientist to take a huge risk. This is called a Moonshot.

The Moonshot Strategy:
Imagine a funder pays a scientist to jump 10 miles into the fog, far beyond where anyone else would dare to go.

The Immediate Problem: This jump is risky. The scientist might fail. Even if they succeed, the new discovery is so far away that it doesn't help much right now. It's like building a bridge to an island that no one can reach yet.
The Long-Term Win: Once that distant island is discovered, it becomes a new lighthouse. Now, the next generation of scientists has a new starting point. They can start exploring the space between the old lighthouse and the new one.

The "Research Cycle":

Step 1 (The Moonshot): A risky jump creates a distant discovery.
Step 2 (The Fill-in): The next scientists rush to fill the gap between the old knowledge and the new moonshot. Because they have two lighthouses to guide them, they can work much faster and with higher success rates.
The Result: The total amount of knowledge created is much higher than if everyone had just taken small, safe steps.

4. When Does This Work?

The paper says this strategy only works under specific conditions:

The Cost Must Be "Just Right": If research is too cheap, scientists will naturally take risks anyway. If it's too expensive, even a moonshot will fail. It needs to be in the middle.
The Funder Must Be Patient: The funder has to be willing to wait. The moonshot might look like a waste of money in the short term, but it pays off in the long run by making future discoveries easier and more frequent.

Summary of the Three Main Points

Knowledge is Connected: Discovering one thing helps us guess the answers to many other related things. The value of a discovery depends on how much "fog" it clears up between known points.
Scientists are Too Conservative: Because it's hard to be right when you are far from what we know, scientists naturally stick to safe, easy questions. This leads to slow progress and frequent failures.
Moonshots are Infrastructure: A "moonshot" (a very distant, risky discovery) acts like building a new bridge. It might not be useful immediately, but it sets the stage for future scientists to cross the gap and discover things much faster than they could have on their own.

In short: To get the most knowledge out of our scientists, we shouldn't just ask them to solve the easiest problems. We should occasionally fund the crazy, risky, "impossible" ideas, because those are the ones that will unlock the next wave of discoveries.

Technical Summary: A Quest for Knowledge

Problem Statement
The paper addresses a fundamental tension in the economics of science: whether more novel research is always desirable. While institutions like the National Science Foundation (NSF) champion scientific freedom and the pursuit of "moonshots" (highly novel, high-risk research), the authors question if researchers, acting in their own self-interest, naturally select the optimal level of novelty. The core problem is that the value of a discovery and the cost of finding it are both endogenous to the existing stock of knowledge. The authors seek to model how knowledge evolves over time and whether a social planner (a "designer") should intervene to incentivize research that exceeds the myopically optimal level of novelty, even if such research has low immediate returns.

Methodology
The authors develop a microfounded dynamic model of knowledge creation involving two agents: a society represented by a single decision-maker and a sequence of short-lived researchers.

Knowledge Structure: The universe of questions is modeled as the real line. The "truth" (the answer to any question $x$ ) is the realization of a standard Brownian motion. Existing knowledge ( $F_k$ ) consists of a finite set of known question-answer pairs.
Conjectures and Decision-Making: Because answers follow a Brownian path, the decision-maker forms conjectures about unknown questions based on the distance to known answers. The precision of these conjectures (variance) depends on the distance to the nearest known points. The decision-maker applies knowledge only if the precision is high enough (uncertainty is below a threshold $q$ ); otherwise, they choose an outside option. The value of knowledge is the integral of the decision-maker's expected payoff across all questions.
Research Process: Researchers select a question $x$ and an effort level that determines the probability $\rho$ of discovering the answer. The cost of research is microfounded: finding an answer with probability $\rho$ is more costly if the conjecture about the answer is imprecise (high variance). This creates an endogenous link between novelty (distance from existing knowledge) and the probability of success.
Dynamic Extension: The model extends to a sequential setting where researchers arrive over time. A long-lived designer can intervene by controlling the actions of specific researchers to alter the trajectory of knowledge accumulation.

Key Contributions
The paper makes three primary contributions to the literature on the economics of science and innovation:

Microfounded Framework for Knowledge Value: The authors quantify the value of a discovery by modeling how it improves decision-making across a continuum of related questions. They distinguish between "expanding knowledge" (discovering answers beyond the current frontier) and "deepening knowledge" (filling gaps between existing points). They show that the benefits of a discovery are non-monotone in novelty; they are maximized at an intermediate distance from existing knowledge.
Endogenous Novelty-Output Trade-off: Unlike previous literature that often treats novelty and output as exogenous or independent, this model links them through a cost function. The authors demonstrate that novelty and the probability of discovery can act as substitutes or complements depending on the structure of existing knowledge. Specifically, in "deepening" scenarios, moving away from one boundary moves closer to the other, altering the marginal cost of success.
Policy Implications for Moonshots: The paper provides a theoretical justification for incentivizing "moonshots"—research questions significantly further from the frontier than what a myopic researcher would choose. It identifies conditions under which such interventions improve the long-run evolution of knowledge.

Results

Researcher's Optimal Choice: In the absence of intervention, researchers choose questions that are too narrow and fail too often. They prefer to "deepen" knowledge in areas of intermediate length rather than "expand" the frontier, because smaller areas offer higher precision and lower costs. Consequently, the natural evolution of knowledge follows a "ladder" structure of step-by-step expansions with small step sizes.
The Moonshot Mechanism: The authors show that a forward-looking designer can improve the evolution of knowledge by inducing a "research cycle." By encouraging a moonshot (a discovery far beyond the frontier, e.g., at distance $6q$ instead of the optimal $3q$ ), the designer creates a large gap in knowledge.
Dynamic Externality: Although the moonshot itself provides little immediate value (as the gap is too large for immediate deepening), it creates a large area for future researchers to fill. Subsequent researchers, aiming to connect the moonshot to the original frontier, are incentivized to work on questions that are more novel than they would have otherwise chosen. This increases their success probability and the overall value of the knowledge stock.
Conditions for Intervention: The paper proves that a designer should induce a moonshot if and only if:
1. The cost of research is intermediate (if costs are too high, future researchers fail; if costs are zero, researchers naturally optimize).
2. The designer is sufficiently patient (high discount factor $\delta$ ).
3. The moonshot is not too distant (it must be close enough to inspire the next researcher to succeed).
Research Cycles: Once a moonshot is made, the next researcher naturally "deepens" the knowledge by filling the gap. This cycle results in a knowledge landscape that is more valuable than one evolved through standard step-by-step expansion.

Significance and Claims
The paper claims to reconcile empirical findings showing a lack of novelty in research (conservative strategies) with the intuition that "moonshots" are valuable. It argues that the lack of novelty is not necessarily a failure of researchers but a rational response to the cost structure and the misalignment of incentives between short-lived researchers and long-term societal goals.

The authors assert that their model offers a new rationale for funding policies: incentivizing distant discoveries is not just about the immediate value of the discovery, but about setting the stage for future researchers to thrive. The paper suggests that "moonshots" function as infrastructure investments: they provide little value in isolation but enable subsequent, more productive research cycles. The findings imply that institutions should consider future-oriented rewards (beyond immediate policy relevance) and that a mix of incentives—perhaps involving research consortia or specific grants for novel directions—may be necessary to optimize the evolution of knowledge.

The authors remain modest, noting that their model is stylized and that real-world frictions (such as publication bias or career concerns) are not explicitly modeled but could be incorporated into their flexible framework. They do not claim to solve the optimal design of all scientific institutions but provide a tractable theoretical basis for understanding the trade-offs between novelty, output, and the dynamic evolution of knowledge.