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Econ-211 · economics · Economics

Redirecting technological change

LLM status Open unverified

Statement

Original subject group: Growth and productivity

Audit classification: Explicit published open question. Redirecting innovation while preserving experimentation is expressly posed; the proposed mechanism is editorial and strategic. Verification concerns the cited version, not first priority or proof that this exact editorial specification remains unsolved on October 8, 2026.

Definitions and precise research target

Editorial mathematical specification.
Fix two research directions $j=1,2$, such as ordinary private productivity and a declared socially valuable health or environmental technology. Firms privately observe project quality $q$, choose direction and research effort $r$, and obtain innovation arrival rate $\lambda_j(r,q)$. Private rewards $v_j(q)$ differ from social rewards $V_j(q)$, including measured spillovers and external damages. A policymaker observes imperfect signals $s$, can offer subsidies $t_j(s,r)$, and faces a stated budget and an explicit probability of political capture or biased project selection. Determine a feasible subsidy or procurement rule maximizing expected discounted social surplus net of research resources, fiscal costs, and capture losses. Require firms’ participation and effort/direction incentive compatibility for every type in the declared quality support. Preserve a specified minimum experimentation probability for projects with uncertain social value, or incorporate the information value of experimentation directly in the objective. Identify the private-response, spillover, learning, and capture parameters needed for policy comparison, and distinguish uncertainty about project returns from discretionary favoritism. Evaluate rules against untargeted support and no-support benchmarks under equal budgets. The target is direction-specific innovation policy with explicit informational constraints; it does not assert that a policymaker knows socially optimal technology ex ante or that one favored sector should receive support universally.

Define an innovation within a finite interval $\Delta>0$ by probability $p_j(r,q)=1-e^{-\lambda_j(r,q)\Delta}$, with $\lambda_j\ge0$; this prevents confusing an arrival intensity with a probability. Let a firm maximize $p_j(r,q)v_j(q)-c_j(r,q)+t_j(s,r)$ over direction and effort after observing quality. Incentive compatibility means the prescribed choice solves this maximization for every quality and observed signal, and report-based schemes require additional truthfulness. For a static benchmark social surplus is $E[p_j(r,q)V_j(q)-c_j(r,q)-C^F(t)-L^{\rm cap}(t)]$, with subsidies counted as transfers except for real financing and capture losses. Experimentation is a positive allocation to a defined uncertain-project set, e.g. $P(j\in U,r\ge r_0)\ge\epsilon$; in a dynamic learning model its option value instead enters continuation welfare. Direction/private-information incentives overlap game theory.

Variants and assumption changes

The following are editorial variants, not additional published open conjectures.
  1. Public research quality. Quality and social value are observable, there is no capture, and effort is verifiable. Derive a direction-specific subsidy benchmark for the private/social return wedge, with a binding common budget.
  2. Learning and capture. Quality is initially unknown to the policymaker, pilot outcomes update a posterior, and biased allocation follows a specified probability kernel. Optimize adaptive subsidies subject to experimentation and fiscal limits and compare with untargeted support.

References and source audit

Redirecting innovation while preserving experimentation is expressly posed; the proposed mechanism is editorial and strategic. This formulation contains strategic incentives and therefore overlaps game theory.
  1. Ufuk Akcigit. 2026. Creative destruction in economic growth. Section7, Open questions, item7. https://onlinelibrary.wiley.com/doi/10.1111/sjoe.70037. DOI: https://doi.org/10.1111/sjoe.70037.

Common conventions: Source mathematical conventions

These conventions apply to each entry unless explicitly replaced.

Models and identification. A primitive model $m$ specifies all probability laws, feasible choices, information, equilibrium and measurement rules used by its target. The admissible class $\mathcal M$ is fixed independently of outcomes. If $P_O(m)$ is its observable probability law and $\tau(m)$ the target, its identified set at observable law $P$ is \[ \mathcal I_\tau(P)=\{\tau(m):m\in\mathcal M,\ P_O(m)=P\}. \] Point identification means that this set is a singleton. An empty set signals incompatibility of data and assumptions. Coordinate bounds need not describe the joint set. Bounds are sharp only if every retained target is attainable or arbitrarily approachable by compatible models. Finite bounds require explicit restrictions on unobserved quantities; unrestricted confounding, hidden wealth, extrapolation or arbitrary equilibrium selection can yield uninformative sets.

Causal interventions. A potential outcome $Y_i(p)$ is the outcome under a complete policy regime $p$, including timing, financing, information and market spillovers. The target population and units are fixed before treatment. With interference, use the complete assignment vector or a justified exposure mapping; individual no-interference notation alone cannot identify an economy-wide intervention. A difference of mean potential outcomes does not require the cross-world joint distribution. Conditioning on post-treatment migration, survival, enrollment or employment changes the estimand and needs separate justification.

Statistical statements. An estimator, confidence set, forecast or test specifies a sampling law, model class and loss/coverage criterion. Uniform $(1-\alpha)$-coverage means $\inf_{m\in\mathcal M}\Pr_m\{\tau(m)\in C_n\}\geq1-\alpha$, or an explicitly asymptotic version. The whole parameter space trivially has coverage, so informativeness requires a stated width, risk or power objective. A forecasting improvement is relative to a named benchmark, information set and evaluation population.

Equilibrium and optimization. An equilibrium comprises feasible plans, optimality, beliefs where needed, budget constraints and all market/resource clearing. The primitives or a stated benchmark define each correspondence $\mathcal E(p;m)$. Nonemptiness is assumed or proved, never inferred just from compact policy sets. A selected-equilibrium target uses a declared selection rule; a robust target quantifies over all permitted equilibria. Use suprema or infima unless attainment is established. An $\varepsilon$-optimal policy is feasible and within $\varepsilon$ of the finite optimum value. Report an empty feasible set separately.

Welfare and accounting. Normative utility, interpersonal normalization, social weights, numeraire, discounting and the use of public receipts are primitives. Behavioral utility need not coincide with the welfare criterion. Household welfare includes ownership income and rents once; adding profits again to compensating variation generally double-counts them. A monetary equivalent is defined by an explicit transfer and price convention, with monotonicity and range conditions. Average effects, mechanism contributions, transfers and welfare losses are different targets. Infinite sums require convergence and dynamic feasible plans require terminal or no-Ponzi conditions.

Source versions. A working-paper date, revision date and journal publication year are distinguished. A DOI for a journal version is not automatically the DOI of an earlier manuscript. Locators refer to the stated version and printed pages where specified. A metadata-only check does not verify a claim about a full-text conclusion. Every entry's source subsection narrows the provenance claim accordingly.

Statement licence: CC-BY-4.0 · Source file

Contributions 1

Econ-211-A1 · Exploration · LLM-generated · gpt 6 astra ultra ·

GPT 6 Astra Ultra attempt on Econ-211

Redirecting technological change: the option value of an experimental direction

GPT 6 Astra Ultra October 9, 2026
Problem reminder.
The original problem asks how to redirect innovation toward social objectives without eliminating useful experimentation, while respecting incentives, information, and public budgets. For a policy $t$, the relevant comparison includes the learning generated by induced research: \[ \Delta W(t)=\mathbb E[W\mid t]-\mathbb E[W\mid 0], \] with expectations over a common physical research environment. Akcigit's open question on the direction of innovation [akcigit] motivates this issue. Here a fully specified two-period experiment isolates one part of the incentive wedge. Effort is fixed and observable; privately informed research quality remains outside the solved benchmark.
Research and information.
At dates zero and one, a planner chooses one project. A safe direction succeeds with known probability $\mu_0\in(0,1)$. An experimental direction has a fixed but unknown success probability $\Theta\in[0,1]$ with a specified common prior and mean $\mu$. Conditional on $\Theta$, its successive outcomes are independent Bernoulli draws. A date-zero experimental outcome $Y$ is publicly observed; a safe project reveals nothing about $\Theta$. Success yields social value one, and equal project costs cancel between directions. The planner discounts date-one output by $\beta\in(0,1]$. Define the posterior means $\mu_Y=\mathbb E[\Theta\mid Y]$ on positive-probability observations; null observations can be assigned arbitrary posteriors.
Theorem (Experimentation can dominate the better current project): In this model the social gain from choosing the experimental direction at date zero, followed by optimal date-one choice, instead of choosing the safe direction first is \[ G=\mu-\mu_0+\beta I,\qquad I=\mathbb E\max\{\mu_0,\mu_Y\}-\max\{\mu_0,\mu\}\geq0. \tag{1} \] The information term is strictly positive if the posterior mean falls strictly on both sides of $\mu_0$ with positive probability. When $\mu<\mu_0$, experimental research is strictly optimal exactly when $\beta I>\mu_0-\mu$.
Proof: The first experimental project's expected output is $\mu$. After observing its outcome, the best available expected output is $\max\{\mu_0,\mu_Y\}$. The experimental path therefore has value $\mu+\beta\mathbb E\max\{\mu_0,\mu_Y\}$. Along the safe-first path there is no information, giving value $\mu_0+\beta\max\{\mu_0,\mu\}$. Subtraction proves the formula. The posterior mean is a martingale: $\mathbb E\mu_Y=\mu$. Convexity of $z\mapsto\max\{\mu_0,z\}$ proves $I\geq0$ by Jensen's inequality. For strictness, if $\mu\leq\mu_0$, then $I=\mathbb E(\mu_Y-\mu_0)_+>0$; if $\mu\geq\mu_0$, then $I=\mathbb E(\mu_0-\mu_Y)_+>0$. The last assertion follows from (1). ∎
Example (An exact prior): Let $\Theta$ equal $0.9$ or $0.1$, each with probability one half, and let $\mu_0=0.6$. Then $\mu=0.5$. Bayes' rule yields posterior means $0.82$ after success and $0.18$ after failure, each outcome having probability one half. Consequently \[ \mathbb E\max\{0.6,\mu_Y\}=0.71, \qquad G=-0.10+0.11\beta. \] A planner with $\beta>10/11$ chooses the direction with the lower contemporaneous success probability. At $\beta=1$ the gain is $0.01$. These are exact arithmetic consequences of the specified prior, not empirical probabilities.
A contractor, capture, and a feasible grant.
A one-period contractor conducts date-zero research and receives private success rewards $v_0,v_E\geq0$. Common real effort cost is $k\geq0$. Assume $v_0\mu_0-k\geq0$ and \[ d=v_0\mu_0-v_E\mu>0. \] Thus absent policy the contractor strictly chooses the safe project and participates. A grant $t$ is paid for the verified experimental direction and effort. A budget requires $0\leq t\leq B$. Grant financing has additional real cost $\lambda t$, $\lambda\geq0$; the grant itself cancels between taxpayer and domestic contractor. All success rewards are transfers already included in social output accounting.

An institutional failure occurs with exogenous probability $\rho\in[0,1)$. In that event verification is corrupted: the grant is disbursed, the safe project is conducted, and an additional real loss $L_{\mathrm{cap}}\geq0$ occurs. Otherwise verification is accurate. Institutional states are resolved before project choice, and this binary capture technology is common knowledge. It is an assumption about implementation, not a derived lobbying equilibrium.

Proposition (A budget and experimentation test): Fix $\varepsilon\in(0,1]$. Suppose accurate-verification ties favor experimentation. A grant implementing experimental research whenever verification is accurate exists within the budget exactly when $B\geq d$. The smallest such grant is $d$. At that grant the unconditional experimentation probability is $1-\rho$ and the social gain is \[ (1-\rho)G-\rho L_{\mathrm{cap}}-\lambda d. \tag{2} \] Thus a weak implementation meeting the experimentation requirement and strictly improving welfare exists whenever \[ B\geq d,\qquad 1-\rho\geq\varepsilon, \qquad (1-\rho)G>\rho L_{\mathrm{cap}}+\lambda d. \] For strict contractor incentives use any $t>d$ satisfying the budget and replace $d$ by $t$ in (2).
Proof: Under accurate verification the experimental payoff minus the safe payoff is $t-d$. This proves the threshold, including the role of tie breaking and the strict variant. The safe payoff is nonnegative, so participation follows. Accurate verification produces social improvement $G$; capture reproduces the baseline project and subtracts $L_{\mathrm{cap}}$. The grant is paid in both states, generating real financing cost $\lambda t$. Taking expectations establishes (2). Choosing the smallest implementing grant weakly minimizes this cost and does not change the induced project or its information. ∎
Attempted extension and residual gap.
The information term in (1) is a value-of-information calculation; no originality claim is made for Jensen's inequality. Its consequence for the policy target is sharper than a ranking by expected current output: even perfect observation of current success probabilities omits a potentially decisive public learning benefit. Equation (2) also shows why identifying that benefit alone is insufficient when verification can be captured.

With privately observed quality $q$, grant acceptance can select different priors and the public posterior need not equal the expression used here. A menu must then satisfy incentive constraints across types as well as directions and effort. Multiperiod experimentation changes the information state and may create endogenous abandonment or excessive continuation. Those are the unresolved parts of the catalogue problem. The explicit benchmark solves a grant threshold and an experimentation tradeoff under known priors and a specified capture process; it does not deliver a generally optimal innovation policy.

Completion Estimate

30%

This is a post hoc, heuristic estimate for the full catalogue target. The attempt computes the public learning value of experimentation and feasible grant thresholds under a two-period prior and specified capture process. Optimal direction and effort incentives with privately observed project quality, type screening and longer adaptive learning remain outside the solved benchmark.

References

  • [akcigit] U. Akcigit (2026), "Creative destruction in economic growth," Scandinavian Journal of Economics, Section 7, question 7. Publisher article.

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