📈 economics

Spillovers, Innovation Difficulty, and the Dynamics of Productivity

Using a medium-scale DSGE model estimated on U.S. data from 1984 to 2019, this paper finds that while innovation difficulty is a persistent factor influencing the probability of successful innovation, aggregate productivity fluctuations are primarily driven by spillover shocks rather than changes in the difficulty of innovating.

Original authors: Alice Albonico, Marco Guerzoni

Published 2026-09-30

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Alice Albonico, Marco Guerzoni

Original paper licensed under CC BY 4.0 (https://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

For decades, the United States has been a powerhouse of invention. New technologies, from digital platforms to artificial intelligence, have emerged at a breathtaking pace, promising to reshape how we live and work. Yet, a puzzling contradiction has settled over the economy: while the rate of new ideas and investments has surged, the overall speed at which the economy produces goods and services has slowed down. This disconnect has left economists searching for an explanation. Is the engine of growth simply running out of fuel, or is the fuel just not reaching the right places? To understand this, one must look at two distinct ways that research and development, or R&D, actually translate into real-world progress. The first is the sheer power of collective effort: how well does the total amount of money and time spent on research push the very edge of what is possible forward? The second is the challenge of the individual attempt: how likely is it that a specific company's research will actually succeed in creating a new, useful product? Distinguishing between these two forces is crucial because a slowdown in one does not necessarily mean a slowdown in the other, and the solution to the economic puzzle depends entirely on which one is the problem.

A team of researchers at the University of Milano-Bicocca set out to untangle these two forces using a detailed computer model of the U.S. economy. They built a simulation that tracks how money flows into research, how that research creates new technologies, and how those technologies spread through the market. The model separates the process into two channels. One channel measures the "spillover" effect, which is the idea that when many firms research together, they collectively push the technological frontier forward, making the next big breakthrough easier for everyone. The other channel measures "innovation difficulty," which represents the probability that a single firm's research effort will actually succeed in creating a new product. The researchers fed their model with real data from 1984 to 2019, including standard economic numbers like GDP and investment, as well as a unique, newly developed measure of technological creativity derived from the text of patents. This patent data acts as a direct window into how often new ideas are actually being successfully generated, rather than just how many attempts are being made.

The results of this simulation offer a clear answer to the mystery of the productivity slowdown. The study finds that the decline in the speed of economic growth is not primarily caused by a drop in the success rate of individual inventions. Instead, the main driver of the slowdown is a weakening in the spillover channel. In simpler terms, the collective effort of all the research happening in the country has become less efficient at pushing the absolute edge of technology forward. The model shows that shocks to this collective efficiency are responsible for the vast majority of the fluctuations in productivity growth, explaining roughly 88 to 97 percent of the variance in TFP growth in the augmented model. In contrast, the difficulty of getting a single invention to succeed plays a much smaller role in the overall speed of the economy. While the probability of success does fluctuate, these changes do not drive the major trends in productivity.

However, the story changes slightly when the researchers look at the nature of the difficulty itself. When they included the patent-based creativity data, the model revealed that the "difficulty" of innovation is not a fast-moving, jittery force that changes every few months. Instead, it behaves like a slow-moving current. Once the model accounts for the real-world success rates found in patents, the difficulty shock appears to be a persistent, long-term force that shapes the landscape of innovation over years, rather than a short-term business cycle disturbance. This suggests that while making a new invention has become harder over time, this increased difficulty is a steady, slow pressure rather than the sudden jolt that caused the recent economic slowdown. The study indicates that the productivity slowdown is not primarily driven by a decline in successful innovation. The data indicates that firms are still finding ways to innovate, but the collective engine that turns those innovations into broad economic growth has lost some of its momentum.

The implications of this finding are significant for how we view the economy and how we might try to fix it. The research suggests that simply encouraging more companies to try to invent new things, or pouring more money into research without addressing how that research connects to the broader economy, may not be enough. If the problem is that the collective spillover of knowledge is weak, then policies need to focus on how ideas spread and how the technological frontier advances for everyone, not just on how many individual attempts are made. The study concludes that the slowdown in productivity is not a failure of the innovators themselves, but a failure in the mechanism that translates their collective work into faster economic growth. By separating the two channels, the researchers have shown that the economy is not running out of ideas, but rather that the path from those ideas to widespread prosperity has become more difficult to navigate.

Technical Summary: Spillovers, Innovation Difficulty, and the Dynamics of Productivity

Problem Statement
The paper addresses the central macroeconomic puzzle of the apparent disconnect between rapid technological change (e.g., digital technologies, AI) and the marked slowdown in aggregate productivity growth in the U.S. since the early 2000s. While existing literature offers various explanations—ranging from slow diffusion and implementation lags to the idea that "ideas are getting harder to find" (Bloom et al., 2020)—these hypotheses often conflate distinct economic mechanisms. The authors argue that the debate requires a structural distinction between two innovation channels:

The Spillover Channel: The efficiency with which aggregate R&D effort advances the technological frontier.
The Difficulty Channel: The probability that sector-level R&D efforts successfully generate innovation and lead to the adoption of frontier technologies (creative destruction).

The core question is whether the productivity slowdown is driven primarily by a decline in the success rate of innovation (difficulty) or by a weakening in the translation of aggregate research into frontier progress (spillovers).

Methodology
The authors develop and estimate a medium-scale Dynamic Stochastic General Equilibrium (DSGE) model with endogenous technological change, building on the framework of Cozzi et al. (2021). The model incorporates standard New Keynesian frictions (habit formation, price rigidities, investment adjustment costs) alongside a Schumpeterian innovation block.

Model Structure:
- Frontier Growth: The growth of the technological frontier ( $g^{A_{max}}$ ) is semi-endogenous, driven by aggregate R&D and knowledge spillovers. It is subject to a spillover shock ( $\sigma^{RD}_t$ ), which alters the efficiency of converting R&D into frontier advancement.
- Innovation Success: Sectoral productivity jumps to the frontier with a probability ( $n_t$ ) determined by R&D investment and a difficulty shock ( $\varepsilon^{n,RD}_t$ ). This shock governs the likelihood of successful innovation for a given level of R&D.
- Aggregate Productivity: Total Factor Productivity (TFP) depends on both the pace of frontier expansion and the rate at which firms successfully innovate and adopt frontier technologies.
Estimation Strategy:
- The model is estimated using Bayesian techniques on U.S. quarterly data from 1984Q1 to 2019Q4.
- Baseline Specification: Uses eight macroeconomic observables (GDP, consumption, investment, R&D, wages, hours, interest rates, inflation).
- Augmented Specification: Incorporates a novel, patent-text-based measure of "technological creativity" (Kalyani, 2024) as an additional observable. This index is designed to capture the probability of innovative success more directly than traditional entry/exit rates, which are influenced by non-technological factors.
- The estimation includes ten fundamental shock processes, explicitly distinguishing between spillover and difficulty shocks.

Key Contributions

Structural Identification: The paper is the first to explicitly separate and identify spillover shocks and difficulty shocks within a single estimated DSGE framework. It demonstrates that these are not merely different names for a general decline in innovation efficiency but represent distinct margins with different macroeconomic transmission mechanisms.
Novel Data Discipline: The authors introduce a patent-text-based measure of technological creativity into the estimation of a DSGE model. This allows for the direct disciplining of the innovation-probability block, offering a more robust identification of the difficulty shock compared to models relying solely on aggregate macro data or firm turnover rates.
Quantitative Decomposition: The study provides a quantitative assessment of the relative importance of these two channels in explaining U.S. productivity fluctuations, moving beyond theoretical speculation to empirical evidence.

Results

Transmission Mechanisms:
- Spillover Shocks: These act directly on the frontier growth margin. An adverse spillover shock causes an immediate and persistent decline in frontier growth, which subsequently lowers TFP, output, investment, and R&D. Innovation probability is largely unaffected because the shock does not change the conditional success rate of R&D.
- Difficulty Shocks: These act directly on the innovation probability margin. An adverse difficulty shock reduces the probability of successful innovation ( $n_t$ ). This slows the diffusion of frontier technology into average productivity, lowering TFP. Interestingly, a difficulty shock can temporarily raise the value of incumbent firms by reducing the risk of creative destruction (displacement), even as aggregate productivity falls.
Quantitative Importance (Variance Decomposition):
- TFP Growth: Spillover shocks are the dominant driver of TFP fluctuations. In the augmented specification, they explain approximately 88–97% of TFP growth variance at short and medium horizons.
- Innovation Probability: Difficulty shocks are the primary driver of fluctuations in the probability of successful innovation, explaining roughly 92–97% of its variance.
- Role of Difficulty: While difficulty shocks significantly shape the probability of innovation, their quantitative contribution to TFP fluctuations is substantially smaller than that of spillover shocks.
Impact of the Creativity Observable:
- Including the creativity measure does not alter the qualitative transmission mechanisms but significantly changes the estimated properties of the difficulty shock.
- In the augmented specification, the difficulty shock becomes less volatile and more persistent. This suggests that innovation difficulty is a slow-moving structural force rather than a high-frequency business cycle disturbance.
- Historical decompositions indicate that while the difficulty shock has increased persistently post-2010 (consistent with the idea that innovation is becoming harder), it remains a secondary factor in explaining the overall productivity slowdown compared to spillover shocks.

Significance and Claims
The paper concludes that the aggregate productivity slowdown in the U.S. is not primarily driven by a decline in the probability of successful innovation. Instead, the slowdown is largely attributable to a weakening in the spillover channel—the mechanism through which aggregate R&D translates into technological frontier advancement.

The authors claim that distinguishing between these channels is crucial for both measurement and policy:

Measurement: A decline in measured innovation performance may reflect weaker spillovers rather than a collapse in the success rate of individual research efforts.
Policy: Policies aimed solely at increasing R&D effort or improving the success rate of innovation (addressing difficulty) may be insufficient if they do not simultaneously strengthen the spillover and diffusion mechanisms that drive frontier growth. Conversely, policies that reduce barriers to successful innovation remain relevant for the pace of creative destruction, even if they are not the primary driver of TFP growth dynamics.

The paper modestly asserts that while innovation difficulty is a real and persistent force shaping the success rate of innovation, it is the spillover channel that quantitatively dominates the dynamics of measured Total Factor Productivity.

Technical Summary: Spillovers, Innovation Difficulty, and the Dynamics of Productivity

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