This dissertation explores the implications of a new model of knowledge production. In my model, researchers have access to a set of primitive knowledge elements that can be combined to form ideas, where a new combination is a new idea. Underlying parameters governing the connections between elements stochastically determine whether a given combination yields a useful idea (some elements tend to work well together, and others do not). These underlying parameters are unknown to researchers, but as they attempt to combine elements and create ideas, they observe signals which they use to improve their beliefs via Bayesian updating. I embed this production function into a simple model of research incentives, where a firms receive a reward for discovering new and useful combinations, but pay a cost to conduct research.

I investigate empirically these predictions using a large dataset on US utility patents: all 8.3 million utility patents granted between 1836 and 2012. From this analysis, I find that the probability a pair of knowledge “elements” (now proxied by technology classifications assigned by patent examiners) will be combined in any given year is increasing in the number of past combinations, decreasing over time, and increasing when both elements in the pair are also used with many other elements. These predictions are consistent with my model. The same work also predicts that patenting activity is positively correlated with changes in researcher knowledge about the connections between elements, and negatively correlated with time. Using panel data on 429 technology classes, I find the growth rate of patents is falling over time, but that increases can be forecast from positive changes in connections between elements 1-5 years earlier, even after controlling for numerous other factors.

In my second paper, I examine the characteristics of the optimal research strategy for a forward-looking researcher using the above framework. To characterize the optimal strategy, I examine two special cases that permit analytic solutions, as well as a set of 100 numerically solved cases. The optimal research strategy reproduces many stylized facts about the innovation process, including the initial dominance of applied research relative to basic research.

The third paper of my dissertation examines the impact of environmental policy choice on innovation, when research is characterized by unobservable (to the policy-maker) variance in technological opportunity. I assume there exist two types of energy, clean and dirty, that are perfect substitutes but for their production costs and a negative externality from dirty energy. Innovators are expected profit maximizers, and their decision to expend resources on R&D depends on technological opportunity, as well as the policy of the government. We show the policy-maker’s decision to use quota or price based incentives matters. Price based incentives such as a carbon tax are characterized by disperse outcomes, with more R&D resources expended when technological opportunity is high, and reduced amounts when technological opportunity is low. Quotas such as mandates, in contrast, lead to a more consistent level of R&D spending across differences in technological opportunity. Thus, price-based systems are more likely to deliver great technological advances or none at all, while mandates are more likely to deliver consistent incremental gains. Moreover, we also show an optimal carbon tax is likely to outperform any mandate in expected welfare terms, and has less information requirements.