Building on the established theoretical framework of directed technological change, this section moves from what is known to what this research project will discover. It articulates the specific, unanswered questions and the precise, testable hypotheses that form the core of the proposed investigation. Furthermore, this section will lay the groundwork for our methodological approach by framing these hypotheses in a way that highlights the necessity of extending the canonical two-factor model to include capital.

3.1 Primary Research Question

The single, overarching question that drives this proposal is:

How does the process of capital accumulation interact with the substitutability between capital, skilled labor, and unskilled labor to endogenously determine the long-run bias of technological change and the path of the skill premium?

3.2 Key Hypotheses

The following specific and testable hypotheses are derived directly from the theoretical principles outlined in the source text and form the pillars of the proposed research.

1. Hypothesis 1 (The Role of Factor Substitutability): The long-run relative demand curve for skilled labor is upward-sloping only when the elasticity of substitution between skilled and unskilled labor (σ) is sufficiently high. This condition is necessary for an increase in the relative supply of skills to generate a sustained, long-run increase in the skill premium.
2. Hypothesis 2 (The Endogeneity of Balanced Growth): The tendency of modern economies toward purely labor-augmenting (Harrod-neutral) technological change, a necessary condition for a balanced growth path, is an endogenous outcome. This stability arises when capital and labor are gross complements (σ < 1). In this case, the ongoing accumulation of capital creates strong price effects (making labor relatively scarce and expensive) that incentivize the development of labor-augmenting technologies to restore factor balance (Chapter 15.6); our three-factor model will investigate whether this result holds when capital-augmenting innovation is also a possibility.
3. Hypothesis 3 (Transitional Dynamics): A rapid and unanticipated increase in the supply of skilled labor will initially depress the skill premium, as the economy moves along a production frontier with fixed technology. Subsequently, the premium will rise, potentially overshooting its initial level, as innovation endogenously becomes more skill-biased in response to the now-larger market for skill-complementary technologies. This dynamic path is consistent with the theoretical response illustrated in Figure 15.4.