The research will employ a two-pronged strategy to address the central questions and test the stated hypotheses. The first prong involves the development of a novel theoretical model that extends the canonical framework of directed technological change. The second prong consists of a calibration and simulation exercise designed to assess the model’s quantitative implications against established empirical facts.

4.1 Theoretical Model Extension

This project will develop a formal economic model that extends the baseline two-factor directed technological change framework of Chapter 15. The key theoretical extension will be the explicit inclusion of physical capital (K) as a distinct, accumulable factor of production alongside skilled (H) and unskilled (L) labor.

This three-factor model will be used to formally derive the equilibrium conditions that determine the direction of innovation. Specifically, the model will characterize the circumstances under which new technologies are endogenously L-biased, H-biased, or K-biased. The direction of bias will be shown to be a function of the relative supplies of the three factors and their pairwise elasticities of substitution. This extension is critical for moving beyond a pure labor market analysis to understand the pivotal role of capital accumulation in shaping wage inequality.

4.2 Model Calibration and Quantitative Analysis

The extended theoretical model will be calibrated using parameter values that are well-grounded in the economic literature and consistent with the source text. Key parameters will include:

• The capital share in national income (α ≈ 1/3, consistent with the stylized facts of capital’s income share discussed in the context of growth accounting in Chapter 3).
• Standard values for the household discount rate (ρ) and the intertemporal elasticity of substitution (1/θ), as used in the neoclassical growth model (Chapter 8).
• Plausible estimates for the elasticities of substitution between the three factors.

Following calibration, a simulation exercise will be performed to analyze the model’s dynamic properties. The model will be used to simulate the response of the skill premium and the bias of innovation to two specific shocks:

1. A sustained increase in the relative supply of skilled labor (H/L), mimicking the postwar U.S. experience.
2. An investment boom, represented by an accelerated rate of capital accumulation (K).

The primary goal of the simulation is to analyze the resulting path of innovation bias and the skill premium. We will assess whether the model can quantitatively replicate the key stylized facts of the modern economy, most notably the concurrent rise in the skill supply and the skill premium as depicted in Figure 15.1.