We construct an endogenous growth model of directed technical change with automation-the introduction of machines which replace low-skill labor and complement high-skill labor-and horizontal innovation-the introduction of new products, which increases demand for both types of labor. Machines are produced with the same technology as the consumption good. The level of technology in the economy is characterized by the number of products and the share of these that are automated. For general processes of technology, we demonstrate that although low-skill wages can drop during periods of increasing automation intensity the asymptotic growth rate is positive, though lower than that of the economy. We then endogenize the evolution of technology and derive an asymptotic steady state. Through numerical simulations, we show that the transitional path follows three phases. First, wages are low such that few machines are used and low-skill wages keep pace with the growth rate of the economy. Then, as wages grow the share of automated products increases and the economy substitutes towards the use of machines which depresses the growth rate of low-skill wages, potentially to negative. Finally, as the economy reaches steady state the share of automated products is constant and the relative growth rate of low-skill wages picks up though it remains lower than that of the economy. We extend the model to include middle-skill workers and demonstrate that the model endogenously captures two important characteristics of the U.S. income distribution over the past 50 years: initially a monotone dispersion of the income distribution, and thereafter a wage growth polarization, in which middle-skill workers experience the lowest wage growth. Finally, in an extension we allow machines to be produced with a different technology than the consumption good. This allows for faster productivity growth for machines which can potentially lead to permanently negative growth of low-skill wages.

We build an endogenous growth model with automation (the replacement of low-skill workers with machines) and horizontal innovation (the creation of new products). Over time, the share of automation innovations endogenously increases through an increase in low-skill wages, leading to an increase in the skill premium and a decline in the labor share. We calibrate the model to the US economy and show that it quantitatively replicates the paths of the skill premium, the labor share, and labor productivity. Our model offers a new perspective on recent trends in the income distribution by showing that they can be explained endogenously. (JEL D31, E25, J24, J31, O33, O41)

Do higher wages lead to more automation innovation? To answer this question, we first introduce a new measure of automation by using the frequency of certain keywords in patent text to identify automation innovations in machinery. We validate our measure by showing that it is correlated with a reduction in routine tasks in a cross-sectoral analysis in the US. Then we build a firm-level panel dataset on automation patents. We combine macroeconomic data from 41 countries and information on geographical patent history to build firm-specific measures of lowskill and high-skill wages. We find that an increase in low-skill wages leads to more automation innovation with an elasticity between 2 and 4. An increase in highskill wages tends to reduce automation innovation. Placebo regressions show that the effect is specific to automation innovations. Finally, we use the Hartz labor market reforms in Germany for an event study and find that they are associated with a relative reduction in automation innovations.

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Innovation is part idea generation and part development. We build a model of "innovating-bydoing," whereby ideas come to practitioners. Successful innovation requires that practitioners' ideas be developed through costly effort. Our model nests existing theories of laboratory research and learning-by-doing. Empirically, we analyze the effect of the U.S. Medicare program on medical equipment innovation. Our model's structure allows us to infer the Medicare program's aggregate effects. We estimate that Medicare's introduction led to a 20 to 30 percent increase in medical equipment patenting across the United States, of which roughly half is due to the innovating-by-doing channel.