This dissertation consists of three essays in economics of innovation and regional economics. The first two essays of my dissertation attempt to fill gaps in the theoretical analysis of the optimal incentive structure when innovation is sequential and cumulative. In particular, the models studied in these chapters feature infinite horizon races with prizes collected continuously and study the effects of the research exemption provision on the incentives for sequential innovation.;In the first essay I develop a dynamic model of duopoly in which firms engage in research and development competition to improve the quality of a final good. The innovation process is sequential and cumulative, and takes place alongside production in an infinite-horizon setting. In this context I study the incentives to invest in R&D resulting from a "research exemption" provision. The model applies closely to the question of the optimal mode of intellectual property right protection for plants, where traditional plant breeder's rights allow for a well-defined research exemption, whereas standard utility patents do not. I specify and solve the duopoly innovation and production model under the two distinct IPR regimes of interest. In particular, the properties of the Markov perfect equilibrium under standard patent protection and under the research exemption are derived, and the impact of the research exemption provision on social welfare is analyzed.;In the second essay I study how the strength of intellectual property rights affects investments in biological innovations when the value of an innovation is stochastically reduced to zero because of the evolution of pest resistance. I frame the problem as a research and development investment game in a duopoly model of sequential innovation. I characterize the incentives to invest in R&D under the two competing IPR regimes, which differ in their treatment of the follow-on innovations that become necessary because of pest adaptation. Depending on the magnitude of the R&D cost, ex ante firms might prefer an intellectual property regime with or without a "research exemption" provision. The study of the welfare function that also accounts for benefit spillovers to consumers---which is possible analytically under some parametric conditions, and numerically otherwise---shows that the ranking of the two IPR regimes depends critically on the extent of the R&D cost.;In the third essay I perform an empirical analysis of the phenomenon of the urban wage premium, which refers the fact that workers in large metropolitan areas earn from 19% to 33% more than those living in non-urban areas. Whereas these differences are usually attributed to various forms of agglomeration economies, this evidence is also consistent with the selection of workers with above-average unobserved ability into large cities. Moreover, with non-random selection both OLS and fixed effects estimates of the wage premium are inconsistent if unobserved ability is correlated with the location choice. In this study we provide selectivity-corrected estimates using data from the National Survey of Families and Households. Empirical results support the view that self-selection can explain substantial part of the urban wage premium.