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Abstract
The step by step model of innovation is a benchmark model in research investigating the relationship between competition and innovation. The model assumes an industry can be in one of two states; leveled or unleveled. In an unleveled state the lagging firm is the only innovator. In a leveled state firms compete in a patent race. In this patent race successful innovation probabilities are mutually exclusive. This formulation provides mathematical tractability, but it has no other justification. I relax this assumption and use numerical simulation to demonstrate that allowing for non mutually exclusive success in innovation has important consequences for the inverted U relationship. The inverted U relationship is no longer a prediction of the model. In addition, the model predicts that patent measures will under count innovation from the leveled state, allowing for an inverted U relationship between competition and patenting under a narrow set of parameter restrictions. This theoretical exercise has important implications for understanding the current state of the empirical record on this topic.

Most growth theorists agree that understanding the economics of innovation and technological change is central to understanding why some countries are richer and/or grow faster than other countries. The driving force behind recent developments in endogenous innovation models of growth is a desire to eliminate population scale effects. In the semi endogenous growth model growth becomes proportional to the exogenous population growth rate but invariant to policy. This paper makes population growth endogenous by modeling fertility along the lines of Barro and Becker (Fertility Choice in a Model of Economic Growth, 1989) and models an array of government policies to demonstrate how some policies can impact levels and growth rates in a scale free endogenous growth model. In the model government policies are categorized according to whether they have level effects only, level and growth effects, or no impact on levels and/or growth.

Urban economists have long recognized that space is economically important. Evidence of the importance of urban agglomeration and the offsetting effects of congestion are provided in a number of studies of productivity and wages. Little attention has been paid to this evidence in the economic growth literature. The new growth research focuses on technological change. We extend the production function for new ideas common to this research in a way that allows for congestion and agglomeration in innovation and test the hypothesis that these forces are important in explaining innovation. Strong evidence is found that agglomeration and congestion are important in explaining the vast differences in per capita patent rates across US states. This suggests an important new agenda in linking studies of urban economics with the rapidly advancing field of endogenous growth.

It is difficult to justify increased state government support for higher education using arguments based only on how higher education contributes to economic growth. The authors find no strong relationship between state funding of higher education and employment concentration in high-technology industries. Instead, they find that investment in public higher education will tend to be lower than justified on economic efficiency grounds because of the incentives for states to free ride off of the investments of other states. A challenge is to build advocacy strategies that take into account some of the realities of the relationship between public expenditures in higher education and economic growth, including the fact that the relationship is strongly influenced by the movement of educated workers across state borders. Other justifications for public higher education will have to be used, including the reduction of transaction costs for businesses in the state and the expansion of knowledge exchange.

This paper employs a hazard model to analyse the impact of education and two types of prison employment programmes on recidivism over a ten‐year period for 4515 prisoners released from Ohio prisons in 1992. Estimations with a Weibull mixture model and propensity score approach provide two means for investigating self‐selection bias. Selection bias is detected for participation in the most common prison job programme but has little effect on estimated marginal savings impacts of prison industry and education programmes. Estimates of the cost savings from postponing return to prison due to programme participation are provided. The potential for cost savings through decreasing or delaying return to prison is an important finding given the substantial and increasing cost of incarceration.