Note on Idea Diffusion Models with Cohort Structures By SANTIAGO CAICEDO University of Chicago Final version received 24 April 2018. In this note I propose two alternative frameworks to study idea diffusion models with cohort structures. Both frameworks fix the Lucas (2009) aggregation mistake while keeping the analytical tractability of the model and its insights. The frameworks differ in their assumptions on the meeting process. I study first a continuous arrival process where agents meet at each point in time, and then a more commonly used Poisson process where meeting opportunities arrive stochastically at some given Poisson rate. I generalize the growth formula in Lucas (2009) and show that both models yield the same growth rate on a balanced growth path. Moreover, I show that the continuous arrival process can be viewed as the limit of Poisson processes where the meeting rate increases but the quality of meetings decreases. INTRODUCTION Every day, people interact and learn from one another. As they age, they accumulate knowledge from these interactions. Lucas (2009) studies this natural learning setting by adding a cohort structure to an idea diffusion model. In his model, all knowledge is embodied in individuals that have the possibility to interact and learn from others. Growth arises endogenously from these interactions. However, there are some mistakes in the aggregation that Lucas uses in his model. In this note, I present two frameworks that use the correct aggregation and still have the rich set of results of Lucas’s original contribution. I argue that these two frameworks are useful in modelling economic problems where agents dynamically learn from each other as they age. I believe that there are many interesting applications and fruitful extensions to these trackable models; for this reason, it is useful to have the corrected version available. 1 The two frameworks have the same learning process but differ in the way in which people meet. In both, whenever individuals meet someone more knowledgeable, they learn and acquire this higher level of knowledge. The difference between the two frameworks comes from how people meet. First I study a continuous arrival model, which is the closest to the one described in Lucas (2009). 2 Agents meet individuals of all ages at each point in time. The fraction of meetings with individuals of each age depends on their share in the total population. In contrast, in the second framework, individuals meet according to a Poisson process with an arrival rate that also depends on the density of individuals of each age. I will refer to this meeting process as the Poisson arrival model.A key difference between the two models is that agents in the continuous arrival model immediately get to learn from others, while in the Poisson arrival model, individuals do not improve their initial productivity until a learning opportunity arrives. However, I will show that the growth rate in a balanced growth path (BGP) is the same for both. Additionally, I generalize the Lucas (2009) growth formula by including the relative distance between the initial distribution and the invariant distribution. If the initial distribution is further away from the invariant one, then there are fewer learning opportunities and hence there is less growth. In Section I, I describe the two frameworks, study the resulting growth rates, and characterize the invariant distributions on a BGP. Then I highlight the common elements © 2018 The London School of Economics and Political Science. Published by Blackwell Publishing, 9600 Garsington Road, Oxford OX4 2DQ, UK and 350 Main St, Malden, MA 02148, USA Economica (2018) doi:10.1111/ecca.12273