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Most college students are required to take at least one mathematics course. Many of these students view mathematics as a dry and tedious subject, where the main task is to “plug and chug” using formulas. In contrast, mathematicians see mathematics as a creative process in which real joy comes from grappling with difficult problems and (hopefully) solving them. In this way, mathematics is like a fun puzzle. The challenge is to get students to view mathematics the same way that their teachers do. Inquiry-based learning (IBL) can help solve this problem. The Academy of Inquiry-Based Learning describes IBL as a pedagogical method that encourages students to conjecture, discover, solve, explore, collaborate, and communicate (What is IBL? (n.d.). Retrieved from http://www.inquirybasedlearning.org/?page=What_is_IBL). With IBL, teachers do not lay out all of the formulas and theorems as previous knowledge. Nor do they provide perfect, easily worked through examples and proofs for every new topic. Instead, IBL courses demonstrate the creative process that is mathematics. IBL makes class more enjoyable for both teachers and students, and can bring students closer to the real experiences of mathematicians.

After briefly reviewing the past history of Bayesian econometrics and Alan Greenspan's (2004) recent description of his use of Bayesian methods in managing policy-making risk, some of the issues and needs that he mentions are discussed and linked to past and present Bayesian econometric research. Then a review of some recent Bayesian econometric research and needs is presented. Finally, some thoughts are presented that relate to the future of Bayesian econometrics.

This chapter provides an alternative interpretation of the emergence of the “Ramsey-Cass-Koopmans” growth model, a framework which, alongside the overlapping generation model, is the dominant approach in today’s macroeconomics. By focusing on the role Paul Samuelson played through the works he developed in the turnpike literature, the author’s goal is to provide a more accurate history of growth theory of the 1940–1960s, one which started before Solow (1956) but never had him as a central reference. Inspired by John von Neumann’s famous 1945 article, Samuelson wrote his first turnpike paper by trying to conjecture an alternative optimal growth path (Samuelson, 1949 [1966]). In the 1960s, after reformulating the intertemporal utility model presented in Ramsey (1928), Samuelson began to propound it as a representative agent model. Through Samuelson’s interactions with colleagues and PhD students at the Massachusetts Institute of Technology (MIT), and given his standing in the profession, he encouraged a broader use of that device in macroeconomics, particularly, in growth theory. With the publication of Samuelson (1965), Tjalling Koopmans and Lionel McKenzie rewrote their own articles in order to account for the new approach. This work complements a recently written account on growth theory by Assaf and Duarte (2018).

The asymptotic bias and variance of a general class of local polynomial estimators of M-regression functions are studied over the whole compact support of the multivariate covariate under a minimal assumption on the support. The support assumption ensures that the vicinity of the boundary of the support will be visited by the multivariate covariate. The results show that like in the univariate case, multivariate local polynomial estimators have good bias and variance properties near the boundary. For the local polynomial regression estimator, we establish its asymptotic normality near the boundary and the usual optimal uniform convergence rate over the whole support. For local polynomial quantile regression, we establish a uniform linearization result which allows us to obtain similar results to the local polynomial regression. We demonstrate both theoretically and numerically that with our uniform results, the common practice of trimming local polynomial regression or quantile estimators to avoid “the boundary effect” is not needed.

The first issue that requires examination is the question of how we got to this point to begin with. The answer to this question, of course, is a function of who “we” happens to be. The lawyers can blame Oliver Wendell Holmes (1897, p. 469), who made “the man of the future … the man of statistics and the master of economics.” The future, it would seem, is now. Legal Realist/Institutionalist lawyer-economists such as Walton Hamilton and Robert Lee Hale, who were economists on law school faculties before that tradition got started at Chicago, had something to do with this too, although neither they nor law-minded economists such as John R. Commons can be given credit or blame for the economic analysis of law – at least not directly.³ The birth of the economic analysis of law is very much a Chicago story – Coase, Becker, and Posner – although we must allow that Guido Calabresi also had more than a bit to do with these things.⁴

X = multiple interpretations

Paul Samuelson was attracted to the irregular economic development pattern of some South American countries because of the links between economic performance and political factors. He discussed the influence of “populist democracy” on Argentina’s relative economic stagnation, which, he argued in the 1970s and early 1980s, served as a dangerous paradigm for the American economy under stagflation. Stagflation phenomena marked the end of Samuelson’s “neoclassical synthesis.” Moreover, he applied his concept of “capitalist fascism” to deal with military dictatorships in Brazil and (especially) in Chile. The Brazilian translation of his Economics in 1973 brought about a correspondence with Brazilian economists about the “fascist” features of the regime. The main variable behind the South American economic and politically unstable processes discussed by Samuelson was economic inequality, which became also a conspicuous feature of the American economy since the adoption of market-based policies in the 1980s and after.

I show that the equilibrium distribution of matches associated with the empirical transferable utility one-to-one matching (TUM) model introduced by Choo and Siow (2006a, 2006b) corresponds to the fixed point of system of K + L nonlinear equations; with K and L respectively equal to the number of discrete types of women and men. I use this representation to derive new comparative static results, showing how the match distribution varies with match surplus and the marginal distributions of agent types.