Origins and Early Development of the Nonlinear Endogenous Mathematical Theory of the Business Cycle: Part I - The Setting

We study the emergence of the nonlinear, endogenous, theory of the business cycle, in mathematical modes, within the framework of a macroeconomic theory, which was itself going through its own formal 'birth pangs' at the same time, in the same years. The first part of the story begins in 1928 and ends, with the publication of Yasui's classic on Kaldor, Hicks and Goodwin, in 1953, and Hudson's classic of 1957. But there were other classics in the 1930s, even within some theories of the business cycles of the time - particularly the Austrian and that which may now be called the 'time-to-build' tradition, which originates in Marx and Aftalion, independently, and reaches its nonlinear formalization origins in Tinbergenís work of 1931, followed by Kalecki's theories of the business cycle, substantially influenced also by Tinbergen's classic for mathematical method. There is also what may, for want of a better name, be called the 'cobweb' tradition, on the one hand, and the tradition of Swedish Sequence Analysis, on the other (especially in the 1937 classic work of Lundberg, summarising the Swedish discussion on business cycle theory). The former having its origins, partly, in Austrian inspired search for an integration of dynamic method with equilibrium economic theory (especially represented by a series of classics by Rosenstein-Rodan, from about 1929); and partly in the well known phenomenon of lagged responses in the supply-demand interactions in agricultural and commodity markets, particularly elegantly formalised by Leontief in 1934. From the point of view of economic theory, they were all part of the emerging consensus on the need to incorporate money and áuctuations in nontrivial ways as intrinsic components of orthodox equilibrium economic theory which was characterised as static theory. The implication was that the search was for a synthesis of dynamic method with traditional static equilibrium economic theory. The origins of macroeconomic theory, generally attributed to the post-depression development of monetary theory, business cycle theory and the theory of policy, could be traced to this particular search for a synthesis and was brilliantly summarised by Kuznets in a series of pioneering contributions in 1929/30. The story we try to tell is of mathematical business cycle theory in its non-linear modes, and how it emerged from one strand of macroeconomic theory, which, as just mentioned, was itself being forged, ab initio, dynamically

25-hydroxyvitamin D is lower in deprived groups, but is not associated with carotid intima media thickness or plaques: results from pSoBid

Objective: The association of the circulating serum vitamin D metabolite 25-hydroxyvitamin D (25OHD) with atherosclerotic burden is unclear, with previous studies reporting disparate results. <p/>Method: Psychological, social and biological determinants of ill health (pSoBid) is a study of participants aged 35–64 years from Glasgow who live at extremes of the socioeconomic spectrum. Vitamin D deficiency was defined as 25OHD < 25nmol/L, as per convention. Cross-sectional associations between circulating 25OHD concentrations and a range of socioeconomic, lifestyle, and biochemistry factors, as well as carotid intima media thickness (cIMT) and plaque presence were assessed in 625 participants. <p/>Results: Geometric mean levels of circulating 25OHD were higher among the least deprived (45.6 nmol/L, 1-SD range 24.4–85.5) versus most deprived (34.2 nmol/L, 1-SD range 16.9–69.2; p < 0.0001). In the least deprived group 15% were “deficient” in circulating 25OHD versus 30.8% in the most deprived (χ2p < 0.0001). Log 25OHD was 27% lower among smokers (p < 0.0001), 20% higher among the physically active versus inactive (p = 0.01), 2% lower per 1 kg/m2 increase in body mass index (BMI) (p < 0.0001), and showed expected seasonal variation (χ2p < 0.0001). Log 25OHD was 13% lower in the most versus least deprived independent of the aforementioned lifestyle confounding factors (p = 0.03). One unit increase in log 25OHD was not associated with atherosclerotic burden in univariable models; cIMT (effect estimate 0.000 mm [95% CI −0.011, 0.012]); plaque presence (OR 0.88 [0.75, 1.03]), or in multivariable models. <p/>Conclusion: There is no strong association of 25OHD with cIMT or plaque presence, despite strong evidence 25OHD associates with lifestyle factors and socioeconomic deprivation

Human and Machine Learning

In this paper, we consider learning by human beings and machines in the light of Herbert Simon’s pioneering contributions to the theory of Human Problem Solving. Using board games of perfect information as a paradigm, we explore differences in human and machine learning in complex strategic environments. In doing so, we contrast theories of learning in classical game theory with computational game theory proposed by Simon. Among theories that invoke computation, we make a further distinction between computable and computational or machine learning theories. We argue that the modern machine learning algorithms, although impressive in terms of their performance, do not necessarily shed enough light on human learning. Instead, they seem to take us further away from Simon’s lifelong quest to understand the mechanics of actual human behaviour

Beginning, crises, and end of the money economy

A crisis is but a crisis when the long run outlook is definitively positive. Then a lower turning point must exist. This implicates a vision or, in the ideal case, a formalized theory of the money economy’s possible end states. This theory has to provide an endogenous explanation of end states and crises. The equilibrium approach excludes endogenous causes in principle. Thus disturbances can only be explained by exogenous random shocks. The structural axiomatic approach, that is applied in the following, consistently defines the potential systemic crisis point and the conditions of an economic happy end