[10/9/19] Lonergan brought a deep knowledge of mathematics and physics to his work in Functional Macroeconomic Dynamics.
Now the principles and laws of a geometry are abstract and generally valid propositions. It follows that the mathematical expression of the principles and laws of a geometry will be invariant under the permissible transformations of that geometry. … Such is the general principle and it admits at least two applications. In the first application one specifies successive sets of transformation equations, determines the mathematical expressions invariant under those transformations, and concludes that the successive sets of invariants represent the principles and laws of successive geometries. In this fashion one may differentiate Euclidean, affine, projective and topological geometries. … A second, slightly different application of the general principle occurs in the theory of Riemannian manifolds. The one basic law governing all such manifolds is given by the equation for the infinitesimal interval, namely,
ds2= Σgijdxidxj [i, j = 1,2…n]
where dx1, dx2… are differentials of the coordinates, and where in general there are n2products under the summation. Since this equation defines the infinitesimal interval, it must be invariant under all permissible transformations. However, instead of working out successive sets of transformations, one considers any transformations to be permissible and effects the differentiation of different manifolds by imposing restrictions upon the coefficients. This is done by appealing to the tensor calculus. … Thus in the familiar Euclidean instance, gij is unity when i equals j; it is zero when i does not equal j; and there are three dimensions. In Minkowski space, the gijis unity or zero as before, but there are four dimensions, and x4 equals ict. In the General Theory of Relativity, the coefficients are symmetrical, so that gij equals gji; and in the Generalized Theory of Gravitation, the coefficients are anti-symmetrical. [CWL 3, 146 -147/170-71]  (Clickhere for previous “Single Paragraphs”)
Part III: A New Textbook, Lonergan’s Macroeconomic Dynamics: A Textbook in Circulation Analysis
Part IV Comments on The Federal Reserve’s Current Framework For Monetary Policy: A Review and Assessment, by Janice C. Eberly, James H. Stock, and Jonathan H Wright.
Part I: The Disorientations of Macroeconomists
One cannot help but admire and be grateful to the Federal Reserve Bank for its Flow of Funds matrices and the National Bureau of Economic Research for its GDP tables. Great information, well done! However, the Fed, the NBER, and the proponents of the DSGE methodology suffer from fundamental disorientations. The NBER’s descriptive, commonsense, national-income accounting must integrate the Fed’s data on credit and to be recast to provide an explanatory systematization of interdependent flows of products and money. Devotees must reorient themselves. (Continue reading)
In his book, FREEFALL (2009, Penguin Books), Joseph Eugene Stiglitz, a professor at Columbia University and a recipient of the Nobel Memorial Prize in Economic Sciences (2001) and the John Bates Clark Medal (1979), states that economics is a predictive science. Now, one must distinguish between predicting a) planetary motion in its scheme of recurrence, and b) this afternoon’s weather vs. next month’s weather, or this afternoon’s prices and quantities vs. next year’s prices and quantities, all subject to to conditions diverging in space and time. Continue reading)
There is required a shift of focus by academics from the concrete secondary determinations of prices and quantities in a non-systematic manifold to the immanent, abstract, primary relativities which may be applied to these secondary determinations to reach particular laws.
Paraphrasing [McShane, 1980, 127]: Taking into account past and (expected) future values does not constitute the creative key transition to Functional Macroeconomic Dynamics.Continue reading →
In this section, we are contrasting familiar textbook models of macrostatic equilibrium, with Lonergan’s explanatory theory of macrodynamic equilibrium. We are contrasting a macrostatic toolkit with a purely relational field theory of macroeconomic dynamics. Lonergan discovered a theory which is more fundamental than the traditional wisdom based upon human psychology and purported endogenous reactions to external forces. His Functional Macroeconomic Dynamics is a set of relationships between n objects, a set of intelligible relations linking what is implicitly defined by the relations themselves, a set of relational forms wherein the form of any element is known through its relations to all other elements. His field theory is a singleexplanatory unity; it is purely relational, completely general, and universally applicable to every configuration in any instance. (Continue reading)