[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 gij is 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]  (Click here for previous “Single Paragraphs”)
We have arranged this Topic into four parts:
- Part I: The Disorientations of Macroeconomists
- Part II: Principles and Precepts of Analysis
- 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)
One cannot help but think that Bernard Lonergan had functional macroeconomic dynamics clearly in mind as he treated the intelligibility of world process in CWL 3, Insight: …, which is very much an implementation of the act of understanding of mathematicians and natural scientists. In his understanding of mathematics, the natural sciences, and the science of macroeconomics in particular, he grasped that the explanation of the dynamic concrete process is expressed by a mathematical conjunction of component abstract primary relativities with component concrete secondary determinations from the non-systematic manifold. And these secondary determinations, such as particular prices and quantities, are to be interpreted in the light of the significant, abstract, explanatory variables rather than in the obscurity of the IS-LM, and AD-AS models. (Continue reading)
Our references in this section are [Burley, 1992-2] and [Burley and Csapo, 1992-1].
Burley, Peter and Csapo, Laszlo, (1992) Money Information in Lonergan-von Neumann Systems, Economic Systems Research, Vol 4, No. 2, 1992 [Burley and Csapo, 1992-1]
Burley, Peter (1992) Evolutionary von Neumann Models, Journal of Evolutionary Economics 2 , 269-80 [Burley, 1992-2]
We consider a game-theoretic, von Neumann model of the transitional process from an initial stationary state to a more abundant stationary state, with matrix A of inputs and matrix B of outputs containing explanatory functional variables. (continue reading)
Philanthropy: Anyone familiar with the medical and cultural institutions of Metropolitan Boston – upon which institutions the regional economy rides piggyback – cannot help but admire the beneficence, wisdom, and benefit of philanthropy: the Connors Center for Women’s Health and Gender Biology at Brigham and Women’s Hospital; the Connors Family Learning Center and the Clough Center for the Study of Constitutional Democracy at Boston College; the Yawkey Center for Outpatient Care and the Wang Building at Mass General; The Rosenberg Building at Beth Israel Hospital; the Salvation Army Kroc Center on Dudley St.; the Harry V. Keefe Library and the Clough Center for Global Understanding at Boston Latin School; the John A. Paulson School of Engineering and Applied Sciences at Harvard; the Carl J. and Ruth Shapiro Cardiovascular Center at Brigham and Women’s Hospital; museums, endowed scholarship funds, hundreds of endowed chairs, stained glass windows, etc. (Continue reading)
DSGE is – to many economists – the standard model and method of macroeconomic analysis. See our treatment of the textbooks’ IS-LM, AD-AS models and the Phillips Curve correlation.
The acronym stands for Dynamic (in Newtonian mechanics an external force causes a change to constant velocity, i.e. an acceleration, which may be negative or positive), Stochastic (random, not according to system, probabilistic, unexplained) General (pertaining to the entire economic process), Equilibrium (essentially Walrasian static equilibrium).
Leon Walras developed the conception of the markets as exchange equilibria. Concentrate all markets into a single hall. Place entrepreneurs behind a central counter. Let all agents of supply offer their services, and the same individuals, as purchasers, state their demands. Then the function of the entrepreneur is to find the equilibrium between these demands and potential supply. … The conception is exact, but it is not complete. It follows from the idea of exchange, but it does not take into account the phases of the productive rhythms. … [CWL 21, 51-52] (Continue reading)
N. Gregory Mankiw wrote an article for the Sunday New York Times, 8/11/19, entitled Ties That Bind Inflation and Unemployment. His final paragraph states:
The Fed’s job is to balance the competing risks of rising unemployment and rising inflation. Striking just the right balance is never easy. The first step, however is to recognize that the Phillips curve is always out there lurking.
We have emphasized that the Fed’s responsibilities are a.) to be admonitory and supervisory to the banking system, and b.) to supply the economy with the quantity of money needed for orderly execution of the magnitudes and frequencies of operative payments. And it is the responsibility of the enlightened private and government sectors – not the Fed, because it does not possess sufficiently effective tools – to manage production, employment, and philanthropy properly. By so doing, enterprise and government can effect production, pricing, interest rates, and dividend rates consistent with the opportunities and risks in the system; and they can achieve the full productivity made possible by the invention, gumption, and hard work of free people, yet properly constrained by the state of technology, culture, and resources. Contrary to what Mankiw seems to be approving in his conclusion, it is wrong to assign responsibility to the Fed for adjusting inflation and unemployment in the economic process by artificially manipulating the interest rate. And, despite all the hype about the effectiveness or ineffectiveness of manipulating the rental price of money (i.e. the interest rate), no one has yet developed the ability to separate the effect of self-healing from the positive or the negative, counterproductive effect of interest-rate manipulation. For further perspective, click here for critical treatment of the IS-LM, AD-AS, and Phillips Curve Models, including notes explaining stagflation and the need to transition from a single-circuit analysis to a double-circuit analysis; here, for Notes Regarding FRB Monetary Policy and a Theoretic of Credit; and here for Practical Precepts for Free People – Consumers, Entrepreneurs, Bankers, Investors. Also see Summary of the Argument (CWL 15, 5-6) and The Cycle of Basic Income (CWL 15, 133-44).