By Steven J. Grisafi, PhD.
During the past few weeks Simon Wren-Lewis has been using an analogy to defend the sometimes ineffectual efforts of the practitioners of economics to guide macroeconomic policy, of which I highly approve. He has explained that, while the practitioners of medicine cannot predict how and when someone may become ill, they can explain, to a satisfactory extent, after someone has become ill, what went wrong with the person”s physiology, and what the best remedy for a cure might be. Prof. Wren-Lewis equates this performance of the practitioners of medicine with those of economics and I consider this analogy satisfactory. To help explain why I do, please allow me to relate a story to you.
Recently a friend of mine from my childhood asked me to model the heat flow created through the use of his new invention, for which he has just received a patent. My friend, a mechanical engineer, spent his entire career in the medical devices industry. His patent is for a device he developed to apply radio frequency induced heat flow into the tissues of living animals in order to alter those tissues for therapeutic purposes. My friend asked me to simulate the heat flow in arbitrary living tissues to provide temperature profiles resulting from an application of the device. After taking a precursory look at what I would be able to do for him, I found two significant obstacles hindering any such attempt to satisfy him. Both obstacles validate Paul Krugman”s often voiced opinion that economics depends upon circumstances. Engineers understand this. Yet, too many economists seem to have been trained to think like physicists. Such persons would look at my friend”s request and consider it to be as easy as pie. I recognized that I would need both the electrical permittivity and the thermal conductivity of this arbitrary living animal tissue. Such information is not available simply because both the animals and their tissue is arbitrary. Consider how much the fat content of tissues of dogs kept as pets can vary within any collection of such animals. Then consider that one cannot know a priori whether or not, when the device probe is inserted into an animal”s tissues, if the probe may find itself in the proximity of a blood vessel. That proximity would alter the boundary conditions for the simulation in that heat would be rapidly transported away from the tissues by the blood flow. One cannot assume that the material properties of the tissues, the electrical permittivity and thermal conductivity, are either homogeneous nor isotropic. Yet, how could one know the spatial and directional variations for these material properties if the tissues are arbitrary? Unknown circumstances inhibit any modeling effort. Recognizing this, I had to recommend to my friend that he lower his expectations for any such modeling effort to include only nominal dimensionless energy transport.
Although I have shifted my modeling efforts from physical systems to economics and finance, from an engineering viewpoint, that modeling effort is little changed. It just so happens that the circumstances of my friend”s device would enable me to model it using essentially the same partial differential equations I use in finance rheology. Whether it is an application in heat transfer or finance rheology one must solve a diffusion equation. The property that is diffusing within an economic system may be different from the property that is diffusing within a physical system, but the random walk character of all diffusion phenomena forms a similarity between the two. More often than not, engineers can do no better at forecasting than economists do.