Analytic functions & the miraculous effectiveness of Taylor series; Mike Konczal on how the “too hot” labor market is over; very briefly noted; did economists “take a beating” in 2023?; will...
For me the fascinating thing is that for a complex-valued function of complex variables, there is no distinction between smooth and analytic; a complex function that is infinitely differentiable necessarily has a power series representation. Then too, the definition of a complex derivative, which is a map from a 2-dimensional real algebra to itself, looks deceptively simpler than the definition of a multivariate real derivative; exactly like a 1-dimensional real derivative in fact. Somehow, the fact that the limit must be the same not only on every path of approach in the domain but also have the same 2-dimensional value in the co-domain makes things simpler instead of more complicated. It is like one of those zen things where extreme levels of mastery circle around to approach the novice again.
Serfs and slaves: I always thought that the difference between serfs and slaves arose out of property law. Slaves were chattels: corporeal and detachable from land. Serfs were part of the real estate, and could only be bought and sold with the land. (This distinction still underlies American law, with most intangible property closer to the law of chattels than realty.)
Hence the slightly redundant term "chattel slavery." Serf status is certainly preferable from the serf's perspective, at least as long as the land isn't populated beyond its carrying capacity.
Thanks very much for the reference to the video - I would not have dreamed when I was a math major (long, long ago) that 100k+ people would be as interested in the fine points of analytic vs. smooth functions! What a delight to see those ideas embodied on screen instead of dusty chalkboard or my equally dusty imagination !
"also believe that while labor demand continues to expand robustly, policy is sufficiently restrictive that it will not remain so for long. But our strong belief that it is time for the Fed to cut—that when inflation is near-target interest rates should be near-neutral"
What does believing in r* have to do with this judgment?
We have an (in principle) highly differentiated model that links Fed policy instruments (ONE of which is control of short terms interest rates) to the optimal (income maximizing) rate of inflation at any one point. Presumably the model can be solved for the short term interest rate (given other policy instruments) that will be needed when the Fed has successfully gotten inflation on an income maximizing target. But why do we need to know THAT rate when inflation is NOT at its income maximizing level?
"[the PC is ]comprehensive filing cabinet for organizing thinking about inflation and demand episodes than a theory that can “take a beating.”
OK but what needs to go into different folders in the filing cabinet is pattern of heterogeneous sectoral shocks and heterogeneous stickiness of nominal prices and wages that makes relative prices more difficult to change with inflation.
Phillips Curve Beating. Would "economists" have had a better year if those who, on Phillips Curve grounds" thought the Fed's efforts to reduce inflation had produced a recession than those "Team Temporary" Philips Curve users who thought the Fed ought t try and had a good chance of achieving a "soft lanking?"
Of course both groups were wrong. The Philips Curve does not exist as a parameter of a model that correctly sees the Fed using inflation to facilitate a multitude of heterogeneous relative price and wage adjustments. A Phillips Curve is a projection onto a two dimension space of the multidimensional adjustments of wages, prices, and product level market clearing. Such a projection can always be made but has little policy relevance. [The lower the dimensionality of the shocks and relative price changes the economy actually exhibits, the Phillips curve will be a better approximation.]
Nimbyism: Partly we are just dealing with garden variety political economy: "losers" are concentrated and self aware, winners even when total benefits exceed total costs, are unidentified future residents or business owners. Showing that the total benefits DO exceed costs and that "losers" may not lose as much as they think, and as citizens, they will benefit from the part of total benefits represented by greater revenues. And in principle why not offset some of the losses? For example, if street parking goes from free to priced, residents could be given part of the revenue.
Reifschneider & Wilcox: The reason for optimism is not that the economy suffered a sectoral shock, but that they saw that the Fed recognized that and was willing to make inflation temporary as relative prices adjusted to the shock. Only a bit of the disinflation was needed to pull back the excess inflation resulting from delaying the movement of the EFFR from Sept 2021 to March 2022.
For me the fascinating thing is that for a complex-valued function of complex variables, there is no distinction between smooth and analytic; a complex function that is infinitely differentiable necessarily has a power series representation. Then too, the definition of a complex derivative, which is a map from a 2-dimensional real algebra to itself, looks deceptively simpler than the definition of a multivariate real derivative; exactly like a 1-dimensional real derivative in fact. Somehow, the fact that the limit must be the same not only on every path of approach in the domain but also have the same 2-dimensional value in the co-domain makes things simpler instead of more complicated. It is like one of those zen things where extreme levels of mastery circle around to approach the novice again.
Serfs and slaves: I always thought that the difference between serfs and slaves arose out of property law. Slaves were chattels: corporeal and detachable from land. Serfs were part of the real estate, and could only be bought and sold with the land. (This distinction still underlies American law, with most intangible property closer to the law of chattels than realty.)
Hence the slightly redundant term "chattel slavery." Serf status is certainly preferable from the serf's perspective, at least as long as the land isn't populated beyond its carrying capacity.
Thanks very much for the reference to the video - I would not have dreamed when I was a math major (long, long ago) that 100k+ people would be as interested in the fine points of analytic vs. smooth functions! What a delight to see those ideas embodied on screen instead of dusty chalkboard or my equally dusty imagination !
"also believe that while labor demand continues to expand robustly, policy is sufficiently restrictive that it will not remain so for long. But our strong belief that it is time for the Fed to cut—that when inflation is near-target interest rates should be near-neutral"
What does believing in r* have to do with this judgment?
We have an (in principle) highly differentiated model that links Fed policy instruments (ONE of which is control of short terms interest rates) to the optimal (income maximizing) rate of inflation at any one point. Presumably the model can be solved for the short term interest rate (given other policy instruments) that will be needed when the Fed has successfully gotten inflation on an income maximizing target. But why do we need to know THAT rate when inflation is NOT at its income maximizing level?
"[the PC is ]comprehensive filing cabinet for organizing thinking about inflation and demand episodes than a theory that can “take a beating.”
OK but what needs to go into different folders in the filing cabinet is pattern of heterogeneous sectoral shocks and heterogeneous stickiness of nominal prices and wages that makes relative prices more difficult to change with inflation.
Phillips Curve Beating. Would "economists" have had a better year if those who, on Phillips Curve grounds" thought the Fed's efforts to reduce inflation had produced a recession than those "Team Temporary" Philips Curve users who thought the Fed ought t try and had a good chance of achieving a "soft lanking?"
Of course both groups were wrong. The Philips Curve does not exist as a parameter of a model that correctly sees the Fed using inflation to facilitate a multitude of heterogeneous relative price and wage adjustments. A Phillips Curve is a projection onto a two dimension space of the multidimensional adjustments of wages, prices, and product level market clearing. Such a projection can always be made but has little policy relevance. [The lower the dimensionality of the shocks and relative price changes the economy actually exhibits, the Phillips curve will be a better approximation.]
Nimbyism: Partly we are just dealing with garden variety political economy: "losers" are concentrated and self aware, winners even when total benefits exceed total costs, are unidentified future residents or business owners. Showing that the total benefits DO exceed costs and that "losers" may not lose as much as they think, and as citizens, they will benefit from the part of total benefits represented by greater revenues. And in principle why not offset some of the losses? For example, if street parking goes from free to priced, residents could be given part of the revenue.
Reifschneider & Wilcox: The reason for optimism is not that the economy suffered a sectoral shock, but that they saw that the Fed recognized that and was willing to make inflation temporary as relative prices adjusted to the shock. Only a bit of the disinflation was needed to pull back the excess inflation resulting from delaying the movement of the EFFR from Sept 2021 to March 2022.