From J* To U*: What My Conjecture Is About

I receive got footling dubiousness that my previous article on J* -- a definition that I invented -- was confusing to most of my readers. As I wrote, I reverted to a mathematical style of writing. It is probable that inventing a concept together with proving it does non be is a pastime that would mainly live on of involvement to mathematicians (and philosophers). However, I receive got a real-world target inward mind: NAIRU. All nosotros demand to exercise generalise the theorem procedure, together with nosotros tin sack essay that a similar concept -- U* -- does non be inward the electrical flow institutional structure. We tin sack thence role that information to annihilate any definition of NAIRU that ends upwards existence equivalent to U*.

Why non receive got on NAIRU directly, a reader mightiness ask? This is because economists are non mathematicians. They role whatever number of unlike concepts, together with assume that they are the same thing. It is a waste product of fourth dimension trying to essay the incoherence of each of these concepts; nosotros but essay that U* cannot exist, together with nosotros tin sack thence but essay the equivalence of whatever item definition of NAIRU to U* equally needed.

Obviously,. that seems to live on a rather grandiose assertion. I could easily live on wrong. The most obvious hurdle is that in that place could live on a flaw inward my J* non-existence proof. I receive got thrown it out there, together with I am waiting for it to live on shot down. Influenza A virus subtype H5N1 to a greater extent than intelligent approach would receive got been to approach people privately together with teach their opinion, but hey, I decided to coil the dice.

The side yesteryear side hurdle is generalisation. I receive got added or thence comments below (which I added to the master article equally well). When I start did the proof, I had really footling thought how to generalise it; I but needed to pivot downward a proof for a unmarried case. However, if nosotros start pulling theoretical tricks out of the nonlinear robust command toolkit, the undertaking mightiness live on easily done. If nosotros desire to generalise the result, things could teach pretty ugly from a mathematical request of view. For example, norms of serial volition non converge. I dealt amongst this inward my doctoral thesis inward an inelegant fashion; mathematicians may receive got a improve agency to approach it.

If my guess is correct, finding a counter-example model is much tougher than it would appear. It is non plenty to alternative a model that violates i of the many assumptions I imposed: the model cannot live on approximated yesteryear whatever such organization inward steady state. Is such a model going to live on anything other than pathological?

Furthermore, lack of a steady soil mightiness non live on enough. If nosotros deed into the frequency domain, nosotros tin sack but pivot downward the nix frequency behaviour. If this works, nosotros tin sack striking whatever organization amongst oscillatory or fifty-fifty chaotic behaviour.

Trivial Definitions of NAIRU

The job amongst mainstream economical analysis is the style to interchange variables that are the outcome of statistical methods together with theoretical concepts. It is obvious that if nosotros define NAIRU to live on the outcome of or thence statistical procedure, it exists. The job is that such a definition is trivial: it has no predictive power.

Imagine that I define "NAIRU" to live on the 12-month moving average of the unemployment rate. We know that if nosotros receive got whatever reasonable definition of steady state, the observed unemployment charge per unit of measurement has to converge to my definition of NAIRU. However, seems clear that this is a trivial observation: this guess of NAIRU has essentially no predictive powerfulness for other steady states.

I imagine that the economists producing NAIRU estimates would live on really unhappy amongst the proposition that their fancy models are equivalent to taking the 12-month moving average of the unemployment rate. However, I encounter no evidence that their estimates receive got whatever to a greater extent than predictive powerfulness than that definition.

What is non Implied yesteryear this Conjecture

My arguments hither are theoretical. I receive got footling dubiousness that they could live on misinterpreted yesteryear those who exercise non sympathize economical theory. I assume that my readers would non brand these item arguments, but i could conceive that individual somewhere mightiness brand comments that are equivalent to the next statements.

• Non-existence of U* implies no trade-off betwixt unemployment together with inflation. This conjecture does non imply that nosotros would non encounter a trade-off betwixt unemployment together with inflation. All the conjecture states is that the trade-off has to include the number of financial policy. We tin sack accommodate the unemployment charge per unit of measurement (within limits) yesteryear changing financial policy, without affecting the steady soil inflation rate.
• Why don't policymakers drive the unemployment charge per unit of measurement to zero? That enquiry presupposes that policymakers care most the fate of the unemployed; I encounter footling evidence of such attention inward the post-1990s world. Secondly, in that place is no machinery -- other than the Job Guarantee -- to forcefulness the "involuntary" unemployment charge per unit of measurement to zero. (If a Job Guarantee were implemented, in that place would yet live on residue unemployment from people on jobless benefits, or conducting a undertaking search. Since they could receive got a Job Guarantee job, such unemployment mightiness live on viewed equally voluntary. Whatever.) Traditional demand-management techniques used inward the 1960s failed, for reasons outlined yesteryear Hyman Minsky (and presumably others) at the time. Within the simplistic degree of models studied, the "fiscal coherence" supposition does imply a non-zero lower jump for the observed J or unemployment charge per unit of measurement does exist: nosotros receive got a theoretical bound for how depression revenue enhancement rates tin sack live on an yet save cost stability. In the existent world, nosotros receive got clearly never flirted amongst that theoretical lower bound.

Remarks on Generalisation

Remark. We exercise non demand to assume that economical models prevarication inward the degree of models described here. It may exclusively live on plenty to specify that they tin sack live on approximated yesteryear such a model inward steady state. This is apparently a much wider degree of model behaviour. We tin sack formalise the notion of approximating a organization yesteryear applying the definitions used inward robust command theory. (My doctoral thesis is the exclusively reference I tin sack offering off-hand that covers the issues I see.)

Remark. The steady soil supposition is needed to permit us to apply algebra inward the proof. If nosotros were willing to delve into to a greater extent than advanced mathematics, it seems possible that nosotros could specify atmospheric condition inward frequency domain terms, together with but facial expression at the nix frequency ("DC") element of signals. Since most fourth dimension serial are expected to live on bounded away from nix for interplanetary space periods of time, in that place would live on obvious convergence issues for the Fourier transform. We would demand to exercise our analysis on finite intervals, together with thence receive got limits. This would live on tedious, but the generalisation may outcome inward a to a greater extent than elegant proof.

(c) Brian Romanchuk 2017