Mathiness

The recent eruption around "mathiness" is the latest burst of discontent almost the dry soil of macroeconomic theory.  There is an undercurrent of politics inside the argument. Once again, I seem to hold upward inward understanding amongst those who likely are on the reverse side of political economic scheme debates from myself. To summarise my views: mathematics is a neutral tool that allows the creation of internally consistent models, but those models may or may non comport whatsoever resemblance to the existent world. And inside the footing of DSGE macro, the fact that the consensus appears to receive got endorsed so-called "New Keynesian" models tells us petty almost their validity.

Mathematics Versus Mathiness

In "Protecting the Norms of Science inward Economics", Paul Romer writes:

About math: I receive got studied physics equally an undergraduate. I’ve seen clear evidence that math tin facilitate scientific progress toward the truth.
If you lot intend that math is worthless or dangerous, I’m certain that at that spot are people who volition hold upward happy to beak over this amongst you. I’m non interested. I’m busy.

I'll come across his undergraduate grade inward physics, as well as enhance him yesteryear a Ph.D. inward applied mathematics (Control Systems Theory). Undergraduate physicists written report highly polished as well as elegant models which receive got been chosen because they line aspects of physical conduct quite well. Conversely, engineers written report complex systems which may or may non appear to follow those simplified laws of nature*, as well as are forced to brand educated guesses on how to simplify the analysis of the systems. Economics is dealing amongst complex systems that are a lot closer to the reality of engineering than the ivory tower of undergraduate physics.

One needs to force downwardly the expectations of what mathematics tin accomplish. Mathematics consists of 2 things:

1. sets; and
2. mathematical (formal) logic, which decide the rules on how nosotros tin manipulate sets to create novel sets. (One tin also laid novel rules for mathematical logic as well as come across what happens, but that is largely the domain of pure mathematicians.)

For example, I took a start twelvemonth graduate course of pedagogy on Linear Systems (taught yesteryear George Zames) when I was an undergraduate, He asked "What is a function?", as well as nobody inward the shape knew the right reply (including me). People were coming amongst definitions involving rules, mappings, et cetera. The existent answer: a component division is a laid of ordered pairs amongst some extra properties tacked on. If nosotros write y=f(x), that is truly precisely specifying that f is a laid of the shape {(x,y)}, with the usual holding that if (x,y) is an chemical factor of f, nosotros cannot receive got some other chemical factor (x,z) in the set, amongst z<>y. Once nosotros create the allowed logical rules, everything inward mathematics is a set, as well as all you lot tin practise is manipulate said sets.

When you lot read modern mainstream economics, this seems to hold upward lost. You read almost things similar "equilibrium", "households", "agents" equally if they are concepts inside mathematics. The exception that I am aware of is Stock-Flow Consistent (SFC) modelling, equally those authors truly write downwardly the scheme equations inward a fashion that is consistent amongst the established norms of mathematics.

As a real basic example, bring 2 optimisation job models.

1. Model M1: Find x such that the component division U(x)= -x^2 is maximised.
2. Model M2: Find x such that the component division U(x) = -(x+1)^2 is maximised. 

It is straightforward to come across that x=0 is the solution to model M1, as well as x=-1 is the solution to model M2. Even though at that spot is a component division amongst the same call (U(x)), as well as it is a component division of a variable amongst the same call (x), most undergraduates volition receive got no difficulty inward understanding that these are truly unlike objects (sets). To what extent these mathematical models as well as solutions fit to real-world optimisation problems, both models tin hold upward viewed equally "valid models" (but presumably non for the same real-world system).

However, Dynamic Stochastic General Equilibrium (DSGE) macro has a hard fourth dimension dealing amongst this distinction. Results from optimisation problems on i laid of mathematical systems ("microeconomics") are imported at random into some other optimisation job (the DSGE model). Which random laid of results which are imported is based on the political biases of the DSGE modeller. To interpret this to my simplified instance above, this is equivalent to proverb that x=0 is the solution to M2, precisely because it is the solution to M1, as well as the variables receive got the same name. I would hold upward hard-pressed to telephone shout out upward this "mathiness"; "Calvinball" is a improve description.

As an example, I volition refer to the instance inward my recent give-and-take of financial policy inward DSGE models that was published at the Real-World Economic Review.

All nosotros tin practise amongst mathematical models of dynamical systems:

1. Write them downwardly clearly, specifying all the sets involved inward the system.
2. Determine the solution(s) to the system.
3. See whether these scheme results fit to real-world behaviour.

Growth Theory

This burst yesteryear Paul Romer was largely triggered yesteryear some academic turf struggle inside the plain of Growth Theory. The theory attempts to characterise the determinants of long-term growth trends. I receive got spent petty fourth dimension looking at growth theory, since it appears self-evidently useless to me. The principal recommendations seem to be: "grow your population", as well as "be to a greater extent than productive, somehow!".

The long run is made upward of curt runs. At present, all of the major countries receive got pose inward house policy settings that leaves a large part of their working population inward unemployment or underemployment. This patently constrains growth, however I receive got non seen whatsoever component division of "Growth Theory" that addresses this problem.

The Tyranny Of Consensus

In "Don't acquire mathy amongst me, or I'll give you lot a skillful shunning", Stephan Williamson responds inward what I persuasion equally effective fashion. It should hold upward noted that Williamson is a Monetarist, non a schoolhouse of thought of economic science that I unremarkably receive got a lot of positive things to say about.

Williamson writes:

Think of truth equally existing at the laissez passer on of a mountain. Once nosotros acquire to the laissez passer on of the mount we'll know it, equally we'll hold upward able to come across a long way, but patch we're climbing the mount we're inward a fog, as well as nosotros can't come across the laissez passer on of the mountain. But nosotros mightiness hold upward able to discern whether we're moving up, down, or precisely sitting inward i place. Paul thinks that nosotros can't precisely allow scientists run loose to bring diverse paths upward the mount amongst unlike kinds of gear, as well as amongst unlike companions of their choosing. According to him, nosotros receive got to organize this enterprise, as well as it's absolutely necessary that nosotros write downwardly a laid of rules that nosotros volition abide by, come upward hell or high water. And when he says "reputational equilibrium" most economists volition know what he has inward heed - at that spot volition hold upward punishments (imposed yesteryear the group) for deviating from the rules.

recent give-and-take of financial policy inward DSGE models that was published at the Real-World Economic Review.

All nosotros tin practise amongst mathematical models of dynamical systems:

1. Write them downwardly clearly, specifying all the sets involved inward the system.
2. Determine the solution(s) to the system.
3. See whether these scheme results fit to real-world behaviour.

Growth Theory

This burst yesteryear Paul Romer was largely triggered yesteryear some academic turf struggle inside the plain of Growth Theory. The theory attempts to characterise the determinants of long-term growth trends. I receive got spent petty fourth dimension looking at growth theory, since it appears self-evidently useless to me. The principal recommendations seem to be: "grow your population", as well as "be to a greater extent than productive, somehow!".

The long run is made upward of curt runs. At present, all of the major countries receive got pose inward house policy settings that leaves a large part of their working population inward unemployment or underemployment. This patently constrains growth, however I receive got non seen whatsoever component division of "Growth Theory" that addresses this problem.

The Tyranny Of Consensus

In "Simon Wren-Lewis objects, defending Romer's views.

But why is it of import to receive got an thought of what that plurality is as well as admit it? I tin intend of 3 reasons. First, it presents an honest motion-picture demo to those learning the discipline. Second, it is real of import that policy makers are told which ideas are widely agreed as well as which are the views of a little minority. That does non halt policy makers going amongst the minority, but they should know what they are doing (as should voters). The public’s trust inward economic science mightiness also growth equally a result. Third, it helps the unity of the subject, usual understanding as well as progress. It becomes clear why those who practise non bring the views of the “plurality” disagree, as well as what they demand to practise to convince the plurality that they are wrong.

Wren-Lewis' persuasion is highly appropriate, given his condition equally a professor of Oxford. I handle a doctorate from the University of Cambridge, but I receive got no illusions almost the intellectual history of the Oxbridge system. Throughout most of their history, Universities were non a centre of independent thought; they trained people to intend at a high story within socially accepted limits. Variations of his declaration receive got been intoned yesteryear Oxbridge dons for centuries.

To exercise political terminology that was likely obsolete when I was an undergraduate, Universities are component division of "the Establishment". Independent thought was largely pursued yesteryear people working exterior the academy system. If the thinkers were component division of a university, they developed their thinking lone inward the library, non inward a collegial atmosphere. Camille Paglia's majority of essays Sex, Art, as well as American Culture: Essays describes this quite well.

Professor Wren-Lewis cites the exercise of New Keynesian models yesteryear primal banks equally back upward for his thesis that they are useful. This is truly an instance of my thesis. Central banks are component division of "the Establishment", as well as so whatever is pop inward academia volition almost yesteryear Definition hold upward used yesteryear primal banks. And what did modern mainstream macro offering primal bankers?

• They were freed from the tiresome project of regulating the financial system.
• DSGE models were laid inward a such a fashion that primal banks allegedly receive got to hold upward independent of the political process, as well as are non dependent to oversight similar whatsoever other means of government.
• Any forecast errors are non the fault of the primal bank; they are due to "unforecastable shocks".
• The neoliberal bias inside DSGE modelling (fiscal policy is allegedly ineffective) helps justify too-tight financial policy, leading to the depression inflation rates that primal banks tin bring credit for.

In summary, mainstream macro is structured to brand primal banks powerful as well as completely unaccountable -- which is a wonderful combination for whatsoever bureaucratic organisation. Is it surprising that they supported DSGE macro?

By contrast, anyone who has a project that depends upon beingness right almost the economic scheme -- for example, marketplace participants -- ignores DSGE macro.

Groupthink And The Natural Rate Of Interest

Mainstream DSGE macro is built around the concept of the natural charge per unit of measurement of interest. I receive got noted earlier that this concept is circular, but I receive got non however had beak over this inward detail. James Montier of GMO has written almost this inward the article "The Idolatry of Interest Rates Part I: Chasing Will-o’-the-Wisp"

I practise non necessarily endorse everything that Montier writes, but the next characterisations appear correct.

One could bring the persuasion that so many brilliant individuals all coalescing around a unmarried framework was evidence of the wisdom of crowds. However, rather than representing the ability of consensus, it appears to me to hold upward evidence of extreme groupthink – it is real telling that non i of the aforementioned luminaries has questioned the framework itself. 

And:

According to the Wicksellian perspective so honey yesteryear Bernanke et al., the natural charge per unit of measurement of involvement is simply assumed to exist. This has disturbing parallels amongst mayhap the oldest joke concerning economists that I know. When I start studied the dependent nigh on xxx years ago, i of my teachers told us the onetime hackneyed tale of the shipwrecked academics: An engineer, a chemist, as well as an economist were all stranded on a desert isle amongst no implements as well as a tin of food. The engineer rigs upward a Heath Robinson-like contraption amongst stick levers as well as vine pulleys. The pharmacist suggests using tabular array salt H2O to erode the tin as well as so heating it in i trial it is weakened. They so plough to the economist who only says, “Let’s assume nosotros receive got a tin opener!” 

Influenza A virus subtype H5N1 consensus has built upward around a theory that the economic scheme is driven yesteryear an non-measurable natural charge per unit of measurement of interest. Meanwhile, this natural charge per unit of measurement of involvement moves inward such a fashion so that it is ever consistent amongst observed data, and its movements cannot hold upward forecast. This is non-falsifiable, as well as should so hold upward rejected equally "anti-Scientific". However, the powerful figures inward academic macro receive got built their reputations using this non-falsifiable theory. Any realistic assessment of academic politics tells us that innovations volition receive got to come upward from exterior of the University system.

Footnote:

* I had a summertime project when I was a senior undergraduate at a enquiry lab for large "electrical machines" (motors or generators). The macroscopic conduct of those motors sometimes changed, fifty-fifty though the electro-mechanical properties of the scheme were supposedly fixed.

(c) Brian Romanchuk 2015