Perverse Effects, Regulatory Arbitrage and Lucas Critique:A Complex System Approach to Policy Design

Endogenous Risk In Policy Design: Significance of Lucas Surprise

Strategy (Modelling of the 1992 Sterling ERM Currency Peg Collapse)

Sheri Markose, James Lukewesa , Frederica Barzi

University of EssexEconomics Dept & CCFEA

Email;scher@essex.ac.uk

Road Map

What is Endogenous Policy Risk in Policy Design?

Policy brings about the crisis it aims to avert

Lucas Critique ; Goodhart’s Law; A.O Hirschman

Events of ‘Black Wednesday’ 16 September 1992 Was there a design flaw in the ERM Peg System? Not free riding but the problem of transparency and self-reflexivity

Why was this not spotted ? Can ACE ‘wind tunnel testing’ help determine

robustness of policy design: Can this be an advance on policy design using say econometrics ? ● CCFEA/ACE Modelling poor policy design leading to collapse of a system: Black

Wednesday and Collapse of the ERM Currency peg on 19 Sept. 2002

30 tests using a ACE wind tunnel test of the currency peg with a central bank intervening to raise the exchange and speculator taking a short position shows that the bank cannot win even once viz. ran out of reserves

Recent Examples of ACE Policy Modelling : Will Tobin Tax work? Westerhoff et. al (2004/5)

Road Map II: Motivation Regulatory Failure and the 2007 economic crisis of this ilk is the result of

deep doctrinal errors

After 20 years of assiduous micro-prudential regulation of capital adequacy (Basel I & II), US and European banks are technically insolvent and 90% of their market value wiped out ;

Only $15 tn assets of banks and near banks remain under reserve regulation and remaining 70% about $50 tn of assets ‘escaped’ into shadow banking sector;

Real economic costs of unemployment, bankruptcies (3000 per week going to wall) and loss of pensions

Following on the heals of this : A Ritualistic observance of a fixed quantitative rule on inflation target by monetary authorities oblivious to all else. This dereliction of duty was ‘rationalized’ on the ground that authorities should not use ‘surprise’

Objective of talk: Contrarian or oppositional structures have special significance in logic and mathematics

● The Gödelian Foundations of Non-Computability, Heterogeneity In Economic Forecasting and Strategic Innovationwill be given

● Transparent, predictable outcomes can be controverted/negated by hostile agents

● Surprises and innovations that arise is a co-evolutionary arms race in a complex adaptive system from which agents cannot withdraw from

this game without ‘losing’

● In economics, Robert Lucas(1972, 76), Ken Binmore (1987) and Markose(2000, 2004, 2005 Section 3) are the few who have raised the crucial strategic significance of this for game theory and policy design

● Deep doctrinal errors regarding policy design have arisen due to a lack of understanding of the consequences of rule breaking contrarian structures

Policy Design and Failure: Lucas Critique (1972, 1976)

● Lucas put an end to the relevance of optimal control (Linear quadratic Guassian models) as a useful tool for policy design; it is a game against nature and regulatees are assumed to be rule abiding

Nobel Prize Winner Robert Lucas made 3 following propositions:

● (i)If private sector can know or rationally expect policy rules and outcomes they can render them ineffective

● (ii)Against such ‘negation’ , policy can succeed only if the private sector can be ‘surprised’

● (iii) Third, the econometric estimation of models to evaluate policy may be difficult or impossible as strategic behaviourial changes to anticipated policy lead to a lack of structural invariance of the models concerned. Strictly speaking, it is the third postulate above in Lucas(1976) that is referred to as the Lucas Critique. However, we will use this term interchangeably with the larger thesis on the trio of postulates on policy design.

The Traditional Linear-Quadratic-Guassian Model of Optimal Control Min (q* - qt)

2 (A) Quadratic Objective Function where the

deviations of the state variable qt from the target q* has to be minimized by optimizing w.r.t policy variable gt .

The state variable dynamics qt = a qt-1 + b gt + t , where t is white noise (B) the state variable is buffeted by white noise and the policy variable on average aims to achieve objective. Substitute (B) into (A) and taking the expected value of the first order conditions for the one period ahead welfare function: Wt = Et-1( q*2 -2 q*qt + qt

2) The optimal rule is a linear function of the lagged state variable gt

* = 1*1

tqb

aq

b. (C )

Substitute gt* in (C ) into (B ) it can be verified that

qt = q* + t . That is the target is achieved on average and deviates from it only by white noise !!

Goodhart’s Law

● Goodhart’s Law claims that “ any observed statistical regularity will tend to collapse once pressure is placed upon it for control purposes” (Goodhart, 1984, p.96)

● Goodhart’s Law is basically an empirical rather than theoretical exegesis of what followed when the Tory chancellor in the mid 1980’s attempted to achieve preannounced nominal monetary targets. As per Goodhart’s Law , these monetary variables became more volatile in the period after they were the object of much concerted effort to control them than in any period before that. Fischer (1994) has given Goodhart’s Law a wide enough theoretical berth to suggest that any formalistic monetary rule will suffer eventual breakdown.

Lucas Critique led to

(i) Demise of macro-econometric models for policy analysis. Few integrative modelling tools currently available for policy design

(ii) However, macro theorists misunderstood what ‘surprise’ strategy mean in a generic setting; in the latter surprises are innovative behaviour and co-evolving policy is needed to keep bad consequences from regulatee arbitrage in check

Adherence to precommitment strategies using simple quantitative rules for monetary authorities specifically to prevent authorities from using ‘surprise’ inflation

Binmore: Modelling Rational Players (1987)

● Binmore controversially raised the “spectre of Gödel” (ibid.) in reference to the general impossibility result of confining rational strategies to predictable functions in the context of eductive game theory

● The strategic use of indeterminism was alluded to in the face of the contrarian or Liar

● The Liar is the Cretan Liar from antiquity

Novelty/Surprises/Innovationsand Undecidable Dynamics of Complex Adaptive Systems

(CAS)

● Despite Binmore (1987)Extant eductive or evolution game theory do not have a Nash Equilibrium in which players use a ‘surprise’ strategy

● Markose, 2003/4 showed this is Nash equilibrium of a very significant game which cannot be analysed in extant game theory framework

● Sine qua non of CAS is its capacity to produce

to produce innovation based undecidable structure changing dynamics (Wolfram-Chomsky ; Langton Casti )

OtherwiseSolitudeEnjoysandNothingDoes

Expectedisor

AnnouncedisVisitorIfinnotishemantainsoroutSteps

Example 1: Major’s Strategy Soon to be referred to as the Liar Strategy ; Note Success of Major’s Liar Strategy is due to the fact that visitors are expected

Major –Major as the Liar Strategy (see, excerpt from Catch 22) The Liar Strategy in a social setting Appleby: ‘About how long will I have to wait before I can go in to see the Major?’ Sergeant Towser: ‘Just until he goes out to lunch. Then you can go right in.’ Appleby: ‘But he won’t be there then. Will he?’ Sergeant Towser : ‘No sir.... . Major Major never sees anyone in his office while he’s in his office.’ Appleby: ‘Sergeant, are you trying to make a fool out of me just because I’m new in the squadron .. ?” Sergeant Towser: ‘Oh, no,sir. Those are my orders. You can ask Major Major when you see him.’ Appleby: ‘ That’s just what I intend to do, Sergeant. When can I see him?’ Sergeant Towser:’Never’. When Major Major looked back on what he had accomplished, he was pleased. With a little ingenuity and vision, he made it all but impossible for anyone in the squadron to talk to him... . No one, it turned out, but that madman Yossarian, who brought him down with a flying tackle one day as he was scooting along the bottom of the ditch to his trailer for lunch.

Catch 22, Joseph Heller.

Despite the obvious hilarity of this episode from Heller’s 20th. century classic, what it underscores is that the Liar strategy can force a no win on the other player who plays transparently.

Goodhart’s Law

● Goodhart’s Law claims that “ any observed statistical regularity will tend to collapse once pressure is placed upon it for control purposes” (Goodhart, 1984, p.96)

● Goodhart’s Law is basically an empirical rather than theoretical exegesis of what followed when the Tory chancellor in the mid 1980’s attempted to achieve preannounced nominal monetary targets. As per Goodhart’s Law , these monetary variables became more volatile in the period after they were the object of much concerted effort to control them than in any period before that. Fischer (1994) has given Goodhart’s Law a wide enough theoretical berth to suggest that any formalistic monetary rule will suffer eventual breakdown.

● A risk model breaks down when used for regulatory purposes. (Daníelsson, 2002)

Borio and White (2003)

● Borio and White (2003) have often been cited as harbouring a less than sanguine view (or one might called the minority dissenting view in legal circles) of the monetary and regulatory arrangements which goes by the term ‘Great Moderation’. The latter conveyed what many in the mainstream academic and policy oriented elites had considered to be the pinnacle of their achievements which sadly has proven to be illusory and the harbinger of a run away boom. Borio and White (2003) states:

● “ as always, we need to remain alert to the possibility that policy actions may, as in the past, have unintended consequences that can alter the nature of the risks in unforeseen ways and lead economic agents and policy makers astray.” These remain pious words in the context of the 21st century when tools from the digital and complexity sciences abound which an economics fraternity that has been cloistered in a twilight world of internal dogma have ignored for over five decades[1][1] at our peril. But were the risk weighted and credit risk transfer rules of Basel II being subjected to stress tests for potential systemic risk consequences ?

●

[1][1] Here one can cite the 1950s Herbert Simon classic Sciences of the Artificial on the need for understanding robust design principles from a procedural and constructive perspective for the stability of large scale models. Also there is Hayek’s call to arms to take a complexity perspective and which resolutely overcomes the siren voices of what he called the wrong kind of maths and science which viewed the whole economy as the work of a single social planner.

A.O Hirschmann

● Policy design should avoid problems of● Futility● Perversity ● Jeopardy ● Hirschman famously said above arguments against

deliberate or conscious design was the ‘rhetoric of reaction’

● The only way to avoid it is laissez faire

Self-Reflexivity

● George Soros made £2bn taking a short position against the Sterling and the Bank of England. He is alleged to have used the Cretan Liar or Contrarian Strategy. Why did Soros win : Or why did all Currency pegs collapse (from Mexico to the Asian ones)

● Soros cut above ordinary speculator: student of Karl Popper and knows the self-reflexive problem of the Cretan Liar. Liar can subvert only from a a point of certainty or computable fixed point. Hence, if the policy position is perfectly known – hostile agents can destroy it. Indeterminism or ambiguity is a essential design element for success of market systems and zero sum games

● Market games or institutions should be designed to satisfy arbitrage free conditions

● Fundamental to this is the absence of transparency or predictability that mitigates computable winning strategies

70

75

80

85

90

95

100

105

110

115

120

Jul-

92

Sep-

92

Nov

-92

Jan-

93

Mac

93

May

-93

Jul-

93

Sep-

93

Nov

-93

Jan-

94

Mac

94

May

-94

Jul-

94

Sep-

94

Nov

-94

Jan-

95

Mac

95

May

-95

Jul-

95

Belgium Denmark France UK

Exchange rates against the deutschemark for the Belgian franc, French franc, Danish krone

and British pound sterling July 1992-July 1995 (index).

Source: Eurostatistik, April 1993, 1994, 1996, August and October 1995

Rules of the ERM Peg: ERM Currency peg requires Central Banks to precommit and support the currency

when the Forex rate falls below peg: Central Bank Rule● ● Central bank rule: ● Defends if £ exchange Rate at lower bound ● ● Do nothing otherwise ●

● The antecedent conditions of this rule, viz. that the currency is overvalued in terms of its official parity can be considered to be common knowledge. The rest of the rule is institutionalized within the structure of the currency peg. Once within the rules of a pegged system, a central bank inevitably stakes its reputation on its capacity to maintain the parity of the exchange rate of its currency.

Figure Gives Evidence of Design Flaw : Requirement to defend in Narrow Band brings about Attack

● Figure shows that the state of the fundamentals relating to the long term viability of the parity was neither necessary nor sufficient for speculative attacks. U.K with a 20% overvalued currency sustained attacks as did the other ERM currencies whose parities appear to be virtually unchanged within the pegged regime and when it effectively floated.

● The only material difference in the case is with the widening of the bands from 2.5 % to 15% was that it rendered the rule dead letter and when the conditions of a defence were made ambiguous, the speculative attacks ceased dramatically.

Speculator Best Response : Short Sterling Borrow Sterling and Sell Immediately in spot market

;When currency has devalued buy back cheap and repay

● | Sell short sterling after defence by C.Bank

● Speculator Liar Strategy |● | Do nothing if C.B

does not defend

Flawed Macro Economic Theory

● Flawed Macro economic literature on precommitment to transparent strategy caused IMF to support currency pegs and led to the worst policy induced failures of our time

● Krugman (1996,p.352) identified one set of conditions in some models for a crisis proof fixed exchange rate lay “with a high cost to abandoning the peg, for e.g, a very strong public commitment .” This paper will challenge such policy prescriptions of this genre of monetary game theory models summarized here in the words of Cukierman(1994, p.1440) : “Precommitment of monetary policy to a pre-announced course is a device for reducing inflation expectations .... . A central bank ... with an unequivocal mandate to focus on price stability, is one institutional device for committing monetary policy. Another device is the maintenance of a fixed parity with the currency of a country that puts high priority on stable prices”.

Commitment to fight to last man

● What provokes the attacks is the transparent defence : Speculator Sells forward after the central bank raises the exchange rate to above the lower bound : Speculator Rule

● Shin and Morris(1998) give a rendering of self-fulfilling currency crisis models with multiple Nash equilibria with either (defence and no attack) and (no defence and attack) being equally feasible. These equilibria do not conform with the stark reality that no currency peg strictly operating rule (A.1, A.2) has survived and every failed currency peg was defended and suffered speculative attacks.

● After the collapse at least Charles Goodhart said : If at the first whiff of trouble the best response is to float : why peg ?

Worst Policy Disaster of Recent Times

● Pegged currency regimes, instituted on grounds of providing an inflation anchor, that have suffered systematic speculative attacks leading to currency crisis and/or economic collapse are the following.

● Jamaica,1990, 1992 ERM crises involving the £-sterling, lira, franc, krona, punt and others, the 1994 peso crisis, the Thai baht (the second wave of attacks on it), the Malaysian ringit and the Indonesain rupiah, 1997.

● Extensive empirical accounts of these currency crises exist, see, Sachs et. al.(1996), Eichengreen et. al. (1996 ). In January 1999, the IMF package of $41bn. was lost in the defence of the dollar peg with the Brazilian real. What constitutes a ‘successful’ speculative attack is contentious.

● For instance, Krugman (1996, p.356) refers to the speculative attack on the krona which netted what appears to be the largest amount of bank reserves of the ERM currencies to speculators as “an attack that failed when the Swedish government proved ready to defend the currency with very high interest rates” of around 500%. Surely, the speculator does not judge his success by whether or not the parity is broken but by how much is netted from the attack and to count on its use as a money pump in the future.

Commitment was for real: Market Believed it : There was no growing interestrate differential between Dm and £

● Norman Lamont, the UK Chancellor, who in the ill fated defence of the £-sterling in the summer of 1992 worked to remove “ ‘any scintilla of doubt’ about the intentions of the government ...that he and the government were ‘going to maintain sterling’s parity and ...do whatever is necessary’ ”, Stephens (1996) (as quoted in Eichengreen,1999

INTRODUCTION ACE MODEL

● To simulate the intervention actions of a central bank agent and a speculator agent given the above scenario

To give the above agents adaptive learning capability during their interactions

Data and events on Black Wednesday declassified:

Web site http://www.hm-treasury.gov.uk/about/information/foi_disclosures/foi_erm4_090205.cfm

Endogenous risk here is with regard to the policy rule/regime set up by regulatory authorities that end up causing the instability and risk that they were

meant to avert

● The game is between the Bank of England and currency speculators wherein the peg on the sterling was attacked after £28 million was spent on the defence on the sterling by the Bank of England. It is argued that precommitment to defend the peg by the central bank and the subsequent transparent defence of the peg, results in a ‘free lunch’ for currency speculators. Facts show that when the exchange rate parity bands were widened and the lower bound violations that prompted central bank defence failed to occur, not only did attacks stop dramatically but the exchange rates remain buoyant

● Some of the events for that period has now been declassified and can be found at

● Web site for 1992 Black Wednesday documents● http://www.hm-treasury.gov.uk/about/information/foi_disclosures/

foi_erm4_090205.cfm● This information is also used to develop an agent based model for the events of

the ERM collapse.

THE MATHEMATICAL MODEL

Random walk model

The two traders model

The model with interest rate policy

e t e t 1 1 R t 1 R t 2 Dt 1 D t t

e t e t 1 1 R t 1 R t 2 Dt 1 D t iF iH a t

e t e t 1 t

THE MATHEMATICAL MODEL (cont'd)

The model with the real money demand

The model with the real national income (GNP)

The three factors can then be combined into one

model

e t e t 1 1 mt 1 R t 2 Dt 1 D t g H g F c t

e t e t 1 1 R t 1 R t 2 Dt 1 D t mF mH b t

e t e t 1 1 Rt 1 Rt 2 D t 1 Dt i F i H mF mH b g H g F c t

EXPERIMENTAL DESIGNModelled around the foregoing mathematical model

Random Walk● Normal distribution white noise fluctuation● No intervention from both players

Two Agents Model● Central bank has fixed reserves● If rate < lower peg, Central bank with amount to

raise rate to mid-point of peg system

EXPERIMENTAL DESIGN (Cont'd)

Two Agents Model (continued)● Speculator has two strategies :

Strategy 1 : Always attack after bank's

defence

Strategy 2 : Attack even if bank has not

defended and exchange rate is

above 3DM

● Intervention amount is intended to drop rate below lower peg

EXPERIMENTAL DESIGN (Cont'd)● Central bank has only one strategy. It simply

defends the peg system whenever the rate gets below or hits lower peg.

● Speculator has two strategies : Stg 1 & 2● Three experiments were carried out.

Experiment 1 : Speculator only attacks after bank – Strategy 1.

Experiment 2 : Speculator attacks even if bank has not defended –

Strategy 2.oo

Experiment 3 incorporates adaptive learning.● Speculator can attack either after the bank's

defence - Strategy 1, or even if bank has not defended – Strategy 2.

● Speculator starts with both strategies having probabilities of 0.5 each.

● A strategy that produces the highest profit from a notional close-out has its probability incremented by 10%, until either one of the probabilities reaches 0.8, when convergence occurs (or generation 300, if earlier)

ADAPTIVE LEARNING

● After convergence, winning strategy becomes the only applicable strategy for the remaining periods

● Stgy 1 wins – speculator only attacks after the bank for all periods after the

point of convergence● Stgy 2 wins – speculator attacks if exch. rate is

>= to an optimal exch. rate achieved at convergence, even

if bank has not defended (will only attack after bank if optimal rate

condition is achieved as well).

ADAPTIVE LEARNING (Cont'd)

Simulation Results

● Endogenous Risk – 1992 ERM Currency Peg

● Experiment 1, 2 and 3

● Summary Results of Experiments - 30 Rounds per Experiment

●

● Experiment 1 Experiment 2 Experiment 3

● Average Profit £1.68m £1.43m £1.94m

● Number of times bank

● reserves exhausted 25 0 24

● Times converging to strategy : Strategy 1 26

● Strategy 2 4

● Average Profit for each strategy : Strategy 1 £ 2.25m

● Strategy 2 £1.86 m

●

DISCUSSIONS/CONCLUSIONS● From our investigation of the strategic interactions between a central bank

and a speculator, shows that the profits for speculator is maximized if attack takes place after the central bank defends and expends foreign reserves

● Therefore, it is transparency of policy and its its implementation that provokes attacks

● To avert this, possible solutions include :

a central bank should use surprise strategies

a central bank should abandon a peg system (e.g. ERM), without any intervention: the design is fatally flawed and any alleged objectives the Central Bank hopes to achieve is jeopardised due to onset of systemic currency collapse