Department of Philosophy, Logic and Scientific MethodLondon School of Economics and Political Science30 April 2015

ECONOMIC POLICY WHEN MODELS DISAGREE

Pauline Barrieu Bernard Sinclair-DesgagnéLondon School of Economics HEC Montréal

Why do models/experts disagree?

Competing theories Growth theory (at least as many as there are

countries…) Monetary policy (nature and role of

expectations) Species survival or extinction; Ecosystem

resilience

Insufficient data Global warming, when and how?

Undetermined empirical specifications Lag length? Measurement and empirical proxies? Nonlinearities?

Policy making based on a particular model might unduly

underestimate the overall uncertainty that surrounds the

effects of a given policy choice.

What can a policy maker currently do?A quick review

1. Model Averaging

Raftery, Madigan, and Hoeting (JASA 1997) Brainard (AER 1967), Chamberlain (2001), Sims (2002)

Gilboa (1987), Schmeidler (1989) Basset, Kroenker, and Kordas (2004)

Enrique Moral-Benito (2015), “Model Averaging in Economics: An Overview,” Journal of Economic Surveys 29(1), p. 46-75

The Bayesian way

E(u(y)| q) = ∑ m ∊ M μ(m) E(u(y)|q,m)

Priordistribution

Non-additive priors /Choquet expectedutility

In some situations, entertaining probabilistic beliefs is hardly achievable or even rational (Gilboa , Postlewaite, and Schmeidler 2008).

In other situations (when models and scenarios are based on different sets of axioms, for instance), how could you even expect holding a prior?

2. Ambiguity aversion

Gilboa and Schmeidler (J. Math.Eco. 1989)Epstein (Review of Economic Studies 1999) Maccheroni, Marinacci and Rustichini (Econometrica 2006)Klibanoff, Marinacci and Mukerji (Econometrica 2006)Maxq minμ∊Δ ∑ m ∊ M μ(m) E(u(y)|q,m)

Maxq ∑μ∊Δ Ψ[∑ m ∊ M μ(m) E(u(y)|q,m)]p(μ)

? ?

Etner, Jeleva, and Tallon (2012), “Decision Theory under Ambiguity,” Journal of Economic Surveys 26(2), p. 234-270

The maximin criterion really corresponds to an extreme form of uncertainty aversion (Adam 2004).

The normative value of ambiguity-averse preferences or nonexpected utility remains debatable (Al-Najar and Weinstein 2009; Wakker 1988). The association made between ambiguity aversion and concerns for robust policies seems unwarranted (Nehring 2009).

3. Robust Control

Hansen and Sargent (1998-2008)Roseta-Palmas and Xepapadeas (2004), Vardas and Xepapapeas (2009)

m

Reference model

AllowedMisspecification(entropy-based

metric)

Maxq minm ∊ Δ(m) E(u(y)|q,m)

Δ(m)

Bertsimas, Brown, and Caramanis (2011), “Theory and Applications of Robust Optimization,” SIAM Review 53(3), p. 464-501

4. Group decision making

• Genest and Zidek (1986), “Combining Probability Distri-butions: A Critique and Annotated Bibliography,” Statistical Science 1(1), p. 114-135

• Osborne and Turner (2010), “Cost-Benefit Analysis versus Referenda,” Journal of Political Economy 118(1), p. 156-187

• March 2015 special issue of Economics and Philosophy on Individual and Social Deliberation.

• Acemoglu, Dahleh, Lobel & Ozdaglar (2011), “Bayesian Learning in Social Networks,” Review of Economic Studies 78, p. 1201-1236

5. Unawareness (?)

Heifetz, Meier, and Schipper (2006), “Interactive Unaware-ness,” Journal of Economic Theory 130, p. 78-94

Galanis (2011), “Syntactic Foundations for Unawareness of Theorems,” Theory and Decision 71(4), p. 593-714

6. Behavioral decision making (?)

Ahn and Ergin (2010), “Framing Contingencies,” Econometrica 78(2), p. 655-695

What are we aiming for in this paper?

A formal unifying approach to policy making which is:

Practical ► can fit a policy-making process(individual DM ≠ group DM)

As undemanding as possible ► requires no representative

agent, probabilities orreference modelbut can use these

Broad in applications ► from macroeconomic, energy, environmental and climate

policy to financial regulation

Based on a clear and► The willingness-to-accept a current

seemingly “reasonable” situation should match the willingness-

prescription to-pay for implementing a remedy

First piece: the so-called Theory of Economic Policy

Tinbergen (1952), Theil (1958)

▪ Target values y ∊ Y

▪ Policy instruments q ∊ Q

▪ Exogenous variables ξ ∊ Ξ

▪ A model of the economy m(y,q;ξ):

If A is non singular, thenthe appropriate policy toachieve target value y* can be set as:

q = A-1 [y* - Bξ]

y = Aq + Bξ

A unifying approach

ω =

[… mi(y,q;ξ)… ]

Models M

Σ

ZScores: WTP

Φpolicyrule

Ωn

v policy evaluation

absolute Unumericalrankings

?m1

….….mn

ScenariosΩn

ω´ =

[… mi(y´,q´;ξ)… ]

welfarelevels

A unifying approach

ω =

[… mi(y,q;ξ)… ]

Ωn

Σ

ω´ =

[… mi(y´,q´;ξ)… ]

WTP

Φpolicyrule

Ωn

v

Uπ

WTA

Willingness- to-accept

v ○ Φ = π ○ U

Z

Fundamental equation

A unifying approach

An effective policy will be such that the willingness-to-pay for it will match the willingness-to-accept the current situation.

Second piece (and main building block): a generalization of Farkas’s lemma [Craven (JOTA 1972)]

If U : Ωn → Σ is surjective, then

U(ωi) = U(ωj) => v ○ Φ(ωi) = v ○ Φ(ωj),

U(ω) ∊ Σ- => v ○ Φ(ω) ∊ Z+

if and only if there exists a function π : Σ → Z such that

π ○ U = v ○ Φ and π(Σ-) Z+ .

A unifying approach

Consistency

Policy Effectiveness

Ωn- = { ω ∊ Ωn | ωi < 0 for some i}

Z+ = Z ∩ ℝ+Existence of policies can be guaranteed by a general versionof the intermediate-value theorem.

A unifying approach

Some implied economic properties

Assumption 1. (Unanimity) ω ∊ Ωn- ⇔ v(ω) ≦ 0 Assumption 2. (Strong WTA) u ∊ Σ- ⇔ π(u) > 0

Prop. 1: (Consensual remedy) For all ω ∊ Ωn- , Φ(ω) ∉ Ωn-Prop. 2: (Self -restraint) For all ω ∊ Ωn

+ , Φ(ω) ∉ Ωn+

Prop. 3: (Non-neutrality) For all ω, Φ(ω) ≠ ω

Prop. 4: (Holism) Φ ≠ (φ1, … , φn)

Prop. 5: (Imperfect enhancement) For at least one ω ∊ Ωn- , ω ⊀ Φ(ω)

Prop. 6: (Simpleness) The “range” of successful q’s decreases with n.

Ωn- = U-1 (Σ-) Ωn+ = Ωn \ Ωn-

Example 1

● Two models (i = 1, 2): ωi = Normal(ai - q, (1- q)σi2)

CARA ranking criterion: U(x) = - e-θx , where θ captures a policy maker’s degree of absolute risk aversion

E[U(x)│q, ωi ] = CEi(q) = ai – q – θ(1- q)σi2 /2

Let π(u1,u2) = - min [ a1 – q0 – θ(1-q0)σ12 /2 , a2 – q0 – θ(1-

q0)σ22 /2]

v(ω1,ω2) = min [ a1 - q´ – θ(1-q´)σ12 /2 , a2 - q´ – θ(1-q

´)σ22 /2]

Then, solving π ○ U = v ○ Φ amounts to solve (for q´):

min [ a1 – q´ – θ (1-q´)σ12 /2 , a2 – q´ – θ(1-q´)σ2

2 /2] = - min [a1 – q0 – θ (1-qo)σ1

2 /2 , a2 – q0 – θ(1-q0)σ2

2 /2]

0 q1

a1–θσ12/2

π[u1,u2]= -a1+θσ1

2/2▪

▪

a2–θσ22/2 ▪

•

CE2(q)

CE1(q)

q* q•Bq•

A

The maximin (q*)and this paper’s ( qA , qB ) solutions; q0 = 0.

Example 2Capital reserves requirements of banking institutions - an eclectic approach

“Scenarios”: credit rating agencies, credit default swaps, value-at-risk schemes, etc.

Let v and U be specified by policymakers (Basel 3)

Policy triggers: for example, U(CDS) < 0 iff prices were above threshold for the last 20 days.

π measures the policymakers’ joint degree of apprehension about the institution’s financial health

Determine the reserves amount using equation (1).

JPMorgan Chase holds $3 billion of “model uncertainty” reserves…The Economist, February 13th 2010

Concluding remarks

Extensions / illustrations Dynamic generalization - Preston (RES 1974) Policy games - Acocella and Di Bartolomeo (Econ

Letters 2006)

Computations use of quasi-inverses

Other issues Elicitation of π Learning Model selection

Φ = v[-1] ○ (π ○ U)

What is simple is always wrong, but what is complex is unusable.- Paul Valéry -