The Epistemology of Simulation, Computation and Dynamics ... Stochastic General Equilibrium (DSGE) theories),

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  • THE EPISTEMOLOGY OF SIMULATION,

    COMPUTATION AND DYNAMICS IN ECONOMICS

    K. VELA VELUPILLAI

    ALGORITHMIC SOCIAL SCIENCES RESEARCH UNIT DEPARTMENT OF ECONOMICS U N I V E R S I T Y O F T R E N T O P R E P A R E D F O R A K E Y N O T E A D D R E S S A T T H E

    4TH WORLD CONGRESS OF THE SOCIETY OF SOCIAL SIMULATION

    NATIONAL CHENGCHI UNIVERSITY, TAIPEI, TAIWAN

    4 – 7, SEPTEMBER, 2012

  • ABSTRACT

    We identify and characterise five frontier research fields, encompassing both micro and macro aspects of economic theory, where machine computation, in its digital mode, play crucial roles in formal modelling exercises: computable general equilibrium theory (CGE) (and its ‘extensions’: Recursive Competitive Equilibrium (RCE) & Dynamic Stochastic General Equilibrium (DSGE) theories), agent based computational economics, computational economics, classical behavioural economics (CBE, as distinct from MBE: Modern Behavioural Economics) and computable economics. These five research frontiers broach, without resolving, many interesting methodological and epistemological issues in economic theorising in (alternative) mathematical modes. The main claim in the paper is that there is a serious epistemological deficit in all of the approaches, but can be ‘discovered’ only in the last two, precisely because the latter are underpinned by computability and constructivity theories, in their strict mathematical senses, and the former are not. However, this claim does not imply that classical behavioural economics and computable economics are ‘complete’ from an epistemological perspective, especially from the point of view of natural or intrinsic dynamics of formal models. The epistemological deficit and the epistemological incompleteness, it is suggested, can be resolved by a theory of simulation, itself based on recognising the ‘duality’ between dynamical systems and numerical analysis, interpreted computably. Hence paying heed to Turing’s Precept: “the inadequacy of ‘reason’ unsupported by common sense.”

  • FOUR SCENES FROM THE THEATRE OF THE ABSURD [PACE: MARTIN ESSLIN]

    "Agent-based computational methods provide the only way in which the self-regulatory capabilities of complex dynamic models can be explored so as to advance our understanding of the adaptive dynamics of actual economies."

    “If you didn’t grow it [the social phenomenon], you didn’t explain its emergence.”

    “We use the term “emergent” to denote stable macroscopic patterns arising from the local interaction of agents.”

    “The weakness of applying GE models to policy issues is twofold: First, they provide non-constructive rather than constructive proofs of the existence of equilibrium; that is, they show that equilibria exist but do not provide techniques by which equilibria can actually be determined. Second, existence per se has no policy significance. .. They can only be employed in this way if they can be made constructive (i.e., be used to find actual equilibria). The extension of the Brouwer and Kakutani fixed point theorems in this direction is what underlies the work of Scarf.... on fixed point algorithms ..."

  • EPISTEMOLOGY, COMPUTATION, DYNAMICS - ECONOMICS

    What is a Computation?

    Kant: What is Man?

     What can I know?

     What must I do?

     What may I hope?

    Every simulation is a computation;

    Every computation is a dynamic process

    What is the epistemological status of a dynamic process?

    What can be computed? What can be simulated? [Philosophy]

    What must be done [to compute, to simulate]? [Methodology]

    What may we expect [from a computation, from a simulation]? [Epistemology]

  • FIVE KINDS OF ECONOMICS UNDERPINNED – OSTENSIBLY -

    BY ‘THEORIES’ OF COMPUTATION

    I. Classical Behavioural Economics (CBE)

    II. Computable General Equilibrium Theory (CGE)

    III. Computational Economics (CE)

    IV. Computable & Constructive Economics (CCE)

    V. Agent-Based Computational Economics & Finance (ABCEF) Remark 1: I divide behavioural economics into a ‘Modern’ and a ‘Classical’ version – MBE & CBE, respectively. CBE is computably underpinned (see Velupillai-Kao).

    Remark 2: CGE forms the ‘CORE’ of RCE which, in turn, is the basis for DSGE

    Remark 3: Endogenous Macrodynamics is, from the point of view of my current research, part of CCE.

    Remark 4: See the following references for detailed discussions, critical comparisons and ‘precise’ definitions of the above:

    • Vela Velupillai & Stefano Zambelli, Computing in Economics, Ch.12, in: The Elgar Companion to Recent Economic Methodology, ed.by John B. Davis and Wade D. Hands, Edward Elgar, Cheltenham, Glos., 2011.

    • Vela Velupillai & Ying-Fang Kao, Origins and Pioneers of Behavioural Economics, Interdisciplinary Journal of Economics & Business Law, Vol. 1, #. 3, 2012.

    • Vela Velupillai, Stefano Zambelli & Stephen Kinsella (eds.), Computable Economics Edward Elgar International Library of Critical Writings, # 259, Edward Elgar, Cheltenham, Glos., 2011.

  • FIVE KINDS OF COMPUTATION THEORIES

    Varieties of Constructive Mathematics and Constructive Analysis (CMCA)

    Computability Theory and Varieties of Computable Analysis (CTCA)

     Interval Analysis (IA)

    Real Computation (RC)

    Numerical Analysis (NA) See:

     K. Vela Velupillai, A Computable Economist’s Perspective on Computational Complexity, ch. 4, in: Handbook of Research on Complexity, ed. by, J. Barkley Rosser, Jr., Edward Elgar, Cheltenham, Glos., 2009.

     Vela Velupillai & Stefano Zambelli, Computing in Economics, Ch.12, in: The Elgar Companion to Recent Economic Methodology, ed.by John B. Davis and Wade D. Hands, Edward Elgar, Cheltenham, Glos., 2011.

  • EPISTEMOLOGICAL DEFICITS & INCOMPLETENESS

    ECONOMICS

    CBE

    CCE

    CGE

    CE

    ABCEF

    MODES OF COMPUTATION

    CMCA

    CTCA

    IA

    RC

    NA

    Every simulation is a computation

    Every mode of computation is a dynamic process

    What is the dynamical system status of Numerical Analysis?

    ?

  • TOWARDS AN EPISTEMOLOGY OF COMPUTATION –

    HENCE OF SIMULATION AND DYNAMICS

    • “Computer science ... is not actually a science. It does not study natural objects. Neither is it, as you might think, mathematics; although it does use mathematical reasoning pretty extensively. Rather, computer science is like engineering - it is all about getting something to do something, rather than just dealing with abstractions ... . ...But this is not to say that computer science is all practical, down to earth bridge-building. Far from it. Computer science touches on a variety of deep issues. ... . It naturally encourages us to ask questions about the limits of computability, about what we can and cannot know about the world around us.”

    Richard Feynman: Feynman Lectures on Computation, Addison-Wesley Publishing Company, Inc., Reading,

    Mass., p. xiii

  • UNDECIDABILITY OF ALGORITHMIC KNOWLEDGE-

    INCOMPLETENESS OF TACIT KNKOWLEDGE

     “I shall reconsider human knowledge by starting from the fact that we can know more than we can tell.”

    [Michael Polanyi, Tacit Knowledge, p. 4; italics in the original]

     “The principle here is that you can know a lot more than you can prove! Unfortunately, it is also possible to think you know a lot more than you actually know. Hence the frequent need for proof.”

    [Richard Feynman, op.cit., p. 90; italics added]

     Michael Polanyi’s caveat (ibid, p.7):

    “We have here examples of knowing, both of a more intellectual and more practical kind; both the ‘wissen’ and ‘können’ of the Germans, or the ‘knowing what’ and the ‘knowing how’ of Gilbert Ryle. These two aspects of knowing have a similar structure and neither is ever present without the other.”

     Algorithmic Knowledge and Tacit Knowledge are capable of being encapsulated in the

    formalisms of CBE & CCE – but not in CGE, CE or ABCEF. Hence: the impossibility of

    discussing epistemological deficits or incompleteness in CGE,CE or ABCEF.

     This is because CGE, CE & ABCEF are not subject to Turing’s Precept 1: ‘[O]f the inadequacy of ‘reason’ unsupported by common sense.’

    Epistemological Deficit

    Epistemological Incompleteness

  • FIVE KINDS OF DYNAMICAL SYSTEMS IN

    ECONOMICS

     Ordinary Differential Equations (Linear & Nonlinear): ODEs – Standard & Nonstandard.

     Partial Differential Equations (Linear & Nonlinear): PDEs.

     Stochastic Differential Equations (Linear, Nonlinear and Partial) SDEs.

     Mixed Dynamic Difference-Differential Equations.

     Difference Equations (Linear & Nonlinear). Remark 1:The above is a ‘descriptive’ delineation. I am able to ‘reduce’ them to two classes – perhaps even one – s.t. all the other forms can be dealt with as ‘special cases’. But this makes the discussion somewhat un-illuminating!

    See:

    • K. Vela Velupillai, Non-Linear Dynamics, Complexity and Randomness: Algorithmic Foundations,