Treatment of Uncertainty in Economics (I)

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Treatment of Uncertainty in Economics (I). Economics 331b. This week. Dynamic deterministic systems Dynamic stochastic systems Optimization (decision making) under uncertainty Uncertainty and learning Uncertainty with extreme distributions (“fat tails”). - PowerPoint PPT Presentation

Transcript of Treatment of Uncertainty in Economics (I)

  • *Economics 331b

    Treatment of Uncertaintyin Economics (I)

  • This weekDynamic deterministic systemsDynamic stochastic systemsOptimization (decision making) under uncertaintyUncertainty and learningUncertainty with extreme distributions (fat tails)*

  • Deterministic dynamic systems (no uncertainty)Consider a dynamic system:

    yt = H(t , t )

    where yt = endogenous variablest = exogenous variables and parameterst = control variablesH = function or mapping.

    *

  • *

  • Deterministic optimization

    Often we have an objective function U(yt ) and want to

    optimize, as inmax U(yt )e-t dt {(t)}Subject to yt = H(t , t )

    As in the optimal growth (Ramsey) model or life-cycle model of consumption.

    *

  • Mankiw, Life Cycle Model, Chapter 17*

  • Stochastic dynamic systems (with uncertainty)Same system:

    yt = H(t , t )

    t = random exogenous variables or parameters

    Examples of stochastic dynamic systems? Help?

    *

  • Which is stock market and random walk?*T=year 0T=year 60

  • Examples: stock market and random walk*RandomwalkUS stock market

  • How can we model this with modern techniques?*

  • Methodology is Monte Carlo technique, like spinning a bunch of roulette wheels at Monte Carlo*How can we model this with modern techniques?

  • Methodology is Monte Carlo technique, like spinning a bunch of roulette wheels at Monte CarloSystem is:

    yt = H(t , t )

    So, You first you find the probability distribution f(t ). Then you simulate (1) with n draws from f(t ). This then produces a distribution, g(yt ).

    *How can we model this with modern techniques?

  • YEcon ModelAn example showing how the results are affected if we make temperature sensitivity a normal random variable N(3, 1.5).*

  • *

  • 50 random runs from RICE model for Temp*

  • Temperature 2100*

  • How do we choose?We have all these runs, ytI , ytII , ytIII ,

    For this, we use expected utility theory.max E[U(yt )]e-t dt Subject to yt = H(t , t ) and with t as control variable.

    We usually assume U( . ) shows risk aversion.

    This produces an optimal policy.*

  • SCC 2015*So, not much difference between mean and best guess. So we can ignore uncertainty (to first approximation.)

    Or can we?

    What is dreadfully wrong with this story?

  • What is dreadfully wrong with this story?The next slide will help us think through why it is wrong and how to fix it.It is an example of 2 states of the world (good and bad with p=0.9 and 0.1), and two potential policies (strong and weak),and payoffs in terms of losses (in % of baseline utility or income).*

  • The payoff matrix (in utility units)*

    ********************