# Treatment of Uncertainty in Economics (I)

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01-Jan-2016Category

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*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.

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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.

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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?

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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).*

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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)*

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