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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)*

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