AGEC 622

• I am James Richardson• I get to be your teacher for the rest of

the semester• Jing Yi will be the grader for this

section.• Brian Herbst will assist in the Labs• If you have problems with homeworks

see Jing, Brian, or me• Are you attending the labs?

– Lab is not required, but highly recommended

Course is about Decision Making

• How do you make decisions?– Do you list all of the possible outcomes

and their consequences?– Do you think about the probabilities for

each possible outcome? P(win) = 25%

– Do you fixate on the outcome you want? P(win) = 100%

– Do you just go through life without planning?

– Systematic consideration of options– Consider probabilities of choices– What ever …..

Topics I cover & their application to life

• Topics: forecasting, risk management, and decision making under risk

• If you live you are faced with decisions– Decisions you make affect how, and how

well you live; and will have consequences forever

– Every decision you make has risk • In business, simulation is the tool we use

to analyze risky decisions– It is used in business, government, and

academia– You already use it, if you think through

possible outcomes for a decision

Simulation for Ag Economists

• Apply econometric equations for forecasting under risk

• Valuing new technology under risk• Test alternative business management

plans with risk• Assess the potential for profits with a

new business with risk• Common theme here is – RISK and

MONEY• Everything we do has risk

Application of Risk in a Decision

• Given two investments, X and Y–Both have the same cash outlay–Return for X averages 30%–Return for Y averages 20%

• If no risk then invest in alternative X

20% Return Y 30% Return X

Application of Risk in a Decision

• Given two investments, X and Y– Cash outlay same for both X and Y– Return for X averages 30%– Return for Y averages 20%

• What if the distributions of returns are known as:

• Simulation estimates the shape of the distribution for returns on risky alternatives

0 10 20 30 40 50 60 70 80 90

-20 -10 0 10 20 30 40 50

X

Y

Simulation Models and Decision Making

• Start with a problem that includes risk• Identify risky variables and control

variables you can change (scenarios)• Gather data, estimate regressions,

and develop equations for model– Generally these are accounting

equations, e.g.Profit = Revenue – Variable and Fixed Costs

• Simulate model under risk• Analyze results and make decisions

for best scenario

Purpose of Simulation• … to estimate distributions that we can

not observe and apply them to economic analysis of risky alternatives (strategies) so the decision maker can make better decisions

• Profit = (P * Ỹ) – FC – (VC * Ỹ)

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Probabilistic Forecast of Profit

~ ~ ~

Two Quotes to Start this Section 622

• “My job is not to be easy on people. My job is to make people better.” Steve Jobs 2008

• “Let’s go do something today rather than dwell on yesterdays mistakes.” JWR 2012– In computer modeling and simulation you

learn by making mistakes, expect to make mistakes

– To learn from your mistakes, you have to figure out how to correct them

– After learning how to fix a mistake move on and prosper

Materials for This Lecture• Read Chapter 16 of Simulation book• Read Chapters 1 and 2• Read first half of Chapter 15 on trend

forecasting• Read journal article “Including Risk in

Economic ..• Readings on the website

– Richardson and Mapp – Including Risk in Economic Feasibility Analyses

…• Before each class review materials on

website– Demo for the days lecture– Overheads for the lecture– Simulation Book is on the website

Forecasting and Simulation

• Forecasters give a point estimate of a variable

• Because we use simulation, we will use probabilistic forecasting– This means we will include risk in our

forecasts for business decision analysis

Simulate a Forecast• Two components to a probabilistic forecast

– AGEC 621 taught you how to develop a deterministic component forecast. It gives a point forecast: Ŷ = a + b1 X + b2 Z

– Stochastic component ẽ was ignored it is used as:Ỹ = Ŷ + ẽ

Which leads to the complete probabilistic forecast model Ỹ = a + b1 X + b2 Z + ẽ

• ẽ makes the deterministic forecast a probabilistic forecast

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Probabilistic Forecast

Steps for Probabilistic Forecasting

• Simulation provides an easy method for incorporating probabilities and confidence intervals into forecasts

• Steps for probabilistic forecasting1. Estimate best econometric model to explain

trend, seasonal, cyclical, structural variability to get ŶT+i

2. Residuals (ê) are unexplained variability or risk; an easy way is to assume ê is distributed normal

3. Simulate risk as ẽ = NORM(0,σe)

4. Probabilistic forecast is ỸT = ŶT+i + ẽ

or ỸT = ŶT+i + NORM(0,σe)

Major Activities in Simulation Modeling

• Estimating parameters for probabilistic forecasts– Ỹt = a + b1 Xt + b2 Zt + b3 Ỹt-1 + ẽ – The risk can be simulated with different distributions, e.g.

• ẽ = NORMAL (Mean, Std Dev) or• ẽ = BETA (Alpha, Beta, Min, Max) or• ẽ = Empirical (Sorted Values) or others

– Estimate parameters (a b1 b2 b3), calculate the residuals (ê) and specify the distribution for ê

• Simulate random values from the distribution (Ỹt)– Validate that simulated values come from their parent

distribution

• Model development, verification, and validation

• Apply the model to analyze risky alternatives and decisions– Statistics and probabilities– Charts and graphs (PDFs, CDFs, StopLight)– Rank risky alternatives

Role of a Forecaster• Analyze historical data series to

quantify patterns that describe the data

• Extrapolate the pattern into the future for a forecast using quantitative models

• In the process, become an expert in the industry so you can identify structural changes before they are observed in the data – incorporate new information into forecasts– In other words, THINK– Look for the unexpected

Types of Forecasts• There are several types of forecast

methods, use best method for problem at hand

• Three types of forecasts– Point or deterministic Ŷ = 10.0000– Range forecast Ŷ = 8.0 to 12.0

– Probabilistic forecast

• Forecasts are never perfect so simulation is a way to protect your job

Forecasting Tools in AGEC 622

• Trend– Linear and non-linear

• Multiple Regression• Seasonal Analysis• Moving Average• Cyclical Analysis• Exponential Smoothing• Time Series Analysis

Define Data Patterns• A time series is a chronological sequence of

observations for a particular variable over fixed intervals of time– Daily– Weekly– Monthly– Quarterly– Annual

• Six patterns for time series data (data we work with is time series data because use data generated over time).– Trend– Cycle– Seasonal variability– Structural variability– Irregular variability– Black Swans

Patterns in Time Series Data

Trend Seasonal

Cycle Mixed

0 10 20 30 40

years

years

monthsperiods J J J J

Trend Seasonal

Cycle Mixed

0 10 20 30 40

years

years

monthsperiods J J J J

Trend • Trend a general up or down movement in

the values of a variable over a historical period

• Most economic data contains at least one trend– Increasing, decreasing or flat

• Trend represents long-term growth or decay• Trends caused by strong underlying forces,

as:– Technological changes, eg., crop yields– Change in tastes and preferences– Change in income and population– Market competition– Inflation and deflation– Policy changes

Simplest Forecast Method • Mean is the simplest forecast method • Deterministic forecast of Mean

Ŷ = Ῡ = ∑ (Yi ) / N• Forecast error (or residual)

êi = Yi – Ŷ• Standard deviation of the residuals is the

measure of the error (or risk) for this forecastσe = [(∑(Yi – Ŷ)2/ (N-1)]1/2

• Probabilistic forecast Ỹ = Ŷ + ẽwhere ẽ represents the stochastic (risky) residual and is simulated from the êi

residuals

Linear Trend Forecast Models

• Deterministic trend modelŶT = a + b TT

where Tt is time; it is a variable expressed as:T = 1, 2, 3, … or T = 1980, 1981, 1982, …

• Estimate parameters for model using OLS• Multiple Regression in Simetar is easy, it does

more than estimate a and b– Std Dev residuals & Std Error Prediction (SEP)

• When available use SEP as the measure of the error (stochastic component) for the probabilistic forecast

• Probabilistic forecast of a trend line becomesỸt = Ŷt + ẽ Which is rewritten using the Normal Distribution for ẽỸt = Ŷt + NORM(0, SEPT) where T is the last actual data

^ ^

^ ^

Non-Linear Trend Forecast Models

• Deterministic trend modelŶt = a + b1 Tt + b2 Tt

2 + b3 Tt

3

where Tt is time variable is

T = 1, 2, 3, …T2 = 1, 4, 9, …T3 = 1, 8, 27, …

Estimate parameters for model using OLS

• Probabilistic forecast from trend becomesỸt = Ŷt + NORM(0, SEPT)

^ ^ ^ ^

Steps to Develop a Trend Forecast

• Plot the data– Identify linear or non-linear trend– Develop T, T2, T3 if necessary

• Estimate trend model using OLS– Observing a low R2 is a usual result– F ratio and t-test will be significant if

trend is statistically present • Simulate model using

Ỹt = Ŷt + NORM(0, SEPT)

• Report probabilistic forecast

Linear Trend Model• F-test, R2, t-test and Prob(t) values• Prediction and Confidence Intervals

Non-Linear Trend Regression

• Add square and cubic terms to capture the trend up and then the trend down

Is a Trend Forecast Enough?

• If we have monthly data, the seasonal pattern may overwhelm the trend, so final model will need both trend and seasonal terms (See the Demo for Lecture 1 ‘MSales’ worksheet)

• If we have annual data, cyclical or structural variability may overwhelm trend so need a more complex model

• Bottom line– Trend is where we start, but we generally

need a more complex model

Types of Forecast Models• Two types of models

– Causal or structural models– Univariate (time series) models

• Causal (structural) models identify the variables (Xs) that explain the variable (Y) we want to forecast, the residuals are the irregular fluctuations to simulateŶ = a + b1 X + b2 Z + ẽ

Note: we will be including ẽ in our forecast models

• Univariate models forecast using past

observations of the same variable– Advantage is you do not have to forecast the structural

variables– Disadvantage is no structural equation to test alternative

assumptions about policy, management, and structural changes

Ŷt = a + b1 Yt-1 + b2 Yt-2 + ẽ

^ ^ ^

^ ^ ^

Meaning of the CI and PI• CI is the confidence for the forecast of

Ŷ– When we compute the 95% CI for Y by

using the sample and calculate an interval of YL to YU we can be 95% confident that the interval contains the true Y0. Because 95% of all CI’s for Y contain Y0 and because we have used one of the CI from this population.

• PI is the confidence for the prediction of Ŷ– When we compute the 95% PI we call a

prediction interval successful if the observed values (samples from the past) fall in the PI we calculated using the sample. We can be 95% confident that we will be successful.

Confidence Intervals in Simetar

Beyond the historical data you will find:

SEP values in column 4

Ŷ values in column 2

Ỹ values in column 1