Course is about Decision Making

1. 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? • OR Systematically consider your options • Consider probabilities of choices • What ever …..

2. Risk and Decision Making • Risk is anything you do not know with certainty, i.e., the grade you will get in 622, the DOW closing value today, or the price a particular stock tomorrow • You are always faced with decisions and risk • Every decision you make has risk or there would not be a decision to make • In business, simulation is the tool used to analyze risky decisions • You already use simulation when you think through possible outcomes for a decision

3. Relationship Between 622 and Your Previous Courses • Statistics • Probabilities • Mean, Variance, Correlation • Statistical tests of significance • Multiple Regression covered in AGECO 621 • Accounting, Finance, Business • I assume you know how to use these tools • I am going to teach you how to use them in a systematic way to forecast risky variables and those forecasts to make better decisions

4. Simulation and Ag Economics • Common theme is – RISK and MONEY • Everything we do has risk • Simple profit equation for a one product firm • If no risk the equation produces one number • Profit = (P * Y) – FC – (VC * Y) • In a risky world there are many outcomes • Profit = (P * Ỹ) – FC – (VC * Ỹ) • In this case yield (Y), price (P), VC are stochastic ~ ~ ~

5. Application of Risk in a Decision • Given two investments, X and Y and no risk • Cash outlay same for both X and Y • Return for X averages 30% • Return for Y averages 20% • Obviously choose X

6. X -20 -10 0 10 20 30 40 50 Y 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: • Simulation estimates the shape of the distribution for returns (or profits) for risky investments 0 10 20 30 40 50 60 70 80 90

7. Purpose of Simulation • … is 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) • Probability (P>14) ~ ~ ~

8. Materials for This Lecture • Simulation Book is on the website at: https://www.afpc.tamu.edu/courses/622/SimulationBook.pdf • Read Chapters 1 and 2 for this lecture • Read first half of Chapter 15 on trend forecasting • Read Chapter 16 of Simulation book by Monday • Journal article readings on the website under “Resources” • Richardson and Mapp journal article on risk analysis • Including Risk in Economic Feasibility Analyses … • Lecture 07 Trend.xlsx

9. Forecasting and Simulation • Forecasters give a point estimate of a variable • Because we use simulation, we will develop and report probabilistic forecasts • This means we will include risk in our forecasts for business decision analysis • Simply this involves adding more than a simple confidence interval about the forecast • Also, it is harder to be proven wrong if you give a range with a probability about the center point

10. Simulate a Forecast • Two components to a probabilistic forecast • AGEC 621 taught you how to develop a Deterministic Forecast which gives a point forecast: Ŷi= a + b1Xi+ b2 Zi The Stochastic Componentẽis generallyignored ẽi= Yi - Ŷi The complete probabilistic forecast model becomes Ỹi= a + b1Xi+ b2 Zi+ ẽ • ẽ makes the deterministic forecast a probabilistic forecast

11. Steps for Probabilistic Forecasting • Steps for probabilistic forecasting • Estimate the besteconometric model to explain trend, seasonal, cyclical, structural variability to get ŶT+i • Residuals (ê) are the unexplained variability or risk; we can assume the residuals are distributed normal • Simulate the risk in Simetar as: ẽ = NORM(0,σe) • Probabilistic forecast is ỸT = ŶT+i + ẽ OR ỸT+1= ŶT+i + NORM(0,σe) or an alternative specification is: ỸT+1 = NORM(ŶT+i , σe) Simulate the ỸT+1 500 times and report the range and probability about the forecasted mean

12. Role of a Forecaster • Analyze historical data series to quantify the patternsfor the variable • 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

13. Types of Forecasts • Three types of forecasts • Point or deterministic forecast Ŷ = 10.0000 • Range forecast Ŷ = 8.0 to 12.0 • Probabilistic forecast • Ŷ = 8.0 to 12.0 with a probability of: P(8<= Ŷ<=12) = 50% P(4.5<=Ŷ<=16) = 95% • Forecasts are never perfect so simulation is a way to protect your job • Harder to prove your forecast is wrong!

14. Forecasting Tools in AGEC 622 • Trend • Linear and non-linear • Multiple Regression • Seasonal Analysis • Moving Average • Cyclical Analysis • Exponential Smoothing • Time Series

15. 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

16. Patterns for Time Series Data

17. Simplest Forecast Method • The Mean is the simplest forecast method • Deterministic forecast of the Mean Ŷ = Ῡ = ∑ (Yi ) / N • Forecast error for a mean forecast is a residual êi= Yi – Ῡ or êi= Yi – Ŷ • Standard deviation of the residuals is the measure of the error (or risk) for the forecast σe = [(∑(Yi – Ŷ)2/ (N-1)]1/2 • Range forecast of: Ŷ ± σe • Probabilistic forecast, where ẽ represents the risk Ỹ = Ŷ + ẽ So the forecast can be presented as P(8<= Ŷ<=12) = 50% (there is a 50% chance Y between 8 and 12)

18. Trend Forecasting • Trend a general up or down movement in the values for 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, e.g., crop yields • Change in tastes and preferences • Change in income and population • Market competition • Inflation and deflation • Policy changes

19. Linear Trend Forecast Models ^ ^ • Deterministic trend model (no risk) Ŷt= a + b Tt where Tt is time and as a variable it is represented as: T = 1, 2, 3, … or T = 1980, 1981, 1982, … , 2017 • Estimate parameters for forecastmodel using OLS • Multiple Regression in Simetar is easy, it does more than estimate a and b • Probabilistic forecast of a trend line becomes Ỹt = Ŷt + ẽ Which is rewritten using the Normal Distribution for ẽ ỸT+t= ŶT+t+ NORM(0, σ) where T is the last actual observed values and σ is the standard deviation of the residuals ^ ^

20. Non-Linear Trend Forecast Models ^ ^ ^ ^ • Deterministic trend model Ŷt = b0+ b1 Tt + b2Tt2+ b3Tt3 where Tt is the time variable and is: T = 1, 2, 3, … T2 = 1, 4, 9, … T3 = 1, 8, 27, … Estimate parameters (beta-hats) using OLS • Probabilistic forecast from trend becomes ỸT+t= ŶT+t+ NORM(0, σ-residuals)

21. Steps to Develop a Trend Forecast • Plot the data • Identify linear or non-linear trend • Develop T, T2, T3 if necessary • Estimate regression model using OLS • Observing a low R2 is a usual result • F ratio and t-test will be significant if a trend is statistically present • Simulate model using Ỹt= Ŷt+ NORM(0, σ-residuals) • Report probabilistic forecast

22. Linear Trend Model Forecast

23. Linear Trend Model Forecast Lecture 07 Trend.xlsx

24. Non-Linear Trend Regression • Estimated equation of Y-Hat = a + b1*Trend + b2*Trend2 +b3*Trend3 This captures the non-linear trend in the data Lecture 07 Trend.xlsx

25. Non-Linear Trend Forecast

26. Is a Trend Forecast Enough? • If we have monthly data, the seasonal pattern may mask the trend, so the final model will need both trend and seasonal terms (See the Demo for Lecture 7 ‘MSales’ worksheet, needs more than a trend) • If we have annual data, cyclical or structural variability may mask the trend so need a more complex model • Bottom line • Trend is where we start, but we generally need a more complex model

27. Types of Forecast Models • Two types of models • Causal or structural models • Univariate (time series) models • Causal (structural) modelsidentify the variables (Xs) that explain the variable (Y) we want to forecast, the residuals are the irregular fluctuations to simulate Ŷ = b0 + b1Py + b2 Px + b3 Z + b4 T + ẽ Ex: Demand models have own and cross prices, income, population, and other variables for tastes and preferences (often includes trend) • 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 + b1Yt-1 + b2 Yt-2 + ẽ ^ ^ ^