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Course is about Decision Making

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%

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Course is about Decision Making

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  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 ^ ^ ^

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