Probability Models for Economic Decisions (The MIT Press)

✍ Scribed by Roger B. Myerson

• Publisher: The MIT Press
• Year: 2019
• Tongue: English
• Leaves: 586
• Edition: 2
• Category: Library

✦ Synopsis

An introduction to the use of probability models for analyzing risk and economic decisions, using spreadsheets to represent and simulate uncertainty.

This textbook offers an introduction to the use of probability models for analyzing risks and economic decisions. It takes a learn-by-doing approach, teaching the student to use spreadsheets to represent and simulate uncertainty and to analyze the effect of such uncertainty on an economic decision. Students in applied business and economics can more easily grasp difficult analytical methods with Excel spreadsheets.

The book covers the basic ideas of probability, how to simulate random variables, and how to compute conditional probabilities via Monte Carlo simulation. The first four chapters use a large collection of probability distributions to simulate a range of problems involving worker efficiency, market entry, oil exploration, repeated investment, and subjective belief elicitation. The book then covers correlation and multivariate normal random variables; conditional expectation; optimization of decision variables, with discussions of the strategic value of information, decision trees, game theory, and adverse selection; risk sharing and finance; dynamic models of growth; dynamic models of arrivals; and model risk.

New material in this second edition includes two new chapters on additional dynamic models and model risk; new sections in every chapter; many new end-of-chapter exercises; and coverage of such topics as simulation model workflow, models of probabilistic electoral forecasting, and real options. The book comes equipped with Simtools, an open-source, free software used througout the book, which allows students to conduct Monte Carlo simulations seamlessly in Excel.

✦ Table of Contents

Cover
Title Page
Copyright
Dedication
Contents
Preface
How Our Book Is Organized
Changes in the Second Edition
Alternative Course Designs
Acknowledgments
1. Simulation and Conditional Probability
1.0 Getting Started with Simtools in Excel
1.1 How to Toss Coins in a Spreadsheet
1.2 A Simulation Model of 20 Sales Calls
1.3 Analysis Using Excel’s Data-Table Command
1.4 Conditional Independence
1.5 A Continuous Random Skill Variable from a Triangular Distribution
1.6 Probability Trees and Bayes’s Rule
1.7 Advanced Spreadsheet Techniques: Constructing a Table with Multiple Inputs
1.8 Using Models
1.9 The Modeling Process
Stage 1: The Decision Problem
a. Goals
b. The Environment
c. Other Players
d. Strategies
Stage 2: The Model
Stage 3: Validation
Stage 4: Integrity in Reporting
Stage 5: Feedback
1.10 Summary
Further Readings
Exercises
2. Discrete Random Variables
2.1 Unknown Quantities in Decisions under Uncertainty
2.2 Charting a Probability Distribution
2.3 Simulating Discrete Random Variables
2.4 Expected Value and Standard Deviation
2.5 Estimates from Sample Data
2.6 Accuracy of Sample Estimates
2.7 Decision Criteria
2.8 Multiple Random Variables
2.9 Summary
Further Readings
Exercises
3. Utility Theory with Constant Risk Tolerance
3.1 Taking Account of Risk Aversion: Utility Analysis with Probabilities
3.2 Utility Analysis from Simulation Data
3.3 The More General Assumption of Linear Risk Tolerance
3.4 Advanced Technical Note on Expected Utility Theory
3.5 Advanced Technical Note on Constant Risk Tolerance
3.6 Limitations of Expected Utility Theory
3.7 Summary
Further Readings
4. Continuous Random Variables
4.1 Normal Distributions
4.2 EXP and LN
4.3 Lognormal Distributions
4.4 Application: The Time Diversification Fallacy
4.5 Generalized Lognormal Distributions
4.6 Subjective Probability Assessment
4.7 A Decision Problem with Discrete and Continuous Unknowns
4.8 Certainty Equivalents of Normal Lotteries
4.9 Other Probability Distributions
Uniform Random Variables
Triangular Random Variables
Beta Random Variables
Exponential Random Variables
Gamma Random Variables
Extreme-Value Random Variables
A Nonparametric Distribution Fitting Sample Data
Binomial Random Variables
Poisson Random Variables
4.10 Summary
Further Readings
Exercises
5. Correlation and Multivariate Normal Random Variables
5.1 Joint Distributions of Discrete Random Variables
5.2 Covariance and Correlation
5.3 Linear Functions of Several Random Variables
5.4 Estimating Correlations from Data
5.5 Making Multivariate Normal Random Variables with CORAND and NORM.INV
5.6 Portfolio Analysis with Multivariate Normal Asset Returns
5.7 Excel Solver and Efficient Portfolio Design
5.8 Political Forecasting
5.9 Subjective Assessment of Correlations
5.10 Using CORAND with Non-Normal Random Variables
5.11 More about Linear Functions of Random Variables
5.12 Summary
Further Readings
Exercises
6. Conditional Expectation
6.1 Dependence among Random Variables
6.2 Estimating Conditional Expectations and Standard Deviations
6.3 The Expected-Posterior Law in a Discrete Example
6.4 Backwards Analysis of Conditional Expectations in Tree Diagrams
6.5 Conditional Expectation Relationships and Correlation
6.6 Uncertainty about a Probability
6.7 Linear Regression Models
6.8 Confidence Intervals and Prediction Intervals
6.9 Regression Analysis and Least Squared Errors
6.10 Summary
Further Readings
Exercises
7. Optimization of Decision Variables
7.1 General Techniques for Using Simulation in Decision Analysis
Method 1: For Each Alternative Strategy, Make a Separate Simulation Table of Payoffs
Method 2: Simultaneously Simulate Payoffs from Several Alternative Strategies
Method 3: Make a Table Listing Simulated Values of All Payoff-Relevant Random Variables
7.2 Strategic Use of Information
7.3 Decision Trees
7.4 Revenue Management
7.5 A Simple Bidding Problem
7.6 The Winner’s Curse
7.7 Analyzing Competitive Behavior
7.8 Summary
Further Readings
Exercises
8. Risk Sharing and Finance
8.1 Optimal Risk Sharing in a Partnership of Individuals with Constant Risk Tolerance
8.2 Optimality of Linear Rules in the Larger Class of Nonlinear Sharing Rules
8.3 Risk Sharing Subject to Moral-Hazard Incentive Constraints
8.4 Piecewise-Linear Sharing Rules with Moral Hazard
8.5 Corporate Decision Making and Asset Pricing in the Stock Market
8.6 Fundamental Ideas of Arbitrage Pricing Theory
8.7 Borrowing and Lending Decisions in Credit Markets with Adverse Selection
8.8 Summary
Further Readings
Exercises
9. Dynamic Models of Growth
9.1 Net Present Value
9.2 Forecasting Models
9.3 Forecasting Example: The Goeing Case
9.4 Brownian-Motion Growth Models
9.5 The Value of Flexibility
9.6 Log-Optimal Investment Strategies
9.7 Some Mathematics of Gambling
9.8 Risk Aversion on Growth Rates
9.9 Summary
Further Readings
Exercises
10. Dynamic Models of Arrivals
10.1 Exponential Arrival Models
10.2 Queueing Models
10.3 A Simple Inventory Model
10.4 The Transmission of Disease: Fixed Population
10.5 The Transmission of Disease: Variable Population
10.6 Project Length and Critical Tasks
10.7 Summary
Further Readings
Exercises
11. Model Risk
11.1 Implementation and Data Errors
11.2 Interpretation Errors
11.3 Model Specification Errors
11.4 Functional Form Mis-specification
11.5 Correlation Mis-specification
11.6 Mis-specification due to Incomplete Information
11.7 Volatility Mis-specification
11.8 Mitigating Model Risk: Estimation, Validation, and Testing
11.9 Mitigating Model Risk: The Precautionary Principle
11.10 Summary
Further Readings
Exercises
Notes
Appendix: Excel Add-Ins for Use with This Book
Installation
References
Index