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BusAd/Econ 533: Economic and Business Decision Tools

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Course Objectives The goal of this course is to provide students with hands-on experience with decision tools used in Economic and Business decision-making.

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Four 3-4 Week Segments Segment 1: Discrete Choice Models (TSP) –Instructor: Joseph Herriges ( Jan. 14, 28 and Feb. 4) Segment 2: Monte Carlo simulation and its applications to Business Finance (Crystal Ball – EXCEL add-in) –Instructor: Travis Sapp ( Feb. 11, 18, 25 and Mar. 3) Segment 2: Geographical Information Systems (GIS) for use in data management, spatial visualization and decision making –Instructor: Brian Mennecke ( Mar. 10, 24, 31 and Apr. 7) Segment 4: Valuing financial options and insurance products using Monte Carlo integration (EXCEL) –Instructor: Arne Hallam ( Apr. 14, 21, 28 and May 5)

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Grading Grading will be separate for each segment (25% each) This segment’s 25%: –10% problem sets –15% exam

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Segment 1: The Basics Objectives: Provide an introduction to modeling the discrete choices made by individual agents Instructor: Joe Herriges –Office: 369 Heady Hall –Office Hours: TR 1 to 2 pm or by appointment Class Meetings: 272 Heady Hall, 6-9 pm Course Syllabus Class Web Page: Software: TSP

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Binary Choice Models Examples abound in studies of –Labor –Union Membership –Education –Housing –Voting –Crime –Purchases of Consumer Durables –Marriage –Transportation –Technology Adoption The simplest of discrete choice models is one between two alternatives

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Segment 1 Outline Class 1 –A review of Linear Regression Models –Introduction to Discrete Choice, particularly the Linear Probability Model –A review of probability distributions –An introduction to TSP Class 2: –Logit/Probit Models –Estimation of Logit and Probit Models Nonlinear Least Squares Maximum Likelihood –Model Interpretation and Inference Class 3: –Extensions Multiple Choices Ordered Choices Sequential Decisions

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Readings Train, K., (2003), Discrete Choice Methods with Simulation, Cambridge, MA: Cambridge University Press, Ch Train, K., (1986), Qualitative Choice Analysis, Cambridge, MA: MIT Press, Ch Greene, W. H., Econometric Analysis, 4 th edition, Upper Saddle River, New Jersey: Prentice-Hall, Inc., Sections 19.1 through 19.5.

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Linear Regression Model Should be a familiar concept Models relationship between –a continuous dependent variable (e.g., wage) –A series of explanatory variables (e.g., years of education, gender, job experience, etc.) Example:

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Wage vs Education

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Ordinary Least Squares (OLS) OLS chooses parameters to minimize where In our example:

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Wage vs Education

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A More Complex Regression Model where Graphing this relationship is difficult, but OLS summarizes the relationships:

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Requirements for OLS to be BLUE Model is linear in the parameters Error term has zero mean Error terms have the same variance across individuals Error terms are uncorrelated across individuals

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Linear Probability Models (LPM) Recall that in our binary choice model, the dependant variable takes on only two values, 0-1 The linear probability model applies the linear regression model to this discrete variable, letting

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Example Suppose that we are modeling the decision of women to enter the labor force, with A simple LPM of labor force entry as a function of education yields

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Implications of the LPM Notice that It is also the case that So that the LPM implies that hence the name – linear probability model

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Predictions for Labor Force Model For a person with no education For a person with a high school education For a person with a Masters and Ph.D. (23 years)

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A More Complex LPM

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Advantages of the LPM Simple to estimate Easy to interpret – the coefficients indicate the marginal impact of an explanatory variable Provides a reasonable approximation for the “average” individual

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Disadvantages of the LPM It will perform poorly –Away from the mean of the sample –When the mean choice probabilities are near zero or one It can predict probabilities of less than zero and greater than 1

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LPM

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Disadvantages of the LPM (cont’d) The LPM specification violates on the assumptions assumed in OLS (i.e., constant variance)

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A more systematic approach, attributed to Goldberger (1964), is that the decision is driven by, an unobserved latent variable; i.e., Latent Variable Models where is referred to as the index function

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We can then note that Latent Variable Models (continued) where F() is a cumulative distribution function for η i

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Graphically 0 1

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Motivation for the Index Function The most common motivation is McFadden’s RUM hypothesis Individual i receives utility from choosing alternative j where x ij and z ij denote, respectively, the observed and unobserved characteristics of both the individuals themselves and the alternatives they are choosing from. Individual i is assumed to choose alternative A if Observability is from the perspective of the analyst.

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RUM Model (Cont’d) Errors can arise from –Omitted variables –Measurement errors –Specification errors due to functional form choice. Analyst specifies a functional form for the representative agent, segmenting individual’s utility into two components where

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Example Suppose that you have two ways of getting to work, train or car, with the utility from getting to work determined by the cost and the travel time; i.e., The individual is assumed to take a car if or

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Example (cont’d) If we know the cost and time variables for an individual, as well as the parameters of the model, then we know what the individual will do Suppose, however, we don’t know the individual’s travel time, but observe their cost of travel by either mode, then

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