# Discrete Choice Model

A discrete choice model is a type of statistical model used to predict a decision outcome where the choices are distinct and limited. These models are especially common in econometrics and behavioral sciences for analyzing decisions where individuals or entities select from a finite set of alternatives.

## Key Characteristics of Discrete Choice Models:β

**Finite, Discrete Alternatives:** The model deals with choices that are distinct and countable. For example, a consumer choosing a brand of a product, a commuter selecting a mode of transportation, or a voter picking a candidate in an election.

**Utility Maximization:** It's often assumed that the decision-maker chooses the option that provides the highest utility (satisfaction or benefit). The concept of utility, however, is broad and can be influenced by various observable and unobservable factors.

**Random Utility Model (RUM):** A common basis for many discrete choice models. It posits that the utility of each choice for an individual is partly deterministic (based on observed attributes) and partly random (due to unobserved factors).

**Probability of Choice**: The model typically predicts the probability of choosing each available alternative. These probabilities are influenced by the attributes of the options and the characteristics of the decision-maker.

**Estimation from Observed Choices:** Parameters in discrete choice models are usually estimated from observed choice data. Various statistical techniques, such as maximum likelihood estimation, are used for this purpose.

## How to Construct a Structural Econometric Modelβ

**Steps in Constructing a Model:**

- Start with economic theory
- Transform economic model into econometric model
- Estimate the econometric model

**Model Framework:**

- Discrete choice to maximize utility
- Random utility model
- Different assumptions about unobservables in the random utility model yielding different econometric models

## Examplesβ

- Decision-making in microeconomics often involves choosing among a discrete set of alternatives.
- Examples include:
- Mode of travel for commuting
- Health insurance plan selection
- Choice of recreation sites
- Consumer goods purchases
- Job selection
- Choice of city for living
- Pollution control equipment for power plants
- Replacement of bus engines
- Automobile purchases
- Crop selection by farmers

## Analyzing a Discrete Choice Problemβ

**Three Steps:**

**Specify the choice set****Formulate a model**of how the agent chooses among the choice set**Estimate unknown parameters**of the model (structural parameters describing decision makerβs behavior, preferences, etc.)

## Choice Setβ

**Defining Choice Set**

- Defines all possible alternatives for the decision maker.
- Example: Methods of commuting to campus (e.g., driving alone, carpooling, bus, biking, walking, using Uber, staying home, etc.)
- Requirements:
*Mutually Exclusive*: Choosing one precludes any other.*Exhaustive*: All possible alternatives must be included.

- Contextual factors like research question and data availability influence choice set definition.

## Modeling and Estimationβ

**Formulating the Model**

- Formulating how an agent chooses among the set using a Random Utility Model (RUM).
- Estimating unknown parameters using various methods.