Linear Probability Model

Background§

The linear probability model (LPM) is a type of discrete choice model used to estimate binary outcome variables. These variables typically take values of 0 or 1, often representing categories such as failure/success, yes/no, or move/stay.

Historical Context§

The linear probability model has been in use since the early 20th century when econometricians began employing regression analysis methods to predict discrete outcomes in areas such as labor economics and consumer choice.

Definitions and Concepts§

The linear probability model assumes a linear relationship between the independent variables and the probability of the dependent binary outcome, represented as:

$$P(Y=1|X) = \beta_0 + \beta_1X_1 + \beta_2X_2 + … + \beta_kX_k$$

where $P(Y=1|X)$ is the probability that the dependent variable $Y$ equals 1, given the predictor variables $X$.

Major Analytical Frameworks§

Classical Economics§

In classical economics, the behavior of binary outcomes can be analyzed to understand economic choices at the micro level, using methods like the LPM.

Neoclassical Economics§

In neoclassical economics, consumer and producer behavior are investigated through models like the LPM to predict discrete decision-making processes based on individual utility maximization.

Keynesian Economics§

Although more focused on macroeconomic factors, Keynesian economics can incorporate LPM analyses to examine micro-level binary decisions, such as employment status.

Marxian Economics§

Marxian economics may apply LPM to study binary labor market outcomes, examining the probabilities that individuals enter different classes within the economic structure.

Institutional Economics§

Institutional economics would use LPMs to analyze the effect of institutions on binary economic decisions, such as compliance with regulations or participation in markets.

Behavioral Economics§

Behavioral economics integrates LPMs to delve into decision-making processes that deviate from rational choice theory, exploring heuristics and biases.

Post-Keynesian Economics§

This framework could utilize LPMs to assess dynamic and uncertain economic environments’ impact on binary decision-making.

Austrian Economics§

Austrian economists might critically evaluate the limitations of LPMs while relying on qualitative approaches to study economic choices.

Development Economics§

Development economists frequently employ LPMs to predict outcomes like adoption of new technologies, health interventions, and educational enrollment in developing countries.

Monetarism§

Traditionally more focused on monetary policy effects, monetarists might use LPMs to study binary decision outcomes affected by changes in money supply.

Comparative Analysis§

The LPM is compared to nonlinear alternatives like the logit and probit models, which can better handle the limitations of the LPM, such as ensuring predicted probabilities remain within the 0 to 1 range.

Case Studies§

Case studies using LPM might include analyses of labor market entry, consumer choice regarding new products, and health behavior adoption, providing a practical understanding of the model’s applications.

Suggested Books for Further Studies§

1. “Econometric Analysis” by William H. Greene
2. “Introduction to Econometrics” by James H. Stock and Mark W. Watson
3. “Discrete Choice Methods with Simulation” by Kenneth Train
4. “Applied Econometric Time Series” by Walter Enders
5. “Econometrics by Example” by Damodar Gujarati

Related Terms with Definitions§

1. Logit Model: A nonlinear model used for predicting binary outcomes, which uses the logistic function to ensure predicted probabilities lie between 0 and 1.
2. Probit Model: Another nonlinear model that applies the cumulative distribution function of the standard normal distribution to constrain predicted probabilities within [0, 1].
3. Discrete Choice Model: Regression models used to predict the choice between two or more discrete alternatives.