Models of Count Data

Abstract

Introduction In many economic contexts the dependent or response variable of interest is a nonnegative integer or count that we wish to explain or analyze in terms of a set of regressors. Unlike the classical regression model, the response variable is discrete, with a distribution that places probability mass at nonnegative integer values only. Several models discussed earlier in the book, such as the binary outcome model and the duration model, can be shown to be closely related to the count data regression model. Regression models for counts, like other limited or discrete dependent variable models such as the logit and probit, are nonlinear with many properties and special features intimately connected to discreteness and nonlinearity. Let us consider some examples from microeconometrics, beginning with sample data that are independent cross-section observations. Fertility studies often model the number of live births over a specified age interval of the mother, with interest in analyzing its variation in terms of, say, mother's schooling, age, and household income (Winkelmann, 1995). In some models of family decisions the number of children may appear as an explanatory variable with the acknowledgment that the variable is endogenous. Accident analysis studies model airline safety as measured by the number of accidents experienced by an airline over some period and seek to determine its relationship to airline profitability and other measures of the financial health of the airline (Rose, 1990).