Chapter 1. Discrete Response Models

1. INTRODUCTION When economic behavior is expressed as a continuous variable, a linear regression model is often adequate to describe the impact of economic factors on this behavior, or to predict this behavior in altered circumstances. For example, a study of food expenditures as a function of price indices for commodity groups and income, using households from the Consumer Expenditure Survey, can start by modeling indirect utility as a translog function and from this derive a linear in logs regression equation for food expenditures that does a good job of describing behavior. This situation remains true even when the behavioral response is limited in range (e.g., food consumption of households is non-negative) or integer-valued (e.g., college enrollment by state), provided these departures from a unrestricted continuous variable are not conspicuous in the data (e.g., food consumption is observed over a range where the non-negativity restriction is clearly not binding; college enrollments are in the thousands, so that round-off of the dependent variable to an integer is negligible relative to other random elements in the model). However, there are a variety of economic behaviors where the continuous approximation is not a good one. Here are some examples: