Relationships between Aggregates and Individual Behaviour: The Nature, Direction and Size of Aggregation Bias

Estimation of relationships between a dependent variable constructed by the aggregation of individual behaviour and aggregate independent variables such as mean income is common. The aim and contribution of the paper is to clarify when and how parameter estimates based on aggregates leads to bias and the likely degree of such bias. It demonstrates that use of aggregate data to estimate parameters associated with a model of individual behaviour when the outcome variable is binary (e.g. a birth) is not advisable. It only ‘works’ when the independent variables do not vary at the individual level (e.g. prices or the unemployment rate). Even then it requires prior distributional knowledge or assumptions. When the individual model also contains variables that vary across individuals, then the analysis in the paper suggests that all parameter estimates based solely on variation in the aggregates usually understate the size of their true value, even ones associated with variables which do not vary over individuals. Indeed, it is often the case that the 95% confidence interval of these latter parameter estimates never contains the parameter’s true value.