Why Threshold Models: A Theoretical Explanation

Abstract

Many economic phenomena are well described by linear models. In such models, the predicted value of the desired quantity – e.g., the future value of an economic characteristic – linearly depends on the current values of this and related economic characteristic and on the numerical values of external effects. Linear models have a clear economic interpretation: they correspond to situations when the overall effect does not depend, e.g., on whether we consider a loose federation as a single country or as several countries. While linear models are often reasonably accurate, to get more accurate predictions, we need to take into account that real-life processes are nonlinear. To take this nonlinearity into account, economists use piece-wise linear (threshold) models, in which we have several different linear dependencies in different domains. Surprisingly, such piece-wise linear models often work better than more traditional models of non-linearity – e.g., models that take quadratic terms into account. In this paper, we provide a theoretical explanation for this empirical success.