Homothetic Efficiency: Theory and Applications

Abstract

We provide a nonparametric revealed preference approach to demand analysis based on homothetic efficiency. Homotheticity is widely assumed (often implicitly) because it is a convenient and often useful restriction. However, this assumption is rarely tested, and data rarely satisfy testable conditions. To overcome this, we provide a way to estimate homothetic efficiency of consumption choices. The method provides considerably higher discriminatory power against random behavior than the commonly used Afriat efficiency. We use experimental and household survey data to illustrate how our approach is useful for different empirical applications and can provide greater predictive success.

Homothetic Preferences Revealed

“…A more extensive overview of the relevant concepts can be found in Sections 2 and 3 of Heufer and Hjertstrand (2017).…”

“…In our approach to homothetic recoverability in Section 2.3, we only make use of the HEV, but the the approach could also be based on the HEI. Heufer and Hjertstrand (2017) propose a linear programming procedure to calculate a first-order approximation of the HEV for observed data. This procedure provides a computationally efficient method for large data sets, and Heufer and Hjertstrand (2017) show that the calculated efficiency vector closely approximates the HEV.…”

“…Heufer and Hjertstrand (2017) propose a linear programming procedure to calculate a first-order approximation of the HEV for observed data. This procedure provides a computationally efficient method for large data sets, and Heufer and Hjertstrand (2017) show that the calculated efficiency vector closely approximates the HEV. An implementation to calculate the HEV for a set of data is available in Matlab ® as supplementary material to Heufer and Hjertstrand (2017).…”

“…Because data rarely satisfies HARP, Heufer (2013) and Heufer and Hjertstrand (2017) develop approaches to measure homothetic efficiency. Similar to the Afriat Efficiency Index (Afriat 1972, also known as the Critical Cost Efficiency Index), their Homothetic Efficiency Index (HEI) is a lower bound that can be interpreted as wasted expenditure.…”

“…In this paper, we show how to implement Knoblauch's method when there are minor violations of homotheticity in the data. Our procedure adjusts the data using the homothetic efficiency approach as suggested by Heufer (2013) and Heufer and Hjertstrand (2017).…”