How Many Price Parameters in Pricing Studies?

Academics often fit a single slope parameter to price, but this assumes linearity across the price continuum. With part-worth (dummy coding), we often estimate utilities for 3 to 5 prices along the price continuum, allowing us to capture thresholds where price sensitivity accelerates. However, what about estimating brand-specific price functions (e.g., brand x price effects or alternative-specific effects)? What about piecewise coding of continuous price functions (such as with summed pricing designs)? As we increase the number of price parameters to estimate, do we risk overfitting? Yet, if we estimate too few price parameters we risk losing the full picture of how price sensitivity differs by brands and differs from low to high price thresholds. This is a tricky area for modelers and we’ll discuss the issues and give some tips for achieving better results in pricing studies!