Quantitative Methods

Estimating a Demand Curve From Your Own Price History

Fit an elasticity to your own transaction history, then learn why the number you just produced is almost certainly wrong in a direction you can predict, and what it costs to get a version you can price against.

  • Advanced
  • 11 min total
  • 12 chapters

What decision this helps you make: Whether the elasticity you estimated from historical sales is good enough to move price on, or whether you need to buy real variation with a randomized test first.

What this topic is

A demand curve tells you how many units you sell at each price. Estimating one from your own history means regressing quantity on price across periods where price moved. Usually you do it in logarithms, so the coefficient reads directly as an elasticity: the percentage change in units for a one percent change in price. The technique is a single line in any statistics package. The difficulty is entirely in whether the price variation you are fitting to was generated by anything other than your own reaction to demand.

Why it matters

Elasticity is the single input that sets the profit-maximizing price, and almost every business that has one got it from a regression on its own sales history. That history was not produced by an experiment. Prices moved because someone in the business looked at demand and decided to move them: raising into a busy season, discounting when stock piled up, promoting when a competitor did. A regression cannot tell those apart from the causal effect of price, so it returns a blend of your pricing policy and your customers' response. The blend is usually biased toward zero, which makes demand look less price-sensitive than it is. That is exactly the error that talks a company into a price increase it cannot survive.

Who should learn it

Owners, pricing leads, finance teams and analysts who have been handed an elasticity number, or are about to produce one, and have to decide what weight it can carry.

What you will understand

  • How to fit a log-log demand model and read the coefficient as an elasticity
  • Why your own price history is contaminated, and which direction the bias runs
  • The one diagnostic that tells you an estimate is self-refuting before you check anything else
  • What an instrumental variable buys you, what it costs in assumptions, and why its answer is local

Prerequisites

Common misconception

"We have four years of our own transaction data, so we can measure our own price sensitivity." Volume of data is not the constraint and never was. The constraint is where the price variation came from. If every price change in those four years was decided by a person looking at demand conditions (and it was), then price and the unobserved demand shock move together, and the regression attributes part of the demand shock to price. More years of that data make the wrong number more precise, not more true. A single month of deliberately randomized prices is worth more than four years of well-intentioned commercial history.